Mercurial > forge
changeset 11532:c0bf85c65b80 octave-forge
maint: remove control-devel (it's been using the hg repo)
author | carandraug |
---|---|
date | Sun, 10 Mar 2013 13:02:11 +0000 |
parents | 92d416c19bea |
children | 761eecba969d |
files | extra/control-devel/COPYING extra/control-devel/DESCRIPTION extra/control-devel/INDEX extra/control-devel/INFO extra/control-devel/Makefile extra/control-devel/devel/CD_player_arm-1.dat extra/control-devel/devel/CDplayer.m extra/control-devel/devel/CDplayerARX.m extra/control-devel/devel/CDplayerVS.m extra/control-devel/devel/CDplayer_a.m extra/control-devel/devel/Destillation.m extra/control-devel/devel/DestillationME.m extra/control-devel/devel/DestillationMEarx.m extra/control-devel/devel/Destillation_a.m extra/control-devel/devel/Destillation_combinations.m extra/control-devel/devel/Evaporator.m extra/control-devel/devel/GlassFurnace.m extra/control-devel/devel/GlassFurnaceARX.m extra/control-devel/devel/HeatingSystem.m extra/control-devel/devel/HeatingSystemKP.m extra/control-devel/devel/HeatingSystemRLS.m extra/control-devel/devel/Ident_results.zip extra/control-devel/devel/LakeErie.m extra/control-devel/devel/LakeErieARX.m extra/control-devel/devel/LakeErieMultiplot.m extra/control-devel/devel/MLexp/mln4sid.m extra/control-devel/devel/MLexp/mlpplant.m extra/control-devel/devel/MLexp/powerplant.dat extra/control-devel/devel/MLexp/pplant.mat extra/control-devel/devel/PowerPlant.m extra/control-devel/devel/PowerPlantFFT.m extra/control-devel/devel/PowerPlantKP.m extra/control-devel/devel/PowerPlantVS.m extra/control-devel/devel/PowerPlant_a.m extra/control-devel/devel/PowerPlant_combinations.m extra/control-devel/devel/REDUCTION_METHODS extra/control-devel/devel/armax.m extra/control-devel/devel/arx_siso.m extra/control-devel/devel/compare_results_hnamodred.m extra/control-devel/devel/destill.dat extra/control-devel/devel/dksyn/AB04MD.f extra/control-devel/devel/dksyn/AB05MD.f extra/control-devel/devel/dksyn/AB07MD.f extra/control-devel/devel/dksyn/AB07ND.f extra/control-devel/devel/dksyn/AB13MD.f extra/control-devel/devel/dksyn/DG01MD.f extra/control-devel/devel/dksyn/MA02AD.f extra/control-devel/devel/dksyn/MA02ED.f extra/control-devel/devel/dksyn/MB01PD.f extra/control-devel/devel/dksyn/MB01QD.f extra/control-devel/devel/dksyn/MB01RU.f extra/control-devel/devel/dksyn/MB01RX.f extra/control-devel/devel/dksyn/MB01RY.f extra/control-devel/devel/dksyn/MB01SD.f extra/control-devel/devel/dksyn/MB01UD.f extra/control-devel/devel/dksyn/MB02PD.f extra/control-devel/devel/dksyn/MB02RZ.f extra/control-devel/devel/dksyn/MB02SZ.f extra/control-devel/devel/dksyn/MB02TZ.f extra/control-devel/devel/dksyn/MB03OY.f extra/control-devel/devel/dksyn/MC01PD.f extra/control-devel/devel/dksyn/SB02MR.f extra/control-devel/devel/dksyn/SB02MS.f extra/control-devel/devel/dksyn/SB02MV.f extra/control-devel/devel/dksyn/SB02MW.f extra/control-devel/devel/dksyn/SB02QD.f extra/control-devel/devel/dksyn/SB02RD.f extra/control-devel/devel/dksyn/SB02RU.f extra/control-devel/devel/dksyn/SB02SD.f extra/control-devel/devel/dksyn/SB03MV.f extra/control-devel/devel/dksyn/SB03MW.f extra/control-devel/devel/dksyn/SB03MX.f extra/control-devel/devel/dksyn/SB03MY.f extra/control-devel/devel/dksyn/SB03QX.f extra/control-devel/devel/dksyn/SB03QY.f extra/control-devel/devel/dksyn/SB03SX.f extra/control-devel/devel/dksyn/SB03SY.f extra/control-devel/devel/dksyn/SB04PX.f extra/control-devel/devel/dksyn/SB10AD.f extra/control-devel/devel/dksyn/SB10LD.f extra/control-devel/devel/dksyn/SB10MD.f extra/control-devel/devel/dksyn/SB10PD.f extra/control-devel/devel/dksyn/SB10QD.f extra/control-devel/devel/dksyn/SB10RD.f extra/control-devel/devel/dksyn/SB10YD.f extra/control-devel/devel/dksyn/SB10ZP.f extra/control-devel/devel/dksyn/TB01ID.f extra/control-devel/devel/dksyn/TB01PD.f extra/control-devel/devel/dksyn/TB01UD.f extra/control-devel/devel/dksyn/TB01XD.f extra/control-devel/devel/dksyn/TB05AD.f extra/control-devel/devel/dksyn/TD03AY.f extra/control-devel/devel/dksyn/TD04AD.f extra/control-devel/devel/dksyn/makefile_dksyn.m extra/control-devel/devel/dksyn/muHopt.f extra/control-devel/devel/dksyn/select.f extra/control-devel/devel/erie.dat extra/control-devel/devel/evaporator.dat extra/control-devel/devel/fixtest.m extra/control-devel/devel/generate_devel_pdf.m extra/control-devel/devel/glassfurnace.dat extra/control-devel/devel/heating_system.dat extra/control-devel/devel/iddata_merge.m extra/control-devel/devel/identVS.m extra/control-devel/devel/ident_combinations.m extra/control-devel/devel/makefile_devel.m extra/control-devel/devel/pH.m extra/control-devel/devel/pH2.m extra/control-devel/devel/pHarx.m extra/control-devel/devel/pHdata.dat extra/control-devel/devel/pdfdoc/collect_texinfo_strings.m extra/control-devel/devel/pdfdoc/control-devel.tex extra/control-devel/devel/pdfdoc/info_generate_manual.txt extra/control-devel/devel/powerplant.dat extra/control-devel/devel/rarx.m extra/control-devel/devel/subsref_problem.m extra/control-devel/devel/test_arx.m extra/control-devel/devel/test_fitfrd.m extra/control-devel/devel/test_frd2iddata.m extra/control-devel/devel/test_iddata.m extra/control-devel/inst/test_devel.m extra/control-devel/src/Makefile extra/control-devel/src/common.cc extra/control-devel/src/common.h extra/control-devel/src/devel_slicot_functions.cc extra/control-devel/src/readme extra/control-devel/src/slicot.tar.gz extra/control-devel/src/slident_a.cc extra/control-devel/src/slident_b.cc extra/control-devel/src/slident_c.cc |
diffstat | 130 files changed, 0 insertions(+), 42673 deletions(-) [+] |
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--- a/extra/control-devel/DESCRIPTION Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,11 +0,0 @@ -Name: Control-Devel -Version: 0.3.0 -Date: 2012-08-14 -Author: Lukas Reichlin <lukas.reichlin@gmail.com> -Maintainer: Lukas Reichlin <lukas.reichlin@gmail.com> -Title: Control Systems Developer's Playground -Description: SLICOT system identification plus model and controller reduction -Depends: octave (>= 3.6.0), control (>= 2.3.49), control (< 2.4.0) -Autoload: yes -License: GPL version 3 or later -Url: http://octave.sf.net, http://www.slicot.org
--- a/extra/control-devel/INDEX Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,31 +0,0 @@ -control-devel >> Control Theory -Examples -Experimental Data Handling - iddata - @iddata/cat - @iddata/detrend - @iddata/diff - @iddata/fft - @iddata/filter - @iddata/get - @iddata/ifft - @iddata/merge - @iddata/nkshift - @iddata/plot - @iddata/resample - @iddata/set - @iddata/size -System Identification - arx - fitfrd - moen4 - moesp - n4sid -Overloaded Operators - @iddata/horzcat - @iddata/subsasgn - @iddata/subsref - @iddata/vertcat -Miscellaneous - options - test_devel \ No newline at end of file
--- a/extra/control-devel/INFO Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,3 +0,0 @@ -This package is just a playground for the author. -All its code will be included in the control package -once it's ready for a release. \ No newline at end of file
--- a/extra/control-devel/Makefile Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,16 +0,0 @@ -sinclude ../../Makeconf - -PKG_FILES = COPYING DESCRIPTION INDEX INFO $(wildcard inst/*) -SUBDIRS = doc/ - -.PHONY: $(SUBDIRS) - -pre-pkg:: - @for _dir in $(SUBDIRS); do \ - $(MAKE) -C $$_dir all; \ - done - -clean: - @for _dir in $(SUBDIRS); do \ - $(MAKE) -C $$_dir $(MAKECMDGOALS); \ - done
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--- a/extra/control-devel/devel/CDplayer.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,71 +0,0 @@ -%{ -Contributed by: - Favoreel - KULeuven - Departement Electrotechniek ESAT/SISTA -Kardinaal Mercierlaan 94 -B-3001 Leuven -Belgium - wouter.favoreel@esat.kuleuven.ac.be -Description: - Data from the mechanical construction of a CD player arm. - The inputs are the forces of the mechanical actuators - while the outputs are related to the tracking accuracy of the arm. - The data was measured in closed loop, and then through a two-step - procedure converted to open loop equivalent data - The inputs are highly colored. -Sampling: -Number: - 2048 -Inputs: - u: forces of the mechanical actuators -Outputs: - y: tracking accuracy of the arm -References: - We are grateful to R. de Callafon of the - Mechanical Engineering Systems and Control group of Delft, who - provided us with these data. - - - Van Den Hof P., Schrama R.J.P., An Indirect Method for Transfer - Function Estimation From Closed Loop Data. Automatica, Vol. 29, - no. 6, pp. 1523-1527, 1993. - -Properties: -Columns: - Column 1: input u1 - Column 2: input u2 - Column 1: output y1 - Column 2: output y2 -Category: - mechanical systems - -%} - -clear all, close all, clc - -load CD_player_arm-1.dat -U=CD_player_arm_1(:,1:2); -Y=CD_player_arm_1(:,3:4); - - -dat = iddata (Y, U) - -% [sys, x0] = moen4 (dat, 8, 's', 15) % s=15, n=8 -[sys, x0] = moen4 (dat, 8, 's', 15, 'noise', 'k') % s=15, n=8 - - - -%[y, t] = lsim (sys, U, [], x0); -[y, t] = lsim (sys, [U, Y], [], x0); - - -err = norm (Y - y, 1) / norm (Y, 1) - -figure (1) -p = columns (Y); -for k = 1 : p - subplot (2, 1, k) - plot (t, Y(:,k), 'b', t, y(:,k), 'r') -endfor - -
--- a/extra/control-devel/devel/CDplayerARX.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,82 +0,0 @@ -%{ -Contributed by: - Favoreel - KULeuven - Departement Electrotechniek ESAT/SISTA -Kardinaal Mercierlaan 94 -B-3001 Leuven -Belgium - wouter.favoreel@esat.kuleuven.ac.be -Description: - Data from the mechanical construction of a CD player arm. - The inputs are the forces of the mechanical actuators - while the outputs are related to the tracking accuracy of the arm. - The data was measured in closed loop, and then through a two-step - procedure converted to open loop equivalent data - The inputs are highly colored. -Sampling: -Number: - 2048 -Inputs: - u: forces of the mechanical actuators -Outputs: - y: tracking accuracy of the arm -References: - We are grateful to R. de Callafon of the - Mechanical Engineering Systems and Control group of Delft, who - provided us with these data. - - - Van Den Hof P., Schrama R.J.P., An Indirect Method for Transfer - Function Estimation From Closed Loop Data. Automatica, Vol. 29, - no. 6, pp. 1523-1527, 1993. - -Properties: -Columns: - Column 1: input u1 - Column 2: input u2 - Column 1: output y1 - Column 2: output y2 -Category: - mechanical systems - -%} - -clear all, close all, clc - -load CD_player_arm-1.dat -U=CD_player_arm_1(:,1:2); -Y=CD_player_arm_1(:,3:4); - - -dat = iddata (Y, U) - -% [sys, x0] = ident (dat, 15, 8) % s=15, n=8 -[sys, x0] = arx (dat, 'na', 8, 'nb', 8) - -[y, t] = lsim (sys, U, [], x0); - -%{ -%[y, t] = lsim (sys, U, [], x0); -%[y, t] = lsim (sys(:,1:2), U); - -[A, B] = filtdata (sys); -%[A, B] = tfdata (sys); - - -y1 = filter (B{1,1}, A{1,1}, U(:,1)) + filter (B{1,2}, A{1,2}, U(:,2)); -y2 = filter (B{2,1}, A{2,1}, U(:,1)) + filter (B{2,2}, A{2,2}, U(:,2)); -y = [y1, y2]; - -t = 0:length(U)-1; -%} - -err = norm (Y - y, 1) / norm (Y, 1) - -figure (1) -p = columns (Y); -for k = 1 : p - subplot (2, 1, k) - plot (t, Y(:,k), 'b', t, y(:,k), 'r') -endfor - -
--- a/extra/control-devel/devel/CDplayerVS.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,67 +0,0 @@ -%{ -Contributed by: - Favoreel - KULeuven - Departement Electrotechniek ESAT/SISTA -Kardinaal Mercierlaan 94 -B-3001 Leuven -Belgium - wouter.favoreel@esat.kuleuven.ac.be -Description: - Data from the mechanical construction of a CD player arm. - The inputs are the forces of the mechanical actuators - while the outputs are related to the tracking accuracy of the arm. - The data was measured in closed loop, and then through a two-step - procedure converted to open loop equivalent data - The inputs are highly colored. -Sampling: -Number: - 2048 -Inputs: - u: forces of the mechanical actuators -Outputs: - y: tracking accuracy of the arm -References: - We are grateful to R. de Callafon of the - Mechanical Engineering Systems and Control group of Delft, who - provided us with these data. - - - Van Den Hof P., Schrama R.J.P., An Indirect Method for Transfer - Function Estimation From Closed Loop Data. Automatica, Vol. 29, - no. 6, pp. 1523-1527, 1993. - -Properties: -Columns: - Column 1: input u1 - Column 2: input u2 - Column 1: output y1 - Column 2: output y2 -Category: - mechanical systems - -%} - -clear all, close all, clc - -load CD_player_arm-1.dat -U=CD_player_arm_1(:,1:2); -Y=CD_player_arm_1(:,3:4); - - -dat = iddata (Y, U) - -[sys, x0] = identVS (dat, 15, 8) % s=15, n=8 - - -[y, t] = lsim (sys, U, [], x0); - -err = norm (Y - y, 1) / norm (Y, 1) - -figure (1) -p = columns (Y); -for k = 1 : p - subplot (2, 1, k) - plot (t, Y(:,k), 'b', t, y(:,k), 'r') -endfor - -
--- a/extra/control-devel/devel/CDplayer_a.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,67 +0,0 @@ -%{ -Contributed by: - Favoreel - KULeuven - Departement Electrotechniek ESAT/SISTA -Kardinaal Mercierlaan 94 -B-3001 Leuven -Belgium - wouter.favoreel@esat.kuleuven.ac.be -Description: - Data from the mechanical construction of a CD player arm. - The inputs are the forces of the mechanical actuators - while the outputs are related to the tracking accuracy of the arm. - The data was measured in closed loop, and then through a two-step - procedure converted to open loop equivalent data - The inputs are highly colored. -Sampling: -Number: - 2048 -Inputs: - u: forces of the mechanical actuators -Outputs: - y: tracking accuracy of the arm -References: - We are grateful to R. de Callafon of the - Mechanical Engineering Systems and Control group of Delft, who - provided us with these data. - - - Van Den Hof P., Schrama R.J.P., An Indirect Method for Transfer - Function Estimation From Closed Loop Data. Automatica, Vol. 29, - no. 6, pp. 1523-1527, 1993. - -Properties: -Columns: - Column 1: input u1 - Column 2: input u2 - Column 1: output y1 - Column 2: output y2 -Category: - mechanical systems - -%} - -close all, clc - -load CD_player_arm-1.dat -U=CD_player_arm_1(:,1:2); -Y=CD_player_arm_1(:,3:4); - - -dat = iddata (Y, U) - -[sys, x0] = ident_a (dat, 15, 8) % s=15, n=8 - - -[y, t] = lsim (sys, U, [], x0); - -err = norm (Y - y, 1) / norm (Y, 1) - -figure (1) -p = columns (Y); -for k = 1 : p - subplot (2, 1, k) - plot (t, Y(:,k), 'b', t, y(:,k), 'r') -endfor - -
--- a/extra/control-devel/devel/Destillation.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,96 +0,0 @@ -%{ -This file describes the data in the destill.dat file. -1. Contributed by: - Peter Van Overschee - K.U.Leuven - ESAT - SISTA - K. Mercierlaan 94 - 3001 Heverlee - Peter.Vanoverschee@esat.kuleuven.ac.be -2. Process/Description: - Data of a simulation (not real !) related to the identification - of an ethane-ethylene destillationcolumn. The series consists of 4 - series: - U_dest, Y_dest: without noise (original series) - U_dest_n10, Y_dest_n10: 10 percent additive white noise - U_dest_n20, Y_dest_n20: 20 percent additive white noise - U_dest_n30, Y_dest_n30: 30 percent additive white noise -3. Sampling time - 15 min. -4. Number of samples: - 90 samples -5. Inputs: - a. ratio between the reboiler duty and the feed flow - b. ratio between the reflux rate and the feed flow - c. ratio between the distillate and the feed flow - d. input ethane composition - e. top pressure -6. Outputs: - a. top ethane composition - b. bottom ethylene composition - c. top-bottom differential pressure. -7. References: - R.P. Guidorzi, M.P. Losito, T. Muratori, The range error test in the - structural identification of linear multivariable systems, - IEEE transactions on automatic control, Vol AC-27, pp 1044-1054, oct. - 1982. -8. Known properties/peculiarities - -9. Some MATLAB-code to retrieve the data - !gunzip destill.dat.Z - load destill.dat - U=destill(:,1:20); - Y=destill(:,21:32); - U_dest=U(:,1:5); - U_dest_n10=U(:,6:10); - U_dest_n20=U(:,11:15); - U_dest_n30=U(:,16:20); - Y_dest=Y(:,1:3); - Y_dest_n10=Y(:,4:6); - Y_dest_n20=Y(:,7:9); - Y_dest_n30=Y(:,10:12); -%} - -clear all, close all, clc - -% DaISy code is wrong, -% first column is sample number -load destill.dat -U=destill(:,2:21); -Y=destill(:,22:33); -U_dest=U(:,1:5); -U_dest_n10=U(:,6:10); -U_dest_n20=U(:,11:15); -U_dest_n30=U(:,16:20); -Y_dest=Y(:,1:3); -Y_dest_n10=Y(:,4:6); -Y_dest_n20=Y(:,7:9); -Y_dest_n30=Y(:,10:12); - -Y = {Y_dest; Y_dest_n10; Y_dest_n20; Y_dest_n30}; -U = {U_dest; U_dest_n10; U_dest_n20; U_dest_n30}; - -dat = iddata (Y, U) - -[sys, x0] = moen4 (dat, 's', 5, 'n', 4, 'noise', 'k') % s=5, n=4 - -x0=x0{1}; - -[y, t] = lsim (sys, [U_dest, Y_dest], [], x0); -%[y, t] = lsim (sys, U_dest); - -err = norm (Y_dest - y, 1) / norm (Y_dest, 1) - -figure (1) -%plot (t, Y_dest, 'b') -plot (t, Y_dest, 'b', t, y, 'r') -legend ('y measured', 'y simulated', 'location', 'southeast') - -figure (2) -p = columns (Y_dest); -for k = 1 : 3 - subplot (3, 1, k) - plot (t, Y_dest(:,k), 'b', t, y(:,k), 'r') - xlim ([0, 90]) -endfor -legend ('y measured', 'y simulated', 'location', 'southeast') -
--- a/extra/control-devel/devel/DestillationME.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,88 +0,0 @@ -%{ -This file describes the data in the destill.dat file. -1. Contributed by: - Peter Van Overschee - K.U.Leuven - ESAT - SISTA - K. Mercierlaan 94 - 3001 Heverlee - Peter.Vanoverschee@esat.kuleuven.ac.be -2. Process/Description: - Data of a simulation (not real !) related to the identification - of an ethane-ethylene destillationcolumn. The series consists of 4 - series: - U_dest, Y_dest: without noise (original series) - U_dest_n10, Y_dest_n10: 10 percent additive white noise - U_dest_n20, Y_dest_n20: 20 percent additive white noise - U_dest_n30, Y_dest_n30: 30 percent additive white noise -3. Sampling time - 15 min. -4. Number of samples: - 90 samples -5. Inputs: - a. ratio between the reboiler duty and the feed flow - b. ratio between the reflux rate and the feed flow - c. ratio between the distillate and the feed flow - d. input ethane composition - e. top pressure -6. Outputs: - a. top ethane composition - b. bottom ethylene composition - c. top-bottom differential pressure. -7. References: - R.P. Guidorzi, M.P. Losito, T. Muratori, The range error test in the - structural identification of linear multivariable systems, - IEEE transactions on automatic control, Vol AC-27, pp 1044-1054, oct. - 1982. -8. Known properties/peculiarities - -9. Some MATLAB-code to retrieve the data - !gunzip destill.dat.Z - load destill.dat - U=destill(:,1:20); - Y=destill(:,21:32); - U_dest=U(:,1:5); - U_dest_n10=U(:,6:10); - U_dest_n20=U(:,11:15); - U_dest_n30=U(:,16:20); - Y_dest=Y(:,1:3); - Y_dest_n10=Y(:,4:6); - Y_dest_n20=Y(:,7:9); - Y_dest_n30=Y(:,10:12); -%} - -clear all, close all, clc - -% DaISy code is wrong, -% first column is sample number -load destill.dat -U=destill(:,2:21); -Y=destill(:,22:33); -U_dest=U(:,1:5); -U_dest_n10=U(:,6:10); -U_dest_n20=U(:,11:15); -U_dest_n30=U(:,16:20); -Y_dest=Y(:,1:3); -Y_dest_n10=Y(:,4:6); -Y_dest_n20=Y(:,7:9); -Y_dest_n30=Y(:,10:12); - -Y = {Y_dest; Y_dest_n10; Y_dest_n20; Y_dest_n30}; -U = {U_dest; U_dest_n10; U_dest_n20; U_dest_n30}; - -dat = iddata (Y, U) - -[sys, x0] = moen4 (dat, 's', 5, 'n', 4) % s=5, n=4 - -x0=x0{1}; - -[y, t] = lsim (sys, U_dest, [], x0); -%[y, t] = lsim (sys, U_dest); - -err = norm (Y_dest - y, 1) / norm (Y_dest, 1) - -figure (1) -%plot (t, Y_dest, 'b') -plot (t, Y_dest, 'b', t, y, 'r') -legend ('y measured', 'y simulated', 'location', 'southeast') - -
--- a/extra/control-devel/devel/DestillationMEarx.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,96 +0,0 @@ -%{ -This file describes the data in the destill.dat file. -1. Contributed by: - Peter Van Overschee - K.U.Leuven - ESAT - SISTA - K. Mercierlaan 94 - 3001 Heverlee - Peter.Vanoverschee@esat.kuleuven.ac.be -2. Process/Description: - Data of a simulation (not real !) related to the identification - of an ethane-ethylene destillationcolumn. The series consists of 4 - series: - U_dest, Y_dest: without noise (original series) - U_dest_n10, Y_dest_n10: 10 percent additive white noise - U_dest_n20, Y_dest_n20: 20 percent additive white noise - U_dest_n30, Y_dest_n30: 30 percent additive white noise -3. Sampling time - 15 min. -4. Number of samples: - 90 samples -5. Inputs: - a. ratio between the reboiler duty and the feed flow - b. ratio between the reflux rate and the feed flow - c. ratio between the distillate and the feed flow - d. input ethane composition - e. top pressure -6. Outputs: - a. top ethane composition - b. bottom ethylene composition - c. top-bottom differential pressure. -7. References: - R.P. Guidorzi, M.P. Losito, T. Muratori, The range error test in the - structural identification of linear multivariable systems, - IEEE transactions on automatic control, Vol AC-27, pp 1044-1054, oct. - 1982. -8. Known properties/peculiarities - -9. Some MATLAB-code to retrieve the data - !gunzip destill.dat.Z - load destill.dat - U=destill(:,1:20); - Y=destill(:,21:32); - U_dest=U(:,1:5); - U_dest_n10=U(:,6:10); - U_dest_n20=U(:,11:15); - U_dest_n30=U(:,16:20); - Y_dest=Y(:,1:3); - Y_dest_n10=Y(:,4:6); - Y_dest_n20=Y(:,7:9); - Y_dest_n30=Y(:,10:12); -%} - -clear all, close all, clc - -% DaISy code is wrong, -% first column is sample number -load destill.dat -U=destill(:,2:21); -Y=destill(:,22:33); -U_dest=U(:,1:5); -U_dest_n10=U(:,6:10); -U_dest_n20=U(:,11:15); -U_dest_n30=U(:,16:20); -Y_dest=Y(:,1:3); -Y_dest_n10=Y(:,4:6); -Y_dest_n20=Y(:,7:9); -Y_dest_n30=Y(:,10:12); - -Y = {Y_dest; Y_dest_n10; Y_dest_n20; Y_dest_n30}; -U = {U_dest; U_dest_n10; U_dest_n20; U_dest_n30}; - -dat = iddata (Y, U) - -[sys, x0] = moen4 (dat, 's', 5, 'n', 4) % s=5, n=4 -sys2 = arx (dat, 'na', 4, 'nb', 4); -[sys2, x02] = arx (dat, 'na', 4, 'nb', 4); - -x0=x0{1}; -x02=x02{1}; - -[y, t] = lsim (sys, U_dest, [], x0); -%[y2, t2] = lsim (sys2(:, 1:5), U_dest); -[y2, t2] = lsim (sys2, U_dest, [], x02); - - -% ARX has no initial conditions, therefore the bad results - -err = norm (Y_dest - y, 1) / norm (Y_dest, 1) -err2 = norm (Y_dest - y2, 1) / norm (Y_dest, 1) - -figure (1) -%plot (t, Y_dest, 'b') -plot (t, Y_dest, t, y, t, y2) -legend ('y measured', 'y MOEN4', 'y ARX', 'location', 'southeast') - -
--- a/extra/control-devel/devel/Destillation_a.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,83 +0,0 @@ -%{ -This file describes the data in the destill.dat file. -1. Contributed by: - Peter Van Overschee - K.U.Leuven - ESAT - SISTA - K. Mercierlaan 94 - 3001 Heverlee - Peter.Vanoverschee@esat.kuleuven.ac.be -2. Process/Description: - Data of a simulation (not real !) related to the identification - of an ethane-ethylene destillationcolumn. The series consists of 4 - series: - U_dest, Y_dest: without noise (original series) - U_dest_n10, Y_dest_n10: 10 percent additive white noise - U_dest_n20, Y_dest_n20: 20 percent additive white noise - U_dest_n30, Y_dest_n30: 30 percent additive white noise -3. Sampling time - 15 min. -4. Number of samples: - 90 samples -5. Inputs: - a. ratio between the reboiler duty and the feed flow - b. ratio between the reflux rate and the feed flow - c. ratio between the distillate and the feed flow - d. input ethane composition - e. top pressure -6. Outputs: - a. top ethane composition - b. bottom ethylene composition - c. top-bottom differential pressure. -7. References: - R.P. Guidorzi, M.P. Losito, T. Muratori, The range error test in the - structural identification of linear multivariable systems, - IEEE transactions on automatic control, Vol AC-27, pp 1044-1054, oct. - 1982. -8. Known properties/peculiarities - -9. Some MATLAB-code to retrieve the data - !gunzip destill.dat.Z - load destill.dat - U=destill(:,1:20); - Y=destill(:,21:32); - U_dest=U(:,1:5); - U_dest_n10=U(:,6:10); - U_dest_n20=U(:,11:15); - U_dest_n30=U(:,16:20); - Y_dest=Y(:,1:3); - Y_dest_n10=Y(:,4:6); - Y_dest_n20=Y(:,7:9); - Y_dest_n30=Y(:,10:12); -%} - - close all, clc - -load destill.dat -U=destill(:,1:20); -Y=destill(:,21:32); -U_dest=U(:,1:5); -U_dest_n10=U(:,6:10); -U_dest_n20=U(:,11:15); -U_dest_n30=U(:,16:20); -Y_dest=Y(:,1:3); -Y_dest_n10=Y(:,4:6); -Y_dest_n20=Y(:,7:9); -Y_dest_n30=Y(:,10:12); - - -dat = iddata (Y_dest, U_dest) - -[sys, x0] = ident_a (dat, 5, 4) % s=5, n=4 - - -[y, t] = lsim (sys, U_dest, [], x0); -%[y, t] = lsim (sys, U_dest); - -err = norm (Y_dest - y, 1) / norm (Y_dest, 1) - -figure (1) -%plot (t, Y_dest, 'b') -plot (t, Y_dest, 'b', t, y, 'r') -legend ('y measured', 'y simulated', 'location', 'southeast') - -
--- a/extra/control-devel/devel/Destillation_combinations.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,90 +0,0 @@ -%{ -This file describes the data in the destill.dat file. -1. Contributed by: - Peter Van Overschee - K.U.Leuven - ESAT - SISTA - K. Mercierlaan 94 - 3001 Heverlee - Peter.Vanoverschee@esat.kuleuven.ac.be -2. Process/Description: - Data of a simulation (not real !) related to the identification - of an ethane-ethylene destillationcolumn. The series consists of 4 - series: - U_dest, Y_dest: without noise (original series) - U_dest_n10, Y_dest_n10: 10 percent additive white noise - U_dest_n20, Y_dest_n20: 20 percent additive white noise - U_dest_n30, Y_dest_n30: 30 percent additive white noise -3. Sampling time - 15 min. -4. Number of samples: - 90 samples -5. Inputs: - a. ratio between the reboiler duty and the feed flow - b. ratio between the reflux rate and the feed flow - c. ratio between the distillate and the feed flow - d. input ethane composition - e. top pressure -6. Outputs: - a. top ethane composition - b. bottom ethylene composition - c. top-bottom differential pressure. -7. References: - R.P. Guidorzi, M.P. Losito, T. Muratori, The range error test in the - structural identification of linear multivariable systems, - IEEE transactions on automatic control, Vol AC-27, pp 1044-1054, oct. - 1982. -8. Known properties/peculiarities - -9. Some MATLAB-code to retrieve the data - !gunzip destill.dat.Z - load destill.dat - U=destill(:,1:20); - Y=destill(:,21:32); - U_dest=U(:,1:5); - U_dest_n10=U(:,6:10); - U_dest_n20=U(:,11:15); - U_dest_n30=U(:,16:20); - Y_dest=Y(:,1:3); - Y_dest_n10=Y(:,4:6); - Y_dest_n20=Y(:,7:9); - Y_dest_n30=Y(:,10:12); -%} - -clear all, close all, clc - -% DaISy code is wrong, -% first column is sample number -load destill.dat -U=destill(:,2:21); -Y=destill(:,22:33); -U_dest=U(:,1:5); -U_dest_n10=U(:,6:10); -U_dest_n20=U(:,11:15); -U_dest_n30=U(:,16:20); -Y_dest=Y(:,1:3); -Y_dest_n10=Y(:,4:6); -Y_dest_n20=Y(:,7:9); -Y_dest_n30=Y(:,10:12); - - -dat = iddata (Y_dest, U_dest); - -err = zeros (3, 3); - -for meth = 0:2 - for alg = 0:2 - [sys, x0] = ident_combinations (dat, 5, 4, meth, alg); % s=5, n=4 - [y, t] = lsim (sys, U_dest, [], x0); - err(meth+1, alg+1) = norm (Y_dest - y, 1) / norm (Y_dest, 1); - endfor -endfor - -err - -%{ -figure (1) -%plot (t, Y_dest, 'b') -plot (t, Y_dest, 'b', t, y, 'r') -legend ('y measured', 'y simulated', 'location', 'southeast') -%} -
--- a/extra/control-devel/devel/Evaporator.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,68 +0,0 @@ -%{ -Contributed by: - Favoreel - KULeuven - Departement Electrotechniek ESAT/SISTA - Kardinaal Mercierlaan 94 - B-3001 Leuven - Belgium - wouter.favoreel@esat.kuleuven.ac.be -Description: - A four-stage evaporator to reduce the water content of a product, - for example milk. The 3 inputs are feed flow, vapor flow to the - first evaporator stage and cooling water flow. The three outputs - are the dry matter content, the flow and the temperature of the - outcoming product. -Sampling: -Number: - 6305 -Inputs: - u1: feed flow to the first evaporator stage - u2: vapor flow to the first evaporator stage - u3: cooling water flow -Outputs: - y1: dry matter content - y2: flow of the outcoming product - y3: temperature of the outcoming product -References: - - Zhu Y., Van Overschee P., De Moor B., Ljung L., Comparison of - three classes of identification methods. Proc. of SYSID '94, - Vol. 1, 4-6 July, Copenhagen, Denmark, pp.~175-180, 1994. -Properties: -Columns: - Column 1: input u1 - Column 2: input u2 - Column 3: input u3 - Column 4: output y1 - Column 5: output y2 - Column 6: output y3 -Category: - Thermic systems -Where: - -%} - -clear all, close all, clc - -load evaporator.dat -U=evaporator(:,1:3); -Y=evaporator(:,4:6); - - -dat = iddata (Y, U) - -[sys, x0] = moen4 (dat, 's', 10, 'n', 4, 'noise', 'k') % s=10, n=4 - - -[y, t] = lsim (sys, [U, Y], [], x0); - -err = norm (Y - y, 1) / norm (Y, 1) - -figure (1) -p = columns (Y); -for k = 1 : p - subplot (3, 1, k) - plot (t, Y(:,k), 'b', t, y(:,k), 'r') -endfor - -
--- a/extra/control-devel/devel/GlassFurnace.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,67 +0,0 @@ -%{ -This file describes the data in the glassfurnace.dat file. -1. Contributed by: - Peter Van Overschee - K.U.Leuven - ESAT - SISTA - K. Mercierlaan 94 - 3001 Heverlee - Peter.Vanoverschee@esat.kuleuven.ac.be -2. Process/Description: - Data of a glassfurnace (Philips) -3. Sampling time - -4. Number of samples: - 1247 samples -5. Inputs: - a. heating input - b. cooling input - c. heating input -6. Outputs: - a. 6 outputs from temperature sensors in a cross section of the - furnace -7. References: - a. Van Overschee P., De Moor B., N4SID : Subspace Algorithms for - the Identification of Combined Deterministic-Stochastic Systems, - Automatica, Special Issue on Statistical Signal Processing and Control, - Vol. 30, No. 1, 1994, pp. 75-93 - b. Van Overschee P., "Subspace identification : Theory, - Implementation, Application" , Ph.D. Thesis, K.U.Leuven, February 1995. -8. Known properties/peculiarities - -9. Some MATLAB-code to retrieve the data - !gunzip glassfurnace.dat.Z - load glassfurnace.dat - T=glassfurnace(:,1); - U=glassfurnace(:,2:4); - Y=glassfurnace(:,5:10); - -%} - - -clear all, close all, clc - -load glassfurnace.dat -T=glassfurnace(:,1); -U=glassfurnace(:,2:4); -Y=glassfurnace(:,5:10); - - -dat = iddata (Y, U) - -[sys, x0, info] = moen4 (dat, 's', 10, 'n', 5, 'noise', 'k') % s=10, n=5 - - -[y, t] = lsim (sys, [U, Y], [], x0); - -err = norm (Y - y, 1) / norm (Y, 1) - -figure (1) -p = columns (Y); -for k = 1 : p - subplot (3, 2, k) - plot (t, Y(:,k), 'b', t, y(:,k), 'r') -endfor -%title ('DaISy: Glass Furnace') -%legend ('y measured', 'y simulated', 'location', 'southeast') - -
--- a/extra/control-devel/devel/GlassFurnaceARX.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,70 +0,0 @@ -%{ -This file describes the data in the glassfurnace.dat file. -1. Contributed by: - Peter Van Overschee - K.U.Leuven - ESAT - SISTA - K. Mercierlaan 94 - 3001 Heverlee - Peter.Vanoverschee@esat.kuleuven.ac.be -2. Process/Description: - Data of a glassfurnace (Philips) -3. Sampling time - -4. Number of samples: - 1247 samples -5. Inputs: - a. heating input - b. cooling input - c. heating input -6. Outputs: - a. 6 outputs from temperature sensors in a cross section of the - furnace -7. References: - a. Van Overschee P., De Moor B., N4SID : Subspace Algorithms for - the Identification of Combined Deterministic-Stochastic Systems, - Automatica, Special Issue on Statistical Signal Processing and Control, - Vol. 30, No. 1, 1994, pp. 75-93 - b. Van Overschee P., "Subspace identification : Theory, - Implementation, Application" , Ph.D. Thesis, K.U.Leuven, February 1995. -8. Known properties/peculiarities - -9. Some MATLAB-code to retrieve the data - !gunzip glassfurnace.dat.Z - load glassfurnace.dat - T=glassfurnace(:,1); - U=glassfurnace(:,2:4); - Y=glassfurnace(:,5:10); - -%} - - -clear all, close all, clc - -load glassfurnace.dat -T=glassfurnace(:,1); -U=glassfurnace(:,2:4); -Y=glassfurnace(:,5:10); - - -dat = iddata (Y, U) - -%[sys, x0] = ident (dat, 10, 5) % s=10, n=5 -%sys = arx (dat, 5) -[sys, x0] = arx (dat, 5) - -%[y, t] = lsim (sys, U, [], x0); -%[y, t] = lsim (sys(:, 1:3), U); -[y, t] = lsim (sys, U, [], x0); - -err = norm (Y - y, 1) / norm (Y, 1) - -figure (1) -p = columns (Y); -for k = 1 : p - subplot (3, 2, k) - plot (t, Y(:,k), 'b', t, y(:,k), 'r') -endfor -%title ('DaISy: Glass Furnace') -%legend ('y measured', 'y simulated', 'location', 'southeast') - -
--- a/extra/control-devel/devel/HeatingSystem.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,99 +0,0 @@ -%{ -1. Contributed by: - - Roy Smith - Dept. of Electrical & Computer Engineering - University of California, - Santa Barbara, CA 93106 - U.S.A. - roy@ece.ucsb.edu - -2. Process/Description: - - The experiment is a simple SISO heating system. - The input drives a 300 Watt Halogen lamp, suspended - several inches above a thin steel plate. The output - is a thermocouple measurement taken from the back of - the plate. - -3. Sampling interval: - - 2.0 seconds - -4. Number of samples - - 801 - -5. Inputs: - - u: input drive voltage - ... -6. Outputs: - - y: temperature (deg. C) - ... -7. References: - - The use of this experiment and data for robust - control model validation is described in: - - "Sampled Data Model Validation: an Algorithm and - Experimental Application," Geir Dullerud & Roy Smith, - International Journal of Robust and Nonlinear Control, - Vol. 6, No. 9/10, pp. 1065-1078, 1996. - -8. Known properties/peculiarities - - The data (and nominal model) is the above paper have the - output expressed in 10's deg. C. This has been rescaled - to the original units of deg. C. in the DaISy data set. - There is also a -1 volt offset in u in the data shown plotted - in the original paper. This has been removed in the - DaISy dataset. - - The data shows evidence of discrepancies. One of the - issues studied in the above paper is the size of these - discrepancies - measured in this case in terms of the norm - of the smallest perturbation required to account for the - difference between the nominal model and the data. - - The steady state input (prior to the start of the experiment) - is u = 6.0 Volts. - -%} - -clear all, close all, clc - -load heating_system.dat -U=heating_system(:,2); -Y=heating_system(:,3); - - -dat = iddata (Y, U, 2.0, 'inname', 'input drive voltage', \ - 'inunit', 'Volt', \ - 'outname', 'temperature', \ - 'outunit', 'Degree Celsius') - -% s=15, n=7 -[sys1, x0] = moen4 (dat, 's', 15, 'n', 7) -%sys2 = arx (dat, 7, 7) % normally na = nb -[sys2, x02] = arx (dat, 7); - -[y1, t1] = lsim (sys1, U, [], x0); -%[y2, t] = lsim (sys2(:, 1), U); -[y2, t] = lsim (sys2, U, [], x02); - - -err1 = norm (Y - y1, 1) / norm (Y, 1) -err2 = norm (Y - y2, 1) / norm (Y, 1) - -figure (1) -plot (t, Y, t, y1, t, y2) -title ('DaISy: Heating System [99-001]') -xlim ([t(1), t(end)]) -xlabel ('Time [s]') -ylabel ('Temperature [Degree Celsius]') -legend ('measurement DaISy', 'simulation MOEN4', 'simulation ARX', 'location', 'northeast') - - -
--- a/extra/control-devel/devel/HeatingSystemKP.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,103 +0,0 @@ -%{ -1. Contributed by: - - Roy Smith - Dept. of Electrical & Computer Engineering - University of California, - Santa Barbara, CA 93106 - U.S.A. - roy@ece.ucsb.edu - -2. Process/Description: - - The experiment is a simple SISO heating system. - The input drives a 300 Watt Halogen lamp, suspended - several inches above a thin steel plate. The output - is a thermocouple measurement taken from the back of - the plate. - -3. Sampling interval: - - 2.0 seconds - -4. Number of samples - - 801 - -5. Inputs: - - u: input drive voltage - ... -6. Outputs: - - y: temperature (deg. C) - ... -7. References: - - The use of this experiment and data for robust - control model validation is described in: - - "Sampled Data Model Validation: an Algorithm and - Experimental Application," Geir Dullerud & Roy Smith, - International Journal of Robust and Nonlinear Control, - Vol. 6, No. 9/10, pp. 1065-1078, 1996. - -8. Known properties/peculiarities - - The data (and nominal model) is the above paper have the - output expressed in 10's deg. C. This has been rescaled - to the original units of deg. C. in the DaISy data set. - There is also a -1 volt offset in u in the data shown plotted - in the original paper. This has been removed in the - DaISy dataset. - - The data shows evidence of discrepancies. One of the - issues studied in the above paper is the size of these - discrepancies - measured in this case in terms of the norm - of the smallest perturbation required to account for the - difference between the nominal model and the data. - - The steady state input (prior to the start of the experiment) - is u = 6.0 Volts. - -%} - -clear all, close all, clc - -load heating_system.dat -U=heating_system(:,2); -Y=heating_system(:,3); - - -dat = iddata (Y, U, 2.0, 'inname', 'input drive voltage', \ - 'inunit', 'Volt', \ - 'outname', 'temperature', \ - 'outunit', '°C') - -% s=15, n=7 -%[sys1, x0] = moen4 (dat, 's', 15, 'n', 7) -[sys1, x0] = moen4 (dat, 's', 15, 'n', 7, 'noise', 'k') - -%sys2 = arx (dat, 7, 7) % normally na = nb -[sys2, x02] = arx (dat, 7); - -%[y1, t1] = lsim (sys1, U, [], x0); -[y1, t1] = lsim (sys1, [U, Y], [], x0); - -%[y2, t] = lsim (sys2(:, 1), U); -[y2, t] = lsim (sys2, U, [], x02); - - -err1 = norm (Y - y1, 1) / norm (Y, 1) -err2 = norm (Y - y2, 1) / norm (Y, 1) - -figure (1) -plot (t, Y, t, y1, t, y2) -title ('DaISy: Heating System [99-001]') -xlim ([t(1), t(end)]) -xlabel ('Time [s]') -ylabel ('Temperature [Degree Celsius]') -legend ('measured', 'simulated subspace', 'simulated ARX', 'location', 'southeast') - - -
--- a/extra/control-devel/devel/HeatingSystemRLS.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,102 +0,0 @@ -%{ -1. Contributed by: - - Roy Smith - Dept. of Electrical & Computer Engineering - University of California, - Santa Barbara, CA 93106 - U.S.A. - roy@ece.ucsb.edu - -2. Process/Description: - - The experiment is a simple SISO heating system. - The input drives a 300 Watt Halogen lamp, suspended - several inches above a thin steel plate. The output - is a thermocouple measurement taken from the back of - the plate. - -3. Sampling interval: - - 2.0 seconds - -4. Number of samples - - 801 - -5. Inputs: - - u: input drive voltage - ... -6. Outputs: - - y: temperature (deg. C) - ... -7. References: - - The use of this experiment and data for robust - control model validation is described in: - - "Sampled Data Model Validation: an Algorithm and - Experimental Application," Geir Dullerud & Roy Smith, - International Journal of Robust and Nonlinear Control, - Vol. 6, No. 9/10, pp. 1065-1078, 1996. - -8. Known properties/peculiarities - - The data (and nominal model) is the above paper have the - output expressed in 10's deg. C. This has been rescaled - to the original units of deg. C. in the DaISy data set. - There is also a -1 volt offset in u in the data shown plotted - in the original paper. This has been removed in the - DaISy dataset. - - The data shows evidence of discrepancies. One of the - issues studied in the above paper is the size of these - discrepancies - measured in this case in terms of the norm - of the smallest perturbation required to account for the - difference between the nominal model and the data. - - The steady state input (prior to the start of the experiment) - is u = 6.0 Volts. - -%} - -clear all, close all, clc - -load heating_system.dat -U=heating_system(:,2); -Y=heating_system(:,3); - - -dat = iddata (Y, U, 2.0, 'inname', 'input drive voltage', \ - 'inunit', 'Volt', \ - 'outname', 'temperature', \ - 'outunit', '°C') - -% s=15, n=7 -[sys1, x0] = moen4 (dat, 's', 15, 'n', 7) -%sys2 = arx (dat, 7, 7) % normally na = nb -[sys2, x02] = arx (dat, 7, 7); -[sys3, x03] = rarx (dat, 7, 7); - -[y1, t1] = lsim (sys1, U, [], x0); -%[y2, t] = lsim (sys2(:, 1), U); -[y2, t] = lsim (sys2, U, [], x02); -[y3, t] = lsim (sys3, U, [], x02); - - -err1 = norm (Y - y1, 1) / norm (Y, 1) -err2 = norm (Y - y2, 1) / norm (Y, 1) -err2 = norm (Y - y3, 1) / norm (Y, 1) - -figure (1) -plot (t, Y, t, y1, t, y2, t, y3) -title ('DaISy: Heating System [99-001]') -xlim ([t(1), t(end)]) -xlabel ('Time [s]') -ylabel ('Temperature [Degree Celsius]') -legend ('measured', 'simulated subspace', 'simulated ARX', 'simulated RLS', 'location', 'southeast') - - -
--- a/extra/control-devel/devel/LakeErie.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,100 +0,0 @@ -%{ -This file describes the data in the erie.dat file. -1. Contributed by: - Peter Van Overschee - K.U.Leuven - ESAT - SISTA - K. Mercierlaan 94 - 3001 Heverlee - Peter.Vanoverschee@esat.kuleuven.ac.be -2. Process/Description: - Data of a simulation (not real !) related to the related to the - identification of the western basin of Lake Erie. The series consists - of 4 series: - U_erie, Y_erie: without noise (original series) - U_erie_n10, Y_erie_n10: 10 percent additive white noise - U_erie_n20, Y_erie_n20: 20 percent additive white noise - U_erie_n30, Y_erie_n30: 30 percent additive white noise -3. Sampling time - 1 month -4. Number of samples: - 57 samples -5. Inputs: - a. water temperature - b. water conductivity - c. water alkalinity - d. NO3 - e. total hardness -6. Outputs: - a. dissolved oxigen - b. algae -7. References: - R.P. Guidorzi, M.P. Losito, T. Muratori, On the last eigenvalue - test in the structural identification of linear multivariable - systems, Proceedings of the V European meeting on cybernetics and - systems research, Vienna, april 1980. -8. Known properties/peculiarities - The considered period runs from march 1968 till november 1972. -9. Some MATLAB-code to retrieve the data - !guzip erie.dat.Z - load erie.dat - U=erie(:,1:20); - Y=erie(:,21:28); - U_erie=U(:,1:5); - U_erie_n10=U(:,6:10); - U_erie_n20=U(:,11:15); - U_erie_n30=U(:,16:20); - Y_erie=Y(:,1:2); - Y_erie_n10=Y(:,3:4); - Y_erie_n20=Y(:,5:6); - Y_erie_n30=Y(:,7:8); -%} - -clear all, close all, clc - -% DaISy code is wrong, -% first column is sample number -load erie.dat -U=erie(:,2:21); -Y=erie(:,22:29); -U_erie=U(:,1:5); -U_erie_n10=U(:,6:10); -U_erie_n20=U(:,11:15); -U_erie_n30=U(:,16:20); -Y_erie=Y(:,1:2); -Y_erie_n10=Y(:,3:4); -Y_erie_n20=Y(:,5:6); -Y_erie_n30=Y(:,7:8); - -Y = {Y_erie; Y_erie_n10; Y_erie_n20; Y_erie_n30}; -U = {U_erie; U_erie_n10; U_erie_n20; U_erie_n30}; - -dat = iddata (Y, U, [], 'inname', {'a. water temperature'; - 'b. water conductivity'; - 'c. water alkalinity'; - 'd. NO3'; - 'e. total hardness'}, \ - 'outname', {'a. dissolved oxygen'; - 'b. algae'}) - -% [sys, x0] = moen4 (dat, 's', 5, 'n', 4) % s=5, n=4 -[sys, x0] = moen4 (dat, 's', 5, 'n', 4, 'noise', 'k') % s=5, n=4 - - -x0=x0{1}; - -[y, t] = lsim (sys, [U_erie, Y_erie], [], x0); -%[y, t] = lsim (sys, U_erie, [], x0); -%[y, t] = lsim (sys, U_erie); - -err = norm (Y_erie - y, 1) / norm (Y_erie, 1) - -figure (1) -p = columns (Y_erie); -for k = 1 : p - subplot (2, 1, k) - plot (t, Y_erie(:,k), 'b', t, y(:,k), 'r') -endfor - -legend ('y measured', 'y simulated', 'location', 'southeast') - -
--- a/extra/control-devel/devel/LakeErieARX.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,155 +0,0 @@ -%{ -This file describes the data in the erie.dat file. -1. Contributed by: - Peter Van Overschee - K.U.Leuven - ESAT - SISTA - K. Mercierlaan 94 - 3001 Heverlee - Peter.Vanoverschee@esat.kuleuven.ac.be -2. Process/Description: - Data of a simulation (not real !) related to the related to the - identification of the western basin of Lake Erie. The series consists - of 4 series: - U_erie, Y_erie: without noise (original series) - U_erie_n10, Y_erie_n10: 10 percent additive white noise - U_erie_n20, Y_erie_n20: 20 percent additive white noise - U_erie_n30, Y_erie_n30: 30 percent additive white noise -3. Sampling time - 1 month -4. Number of samples: - 57 samples -5. Inputs: - a. water temperature - b. water conductivity - c. water alkalinity - d. NO3 - e. total hardness -6. Outputs: - a. dissolved oxygen - b. algae -7. References: - R.P. Guidorzi, M.P. Losito, T. Muratori, On the last eigenvalue - test in the structural identification of linear multivariable - systems, Proceedings of the V European meeting on cybernetics and - systems research, Vienna, april 1980. -8. Known properties/peculiarities - The considered period runs from march 1968 till november 1972. -9. Some MATLAB-code to retrieve the data - !guzip erie.dat.Z - load erie.dat - U=erie(:,1:20); - Y=erie(:,21:28); - U_erie=U(:,1:5); - U_erie_n10=U(:,6:10); - U_erie_n20=U(:,11:15); - U_erie_n30=U(:,16:20); - Y_erie=Y(:,1:2); - Y_erie_n10=Y(:,3:4); - Y_erie_n20=Y(:,5:6); - Y_erie_n30=Y(:,7:8); -%} - -clear all, close all, clc - -% DaISy code is wrong, -% first column is sample number -load erie.dat -U=erie(:,2:21); -Y=erie(:,22:29); -U_erie=U(:,1:5); -U_erie_n10=U(:,6:10); -U_erie_n20=U(:,11:15); -U_erie_n30=U(:,16:20); -Y_erie=Y(:,1:2); -Y_erie_n10=Y(:,3:4); -Y_erie_n20=Y(:,5:6); -Y_erie_n30=Y(:,7:8); - -Y = {Y_erie; Y_erie_n10; Y_erie_n20; Y_erie_n30}; -U = {U_erie; U_erie_n10; U_erie_n20; U_erie_n30}; - -dat = iddata (Y, U, [], 'inname', {'a. water temperature'; - 'b. water conductivity'; - 'c. water alkalinity'; - 'd. NO3'; - 'e. total hardness'}, \ - 'outname', {'a. dissolved oxygen'; - 'b. algae'}) - -[sys, x0, info] = moen4 (dat, 's', 5, 'n', 4) % s=5, n=4 -% sys2 = arx (dat, 4, 4) -[sys2, x02] = arx (dat, 4) - -x0=x0{1}; -x02=x02{1}; - -[y, t] = lsim (sys, U_erie, [], x0); -% [y2, t2] = lsim (sys2(:, 1:5), U_erie); -[y2, t2] = lsim (sys2, U_erie, [], x02); - - -err = norm (Y_erie - y, 1) / norm (Y_erie, 1) -err2 = norm (Y_erie - y2, 1) / norm (Y_erie, 1) - - -figure (1) -p = columns (Y_erie); -for k = 1 : p - subplot (2, 1, k) - plot (t, Y_erie(:,k), t, y(:,k), t, y2(:,k)) - grid on -endfor - -subplot (2, 1, 1) -title ('DaISy: Lake Erie [96-005]') -ylabel ('Dissolved Oxygen [n.s.]') -xlim ([0, 56]) - -subplot (2, 1, 2) -ylabel ('Algae [n.s.]') -xlabel ('Time [months]') -xlim ([0, 56]) - -legend ('measurement DaISy', 'simulation MOEN4', 'simulation ARX', 'location', 'northeast') - - - - - -l = lqe (sys, info.Q, 100*info.Ry, info.S) - - - -[a, b, c, d] = ssdata (sys); - -sys2 = ss ([a-l*c], [b-l*d, l], c, [d, zeros(2)], -1) - -[sys, ~, info] = moen4 (dat, 's', 5, 'n', 4, 'noise', 'k') - -[y, t] = lsim (sys, [U_erie, Y_erie], [], x0); -[y2, t2] = lsim (sys2, [U_erie, Y_erie], [], x0); - -errkp = norm (Y_erie - y, 1) / norm (Y_erie, 1) -err2kp = norm (Y_erie - y2, 1) / norm (Y_erie, 1) - -figure (2) -p = columns (Y_erie); -for k = 1 : p - subplot (2, 1, k) - plot (t, Y_erie(:,k), t, y(:,k), t, y2(:,k)) - grid on -endfor - -subplot (2, 1, 1) -title ('DaISy: Lake Erie [96-005]') -ylabel ('Dissolved Oxygen [n.s.]') -xlim ([0, 56]) - -subplot (2, 1, 2) -ylabel ('Algae [n.s.]') -xlabel ('Time [months]') -xlim ([0, 56]) - -legend ('Measurement DaISy', 'MOEN4 Kalman Predictor', 'MOEN4 Observer', 'location', 'northeast') - -
--- a/extra/control-devel/devel/LakeErieMultiplot.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,159 +0,0 @@ -%{ -This file describes the data in the erie.dat file. -1. Contributed by: - Peter Van Overschee - K.U.Leuven - ESAT - SISTA - K. Mercierlaan 94 - 3001 Heverlee - Peter.Vanoverschee@esat.kuleuven.ac.be -2. Process/Description: - Data of a simulation (not real !) related to the related to the - identification of the western basin of Lake Erie. The series consists - of 4 series: - U_erie, Y_erie: without noise (original series) - U_erie_n10, Y_erie_n10: 10 percent additive white noise - U_erie_n20, Y_erie_n20: 20 percent additive white noise - U_erie_n30, Y_erie_n30: 30 percent additive white noise -3. Sampling time - 1 month -4. Number of samples: - 57 samples -5. Inputs: - a. water temperature - b. water conductivity - c. water alkalinity - d. NO3 - e. total hardness -6. Outputs: - a. dissolved oxygen - b. algae -7. References: - R.P. Guidorzi, M.P. Losito, T. Muratori, On the last eigenvalue - test in the structural identification of linear multivariable - systems, Proceedings of the V European meeting on cybernetics and - systems research, Vienna, april 1980. -8. Known properties/peculiarities - The considered period runs from march 1968 till november 1972. -9. Some MATLAB-code to retrieve the data - !guzip erie.dat.Z - load erie.dat - U=erie(:,1:20); - Y=erie(:,21:28); - U_erie=U(:,1:5); - U_erie_n10=U(:,6:10); - U_erie_n20=U(:,11:15); - U_erie_n30=U(:,16:20); - Y_erie=Y(:,1:2); - Y_erie_n10=Y(:,3:4); - Y_erie_n20=Y(:,5:6); - Y_erie_n30=Y(:,7:8); -%} - -clear all, close all, clc - -% DaISy code is wrong, -% first column is sample number -load erie.dat -U=erie(:,2:21); -Y=erie(:,22:29); -U_erie=U(:,1:5); -U_erie_n10=U(:,6:10); -U_erie_n20=U(:,11:15); -U_erie_n30=U(:,16:20); -Y_erie=Y(:,1:2); -Y_erie_n10=Y(:,3:4); -Y_erie_n20=Y(:,5:6); -Y_erie_n30=Y(:,7:8); - -Y = {Y_erie; Y_erie_n10; Y_erie_n20; Y_erie_n30}; -U = {U_erie; U_erie_n10; U_erie_n20; U_erie_n30}; - -dat = iddata (Y, U, [], 'inname', {'a. water temperature'; - 'b. water conductivity'; - 'c. water alkalinity'; - 'd. NO3'; - 'e. total hardness'}, \ - 'outname', {'a. dissolved oxygen'; - 'b. algae'}) - -[sys, x0, info] = moen4 (dat, 's', 5, 'n', 4) % s=5, n=4 -% sys2 = arx (dat, 4, 4) -[sys2, x02] = arx (dat, 4) - -x0=x0{1}; -x02=x02{1}; - -lsim (sys, sys2, U_erie) - -%{ -[y, t] = lsim (sys, U_erie, [], x0); -% [y2, t2] = lsim (sys2(:, 1:5), U_erie); -[y2, t2] = lsim (sys2, U_erie, [], x02); - - -err = norm (Y_erie - y, 1) / norm (Y_erie, 1) -err2 = norm (Y_erie - y2, 1) / norm (Y_erie, 1) - - -figure (1) -p = columns (Y_erie); -for k = 1 : p - subplot (2, 1, k) - plot (t, Y_erie(:,k), t, y(:,k), t, y2(:,k)) - grid on -endfor - -subplot (2, 1, 1) -title ('DaISy: Lake Erie [96-005]') -ylabel ('Dissolved Oxygen [n.s.]') -xlim ([0, 56]) - -subplot (2, 1, 2) -ylabel ('Algae [n.s.]') -xlabel ('Time [months]') -xlim ([0, 56]) - -legend ('measurement DaISy', 'simulation MOEN4', 'simulation ARX', 'location', 'northeast') - - - - - -l = lqe (sys, info.Q, 100*info.Ry, info.S) - - - -[a, b, c, d] = ssdata (sys); - -sys2 = ss ([a-l*c], [b-l*d, l], c, [d, zeros(2)], -1) - -[sys, ~, info] = moen4 (dat, 's', 5, 'n', 4, 'noise', 'k') - -[y, t] = lsim (sys, [U_erie, Y_erie], [], x0); -[y2, t2] = lsim (sys2, [U_erie, Y_erie], [], x0); - -errkp = norm (Y_erie - y, 1) / norm (Y_erie, 1) -err2kp = norm (Y_erie - y2, 1) / norm (Y_erie, 1) - - -figure (2) -p = columns (Y_erie); -for k = 1 : p - subplot (2, 1, k) - plot (t, Y_erie(:,k), t, y(:,k), t, y2(:,k)) - grid on -endfor - -subplot (2, 1, 1) -title ('DaISy: Lake Erie [96-005]') -ylabel ('Dissolved Oxygen [n.s.]') -xlim ([0, 56]) - -subplot (2, 1, 2) -ylabel ('Algae [n.s.]') -xlabel ('Time [months]') -xlim ([0, 56]) - -legend ('Measurement DaISy', 'MOEN4 Kalman Predictor', 'MOEN4 Kalman Predictor (weak)', 'location', 'northeast') -%} -
--- a/extra/control-devel/devel/MLexp/mln4sid.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,90 +0,0 @@ -%{ -This file describes the data in the powerplant.dat file. -1. Contributed by: - Peter Van Overschee - K.U.Leuven - ESAT - SISTA - K. Mercierlaan 94 - 3001 Heverlee - Peter.Vanoverschee@esat.kuleuven.ac.be -2. Process/Description: - data of a power plant (Pont-sur-Sambre (France)) of 120 MW -3. Sampling time - 1228.8 sec -4. Number of samples: - 200 samples -5. Inputs: - 1. gas flow - 2. turbine valves opening - 3. super heater spray flow - 4. gas dampers - 5. air flow -6. Outputs: - 1. steam pressure - 2. main stem temperature - 3. reheat steam temperature -7. References: - a. R.P. Guidorzi, P. Rossi, Identification of a power plant from normal - operating records. Automatic control theory and applications (Canada, - Vol 2, pp 63-67, sept 1974. - b. Moonen M., De Moor B., Vandenberghe L., Vandewalle J., On- and - off-line identification of linear state-space models, International - Journal of Control, Vol. 49, Jan. 1989, pp.219-232 -8. Known properties/peculiarities - -9. Some MATLAB-code to retrieve the data - !gunzip powerplant.dat.Z - load powerplant.dat - U=powerplant(:,1:5); - Y=powerplant(:,6:8); - Yr=powerplant(:,9:11); - -%} - -clear all, close all, clc - -load powerplant.dat -U=powerplant(:,1:5); -Y=powerplant(:,6:8); -Yr=powerplant(:,9:11); - -inname = {'gas flow', - 'turbine valves opening', - 'super heater spray flow', - 'gas dampers', - 'air flow'}; - -outname = {'steam pressure', - 'main steam temperature', - 'reheat steam temperature'}; - -tsam = 1228.8; - -dat = iddata (Y, U, tsam, 'outputname', outname, 'inputname', inname) - - - -[sys, x0] = n4sid (dat, 8); % s=10, n=8 - - -%sys = ss (a, b, c, d, 1); - -x0 = sys.x0 -sys = ss (sys); -sys = sys(:, 'Measured') - -[y, t] = lsim (sys, U, [], x0); -%[y, t] = lsim (sys, U, 1:size(U,1)); - - -err = norm (Y - y, 1) / norm (Y, 1) - -figure (1) -p = size (Y, 2); -for k = 1 : p - subplot (3, 1, k) - plot (t, Y(:,k), 'b', t, y(:,k), 'r') -end -%title ('DaISy: Power Plant') -%legend ('y measured', 'y simulated', 'location', 'southeast') - -
--- a/extra/control-devel/devel/MLexp/mlpplant.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,72 +0,0 @@ -%{ -This file describes the data in the powerplant.dat file. -1. Contributed by: - Peter Van Overschee - K.U.Leuven - ESAT - SISTA - K. Mercierlaan 94 - 3001 Heverlee - Peter.Vanoverschee@esat.kuleuven.ac.be -2. Process/Description: - data of a power plant (Pont-sur-Sambre (France)) of 120 MW -3. Sampling time - 1228.8 sec -4. Number of samples: - 200 samples -5. Inputs: - 1. gas flow - 2. turbine valves opening - 3. super heater spray flow - 4. gas dampers - 5. air flow -6. Outputs: - 1. steam pressure - 2. main stem temperature - 3. reheat steam temperature -7. References: - a. R.P. Guidorzi, P. Rossi, Identification of a power plant from normal - operating records. Automatic control theory and applications (Canada, - Vol 2, pp 63-67, sept 1974. - b. Moonen M., De Moor B., Vandenberghe L., Vandewalle J., On- and - off-line identification of linear state-space models, International - Journal of Control, Vol. 49, Jan. 1989, pp.219-232 -8. Known properties/peculiarities - -9. Some MATLAB-code to retrieve the data - !gunzip powerplant.dat.Z - load powerplant.dat - U=powerplant(:,1:5); - Y=powerplant(:,6:8); - Yr=powerplant(:,9:11); - -%} - -clear all, close all, clc - -load powerplant.dat -U=powerplant(:,1:5); -Y=powerplant(:,6:8); -Yr=powerplant(:,9:11); - -%{ -dat = iddata (Y, U) - -[sys, x0] = ident (dat, 10, 8) % s=10, n=8 -%} -load pplant - -sys = ss (a, b, c, d, 1); - -[y, t] = lsim (sys, U, 1:size(U,1), x0); - -err = norm (Y - y, 1) / norm (Y, 1) - -figure (1) -p = size (Y, 2); -for k = 1 : p - subplot (3, 1, k) - plot (t, Y(:,k), 'b', t, y(:,k), 'r') -end -%title ('DaISy: Power Plant') -%legend ('y measured', 'y simulated', 'location', 'southeast') - -
--- a/extra/control-devel/devel/MLexp/powerplant.dat Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,200 +0,0 @@ - 1.0000000e+00 -8.1100000e+02 -5.9200000e+02 4.2100000e+02 -6.8000000e+02 -6.8100000e+02 1.1700000e+02 1.2900000e+02 -4.7000000e+01 1.2005000e+02 1.2904000e+02 -4.8588000e+01 - 2.0000000e+00 -8.1200000e+02 -6.1900000e+02 4.7700000e+02 -6.8500000e+02 -6.5100000e+02 1.1300000e+02 1.4100000e+02 -4.2000000e+01 1.0881000e+02 1.3890000e+02 -4.2329000e+01 - 3.0000000e+00 -8.1700000e+02 -5.6500000e+02 5.3800000e+02 -6.7800000e+02 -6.7700000e+02 8.3000000e+01 1.5000000e+02 -3.7000000e+01 8.4903000e+01 1.5790000e+02 -2.9271000e+01 - 4.0000000e+00 -6.9500000e+02 -7.2500000e+02 5.3600000e+02 -6.7400000e+02 -7.0200000e+02 1.4400000e+02 1.7400000e+02 -3.0000000e+00 1.4232000e+02 1.6939000e+02 -9.7179000e+00 - 5.0000000e+00 -6.9700000e+02 -5.7100000e+02 5.3100000e+02 -6.7600000e+02 -6.8500000e+02 1.5600000e+02 1.9600000e+02 1.9000000e+01 1.6235000e+02 1.9724000e+02 4.0350000e+01 - 6.0000000e+00 -6.9700000e+02 -6.1800000e+02 5.3300000e+02 -6.8100000e+02 -7.2100000e+02 1.7400000e+02 1.9200000e+02 6.0000000e+00 2.0722000e+02 2.1180000e+02 4.7120000e+01 - 7.0000000e+00 -7.0200000e+02 -5.7900000e+02 5.4900000e+02 -6.7700000e+02 -6.9900000e+02 1.7100000e+02 1.9300000e+02 3.0000000e+00 2.2415000e+02 2.1638000e+02 4.6753000e+01 - 8.0000000e+00 -7.0300000e+02 -4.8700000e+02 5.7500000e+02 -6.7700000e+02 -6.9400000e+02 1.6900000e+02 2.2400000e+02 1.4000000e+01 2.0604000e+02 2.0174000e+02 3.2968000e+01 - 9.0000000e+00 -7.0500000e+02 -4.4900000e+02 5.6100000e+02 -6.7900000e+02 -6.7800000e+02 1.5500000e+02 2.1100000e+02 1.4000000e+01 1.7784000e+02 1.8128000e+02 1.4550000e+01 - 1.0000000e+01 -7.0500000e+02 -4.3100000e+02 5.6300000e+02 -6.8000000e+02 -6.9200000e+02 1.3700000e+02 1.7500000e+02 4.0000000e+00 1.4376000e+02 1.5895000e+02 2.6711000e-01 - 1.1000000e+01 -7.0700000e+02 -5.0200000e+02 5.6100000e+02 -6.7900000e+02 -6.8600000e+02 1.3000000e+02 1.6500000e+02 1.3000000e+01 1.3855000e+02 1.4555000e+02 -3.0633000e+00 - 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1.8600000e+02 1.5700000e+02 5.7000000e+02 1.3400000e+03 -1.6570000e+03 2.6700000e+02 6.9000000e+01 1.4200000e+02 3.1200000e+02 -2.5199000e+02 -5.5578000e+02 -5.2904000e+02 - 1.8700000e+02 1.5400000e+02 5.5600000e+02 1.3430000e+03 -1.6570000e+03 2.6800000e+02 7.4000000e+01 1.3600000e+02 3.0600000e+02 -2.4545000e+02 -5.5582000e+02 -5.3401000e+02 - 1.8800000e+02 1.5700000e+02 5.3700000e+02 1.3450000e+03 -1.6570000e+03 -4.2500000e+02 1.9600000e+02 1.6400000e+02 2.7700000e+02 -2.8011000e+02 -5.4967000e+02 -5.7073000e+02 - 1.8900000e+02 1.5800000e+02 5.5500000e+02 1.3310000e+03 -1.6530000e+03 -5.8100000e+02 3.4700000e+02 2.0800000e+02 1.3300000e+02 -3.1995000e+02 -4.9697000e+02 -6.1617000e+02 - 1.9000000e+02 1.5800000e+02 5.5100000e+02 1.3150000e+03 -1.6540000e+03 -6.4300000e+02 4.6100000e+02 2.3000000e+02 -5.8000000e+01 -3.2126000e+02 -4.1269000e+02 -6.4590000e+02 - 1.9100000e+02 1.5900000e+02 5.9000000e+02 1.3220000e+03 -1.6560000e+03 -6.8700000e+02 5.2600000e+02 2.0400000e+02 -2.5100000e+02 -3.1328000e+02 -3.0600000e+02 -6.5649000e+02 - 1.9200000e+02 1.6000000e+02 5.6600000e+02 1.3150000e+03 -1.6570000e+03 -7.3700000e+02 5.8100000e+02 1.6100000e+02 -3.8500000e+02 -2.7765000e+02 -1.9647000e+02 -6.5015000e+02 - 1.9300000e+02 1.6000000e+02 5.5300000e+02 1.3150000e+03 -1.6530000e+03 -7.6700000e+02 5.8800000e+02 1.1900000e+02 -4.5800000e+02 -2.2465000e+02 -9.2677000e+01 -6.1837000e+02 - 1.9400000e+02 1.6100000e+02 6.4400000e+02 1.3270000e+03 -1.3960000e+03 -7.3100000e+02 5.4900000e+02 6.3000000e+01 -5.2800000e+02 -1.8456000e+02 -2.2277000e+00 -5.7001000e+02 - 1.9500000e+02 1.5900000e+02 6.4000000e+02 1.3350000e+03 -5.7700000e+02 -6.3900000e+02 4.9700000e+02 5.0000000e+00 -5.5000000e+02 -1.1778000e+02 7.2004000e+01 -5.0293000e+02 - 1.9600000e+02 1.6100000e+02 7.2600000e+02 1.3340000e+03 -5.7700000e+02 -7.3000000e+02 4.2000000e+02 -2.0000000e+01 -4.9800000e+02 -9.6611000e+01 1.2077000e+02 -3.9313000e+02 - 1.9700000e+02 1.7500000e+02 7.2900000e+02 1.3100000e+03 -5.7300000e+02 -7.1100000e+02 3.2700000e+02 -4.9000000e+01 -4.6400000e+02 -6.9050000e+01 1.5983000e+02 -2.8852000e+02 - 1.9800000e+02 1.7500000e+02 8.5400000e+02 1.3300000e+03 -5.7600000e+02 -6.9000000e+02 1.9800000e+02 -7.8000000e+01 -4.3800000e+02 -7.2970000e+01 1.8176000e+02 -1.9352000e+02 - 1.9900000e+02 1.6100000e+02 7.2900000e+02 1.3130000e+03 -5.7300000e+02 -6.3600000e+02 1.5400000e+02 -8.0000000e+01 -4.0900000e+02 -1.7599000e+01 2.0261000e+02 -1.1462000e+02 - 2.0000000e+02 1.7600000e+02 7.0600000e+02 1.3140000e+03 -5.8300000e+02 -7.4500000e+02 1.3000000e+02 -6.0000000e+01 -3.7700000e+02 2.7441000e+01 2.2371000e+02 -4.0925000e+01
--- a/extra/control-devel/devel/PowerPlant.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,85 +0,0 @@ -%{ -This file describes the data in the powerplant.dat file. -1. Contributed by: - Peter Van Overschee - K.U.Leuven - ESAT - SISTA - K. Mercierlaan 94 - 3001 Heverlee - Peter.Vanoverschee@esat.kuleuven.ac.be -2. Process/Description: - data of a power plant (Pont-sur-Sambre (France)) of 120 MW -3. Sampling time - 1228.8 sec -4. Number of samples: - 200 samples -5. Inputs: - 1. gas flow - 2. turbine valves opening - 3. super heater spray flow - 4. gas dampers - 5. air flow -6. Outputs: - 1. steam pressure - 2. main stem temperature - 3. reheat steam temperature -7. References: - a. R.P. Guidorzi, P. Rossi, Identification of a power plant from normal - operating records. Automatic control theory and applications (Canada, - Vol 2, pp 63-67, sept 1974. - b. Moonen M., De Moor B., Vandenberghe L., Vandewalle J., On- and - off-line identification of linear state-space models, International - Journal of Control, Vol. 49, Jan. 1989, pp.219-232 -8. Known properties/peculiarities - -9. Some MATLAB-code to retrieve the data - !gunzip powerplant.dat.Z - load powerplant.dat - U=powerplant(:,1:5); - Y=powerplant(:,6:8); - Yr=powerplant(:,9:11); - -%} - -clear all, close all, clc - -% NB: the code from DaISy is wrong: -% powerplant(:,1) is just the sample number -% therefore increase indices by one -% it took me weeks to find that silly mistake ... -load powerplant.dat -U=powerplant(:,2:6); -Y=powerplant(:,7:9); -Yr=powerplant(:,10:12); - -inname = {'gas flow', - 'turbine valves opening', - 'super heater spray flow', - 'gas dampers', - 'air flow'}; - -outname = {'steam pressure', - 'main steam temperature', - 'reheat steam temperature'}; - -tsam = 1228.8; - -dat = iddata (Y, U, tsam, 'outname', outname, 'inname', inname) - -[sys, x0] = moen4 (dat, 's', 10, 'n', 8) % s=10, n=8 - - -[y, t] = lsim (sys, U, [], x0); - -err = norm (Y - y, 1) / norm (Y, 1) - -figure (1) -p = columns (Y); -for k = 1 : p - subplot (3, 1, k) - plot (t, Y(:,k), 'b', t, y(:,k), 'r') -endfor -%title ('DaISy: Power Plant') -%legend ('y measured', 'y simulated', 'location', 'southeast') - -st = isstable (sys) -
--- a/extra/control-devel/devel/PowerPlantFFT.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,68 +0,0 @@ -%{ -This file describes the data in the powerplant.dat file. -1. Contributed by: - Peter Van Overschee - K.U.Leuven - ESAT - SISTA - K. Mercierlaan 94 - 3001 Heverlee - Peter.Vanoverschee@esat.kuleuven.ac.be -2. Process/Description: - data of a power plant (Pont-sur-Sambre (France)) of 120 MW -3. Sampling time - 1228.8 sec -4. Number of samples: - 200 samples -5. Inputs: - 1. gas flow - 2. turbine valves opening - 3. super heater spray flow - 4. gas dampers - 5. air flow -6. Outputs: - 1. steam pressure - 2. main stem temperature - 3. reheat steam temperature -7. References: - a. R.P. Guidorzi, P. Rossi, Identification of a power plant from normal - operating records. Automatic control theory and applications (Canada, - Vol 2, pp 63-67, sept 1974. - b. Moonen M., De Moor B., Vandenberghe L., Vandewalle J., On- and - off-line identification of linear state-space models, International - Journal of Control, Vol. 49, Jan. 1989, pp.219-232 -8. Known properties/peculiarities - -9. Some MATLAB-code to retrieve the data - !gunzip powerplant.dat.Z - load powerplant.dat - U=powerplant(:,1:5); - Y=powerplant(:,6:8); - Yr=powerplant(:,9:11); - -%} - -clear all, close all, clc - -load powerplant.dat -U=powerplant(:,1:5); -Y=powerplant(:,6:8); -Yr=powerplant(:,9:11); - -inname = {'gas flow', - 'turbine valves opening', - 'super heater spray flow', - 'gas dampers', - 'air flow'}; - -outname = {'steam pressure', - 'main steam temperature', - 'reheat steam temperature'}; - -tsam = 1228.8; - -dat = iddata (Y, U, tsam, 'outputname', outname, 'inputname', inname) - - -a = fft (dat) - -b = ifft (a) -
--- a/extra/control-devel/devel/PowerPlantKP.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,84 +0,0 @@ -%{ -This file describes the data in the powerplant.dat file. -1. Contributed by: - Peter Van Overschee - K.U.Leuven - ESAT - SISTA - K. Mercierlaan 94 - 3001 Heverlee - Peter.Vanoverschee@esat.kuleuven.ac.be -2. Process/Description: - data of a power plant (Pont-sur-Sambre (France)) of 120 MW -3. Sampling time - 1228.8 sec -4. Number of samples: - 200 samples -5. Inputs: - 1. gas flow - 2. turbine valves opening - 3. super heater spray flow - 4. gas dampers - 5. air flow -6. Outputs: - 1. steam pressure - 2. main stem temperature - 3. reheat steam temperature -7. References: - a. R.P. Guidorzi, P. Rossi, Identification of a power plant from normal - operating records. Automatic control theory and applications (Canada, - Vol 2, pp 63-67, sept 1974. - b. Moonen M., De Moor B., Vandenberghe L., Vandewalle J., On- and - off-line identification of linear state-space models, International - Journal of Control, Vol. 49, Jan. 1989, pp.219-232 -8. Known properties/peculiarities - -9. Some MATLAB-code to retrieve the data - !gunzip powerplant.dat.Z - load powerplant.dat - U=powerplant(:,1:5); - Y=powerplant(:,6:8); - Yr=powerplant(:,9:11); - -%} - -clear all, close all, clc - -% NB: the code from DaISy is wrong: -% powerplant(:,1) is just the sample number -% therefore increase indices by one -% it took me weeks to find that silly mistake ... -load powerplant.dat -U=powerplant(:,2:6); -Y=powerplant(:,7:9); -Yr=powerplant(:,10:12); - -inname = {'gas flow', - 'turbine valves opening', - 'super heater spray flow', - 'gas dampers', - 'air flow'}; - -outname = {'steam pressure', - 'main steam temperature', - 'reheat steam temperature'}; - -tsam = 1228.8; - -dat = iddata (Y, U, tsam, 'outname', outname, 'inname', inname) - -[sys, x0] = moen4 (dat, 's', 10, 'n', 8, 'noise', 'k') % s=10, n=8 - -[y, t] = lsim (sys, [U, Y], [], x0); - -err = norm (Y - y, 1) / norm (Y, 1) - -figure (1) -p = columns (Y); -for k = 1 : p - subplot (3, 1, k) - plot (t, Y(:,k), 'b', t, y(:,k), 'r') -endfor -%title ('DaISy: Power Plant') -%legend ('y measured', 'y simulated', 'location', 'southeast') - -st = isstable (sys) -
--- a/extra/control-devel/devel/PowerPlantVS.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,85 +0,0 @@ -%{ -This file describes the data in the powerplant.dat file. -1. Contributed by: - Peter Van Overschee - K.U.Leuven - ESAT - SISTA - K. Mercierlaan 94 - 3001 Heverlee - Peter.Vanoverschee@esat.kuleuven.ac.be -2. Process/Description: - data of a power plant (Pont-sur-Sambre (France)) of 120 MW -3. Sampling time - 1228.8 sec -4. Number of samples: - 200 samples -5. Inputs: - 1. gas flow - 2. turbine valves opening - 3. super heater spray flow - 4. gas dampers - 5. air flow -6. Outputs: - 1. steam pressure - 2. main stem temperature - 3. reheat steam temperature -7. References: - a. R.P. Guidorzi, P. Rossi, Identification of a power plant from normal - operating records. Automatic control theory and applications (Canada, - Vol 2, pp 63-67, sept 1974. - b. Moonen M., De Moor B., Vandenberghe L., Vandewalle J., On- and - off-line identification of linear state-space models, International - Journal of Control, Vol. 49, Jan. 1989, pp.219-232 -8. Known properties/peculiarities - -9. Some MATLAB-code to retrieve the data - !gunzip powerplant.dat.Z - load powerplant.dat - U=powerplant(:,1:5); - Y=powerplant(:,6:8); - Yr=powerplant(:,9:11); - -%} - - close all, clc - -% NB: the code from DaISy is wrong: -% powerplant(:,1) is just the sample number -% therefore increase indices by one -% it took me weeks to find that silly mistake ... -load powerplant.dat -U=powerplant(:,2:6); -Y=powerplant(:,7:9); -Yr=powerplant(:,10:12); - -inname = {'gas flow', - 'turbine valves opening', - 'super heater spray flow', - 'gas dampers', - 'air flow'}; - -outname = {'steam pressure', - 'main steam temperature', - 'reheat steam temperature'}; - -tsam = 1228.8; - -dat = iddata (Y, U, tsam, 'outname', outname, 'inname', inname) - -[sys, x0] = identVS (dat, 10, 8) % s=10, n=8 - - -[y, t] = lsim (sys, U, [], x0); - -err = norm (Y - y, 1) / norm (Y, 1) - -figure (1) -p = columns (Y); -for k = 1 : p - subplot (3, 1, k) - plot (t, Y(:,k), 'b', t, y(:,k), 'r') -endfor -%title ('DaISy: Power Plant') -%legend ('y measured', 'y simulated', 'location', 'southeast') - -st = isstable (sys) -
--- a/extra/control-devel/devel/PowerPlant_a.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,81 +0,0 @@ -%{ -This file describes the data in the powerplant.dat file. -1. Contributed by: - Peter Van Overschee - K.U.Leuven - ESAT - SISTA - K. Mercierlaan 94 - 3001 Heverlee - Peter.Vanoverschee@esat.kuleuven.ac.be -2. Process/Description: - data of a power plant (Pont-sur-Sambre (France)) of 120 MW -3. Sampling time - 1228.8 sec -4. Number of samples: - 200 samples -5. Inputs: - 1. gas flow - 2. turbine valves opening - 3. super heater spray flow - 4. gas dampers - 5. air flow -6. Outputs: - 1. steam pressure - 2. main stem temperature - 3. reheat steam temperature -7. References: - a. R.P. Guidorzi, P. Rossi, Identification of a power plant from normal - operating records. Automatic control theory and applications (Canada, - Vol 2, pp 63-67, sept 1974. - b. Moonen M., De Moor B., Vandenberghe L., Vandewalle J., On- and - off-line identification of linear state-space models, International - Journal of Control, Vol. 49, Jan. 1989, pp.219-232 -8. Known properties/peculiarities - -9. Some MATLAB-code to retrieve the data - !gunzip powerplant.dat.Z - load powerplant.dat - U=powerplant(:,1:5); - Y=powerplant(:,6:8); - Yr=powerplant(:,9:11); - -%} - - close all, clc - -load powerplant.dat -U=powerplant(:,1:5); -Y=powerplant(:,6:8); -Yr=powerplant(:,9:11); - -inname = {'gas flow', - 'turbine valves opening', - 'super heater spray flow', - 'gas dampers', - 'air flow'}; - -outname = {'steam pressure', - 'main steam temperature', - 'reheat steam temperature'}; - -tsam = 1228.8; - -dat = iddata (Y, U, tsam, 'outname', outname, 'inname', inname) - -[sys, x0] = ident_a (dat, 10, 8) % s=10, n=8 - - -[y, t] = lsim (sys, U, [], x0); - -err = norm (Y - y, 1) / norm (Y, 1) - -figure (1) -p = columns (Y); -for k = 1 : p - subplot (3, 1, k) - plot (t, Y(:,k), 'b', t, y(:,k), 'r') -endfor -%title ('DaISy: Power Plant') -%legend ('y measured', 'y simulated', 'location', 'southeast') - -st = isstable (sys) -
--- a/extra/control-devel/devel/PowerPlant_combinations.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,92 +0,0 @@ -%{ -This file describes the data in the powerplant.dat file. -1. Contributed by: - Peter Van Overschee - K.U.Leuven - ESAT - SISTA - K. Mercierlaan 94 - 3001 Heverlee - Peter.Vanoverschee@esat.kuleuven.ac.be -2. Process/Description: - data of a power plant (Pont-sur-Sambre (France)) of 120 MW -3. Sampling time - 1228.8 sec -4. Number of samples: - 200 samples -5. Inputs: - 1. gas flow - 2. turbine valves opening - 3. super heater spray flow - 4. gas dampers - 5. air flow -6. Outputs: - 1. steam pressure - 2. main stem temperature - 3. reheat steam temperature -7. References: - a. R.P. Guidorzi, P. Rossi, Identification of a power plant from normal - operating records. Automatic control theory and applications (Canada, - Vol 2, pp 63-67, sept 1974. - b. Moonen M., De Moor B., Vandenberghe L., Vandewalle J., On- and - off-line identification of linear state-space models, International - Journal of Control, Vol. 49, Jan. 1989, pp.219-232 -8. Known properties/peculiarities - -9. Some MATLAB-code to retrieve the data - !gunzip powerplant.dat.Z - load powerplant.dat - U=powerplant(:,1:5); - Y=powerplant(:,6:8); - Yr=powerplant(:,9:11); - -%} - -clear all, close all, clc - -% NB: the code from DaISy is wrong: -% powerplant(:,1) is just the sample number -% therefore increase indices by one -% it took me weeks to find that silly mistake ... -load powerplant.dat -U=powerplant(:,2:6); -Y=powerplant(:,7:9); -Yr=powerplant(:,10:12); - -inname = {'gas flow', - 'turbine valves opening', - 'super heater spray flow', - 'gas dampers', - 'air flow'}; - -outname = {'steam pressure', - 'main steam temperature', - 'reheat steam temperature'}; - -tsam = 1228.8; - -dat = iddata (Y, U, tsam, 'outname', outname, 'inname', inname) - - -err = zeros (3, 3); - -for meth = 0:2 - for alg = 0:2 - [sys, x0] = ident_combinations (dat, 10, 8, meth, alg); % s=10, n=8 - [y, t] = lsim (sys, U, [], x0); - err(meth+1, alg+1) = norm (Y - y, 1) / norm (Y, 1); - endfor -endfor - -err - -%{ -figure (1) -p = columns (Y); -for k = 1 : p - subplot (3, 1, k) - plot (t, Y(:,k), 'b', t, y(:,k), 'r') -endfor -%title ('DaISy: Power Plant') -%legend ('y measured', 'y simulated', 'location', 'southeast') - -st = isstable (sys) -%}
--- a/extra/control-devel/devel/REDUCTION_METHODS Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,57 +0,0 @@ -Reduction Methods - -absolute/additive error - BTA balanced truncation - SPA singular perturbation approximation - HNA Hankel-norm approximation - -relative/multiplicative error - BST balanced stochastic truncation - - -modred Model Reduction - -AB 09 ID - BTA SR - - BTA BFSR - - SPA SR - - SPA BFSR - FW BTA SR - FW BTA BFSR - FW SPA SR - FW SPA BFSR - -AB 09 JD - HNA - FW HNA - -AB 09 HD BST BTA SR - BST BTA BFSR - BST SPA SR - BST SPA BFSR - - -conred Controller Reduction - -SB 16 AD - BTA SR - - BTA BFSR - - SPA SR - - SPA BFSR - FW BTA SR - FW BTA BFSR - FW SPA SR - FW SPA BFSR - -SB 16 BD CF BTA SR - CF BTA BFSR - CF SPA SR - CF SPA BFSR - -SB 16 CD FWCF BTA SR - FWCF BTA BFSR - - - -FW frequency-weighted -CF coprime factorization - -SR square-root -BFSR balancing-free square-root \ No newline at end of file
--- a/extra/control-devel/devel/armax.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,215 +0,0 @@ -## Copyright (C) 2012 Lukas F. Reichlin -## -## This file is part of LTI Syncope. -## -## LTI Syncope is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## LTI Syncope is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with LTI Syncope. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{sys} =} arx (@var{dat}, @var{na}, @var{nb}) -## ARX -## @end deftypefn - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: April 2012 -## Version: 0.1 - -function [sys, varargout] = armax (dat, na, nb, nc) - - ## TODO: delays - - if (nargin != 3) - print_usage (); - endif - - if (! isa (dat, "iddata")) - error ("arx: first argument must be an iddata dataset"); - endif - - ## p: outputs, m: inputs, ex: experiments - [~, p, m, ex] = size (dat); - - ## extract data - Y = dat.y; - U = dat.u; - tsam = dat.tsam; - - ## multi-experiment data requires equal sampling times - if (ex > 1 && ! isequal (tsam{:})) - error ("arx: require equally sampled experiments"); - else - tsam = tsam{1}; - endif - - - if (is_real_scalar (na, nb)) - na = repmat (na, p, 1); # na(p-by-1) - nb = repmat (nb, p, m); # nb(p-by-m) - elseif (! (is_real_vector (na) && is_real_matrix (nb) \ - && rows (na) == p && rows (nb) == p && columns (nb) == m)) - error ("arx: require na(%dx1) instead of (%dx%d) and nb(%dx%d) instead of (%dx%d)", \ - p, rows (na), columns (na), p, m, rows (nb), columns (nb)); - endif - - max_nb = max (nb, [], 2); # one maximum for each row/output, max_nb(p-by-1) - n = max (na, max_nb); # n(p-by-1) - - ## create empty cells for numerator and denominator polynomials - num = cell (p, m+p); - den = cell (p, m+p); - - ## MIMO (p-by-m) models are identified as p MISO (1-by-m) models - ## For multi-experiment data, minimize the trace of the error - for i = 1 : p # for every output - Phi = cell (ex, 1); # one regression matrix per experiment - for e = 1 : ex # for every experiment - ## avoid warning: toeplitz: column wins anti-diagonal conflict - ## therefore set first row element equal to y(1) - PhiY = toeplitz (Y{e}(1:end-1, i), [Y{e}(1, i); zeros(na(i)-1, 1)]); - ## create MISO Phi for every experiment - PhiU = arrayfun (@(x) toeplitz (U{e}(1:end-1, x), [U{e}(1, x); zeros(nb(i,x)-1, 1)]), 1:m, "uniformoutput", false); - Phi{e} = (horzcat (-PhiY, PhiU{:}))(n(i):end, :); - endfor - - ## compute parameter vector Theta - Theta = __theta__ (Phi, Y, i, n); - - ## extract polynomial matrices A and B from Theta - ## A is a scalar polynomial for output i, i=1:p - ## B is polynomial row vector (1-by-m) for output i - A = [1; Theta(1:na(i))]; # a0 = 1, a1 = Theta(1), an = Theta(n) - ThetaB = Theta(na(i)+1:end); # all polynomials from B are in one column vector - B = mat2cell (ThetaB, nb(i,:)); # now separate the polynomials, one for each input - B = reshape (B, 1, []); # make B a row cell (1-by-m) - B = cellfun (@(x) [0; x], B, "uniformoutput", false); # b0 = 0 (leading zero required by filt) - - ## add error inputs - Be = repmat ({0}, 1, p); # there are as many error inputs as system outputs (p) - Be(i) = 1; # inputs m+1:m+p are zero, except m+i which is one - num(i, :) = [B, Be]; # numerator polynomials for output i, individual for each input - den(i, :) = repmat ({A}, 1, m+p); # in a row (output i), all inputs have the same denominator polynomial - endfor - - ## A(q) y(t) = B(q) u(t) + e(t) - ## there is only one A per row - ## B(z) and A(z) are a Matrix Fraction Description (MFD) - ## y = A^-1(q) B(q) u(t) + A^-1(q) e(t) - ## since A(q) is a diagonal polynomial matrix, its inverse is trivial: - ## the corresponding transfer function has common row denominators. - - sys = filt (num, den, tsam); # filt creates a transfer function in z^-1 - - ## compute initial state vector x0 if requested - ## this makes only sense for state-space models, therefore convert TF to SS - if (nargout > 1) - sys = prescale (ss (sys(:,1:m))); - x0 = slib01cd (Y, U, sys.a, sys.b, sys.c, sys.d, 0.0); - ## return x0 as vector for single-experiment data - ## instead of a cell containing one vector - if (numel (x0) == 1) - x0 = x0{1}; - endif - varargout{1} = x0; - endif - -endfunction - - -%function theta = __theta__ (phi, y, i, n) -function Theta = __theta__ (Phi, Y, i, n) - - - if (numel (Phi) == 1) # single-experiment dataset - % recursive pseudolinear regression, naive formula - gamma = ? - Theta = ? - R = ? - for t = 1 : rows (Phi{1}) - phi = Phi{1}(t,:); # note that my phi is Ljung's phi.' - y = Y{1}(t+n(i), :); - epsilon = y - phi*Theta; - R += gamma * (phi.'*phi - R) - Theta += gamma * R \ phi.' * epsilon; - endfor -%{ - % recursive least-squares with efficient matrix inversion - [pr, pc] = size (Phi{1}); - lambda = 1; % default 1 - Theta = zeros (pc, 1); - P = 10 * eye (pc); - for t = 1 : pr - phi = Phi{1}(t,:); # note that my phi is Ljung's phi.' - y = Y{1}(t+n(i), :); - den = lambda + phi*P*phi.'; - L = P * phi.' / den; - P = (P - (P * phi.' * phi * P) / den) / lambda; - Theta += L * (y - phi*Theta); - endfor -%} -%{ - ## use "square-root algorithm" - A = horzcat (phi{1}, y{1}(n(i)+1:end, i)); # [Phi, Y] - R0 = triu (qr (A, 0)); # 0 for economy-size R (without zero rows) - R1 = R0(1:end-1, 1:end-1); # R1 is triangular - can we exploit this in R1\R2? - R2 = R0(1:end-1, end); - theta = __ls_svd__ (R1, R2); # R1 \ R2 - - ## Theta = Phi \ Y(n+1:end, :); # naive formula - ## theta = __ls_svd__ (phi{1}, y{1}(n(i)+1:end, i)); -%} - else # multi-experiment dataset - ## TODO: find more sophisticated formula than - ## Theta = (Phi1' Phi + Phi2' Phi2 + ...) \ (Phi1' Y1 + Phi2' Y2 + ...) - - ## covariance matrix C = (Phi1' Phi + Phi2' Phi2 + ...) - tmp = cellfun (@(Phi) Phi.' * Phi, phi, "uniformoutput", false); - rc = cellfun (@rcond, tmp); # C auch noch testen? QR oder SVD? - C = plus (tmp{:}); - - ## PhiTY = (Phi1' Y1 + Phi2' Y2 + ...) - tmp = cellfun (@(Phi, Y) Phi.' * Y(n(i)+1:end, i), phi, y, "uniformoutput", false); - PhiTY = plus (tmp{:}); - - ## pseudoinverse Theta = C \ Phi'Y - theta = __ls_svd__ (C, PhiTY); - endif - -endfunction - - -function x = __ls_svd__ (A, b) - - ## solve the problem Ax=b - ## x = A\b would also work, - ## but this way we have better control and warnings - - ## solve linear least squares problem by pseudoinverse - ## the pseudoinverse is computed by singular value decomposition - ## M = U S V* ---> M+ = V S+ U* - ## Th = Ph \ Y = Ph+ Y - ## Th = V S+ U* Y, S+ = 1 ./ diag (S) - - [U, S, V] = svd (A, 0); # 0 for "economy size" decomposition - S = diag (S); # extract main diagonal - r = sum (S > eps*S(1)); - if (r < length (S)) - warning ("arx: rank-deficient coefficient matrix"); - warning ("sampling time too small"); - warning ("persistence of excitation"); - endif - V = V(:, 1:r); - S = S(1:r); - U = U(:, 1:r); - x = V * (S .\ (U' * b)); # U' is the conjugate transpose - -endfunction
--- a/extra/control-devel/devel/arx_siso.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,229 +0,0 @@ -## Copyright (C) 2012 Lukas F. Reichlin -## -## This file is part of LTI Syncope. -## -## LTI Syncope is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## LTI Syncope is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with LTI Syncope. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{sys} =} arx (@var{dat}, @var{na}, @var{nb}) -## ARX -## @end deftypefn - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: April 2012 -## Version: 0.1 - -function [sys, varargout] = arx (dat, varargin) - - ## TODO: delays - - if (nargin < 2) - print_usage (); - endif - - if (! isa (dat, "iddata")) - error ("arx: first argument must be an iddata dataset"); - endif - -% if (nargin > 2) # arx (dat, ...) - if (is_real_scalar (varargin{1})) # arx (dat, n, ...) - varargin = horzcat (varargin(2:end), {"na"}, varargin(1), {"nb"}, varargin(1)); - endif - if (isstruct (varargin{1})) # arx (dat, opt, ...), arx (dat, n, opt, ...) - varargin = horzcat (__opt2cell__ (varargin{1}), varargin(2:end)); - endif -% endif - - nkv = numel (varargin); # number of keys and values - - if (rem (nkv, 2)) - error ("arx: keys and values must come in pairs"); - endif - - - ## p: outputs, m: inputs, ex: experiments - [~, p, m, ex] = size (dat); # dataset dimensions - - ## extract data - Y = dat.y; - U = dat.u; - tsam = dat.tsam; - - ## multi-experiment data requires equal sampling times - if (ex > 1 && ! isequal (tsam{:})) - error ("arx: require equally sampled experiments"); - else - tsam = tsam{1}; - endif - - - ## default arguments - na = []; - nb = []; % ??? - nk = []; - - ## handle keys and values - for k = 1 : 2 : nkv - key = lower (varargin{k}); - val = varargin{k+1}; - switch (key) - ## TODO: proper argument checking - case "na" - na = val; - case "nb" - nb = val; - case "nk" - error ("nk"); - otherwise - warning ("arx: invalid property name '%s' ignored", key); - endswitch - endfor - - - if (is_real_scalar (na, nb)) - na = repmat (na, p, 1); # na(p-by-1) - nb = repmat (nb, p, m); # nb(p-by-m) - elseif (! (is_real_vector (na) && is_real_matrix (nb) \ - && rows (na) == p && rows (nb) == p && columns (nb) == m)) - error ("arx: require na(%dx1) instead of (%dx%d) and nb(%dx%d) instead of (%dx%d)", \ - p, rows (na), columns (na), p, m, rows (nb), columns (nb)); - endif - - max_nb = max (nb, [], 2); # one maximum for each row/output, max_nb(p-by-1) - n = max (na, max_nb); # n(p-by-1) - - ## create empty cells for numerator and denominator polynomials - % num = cell (p, m+p); - % den = cell (p, m+p); - num = cell (p, m); - den = cell (p, m); - - ## MIMO (p-by-m) models are identified as pm SISO models - ## For multi-experiment data, minimize the trace of the error - for i = 1 : p # for every output - for j = 1 : m # for every input - Phi = cell (ex, 1); # one regression matrix per experiment - for e = 1 : ex # for every experiment - ## avoid warning: toeplitz: column wins anti-diagonal conflict - ## therefore set first row element equal to y(1) - PhiY = toeplitz (Y{e}(1:end-1, i), [Y{e}(1, i); zeros(na(i,j)-1, 1)]); - PhiU = toeplitz (U{e}(1:end-1, j), [U{e}(1, j); zeros(nb(i,j)-1, 1)]); - Phi{e} = [-PhiY, PhiU](n(i):end, :); - endfor - - ## compute parameter vector Theta - Theta = __theta__ (Phi, Y, i, n); - - ## extract polynomials A and B from Theta - A = [1; Theta(1:na(i,j))]; # a0 = 1, a1 = Theta(1), an = Theta(n) - B = [0; Theta(na(i,j)+1:end)]; # b0 = 0 (leading zero required by filt) - - num(i,j) = A; - den(i,j) = B; - - %{ - ## add error inputs - Be = repmat ({0}, 1, p); # there are as many error inputs as system outputs (p) - Be(i) = 1; # inputs m+1:m+p are zero, except m+i which is one - num(i, :) = [B, Be]; # numerator polynomials for output i, individual for each input - den(i, :) = repmat ({A}, 1, m+p); # in a row (output i), all inputs have the same denominator polynomial - %} - endfor - endfor - - %{ - ## A(q) y(t) = B(q) u(t) + e(t) - ## there is only one A per row - ## B(z) and A(z) are a Matrix Fraction Description (MFD) - ## y = A^-1(q) B(q) u(t) + A^-1(q) e(t) - ## since A(q) is a diagonal polynomial matrix, its inverse is trivial: - ## the corresponding transfer function has common row denominators. - %} - - sys = filt (num, den, tsam); # filt creates a transfer function in z^-1 - - ## compute initial state vector x0 if requested - ## this makes only sense for state-space models, therefore convert TF to SS - if (nargout > 1) - sys = prescale (ss (sys(:,1:m))); - x0 = slib01cd (Y, U, sys.a, sys.b, sys.c, sys.d, 0.0); - ## return x0 as vector for single-experiment data - ## instead of a cell containing one vector - if (numel (x0) == 1) - x0 = x0{1}; - endif - varargout{1} = x0; - endif - -endfunction - - -function theta = __theta__ (phi, y, i, n) - - if (numel (phi) == 1) # single-experiment dataset - ## use "square-root algorithm" - A = horzcat (phi{1}, y{1}(n(i)+1:end, i)); # [Phi, Y] - R0 = triu (qr (A, 0)); # 0 for economy-size R (without zero rows) - R1 = R0(1:end-1, 1:end-1); # R1 is triangular - can we exploit this in R1\R2? - R2 = R0(1:end-1, end); - theta = __ls_svd__ (R1, R2); # R1 \ R2 - - ## Theta = Phi \ Y(n+1:end, :); # naive formula - ## theta = __ls_svd__ (phi{1}, y{1}(n(i)+1:end, i)); - else # multi-experiment dataset - ## TODO: find more sophisticated formula than - ## Theta = (Phi1' Phi + Phi2' Phi2 + ...) \ (Phi1' Y1 + Phi2' Y2 + ...) - - ## covariance matrix C = (Phi1' Phi + Phi2' Phi2 + ...) - tmp = cellfun (@(Phi) Phi.' * Phi, phi, "uniformoutput", false); - % rc = cellfun (@rcond, tmp); # C auch noch testen? QR oder SVD? - C = plus (tmp{:}); - - ## PhiTY = (Phi1' Y1 + Phi2' Y2 + ...) - tmp = cellfun (@(Phi, Y) Phi.' * Y(n(i)+1:end, i), phi, y, "uniformoutput", false); - PhiTY = plus (tmp{:}); - - ## pseudoinverse Theta = C \ Phi'Y - theta = __ls_svd__ (C, PhiTY); - endif - -endfunction - - -function x = __ls_svd__ (A, b) - - ## solve the problem Ax=b - ## x = A\b would also work, - ## but this way we have better control and warnings - - ## solve linear least squares problem by pseudoinverse - ## the pseudoinverse is computed by singular value decomposition - ## M = U S V* ---> M+ = V S+ U* - ## Th = Ph \ Y = Ph+ Y - ## Th = V S+ U* Y, S+ = 1 ./ diag (S) - - [U, S, V] = svd (A, 0); # 0 for "economy size" decomposition - S = diag (S); # extract main diagonal - r = sum (S > eps*S(1)); - if (r < length (S)) - warning ("arx: rank-deficient coefficient matrix"); - warning ("sampling time too small"); - warning ("persistence of excitation"); - endif - V = V(:, 1:r); - S = S(1:r); - U = U(:, 1:r); - x = V * (S .\ (U' * b)); # U' is the conjugate transpose - -endfunction
--- a/extra/control-devel/devel/compare_results_hnamodred.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,33 +0,0 @@ - Mo = [ - - -0.23915 0.30723 1.16297 -1.19671 1.04965 - -2.97091 -0.23915 2.62702 -3.10273 3.70515 - 0.00000 0.00000 -0.51368 1.28421 -0.82227 - 0.00000 0.00000 -0.15189 -0.51368 0.74348 - 0.44660 -0.01427 0.47803 -0.20129 0.02190 -]; - - Me = [ - - -0.23910 0.30720 1.16300 1.19670 -1.04970 - -2.97090 -0.23910 2.62700 3.10270 -3.70520 - 0.00000 0.00000 -0.51370 -1.28420 0.82230 - 0.00000 0.00000 0.15190 -0.51370 0.74350 - -0.44660 0.01430 -0.47800 -0.20130 0.02190 -]; - -syso = ss (Mo(1:4, 1:4), Mo(1:4, 5), Mo(5, 1:4), Mo(5, 5)) - -syse = ss (Me(1:4, 1:4), Me(1:4, 5), Me(5, 1:4), Me(5, 5)) - -figure (1) -bode (syso) - -figure (2) -bode (syse) - -figure (3) -step (syso) - -figure (4) -step (syse) \ No newline at end of file
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--- a/extra/control-devel/devel/dksyn/AB04MD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,345 +0,0 @@ - SUBROUTINE AB04MD( TYPE, N, M, P, ALPHA, BETA, A, LDA, B, LDB, C, - $ LDC, D, LDD, IWORK, DWORK, LDWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To perform a transformation on the parameters (A,B,C,D) of a -C system, which is equivalent to a bilinear transformation of the -C corresponding transfer function matrix. -C -C ARGUMENTS -C -C Mode Parameters -C -C TYPE CHARACTER*1 -C Indicates the type of the original system and the -C transformation to be performed as follows: -C = 'D': discrete-time -> continuous-time; -C = 'C': continuous-time -> discrete-time. -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the state matrix A. N >= 0. -C -C M (input) INTEGER -C The number of system inputs. M >= 0. -C -C P (input) INTEGER -C The number of system outputs. P >= 0. -C -C ALPHA, (input) DOUBLE PRECISION -C BETA Parameters specifying the bilinear transformation. -C Recommended values for stable systems: ALPHA = 1, -C BETA = 1. ALPHA <> 0, BETA <> 0. -C -C A (input/output) DOUBLE PRECISION array, dimension (LDA,N) -C On entry, the leading N-by-N part of this array must -C contain the state matrix A of the original system. -C On exit, the leading N-by-N part of this array contains -C _ -C the state matrix A of the transformed system. -C -C LDA INTEGER -C The leading dimension of array A. LDA >= MAX(1,N). -C -C B (input/output) DOUBLE PRECISION array, dimension (LDB,M) -C On entry, the leading N-by-M part of this array must -C contain the input matrix B of the original system. -C On exit, the leading N-by-M part of this array contains -C _ -C the input matrix B of the transformed system. -C -C LDB INTEGER -C The leading dimension of array B. LDB >= MAX(1,N). -C -C C (input/output) DOUBLE PRECISION array, dimension (LDC,N) -C On entry, the leading P-by-N part of this array must -C contain the output matrix C of the original system. -C On exit, the leading P-by-N part of this array contains -C _ -C the output matrix C of the transformed system. -C -C LDC INTEGER -C The leading dimension of array C. LDC >= MAX(1,P). -C -C D (input/output) DOUBLE PRECISION array, dimension (LDD,M) -C On entry, the leading P-by-M part of this array must -C contain the input/output matrix D for the original system. -C On exit, the leading P-by-M part of this array contains -C _ -C the input/output matrix D of the transformed system. -C -C LDD INTEGER -C The leading dimension of array D. LDD >= MAX(1,P). -C -C Workspace -C -C IWORK INTEGER array, dimension (N) -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C On exit, if INFO = 0, DWORK(1) returns the optimal value -C of LDWORK. -C -C LDWORK INTEGER -C The length of the array DWORK. LDWORK >= MAX(1,N). -C For optimum performance LDWORK >= MAX(1,N*NB), where NB -C is the optimal blocksize. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C = 1: if the matrix (ALPHA*I + A) is exactly singular; -C = 2: if the matrix (BETA*I - A) is exactly singular. -C -C METHOD -C -C The parameters of the discrete-time system are transformed into -C the parameters of the continuous-time system (TYPE = 'D'), or -C vice-versa (TYPE = 'C') by the transformation: -C -C 1. Discrete -> continuous -C _ -1 -C A = beta*(alpha*I + A) * (A - alpha*I) -C _ -1 -C B = sqrt(2*alpha*beta) * (alpha*I + A) * B -C _ -1 -C C = sqrt(2*alpha*beta) * C * (alpha*I + A) -C _ -1 -C D = D - C * (alpha*I + A) * B -C -C which is equivalent to the bilinear transformation -C -C z - alpha -C z -> s = beta --------- . -C z + alpha -C -C of one transfer matrix onto the other. -C -C 2. Continuous -> discrete -C _ -1 -C A = alpha*(beta*I - A) * (beta*I + A) -C _ -1 -C B = sqrt(2*alpha*beta) * (beta*I - A) * B -C _ -1 -C C = sqrt(2*alpha*beta) * C * (beta*I - A) -C _ -1 -C D = D + C * (beta*I - A) * B -C -C which is equivalent to the bilinear transformation -C -C beta + s -C s -> z = alpha -------- . -C beta - s -C -C of one transfer matrix onto the other. -C -C REFERENCES -C -C [1] Al-Saggaf, U.M. and Franklin, G.F. -C Model reduction via balanced realizations: a extension and -C frequency weighting techniques. -C IEEE Trans. Autom. Contr., AC-33, pp. 687-692, 1988. -C -C NUMERICAL ASPECTS -C 3 -C The time taken is approximately proportional to N . -C The accuracy depends mainly on the condition number of the matrix -C to be inverted. -C -C CONTRIBUTORS -C -C Release 3.0: V. Sima, Katholieke Univ. Leuven, Belgium, and -C A. Varga, German Aerospace Research Establishment, -C Oberpfaffenhofen, Germany, Nov. 1996. -C Supersedes Release 2.0 routine AB04AD by W. van der Linden, and -C A.J. Geurts, Technische Hogeschool Eindhoven, Holland. -C -C REVISIONS -C -C - -C -C KEYWORDS -C -C Bilinear transformation, continuous-time system, discrete-time -C system, state-space model. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE, TWO - PARAMETER ( ZERO=0.0D0, ONE=1.0D0, TWO=2.0D0 ) -C .. Scalar Arguments .. - CHARACTER TYPE - INTEGER INFO, LDA, LDB, LDC, LDD, LDWORK, M, N, P - DOUBLE PRECISION ALPHA, BETA -C .. Array Arguments .. - INTEGER IWORK(*) - DOUBLE PRECISION A(LDA,*), B(LDB,*), C(LDC,*), D(LDD,*), DWORK(*) -C .. Local Scalars .. - LOGICAL LTYPE - INTEGER I, IP - DOUBLE PRECISION AB2, PALPHA, PBETA, SQRAB2 -C .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -C .. External Subroutines .. - EXTERNAL DGEMM, DGETRF, DGETRS, DGETRI, DLASCL, DSCAL, - $ DSWAP, XERBLA -C .. Intrinsic Functions .. - INTRINSIC ABS, MAX, SIGN, SQRT -C .. Executable Statements .. -C - INFO = 0 - LTYPE = LSAME( TYPE, 'D' ) -C -C Test the input scalar arguments. -C - IF( .NOT.LTYPE .AND. .NOT.LSAME( TYPE, 'C' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( M.LT.0 ) THEN - INFO = -3 - ELSE IF( P.LT.0 ) THEN - INFO = -4 - ELSE IF( ALPHA.EQ.ZERO ) THEN - INFO = -5 - ELSE IF( BETA.EQ.ZERO ) THEN - INFO = -6 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -8 - ELSE IF( LDB.LT.MAX( 1, N ) ) THEN - INFO = -10 - ELSE IF( LDC.LT.MAX( 1, P ) ) THEN - INFO = -12 - ELSE IF( LDD.LT.MAX( 1, P ) ) THEN - INFO = -14 - ELSE IF( LDWORK.LT.MAX( 1, N ) ) THEN - INFO = -17 - END IF -C - IF ( INFO.NE.0 ) THEN -C -C Error return. -C - CALL XERBLA( 'AB04MD', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF ( MAX( N, M, P ).EQ.0 ) - $ RETURN -C -C (Note: Comments in the code beginning "Workspace:" describe the -C minimal amount of real workspace needed at that point in the -C code, as well as the preferred amount for good performance. -C NB refers to the optimal block size for the immediately -C following subroutine, as returned by ILAENV.) -C - IF (LTYPE) THEN -C -C Discrete-time to continuous-time with (ALPHA, BETA). -C - PALPHA = ALPHA - PBETA = BETA - ELSE -C -C Continuous-time to discrete-time with (ALPHA, BETA) is -C equivalent with discrete-time to continuous-time with -C (-BETA, -ALPHA), if B and C change the sign. -C - PALPHA = -BETA - PBETA = -ALPHA - END IF -C - AB2 = PALPHA*PBETA*TWO - SQRAB2 = SIGN( SQRT( ABS( AB2 ) ), PALPHA ) -C -1 -C Compute (alpha*I + A) . -C - DO 10 I = 1, N - A(I,I) = A(I,I) + PALPHA - 10 CONTINUE -C - CALL DGETRF( N, N, A, LDA, IWORK, INFO ) -C - IF (INFO.NE.0) THEN -C -C Error return. -C - IF (LTYPE) THEN - INFO = 1 - ELSE - INFO = 2 - END IF - RETURN - END IF -C -1 -C Compute (alpha*I+A) *B. -C - CALL DGETRS( 'No transpose', N, M, A, LDA, IWORK, B, LDB, INFO ) -C -1 -C Compute D - C*(alpha*I+A) *B. -C - CALL DGEMM( 'No transpose', 'No transpose', P, M, N, -ONE, C, - $ LDC, B, LDB, ONE, D, LDD ) -C -C Scale B by sqrt(2*alpha*beta). -C - CALL DLASCL( 'General', 0, 0, ONE, SQRAB2, N, M, B, LDB, INFO ) -C -1 -C Compute sqrt(2*alpha*beta)*C*(alpha*I + A) . -C - CALL DTRSM( 'Right', 'Upper', 'No transpose', 'Non-unit', P, N, - $ SQRAB2, A, LDA, C, LDC ) -C - CALL DTRSM( 'Right', 'Lower', 'No transpose', 'Unit', P, N, ONE, - $ A, LDA, C, LDC ) -C -C Apply column interchanges to the solution matrix. -C - DO 20 I = N-1, 1, -1 - IP = IWORK(I) - IF ( IP.NE.I ) - $ CALL DSWAP( P, C(1,I), 1, C(1,IP), 1 ) - 20 CONTINUE -C -1 -C Compute beta*(alpha*I + A) *(A - alpha*I) as -C -1 -C beta*I - 2*alpha*beta*(alpha*I + A) . -C -C Workspace: need N; prefer N*NB. -C - CALL DGETRI( N, A, LDA, IWORK, DWORK, LDWORK, INFO ) -C - DO 30 I = 1, N - CALL DSCAL(N, -AB2, A(1,I), 1) - A(I,I) = A(I,I) + PBETA - 30 CONTINUE -C - RETURN -C *** Last line of AB04MD *** - END
--- a/extra/control-devel/devel/dksyn/AB05MD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,547 +0,0 @@ - SUBROUTINE AB05MD( UPLO, OVER, N1, M1, P1, N2, P2, A1, LDA1, B1, - $ LDB1, C1, LDC1, D1, LDD1, A2, LDA2, B2, LDB2, - $ C2, LDC2, D2, LDD2, N, A, LDA, B, LDB, C, LDC, - $ D, LDD, DWORK, LDWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To obtain the state-space model (A,B,C,D) for the cascaded -C inter-connection of two systems, each given in state-space form. -C -C ARGUMENTS -C -C Mode Parameters -C -C UPLO CHARACTER*1 -C Indicates whether the user wishes to obtain the matrix A -C in the upper or lower block diagonal form, as follows: -C = 'U': Obtain A in the upper block diagonal form; -C = 'L': Obtain A in the lower block diagonal form. -C -C OVER CHARACTER*1 -C Indicates whether the user wishes to overlap pairs of -C arrays, as follows: -C = 'N': Do not overlap; -C = 'O': Overlap pairs of arrays: A1 and A, B1 and B, -C C1 and C, and D1 and D (for UPLO = 'L'), or A2 -C and A, B2 and B, C2 and C, and D2 and D (for -C UPLO = 'U'), i.e. the same name is effectively -C used for each pair (for all pairs) in the routine -C call. In this case, setting LDA1 = LDA, -C LDB1 = LDB, LDC1 = LDC, and LDD1 = LDD, or -C LDA2 = LDA, LDB2 = LDB, LDC2 = LDC, and LDD2 = LDD -C will give maximum efficiency. -C -C Input/Output Parameters -C -C N1 (input) INTEGER -C The number of state variables in the first system, i.e. -C the order of the matrix A1. N1 >= 0. -C -C M1 (input) INTEGER -C The number of input variables for the first system. -C M1 >= 0. -C -C P1 (input) INTEGER -C The number of output variables from the first system and -C the number of input variables for the second system. -C P1 >= 0. -C -C N2 (input) INTEGER -C The number of state variables in the second system, i.e. -C the order of the matrix A2. N2 >= 0. -C -C P2 (input) INTEGER -C The number of output variables from the second system. -C P2 >= 0. -C -C A1 (input) DOUBLE PRECISION array, dimension (LDA1,N1) -C The leading N1-by-N1 part of this array must contain the -C state transition matrix A1 for the first system. -C -C LDA1 INTEGER -C The leading dimension of array A1. LDA1 >= MAX(1,N1). -C -C B1 (input) DOUBLE PRECISION array, dimension (LDB1,M1) -C The leading N1-by-M1 part of this array must contain the -C input/state matrix B1 for the first system. -C -C LDB1 INTEGER -C The leading dimension of array B1. LDB1 >= MAX(1,N1). -C -C C1 (input) DOUBLE PRECISION array, dimension (LDC1,N1) -C The leading P1-by-N1 part of this array must contain the -C state/output matrix C1 for the first system. -C -C LDC1 INTEGER -C The leading dimension of array C1. -C LDC1 >= MAX(1,P1) if N1 > 0. -C LDC1 >= 1 if N1 = 0. -C -C D1 (input) DOUBLE PRECISION array, dimension (LDD1,M1) -C The leading P1-by-M1 part of this array must contain the -C input/output matrix D1 for the first system. -C -C LDD1 INTEGER -C The leading dimension of array D1. LDD1 >= MAX(1,P1). -C -C A2 (input) DOUBLE PRECISION array, dimension (LDA2,N2) -C The leading N2-by-N2 part of this array must contain the -C state transition matrix A2 for the second system. -C -C LDA2 INTEGER -C The leading dimension of array A2. LDA2 >= MAX(1,N2). -C -C B2 (input) DOUBLE PRECISION array, dimension (LDB2,P1) -C The leading N2-by-P1 part of this array must contain the -C input/state matrix B2 for the second system. -C -C LDB2 INTEGER -C The leading dimension of array B2. LDB2 >= MAX(1,N2). -C -C C2 (input) DOUBLE PRECISION array, dimension (LDC2,N2) -C The leading P2-by-N2 part of this array must contain the -C state/output matrix C2 for the second system. -C -C LDC2 INTEGER -C The leading dimension of array C2. -C LDC2 >= MAX(1,P2) if N2 > 0. -C LDC2 >= 1 if N2 = 0. -C -C D2 (input) DOUBLE PRECISION array, dimension (LDD2,P1) -C The leading P2-by-P1 part of this array must contain the -C input/output matrix D2 for the second system. -C -C LDD2 INTEGER -C The leading dimension of array D2. LDD2 >= MAX(1,P2). -C -C N (output) INTEGER -C The number of state variables (N1 + N2) in the resulting -C system, i.e. the order of the matrix A, the number of rows -C of B and the number of columns of C. -C -C A (output) DOUBLE PRECISION array, dimension (LDA,N1+N2) -C The leading N-by-N part of this array contains the state -C transition matrix A for the cascaded system. -C If OVER = 'O', the array A can overlap A1, if UPLO = 'L', -C or A2, if UPLO = 'U'. -C -C LDA INTEGER -C The leading dimension of array A. LDA >= MAX(1,N1+N2). -C -C B (output) DOUBLE PRECISION array, dimension (LDB,M1) -C The leading N-by-M1 part of this array contains the -C input/state matrix B for the cascaded system. -C If OVER = 'O', the array B can overlap B1, if UPLO = 'L', -C or B2, if UPLO = 'U'. -C -C LDB INTEGER -C The leading dimension of array B. LDB >= MAX(1,N1+N2). -C -C C (output) DOUBLE PRECISION array, dimension (LDC,N1+N2) -C The leading P2-by-N part of this array contains the -C state/output matrix C for the cascaded system. -C If OVER = 'O', the array C can overlap C1, if UPLO = 'L', -C or C2, if UPLO = 'U'. -C -C LDC INTEGER -C The leading dimension of array C. -C LDC >= MAX(1,P2) if N1+N2 > 0. -C LDC >= 1 if N1+N2 = 0. -C -C D (output) DOUBLE PRECISION array, dimension (LDD,M1) -C The leading P2-by-M1 part of this array contains the -C input/output matrix D for the cascaded system. -C If OVER = 'O', the array D can overlap D1, if UPLO = 'L', -C or D2, if UPLO = 'U'. -C -C LDD INTEGER -C The leading dimension of array D. LDD >= MAX(1,P2). -C -C Workspace -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C The array DWORK is not referenced if OVER = 'N'. -C -C LDWORK INTEGER -C The length of the array DWORK. -C LDWORK >= MAX( 1, P1*MAX(N1, M1, N2, P2) ) if OVER = 'O'. -C LDWORK >= 1 if OVER = 'N'. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value. -C -C METHOD -C -C After cascaded inter-connection of the two systems -C -C X1' = A1*X1 + B1*U -C V = C1*X1 + D1*U -C -C X2' = A2*X2 + B2*V -C Y = C2*X2 + D2*V -C -C (where ' denotes differentiation with respect to time) -C -C the following state-space model will be obtained: -C -C X' = A*X + B*U -C Y = C*X + D*U -C -C where matrix A has the form ( A1 0 ), -C ( B2*C1 A2) -C -C matrix B has the form ( B1 ), -C ( B2*D1 ) -C -C matrix C has the form ( D2*C1 C2 ) and -C -C matrix D has the form ( D2*D1 ). -C -C This form is returned by the routine when UPLO = 'L'. Note that -C when A1 and A2 are block lower triangular, the resulting state -C matrix is also block lower triangular. -C -C By applying a similarity transformation to the system above, -C using the matrix ( 0 I ), where I is the identity matrix of -C ( J 0 ) -C order N2, and J is the identity matrix of order N1, the -C system matrices become -C -C A = ( A2 B2*C1 ), -C ( 0 A1 ) -C -C B = ( B2*D1 ), -C ( B1 ) -C -C C = ( C2 D2*C1 ) and -C -C D = ( D2*D1 ). -C -C This form is returned by the routine when UPLO = 'U'. Note that -C when A1 and A2 are block upper triangular (for instance, in the -C real Schur form), the resulting state matrix is also block upper -C triangular. -C -C REFERENCES -C -C None -C -C NUMERICAL ASPECTS -C -C The algorithm requires P1*(N1+M1)*(N2+P2) operations. -C -C CONTRIBUTORS -C -C Release 3.0: V. Sima, Katholieke Univ. Leuven, Belgium, and -C A. Varga, German Aerospace Research Establishment, -C Oberpfaffenhofen, Germany, Nov. 1996. -C Supersedes Release 2.0 routine AB05AD by C.J.Benson, Kingston -C Polytechnic, United Kingdom, January 1982. -C -C REVISIONS -C -C V. Sima, Research Institute for Informatics, Bucharest, July 2003, -C Feb. 2004. -C -C KEYWORDS -C -C Cascade control, continuous-time system, multivariable -C system, state-space model, state-space representation. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) -C .. Scalar Arguments .. - CHARACTER OVER, UPLO - INTEGER INFO, LDA, LDA1, LDA2, LDB, LDB1, LDB2, LDC, - $ LDC1, LDC2, LDD, LDD1, LDD2, LDWORK, M1, N, N1, - $ N2, P1, P2 -C .. Array Arguments .. - DOUBLE PRECISION A(LDA,*), A1(LDA1,*), A2(LDA2,*), B(LDB,*), - $ B1(LDB1,*), B2(LDB2,*), C(LDC,*), C1(LDC1,*), - $ C2(LDC2,*), D(LDD,*), D1(LDD1,*), D2(LDD2,*), - $ DWORK(*) -C .. Local Scalars .. - LOGICAL LOVER, LUPLO - INTEGER I, I1, I2, J, LDWN2, LDWP1, LDWP2 -C .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -C .. External Subroutines .. - EXTERNAL DGEMM, DLACPY, DLASET, XERBLA -C .. Intrinsic Functions .. - INTRINSIC MAX, MIN -C .. Executable Statements .. -C - LOVER = LSAME( OVER, 'O' ) - LUPLO = LSAME( UPLO, 'L' ) - N = N1 + N2 - INFO = 0 -C -C Test the input scalar arguments. -C - IF( .NOT.LUPLO .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN - INFO = -1 - ELSE IF( .NOT.LOVER .AND. .NOT.LSAME( OVER, 'N' ) ) THEN - INFO = -2 - ELSE IF( N1.LT.0 ) THEN - INFO = -3 - ELSE IF( M1.LT.0 ) THEN - INFO = -4 - ELSE IF( P1.LT.0 ) THEN - INFO = -5 - ELSE IF( N2.LT.0 ) THEN - INFO = -6 - ELSE IF( P2.LT.0 ) THEN - INFO = -7 - ELSE IF( LDA1.LT.MAX( 1, N1 ) ) THEN - INFO = -9 - ELSE IF( LDB1.LT.MAX( 1, N1 ) ) THEN - INFO = -11 - ELSE IF( ( N1.GT.0 .AND. LDC1.LT.MAX( 1, P1 ) ) .OR. - $ ( N1.EQ.0 .AND. LDC1.LT.1 ) ) THEN - INFO = -13 - ELSE IF( LDD1.LT.MAX( 1, P1 ) ) THEN - INFO = -15 - ELSE IF( LDA2.LT.MAX( 1, N2 ) ) THEN - INFO = -17 - ELSE IF( LDB2.LT.MAX( 1, N2 ) ) THEN - INFO = -19 - ELSE IF( ( N2.GT.0 .AND. LDC2.LT.MAX( 1, P2 ) ) .OR. - $ ( N2.EQ.0 .AND. LDC2.LT.1 ) ) THEN - INFO = -21 - ELSE IF( LDD2.LT.MAX( 1, P2 ) ) THEN - INFO = -23 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -26 - ELSE IF( LDB.LT.MAX( 1, N ) ) THEN - INFO = -28 - ELSE IF( ( N.GT.0 .AND. LDC.LT.MAX( 1, P2 ) ) .OR. - $ ( N.EQ.0 .AND. LDC.LT.1 ) ) THEN - INFO = -30 - ELSE IF( LDD.LT.MAX( 1, P2 ) ) THEN - INFO = -32 - ELSE IF( ( LOVER.AND.LDWORK.LT.MAX( 1, P1*MAX( N1, M1, N2, P2 )) ) - $.OR.( .NOT.LOVER.AND.LDWORK.LT.1 ) ) THEN - INFO = -34 - END IF -C - IF ( INFO.NE.0 ) THEN -C -C Error return. -C - CALL XERBLA( 'AB05MD', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF ( MAX( N, MIN( M1, P2 ) ).EQ.0 ) - $ RETURN -C -C Set row/column indices for storing the results. -C - IF ( LUPLO ) THEN - I1 = 1 - I2 = MIN( N1 + 1, N ) - ELSE - I1 = MIN( N2 + 1, N ) - I2 = 1 - END IF -C - LDWN2 = MAX( 1, N2 ) - LDWP1 = MAX( 1, P1 ) - LDWP2 = MAX( 1, P2 ) -C -C Construct the cascaded system matrices, taking the desired block -C structure and possible overwriting into account. -C -C Form the diagonal blocks of matrix A. -C - IF ( LUPLO ) THEN -C -C Lower block diagonal structure. -C - IF ( LOVER .AND. LDA1.LE.LDA ) THEN - IF ( LDA1.LT.LDA ) THEN -C - DO 20 J = N1, 1, -1 - DO 10 I = N1, 1, -1 - A(I,J) = A1(I,J) - 10 CONTINUE - 20 CONTINUE -C - END IF - ELSE - CALL DLACPY( 'F', N1, N1, A1, LDA1, A, LDA ) - END IF - IF ( N2.GT.0 ) - $ CALL DLACPY( 'F', N2, N2, A2, LDA2, A(I2,I2), LDA ) - ELSE -C -C Upper block diagonal structure. -C - IF ( LOVER .AND. LDA2.LE.LDA ) THEN - IF ( LDA2.LT.LDA ) THEN -C - DO 40 J = N2, 1, -1 - DO 30 I = N2, 1, -1 - A(I,J) = A2(I,J) - 30 CONTINUE - 40 CONTINUE -C - END IF - ELSE - CALL DLACPY( 'F', N2, N2, A2, LDA2, A, LDA ) - END IF - IF ( N1.GT.0 ) - $ CALL DLACPY( 'F', N1, N1, A1, LDA1, A(I1,I1), LDA ) - END IF -C -C Form the off-diagonal blocks of matrix A. -C - IF ( MIN( N1, N2 ).GT.0 ) THEN - CALL DLASET( 'F', N1, N2, ZERO, ZERO, A(I1,I2), LDA ) - CALL DGEMM ( 'No transpose', 'No transpose', N2, N1, P1, ONE, - $ B2, LDB2, C1, LDC1, ZERO, A(I2,I1), LDA ) - END IF -C - IF ( LUPLO ) THEN -C -C Form the matrix B. -C - IF ( LOVER .AND. LDB1.LE.LDB ) THEN - IF ( LDB1.LT.LDB ) THEN -C - DO 60 J = M1, 1, -1 - DO 50 I = N1, 1, -1 - B(I,J) = B1(I,J) - 50 CONTINUE - 60 CONTINUE -C - END IF - ELSE - CALL DLACPY( 'F', N1, M1, B1, LDB1, B, LDB ) - END IF -C - IF ( MIN( N2, M1 ).GT.0 ) - $ CALL DGEMM ( 'No transpose', 'No transpose', N2, M1, P1, - $ ONE, B2, LDB2, D1, LDD1, ZERO, B(I2,1), LDB ) -C -C Form the matrix C. -C - IF ( N1.GT.0 ) THEN - IF ( LOVER ) THEN -C -C Workspace: P1*N1. -C - CALL DLACPY( 'F', P1, N1, C1, LDC1, DWORK, LDWP1 ) - CALL DGEMM ( 'No transpose', 'No transpose', P2, N1, P1, - $ ONE, D2, LDD2, DWORK, LDWP1, ZERO, C, LDC ) - ELSE - CALL DGEMM ( 'No transpose', 'No transpose', P2, N1, P1, - $ ONE, D2, LDD2, C1, LDC1, ZERO, C, LDC ) - END IF - END IF -C - IF ( MIN( P2, N2 ).GT.0 ) - $ CALL DLACPY( 'F', P2, N2, C2, LDC2, C(1,I2), LDC ) -C -C Now form the matrix D. -C - IF ( LOVER ) THEN -C -C Workspace: P1*M1. -C - CALL DLACPY( 'F', P1, M1, D1, LDD1, DWORK, LDWP1 ) - CALL DGEMM ( 'No transpose', 'No transpose', P2, M1, P1, - $ ONE, D2, LDD2, DWORK, LDWP1, ZERO, D, LDD ) - ELSE - CALL DGEMM ( 'No transpose', 'No transpose', P2, M1, P1, - $ ONE, D2, LDD2, D1, LDD1, ZERO, D, LDD ) - END IF -C - ELSE -C -C Form the matrix B. -C - IF ( LOVER ) THEN -C -C Workspace: N2*P1. -C - CALL DLACPY( 'F', N2, P1, B2, LDB2, DWORK, LDWN2 ) - IF ( MIN( N2, M1 ).GT.0 ) - $ CALL DGEMM ( 'No transpose', 'No transpose', N2, M1, P1, - $ ONE, DWORK, LDWN2, D1, LDD1, ZERO, B(I2,1), - $ LDB ) - ELSE - CALL DGEMM ( 'No transpose', 'No transpose', N2, M1, P1, - $ ONE, B2, LDB2, D1, LDD1, ZERO, B, LDB ) - END IF -C - IF ( MIN( N1, M1 ).GT.0 ) - $ CALL DLACPY( 'F', N1, M1, B1, LDB1, B(I1,1), LDB ) -C -C Form the matrix C. -C - IF ( LOVER .AND. LDC2.LE.LDC ) THEN - IF ( LDC2.LT.LDC ) THEN -C - DO 80 J = N2, 1, -1 - DO 70 I = P2, 1, -1 - C(I,J) = C2(I,J) - 70 CONTINUE - 80 CONTINUE -C - END IF - ELSE - CALL DLACPY( 'F', P2, N2, C2, LDC2, C, LDC ) - END IF -C - IF ( MIN( P2, N1 ).GT.0 ) - $ CALL DGEMM ( 'No transpose', 'No transpose', P2, N1, P1, - $ ONE, D2, LDD2, C1, LDC1, ZERO, C(1,I1), LDC ) -C -C Now form the matrix D. -C - IF ( LOVER ) THEN -C -C Workspace: P2*P1. -C - CALL DLACPY( 'F', P2, P1, D2, LDD2, DWORK, LDWP2 ) - CALL DGEMM ( 'No transpose', 'No transpose', P2, M1, P1, - $ ONE, DWORK, LDWP2, D1, LDD1, ZERO, D, LDD ) - ELSE - CALL DGEMM ( 'No transpose', 'No transpose', P2, M1, P1, - $ ONE, D2, LDD2, D1, LDD1, ZERO, D, LDD ) - END IF - END IF -C - RETURN -C *** Last line of AB05MD *** - END
--- a/extra/control-devel/devel/dksyn/AB07MD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,224 +0,0 @@ - SUBROUTINE AB07MD( JOBD, N, M, P, A, LDA, B, LDB, C, LDC, D, LDD, - $ INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To find the dual of a given state-space representation. -C -C ARGUMENTS -C -C Mode Parameters -C -C JOBD CHARACTER*1 -C Specifies whether or not a non-zero matrix D appears in -C the given state space model: -C = 'D': D is present; -C = 'Z': D is assumed a zero matrix. -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the state-space representation. N >= 0. -C -C M (input) INTEGER -C The number of system inputs. M >= 0. -C -C P (input) INTEGER -C The number of system outputs. P >= 0. -C -C A (input/output) DOUBLE PRECISION array, dimension (LDA,N) -C On entry, the leading N-by-N part of this array must -C contain the original state dynamics matrix A. -C On exit, the leading N-by-N part of this array contains -C the dual state dynamics matrix A'. -C -C LDA INTEGER -C The leading dimension of array A. LDA >= MAX(1,N). -C -C B (input/output) DOUBLE PRECISION array, dimension -C (LDB,MAX(M,P)) -C On entry, the leading N-by-M part of this array must -C contain the original input/state matrix B. -C On exit, the leading N-by-P part of this array contains -C the dual input/state matrix C'. -C -C LDB INTEGER -C The leading dimension of array B. LDB >= MAX(1,N). -C -C C (input/output) DOUBLE PRECISION array, dimension (LDC,N) -C On entry, the leading P-by-N part of this array must -C contain the original state/output matrix C. -C On exit, the leading M-by-N part of this array contains -C the dual state/output matrix B'. -C -C LDC INTEGER -C The leading dimension of array C. -C LDC >= MAX(1,M,P) if N > 0. -C LDC >= 1 if N = 0. -C -C D (input/output) DOUBLE PRECISION array, dimension -C (LDD,MAX(M,P)) -C On entry, if JOBD = 'D', the leading P-by-M part of this -C array must contain the original direct transmission -C matrix D. -C On exit, if JOBD = 'D', the leading M-by-P part of this -C array contains the dual direct transmission matrix D'. -C The array D is not referenced if JOBD = 'Z'. -C -C LDD INTEGER -C The leading dimension of array D. -C LDD >= MAX(1,M,P) if JOBD = 'D'. -C LDD >= 1 if JOBD = 'Z'. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value. -C -C METHOD -C -C If the given state-space representation is the M-input/P-output -C (A,B,C,D), its dual is simply the P-input/M-output (A',C',B',D'). -C -C REFERENCES -C -C None -C -C NUMERICAL ASPECTS -C -C None -C -C CONTRIBUTOR -C -C Release 3.0: V. Sima, Katholieke Univ. Leuven, Belgium, Dec. 1996. -C Supersedes Release 2.0 routine AB07AD by T.W.C.Williams, Kingston -C Polytechnic, United Kingdom, March 1982. -C -C REVISIONS -C -C V. Sima, Research Institute for Informatics, Bucharest, Feb. 2004. -C -C KEYWORDS -C -C Dual system, state-space model, state-space representation. -C -C ****************************************************************** -C -C .. Scalar Arguments .. - CHARACTER JOBD - INTEGER INFO, LDA, LDB, LDC, LDD, M, N, P -C .. Array Arguments .. - DOUBLE PRECISION A(LDA,*), B(LDB,*), C(LDC,*), D(LDD,*) -C .. Local Scalars .. - LOGICAL LJOBD - INTEGER J, MINMP, MPLIM -C .. External functions .. - LOGICAL LSAME - EXTERNAL LSAME -C .. External subroutines .. - EXTERNAL DCOPY, DSWAP, XERBLA -C .. Intrinsic Functions .. - INTRINSIC MAX, MIN -C .. Executable Statements .. -C - INFO = 0 - LJOBD = LSAME( JOBD, 'D' ) - MPLIM = MAX( M, P ) - MINMP = MIN( M, P ) -C -C Test the input scalar arguments. -C - IF( .NOT.LJOBD .AND. .NOT.LSAME( JOBD, 'Z' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( M.LT.0 ) THEN - INFO = -3 - ELSE IF( P.LT.0 ) THEN - INFO = -4 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -6 - ELSE IF( LDB.LT.MAX( 1, N ) ) THEN - INFO = -8 - ELSE IF( ( N.GT.0 .AND. LDC.LT.MAX( 1, MPLIM ) ) .OR. - $ ( N.EQ.0 .AND. LDC.LT.1 ) ) THEN - INFO = -10 - ELSE IF( ( LJOBD .AND. LDD.LT.MAX( 1, MPLIM ) ) .OR. - $ ( .NOT.LJOBD .AND. LDD.LT.1 ) ) THEN - INFO = -12 - END IF -C - IF ( INFO.NE.0 ) THEN -C -C Error return. -C - CALL XERBLA( 'AB07MD', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF ( MAX( N, MINMP ).EQ.0 ) - $ RETURN -C - IF ( N.GT.0 ) THEN -C -C Transpose A, if non-scalar. -C - DO 10 J = 1, N - 1 - CALL DSWAP( N-J, A(J+1,J), 1, A(J,J+1), LDA ) - 10 CONTINUE -C -C Replace B by C' and C by B'. -C - DO 20 J = 1, MPLIM - IF ( J.LE.MINMP ) THEN - CALL DSWAP( N, B(1,J), 1, C(J,1), LDC ) - ELSE IF ( J.GT.P ) THEN - CALL DCOPY( N, B(1,J), 1, C(J,1), LDC ) - ELSE - CALL DCOPY( N, C(J,1), LDC, B(1,J), 1 ) - END IF - 20 CONTINUE -C - END IF -C - IF ( LJOBD .AND. MINMP.GT.0 ) THEN -C -C Transpose D, if non-scalar. -C - DO 30 J = 1, MPLIM - IF ( J.LT.MINMP ) THEN - CALL DSWAP( MINMP-J, D(J+1,J), 1, D(J,J+1), LDD ) - ELSE IF ( J.GT.P ) THEN - CALL DCOPY( P, D(1,J), 1, D(J,1), LDD ) - ELSE IF ( J.GT.M ) THEN - CALL DCOPY( M, D(J,1), LDD, D(1,J), 1 ) - END IF - 30 CONTINUE -C - END IF -C - RETURN -C *** Last line of AB07MD *** - END
--- a/extra/control-devel/devel/dksyn/AB07ND.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,303 +0,0 @@ - SUBROUTINE AB07ND( N, M, A, LDA, B, LDB, C, LDC, D, LDD, RCOND, - $ IWORK, DWORK, LDWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To compute the inverse (Ai,Bi,Ci,Di) of a given system (A,B,C,D). -C -C ARGUMENTS -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the state matrix A. N >= 0. -C -C M (input) INTEGER -C The number of system inputs and outputs. M >= 0. -C -C A (input/output) DOUBLE PRECISION array, dimension (LDA,N) -C On entry, the leading N-by-N part of this array must -C contain the state matrix A of the original system. -C On exit, the leading N-by-N part of this array contains -C the state matrix Ai of the inverse system. -C -C LDA INTEGER -C The leading dimension of the array A. LDA >= MAX(1,N). -C -C B (input/output) DOUBLE PRECISION array, dimension (LDB,M) -C On entry, the leading N-by-M part of this array must -C contain the input matrix B of the original system. -C On exit, the leading N-by-M part of this array contains -C the input matrix Bi of the inverse system. -C -C LDB INTEGER -C The leading dimension of the array B. LDB >= MAX(1,N). -C -C C (input/output) DOUBLE PRECISION array, dimension (LDC,N) -C On entry, the leading M-by-N part of this array must -C contain the output matrix C of the original system. -C On exit, the leading M-by-N part of this array contains -C the output matrix Ci of the inverse system. -C -C LDC INTEGER -C The leading dimension of the array C. LDC >= MAX(1,M). -C -C D (input/output) DOUBLE PRECISION array, dimension (LDD,M) -C On entry, the leading M-by-M part of this array must -C contain the feedthrough matrix D of the original system. -C On exit, the leading M-by-M part of this array contains -C the feedthrough matrix Di of the inverse system. -C -C LDD INTEGER -C The leading dimension of the array D. LDD >= MAX(1,M). -C -C RCOND (output) DOUBLE PRECISION -C The estimated reciprocal condition number of the -C feedthrough matrix D of the original system. -C -C Workspace -C -C IWORK INTEGER array, dimension (2*M) -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C On exit, if INFO = 0 or M+1, DWORK(1) returns the optimal -C value of LDWORK. -C -C LDWORK INTEGER -C The length of the array DWORK. LDWORK >= MAX(1,4*M). -C For good performance, LDWORK should be larger. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C = i: the matrix D is exactly singular; the (i,i) diagonal -C element is zero, i <= M; RCOND was set to zero; -C = M+1: the matrix D is numerically singular, i.e., RCOND -C is less than the relative machine precision, EPS -C (see LAPACK Library routine DLAMCH). The -C calculations have been completed, but the results -C could be very inaccurate. -C -C METHOD -C -C The matrices of the inverse system are computed with the formulas: -C -1 -1 -1 -1 -C Ai = A - B*D *C, Bi = -B*D , Ci = D *C, Di = D . -C -C NUMERICAL ASPECTS -C -C The accuracy depends mainly on the condition number of the matrix -C D to be inverted. The estimated reciprocal condition number is -C returned in RCOND. -C -C CONTRIBUTORS -C -C A. Varga, German Aerospace Center, Oberpfaffenhofen, March 2000. -C D. Sima, University of Bucharest, April 2000. -C V. Sima, Research Institute for Informatics, Bucharest, Apr. 2000. -C Based on the routine SYSINV, A. Varga, 1992. -C -C REVISIONS -C -C A. Varga, German Aerospace Center, Oberpfaffenhofen, July 2000. -C -C KEYWORDS -C -C Inverse system, state-space model, state-space representation. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) -C .. Scalar Arguments .. - DOUBLE PRECISION RCOND - INTEGER INFO, LDA, LDB, LDC, LDD, LDWORK, M, N -C .. Array Arguments .. - DOUBLE PRECISION A(LDA,*), B(LDB,*), C(LDC,*), D(LDD,*), - $ DWORK(*) - INTEGER IWORK(*) -C .. Local Scalars .. - DOUBLE PRECISION DNORM - INTEGER BL, CHUNK, I, IERR, J, MAXWRK - LOGICAL BLAS3, BLOCK -C .. External Functions .. - DOUBLE PRECISION DLAMCH, DLANGE - INTEGER ILAENV - EXTERNAL DLAMCH, DLANGE, ILAENV -C .. External Subroutines .. - EXTERNAL DCOPY, DGECON, DGEMM, DGEMV, DGETRF, DGETRI, - $ DLACPY, XERBLA -C .. Intrinsic Functions .. - INTRINSIC DBLE, MAX, MIN -C .. Executable Statements .. -C - INFO = 0 -C -C Test the input scalar arguments. -C - IF( N.LT.0 ) THEN - INFO = -1 - ELSE IF( M.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -4 - ELSE IF( LDB.LT.MAX( 1, N ) ) THEN - INFO = -6 - ELSE IF( LDC.LT.MAX( 1, M ) ) THEN - INFO = -8 - ELSE IF( LDD.LT.MAX( 1, M ) ) THEN - INFO = -10 - ELSE IF( LDWORK.LT.MAX( 1, 4*M ) ) THEN - INFO = -14 - END IF -C - IF ( INFO.NE.0 ) THEN -C -C Error return. -C - CALL XERBLA( 'AB07ND', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF ( M.EQ.0 ) THEN - RCOND = ONE - DWORK(1) = ONE - RETURN - END IF -C -C Factorize D. -C - CALL DGETRF( M, M, D, LDD, IWORK, INFO ) - IF ( INFO.NE.0 ) THEN - RCOND = ZERO - RETURN - END IF -C -C Compute the reciprocal condition number of the matrix D. -C Workspace: need 4*M. -C (Note: Comments in the code beginning "Workspace:" describe the -C minimal amount of workspace needed at that point in the code, -C as well as the preferred amount for good performance. -C NB refers to the optimal block size for the immediately -C following subroutine, as returned by ILAENV.) -C - DNORM = DLANGE( '1-norm', M, M, D, LDD, DWORK ) - CALL DGECON( '1-norm', M, D, LDD, DNORM, RCOND, DWORK, IWORK(M+1), - $ IERR ) - IF ( RCOND.LT.DLAMCH( 'Epsilon' ) ) - $ INFO = M + 1 -C -1 -C Compute Di = D . -C Workspace: need M; -C prefer M*NB. -C - MAXWRK = MAX( 4*M, M*ILAENV( 1, 'DGETRI', ' ', M, -1, -1, -1 ) ) - CALL DGETRI( M, D, LDD, IWORK, DWORK, LDWORK, IERR ) - IF ( N.GT.0 ) THEN - CHUNK = LDWORK / M - BLAS3 = CHUNK.GE.N .AND. M.GT.1 - BLOCK = MIN( CHUNK, M ).GT.1 -C -1 -C Compute Bi = -B*D . -C - IF ( BLAS3 ) THEN -C -C Enough workspace for a fast BLAS 3 algorithm. -C - CALL DLACPY( 'Full', N, M, B, LDB, DWORK, N ) - CALL DGEMM( 'NoTranspose', 'NoTranspose', N, M, M, -ONE, - $ DWORK, N, D, LDD, ZERO, B, LDB ) -C - ELSE IF( BLOCK ) THEN -C -C Use as many rows of B as possible. -C - DO 10 I = 1, N, CHUNK - BL = MIN( N-I+1, CHUNK ) - CALL DLACPY( 'Full', BL, M, B(I,1), LDB, DWORK, BL ) - CALL DGEMM( 'NoTranspose', 'NoTranspose', BL, M, M, -ONE, - $ DWORK, BL, D, LDD, ZERO, B(I,1), LDB ) - 10 CONTINUE -C - ELSE -C -C Use a BLAS 2 algorithm. -C - DO 20 I = 1, N - CALL DCOPY( M, B(I,1), LDB, DWORK, 1 ) - CALL DGEMV( 'Transpose', M, M, -ONE, D, LDD, DWORK, 1, - $ ZERO, B(I,1), LDB ) - 20 CONTINUE -C - END IF -C -C Compute Ai = A + Bi*C. -C - CALL DGEMM( 'NoTranspose', 'NoTranspose', N, N, M, ONE, B, LDB, - $ C, LDC, ONE, A, LDA ) -C -1 -C Compute C <-- D *C. -C - IF ( BLAS3 ) THEN -C -C Enough workspace for a fast BLAS 3 algorithm. -C - CALL DLACPY( 'Full', M, N, C, LDC, DWORK, M ) - CALL DGEMM( 'NoTranspose', 'NoTranspose', M, N, M, ONE, - $ D, LDD, DWORK, M, ZERO, C, LDC ) -C - ELSE IF( BLOCK ) THEN -C -C Use as many columns of C as possible. -C - DO 30 J = 1, N, CHUNK - BL = MIN( N-J+1, CHUNK ) - CALL DLACPY( 'Full', M, BL, C(1,J), LDC, DWORK, M ) - CALL DGEMM( 'NoTranspose', 'NoTranspose', M, BL, M, ONE, - $ D, LDD, DWORK, M, ZERO, C(1,J), LDC ) - 30 CONTINUE -C - ELSE -C -C Use a BLAS 2 algorithm. -C - DO 40 J = 1, N - CALL DCOPY( M, C(1,J), 1, DWORK, 1 ) - CALL DGEMV( 'NoTranspose', M, M, ONE, D, LDD, DWORK, 1, - $ ZERO, C(1,J), 1 ) - 40 CONTINUE -C - END IF - END IF -C -C Return optimal workspace in DWORK(1). -C - DWORK(1) = DBLE( MAX( MAXWRK, N*M ) ) - RETURN -C -C *** Last line of AB07ND *** - END
--- a/extra/control-devel/devel/dksyn/AB13MD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,1782 +0,0 @@ - SUBROUTINE AB13MD( FACT, N, Z, LDZ, M, NBLOCK, ITYPE, X, BOUND, D, - $ G, IWORK, DWORK, LDWORK, ZWORK, LZWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To compute an upper bound on the structured singular value for a -C given square complex matrix and a given block structure of the -C uncertainty. -C -C ARGUMENTS -C -C Mode Parameters -C -C FACT CHARACTER*1 -C Specifies whether or not an information from the -C previous call is supplied in the vector X. -C = 'F': On entry, X contains information from the -C previous call. -C = 'N': On entry, X does not contain an information from -C the previous call. -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the matrix Z. N >= 0. -C -C Z (input) COMPLEX*16 array, dimension (LDZ,N) -C The leading N-by-N part of this array must contain the -C complex matrix Z for which the upper bound on the -C structured singular value is to be computed. -C -C LDZ INTEGER -C The leading dimension of the array Z. LDZ >= max(1,N). -C -C M (input) INTEGER -C The number of diagonal blocks in the block structure of -C the uncertainty. M >= 1. -C -C NBLOCK (input) INTEGER array, dimension (M) -C The vector of length M containing the block structure -C of the uncertainty. NBLOCK(I), I = 1:M, is the size of -C each block. -C -C ITYPE (input) INTEGER array, dimension (M) -C The vector of length M indicating the type of each block. -C For I = 1:M, -C ITYPE(I) = 1 indicates that the corresponding block is a -C real block, and -C ITYPE(I) = 2 indicates that the corresponding block is a -C complex block. -C NBLOCK(I) must be equal to 1 if ITYPE(I) is equal to 1. -C -C X (input/output) DOUBLE PRECISION array, dimension -C ( M + MR - 1 ), where MR is the number of the real blocks. -C On entry, if FACT = 'F' and NBLOCK(1) < N, this array -C must contain information from the previous call to AB13MD. -C If NBLOCK(1) = N, this array is not used. -C On exit, if NBLOCK(1) < N, this array contains information -C that can be used in the next call to AB13MD for a matrix -C close to Z. -C -C BOUND (output) DOUBLE PRECISION -C The upper bound on the structured singular value. -C -C D, G (output) DOUBLE PRECISION arrays, dimension (N) -C The vectors of length N containing the diagonal entries -C of the diagonal N-by-N matrices D and G, respectively, -C such that the matrix -C Z'*D^2*Z + sqrt(-1)*(G*Z-Z'*G) - BOUND^2*D^2 -C is negative semidefinite. -C -C Workspace -C -C IWORK INTEGER array, dimension MAX(4*M-2,N) -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C On exit, if INFO = 0, DWORK(1) contains the optimal value -C of LDWORK. -C -C LDWORK INTEGER -C The dimension of the array DWORK. -C LDWORK >= 2*N*N*M - N*N + 9*M*M + N*M + 11*N + 33*M - 11. -C For best performance -C LDWORK >= 2*N*N*M - N*N + 9*M*M + N*M + 6*N + 33*M - 11 + -C MAX( 5*N,2*N*NB ) -C where NB is the optimal blocksize returned by ILAENV. -C -C ZWORK COMPLEX*16 array, dimension (LZWORK) -C On exit, if INFO = 0, ZWORK(1) contains the optimal value -C of LZWORK. -C -C LZWORK INTEGER -C The dimension of the array ZWORK. -C LZWORK >= 6*N*N*M + 12*N*N + 6*M + 6*N - 3. -C For best performance -C LZWORK >= 6*N*N*M + 12*N*N + 6*M + 3*N - 3 + -C MAX( 3*N,N*NB ) -C where NB is the optimal blocksize returned by ILAENV. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C = 1: the block sizes must be positive integers; -C = 2: the sum of block sizes must be equal to N; -C = 3: the size of a real block must be equal to 1; -C = 4: the block type must be either 1 or 2; -C = 5: errors in solving linear equations or in matrix -C inversion; -C = 6: errors in computing eigenvalues or singular values. -C -C METHOD -C -C The routine computes the upper bound proposed in [1]. -C -C REFERENCES -C -C [1] Fan, M.K.H., Tits, A.L., and Doyle, J.C. -C Robustness in the presence of mixed parametric uncertainty -C and unmodeled dynamics. -C IEEE Trans. Automatic Control, vol. AC-36, 1991, pp. 25-38. -C -C NUMERICAL ASPECTS -C -C The accuracy and speed of computation depend on the value of -C the internal threshold TOL. -C -C CONTRIBUTORS -C -C P.Hr. Petkov, F. Delebecque, D.W. Gu, M.M. Konstantinov and -C S. Steer with the assistance of V. Sima, September 2000. -C -C REVISIONS -C -C V. Sima, Katholieke Universiteit Leuven, February 2001. -C -C KEYWORDS -C -C H-infinity optimal control, Robust control, Structured singular -C value. -C -C ****************************************************************** -C -C .. Parameters .. - COMPLEX*16 CZERO, CONE, CIMAG - PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), - $ CONE = ( 1.0D+0, 0.0D+0 ), - $ CIMAG = ( 0.0D+0, 1.0D+0 ) ) - DOUBLE PRECISION ZERO, ONE, TWO, FOUR, FIVE, EIGHT, TEN, FORTY, - $ FIFTY - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0, - $ FOUR = 4.0D+0, FIVE = 5.0D+0, EIGHT = 8.0D+0, - $ TEN = 1.0D+1, FORTY = 4.0D+1, FIFTY = 5.0D+1 - $ ) - DOUBLE PRECISION ALPHA, BETA, THETA - PARAMETER ( ALPHA = 100.0D+0, BETA = 1.0D-2, - $ THETA = 1.0D-2 ) - DOUBLE PRECISION C1, C2, C3, C4, C5, C6, C7, C8, C9 - PARAMETER ( C1 = 1.0D-3, C2 = 1.0D-2, C3 = 0.25D+0, - $ C4 = 0.9D+0, C5 = 1.5D+0, C6 = 1.0D+1, - $ C7 = 1.0D+2, C8 = 1.0D+3, C9 = 1.0D+4 ) -C .. -C .. Scalar Arguments .. - CHARACTER FACT - INTEGER INFO, LDWORK, LDZ, LZWORK, M, N - DOUBLE PRECISION BOUND -C .. -C .. Array Arguments .. - INTEGER ITYPE( * ), IWORK( * ), NBLOCK( * ) - COMPLEX*16 Z( LDZ, * ), ZWORK( * ) - DOUBLE PRECISION D( * ), DWORK( * ), G( * ), X( * ) -C .. -C .. Local Scalars .. - INTEGER I, INFO2, ISUM, ITER, IW2, IW3, IW4, IW5, IW6, - $ IW7, IW8, IW9, IW10, IW11, IW12, IW13, IW14, - $ IW15, IW16, IW17, IW18, IW19, IW20, IW21, IW22, - $ IW23, IW24, IW25, IW26, IW27, IW28, IW29, IW30, - $ IW31, IW32, IW33, IWRK, IZ2, IZ3, IZ4, IZ5, - $ IZ6, IZ7, IZ8, IZ9, IZ10, IZ11, IZ12, IZ13, - $ IZ14, IZ15, IZ16, IZ17, IZ18, IZ19, IZ20, IZ21, - $ IZ22, IZ23, IZ24, IZWRK, J, K, L, LWA, LWAMAX, - $ LZA, LZAMAX, MINWRK, MINZRK, MR, MT, NSUM, SDIM - COMPLEX*16 DETF, TEMPIJ, TEMPJI - DOUBLE PRECISION C, COLSUM, DELTA, DLAMBD, E, EMAX, EMIN, EPS, - $ HN, HNORM, HNORM1, PHI, PP, PROD, RAT, RCOND, - $ REGPAR, ROWSUM, SCALE, SNORM, STSIZE, SVLAM, - $ T1, T2, T3, TAU, TEMP, TOL, TOL2, TOL3, TOL4, - $ TOL5, YNORM1, YNORM2, ZNORM, ZNORM2 - LOGICAL GTEST, POS, XFACT -C .. -C .. Local Arrays .. - LOGICAL BWORK( 1 ) -C .. -C .. External Functions - DOUBLE PRECISION DDOT, DLAMCH, DLANGE, ZLANGE - LOGICAL LSAME, SELECT - EXTERNAL DDOT, DLAMCH, DLANGE, LSAME, SELECT, ZLANGE -C .. -C .. External Subroutines .. - EXTERNAL DCOPY, DGEMV, DLACPY, DLASET, DSCAL, DSYCON, - $ DSYSV, DSYTRF, DSYTRS, XERBLA, ZCOPY, ZGEES, - $ ZGEMM, ZGEMV, ZGESVD, ZGETRF, ZGETRI, ZLACPY, - $ ZLASCL -C .. -C .. Intrinsic Functions .. - INTRINSIC ABS, DCMPLX, DCONJG, DFLOAT, DREAL, INT, LOG, - $ MAX, SQRT -C .. -C .. Executable Statements .. -C -C Compute workspace. -C - MINWRK = 2*N*N*M - N*N + 9*M*M + N*M + 11*N + 33*M - 11 - MINZRK = 6*N*N*M + 12*N*N + 6*M + 6*N - 3 -C -C Decode and Test input parameters. -C - INFO = 0 - XFACT = LSAME( FACT, 'F' ) - IF( .NOT.XFACT .AND. .NOT.LSAME( FACT, 'N' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDZ.LT.MAX( 1, N ) ) THEN - INFO = -4 - ELSE IF( M.LT.1 ) THEN - INFO = -5 - ELSE IF( LDWORK.LT.MINWRK ) THEN - INFO = -14 - ELSE IF( LZWORK.LT.MINZRK ) THEN - INFO = -16 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'AB13MD', -INFO ) - RETURN - END IF -C - NSUM = 0 - ISUM = 0 - MR = 0 - DO 10 I = 1, M - IF( NBLOCK( I ).LT.1 ) THEN - INFO = 1 - RETURN - END IF - IF( ITYPE( I ).EQ.1 .AND. NBLOCK( I ).GT.1 ) THEN - INFO = 3 - RETURN - END IF - NSUM = NSUM + NBLOCK( I ) - IF( ITYPE( I ).EQ.1 ) MR = MR + 1 - IF( ITYPE( I ).EQ.1 .OR. ITYPE( I ).EQ.2 ) ISUM = ISUM + 1 - 10 CONTINUE - IF( NSUM.NE.N ) THEN - INFO = 2 - RETURN - END IF - IF( ISUM.NE.M ) THEN - INFO = 4 - RETURN - END IF - MT = M + MR - 1 -C - LWAMAX = 0 - LZAMAX = 0 -C -C Set D = In, G = 0. -C - CALL DLASET( 'Full', N, 1, ONE, ONE, D, N ) - CALL DLASET( 'Full', N, 1, ZERO, ZERO, G, N ) -C -C Quick return if possible. -C - ZNORM = ZLANGE( 'F', N, N, Z, LDZ, DWORK ) - IF( ZNORM.EQ.ZERO ) THEN - BOUND = ZERO - DWORK( 1 ) = ONE - ZWORK( 1 ) = CONE - RETURN - END IF -C -C Copy Z into ZWORK. -C - CALL ZLACPY( 'Full', N, N, Z, LDZ, ZWORK, N ) -C -C Exact bound for the case NBLOCK( 1 ) = N. -C - IF( NBLOCK( 1 ).EQ.N ) THEN - IF( ITYPE( 1 ).EQ.1 ) THEN -C -C 1-by-1 real block. -C - BOUND = ZERO - DWORK( 1 ) = ONE - ZWORK( 1 ) = CONE - ELSE -C -C N-by-N complex block. -C - CALL ZGESVD( 'N', 'N', N, N, ZWORK, N, DWORK, ZWORK, 1, - $ ZWORK, 1, ZWORK( N*N+1 ), LZWORK, - $ DWORK( N+1 ), INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 6 - RETURN - END IF - BOUND = DWORK( 1 ) - LZA = N*N + INT( ZWORK( N*N+1 ) ) - DWORK( 1 ) = 5*N - ZWORK( 1 ) = DCMPLX( LZA ) - END IF - RETURN - END IF -C -C Get machine precision. -C - EPS = DLAMCH( 'P' ) -C -C Set tolerances. -C - TOL = C7*SQRT( EPS ) - TOL2 = C9*EPS - TOL3 = C6*EPS - TOL4 = C1 - TOL5 = C1 - REGPAR = C8*EPS -C -C Real workspace usage. -C - IW2 = M*M - IW3 = IW2 + M - IW4 = IW3 + N - IW5 = IW4 + M - IW6 = IW5 + M - IW7 = IW6 + N - IW8 = IW7 + N - IW9 = IW8 + N*( M - 1 ) - IW10 = IW9 + N*N*MT - IW11 = IW10 + MT - IW12 = IW11 + MT*MT - IW13 = IW12 + N - IW14 = IW13 + MT + 1 - IW15 = IW14 + MT + 1 - IW16 = IW15 + MT + 1 - IW17 = IW16 + MT + 1 - IW18 = IW17 + MT + 1 - IW19 = IW18 + MT - IW20 = IW19 + MT - IW21 = IW20 + MT - IW22 = IW21 + N - IW23 = IW22 + M - 1 - IW24 = IW23 + MR - IW25 = IW24 + N - IW26 = IW25 + 2*MT - IW27 = IW26 + MT - IW28 = IW27 + MT - IW29 = IW28 + M - 1 - IW30 = IW29 + MR - IW31 = IW30 + N + 2*MT - IW32 = IW31 + MT*MT - IW33 = IW32 + MT - IWRK = IW33 + MT + 1 -C -C Double complex workspace usage. -C - IZ2 = N*N - IZ3 = IZ2 + N*N - IZ4 = IZ3 + N*N - IZ5 = IZ4 + N*N - IZ6 = IZ5 + N*N - IZ7 = IZ6 + N*N*MT - IZ8 = IZ7 + N*N - IZ9 = IZ8 + N*N - IZ10 = IZ9 + N*N - IZ11 = IZ10 + MT - IZ12 = IZ11 + N*N - IZ13 = IZ12 + N - IZ14 = IZ13 + N*N - IZ15 = IZ14 + N - IZ16 = IZ15 + N*N - IZ17 = IZ16 + N - IZ18 = IZ17 + N*N - IZ19 = IZ18 + N*N*MT - IZ20 = IZ19 + MT - IZ21 = IZ20 + N*N*MT - IZ22 = IZ21 + N*N - IZ23 = IZ22 + N*N - IZ24 = IZ23 + N*N - IZWRK = IZ24 + MT -C -C Compute the cumulative sums of blocks dimensions. -C - IWORK( 1 ) = 0 - DO 20 I = 2, M+1 - IWORK( I ) = IWORK( I - 1 ) + NBLOCK( I - 1 ) - 20 CONTINUE -C -C Find Osborne scaling if initial scaling is not given. -C - IF( .NOT.XFACT ) THEN - CALL DLASET( 'Full', M, M, ZERO, ZERO, DWORK, M ) - CALL DLASET( 'Full', M, 1, ONE, ONE, DWORK( IW2+1 ), M ) - ZNORM = ZLANGE( 'F', N, N, ZWORK, N, DWORK ) - DO 40 J = 1, M - DO 30 I = 1, M - IF( I.NE.J ) THEN - CALL ZLACPY( 'Full', IWORK( I+1 )-IWORK( I ), - $ IWORK( J+1 )-IWORK( J ), - $ Z( IWORK( I )+1, IWORK( J )+1 ), LDZ, - $ ZWORK( IZ2+1 ), N ) - CALL ZGESVD( 'N', 'N', IWORK( I+1 )-IWORK( I ), - $ IWORK( J+1 )-IWORK( J ), ZWORK( IZ2+1 ), - $ N, DWORK( IW3+1 ), ZWORK, 1, ZWORK, 1, - $ ZWORK( IZWRK+1 ), LZWORK-IZWRK, - $ DWORK( IWRK+1 ), INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 6 - RETURN - END IF - LZA = INT( ZWORK( IZWRK+1 ) ) - LZAMAX = MAX( LZA, LZAMAX ) - ZNORM2 = DWORK( IW3+1 ) - DWORK( I+(J-1)*M ) = ZNORM2 + ZNORM*TOL2 - END IF - 30 CONTINUE - 40 CONTINUE - CALL DLASET( 'Full', M, 1, ZERO, ZERO, DWORK( IW4+1 ), M ) - 50 DO 60 I = 1, M - DWORK( IW5+I ) = DWORK( IW4+I ) - ONE - 60 CONTINUE - HNORM = DLANGE( 'F', M, 1, DWORK( IW5+1 ), M, DWORK ) - IF( HNORM.LE.TOL2 ) GO TO 120 - DO 110 K = 1, M - COLSUM = ZERO - DO 70 I = 1, M - COLSUM = COLSUM + DWORK( I+(K-1)*M ) - 70 CONTINUE - ROWSUM = ZERO - DO 80 J = 1, M - ROWSUM = ROWSUM + DWORK( K+(J-1)*M ) - 80 CONTINUE - RAT = SQRT( COLSUM / ROWSUM ) - DWORK( IW4+K ) = RAT - DO 90 I = 1, M - DWORK( I+(K-1)*M ) = DWORK( I+(K-1)*M ) / RAT - 90 CONTINUE - DO 100 J = 1, M - DWORK( K+(J-1)*M ) = DWORK( K+(J-1)*M )*RAT - 100 CONTINUE - DWORK( IW2+K ) = DWORK( IW2+K )*RAT - 110 CONTINUE - GO TO 50 - 120 SCALE = ONE / DWORK( IW2+1 ) - CALL DSCAL( M, SCALE, DWORK( IW2+1 ), 1 ) - ELSE - DWORK( IW2+1 ) = ONE - DO 130 I = 2, M - DWORK( IW2+I ) = SQRT( X( I-1 ) ) - 130 CONTINUE - END IF - DO 150 J = 1, M - DO 140 I = 1, M - IF( I.NE.J ) THEN - CALL ZLASCL( 'G', M, M, DWORK( IW2+J ), DWORK( IW2+I ), - $ IWORK( I+1 )-IWORK( I ), - $ IWORK( J+1 )-IWORK( J ), - $ ZWORK( IWORK( I )+1+IWORK( J )*N ), N, - $ INFO2 ) - END IF - 140 CONTINUE - 150 CONTINUE -C -C Scale Z by its 2-norm. -C - CALL ZLACPY( 'Full', N, N, ZWORK, N, ZWORK( IZ2+1 ), N ) - CALL ZGESVD( 'N', 'N', N, N, ZWORK( IZ2+1 ), N, DWORK( IW3+1 ), - $ ZWORK, 1, ZWORK, 1, ZWORK( IZWRK+1 ), LZWORK-IZWRK, - $ DWORK( IWRK+1 ), INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 6 - RETURN - END IF - LZA = INT( ZWORK( IZWRK+1 ) ) - LZAMAX = MAX( LZA, LZAMAX ) - ZNORM = DWORK( IW3+1 ) - CALL ZLASCL( 'G', M, M, ZNORM, ONE, N, N, ZWORK, N, INFO2 ) -C -C Set BB. -C - CALL DLASET( 'Full', N*N, MT, ZERO, ZERO, DWORK( IW9+1 ), N*N ) -C -C Set P. -C - DO 160 I = 1, NBLOCK( 1 ) - DWORK( IW6+I ) = ONE - 160 CONTINUE - DO 170 I = NBLOCK( 1 )+1, N - DWORK( IW6+I ) = ZERO - 170 CONTINUE -C -C Compute P*Z. -C - DO 190 J = 1, N - DO 180 I = 1, N - ZWORK( IZ3+I+(J-1)*N ) = DCMPLX( DWORK( IW6+I ) )* - $ ZWORK( I+(J-1)*N ) - 180 CONTINUE - 190 CONTINUE -C -C Compute Z'*P*Z. -C - CALL ZGEMM( 'C', 'N', N, N, N, CONE, ZWORK, N, ZWORK( IZ3+1 ), N, - $ CZERO, ZWORK( IZ4+1 ), N ) -C -C Copy Z'*P*Z into A0. -C - CALL ZLACPY( 'Full', N, N, ZWORK( IZ4+1 ), N, ZWORK( IZ5+1 ), N ) -C -C Copy diag(P) into B0d. -C - CALL DCOPY( N, DWORK( IW6+1 ), 1, DWORK( IW7+1 ), 1 ) -C - DO 270 K = 2, M -C -C Set P. -C - DO 200 I = 1, IWORK( K ) - DWORK( IW6+I ) = ZERO - 200 CONTINUE - DO 210 I = IWORK( K )+1, IWORK( K )+NBLOCK( K ) - DWORK( IW6+I ) = ONE - 210 CONTINUE - IF( K.LT.M ) THEN - DO 220 I = IWORK( K+1 )+1, N - DWORK( IW6+I ) = ZERO - 220 CONTINUE - END IF -C -C Compute P*Z. -C - DO 240 J = 1, N - DO 230 I = 1, N - ZWORK( IZ3+I+(J-1)*N ) = DCMPLX( DWORK( IW6+I ) )* - $ ZWORK( I+(J-1)*N ) - 230 CONTINUE - 240 CONTINUE -C -C Compute t = Z'*P*Z. -C - CALL ZGEMM( 'C', 'N', N, N, N, CONE, ZWORK, N, ZWORK( IZ3+1 ), - $ N, CZERO, ZWORK( IZ4+1 ), N ) -C -C Copy t(:) into the (k-1)-th column of AA. -C - CALL ZCOPY( N*N, ZWORK( IZ4+1 ), 1, ZWORK( IZ6+1+(K-2)*N*N ), - $ 1 ) -C -C Copy diag(P) into the (k-1)-th column of BBd. -C - CALL DCOPY( N, DWORK( IW6+1 ), 1, DWORK( IW8+1+(K-2)*N ), 1 ) -C -C Copy P(:) into the (k-1)-th column of BB. -C - DO 260 I = 1, N - DWORK( IW9+I+(I-1)*N+(K-2)*N*N ) = DWORK( IW6+I ) - 260 CONTINUE - 270 CONTINUE -C - L = 0 -C - DO 350 K = 1, M - IF( ITYPE( K ).EQ.1 ) THEN - L = L + 1 -C -C Set P. -C - DO 280 I = 1, IWORK( K ) - DWORK( IW6+I ) = ZERO - 280 CONTINUE - DO 290 I = IWORK( K )+1, IWORK( K )+NBLOCK( K ) - DWORK( IW6+I ) = ONE - 290 CONTINUE - IF( K.LT.M ) THEN - DO 300 I = IWORK( K+1 )+1, N - DWORK( IW6+I ) = ZERO - 300 CONTINUE - END IF -C -C Compute P*Z. -C - DO 320 J = 1, N - DO 310 I = 1, N - ZWORK( IZ3+I+(J-1)*N ) = DCMPLX( DWORK( IW6+I ) )* - $ ZWORK( I+(J-1)*N ) - 310 CONTINUE - 320 CONTINUE -C -C Compute t = sqrt(-1)*( P*Z - Z'*P ). -C - DO 340 J = 1, N - DO 330 I = 1, J - TEMPIJ = ZWORK( IZ3+I+(J-1)*N ) - TEMPJI = ZWORK( IZ3+J+(I-1)*N ) - ZWORK( IZ4+I+(J-1)*N ) = CIMAG*( TEMPIJ - - $ DCONJG( TEMPJI ) ) - ZWORK( IZ4+J+(I-1)*N ) = CIMAG*( TEMPJI - - $ DCONJG( TEMPIJ ) ) - 330 CONTINUE - 340 CONTINUE -C -C Copy t(:) into the (m-1+l)-th column of AA. -C - CALL ZCOPY( N*N, ZWORK( IZ4+1 ), 1, - $ ZWORK( IZ6+1+(M-2+L)*N*N ), 1 ) - END IF - 350 CONTINUE -C -C Set initial X. -C - DO 360 I = 1, M - 1 - X( I ) = ONE - 360 CONTINUE - IF( MR.GT.0 ) THEN - IF( .NOT.XFACT ) THEN - DO 370 I = 1, MR - X( M-1+I ) = ZERO - 370 CONTINUE - ELSE - L = 0 - DO 380 K = 1, M - IF( ITYPE( K ).EQ.1 ) THEN - L = L + 1 - X( M-1+L ) = X( M-1+L ) / DWORK( IW2+K )**2 - END IF - 380 CONTINUE - END IF - END IF -C -C Set constants. -C - SVLAM = ONE / EPS - C = ONE -C -C Set H. -C - CALL DLASET( 'Full', MT, MT, ZERO, ONE, DWORK( IW11+1 ), MT ) -C - ITER = -1 -C -C Main iteration loop. -C - 390 ITER = ITER + 1 -C -C Compute A(:) = A0 + AA*x. -C - DO 400 I = 1, MT - ZWORK( IZ10+I ) = DCMPLX( X( I ) ) - 400 CONTINUE - CALL ZCOPY( N*N, ZWORK( IZ5+1 ), 1, ZWORK( IZ7+1 ), 1 ) - CALL ZGEMV( 'N', N*N, MT, CONE, ZWORK( IZ6+1 ), N*N, - $ ZWORK( IZ10+1 ), 1, CONE, ZWORK( IZ7+1 ), 1 ) -C -C Compute diag( Binv ). -C - CALL DCOPY( N, DWORK( IW7+1 ), 1, DWORK( IW12+1 ), 1 ) - CALL DGEMV( 'N', N, M-1, ONE, DWORK( IW8+1 ), N, X, 1, ONE, - $ DWORK( IW12+1 ), 1 ) - DO 410 I = 1, N - DWORK( IW12+I ) = ONE / DWORK( IW12+I ) - 410 CONTINUE -C -C Compute Binv*A. -C - DO 430 J = 1, N - DO 420 I = 1, N - ZWORK( IZ11+I+(J-1)*N ) = DCMPLX( DWORK( IW12+I ) )* - $ ZWORK( IZ7+I+(J-1)*N ) - 420 CONTINUE - 430 CONTINUE -C -C Compute eig( Binv*A ). -C - CALL ZGEES( 'N', 'N', SELECT, N, ZWORK( IZ11+1 ), N, SDIM, - $ ZWORK( IZ12+1 ), ZWORK, N, ZWORK( IZWRK+1 ), - $ LZWORK-IZWRK, DWORK( IWRK+1 ), BWORK, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 6 - RETURN - END IF - LZA = INT( ZWORK( IZWRK+1 ) ) - LZAMAX = MAX( LZA, LZAMAX ) - E = DREAL( ZWORK( IZ12+1 ) ) - IF( N.GT.1 ) THEN - DO 440 I = 2, N - IF( DREAL( ZWORK( IZ12+I ) ).GT.E ) - $ E = DREAL( ZWORK( IZ12+I ) ) - 440 CONTINUE - END IF -C -C Set tau. -C - IF( MR.GT.0 ) THEN - SNORM = ABS( X( M ) ) - IF( MR.GT.1 ) THEN - DO 450 I = M+1, MT - IF( ABS( X( I ) ).GT.SNORM ) SNORM = ABS( X( I ) ) - 450 CONTINUE - END IF - IF( SNORM.GT.FORTY ) THEN - TAU = C7 - ELSE IF( SNORM.GT.EIGHT ) THEN - TAU = FIFTY - ELSE IF( SNORM.GT.FOUR ) THEN - TAU = TEN - ELSE IF( SNORM.GT.ONE ) THEN - TAU = FIVE - ELSE - TAU = TWO - END IF - END IF - IF( ITER.EQ.0 ) THEN - DLAMBD = E + C1 - ELSE - DWORK( IW13+1 ) = E - CALL DCOPY( MT, X, 1, DWORK( IW13+2 ), 1 ) - DLAMBD = ( ONE - THETA )*DWORK( IW13+1 ) + - $ THETA*DWORK( IW14+1 ) - CALL DCOPY( MT, DWORK( IW13+2 ), 1, DWORK( IW18+1 ), 1 ) - CALL DCOPY( MT, DWORK( IW14+2 ), 1, DWORK( IW19+1 ), 1 ) - L = 0 - 460 DO 470 I = 1, MT - X( I ) = ( ONE - THETA / TWO**L )*DWORK( IW18+I ) + - $ ( THETA / TWO**L )*DWORK( IW19+I ) - 470 CONTINUE -C -C Compute At(:) = A0 + AA*x. -C - DO 480 I = 1, MT - ZWORK( IZ10+I ) = DCMPLX( X( I ) ) - 480 CONTINUE - CALL ZCOPY( N*N, ZWORK( IZ5+1 ), 1, ZWORK( IZ9+1 ), 1 ) - CALL ZGEMV( 'N', N*N, MT, CONE, ZWORK( IZ6+1 ), N*N, - $ ZWORK( IZ10+1 ), 1, CONE, ZWORK( IZ9+1 ), 1 ) -C -C Compute diag(Bt). -C - CALL DCOPY( N, DWORK( IW7+1 ), 1, DWORK( IW21+1 ), 1 ) - CALL DGEMV( 'N', N, M-1, ONE, DWORK( IW8+1 ), N, X, 1, ONE, - $ DWORK( IW21+1 ), 1 ) -C -C Compute W. -C - DO 500 J = 1, N - DO 490 I = 1, N - IF( I.EQ.J ) THEN - ZWORK( IZ13+I+(I-1)*N ) = DCMPLX( THETA*BETA* - $ ( DWORK( IW14+1 ) - DWORK( IW13+1 ) ) /TWO - - $ DLAMBD*DWORK( IW21+I ) ) + - $ ZWORK( IZ9+I+(I-1)*N ) - ELSE - ZWORK( IZ13+I+(J-1)*N ) = ZWORK( IZ9+I+(J-1)*N ) - END IF - 490 CONTINUE - 500 CONTINUE -C -C Compute eig( W ). -C - CALL ZGEES( 'N', 'N', SELECT, N, ZWORK( IZ13+1 ), N, SDIM, - $ ZWORK( IZ14+1 ), ZWORK, N, ZWORK( IZWRK+1 ), - $ LZWORK-IZWRK, DWORK( IWRK+1 ), BWORK, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 6 - RETURN - END IF - LZA = INT( ZWORK( IZWRK+1 ) ) - LZAMAX = MAX( LZA, LZAMAX ) - EMAX = DREAL( ZWORK( IZ14+1 ) ) - IF( N.GT.1 ) THEN - DO 510 I = 2, N - IF( DREAL( ZWORK( IZ14+I ) ).GT.EMAX ) - $ EMAX = DREAL( ZWORK( IZ14+I ) ) - 510 CONTINUE - END IF - IF( EMAX.LE.ZERO ) THEN - GO TO 515 - ELSE - L = L + 1 - GO TO 460 - END IF - END IF -C -C Set y. -C - 515 DWORK( IW13+1 ) = DLAMBD - CALL DCOPY( MT, X, 1, DWORK( IW13+2 ), 1 ) -C - IF( ( SVLAM - DLAMBD ).LT.TOL ) THEN - BOUND = SQRT( MAX( E, ZERO ) )*ZNORM - DO 520 I = 1, M - 1 - X( I ) = X( I )*DWORK( IW2+I+1 )**2 - 520 CONTINUE -C -C Compute sqrt( x ). -C - DO 530 I = 1, M-1 - DWORK( IW20+I ) = SQRT( X( I ) ) - 530 CONTINUE -C -C Compute diag( D ). -C - CALL DCOPY( N, DWORK( IW7+1 ), 1, D, 1 ) - CALL DGEMV( 'N', N, M-1, ONE, DWORK( IW8+1 ), N, - $ DWORK( IW20+1 ), 1, ONE, D, 1 ) -C -C Compute diag( G ). -C - J = 0 - L = 0 - DO 540 K = 1, M - J = J + NBLOCK( K ) - IF( ITYPE( K ).EQ.1 ) THEN - L = L + 1 - X( M-1+L ) = X( M-1+L )*DWORK( IW2+K )**2 - G( J ) = X( M-1+L ) - END IF - 540 CONTINUE - CALL DSCAL( N, ZNORM, G, 1 ) - DWORK( 1 ) = DFLOAT( MINWRK - 5*N + LWAMAX ) - ZWORK( 1 ) = DCMPLX( MINZRK - 3*N + LZAMAX ) - RETURN - END IF - SVLAM = DLAMBD - DO 800 K = 1, M -C -C Store xD. -C - CALL DCOPY( M-1, X, 1, DWORK( IW22+1 ), 1 ) - IF( MR.GT.0 ) THEN -C -C Store xG. -C - CALL DCOPY( MR, X( M ), 1, DWORK( IW23+1 ), 1 ) - END IF -C -C Compute A(:) = A0 + AA*x. -C - DO 550 I = 1, MT - ZWORK( IZ10+I ) = DCMPLX( X( I ) ) - 550 CONTINUE - CALL ZCOPY( N*N, ZWORK( IZ5+1 ), 1, ZWORK( IZ7+1 ), 1 ) - CALL ZGEMV( 'N', N*N, MT, CONE, ZWORK( IZ6+1 ), N*N, - $ ZWORK( IZ10+1 ), 1, CONE, ZWORK( IZ7+1 ), 1 ) -C -C Compute B = B0d + BBd*xD. -C - CALL DCOPY( N, DWORK( IW7+1 ), 1, DWORK( IW24+1 ), 1 ) - CALL DGEMV( 'N', N, M-1, ONE, DWORK( IW8+1 ), N, - $ DWORK( IW22+1 ), 1, ONE, DWORK( IW24+1 ), 1 ) -C -C Compute F. -C - DO 556 J = 1, N - DO 555 I = 1, N - IF( I.EQ.J ) THEN - ZWORK( IZ15+I+(I-1)*N ) = DCMPLX( DLAMBD* - $ DWORK( IW24+I ) ) - ZWORK( IZ7+I+(I-1)*N ) - ELSE - ZWORK( IZ15+I+(J-1)*N ) = -ZWORK( IZ7+I+(J-1)*N ) - END IF - 555 CONTINUE - 556 CONTINUE - CALL ZLACPY( 'Full', N, N, ZWORK( IZ15+1 ), N, - $ ZWORK( IZ17+1 ), N ) -C -C Compute det( F ). -C - CALL ZGEES( 'N', 'N', SELECT, N, ZWORK( IZ15+1 ), N, SDIM, - $ ZWORK( IZ16+1 ), ZWORK, N, ZWORK( IZWRK+1 ), - $ LZWORK-IZWRK, DWORK( IWRK+1 ), BWORK, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 6 - RETURN - END IF - LZA = INT( ZWORK( IZWRK+1 ) ) - LZAMAX = MAX( LZA, LZAMAX ) - DETF = CONE - DO 560 I = 1, N - DETF = DETF*ZWORK( IZ16+I ) - 560 CONTINUE -C -C Compute Finv. -C - CALL ZGETRF( N, N, ZWORK( IZ17+1 ), N, IWORK, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 5 - RETURN - END IF - CALL ZGETRI( N, ZWORK( IZ17+1 ), N, IWORK, ZWORK( IZWRK+1 ), - $ LDWORK-IWRK, INFO2 ) - LZA = INT( ZWORK( IZWRK+1 ) ) - LZAMAX = MAX( LZA, LZAMAX ) -C -C Compute phi. -C - DO 570 I = 1, M-1 - DWORK( IW25+I ) = DWORK( IW22+I ) - BETA - DWORK( IW25+M-1+I ) = ALPHA - DWORK( IW22+I ) - 570 CONTINUE - IF( MR.GT.0 ) THEN - DO 580 I = 1, MR - DWORK( IW25+2*(M-1)+I ) = DWORK( IW23+I ) + TAU - DWORK( IW25+2*(M-1)+MR+I ) = TAU - DWORK( IW23+I ) - 580 CONTINUE - END IF - PROD = ONE - DO 590 I = 1, 2*MT - PROD = PROD*DWORK( IW25+I ) - 590 CONTINUE - TEMP = DREAL( DETF ) - IF( TEMP.LT.EPS ) TEMP = EPS - PHI = -LOG( TEMP ) - LOG( PROD ) -C -C Compute g. -C - DO 610 J = 1, MT - DO 600 I = 1, N*N - ZWORK( IZ18+I+(J-1)*N*N ) = DCMPLX( DLAMBD* - $ DWORK( IW9+I+(J-1)*N*N ) ) - ZWORK( IZ6+I+(J-1)*N*N ) - 600 CONTINUE - 610 CONTINUE - CALL ZGEMV( 'C', N*N, MT, CONE, ZWORK( IZ18+1 ), N*N, - $ ZWORK( IZ17+1 ), 1, CZERO, ZWORK( IZ19+1 ), 1 ) - DO 620 I = 1, M-1 - DWORK( IW26+I ) = ONE / ( DWORK( IW22+I ) - BETA ) - - $ ONE / ( ALPHA - DWORK( IW22+I ) ) - 620 CONTINUE - IF( MR.GT.0 ) THEN - DO 630 I = 1, MR - DWORK( IW26+M-1+I ) = ONE / ( DWORK( IW23+I ) + TAU ) - $ -ONE / ( TAU - DWORK( IW23+I ) ) - 630 CONTINUE - END IF - DO 640 I = 1, MT - DWORK( IW26+I ) = -DREAL( ZWORK( IZ19+I ) ) - - $ DWORK( IW26+I ) - 640 CONTINUE -C -C Compute h. -C - CALL DLACPY( 'Full', MT, MT, DWORK( IW11+1 ), MT, - $ DWORK( IW31+1 ), MT ) - CALL DCOPY( MT, DWORK( IW26+1 ), 1, DWORK( IW27+1 ), 1 ) - CALL DSYSV( 'U', MT, 1, DWORK( IW31+1 ), MT, IWORK, - $ DWORK( IW27+1 ), MT, DWORK( IWRK+1 ), - $ LDWORK-IWRK, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 5 - RETURN - END IF - LWA = INT( DWORK( IWRK+1 ) ) - LWAMAX = MAX( LWA, LWAMAX ) - STSIZE = ONE -C -C Store hD. -C - CALL DCOPY( M-1, DWORK( IW27+1 ), 1, DWORK( IW28+1 ), 1 ) -C -C Determine stepsize. -C - L = 0 - DO 650 I = 1, M-1 - IF( DWORK( IW28+I ).GT.ZERO ) THEN - L = L + 1 - IF( L.EQ.1 ) THEN - TEMP = ( DWORK( IW22+I ) - BETA ) / DWORK( IW28+I ) - ELSE - TEMP = MIN( TEMP, ( DWORK( IW22+I ) - BETA ) / - $ DWORK( IW28+I ) ) - END IF - END IF - 650 CONTINUE - IF( L.GT.0 ) STSIZE = MIN( STSIZE, TEMP ) - L = 0 - DO 660 I = 1, M-1 - IF( DWORK( IW28+I ).LT.ZERO ) THEN - L = L + 1 - IF( L.EQ.1 ) THEN - TEMP = ( ALPHA - DWORK( IW22+I ) ) / - $ ( -DWORK( IW28+I ) ) - ELSE - TEMP = MIN( TEMP, ( ALPHA - DWORK( IW22+I ) ) / - $ ( -DWORK( IW28+I ) ) ) - END IF - END IF - 660 CONTINUE - IF( L.GT.0 ) STSIZE = MIN( STSIZE, TEMP ) - IF( MR.GT.0 ) THEN -C -C Store hG. -C - CALL DCOPY( MR, DWORK( IW27+M ), 1, DWORK( IW29+1 ), 1 ) -C -C Determine stepsize. -C - L = 0 - DO 670 I = 1, MR - IF( DWORK( IW29+I ).GT.ZERO ) THEN - L = L + 1 - IF( L.EQ.1 ) THEN - TEMP = ( DWORK( IW23+I ) + TAU ) / - $ DWORK( IW29+I ) - ELSE - TEMP = MIN( TEMP, ( DWORK( IW23+I ) + TAU ) / - $ DWORK( IW29+I ) ) - END IF - END IF - 670 CONTINUE - IF( L.GT.0 ) STSIZE = MIN( STSIZE, TEMP ) - L = 0 - DO 680 I = 1, MR - IF( DWORK( IW29+I ).LT.ZERO ) THEN - L = L + 1 - IF( L.EQ.1 ) THEN - TEMP = ( TAU - DWORK( IW23+I ) ) / - $ ( -DWORK( IW29+I ) ) - ELSE - TEMP = MIN( TEMP, ( TAU - DWORK( IW23+I ) ) / - $ ( -DWORK( IW29+I ) ) ) - END IF - END IF - 680 CONTINUE - END IF - IF( L.GT.0 ) STSIZE = MIN( STSIZE, TEMP ) - STSIZE = C4*STSIZE - IF( STSIZE.GE.TOL4 ) THEN -C -C Compute x_new. -C - DO 700 I = 1, MT - DWORK( IW20+I ) = X( I ) - STSIZE*DWORK( IW27+I ) - 700 CONTINUE -C -C Store xD. -C - CALL DCOPY( M-1, DWORK( IW20+1 ), 1, DWORK( IW22+1 ), 1 ) - IF( MR.GT.0 ) THEN -C -C Store xG. -C - CALL DCOPY( MR, DWORK( IW20+M ), 1, DWORK( IW23+1 ), - $ 1 ) - END IF -C -C Compute A(:) = A0 + AA*x_new. -C - DO 710 I = 1, MT - ZWORK( IZ10+I ) = DCMPLX( DWORK( IW20+I ) ) - 710 CONTINUE - CALL ZCOPY( N*N, ZWORK( IZ5+1 ), 1, ZWORK( IZ7+1 ), 1 ) - CALL ZGEMV( 'N', N*N, MT, CONE, ZWORK( IZ6+1 ), N*N, - $ ZWORK( IZ10+1 ), 1, CONE, ZWORK( IZ7+1 ), 1 ) -C -C Compute B = B0d + BBd*xD. -C - CALL DCOPY( N, DWORK( IW7+1 ), 1, DWORK( IW24+1 ), 1 ) - CALL DGEMV( 'N', N, M-1, ONE, DWORK( IW8+1 ), N, - $ DWORK( IW22+1 ), 1, ONE, DWORK( IW24+1 ), 1 ) -C -C Compute lambda*diag(B) - A. -C - DO 730 J = 1, N - DO 720 I = 1, N - IF( I.EQ.J ) THEN - ZWORK( IZ15+I+(I-1)*N ) = DCMPLX( DLAMBD* - $ DWORK( IW24+I ) ) - ZWORK( IZ7+I+(I-1)*N ) - ELSE - ZWORK( IZ15+I+(J-1)*N ) = - $ -ZWORK( IZ7+I+(J-1)*N ) - END IF - 720 CONTINUE - 730 CONTINUE -C -C Compute eig( lambda*diag(B)-A ). -C - CALL ZGEES( 'N', 'N', SELECT, N, ZWORK( IZ15+1 ), N, - $ SDIM, ZWORK( IZ16+1 ), ZWORK, N, - $ ZWORK( IZWRK+1 ), LZWORK-IZWRK, - $ DWORK( IWRK+1 ), BWORK, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 6 - RETURN - END IF - LZA = INT( ZWORK( IZWRK+1 ) ) - LZAMAX = MAX( LZA, LZAMAX ) - EMIN = DREAL( ZWORK( IZ16+1 ) ) - IF( N.GT.1 ) THEN - DO 740 I = 2, N - IF( DREAL( ZWORK( IZ16+I ) ).LT.EMIN ) - $ EMIN = DREAL( ZWORK( IZ16+I ) ) - 740 CONTINUE - END IF - DO 750 I = 1, N - DWORK( IW30+I ) = DREAL( ZWORK( IZ16+I ) ) - 750 CONTINUE - DO 760 I = 1, M-1 - DWORK( IW30+N+I ) = DWORK( IW22+I ) - BETA - DWORK( IW30+N+M-1+I ) = ALPHA - DWORK( IW22+I ) - 760 CONTINUE - IF( MR.GT.0 ) THEN - DO 770 I = 1, MR - DWORK( IW30+N+2*(M-1)+I ) = DWORK( IW23+I ) + TAU - DWORK( IW30+N+2*(M-1)+MR+I ) = TAU - - $ DWORK( IW23+I ) - 770 CONTINUE - END IF - PROD = ONE - DO 780 I = 1, N+2*MT - PROD = PROD*DWORK( IW30+I ) - 780 CONTINUE - IF( EMIN.LE.ZERO .OR. ( -LOG( PROD ) ).GE.PHI ) THEN - STSIZE = STSIZE / TEN - ELSE - CALL DCOPY( MT, DWORK( IW20+1 ), 1, X, 1 ) - END IF - END IF - IF( STSIZE.LT.TOL4 ) GO TO 810 - 800 CONTINUE -C - 810 CONTINUE -C -C Store xD. -C - CALL DCOPY( M-1, X, 1, DWORK( IW22+1 ), 1 ) - IF( MR.GT.0 ) THEN -C -C Store xG. -C - CALL DCOPY( MR, X( M ), 1, DWORK( IW23+1 ), 1 ) - END IF -C -C Compute A(:) = A0 + AA*x. -C - DO 820 I = 1, MT - ZWORK( IZ10+I ) = DCMPLX( X( I ) ) - 820 CONTINUE - CALL ZCOPY( N*N, ZWORK( IZ5+1 ), 1, ZWORK( IZ7+1 ), 1 ) - CALL ZGEMV( 'N', N*N, MT, CONE, ZWORK( IZ6+1 ), N*N, - $ ZWORK( IZ10+1 ), 1, CONE, ZWORK( IZ7+1 ), 1 ) -C -C Compute diag( B ) = B0d + BBd*xD. -C - CALL DCOPY( N, DWORK( IW7+1 ), 1, DWORK( IW24+1 ), 1 ) - CALL DGEMV( 'N', N, M-1, ONE, DWORK( IW8+1 ), N, - $ DWORK( IW22+1 ), 1, ONE, DWORK( IW24+1 ), 1 ) -C -C Compute F. -C - DO 840 J = 1, N - DO 830 I = 1, N - IF( I.EQ.J ) THEN - ZWORK( IZ15+I+(I-1)*N ) = DCMPLX( DLAMBD* - $ DWORK( IW24+I ) ) - ZWORK( IZ7+I+(I-1)*N ) - ELSE - ZWORK( IZ15+I+(J-1)*N ) = -ZWORK( IZ7+I+(J-1)*N ) - END IF - 830 CONTINUE - 840 CONTINUE - CALL ZLACPY( 'Full', N, N, ZWORK( IZ15+1 ), N, - $ ZWORK( IZ17+1 ), N ) -C -C Compute det( F ). -C - CALL ZGEES( 'N', 'N', SELECT, N, ZWORK( IZ15+1 ), N, SDIM, - $ ZWORK( IZ16+1 ), ZWORK, N, ZWORK( IZWRK+1 ), - $ LZWORK-IZWRK, DWORK( IWRK+1 ), BWORK, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 6 - RETURN - END IF - LZA = INT( ZWORK( IZWRK+1 ) ) - LZAMAX = MAX( LZA, LZAMAX ) - DETF = CONE - DO 850 I = 1, N - DETF = DETF*ZWORK( IZ16+I ) - 850 CONTINUE -C -C Compute Finv. -C - CALL ZGETRF( N, N, ZWORK( IZ17+1 ), N, IWORK, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 5 - RETURN - END IF - CALL ZGETRI( N, ZWORK( IZ17+1 ), N, IWORK, ZWORK( IZWRK+1 ), - $ LDWORK-IWRK, INFO2 ) - LZA = INT( ZWORK( IZWRK+1 ) ) - LZAMAX = MAX( LZA, LZAMAX ) -C -C Compute the barrier function. -C - DO 860 I = 1, M-1 - DWORK( IW25+I ) = DWORK( IW22+I ) - BETA - DWORK( IW25+M-1+I ) = ALPHA - DWORK( IW22+I ) - 860 CONTINUE - IF( MR.GT.0 ) THEN - DO 870 I = 1, MR - DWORK( IW25+2*(M-1)+I ) = DWORK( IW23+I ) + TAU - DWORK( IW25+2*(M-1)+MR+I ) = TAU - DWORK( IW23+I ) - 870 CONTINUE - END IF - PROD = ONE - DO 880 I = 1, 2*MT - PROD = PROD*DWORK( IW25+I ) - 880 CONTINUE - TEMP = DREAL( DETF ) - IF( TEMP.LT.EPS ) TEMP = EPS - PHI = -LOG( TEMP ) - LOG( PROD ) -C -C Compute the gradient of the barrier function. -C - DO 900 J = 1, MT - DO 890 I = 1, N*N - ZWORK( IZ18+I+(J-1)*N*N ) = DCMPLX( DLAMBD* - $ DWORK( IW9+I+(J-1)*N*N ) ) - ZWORK( IZ6+I+(J-1)*N*N ) - 890 CONTINUE - 900 CONTINUE - CALL ZGEMV( 'C', N*N, MT, CONE, ZWORK( IZ18+1 ), N*N, - $ ZWORK( IZ17+1 ), 1, CZERO, ZWORK( IZ19+1 ), 1 ) - DO 910 I = 1, M-1 - DWORK( IW26+I ) = ONE / ( DWORK( IW22+I ) - BETA ) - - $ ONE / ( ALPHA - DWORK( IW22+I ) ) - 910 CONTINUE - IF( MR.GT.0 ) THEN - DO 920 I = 1, MR - DWORK( IW26+M-1+I ) = ONE / ( DWORK( IW23+I ) + TAU ) - $ -ONE / ( TAU - DWORK( IW23+I ) ) - 920 CONTINUE - END IF - DO 925 I = 1, MT - DWORK( IW26+I ) = -DREAL( ZWORK( IZ19+I ) ) - - $ DWORK( IW26+I ) - 925 CONTINUE -C -C Compute the Hessian of the barrier function. -C - CALL ZGEMM( 'N', 'N', N, N*MT, N, CONE, ZWORK( IZ17+1 ), N, - $ ZWORK( IZ18+1 ), N, CZERO, ZWORK( IZ20+1 ), N ) - - CALL DLASET( 'Full', MT, MT, ZERO, ZERO, DWORK( IW11+1 ), - $ MT ) - DO 960 K = 1, MT - CALL ZCOPY( N*N, ZWORK( IZ20+1+(K-1)*N*N ), 1, - $ ZWORK( IZ22+1 ), 1 ) - DO 940 J = 1, N - DO 930 I = 1, N - ZWORK( IZ23+I+(J-1)*N ) = - $ DCONJG( ZWORK( IZ22+J+(I-1)*N ) ) - 930 CONTINUE - 940 CONTINUE - CALL ZGEMV( 'C', N*N, K, CONE, ZWORK( IZ20+1 ), N*N, - $ ZWORK( IZ23+1 ), 1, CZERO, ZWORK( IZ24+1 ), - $ 1 ) - DO 950 J = 1, K - DWORK( IW11+K+(J-1)*MT ) = - $ DREAL( DCONJG( ZWORK( IZ24+J ) ) ) - 950 CONTINUE - 960 CONTINUE - DO 970 I = 1, M-1 - DWORK( IW10+I ) = ONE / ( DWORK( IW22+I ) - BETA )**2 + - $ ONE / ( ALPHA - DWORK( IW22+I ) )**2 - 970 CONTINUE - IF( MR.GT.0 ) THEN - DO 980 I = 1, MR - DWORK( IW10+M-1+I ) = - $ ONE / ( DWORK( IW23+I ) + TAU )**2 + - $ ONE / ( TAU - DWORK( IW23+I ) )**2 - 980 CONTINUE - END IF - DO 990 I = 1, MT - DWORK( IW11+I+(I-1)*MT ) = DWORK( IW11+I+(I-1)*MT ) + - $ DWORK( IW10+I ) - 990 CONTINUE - DO 1100 J = 1, MT - DO 1000 I = 1, J - IF( I.NE.J ) THEN - T1 = DWORK( IW11+I+(J-1)*MT ) - T2 = DWORK( IW11+J+(I-1)*MT ) - DWORK( IW11+I+(J-1)*MT ) = T1 + T2 - DWORK( IW11+J+(I-1)*MT ) = T1 + T2 - END IF - 1000 CONTINUE - 1100 CONTINUE -C -C Compute norm( H ). -C - 1110 HNORM = DLANGE( 'F', MT, MT, DWORK( IW11+1 ), MT, DWORK ) -C -C Compute rcond( H ). -C - CALL DLACPY( 'Full', MT, MT, DWORK( IW11+1 ), MT, - $ DWORK( IW31+1 ), MT ) - HNORM1 = DLANGE( '1', MT, MT, DWORK( IW31+1 ), MT, DWORK ) - CALL DSYTRF( 'U', MT, DWORK( IW31+1 ), MT, IWORK, - $ DWORK( IWRK+1 ), LDWORK-IWRK, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 5 - RETURN - END IF - LWA = INT( DWORK( IWRK+1 ) ) - LWAMAX = MAX( LWA, LWAMAX ) - CALL DSYCON( 'U', MT, DWORK( IW31+1 ), MT, IWORK, HNORM1, - $ RCOND, DWORK( IWRK+1 ), IWORK( MT+1 ), INFO2 ) - IF( RCOND.LT.TOL3 ) THEN - DO 1120 I = 1, MT - DWORK( IW11+I+(I-1)*MT ) = DWORK( IW11+I+(I-1)*MT ) + - $ HNORM*REGPAR - 1120 CONTINUE - GO TO 1110 - END IF -C -C Compute the tangent line to path of center. -C - CALL DCOPY( MT, DWORK( IW26+1 ), 1, DWORK( IW27+1 ), 1 ) - CALL DSYTRS( 'U', MT, 1, DWORK( IW31+1 ), MT, IWORK, - $ DWORK( IW27+1 ), MT, INFO2 ) -C -C Check if x-h satisfies the Goldstein test. -C - GTEST = .FALSE. - DO 1130 I = 1, MT - DWORK( IW20+I ) = X( I ) - DWORK( IW27+I ) - 1130 CONTINUE -C -C Store xD. -C - CALL DCOPY( M-1, DWORK( IW20+1 ), 1, DWORK( IW22+1 ), 1 ) - IF( MR.GT.0 ) THEN -C -C Store xG. -C - CALL DCOPY( MR, DWORK( IW20+M ), 1, DWORK( IW23+1 ), 1 ) - END IF -C -C Compute A(:) = A0 + AA*x_new. -C - DO 1140 I = 1, MT - ZWORK( IZ10+I ) = DCMPLX( DWORK( IW20+I ) ) - 1140 CONTINUE - CALL ZCOPY( N*N, ZWORK( IZ5+1 ), 1, ZWORK( IZ7+1 ), 1 ) - CALL ZGEMV( 'N', N*N, MT, CONE, ZWORK( IZ6+1 ), N*N, - $ ZWORK( IZ10+1 ), 1, CONE, ZWORK( IZ7+1 ), 1 ) -C -C Compute diag( B ) = B0d + BBd*xD. -C - CALL DCOPY( N, DWORK( IW7+1 ), 1, DWORK( IW24+1 ), 1 ) - CALL DGEMV( 'N', N, M-1, ONE, DWORK( IW8+1 ), N, - $ DWORK( IW22+1 ), 1, ONE, DWORK( IW24+1 ), 1 ) -C -C Compute lambda*diag(B) - A. -C - DO 1160 J = 1, N - DO 1150 I = 1, N - IF( I.EQ.J ) THEN - ZWORK( IZ15+I+(I-1)*N ) = DCMPLX( DLAMBD* - $ DWORK( IW24+I ) ) - ZWORK( IZ7+I+(I-1)*N ) - ELSE - ZWORK( IZ15+I+(J-1)*N ) = -ZWORK( IZ7+I+(J-1)*N ) - END IF - 1150 CONTINUE - 1160 CONTINUE -C -C Compute eig( lambda*diag(B)-A ). -C - CALL ZGEES( 'N', 'N', SELECT, N, ZWORK( IZ15+1 ), N, SDIM, - $ ZWORK( IZ16+1 ), ZWORK, N, ZWORK( IZWRK+1 ), - $ LZWORK-IZWRK, DWORK( IWRK+1 ), BWORK, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 6 - RETURN - END IF - LZA = INT( ZWORK( IZWRK+1 ) ) - LZAMAX = MAX( LZA, LZAMAX ) - DO 1190 I = 1, N - DWORK( IW30+I ) = DREAL( ZWORK( IZ16+I ) ) - 1190 CONTINUE - DO 1200 I = 1, M-1 - DWORK( IW30+N+I ) = DWORK( IW22+I ) - BETA - DWORK( IW30+N+M-1+I ) = ALPHA - DWORK( IW22+I ) - 1200 CONTINUE - IF( MR.GT.0 ) THEN - DO 1210 I = 1, MR - DWORK( IW30+N+2*(M-1)+I ) = DWORK( IW23+I ) + TAU - DWORK( IW30+N+2*(M-1)+MR+I ) = TAU - DWORK( IW23+I ) - 1210 CONTINUE - END IF - EMIN = DWORK( IW30+1 ) - DO 1220 I = 1, N+2*MT - IF( DWORK( IW30+I ).LT.EMIN ) EMIN = DWORK( IW30+I ) - 1220 CONTINUE - IF( EMIN.LE.ZERO ) THEN - GTEST = .FALSE. - ELSE - PP = DDOT( MT, DWORK( IW26+1 ), 1, DWORK( IW27+1 ), 1 ) - PROD = ONE - DO 1230 I = 1, N+2*MT - PROD = PROD*DWORK( IW30+I ) - 1230 CONTINUE - T1 = -LOG( PROD ) - T2 = PHI - C2*PP - T3 = PHI - C4*PP - IF( T1.GE.T3 .AND. T1.LT.T2 ) GTEST = .TRUE. - END IF -C -C Use x-h if Goldstein test is satisfied. Otherwise use -C Nesterov-Nemirovsky's stepsize length. -C - PP = DDOT( MT, DWORK( IW26+1 ), 1, DWORK( IW27+1 ), 1 ) - DELTA = SQRT( PP ) - IF( GTEST .OR. DELTA.LE.C3 ) THEN - DO 1240 I = 1, MT - X( I ) = X( I ) - DWORK( IW27+I ) - 1240 CONTINUE - ELSE - DO 1250 I = 1, MT - X( I ) = X( I ) - DWORK( IW27+I ) / ( ONE + DELTA ) - 1250 CONTINUE - END IF -C -C Analytic center is found if delta is sufficiently small. -C - IF( DELTA.LT.TOL5 ) GO TO 1260 - GO TO 810 -C -C Set yf. -C - 1260 DWORK( IW14+1 ) = DLAMBD - CALL DCOPY( MT, X, 1, DWORK( IW14+2 ), 1 ) -C -C Set yw. -C - CALL DCOPY( MT+1, DWORK( IW14+1 ), 1, DWORK( IW15+1 ), 1 ) -C -C Compute Fb. -C - DO 1280 J = 1, N - DO 1270 I = 1, N - ZWORK( IZ21+I+(J-1)*N ) = DCMPLX( DWORK( IW24+I ) )* - $ DCONJG( ZWORK( IZ17+J+(I-1)*N ) ) - 1270 CONTINUE - 1280 CONTINUE - CALL ZGEMV( 'C', N*N, MT, CONE, ZWORK( IZ20+1 ), N*N, - $ ZWORK( IZ21+1 ), 1, CZERO, ZWORK( IZ24+1 ), 1 ) - DO 1300 I = 1, MT - DWORK( IW32+I ) = DREAL( ZWORK( IZ24+I ) ) - 1300 CONTINUE -C -C Compute h1. -C - CALL DLACPY( 'Full', MT, MT, DWORK( IW11+1 ), MT, - $ DWORK( IW31+1 ), MT ) - CALL DSYSV( 'U', MT, 1, DWORK( IW31+1 ), MT, IWORK, - $ DWORK( IW32+1 ), MT, DWORK( IWRK+1 ), - $ LDWORK-IWRK, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 5 - RETURN - END IF - LWA = INT( DWORK( IWRK+1 ) ) - LWAMAX = MAX( LWA, LWAMAX ) -C -C Compute hn. -C - HN = DLANGE( 'F', MT, 1, DWORK( IW32+1 ), MT, DWORK ) -C -C Compute y. -C - DWORK( IW13+1 ) = DLAMBD - C / HN - DO 1310 I = 1, MT - DWORK( IW13+1+I ) = X( I ) + C*DWORK( IW32+I ) / HN - 1310 CONTINUE -C -C Store xD. -C - CALL DCOPY( M-1, DWORK( IW13+2 ), 1, DWORK( IW22+1 ), 1 ) - IF( MR.GT.0 ) THEN -C -C Store xG. -C - CALL DCOPY( MR, DWORK( IW13+M+1 ), 1, DWORK( IW23+1 ), 1 ) - END IF -C -C Compute A(:) = A0 + AA*y(2:mt+1). -C - DO 1320 I = 1, MT - ZWORK( IZ10+I ) = DCMPLX( DWORK( IW13+1+I ) ) - 1320 CONTINUE - CALL ZCOPY( N*N, ZWORK( IZ5+1 ), 1, ZWORK( IZ7+1 ), 1 ) - CALL ZGEMV( 'N', N*N, MT, CONE, ZWORK( IZ6+1 ), N*N, - $ ZWORK( IZ10+1 ), 1, CONE, ZWORK( IZ7+1 ), 1 ) -C -C Compute B = B0d + BBd*xD. -C - CALL DCOPY( N, DWORK( IW7+1 ), 1, DWORK( IW24+1 ), 1 ) - CALL DGEMV( 'N', N, M-1, ONE, DWORK( IW8+1 ), N, - $ DWORK( IW22+1 ), 1, ONE, DWORK( IW24+1 ), 1 ) -C -C Compute y(1)*diag(B) - A. -C - DO 1340 J = 1, N - DO 1330 I = 1, N - IF( I.EQ.J ) THEN - ZWORK( IZ15+I+(I-1)*N ) = DCMPLX( DWORK( IW13+1 )* - $ DWORK( IW24+I ) ) - ZWORK( IZ7+I+(I-1)*N ) - ELSE - ZWORK( IZ15+I+(J-1)*N ) = -ZWORK( IZ7+I+(J-1)*N ) - END IF - 1330 CONTINUE - 1340 CONTINUE -C -C Compute eig( y(1)*diag(B)-A ). -C - CALL ZGEES( 'N', 'N', SELECT, N, ZWORK( IZ15+1 ), N, SDIM, - $ ZWORK( IZ16+1 ), ZWORK, N, ZWORK( IZWRK+1 ), - $ LZWORK-IZWRK, DWORK( IWRK+1 ), BWORK, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 6 - RETURN - END IF - LZA = INT( ZWORK( IZWRK+1 ) ) - LZAMAX = MAX( LZA, LZAMAX ) - EMIN = DREAL( ZWORK( IZ16+1 ) ) - IF( N.GT.1 ) THEN - DO 1350 I = 2, N - IF( DREAL( ZWORK( IZ16+I ) ).LT.EMIN ) - $ EMIN = DREAL( ZWORK( IZ16+I ) ) - 1350 CONTINUE - END IF - POS = .TRUE. - DO 1360 I = 1, M-1 - DWORK( IW25+I ) = DWORK( IW22+I ) - BETA - DWORK( IW25+M-1+I ) = ALPHA - DWORK( IW22+I ) - 1360 CONTINUE - IF( MR.GT.0 ) THEN - DO 1370 I = 1, MR - DWORK( IW25+2*(M-1)+I ) = DWORK( IW23+I ) + TAU - DWORK( IW25+2*(M-1)+MR+I ) = TAU - DWORK( IW23+I ) - 1370 CONTINUE - END IF - TEMP = DWORK( IW25+1 ) - DO 1380 I = 2, 2*MT - IF( DWORK( IW25+I ).LT.TEMP ) TEMP = DWORK( IW25+I ) - 1380 CONTINUE - IF( TEMP.LE.ZERO .OR. EMIN.LE.ZERO ) POS = .FALSE. - 1390 IF( POS ) THEN -C -C Set y2 = y. -C - CALL DCOPY( MT+1, DWORK( IW13+1 ), 1, DWORK( IW17+1 ), 1 ) -C -C Compute y = y + 1.5*( y - yw ). -C - DO 1400 I = 1, MT+1 - DWORK( IW13+I ) = DWORK( IW13+I ) + - $ C5*( DWORK( IW13+I ) - DWORK( IW15+I ) ) - 1400 CONTINUE -C -C Store xD. -C - CALL DCOPY( M-1, DWORK( IW13+2 ), 1, DWORK( IW22+1 ), 1 ) - IF( MR.GT.0 ) THEN -C -C Store xG. -C - CALL DCOPY( MR, DWORK( IW13+M+1 ), 1, - $ DWORK( IW23+1 ), 1 ) - END IF -C -C Compute A(:) = A0 + AA*y(2:mt+1). -C - DO 1420 I = 1, MT - ZWORK( IZ10+I ) = DCMPLX( DWORK( IW13+1+I ) ) - 1420 CONTINUE - CALL ZCOPY( N*N, ZWORK( IZ5+1 ), 1, ZWORK( IZ7+1 ), 1 ) - CALL ZGEMV( 'N', N*N, MT, CONE, ZWORK( IZ6+1 ), N*N, - $ ZWORK( IZ10+1 ), 1, CONE, ZWORK( IZ7+1 ), 1 ) -C -C Compute diag( B ) = B0d + BBd*xD. -C - CALL DCOPY( N, DWORK( IW7+1 ), 1, DWORK( IW24+1 ), 1 ) - CALL DGEMV( 'N', N, M-1, ONE, DWORK( IW8+1 ), N, - $ DWORK( IW22+1 ), 1, ONE, DWORK( IW24+1 ), 1 ) -C -C Set yw = y2. -C - CALL DCOPY( MT+1, DWORK( IW17+1 ), 1, DWORK( IW15+1 ), 1 ) -C -C Compute y(1)*diag(B) - A. -C - DO 1440 J = 1, N - DO 1430 I = 1, N - IF( I.EQ.J ) THEN - ZWORK( IZ15+I+(I-1)*N ) = DCMPLX( DWORK( IW13+1 )* - $ DWORK( IW24+I ) ) - ZWORK( IZ7+I+(I-1)*N ) - ELSE - ZWORK( IZ15+I+(J-1)*N ) = -ZWORK( IZ7+I+(J-1)*N ) - END IF - 1430 CONTINUE - 1440 CONTINUE -C -C Compute eig( y(1)*diag(B)-A ). -C - CALL ZGEES( 'N', 'N', SELECT, N, ZWORK( IZ15+1 ), N, SDIM, - $ ZWORK( IZ16+1 ), ZWORK, N, ZWORK( IZWRK+1 ), - $ LZWORK-IZWRK, DWORK( IWRK+1 ), BWORK, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 6 - RETURN - END IF - LZA = INT( ZWORK( IZWRK+1 ) ) - LZAMAX = MAX( LZA, LZAMAX ) - EMIN = DREAL( ZWORK( IZ16+1 ) ) - IF( N.GT.1 ) THEN - DO 1450 I = 2, N - IF( DREAL( ZWORK( IZ16+I ) ).LT.EMIN ) - $ EMIN = DREAL( ZWORK( IZ16+I ) ) - 1450 CONTINUE - END IF - POS = .TRUE. - DO 1460 I = 1, M-1 - DWORK( IW25+I ) = DWORK( IW22+I ) - BETA - DWORK( IW25+M-1+I ) = ALPHA - DWORK( IW22+I ) - 1460 CONTINUE - IF( MR.GT.0 ) THEN - DO 1470 I = 1, MR - DWORK( IW25+2*(M-1)+I ) = DWORK( IW23+I ) + TAU - DWORK( IW25+2*(M-1)+MR+I ) = TAU - DWORK( IW23+I ) - 1470 CONTINUE - END IF - TEMP = DWORK( IW25+1 ) - DO 1480 I = 2, 2*MT - IF( DWORK( IW25+I ).LT.TEMP ) TEMP = DWORK( IW25+I ) - 1480 CONTINUE - IF( TEMP.LE.ZERO .OR. EMIN.LE.ZERO ) POS = .FALSE. - GO TO 1390 - END IF - 1490 CONTINUE -C -C Set y1 = ( y + yw ) / 2. -C - DO 1500 I = 1, MT+1 - DWORK( IW16+I ) = ( DWORK( IW13+I ) + DWORK( IW15+I ) ) - $ / TWO - 1500 CONTINUE -C -C Store xD. -C - CALL DCOPY( M-1, DWORK( IW16+2 ), 1, DWORK( IW22+1 ), 1 ) - IF( MR.GT.0 ) THEN -C -C Store xG. -C - CALL DCOPY( MR, DWORK( IW16+M+1 ), 1, DWORK( IW23+1 ), 1 ) - END IF -C -C Compute A(:) = A0 + AA*y1(2:mt+1). -C - DO 1510 I = 1, MT - ZWORK( IZ10+I ) = DCMPLX( DWORK( IW16+1+I ) ) - 1510 CONTINUE - CALL ZCOPY( N*N, ZWORK( IZ5+1 ), 1, ZWORK( IZ7+1 ), 1 ) - CALL ZGEMV( 'N', N*N, MT, CONE, ZWORK( IZ6+1 ), N*N, - $ ZWORK( IZ10+1 ), 1, CONE, ZWORK( IZ7+1 ), 1 ) -C -C Compute diag( B ) = B0d + BBd*xD. -C - CALL DCOPY( N, DWORK( IW7+1 ), 1, DWORK( IW24+1 ), 1 ) - CALL DGEMV( 'N', N, M-1, ONE, DWORK( IW8+1 ), N, - $ DWORK( IW22+1 ), 1, ONE, DWORK( IW24+1 ), 1 ) -C -C Compute y1(1)*diag(B) - A. -C - DO 1530 J = 1, N - DO 1520 I = 1, N - IF( I.EQ.J ) THEN - ZWORK( IZ15+I+(I-1)*N ) = DCMPLX( DWORK( IW16+1 )* - $ DWORK( IW24+I ) ) - ZWORK( IZ7+I+(I-1)*N ) - ELSE - ZWORK( IZ15+I+(J-1)*N ) = -ZWORK( IZ7+I+(J-1)*N ) - END IF - 1520 CONTINUE - 1530 CONTINUE -C -C Compute eig( y1(1)*diag(B)-A ). -C - CALL ZGEES( 'N', 'N', SELECT, N, ZWORK( IZ15+1 ), N, SDIM, - $ ZWORK( IZ16+1 ), ZWORK, N, ZWORK( IZWRK+1 ), - $ LZWORK-IZWRK, DWORK( IWRK+1 ), BWORK, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 6 - RETURN - END IF - LZA = INT( ZWORK( IZWRK+1 ) ) - LZAMAX = MAX( LZA, LZAMAX ) - EMIN = DREAL( ZWORK( IZ16+1 ) ) - IF( N.GT.1 ) THEN - DO 1540 I = 2, N - IF( DREAL( ZWORK( IZ16+I ) ).LT.EMIN ) - $ EMIN = DREAL( ZWORK( IZ16+I ) ) - 1540 CONTINUE - END IF - POS = .TRUE. - DO 1550 I = 1, M-1 - DWORK( IW25+I ) = DWORK( IW22+I ) - BETA - DWORK( IW25+M-1+I ) = ALPHA - DWORK( IW22+I ) - 1550 CONTINUE - IF( MR.GT.0 ) THEN - DO 1560 I = 1, MR - DWORK( IW25+2*(M-1)+I ) = DWORK( IW23+I ) + TAU - DWORK( IW25+2*(M-1)+MR+I ) = TAU - DWORK( IW23+I ) - 1560 CONTINUE - END IF - TEMP = DWORK( IW25+1 ) - DO 1570 I = 2, 2*MT - IF( DWORK( IW25+I ).LT.TEMP ) TEMP = DWORK( IW25+I ) - 1570 CONTINUE - IF( TEMP.LE.ZERO .OR. EMIN.LE.ZERO ) POS = .FALSE. - IF( POS ) THEN -C -C Set yw = y1. -C - CALL DCOPY( MT+1, DWORK( IW16+1 ), 1, DWORK( IW15+1 ), 1 ) - ELSE -C -C Set y = y1. -C - CALL DCOPY( MT+1, DWORK( IW16+1 ), 1, DWORK( IW13+1 ), 1 ) - END IF - DO 1580 I = 1, MT+1 - DWORK( IW33+I ) = DWORK( IW13+I ) - DWORK( IW15+I ) - 1580 CONTINUE - YNORM1 = DLANGE( 'F', MT+1, 1, DWORK( IW33+1 ), MT+1, DWORK ) - DO 1590 I = 1, MT+1 - DWORK( IW33+I ) = DWORK( IW13+I ) - DWORK( IW14+I ) - 1590 CONTINUE - YNORM2 = DLANGE( 'F', MT+1, 1, DWORK( IW33+1 ), MT+1, DWORK ) - IF( YNORM1.LT.YNORM2*THETA ) GO TO 1600 - GO TO 1490 -C -C Compute c. -C - 1600 DO 1610 I = 1, MT+1 - DWORK( IW33+I ) = DWORK( IW15+I ) - DWORK( IW14+I ) - 1610 CONTINUE - C = DLANGE( 'F', MT+1, 1, DWORK( IW33+1 ), MT+1, DWORK ) -C -C Set x = yw(2:mt+1). -C - CALL DCOPY( MT, DWORK( IW15+2 ), 1, X, 1 ) - GO TO 390 -C -C *** Last line of AB13MD *** - END
--- a/extra/control-devel/devel/dksyn/DG01MD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,235 +0,0 @@ - SUBROUTINE DG01MD( INDI, N, XR, XI, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To compute the discrete Fourier transform, or inverse transform, -C of a complex signal. -C -C ARGUMENTS -C -C Mode Parameters -C -C INDI CHARACTER*1 -C Indicates whether a Fourier transform or inverse Fourier -C transform is to be performed as follows: -C = 'D': (Direct) Fourier transform; -C = 'I': Inverse Fourier transform. -C -C Input/Output Parameters -C -C N (input) INTEGER -C The number of complex samples. N must be a power of 2. -C N >= 2. -C -C XR (input/output) DOUBLE PRECISION array, dimension (N) -C On entry, this array must contain the real part of either -C the complex signal z if INDI = 'D', or f(z) if INDI = 'I'. -C On exit, this array contains either the real part of the -C computed Fourier transform f(z) if INDI = 'D', or the -C inverse Fourier transform z of f(z) if INDI = 'I'. -C -C XI (input/output) DOUBLE PRECISION array, dimension (N) -C On entry, this array must contain the imaginary part of -C either z if INDI = 'D', or f(z) if INDI = 'I'. -C On exit, this array contains either the imaginary part of -C f(z) if INDI = 'D', or z if INDI = 'I'. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value. -C -C METHOD -C -C If INDI = 'D', then the routine performs a discrete Fourier -C transform on the complex signal Z(i), i = 1,2,...,N. If the result -C is denoted by FZ(k), k = 1,2,...,N, then the relationship between -C Z and FZ is given by the formula: -C -C N ((k-1)*(i-1)) -C FZ(k) = SUM ( Z(i) * V ), -C i=1 -C 2 -C where V = exp( -2*pi*j/N ) and j = -1. -C -C If INDI = 'I', then the routine performs an inverse discrete -C Fourier transform on the complex signal FZ(k), k = 1,2,...,N. If -C the result is denoted by Z(i), i = 1,2,...,N, then the -C relationship between Z and FZ is given by the formula: -C -C N ((k-1)*(i-1)) -C Z(i) = SUM ( FZ(k) * W ), -C k=1 -C -C where W = exp( 2*pi*j/N ). -C -C Note that a discrete Fourier transform, followed by an inverse -C discrete Fourier transform, will result in a signal which is a -C factor N larger than the original input signal. -C -C REFERENCES -C -C [1] Rabiner, L.R. and Rader, C.M. -C Digital Signal Processing. -C IEEE Press, 1972. -C -C NUMERICAL ASPECTS -C -C The algorithm requires 0( N*log(N) ) operations. -C -C CONTRIBUTOR -C -C Release 3.0: V. Sima, Katholieke Univ. Leuven, Belgium, Feb. 1997. -C Supersedes Release 2.0 routine DG01AD by R. Dekeyser, State -C University of Gent, Belgium. -C -C REVISIONS -C -C - -C -C KEYWORDS -C -C Complex signals, digital signal processing, fast Fourier -C transform. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, HALF, ONE, TWO, EIGHT - PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0, - $ TWO = 2.0D0, EIGHT = 8.0D0 ) -C .. Scalar Arguments .. - CHARACTER INDI - INTEGER INFO, N -C .. Array Arguments .. - DOUBLE PRECISION XI(*), XR(*) -C .. Local Scalars .. - LOGICAL LINDI - INTEGER I, J, K, L, M - DOUBLE PRECISION PI2, TI, TR, WHELP, WI, WR, WSTPI, WSTPR -C .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -C .. External Subroutines .. - EXTERNAL XERBLA -C .. Intrinsic Functions .. - INTRINSIC ATAN, DBLE, MOD, SIN -C .. Executable Statements .. -C - INFO = 0 - LINDI = LSAME( INDI, 'D' ) -C -C Test the input scalar arguments. -C - IF( .NOT.LINDI .AND. .NOT.LSAME( INDI, 'I' ) ) THEN - INFO = -1 - ELSE - J = 0 - IF( N.GE.2 ) THEN - J = N -C WHILE ( MOD( J, 2 ).EQ.0 ) DO - 10 CONTINUE - IF ( MOD( J, 2 ).EQ.0 ) THEN - J = J/2 - GO TO 10 - END IF -C END WHILE 10 - END IF - IF ( J.NE.1 ) INFO = -2 - END IF -C - IF ( INFO.NE.0 ) THEN -C -C Error return. -C - CALL XERBLA( 'DG01MD', -INFO ) - RETURN - END IF -C -C Inplace shuffling of data. -C - J = 1 -C - DO 30 I = 1, N - IF ( J.GT.I ) THEN - TR = XR(I) - TI = XI(I) - XR(I) = XR(J) - XI(I) = XI(J) - XR(J) = TR - XI(J) = TI - END IF - K = N/2 -C REPEAT - 20 IF ( J.GT.K ) THEN - J = J - K - K = K/2 - IF ( K.GE.2 ) GO TO 20 - END IF -C UNTIL ( K.LT.2 ) - J = J + K - 30 CONTINUE -C -C Transform by decimation in time. -C - PI2 = EIGHT*ATAN( ONE ) - IF ( LINDI ) PI2 = -PI2 -C - I = 1 -C -C WHILE ( I.LT.N ) DO -C - 40 IF ( I.LT.N ) THEN - L = 2*I - WHELP = PI2/DBLE( L ) - WSTPI = SIN( WHELP ) - WHELP = SIN( HALF*WHELP ) - WSTPR = -TWO*WHELP*WHELP - WR = ONE - WI = ZERO -C - DO 60 J = 1, I -C - DO 50 K = J, N, L - M = K + I - TR = WR*XR(M) - WI*XI(M) - TI = WR*XI(M) + WI*XR(M) - XR(M) = XR(K) - TR - XI(M) = XI(K) - TI - XR(K) = XR(K) + TR - XI(K) = XI(K) + TI - 50 CONTINUE -C - WHELP = WR - WR = WR + WR*WSTPR - WI*WSTPI - WI = WI + WHELP*WSTPI + WI*WSTPR - 60 CONTINUE -C - I = L - GO TO 40 -C END WHILE 40 - END IF -C - RETURN -C *** Last line of DG01MD *** - END
--- a/extra/control-devel/devel/dksyn/MA02AD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,108 +0,0 @@ - SUBROUTINE MA02AD( JOB, M, N, A, LDA, B, LDB ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To transpose all or part of a two-dimensional matrix A into -C another matrix B. -C -C ARGUMENTS -C -C Mode Parameters -C -C JOB CHARACTER*1 -C Specifies the part of the matrix A to be transposed into B -C as follows: -C = 'U': Upper triangular part; -C = 'L': Lower triangular part; -C Otherwise: All of the matrix A. -C -C Input/Output Parameters -C -C M (input) INTEGER -C The number of rows of the matrix A. M >= 0. -C -C N (input) INTEGER -C The number of columns of the matrix A. N >= 0. -C -C A (input) DOUBLE PRECISION array, dimension (LDA,N) -C The m-by-n matrix A. If JOB = 'U', only the upper -C triangle or trapezoid is accessed; if JOB = 'L', only the -C lower triangle or trapezoid is accessed. -C -C LDA INTEGER -C The leading dimension of the array A. LDA >= max(1,M). -C -C B (output) DOUBLE PRECISION array, dimension (LDB,M) -C B = A' in the locations specified by JOB. -C -C LDB INTEGER -C The leading dimension of the array B. LDB >= max(1,N). -C -C CONTRIBUTOR -C -C A. Varga, German Aerospace Center, -C DLR Oberpfaffenhofen, March 1998. -C Based on the RASP routine DMTRA. -C -C REVISIONS -C -C - -C -C ****************************************************************** -C -C .. Scalar Arguments .. - CHARACTER JOB - INTEGER LDA, LDB, M, N -C .. Array Arguments .. - DOUBLE PRECISION A(LDA,*), B(LDB,*) -C .. Local Scalars .. - INTEGER I, J -C .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -C .. Intrinsic Functions .. - INTRINSIC MIN -C -C .. Executable Statements .. -C - IF( LSAME( JOB, 'U' ) ) THEN - DO 20 J = 1, N - DO 10 I = 1, MIN( J, M ) - B(J,I) = A(I,J) - 10 CONTINUE - 20 CONTINUE - ELSE IF( LSAME( JOB, 'L' ) ) THEN - DO 40 J = 1, N - DO 30 I = J, M - B(J,I) = A(I,J) - 30 CONTINUE - 40 CONTINUE - ELSE - DO 60 J = 1, N - DO 50 I = 1, M - B(J,I) = A(I,J) - 50 CONTINUE - 60 CONTINUE - END IF -C - RETURN -C *** Last line of MA02AD *** - END
--- a/extra/control-devel/devel/dksyn/MA02ED.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,99 +0,0 @@ - SUBROUTINE MA02ED( UPLO, N, A, LDA ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To store by symmetry the upper or lower triangle of a symmetric -C matrix, given the other triangle. -C -C ARGUMENTS -C -C Mode Parameters -C -C UPLO CHARACTER*1 -C Specifies which part of the matrix is given as follows: -C = 'U': Upper triangular part; -C = 'L': Lower triangular part. -C For all other values, the array A is not referenced. -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the matrix A. N >= 0. -C -C A (input/output) DOUBLE PRECISION array, dimension (LDA,N) -C On entry, the leading N-by-N upper triangular part -C (if UPLO = 'U'), or lower triangular part (if UPLO = 'L'), -C of this array must contain the corresponding upper or -C lower triangle of the symmetric matrix A. -C On exit, the leading N-by-N part of this array contains -C the symmetric matrix A with all elements stored. -C -C LDA INTEGER -C The leading dimension of the array A. LDA >= max(1,N). -C -C CONTRIBUTOR -C -C V. Sima, Research Institute for Informatics, Bucharest, Romania, -C Oct. 1998. -C -C REVISIONS -C -C - -C -C ****************************************************************** -C -C .. Scalar Arguments .. - CHARACTER UPLO - INTEGER LDA, N -C .. Array Arguments .. - DOUBLE PRECISION A(LDA,*) -C .. Local Scalars .. - INTEGER J -C .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -C .. External Subroutines .. - EXTERNAL DCOPY -C -C .. Executable Statements .. -C -C For efficiency reasons, the parameters are not checked for errors. -C - IF( LSAME( UPLO, 'L' ) ) THEN -C -C Construct the upper triangle of A. -C - DO 20 J = 2, N - CALL DCOPY( J-1, A(J,1), LDA, A(1,J), 1 ) - 20 CONTINUE -C - ELSE IF( LSAME( UPLO, 'U' ) ) THEN -C -C Construct the lower triangle of A. -C - DO 40 J = 2, N - CALL DCOPY( J-1, A(1,J), 1, A(J,1), LDA ) - 40 CONTINUE -C - END IF - RETURN -C *** Last line of MA02ED *** - END
--- a/extra/control-devel/devel/dksyn/MB01PD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,271 +0,0 @@ - SUBROUTINE MB01PD( SCUN, TYPE, M, N, KL, KU, ANRM, NBL, NROWS, A, - $ LDA, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To scale a matrix or undo scaling. Scaling is performed, if -C necessary, so that the matrix norm will be in a safe range of -C representable numbers. -C -C ARGUMENTS -C -C Mode Parameters -C -C SCUN CHARACTER*1 -C SCUN indicates the operation to be performed. -C = 'S': scale the matrix. -C = 'U': undo scaling of the matrix. -C -C TYPE CHARACTER*1 -C TYPE indicates the storage type of the input matrix. -C = 'G': A is a full matrix. -C = 'L': A is a (block) lower triangular matrix. -C = 'U': A is an (block) upper triangular matrix. -C = 'H': A is an (block) upper Hessenberg matrix. -C = 'B': A is a symmetric band matrix with lower bandwidth -C KL and upper bandwidth KU and with the only the -C lower half stored. -C = 'Q': A is a symmetric band matrix with lower bandwidth -C KL and upper bandwidth KU and with the only the -C upper half stored. -C = 'Z': A is a band matrix with lower bandwidth KL and -C upper bandwidth KU. -C -C Input/Output Parameters -C -C M (input) INTEGER -C The number of rows of the matrix A. M >= 0. -C -C N (input) INTEGER -C The number of columns of the matrix A. N >= 0. -C -C KL (input) INTEGER -C The lower bandwidth of A. Referenced only if TYPE = 'B', -C 'Q' or 'Z'. -C -C KU (input) INTEGER -C The upper bandwidth of A. Referenced only if TYPE = 'B', -C 'Q' or 'Z'. -C -C ANRM (input) DOUBLE PRECISION -C The norm of the initial matrix A. ANRM >= 0. -C When ANRM = 0 then an immediate return is effected. -C ANRM should be preserved between the call of the routine -C with SCUN = 'S' and the corresponding one with SCUN = 'U'. -C -C NBL (input) INTEGER -C The number of diagonal blocks of the matrix A, if it has a -C block structure. To specify that matrix A has no block -C structure, set NBL = 0. NBL >= 0. -C -C NROWS (input) INTEGER array, dimension max(1,NBL) -C NROWS(i) contains the number of rows and columns of the -C i-th diagonal block of matrix A. The sum of the values -C NROWS(i), for i = 1: NBL, should be equal to min(M,N). -C The elements of the array NROWS are not referenced if -C NBL = 0. -C -C A (input/output) DOUBLE PRECISION array, dimension (LDA,N) -C On entry, the leading M by N part of this array must -C contain the matrix to be scaled/unscaled. -C On exit, the leading M by N part of A will contain -C the modified matrix. -C The storage mode of A is specified by TYPE. -C -C LDA (input) INTEGER -C The leading dimension of the array A. LDA >= max(1,M). -C -C Error Indicator -C -C INFO (output) INTEGER -C = 0: successful exit -C < 0: if INFO = -i, the i-th argument had an illegal -C value. -C -C METHOD -C -C Denote by ANRM the norm of the matrix, and by SMLNUM and BIGNUM, -C two positive numbers near the smallest and largest safely -C representable numbers, respectively. The matrix is scaled, if -C needed, such that the norm of the result is in the range -C [SMLNUM, BIGNUM]. The scaling factor is represented as a ratio -C of two numbers, one of them being ANRM, and the other one either -C SMLNUM or BIGNUM, depending on ANRM being less than SMLNUM or -C larger than BIGNUM, respectively. For undoing the scaling, the -C norm is again compared with SMLNUM or BIGNUM, and the reciprocal -C of the previous scaling factor is used. -C -C CONTRIBUTOR -C -C V. Sima, Katholieke Univ. Leuven, Belgium, Nov. 1996. -C -C REVISIONS -C -C Oct. 2001, V. Sima, Research Institute for Informatics, Bucharest. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) -C .. Scalar Arguments .. - CHARACTER SCUN, TYPE - INTEGER INFO, KL, KU, LDA, M, MN, N, NBL - DOUBLE PRECISION ANRM -C .. Array Arguments .. - INTEGER NROWS ( * ) - DOUBLE PRECISION A( LDA, * ) -C .. Local Scalars .. - LOGICAL FIRST, LSCALE - INTEGER I, ISUM, ITYPE - DOUBLE PRECISION BIGNUM, SMLNUM -C .. External Functions .. - LOGICAL LSAME - DOUBLE PRECISION DLAMCH - EXTERNAL DLAMCH, LSAME -C .. -C .. External Subroutines .. - EXTERNAL DLABAD, MB01QD, XERBLA -C .. Intrinsic Functions .. - INTRINSIC MAX, MIN -C .. Save statement .. - SAVE BIGNUM, FIRST, SMLNUM -C .. Data statements .. - DATA FIRST/.TRUE./ -C .. -C .. Executable Statements .. -C -C Test the input scalar arguments. -C - INFO = 0 - LSCALE = LSAME( SCUN, 'S' ) - IF( LSAME( TYPE, 'G' ) ) THEN - ITYPE = 0 - ELSE IF( LSAME( TYPE, 'L' ) ) THEN - ITYPE = 1 - ELSE IF( LSAME( TYPE, 'U' ) ) THEN - ITYPE = 2 - ELSE IF( LSAME( TYPE, 'H' ) ) THEN - ITYPE = 3 - ELSE IF( LSAME( TYPE, 'B' ) ) THEN - ITYPE = 4 - ELSE IF( LSAME( TYPE, 'Q' ) ) THEN - ITYPE = 5 - ELSE IF( LSAME( TYPE, 'Z' ) ) THEN - ITYPE = 6 - ELSE - ITYPE = -1 - END IF -C - MN = MIN( M, N ) -C - ISUM = 0 - IF( NBL.GT.0 ) THEN - DO 10 I = 1, NBL - ISUM = ISUM + NROWS(I) - 10 CONTINUE - END IF -C - IF( .NOT.LSCALE .AND. .NOT.LSAME( SCUN, 'U' ) ) THEN - INFO = -1 - ELSE IF( ITYPE.EQ.-1 ) THEN - INFO = -2 - ELSE IF( M.LT.0 ) THEN - INFO = -3 - ELSE IF( N.LT.0 .OR. - $ ( ( ITYPE.EQ.4 .OR. ITYPE.EQ.5 ) .AND. N.NE.M ) ) THEN - INFO = -4 - ELSE IF( ANRM.LT.ZERO ) THEN - INFO = -7 - ELSE IF( NBL.LT.0 ) THEN - INFO = -8 - ELSE IF( NBL.GT.0 .AND. ISUM.NE.MN ) THEN - INFO = -9 - ELSE IF( ITYPE.LE.3 .AND. LDA.LT.MAX( 1, M ) ) THEN - INFO = -11 - ELSE IF( ITYPE.GE.4 ) THEN - IF( KL.LT.0 .OR. KL.GT.MAX( M-1, 0 ) ) THEN - INFO = -5 - ELSE IF( KU.LT.0 .OR. KU.GT.MAX( N-1, 0 ) .OR. - $ ( ( ITYPE.EQ.4 .OR. ITYPE.EQ.5 ) .AND. KL.NE.KU ) ) - $ THEN - INFO = -6 - ELSE IF( ( ITYPE.EQ.4 .AND. LDA.LT.KL+1 ) .OR. - $ ( ITYPE.EQ.5 .AND. LDA.LT.KU+1 ) .OR. - $ ( ITYPE.EQ.6 .AND. LDA.LT.2*KL+KU+1 ) ) THEN - INFO = -11 - END IF - END IF -C - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'MB01PD', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF( MN.EQ.0 .OR. ANRM.EQ.ZERO ) - $ RETURN -C - IF ( FIRST ) THEN -C -C Get machine parameters. -C - SMLNUM = DLAMCH( 'S' ) / DLAMCH( 'P' ) - BIGNUM = ONE / SMLNUM - CALL DLABAD( SMLNUM, BIGNUM ) - FIRST = .FALSE. - END IF -C - IF ( LSCALE ) THEN -C -C Scale A, if its norm is outside range [SMLNUM,BIGNUM]. -C - IF( ANRM.LT.SMLNUM ) THEN -C -C Scale matrix norm up to SMLNUM. -C - CALL MB01QD( TYPE, M, N, KL, KU, ANRM, SMLNUM, NBL, NROWS, - $ A, LDA, INFO ) - ELSE IF( ANRM.GT.BIGNUM ) THEN -C -C Scale matrix norm down to BIGNUM. -C - CALL MB01QD( TYPE, M, N, KL, KU, ANRM, BIGNUM, NBL, NROWS, - $ A, LDA, INFO ) - END IF -C - ELSE -C -C Undo scaling. -C - IF( ANRM.LT.SMLNUM ) THEN - CALL MB01QD( TYPE, M, N, KL, KU, SMLNUM, ANRM, NBL, NROWS, - $ A, LDA, INFO ) - ELSE IF( ANRM.GT.BIGNUM ) THEN - CALL MB01QD( TYPE, M, N, KL, KU, BIGNUM, ANRM, NBL, NROWS, - $ A, LDA, INFO ) - END IF - END IF -C - RETURN -C *** Last line of MB01PD *** - END
--- a/extra/control-devel/devel/dksyn/MB01QD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,334 +0,0 @@ - SUBROUTINE MB01QD( TYPE, M, N, KL, KU, CFROM, CTO, NBL, NROWS, A, - $ LDA, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To multiply the M by N real matrix A by the real scalar CTO/CFROM. -C This is done without over/underflow as long as the final result -C CTO*A(I,J)/CFROM does not over/underflow. TYPE specifies that -C A may be full, (block) upper triangular, (block) lower triangular, -C (block) upper Hessenberg, or banded. -C -C ARGUMENTS -C -C Mode Parameters -C -C TYPE CHARACTER*1 -C TYPE indices the storage type of the input matrix. -C = 'G': A is a full matrix. -C = 'L': A is a (block) lower triangular matrix. -C = 'U': A is a (block) upper triangular matrix. -C = 'H': A is a (block) upper Hessenberg matrix. -C = 'B': A is a symmetric band matrix with lower bandwidth -C KL and upper bandwidth KU and with the only the -C lower half stored. -C = 'Q': A is a symmetric band matrix with lower bandwidth -C KL and upper bandwidth KU and with the only the -C upper half stored. -C = 'Z': A is a band matrix with lower bandwidth KL and -C upper bandwidth KU. -C -C Input/Output Parameters -C -C M (input) INTEGER -C The number of rows of the matrix A. M >= 0. -C -C N (input) INTEGER -C The number of columns of the matrix A. N >= 0. -C -C KL (input) INTEGER -C The lower bandwidth of A. Referenced only if TYPE = 'B', -C 'Q' or 'Z'. -C -C KU (input) INTEGER -C The upper bandwidth of A. Referenced only if TYPE = 'B', -C 'Q' or 'Z'. -C -C CFROM (input) DOUBLE PRECISION -C CTO (input) DOUBLE PRECISION -C The matrix A is multiplied by CTO/CFROM. A(I,J) is -C computed without over/underflow if the final result -C CTO*A(I,J)/CFROM can be represented without over/ -C underflow. CFROM must be nonzero. -C -C NBL (input) INTEGER -C The number of diagonal blocks of the matrix A, if it has a -C block structure. To specify that matrix A has no block -C structure, set NBL = 0. NBL >= 0. -C -C NROWS (input) INTEGER array, dimension max(1,NBL) -C NROWS(i) contains the number of rows and columns of the -C i-th diagonal block of matrix A. The sum of the values -C NROWS(i), for i = 1: NBL, should be equal to min(M,N). -C The array NROWS is not referenced if NBL = 0. -C -C A (input/output) DOUBLE PRECISION array, dimension (LDA,N) -C The matrix to be multiplied by CTO/CFROM. See TYPE for -C the storage type. -C -C LDA (input) INTEGER -C The leading dimension of the array A. LDA >= max(1,M). -C -C Error Indicator -C -C INFO INTEGER -C Not used in this implementation. -C -C METHOD -C -C Matrix A is multiplied by the real scalar CTO/CFROM, taking into -C account the specified storage mode of the matrix. -C MB01QD is a version of the LAPACK routine DLASCL, modified for -C dealing with block triangular, or block Hessenberg matrices. -C For efficiency, no tests of the input scalar parameters are -C performed. -C -C CONTRIBUTOR -C -C V. Sima, Katholieke Univ. Leuven, Belgium, Nov. 1996. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) -C .. -C .. Scalar Arguments .. - CHARACTER TYPE - INTEGER INFO, KL, KU, LDA, M, N, NBL - DOUBLE PRECISION CFROM, CTO -C .. -C .. Array Arguments .. - INTEGER NROWS ( * ) - DOUBLE PRECISION A( LDA, * ) -C .. -C .. Local Scalars .. - LOGICAL DONE, NOBLC - INTEGER I, IFIN, ITYPE, J, JFIN, JINI, K, K1, K2, K3, - $ K4 - DOUBLE PRECISION BIGNUM, CFROM1, CFROMC, CTO1, CTOC, MUL, SMLNUM -C .. -C .. External Functions .. - LOGICAL LSAME - DOUBLE PRECISION DLAMCH - EXTERNAL LSAME, DLAMCH -C .. -C .. Intrinsic Functions .. - INTRINSIC ABS, MAX, MIN -C .. -C .. Executable Statements .. -C - IF( LSAME( TYPE, 'G' ) ) THEN - ITYPE = 0 - ELSE IF( LSAME( TYPE, 'L' ) ) THEN - ITYPE = 1 - ELSE IF( LSAME( TYPE, 'U' ) ) THEN - ITYPE = 2 - ELSE IF( LSAME( TYPE, 'H' ) ) THEN - ITYPE = 3 - ELSE IF( LSAME( TYPE, 'B' ) ) THEN - ITYPE = 4 - ELSE IF( LSAME( TYPE, 'Q' ) ) THEN - ITYPE = 5 - ELSE - ITYPE = 6 - END IF -C -C Quick return if possible. -C - IF( MIN( M, N ).EQ.0 ) - $ RETURN -C -C Get machine parameters. -C - SMLNUM = DLAMCH( 'S' ) - BIGNUM = ONE / SMLNUM -C - CFROMC = CFROM - CTOC = CTO -C - 10 CONTINUE - CFROM1 = CFROMC*SMLNUM - CTO1 = CTOC / BIGNUM - IF( ABS( CFROM1 ).GT.ABS( CTOC ) .AND. CTOC.NE.ZERO ) THEN - MUL = SMLNUM - DONE = .FALSE. - CFROMC = CFROM1 - ELSE IF( ABS( CTO1 ).GT.ABS( CFROMC ) ) THEN - MUL = BIGNUM - DONE = .FALSE. - CTOC = CTO1 - ELSE - MUL = CTOC / CFROMC - DONE = .TRUE. - END IF -C - NOBLC = NBL.EQ.0 -C - IF( ITYPE.EQ.0 ) THEN -C -C Full matrix -C - DO 30 J = 1, N - DO 20 I = 1, M - A( I, J ) = A( I, J )*MUL - 20 CONTINUE - 30 CONTINUE -C - ELSE IF( ITYPE.EQ.1 ) THEN -C - IF ( NOBLC ) THEN -C -C Lower triangular matrix -C - DO 50 J = 1, N - DO 40 I = J, M - A( I, J ) = A( I, J )*MUL - 40 CONTINUE - 50 CONTINUE -C - ELSE -C -C Block lower triangular matrix -C - JFIN = 0 - DO 80 K = 1, NBL - JINI = JFIN + 1 - JFIN = JFIN + NROWS( K ) - DO 70 J = JINI, JFIN - DO 60 I = JINI, M - A( I, J ) = A( I, J )*MUL - 60 CONTINUE - 70 CONTINUE - 80 CONTINUE - END IF -C - ELSE IF( ITYPE.EQ.2 ) THEN -C - IF ( NOBLC ) THEN -C -C Upper triangular matrix -C - DO 100 J = 1, N - DO 90 I = 1, MIN( J, M ) - A( I, J ) = A( I, J )*MUL - 90 CONTINUE - 100 CONTINUE -C - ELSE -C -C Block upper triangular matrix -C - JFIN = 0 - DO 130 K = 1, NBL - JINI = JFIN + 1 - JFIN = JFIN + NROWS( K ) - IF ( K.EQ.NBL ) JFIN = N - DO 120 J = JINI, JFIN - DO 110 I = 1, MIN( JFIN, M ) - A( I, J ) = A( I, J )*MUL - 110 CONTINUE - 120 CONTINUE - 130 CONTINUE - END IF -C - ELSE IF( ITYPE.EQ.3 ) THEN -C - IF ( NOBLC ) THEN -C -C Upper Hessenberg matrix -C - DO 150 J = 1, N - DO 140 I = 1, MIN( J+1, M ) - A( I, J ) = A( I, J )*MUL - 140 CONTINUE - 150 CONTINUE -C - ELSE -C -C Block upper Hessenberg matrix -C - JFIN = 0 - DO 180 K = 1, NBL - JINI = JFIN + 1 - JFIN = JFIN + NROWS( K ) -C - IF ( K.EQ.NBL ) THEN - JFIN = N - IFIN = N - ELSE - IFIN = JFIN + NROWS( K+1 ) - END IF -C - DO 170 J = JINI, JFIN - DO 160 I = 1, MIN( IFIN, M ) - A( I, J ) = A( I, J )*MUL - 160 CONTINUE - 170 CONTINUE - 180 CONTINUE - END IF -C - ELSE IF( ITYPE.EQ.4 ) THEN -C -C Lower half of a symmetric band matrix -C - K3 = KL + 1 - K4 = N + 1 - DO 200 J = 1, N - DO 190 I = 1, MIN( K3, K4-J ) - A( I, J ) = A( I, J )*MUL - 190 CONTINUE - 200 CONTINUE -C - ELSE IF( ITYPE.EQ.5 ) THEN -C -C Upper half of a symmetric band matrix -C - K1 = KU + 2 - K3 = KU + 1 - DO 220 J = 1, N - DO 210 I = MAX( K1-J, 1 ), K3 - A( I, J ) = A( I, J )*MUL - 210 CONTINUE - 220 CONTINUE -C - ELSE IF( ITYPE.EQ.6 ) THEN -C -C Band matrix -C - K1 = KL + KU + 2 - K2 = KL + 1 - K3 = 2*KL + KU + 1 - K4 = KL + KU + 1 + M - DO 240 J = 1, N - DO 230 I = MAX( K1-J, K2 ), MIN( K3, K4-J ) - A( I, J ) = A( I, J )*MUL - 230 CONTINUE - 240 CONTINUE -C - END IF -C - IF( .NOT.DONE ) - $ GO TO 10 -C - RETURN -C *** Last line of MB01QD *** - END
--- a/extra/control-devel/devel/dksyn/MB01RU.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,282 +0,0 @@ - SUBROUTINE MB01RU( UPLO, TRANS, M, N, ALPHA, BETA, R, LDR, A, LDA, - $ X, LDX, DWORK, LDWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To compute the matrix formula -C _ -C R = alpha*R + beta*op( A )*X*op( A )', -C _ -C where alpha and beta are scalars, R, X, and R are symmetric -C matrices, A is a general matrix, and op( A ) is one of -C -C op( A ) = A or op( A ) = A'. -C -C The result is overwritten on R. -C -C ARGUMENTS -C -C Mode Parameters -C -C UPLO CHARACTER*1 -C Specifies which triangles of the symmetric matrices R -C and X are given as follows: -C = 'U': the upper triangular part is given; -C = 'L': the lower triangular part is given. -C -C TRANS CHARACTER*1 -C Specifies the form of op( A ) to be used in the matrix -C multiplication as follows: -C = 'N': op( A ) = A; -C = 'T': op( A ) = A'; -C = 'C': op( A ) = A'. -C -C Input/Output Parameters -C -C M (input) INTEGER _ -C The order of the matrices R and R and the number of rows -C of the matrix op( A ). M >= 0. -C -C N (input) INTEGER -C The order of the matrix X and the number of columns of the -C the matrix op( A ). N >= 0. -C -C ALPHA (input) DOUBLE PRECISION -C The scalar alpha. When alpha is zero then R need not be -C set before entry, except when R is identified with X in -C the call. -C -C BETA (input) DOUBLE PRECISION -C The scalar beta. When beta is zero then A and X are not -C referenced. -C -C R (input/output) DOUBLE PRECISION array, dimension (LDR,M) -C On entry with UPLO = 'U', the leading M-by-M upper -C triangular part of this array must contain the upper -C triangular part of the symmetric matrix R. -C On entry with UPLO = 'L', the leading M-by-M lower -C triangular part of this array must contain the lower -C triangular part of the symmetric matrix R. -C On exit, the leading M-by-M upper triangular part (if -C UPLO = 'U'), or lower triangular part (if UPLO = 'L'), of -C this array contains the corresponding triangular part of -C _ -C the computed matrix R. -C -C LDR INTEGER -C The leading dimension of array R. LDR >= MAX(1,M). -C -C A (input) DOUBLE PRECISION array, dimension (LDA,k) -C where k is N when TRANS = 'N' and is M when TRANS = 'T' or -C TRANS = 'C'. -C On entry with TRANS = 'N', the leading M-by-N part of this -C array must contain the matrix A. -C On entry with TRANS = 'T' or TRANS = 'C', the leading -C N-by-M part of this array must contain the matrix A. -C -C LDA INTEGER -C The leading dimension of array A. LDA >= MAX(1,k), -C where k is M when TRANS = 'N' and is N when TRANS = 'T' or -C TRANS = 'C'. -C -C X (input) DOUBLE PRECISION array, dimension (LDX,N) -C On entry, if UPLO = 'U', the leading N-by-N upper -C triangular part of this array must contain the upper -C triangular part of the symmetric matrix X and the strictly -C lower triangular part of the array is not referenced. -C On entry, if UPLO = 'L', the leading N-by-N lower -C triangular part of this array must contain the lower -C triangular part of the symmetric matrix X and the strictly -C upper triangular part of the array is not referenced. -C The diagonal elements of this array are modified -C internally, but are restored on exit. -C -C LDX INTEGER -C The leading dimension of array X. LDX >= MAX(1,N). -C -C Workspace -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C This array is not referenced when beta = 0, or M*N = 0. -C -C LDWORK The length of the array DWORK. -C LDWORK >= M*N, if beta <> 0; -C LDWORK >= 0, if beta = 0. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -k, the k-th argument had an illegal -C value. -C -C METHOD -C -C The matrix expression is efficiently evaluated taking the symmetry -C into account. Specifically, let X = T + T', with T an upper or -C lower triangular matrix, defined by -C -C T = triu( X ) - (1/2)*diag( X ), if UPLO = 'U', -C T = tril( X ) - (1/2)*diag( X ), if UPLO = 'L', -C -C where triu, tril, and diag denote the upper triangular part, lower -C triangular part, and diagonal part of X, respectively. Then, -C -C A*X*A' = ( A*T )*A' + A*( A*T )', for TRANS = 'N', -C A'*X*A = A'*( T*A ) + ( T*A )'*A, for TRANS = 'T', or 'C', -C -C which involve BLAS 3 operations (DTRMM and DSYR2K). -C -C NUMERICAL ASPECTS -C -C The algorithm requires approximately -C -C 2 2 -C 3/2 x M x N + 1/2 x M -C -C operations. -C -C FURTHER COMMENTS -C -C This is a simpler version for MB01RD. -C -C CONTRIBUTORS -C -C V. Sima, Katholieke Univ. Leuven, Belgium, Jan. 1999. -C -C REVISIONS -C -C A. Varga, German Aerospace Center, Oberpfaffenhofen, March 2004. -C V. Sima, Research Institute for Informatics, Bucharest, Mar. 2004. -C -C KEYWORDS -C -C Elementary matrix operations, matrix algebra, matrix operations. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE, TWO, HALF - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0, - $ HALF = 0.5D0 ) -C .. Scalar Arguments .. - CHARACTER TRANS, UPLO - INTEGER INFO, LDA, LDR, LDWORK, LDX, M, N - DOUBLE PRECISION ALPHA, BETA -C .. Array Arguments .. - DOUBLE PRECISION A(LDA,*), DWORK(*), R(LDR,*), X(LDX,*) -C .. Local Scalars .. - LOGICAL LTRANS, LUPLO -C .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -C .. External Subroutines .. - EXTERNAL DLACPY, DLASCL, DLASET, DSCAL, DSYR2K, DTRMM, - $ XERBLA -C .. Intrinsic Functions .. - INTRINSIC MAX -C .. Executable Statements .. -C -C Test the input scalar arguments. -C - INFO = 0 - LUPLO = LSAME( UPLO, 'U' ) - LTRANS = LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' ) -C - IF( ( .NOT.LUPLO ).AND.( .NOT.LSAME( UPLO, 'L' ) ) )THEN - INFO = -1 - ELSE IF( ( .NOT.LTRANS ).AND.( .NOT.LSAME( TRANS, 'N' ) ) )THEN - INFO = -2 - ELSE IF( M.LT.0 ) THEN - INFO = -3 - ELSE IF( N.LT.0 ) THEN - INFO = -4 - ELSE IF( LDR.LT.MAX( 1, M ) ) THEN - INFO = -8 - ELSE IF( LDA.LT.1 .OR. ( LTRANS .AND. LDA.LT.N ) .OR. - $ ( .NOT.LTRANS .AND. LDA.LT.M ) ) THEN - INFO = -10 - ELSE IF( LDX.LT.MAX( 1, N ) ) THEN - INFO = -12 - ELSE IF( ( BETA.NE.ZERO .AND. LDWORK.LT.M*N ) - $ .OR.( BETA.EQ.ZERO .AND. LDWORK.LT.0 ) ) THEN - INFO = -14 - END IF -C - IF ( INFO.NE.0 ) THEN -C -C Error return. -C - CALL XERBLA( 'MB01RU', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF ( M.EQ.0 ) - $ RETURN -C - IF ( BETA.EQ.ZERO .OR. N.EQ.0 ) THEN - IF ( ALPHA.EQ.ZERO ) THEN -C -C Special case alpha = 0. -C - CALL DLASET( UPLO, M, M, ZERO, ZERO, R, LDR ) - ELSE -C -C Special case beta = 0 or N = 0. -C - IF ( ALPHA.NE.ONE ) - $ CALL DLASCL( UPLO, 0, 0, ONE, ALPHA, M, M, R, LDR, INFO ) - END IF - RETURN - END IF -C -C General case: beta <> 0. -C Compute W = op( A )*T or W = T*op( A ) in DWORK, and apply the -C updating formula (see METHOD section). -C Workspace: need M*N. -C - CALL DSCAL( N, HALF, X, LDX+1 ) -C - IF( LTRANS ) THEN -C - CALL DLACPY( 'Full', N, M, A, LDA, DWORK, N ) - CALL DTRMM( 'Left', UPLO, 'NoTranspose', 'Non-unit', N, M, - $ ONE, X, LDX, DWORK, N ) - CALL DSYR2K( UPLO, TRANS, M, N, BETA, DWORK, N, A, LDA, ALPHA, - $ R, LDR ) -C - ELSE -C - CALL DLACPY( 'Full', M, N, A, LDA, DWORK, M ) - CALL DTRMM( 'Right', UPLO, 'NoTranspose', 'Non-unit', M, N, - $ ONE, X, LDX, DWORK, M ) - CALL DSYR2K( UPLO, TRANS, M, N, BETA, DWORK, M, A, LDA, ALPHA, - $ R, LDR ) -C - END IF -C - CALL DSCAL( N, TWO, X, LDX+1 ) -C - RETURN -C *** Last line of MB01RU *** - END
--- a/extra/control-devel/devel/dksyn/MB01RX.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,315 +0,0 @@ - SUBROUTINE MB01RX( SIDE, UPLO, TRANS, M, N, ALPHA, BETA, R, LDR, - $ A, LDA, B, LDB, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To compute either the upper or lower triangular part of one of the -C matrix formulas -C _ -C R = alpha*R + beta*op( A )*B, (1) -C _ -C R = alpha*R + beta*B*op( A ), (2) -C _ -C where alpha and beta are scalars, R and R are m-by-m matrices, -C op( A ) and B are m-by-n and n-by-m matrices for (1), or n-by-m -C and m-by-n matrices for (2), respectively, and op( A ) is one of -C -C op( A ) = A or op( A ) = A', the transpose of A. -C -C The result is overwritten on R. -C -C ARGUMENTS -C -C Mode Parameters -C -C SIDE CHARACTER*1 -C Specifies whether the matrix A appears on the left or -C right in the matrix product as follows: -C _ -C = 'L': R = alpha*R + beta*op( A )*B; -C _ -C = 'R': R = alpha*R + beta*B*op( A ). -C -C UPLO CHARACTER*1 _ -C Specifies which triangles of the matrices R and R are -C computed and given, respectively, as follows: -C = 'U': the upper triangular part; -C = 'L': the lower triangular part. -C -C TRANS CHARACTER*1 -C Specifies the form of op( A ) to be used in the matrix -C multiplication as follows: -C = 'N': op( A ) = A; -C = 'T': op( A ) = A'; -C = 'C': op( A ) = A'. -C -C Input/Output Parameters -C -C M (input) INTEGER _ -C The order of the matrices R and R, the number of rows of -C the matrix op( A ) and the number of columns of the -C matrix B, for SIDE = 'L', or the number of rows of the -C matrix B and the number of columns of the matrix op( A ), -C for SIDE = 'R'. M >= 0. -C -C N (input) INTEGER -C The number of rows of the matrix B and the number of -C columns of the matrix op( A ), for SIDE = 'L', or the -C number of rows of the matrix op( A ) and the number of -C columns of the matrix B, for SIDE = 'R'. N >= 0. -C -C ALPHA (input) DOUBLE PRECISION -C The scalar alpha. When alpha is zero then R need not be -C set before entry. -C -C BETA (input) DOUBLE PRECISION -C The scalar beta. When beta is zero then A and B are not -C referenced. -C -C R (input/output) DOUBLE PRECISION array, dimension (LDR,M) -C On entry with UPLO = 'U', the leading M-by-M upper -C triangular part of this array must contain the upper -C triangular part of the matrix R; the strictly lower -C triangular part of the array is not referenced. -C On entry with UPLO = 'L', the leading M-by-M lower -C triangular part of this array must contain the lower -C triangular part of the matrix R; the strictly upper -C triangular part of the array is not referenced. -C On exit, the leading M-by-M upper triangular part (if -C UPLO = 'U'), or lower triangular part (if UPLO = 'L') of -C this array contains the corresponding triangular part of -C _ -C the computed matrix R. -C -C LDR INTEGER -C The leading dimension of array R. LDR >= MAX(1,M). -C -C A (input) DOUBLE PRECISION array, dimension (LDA,k), where -C k = N when SIDE = 'L', and TRANS = 'N', or -C SIDE = 'R', and TRANS = 'T'; -C k = M when SIDE = 'R', and TRANS = 'N', or -C SIDE = 'L', and TRANS = 'T'. -C On entry, if SIDE = 'L', and TRANS = 'N', or -C SIDE = 'R', and TRANS = 'T', -C the leading M-by-N part of this array must contain the -C matrix A. -C On entry, if SIDE = 'R', and TRANS = 'N', or -C SIDE = 'L', and TRANS = 'T', -C the leading N-by-M part of this array must contain the -C matrix A. -C -C LDA INTEGER -C The leading dimension of array A. LDA >= MAX(1,l), where -C l = M when SIDE = 'L', and TRANS = 'N', or -C SIDE = 'R', and TRANS = 'T'; -C l = N when SIDE = 'R', and TRANS = 'N', or -C SIDE = 'L', and TRANS = 'T'. -C -C B (input) DOUBLE PRECISION array, dimension (LDB,p), where -C p = M when SIDE = 'L'; -C p = N when SIDE = 'R'. -C On entry, the leading N-by-M part, if SIDE = 'L', or -C M-by-N part, if SIDE = 'R', of this array must contain the -C matrix B. -C -C LDB INTEGER -C The leading dimension of array B. -C LDB >= MAX(1,N), if SIDE = 'L'; -C LDB >= MAX(1,M), if SIDE = 'R'. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value. -C -C METHOD -C -C The matrix expression is evaluated taking the triangular -C structure into account. BLAS 2 operations are used. A block -C algorithm can be easily constructed; it can use BLAS 3 GEMM -C operations for most computations, and calls of this BLAS 2 -C algorithm for computing the triangles. -C -C FURTHER COMMENTS -C -C The main application of this routine is when the result should -C be a symmetric matrix, e.g., when B = X*op( A )', for (1), or -C B = op( A )'*X, for (2), where B is already available and X = X'. -C -C CONTRIBUTORS -C -C V. Sima, Katholieke Univ. Leuven, Belgium, Feb. 1999. -C -C REVISIONS -C -C V. Sima, Research Institute for Informatics, Bucharest, Mar. 2004. -C -C KEYWORDS -C -C Elementary matrix operations, matrix algebra, matrix operations. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) -C .. Scalar Arguments .. - CHARACTER SIDE, TRANS, UPLO - INTEGER INFO, LDA, LDB, LDR, M, N - DOUBLE PRECISION ALPHA, BETA -C .. Array Arguments .. - DOUBLE PRECISION A(LDA,*), B(LDB,*), R(LDR,*) -C .. Local Scalars .. - LOGICAL LSIDE, LTRANS, LUPLO - INTEGER J -C .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -C .. External Subroutines .. - EXTERNAL DGEMV, DLASCL, DLASET, XERBLA -C .. Intrinsic Functions .. - INTRINSIC MAX -C .. Executable Statements .. -C -C Test the input scalar arguments. -C - INFO = 0 - LSIDE = LSAME( SIDE, 'L' ) - LUPLO = LSAME( UPLO, 'U' ) - LTRANS = LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' ) -C - IF( ( .NOT.LSIDE ).AND.( .NOT.LSAME( SIDE, 'R' ) ) )THEN - INFO = -1 - ELSE IF( ( .NOT.LUPLO ).AND.( .NOT.LSAME( UPLO, 'L' ) ) )THEN - INFO = -2 - ELSE IF( ( .NOT.LTRANS ).AND.( .NOT.LSAME( TRANS, 'N' ) ) )THEN - INFO = -3 - ELSE IF( M.LT.0 ) THEN - INFO = -4 - ELSE IF( N.LT.0 ) THEN - INFO = -5 - ELSE IF( LDR.LT.MAX( 1, M ) ) THEN - INFO = -9 - ELSE IF( LDA.LT.1 .OR. - $ ( ( ( LSIDE .AND. .NOT.LTRANS ) .OR. - $ ( .NOT.LSIDE .AND. LTRANS ) ) .AND. LDA.LT.M ) .OR. - $ ( ( ( LSIDE .AND. LTRANS ) .OR. - $ ( .NOT.LSIDE .AND. .NOT.LTRANS ) ) .AND. LDA.LT.N ) ) THEN - INFO = -11 - ELSE IF( LDB.LT.1 .OR. - $ ( LSIDE .AND. LDB.LT.N ) .OR. - $ ( .NOT.LSIDE .AND. LDB.LT.M ) ) THEN - INFO = -13 - END IF -C - IF ( INFO.NE.0 ) THEN -C -C Error return. -C - CALL XERBLA( 'MB01RX', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF ( M.EQ.0 ) - $ RETURN -C - IF ( BETA.EQ.ZERO .OR. N.EQ.0 ) THEN - IF ( ALPHA.EQ.ZERO ) THEN -C -C Special case alpha = 0. -C - CALL DLASET( UPLO, M, M, ZERO, ZERO, R, LDR ) - ELSE -C -C Special case beta = 0 or N = 0. -C - IF ( ALPHA.NE.ONE ) - $ CALL DLASCL( UPLO, 0, 0, ONE, ALPHA, M, M, R, LDR, INFO ) - END IF - RETURN - END IF -C -C General case: beta <> 0. -C Compute the required triangle of (1) or (2) using BLAS 2 -C operations. -C - IF( LSIDE ) THEN - IF( LUPLO ) THEN - IF ( LTRANS ) THEN - DO 10 J = 1, M - CALL DGEMV( TRANS, N, J, BETA, A, LDA, B(1,J), 1, - $ ALPHA, R(1,J), 1 ) - 10 CONTINUE - ELSE - DO 20 J = 1, M - CALL DGEMV( TRANS, J, N, BETA, A, LDA, B(1,J), 1, - $ ALPHA, R(1,J), 1 ) - 20 CONTINUE - END IF - ELSE - IF ( LTRANS ) THEN - DO 30 J = 1, M - CALL DGEMV( TRANS, N, M-J+1, BETA, A(1,J), LDA, - $ B(1,J), 1, ALPHA, R(J,J), 1 ) - 30 CONTINUE - ELSE - DO 40 J = 1, M - CALL DGEMV( TRANS, M-J+1, N, BETA, A(J,1), LDA, - $ B(1,J), 1, ALPHA, R(J,J), 1 ) - 40 CONTINUE - END IF - END IF -C - ELSE - IF( LUPLO ) THEN - IF( LTRANS ) THEN - DO 50 J = 1, M - CALL DGEMV( 'NoTranspose', J, N, BETA, B, LDB, A(J,1), - $ LDA, ALPHA, R(1,J), 1 ) - 50 CONTINUE - ELSE - DO 60 J = 1, M - CALL DGEMV( 'NoTranspose', J, N, BETA, B, LDB, A(1,J), - $ 1, ALPHA, R(1,J), 1 ) - 60 CONTINUE - END IF - ELSE - IF( LTRANS ) THEN - DO 70 J = 1, M - CALL DGEMV( 'NoTranspose', M-J+1, N, BETA, B(J,1), - $ LDB, A(J,1), LDA, ALPHA, R(J,J), 1 ) - 70 CONTINUE - ELSE - DO 80 J = 1, M - CALL DGEMV( 'NoTranspose', M-J+1, N, BETA, B(J,1), - $ LDB, A(1,J), 1, ALPHA, R(J,J), 1 ) - 80 CONTINUE - END IF - END IF - END IF -C - RETURN -C *** Last line of MB01RX *** - END
--- a/extra/control-devel/devel/dksyn/MB01RY.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,429 +0,0 @@ - SUBROUTINE MB01RY( SIDE, UPLO, TRANS, M, ALPHA, BETA, R, LDR, H, - $ LDH, B, LDB, DWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To compute either the upper or lower triangular part of one of the -C matrix formulas -C _ -C R = alpha*R + beta*op( H )*B, (1) -C _ -C R = alpha*R + beta*B*op( H ), (2) -C _ -C where alpha and beta are scalars, H, B, R, and R are m-by-m -C matrices, H is an upper Hessenberg matrix, and op( H ) is one of -C -C op( H ) = H or op( H ) = H', the transpose of H. -C -C The result is overwritten on R. -C -C ARGUMENTS -C -C Mode Parameters -C -C SIDE CHARACTER*1 -C Specifies whether the Hessenberg matrix H appears on the -C left or right in the matrix product as follows: -C _ -C = 'L': R = alpha*R + beta*op( H )*B; -C _ -C = 'R': R = alpha*R + beta*B*op( H ). -C -C UPLO CHARACTER*1 _ -C Specifies which triangles of the matrices R and R are -C computed and given, respectively, as follows: -C = 'U': the upper triangular part; -C = 'L': the lower triangular part. -C -C TRANS CHARACTER*1 -C Specifies the form of op( H ) to be used in the matrix -C multiplication as follows: -C = 'N': op( H ) = H; -C = 'T': op( H ) = H'; -C = 'C': op( H ) = H'. -C -C Input/Output Parameters -C -C M (input) INTEGER _ -C The order of the matrices R, R, H and B. M >= 0. -C -C ALPHA (input) DOUBLE PRECISION -C The scalar alpha. When alpha is zero then R need not be -C set before entry. -C -C BETA (input) DOUBLE PRECISION -C The scalar beta. When beta is zero then H and B are not -C referenced. -C -C R (input/output) DOUBLE PRECISION array, dimension (LDR,M) -C On entry with UPLO = 'U', the leading M-by-M upper -C triangular part of this array must contain the upper -C triangular part of the matrix R; the strictly lower -C triangular part of the array is not referenced. -C On entry with UPLO = 'L', the leading M-by-M lower -C triangular part of this array must contain the lower -C triangular part of the matrix R; the strictly upper -C triangular part of the array is not referenced. -C On exit, the leading M-by-M upper triangular part (if -C UPLO = 'U'), or lower triangular part (if UPLO = 'L') of -C this array contains the corresponding triangular part of -C _ -C the computed matrix R. -C -C LDR INTEGER -C The leading dimension of array R. LDR >= MAX(1,M). -C -C H (input) DOUBLE PRECISION array, dimension (LDH,M) -C On entry, the leading M-by-M upper Hessenberg part of -C this array must contain the upper Hessenberg part of the -C matrix H. -C The elements below the subdiagonal are not referenced, -C except possibly for those in the first column, which -C could be overwritten, but are restored on exit. -C -C LDH INTEGER -C The leading dimension of array H. LDH >= MAX(1,M). -C -C B (input) DOUBLE PRECISION array, dimension (LDB,M) -C On entry, the leading M-by-M part of this array must -C contain the matrix B. -C -C LDB INTEGER -C The leading dimension of array B. LDB >= MAX(1,M). -C -C Workspace -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C LDWORK >= M, if beta <> 0 and SIDE = 'L'; -C LDWORK >= 0, if beta = 0 or SIDE = 'R'. -C This array is not referenced when beta = 0 or SIDE = 'R'. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value. -C -C METHOD -C -C The matrix expression is efficiently evaluated taking the -C Hessenberg/triangular structure into account. BLAS 2 operations -C are used. A block algorithm can be constructed; it can use BLAS 3 -C GEMM operations for most computations, and calls of this BLAS 2 -C algorithm for computing the triangles. -C -C FURTHER COMMENTS -C -C The main application of this routine is when the result should -C be a symmetric matrix, e.g., when B = X*op( H )', for (1), or -C B = op( H )'*X, for (2), where B is already available and X = X'. -C -C CONTRIBUTORS -C -C V. Sima, Katholieke Univ. Leuven, Belgium, Feb. 1999. -C -C REVISIONS -C -C - -C -C KEYWORDS -C -C Elementary matrix operations, matrix algebra, matrix operations. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) -C .. Scalar Arguments .. - CHARACTER SIDE, TRANS, UPLO - INTEGER INFO, LDB, LDH, LDR, M - DOUBLE PRECISION ALPHA, BETA -C .. Array Arguments .. - DOUBLE PRECISION B(LDB,*), DWORK(*), H(LDH,*), R(LDR,*) -C .. Local Scalars .. - LOGICAL LSIDE, LTRANS, LUPLO - INTEGER I, J -C .. External Functions .. - LOGICAL LSAME - DOUBLE PRECISION DDOT - EXTERNAL DDOT, LSAME -C .. External Subroutines .. - EXTERNAL DCOPY, DGEMV, DLASCL, DLASET, DSCAL, DSWAP, - $ DTRMV, XERBLA -C .. Intrinsic Functions .. - INTRINSIC MAX, MIN -C .. Executable Statements .. -C -C Test the input scalar arguments. -C - INFO = 0 - LSIDE = LSAME( SIDE, 'L' ) - LUPLO = LSAME( UPLO, 'U' ) - LTRANS = LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' ) -C - IF( ( .NOT.LSIDE ).AND.( .NOT.LSAME( SIDE, 'R' ) ) )THEN - INFO = -1 - ELSE IF( ( .NOT.LUPLO ).AND.( .NOT.LSAME( UPLO, 'L' ) ) )THEN - INFO = -2 - ELSE IF( ( .NOT.LTRANS ).AND.( .NOT.LSAME( TRANS, 'N' ) ) )THEN - INFO = -3 - ELSE IF( M.LT.0 ) THEN - INFO = -4 - ELSE IF( LDR.LT.MAX( 1, M ) ) THEN - INFO = -8 - ELSE IF( LDH.LT.MAX( 1, M ) ) THEN - INFO = -10 - ELSE IF( LDB.LT.MAX( 1, M ) ) THEN - INFO = -12 - END IF -C - IF ( INFO.NE.0 ) THEN -C -C Error return. -C - CALL XERBLA( 'MB01RY', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF ( M.EQ.0 ) - $ RETURN -C - IF ( BETA.EQ.ZERO ) THEN - IF ( ALPHA.EQ.ZERO ) THEN -C -C Special case when both alpha = 0 and beta = 0. -C - CALL DLASET( UPLO, M, M, ZERO, ZERO, R, LDR ) - ELSE -C -C Special case beta = 0. -C - IF ( ALPHA.NE.ONE ) - $ CALL DLASCL( UPLO, 0, 0, ONE, ALPHA, M, M, R, LDR, INFO ) - END IF - RETURN - END IF -C -C General case: beta <> 0. -C Compute the required triangle of (1) or (2) using BLAS 2 -C operations. -C - IF( LSIDE ) THEN -C -C To avoid repeated references to the subdiagonal elements of H, -C these are swapped with the corresponding elements of H in the -C first column, and are finally restored. -C - IF( M.GT.2 ) - $ CALL DSWAP( M-2, H( 3, 2 ), LDH+1, H( 3, 1 ), 1 ) -C - IF( LUPLO ) THEN - IF ( LTRANS ) THEN -C - DO 20 J = 1, M -C -C Multiply the transposed upper triangle of the leading -C j-by-j submatrix of H by the leading part of the j-th -C column of B. -C - CALL DCOPY( J, B( 1, J ), 1, DWORK, 1 ) - CALL DTRMV( 'Upper', TRANS, 'Non-unit', J, H, LDH, - $ DWORK, 1 ) -C -C Add the contribution of the subdiagonal of H to -C the j-th column of the product. -C - DO 10 I = 1, MIN( J, M - 1 ) - R( I, J ) = ALPHA*R( I, J ) + BETA*( DWORK( I ) + - $ H( I+1, 1 )*B( I+1, J ) ) - 10 CONTINUE -C - 20 CONTINUE -C - R( M, M ) = ALPHA*R( M, M ) + BETA*DWORK( M ) -C - ELSE -C - DO 40 J = 1, M -C -C Multiply the upper triangle of the leading j-by-j -C submatrix of H by the leading part of the j-th column -C of B. -C - CALL DCOPY( J, B( 1, J ), 1, DWORK, 1 ) - CALL DTRMV( 'Upper', TRANS, 'Non-unit', J, H, LDH, - $ DWORK, 1 ) - IF( J.LT.M ) THEN -C -C Multiply the remaining right part of the leading -C j-by-M submatrix of H by the trailing part of the -C j-th column of B. -C - CALL DGEMV( TRANS, J, M-J, BETA, H( 1, J+1 ), LDH, - $ B( J+1, J ), 1, ALPHA, R( 1, J ), 1 ) - ELSE - CALL DSCAL( M, ALPHA, R( 1, M ), 1 ) - END IF -C -C Add the contribution of the subdiagonal of H to -C the j-th column of the product. -C - R( 1, J ) = R( 1, J ) + BETA*DWORK( 1 ) -C - DO 30 I = 2, J - R( I, J ) = R( I, J ) + BETA*( DWORK( I ) + - $ H( I, 1 )*B( I-1, J ) ) - 30 CONTINUE -C - 40 CONTINUE -C - END IF -C - ELSE -C - IF ( LTRANS ) THEN -C - DO 60 J = M, 1, -1 -C -C Multiply the transposed upper triangle of the trailing -C (M-j+1)-by-(M-j+1) submatrix of H by the trailing part -C of the j-th column of B. -C - CALL DCOPY( M-J+1, B( J, J ), 1, DWORK( J ), 1 ) - CALL DTRMV( 'Upper', TRANS, 'Non-unit', M-J+1, - $ H( J, J ), LDH, DWORK( J ), 1 ) - IF( J.GT.1 ) THEN -C -C Multiply the remaining left part of the trailing -C (M-j+1)-by-(j-1) submatrix of H' by the leading -C part of the j-th column of B. -C - CALL DGEMV( TRANS, J-1, M-J+1, BETA, H( 1, J ), - $ LDH, B( 1, J ), 1, ALPHA, R( J, J ), - $ 1 ) - ELSE - CALL DSCAL( M, ALPHA, R( 1, 1 ), 1 ) - END IF -C -C Add the contribution of the subdiagonal of H to -C the j-th column of the product. -C - DO 50 I = J, M - 1 - R( I, J ) = R( I, J ) + BETA*( DWORK( I ) + - $ H( I+1, 1 )*B( I+1, J ) ) - 50 CONTINUE -C - R( M, J ) = R( M, J ) + BETA*DWORK( M ) - 60 CONTINUE -C - ELSE -C - DO 80 J = M, 1, -1 -C -C Multiply the upper triangle of the trailing -C (M-j+1)-by-(M-j+1) submatrix of H by the trailing -C part of the j-th column of B. -C - CALL DCOPY( M-J+1, B( J, J ), 1, DWORK( J ), 1 ) - CALL DTRMV( 'Upper', TRANS, 'Non-unit', M-J+1, - $ H( J, J ), LDH, DWORK( J ), 1 ) -C -C Add the contribution of the subdiagonal of H to -C the j-th column of the product. -C - DO 70 I = MAX( J, 2 ), M - R( I, J ) = ALPHA*R( I, J ) + BETA*( DWORK( I ) - $ + H( I, 1 )*B( I-1, J ) ) - 70 CONTINUE -C - 80 CONTINUE -C - R( 1, 1 ) = ALPHA*R( 1, 1 ) + BETA*DWORK( 1 ) -C - END IF - END IF -C - IF( M.GT.2 ) - $ CALL DSWAP( M-2, H( 3, 2 ), LDH+1, H( 3, 1 ), 1 ) -C - ELSE -C -C Row-wise calculations are used for H, if SIDE = 'R' and -C TRANS = 'T'. -C - IF( LUPLO ) THEN - IF( LTRANS ) THEN - R( 1, 1 ) = ALPHA*R( 1, 1 ) + - $ BETA*DDOT( M, B, LDB, H, LDH ) -C - DO 90 J = 2, M - CALL DGEMV( 'NoTranspose', J, M-J+2, BETA, - $ B( 1, J-1 ), LDB, H( J, J-1 ), LDH, - $ ALPHA, R( 1, J ), 1 ) - 90 CONTINUE -C - ELSE -C - DO 100 J = 1, M - 1 - CALL DGEMV( 'NoTranspose', J, J+1, BETA, B, LDB, - $ H( 1, J ), 1, ALPHA, R( 1, J ), 1 ) - 100 CONTINUE -C - CALL DGEMV( 'NoTranspose', M, M, BETA, B, LDB, - $ H( 1, M ), 1, ALPHA, R( 1, M ), 1 ) -C - END IF -C - ELSE -C - IF( LTRANS ) THEN -C - CALL DGEMV( 'NoTranspose', M, M, BETA, B, LDB, H, LDH, - $ ALPHA, R( 1, 1 ), 1 ) -C - DO 110 J = 2, M - CALL DGEMV( 'NoTranspose', M-J+1, M-J+2, BETA, - $ B( J, J-1 ), LDB, H( J, J-1 ), LDH, ALPHA, - $ R( J, J ), 1 ) - 110 CONTINUE -C - ELSE -C - DO 120 J = 1, M - 1 - CALL DGEMV( 'NoTranspose', M-J+1, J+1, BETA, - $ B( J, 1 ), LDB, H( 1, J ), 1, ALPHA, - $ R( J, J ), 1 ) - 120 CONTINUE -C - R( M, M ) = ALPHA*R( M, M ) + - $ BETA*DDOT( M, B( M, 1 ), LDB, H( 1, M ), 1 ) -C - END IF - END IF - END IF -C - RETURN -C *** Last line of MB01RY *** - END
--- a/extra/control-devel/devel/dksyn/MB01SD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,123 +0,0 @@ - SUBROUTINE MB01SD( JOBS, M, N, A, LDA, R, C ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To scale a general M-by-N matrix A using the row and column -C scaling factors in the vectors R and C. -C -C ARGUMENTS -C -C Mode Parameters -C -C JOBS CHARACTER*1 -C Specifies the scaling operation to be done, as follows: -C = 'R': row scaling, i.e., A will be premultiplied -C by diag(R); -C = 'C': column scaling, i.e., A will be postmultiplied -C by diag(C); -C = 'B': both row and column scaling, i.e., A will be -C replaced by diag(R) * A * diag(C). -C -C Input/Output Parameters -C -C M (input) INTEGER -C The number of rows of the matrix A. M >= 0. -C -C N (input) INTEGER -C The number of columns of the matrix A. N >= 0. -C -C A (input/output) DOUBLE PRECISION array, dimension (LDA,N) -C On entry, the M-by-N matrix A. -C On exit, the scaled matrix. See JOBS for the form of the -C scaled matrix. -C -C LDA INTEGER -C The leading dimension of the array A. LDA >= max(1,M). -C -C R (input) DOUBLE PRECISION array, dimension (M) -C The row scale factors for A. -C R is not referenced if JOBS = 'C'. -C -C C (input) DOUBLE PRECISION array, dimension (N) -C The column scale factors for A. -C C is not referenced if JOBS = 'R'. -C -C -C CONTRIBUTOR -C -C A. Varga, German Aerospace Center, -C DLR Oberpfaffenhofen, April 1998. -C Based on the RASP routine DMSCAL. -C -C ****************************************************************** -C -C .. Scalar Arguments .. - CHARACTER JOBS - INTEGER LDA, M, N -C .. Array Arguments .. - DOUBLE PRECISION A(LDA,*), C(*), R(*) -C .. Local Scalars .. - INTEGER I, J - DOUBLE PRECISION CJ -C .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -C .. Executable Statements .. -C -C Quick return if possible. -C - IF( M.EQ.0 .OR. N.EQ.0 ) - $ RETURN -C - IF( LSAME( JOBS, 'C' ) ) THEN -C -C Column scaling, no row scaling. -C - DO 20 J = 1, N - CJ = C(J) - DO 10 I = 1, M - A(I,J) = CJ*A(I,J) - 10 CONTINUE - 20 CONTINUE - ELSE IF( LSAME( JOBS, 'R' ) ) THEN -C -C Row scaling, no column scaling. -C - DO 40 J = 1, N - DO 30 I = 1, M - A(I,J) = R(I)*A(I,J) - 30 CONTINUE - 40 CONTINUE - ELSE IF( LSAME( JOBS, 'B' ) ) THEN -C -C Row and column scaling. -C - DO 60 J = 1, N - CJ = C(J) - DO 50 I = 1, M - A(I,J) = CJ*R(I)*A(I,J) - 50 CONTINUE - 60 CONTINUE - END IF -C - RETURN -C *** Last line of MB01SD *** - END
--- a/extra/control-devel/devel/dksyn/MB01UD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,238 +0,0 @@ - SUBROUTINE MB01UD( SIDE, TRANS, M, N, ALPHA, H, LDH, A, LDA, B, - $ LDB, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To compute one of the matrix products -C -C B = alpha*op( H ) * A, or B = alpha*A * op( H ), -C -C where alpha is a scalar, A and B are m-by-n matrices, H is an -C upper Hessenberg matrix, and op( H ) is one of -C -C op( H ) = H or op( H ) = H', the transpose of H. -C -C ARGUMENTS -C -C Mode Parameters -C -C SIDE CHARACTER*1 -C Specifies whether the Hessenberg matrix H appears on the -C left or right in the matrix product as follows: -C = 'L': B = alpha*op( H ) * A; -C = 'R': B = alpha*A * op( H ). -C -C TRANS CHARACTER*1 -C Specifies the form of op( H ) to be used in the matrix -C multiplication as follows: -C = 'N': op( H ) = H; -C = 'T': op( H ) = H'; -C = 'C': op( H ) = H'. -C -C Input/Output Parameters -C -C M (input) INTEGER -C The number of rows of the matrices A and B. M >= 0. -C -C N (input) INTEGER -C The number of columns of the matrices A and B. N >= 0. -C -C ALPHA (input) DOUBLE PRECISION -C The scalar alpha. When alpha is zero then H is not -C referenced and A need not be set before entry. -C -C H (input) DOUBLE PRECISION array, dimension (LDH,k) -C where k is M when SIDE = 'L' and is N when SIDE = 'R'. -C On entry with SIDE = 'L', the leading M-by-M upper -C Hessenberg part of this array must contain the upper -C Hessenberg matrix H. -C On entry with SIDE = 'R', the leading N-by-N upper -C Hessenberg part of this array must contain the upper -C Hessenberg matrix H. -C The elements below the subdiagonal are not referenced, -C except possibly for those in the first column, which -C could be overwritten, but are restored on exit. -C -C LDH INTEGER -C The leading dimension of the array H. LDH >= max(1,k), -C where k is M when SIDE = 'L' and is N when SIDE = 'R'. -C -C A (input) DOUBLE PRECISION array, dimension (LDA,N) -C The leading M-by-N part of this array must contain the -C matrix A. -C -C LDA INTEGER -C The leading dimension of the array A. LDA >= max(1,M). -C -C B (output) DOUBLE PRECISION array, dimension (LDB,N) -C The leading M-by-N part of this array contains the -C computed product. -C -C LDB INTEGER -C The leading dimension of the array B. LDB >= max(1,M). -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value. -C -C METHOD -C -C The required matrix product is computed in two steps. In the first -C step, the upper triangle of H is used; in the second step, the -C contribution of the subdiagonal is added. A fast BLAS 3 DTRMM -C operation is used in the first step. -C -C CONTRIBUTOR -C -C V. Sima, Katholieke Univ. Leuven, Belgium, January 1999. -C -C REVISIONS -C -C - -C -C KEYWORDS -C -C Elementary matrix operations, matrix operations. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) -C .. Scalar Arguments .. - CHARACTER SIDE, TRANS - INTEGER INFO, LDA, LDB, LDH, M, N - DOUBLE PRECISION ALPHA -C .. Array Arguments .. - DOUBLE PRECISION A(LDA,*), B(LDB,*), H(LDH,*) -C .. Local Scalars .. - LOGICAL LSIDE, LTRANS - INTEGER I, J -C .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -C .. External Subroutines .. - EXTERNAL DAXPY, DLACPY, DLASET, DSWAP, DTRMM, XERBLA -C .. Intrinsic Functions .. - INTRINSIC MAX, MIN -C -C .. Executable Statements .. -C -C Test the input scalar arguments. -C - INFO = 0 - LSIDE = LSAME( SIDE, 'L' ) - LTRANS = LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' ) -C - IF( ( .NOT.LSIDE ).AND.( .NOT.LSAME( SIDE, 'R' ) ) )THEN - INFO = -1 - ELSE IF( ( .NOT.LTRANS ).AND.( .NOT.LSAME( TRANS, 'N' ) ) )THEN - INFO = -2 - ELSE IF( M.LT.0 ) THEN - INFO = -3 - ELSE IF( N.LT.0 ) THEN - INFO = -4 - ELSE IF( LDH.LT.1 .OR. ( LSIDE .AND. LDH.LT.M ) .OR. - $ ( .NOT.LSIDE .AND. LDH.LT.N ) ) THEN - INFO = -7 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -9 - ELSE IF( LDB.LT.MAX( 1, M ) ) THEN - INFO = -11 - END IF -C - IF ( INFO.NE.0 ) THEN -C -C Error return. -C - CALL XERBLA( 'MB01UD', -INFO ) - RETURN - END IF -C -C Quick return, if possible. -C - IF ( MIN( M, N ).EQ.0 ) - $ RETURN -C - IF( ALPHA.EQ.ZERO ) THEN -C -C Set B to zero and return. -C - CALL DLASET( 'Full', M, N, ZERO, ZERO, B, LDB ) - RETURN - END IF -C -C Copy A in B and compute one of the matrix products -C B = alpha*op( triu( H ) ) * A, or -C B = alpha*A * op( triu( H ) ), -C involving the upper triangle of H. -C - CALL DLACPY( 'Full', M, N, A, LDA, B, LDB ) - CALL DTRMM( SIDE, 'Upper', TRANS, 'Non-unit', M, N, ALPHA, H, - $ LDH, B, LDB ) -C -C Add the contribution of the subdiagonal of H. -C If SIDE = 'L', the subdiagonal of H is swapped with the -C corresponding elements in the first column of H, and the -C calculations are organized for column operations. -C - IF( LSIDE ) THEN - IF( M.GT.2 ) - $ CALL DSWAP( M-2, H( 3, 2 ), LDH+1, H( 3, 1 ), 1 ) - IF( LTRANS ) THEN - DO 20 J = 1, N - DO 10 I = 1, M - 1 - B( I, J ) = B( I, J ) + ALPHA*H( I+1, 1 )*A( I+1, J ) - 10 CONTINUE - 20 CONTINUE - ELSE - DO 40 J = 1, N - DO 30 I = 2, M - B( I, J ) = B( I, J ) + ALPHA*H( I, 1 )*A( I-1, J ) - 30 CONTINUE - 40 CONTINUE - END IF - IF( M.GT.2 ) - $ CALL DSWAP( M-2, H( 3, 2 ), LDH+1, H( 3, 1 ), 1 ) -C - ELSE -C - IF( LTRANS ) THEN - DO 50 J = 1, N - 1 - IF ( H( J+1, J ).NE.ZERO ) - $ CALL DAXPY( M, ALPHA*H( J+1, J ), A( 1, J ), 1, - $ B( 1, J+1 ), 1 ) - 50 CONTINUE - ELSE - DO 60 J = 1, N - 1 - IF ( H( J+1, J ).NE.ZERO ) - $ CALL DAXPY( M, ALPHA*H( J+1, J ), A( 1, J+1 ), 1, - $ B( 1, J ), 1 ) - 60 CONTINUE - END IF - END IF -C - RETURN -C *** Last line of MB01UD *** - END
--- a/extra/control-devel/devel/dksyn/MB02PD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,553 +0,0 @@ - SUBROUTINE MB02PD( FACT, TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, - $ EQUED, R, C, B, LDB, X, LDX, RCOND, FERR, BERR, - $ IWORK, DWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To solve (if well-conditioned) the matrix equations -C -C op( A )*X = B, -C -C where X and B are N-by-NRHS matrices, A is an N-by-N matrix and -C op( A ) is one of -C -C op( A ) = A or op( A ) = A'. -C -C Error bounds on the solution and a condition estimate are also -C provided. -C -C ARGUMENTS -C -C Mode Parameters -C -C FACT CHARACTER*1 -C Specifies whether or not the factored form of the matrix A -C is supplied on entry, and if not, whether the matrix A -C should be equilibrated before it is factored. -C = 'F': On entry, AF and IPIV contain the factored form -C of A. If EQUED is not 'N', the matrix A has been -C equilibrated with scaling factors given by R -C and C. A, AF, and IPIV are not modified. -C = 'N': The matrix A will be copied to AF and factored. -C = 'E': The matrix A will be equilibrated if necessary, -C then copied to AF and factored. -C -C TRANS CHARACTER*1 -C Specifies the form of the system of equations as follows: -C = 'N': A * X = B (No transpose); -C = 'T': A**T * X = B (Transpose); -C = 'C': A**H * X = B (Transpose). -C -C Input/Output Parameters -C -C N (input) INTEGER -C The number of linear equations, i.e., the order of the -C matrix A. N >= 0. -C -C NRHS (input) INTEGER -C The number of right hand sides, i.e., the number of -C columns of the matrices B and X. NRHS >= 0. -C -C A (input/output) DOUBLE PRECISION array, dimension (LDA,N) -C On entry, the leading N-by-N part of this array must -C contain the matrix A. If FACT = 'F' and EQUED is not 'N', -C then A must have been equilibrated by the scaling factors -C in R and/or C. A is not modified if FACT = 'F' or 'N', -C or if FACT = 'E' and EQUED = 'N' on exit. -C On exit, if EQUED .NE. 'N', the leading N-by-N part of -C this array contains the matrix A scaled as follows: -C EQUED = 'R': A := diag(R) * A; -C EQUED = 'C': A := A * diag(C); -C EQUED = 'B': A := diag(R) * A * diag(C). -C -C LDA INTEGER -C The leading dimension of the array A. LDA >= max(1,N). -C -C AF (input or output) DOUBLE PRECISION array, dimension -C (LDAF,N) -C If FACT = 'F', then AF is an input argument and on entry -C the leading N-by-N part of this array must contain the -C factors L and U from the factorization A = P*L*U as -C computed by DGETRF. If EQUED .NE. 'N', then AF is the -C factored form of the equilibrated matrix A. -C If FACT = 'N', then AF is an output argument and on exit -C the leading N-by-N part of this array contains the factors -C L and U from the factorization A = P*L*U of the original -C matrix A. -C If FACT = 'E', then AF is an output argument and on exit -C the leading N-by-N part of this array contains the factors -C L and U from the factorization A = P*L*U of the -C equilibrated matrix A (see the description of A for the -C form of the equilibrated matrix). -C -C LDAF (input) INTEGER -C The leading dimension of the array AF. LDAF >= max(1,N). -C -C IPIV (input or output) INTEGER array, dimension (N) -C If FACT = 'F', then IPIV is an input argument and on entry -C it must contain the pivot indices from the factorization -C A = P*L*U as computed by DGETRF; row i of the matrix was -C interchanged with row IPIV(i). -C If FACT = 'N', then IPIV is an output argument and on exit -C it contains the pivot indices from the factorization -C A = P*L*U of the original matrix A. -C If FACT = 'E', then IPIV is an output argument and on exit -C it contains the pivot indices from the factorization -C A = P*L*U of the equilibrated matrix A. -C -C EQUED (input or output) CHARACTER*1 -C Specifies the form of equilibration that was done as -C follows: -C = 'N': No equilibration (always true if FACT = 'N'); -C = 'R': Row equilibration, i.e., A has been premultiplied -C by diag(R); -C = 'C': Column equilibration, i.e., A has been -C postmultiplied by diag(C); -C = 'B': Both row and column equilibration, i.e., A has -C been replaced by diag(R) * A * diag(C). -C EQUED is an input argument if FACT = 'F'; otherwise, it is -C an output argument. -C -C R (input or output) DOUBLE PRECISION array, dimension (N) -C The row scale factors for A. If EQUED = 'R' or 'B', A is -C multiplied on the left by diag(R); if EQUED = 'N' or 'C', -C R is not accessed. R is an input argument if FACT = 'F'; -C otherwise, R is an output argument. If FACT = 'F' and -C EQUED = 'R' or 'B', each element of R must be positive. -C -C C (input or output) DOUBLE PRECISION array, dimension (N) -C The column scale factors for A. If EQUED = 'C' or 'B', -C A is multiplied on the right by diag(C); if EQUED = 'N' -C or 'R', C is not accessed. C is an input argument if -C FACT = 'F'; otherwise, C is an output argument. If -C FACT = 'F' and EQUED = 'C' or 'B', each element of C must -C be positive. -C -C B (input/output) DOUBLE PRECISION array, dimension -C (LDB,NRHS) -C On entry, the leading N-by-NRHS part of this array must -C contain the right-hand side matrix B. -C On exit, -C if EQUED = 'N', B is not modified; -C if TRANS = 'N' and EQUED = 'R' or 'B', the leading -C N-by-NRHS part of this array contains diag(R)*B; -C if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', the leading -C N-by-NRHS part of this array contains diag(C)*B. -C -C LDB INTEGER -C The leading dimension of the array B. LDB >= max(1,N). -C -C X (output) DOUBLE PRECISION array, dimension (LDX,NRHS) -C If INFO = 0 or INFO = N+1, the leading N-by-NRHS part of -C this array contains the solution matrix X to the original -C system of equations. Note that A and B are modified on -C exit if EQUED .NE. 'N', and the solution to the -C equilibrated system is inv(diag(C))*X if TRANS = 'N' and -C EQUED = 'C' or 'B', or inv(diag(R))*X if TRANS = 'T' or -C 'C' and EQUED = 'R' or 'B'. -C -C LDX (input) INTEGER -C The leading dimension of the array X. LDX >= max(1,N). -C -C RCOND (output) DOUBLE PRECISION -C The estimate of the reciprocal condition number of the -C matrix A after equilibration (if done). If RCOND is less -C than the machine precision (in particular, if RCOND = 0), -C the matrix is singular to working precision. This -C condition is indicated by a return code of INFO > 0. -C For efficiency reasons, RCOND is computed only when the -C matrix A is factored, i.e., for FACT = 'N' or 'E'. For -C FACT = 'F', RCOND is not used, but it is assumed that it -C has been computed and checked before the routine call. -C -C FERR (output) DOUBLE PRECISION array, dimension (NRHS) -C The estimated forward error bound for each solution vector -C X(j) (the j-th column of the solution matrix X). -C If XTRUE is the true solution corresponding to X(j), -C FERR(j) is an estimated upper bound for the magnitude of -C the largest element in (X(j) - XTRUE) divided by the -C magnitude of the largest element in X(j). The estimate -C is as reliable as the estimate for RCOND, and is almost -C always a slight overestimate of the true error. -C -C BERR (output) DOUBLE PRECISION array, dimension (NRHS) -C The componentwise relative backward error of each solution -C vector X(j) (i.e., the smallest relative change in -C any element of A or B that makes X(j) an exact solution). -C -C Workspace -C -C IWORK INTEGER array, dimension (N) -C -C DWORK DOUBLE PRECISION array, dimension (4*N) -C On exit, DWORK(1) contains the reciprocal pivot growth -C factor norm(A)/norm(U). The "max absolute element" norm is -C used. If DWORK(1) is much less than 1, then the stability -C of the LU factorization of the (equilibrated) matrix A -C could be poor. This also means that the solution X, -C condition estimator RCOND, and forward error bound FERR -C could be unreliable. If factorization fails with -C 0 < INFO <= N, then DWORK(1) contains the reciprocal pivot -C growth factor for the leading INFO columns of A. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C > 0: if INFO = i, and i is -C <= N: U(i,i) is exactly zero. The factorization -C has been completed, but the factor U is -C exactly singular, so the solution and error -C bounds could not be computed. RCOND = 0 is -C returned. -C = N+1: U is nonsingular, but RCOND is less than -C machine precision, meaning that the matrix is -C singular to working precision. Nevertheless, -C the solution and error bounds are computed -C because there are a number of situations -C where the computed solution can be more -C accurate than the value of RCOND would -C suggest. -C The positive values for INFO are set only when the -C matrix A is factored, i.e., for FACT = 'N' or 'E'. -C -C METHOD -C -C The following steps are performed: -C -C 1. If FACT = 'E', real scaling factors are computed to equilibrate -C the system: -C -C TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B -C TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B -C TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B -C -C Whether or not the system will be equilibrated depends on the -C scaling of the matrix A, but if equilibration is used, A is -C overwritten by diag(R)*A*diag(C) and B by diag(R)*B -C (if TRANS='N') or diag(C)*B (if TRANS = 'T' or 'C'). -C -C 2. If FACT = 'N' or 'E', the LU decomposition is used to factor -C the matrix A (after equilibration if FACT = 'E') as -C A = P * L * U, -C where P is a permutation matrix, L is a unit lower triangular -C matrix, and U is upper triangular. -C -C 3. If some U(i,i)=0, so that U is exactly singular, then the -C routine returns with INFO = i. Otherwise, the factored form -C of A is used to estimate the condition number of the matrix A. -C If the reciprocal of the condition number is less than machine -C precision, INFO = N+1 is returned as a warning, but the routine -C still goes on to solve for X and compute error bounds as -C described below. -C -C 4. The system of equations is solved for X using the factored form -C of A. -C -C 5. Iterative refinement is applied to improve the computed -C solution matrix and calculate error bounds and backward error -C estimates for it. -C -C 6. If equilibration was used, the matrix X is premultiplied by -C diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so -C that it solves the original system before equilibration. -C -C REFERENCES -C -C [1] Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J., -C Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., -C Ostrouchov, S., Sorensen, D. -C LAPACK Users' Guide: Second Edition, SIAM, Philadelphia, 1995. -C -C FURTHER COMMENTS -C -C This is a simplified version of the LAPACK Library routine DGESVX, -C useful when several sets of matrix equations with the same -C coefficient matrix A and/or A' should be solved. -C -C NUMERICAL ASPECTS -C 3 -C The algorithm requires 0(N ) operations. -C -C CONTRIBUTORS -C -C V. Sima, Research Institute for Informatics, Bucharest, Apr. 1999. -C -C REVISIONS -C -C - -C -C KEYWORDS -C -C Condition number, matrix algebra, matrix operations. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) -C .. Scalar Arguments .. - CHARACTER EQUED, FACT, TRANS - INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS - DOUBLE PRECISION RCOND -C .. -C .. Array Arguments .. - INTEGER IPIV( * ), IWORK( * ) - DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ), - $ BERR( * ), C( * ), DWORK( * ), FERR( * ), - $ R( * ), X( LDX, * ) -C .. -C .. Local Scalars .. - LOGICAL COLEQU, EQUIL, NOFACT, NOTRAN, ROWEQU - CHARACTER NORM - INTEGER I, INFEQU, J - DOUBLE PRECISION AMAX, ANORM, BIGNUM, COLCND, RCMAX, RCMIN, - $ ROWCND, RPVGRW, SMLNUM -C .. -C .. External Functions .. - LOGICAL LSAME - DOUBLE PRECISION DLAMCH, DLANGE, DLANTR - EXTERNAL LSAME, DLAMCH, DLANGE, DLANTR -C .. -C .. External Subroutines .. - EXTERNAL DGECON, DGEEQU, DGERFS, DGETRF, DGETRS, DLACPY, - $ DLAQGE, XERBLA -C .. -C .. Intrinsic Functions .. - INTRINSIC MAX, MIN -C .. -C .. Save Statement .. - SAVE RPVGRW -C .. -C .. Executable Statements .. -C - INFO = 0 - NOFACT = LSAME( FACT, 'N' ) - EQUIL = LSAME( FACT, 'E' ) - NOTRAN = LSAME( TRANS, 'N' ) - IF( NOFACT .OR. EQUIL ) THEN - EQUED = 'N' - ROWEQU = .FALSE. - COLEQU = .FALSE. - ELSE - ROWEQU = LSAME( EQUED, 'R' ) .OR. LSAME( EQUED, 'B' ) - COLEQU = LSAME( EQUED, 'C' ) .OR. LSAME( EQUED, 'B' ) - SMLNUM = DLAMCH( 'Safe minimum' ) - BIGNUM = ONE / SMLNUM - END IF -C -C Test the input parameters. -C - IF( .NOT.NOFACT .AND. .NOT.EQUIL .AND. .NOT.LSAME( FACT, 'F' ) ) - $ THEN - INFO = -1 - ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT. - $ LSAME( TRANS, 'C' ) ) THEN - INFO = -2 - ELSE IF( N.LT.0 ) THEN - INFO = -3 - ELSE IF( NRHS.LT.0 ) THEN - INFO = -4 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -6 - ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN - INFO = -8 - ELSE IF( LSAME( FACT, 'F' ) .AND. .NOT. - $ ( ROWEQU .OR. COLEQU .OR. LSAME( EQUED, 'N' ) ) ) THEN - INFO = -10 - ELSE - IF( ROWEQU ) THEN - RCMIN = BIGNUM - RCMAX = ZERO - DO 10 J = 1, N - RCMIN = MIN( RCMIN, R( J ) ) - RCMAX = MAX( RCMAX, R( J ) ) - 10 CONTINUE - IF( RCMIN.LE.ZERO ) THEN - INFO = -11 - ELSE IF( N.GT.0 ) THEN - ROWCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM ) - ELSE - ROWCND = ONE - END IF - END IF - IF( COLEQU .AND. INFO.EQ.0 ) THEN - RCMIN = BIGNUM - RCMAX = ZERO - DO 20 J = 1, N - RCMIN = MIN( RCMIN, C( J ) ) - RCMAX = MAX( RCMAX, C( J ) ) - 20 CONTINUE - IF( RCMIN.LE.ZERO ) THEN - INFO = -12 - ELSE IF( N.GT.0 ) THEN - COLCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM ) - ELSE - COLCND = ONE - END IF - END IF - IF( INFO.EQ.0 ) THEN - IF( LDB.LT.MAX( 1, N ) ) THEN - INFO = -14 - ELSE IF( LDX.LT.MAX( 1, N ) ) THEN - INFO = -16 - END IF - END IF - END IF -C - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'MB02PD', -INFO ) - RETURN - END IF -C - IF( EQUIL ) THEN -C -C Compute row and column scalings to equilibrate the matrix A. -C - CALL DGEEQU( N, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFEQU ) - IF( INFEQU.EQ.0 ) THEN -C -C Equilibrate the matrix. -C - CALL DLAQGE( N, N, A, LDA, R, C, ROWCND, COLCND, AMAX, - $ EQUED ) - ROWEQU = LSAME( EQUED, 'R' ) .OR. LSAME( EQUED, 'B' ) - COLEQU = LSAME( EQUED, 'C' ) .OR. LSAME( EQUED, 'B' ) - END IF - END IF -C -C Scale the right hand side. -C - IF( NOTRAN ) THEN - IF( ROWEQU ) THEN - DO 40 J = 1, NRHS - DO 30 I = 1, N - B( I, J ) = R( I )*B( I, J ) - 30 CONTINUE - 40 CONTINUE - END IF - ELSE IF( COLEQU ) THEN - DO 60 J = 1, NRHS - DO 50 I = 1, N - B( I, J ) = C( I )*B( I, J ) - 50 CONTINUE - 60 CONTINUE - END IF -C - IF( NOFACT .OR. EQUIL ) THEN -C -C Compute the LU factorization of A. -C - CALL DLACPY( 'Full', N, N, A, LDA, AF, LDAF ) - CALL DGETRF( N, N, AF, LDAF, IPIV, INFO ) -C -C Return if INFO is non-zero. -C - IF( INFO.NE.0 ) THEN - IF( INFO.GT.0 ) THEN -C -C Compute the reciprocal pivot growth factor of the -C leading rank-deficient INFO columns of A. -C - RPVGRW = DLANTR( 'M', 'U', 'N', INFO, INFO, AF, LDAF, - $ DWORK ) - IF( RPVGRW.EQ.ZERO ) THEN - RPVGRW = ONE - ELSE - RPVGRW = DLANGE( 'M', N, INFO, A, LDA, DWORK ) / - $ RPVGRW - END IF - DWORK( 1 ) = RPVGRW - RCOND = ZERO - END IF - RETURN - END IF -C -C Compute the norm of the matrix A and the -C reciprocal pivot growth factor RPVGRW. -C - IF( NOTRAN ) THEN - NORM = '1' - ELSE - NORM = 'I' - END IF - ANORM = DLANGE( NORM, N, N, A, LDA, DWORK ) - RPVGRW = DLANTR( 'M', 'U', 'N', N, N, AF, LDAF, DWORK ) - IF( RPVGRW.EQ.ZERO ) THEN - RPVGRW = ONE - ELSE - RPVGRW = DLANGE( 'M', N, N, A, LDA, DWORK ) / RPVGRW - END IF -C -C Compute the reciprocal of the condition number of A. -C - CALL DGECON( NORM, N, AF, LDAF, ANORM, RCOND, DWORK, IWORK, - $ INFO ) -C -C Set INFO = N+1 if the matrix is singular to working precision. -C - IF( RCOND.LT.DLAMCH( 'Epsilon' ) ) - $ INFO = N + 1 - END IF -C -C Compute the solution matrix X. -C - CALL DLACPY( 'Full', N, NRHS, B, LDB, X, LDX ) - CALL DGETRS( TRANS, N, NRHS, AF, LDAF, IPIV, X, LDX, INFO ) -C -C Use iterative refinement to improve the computed solution and -C compute error bounds and backward error estimates for it. -C - CALL DGERFS( TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, - $ LDX, FERR, BERR, DWORK, IWORK, INFO ) -C -C Transform the solution matrix X to a solution of the original -C system. -C - IF( NOTRAN ) THEN - IF( COLEQU ) THEN - DO 80 J = 1, NRHS - DO 70 I = 1, N - X( I, J ) = C( I )*X( I, J ) - 70 CONTINUE - 80 CONTINUE - DO 90 J = 1, NRHS - FERR( J ) = FERR( J ) / COLCND - 90 CONTINUE - END IF - ELSE IF( ROWEQU ) THEN - DO 110 J = 1, NRHS - DO 100 I = 1, N - X( I, J ) = R( I )*X( I, J ) - 100 CONTINUE - 110 CONTINUE - DO 120 J = 1, NRHS - FERR( J ) = FERR( J ) / ROWCND - 120 CONTINUE - END IF -C - DWORK( 1 ) = RPVGRW - RETURN -C -C *** Last line of MB02PD *** - END
--- a/extra/control-devel/devel/dksyn/MB02RZ.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,216 +0,0 @@ - SUBROUTINE MB02RZ( TRANS, N, NRHS, H, LDH, IPIV, B, LDB, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To solve a system of linear equations -C H * X = B, H' * X = B or H**H * X = B -C with a complex upper Hessenberg N-by-N matrix H using the LU -C factorization computed by MB02SZ. -C -C ARGUMENTS -C -C Mode Parameters -C -C TRANS CHARACTER*1 -C Specifies the form of the system of equations: -C = 'N': H * X = B (No transpose) -C = 'T': H'* X = B (Transpose) -C = 'C': H**H * X = B (Conjugate transpose) -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the matrix H. N >= 0. -C -C NRHS (input) INTEGER -C The number of right hand sides, i.e., the number of -C columns of the matrix B. NRHS >= 0. -C -C H (input) COMPLEX*16 array, dimension (LDH,N) -C The factors L and U from the factorization H = P*L*U -C as computed by MB02SZ. -C -C LDH INTEGER -C The leading dimension of the array H. LDH >= max(1,N). -C -C IPIV (input) INTEGER array, dimension (N) -C The pivot indices from MB02SZ; for 1<=i<=N, row i of the -C matrix was interchanged with row IPIV(i). -C -C B (input/output) COMPLEX*16 array, dimension (LDB,NRHS) -C On entry, the right hand side matrix B. -C On exit, the solution matrix X. -C -C LDB INTEGER -C The leading dimension of the array B. LDB >= max(1,N). -C -C INFO (output) INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value. -C -C METHOD -C -C The routine uses the factorization -C H = P * L * U -C where P is a permutation matrix, L is lower triangular with unit -C diagonal elements (and one nonzero subdiagonal), and U is upper -C triangular. -C -C REFERENCES -C -C - -C -C NUMERICAL ASPECTS -C 2 -C The algorithm requires 0( N x NRHS ) complex operations. -C -C CONTRIBUTOR -C -C Release 3.0: V. Sima, Katholieke Univ. Leuven, Belgium, Dec. 1996. -C Supersedes Release 2.0 routine TB01FW by A.J. Laub, University of -C Southern California, United States of America, May 1980. -C -C REVISIONS -C -C - -C -C KEYWORDS -C -C Frequency response, Hessenberg form, matrix algebra. -C -C ****************************************************************** -C -C .. Parameters .. - COMPLEX*16 ONE - PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) -C .. Scalar Arguments .. - CHARACTER TRANS - INTEGER INFO, LDB, LDH, N, NRHS -C .. -C .. Array Arguments .. - INTEGER IPIV( * ) - COMPLEX*16 B( LDB, * ), H( LDH, * ) -C .. Local Scalars .. - LOGICAL NOTRAN - INTEGER J, JP -C .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -C .. External Subroutines .. - EXTERNAL XERBLA, ZAXPY, ZSWAP, ZTRSM -C .. Intrinsic Functions .. - INTRINSIC DCONJG, MAX -C .. Executable Statements .. -C -C Test the input parameters. -C - INFO = 0 - NOTRAN = LSAME( TRANS, 'N' ) - IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT. - $ LSAME( TRANS, 'C' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( NRHS.LT.0 ) THEN - INFO = -3 - ELSE IF( LDH.LT.MAX( 1, N ) ) THEN - INFO = -5 - ELSE IF( LDB.LT.MAX( 1, N ) ) THEN - INFO = -8 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'MB02RZ', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF( N.EQ.0 .OR. NRHS.EQ.0 ) - $ RETURN -C - IF( NOTRAN ) THEN -C -C Solve H * X = B. -C -C Solve L * X = B, overwriting B with X. -C -C L is represented as a product of permutations and unit lower -C triangular matrices L = P(1) * L(1) * ... * P(n-1) * L(n-1), -C where each transformation L(i) is a rank-one modification of -C the identity matrix. -C - DO 10 J = 1, N - 1 - JP = IPIV( J ) - IF( JP.NE.J ) - $ CALL ZSWAP( NRHS, B( JP, 1 ), LDB, B( J, 1 ), LDB ) - CALL ZAXPY( NRHS, -H( J+1, J ), B( J, 1 ), LDB, B( J+1, 1 ), - $ LDB ) - 10 CONTINUE -C -C Solve U * X = B, overwriting B with X. -C - CALL ZTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', N, - $ NRHS, ONE, H, LDH, B, LDB ) -C - ELSE IF( LSAME( TRANS, 'T' ) ) THEN -C -C Solve H' * X = B. -C -C Solve U' * X = B, overwriting B with X. -C - CALL ZTRSM( 'Left', 'Upper', TRANS, 'Non-unit', N, NRHS, ONE, - $ H, LDH, B, LDB ) -C -C Solve L' * X = B, overwriting B with X. -C - DO 20 J = N - 1, 1, -1 - CALL ZAXPY( NRHS, -H( J+1, J ), B( J+1, 1 ), LDB, B( J, 1 ), - $ LDB ) - JP = IPIV( J ) - IF( JP.NE.J ) - $ CALL ZSWAP( NRHS, B( JP, 1 ), LDB, B( J, 1 ), LDB ) - 20 CONTINUE -C - ELSE -C -C Solve H**H * X = B. -C -C Solve U**H * X = B, overwriting B with X. -C - CALL ZTRSM( 'Left', 'Upper', TRANS, 'Non-unit', N, NRHS, ONE, - $ H, LDH, B, LDB ) -C -C Solve L**H * X = B, overwriting B with X. -C - DO 30 J = N - 1, 1, -1 - CALL ZAXPY( NRHS, -DCONJG( H( J+1, J ) ), B( J+1, 1 ), LDB, - $ B( J, 1 ), LDB ) - JP = IPIV( J ) - IF( JP.NE.J ) - $ CALL ZSWAP( NRHS, B( JP, 1 ), LDB, B( J, 1 ), LDB ) - 30 CONTINUE -C - END IF -C - RETURN -C *** Last line of MB02RZ *** - END
--- a/extra/control-devel/devel/dksyn/MB02SZ.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,169 +0,0 @@ - SUBROUTINE MB02SZ( N, H, LDH, IPIV, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To compute an LU factorization of a complex n-by-n upper -C Hessenberg matrix H using partial pivoting with row interchanges. -C -C ARGUMENTS -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the matrix H. N >= 0. -C -C H (input/output) COMPLEX*16 array, dimension (LDH,N) -C On entry, the n-by-n upper Hessenberg matrix to be -C factored. -C On exit, the factors L and U from the factorization -C H = P*L*U; the unit diagonal elements of L are not stored, -C and L is lower bidiagonal. -C -C LDH INTEGER -C The leading dimension of the array H. LDH >= max(1,N). -C -C IPIV (output) INTEGER array, dimension (N) -C The pivot indices; for 1 <= i <= N, row i of the matrix -C was interchanged with row IPIV(i). -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C > 0: if INFO = i, U(i,i) is exactly zero. The -C factorization has been completed, but the factor U -C is exactly singular, and division by zero will occur -C if it is used to solve a system of equations. -C -C METHOD -C -C The factorization has the form -C H = P * L * U -C where P is a permutation matrix, L is lower triangular with unit -C diagonal elements (and one nonzero subdiagonal), and U is upper -C triangular. -C -C This is the right-looking Level 2 BLAS version of the algorithm -C (adapted after ZGETF2). -C -C REFERENCES -C -C - -C -C NUMERICAL ASPECTS -C 2 -C The algorithm requires 0( N ) complex operations. -C -C CONTRIBUTOR -C -C Release 3.0: V. Sima, Katholieke Univ. Leuven, Belgium, Dec. 1996. -C Supersedes Release 2.0 routine TB01FX by A.J. Laub, University of -C Southern California, United States of America, May 1980. -C -C REVISIONS -C -C V. Sima, Research Institute for Informatics, Bucharest, Oct. 2000, -C Jan. 2005. -C -C KEYWORDS -C -C Frequency response, Hessenberg form, matrix algebra. -C -C ****************************************************************** -C -C .. Parameters .. - COMPLEX*16 ZERO - PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) -C .. Scalar Arguments .. - INTEGER INFO, LDH, N -C .. Array Arguments .. - INTEGER IPIV(*) - COMPLEX*16 H(LDH,*) -C .. Local Scalars .. - INTEGER J, JP -C .. External Functions .. - DOUBLE PRECISION DCABS1 - EXTERNAL DCABS1 -C .. External Subroutines .. - EXTERNAL XERBLA, ZAXPY, ZSWAP -C .. Intrinsic Functions .. - INTRINSIC MAX -C .. -C .. Executable Statements .. -C -C Check the scalar input parameters. -C - INFO = 0 - IF( N.LT.0 ) THEN - INFO = -1 - ELSE IF( LDH.LT.MAX( 1, N ) ) THEN - INFO = -3 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'MB02SZ', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF( N.EQ.0 ) - $ RETURN -C - DO 10 J = 1, N -C -C Find pivot and test for singularity. -C - JP = J - IF ( J.LT.N ) THEN - IF ( DCABS1( H( J+1, J ) ).GT.DCABS1( H( J, J ) ) ) - $ JP = J + 1 - END IF - IPIV( J ) = JP - IF( H( JP, J ).NE.ZERO ) THEN -C -C Apply the interchange to columns J:N. -C - IF( JP.NE.J ) - $ CALL ZSWAP( N-J+1, H( J, J ), LDH, H( JP, J ), LDH ) -C -C Compute element J+1 of J-th column. -C - IF( J.LT.N ) - $ H( J+1, J ) = H( J+1, J )/H( J, J ) -C - ELSE IF( INFO.EQ.0 ) THEN -C - INFO = J - END IF -C - IF( J.LT.N ) THEN -C -C Update trailing submatrix. -C - CALL ZAXPY( N-J, -H( J+1, J ), H( J, J+1 ), LDH, - $ H( J+1, J+1 ), LDH ) - END IF - 10 CONTINUE - RETURN -C *** Last line of MB02SZ *** - END
--- a/extra/control-devel/devel/dksyn/MB02TZ.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,247 +0,0 @@ - SUBROUTINE MB02TZ( NORM, N, HNORM, H, LDH, IPIV, RCOND, DWORK, - $ ZWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To estimate the reciprocal of the condition number of a complex -C upper Hessenberg matrix H, in either the 1-norm or the -C infinity-norm, using the LU factorization computed by MB02SZ. -C -C ARGUMENTS -C -C Mode Parameters -C -C NORM CHARACTER*1 -C Specifies whether the 1-norm condition number or the -C infinity-norm condition number is required: -C = '1' or 'O': 1-norm; -C = 'I': Infinity-norm. -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the matrix H. N >= 0. -C -C HNORM (input) DOUBLE PRECISION -C If NORM = '1' or 'O', the 1-norm of the original matrix H. -C If NORM = 'I', the infinity-norm of the original matrix H. -C -C H (input) COMPLEX*16 array, dimension (LDH,N) -C The factors L and U from the factorization H = P*L*U -C as computed by MB02SZ. -C -C LDH INTEGER -C The leading dimension of the array H. LDH >= max(1,N). -C -C IPIV (input) INTEGER array, dimension (N) -C The pivot indices; for 1 <= i <= N, row i of the matrix -C was interchanged with row IPIV(i). -C -C RCOND (output) DOUBLE PRECISION -C The reciprocal of the condition number of the matrix H, -C computed as RCOND = 1/(norm(H) * norm(inv(H))). -C -C Workspace -C -C DWORK DOUBLE PRECISION array, dimension (N) -C -C ZWORK COMPLEX*16 array, dimension (2*N) -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value. -C -C METHOD -C -C An estimate is obtained for norm(inv(H)), and the reciprocal of -C the condition number is computed as -C RCOND = 1 / ( norm(H) * norm(inv(H)) ). -C -C REFERENCES -C -C - -C -C NUMERICAL ASPECTS -C 2 -C The algorithm requires 0( N ) complex operations. -C -C CONTRIBUTOR -C -C Release 3.0: V. Sima, Katholieke Univ. Leuven, Belgium, Dec. 1996. -C Supersedes Release 2.0 routine TB01FY by A.J. Laub, University of -C Southern California, United States of America, May 1980. -C -C REVISIONS -C -C V. Sima, Research Institute for Informatics, Bucharest, Feb. 2005. -C -C KEYWORDS -C -C Frequency response, Hessenberg form, matrix algebra. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -C .. Scalar Arguments .. - CHARACTER NORM - INTEGER INFO, LDH, N - DOUBLE PRECISION HNORM, RCOND -C .. -C .. Array Arguments .. - INTEGER IPIV(*) - DOUBLE PRECISION DWORK( * ) - COMPLEX*16 H( LDH, * ), ZWORK( * ) -C .. Local Scalars .. - LOGICAL ONENRM - CHARACTER NORMIN - INTEGER IX, J, JP, KASE, KASE1 -C - DOUBLE PRECISION HINVNM, SCALE, SMLNUM - COMPLEX*16 T, ZDUM -C .. -C .. External Functions .. - LOGICAL LSAME - INTEGER IZAMAX - DOUBLE PRECISION DLAMCH - EXTERNAL DLAMCH, IZAMAX, LSAME -C .. -C .. External Subroutines .. - EXTERNAL XERBLA, ZDRSCL, ZLACON, ZLATRS -C .. -C .. Intrinsic Functions .. - INTRINSIC ABS, DBLE, DCONJG, DIMAG, MAX -C .. -C .. Statement Functions .. - DOUBLE PRECISION CABS1 -C .. -C .. Statement Function definitions .. - CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) -C .. -C .. Executable Statements .. -C -C Test the input parameters. -C - INFO = 0 - ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' ) - IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( HNORM.LT.ZERO ) THEN - INFO = -3 - ELSE IF( LDH.LT.MAX( 1, N ) ) THEN - INFO = -5 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'MB02TZ', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - RCOND = ZERO - IF( N.EQ.0 ) THEN - RCOND = ONE - RETURN - ELSE IF( HNORM.EQ.ZERO ) THEN - RETURN - END IF -C - SMLNUM = DLAMCH( 'Safe minimum' ) -C -C Estimate the norm of inv(H). -C - HINVNM = ZERO - NORMIN = 'N' - IF( ONENRM ) THEN - KASE1 = 1 - ELSE - KASE1 = 2 - END IF - KASE = 0 - 10 CONTINUE - CALL ZLACON( N, ZWORK( N+1 ), ZWORK, HINVNM, KASE ) - IF( KASE.NE.0 ) THEN - IF( KASE.EQ.KASE1 ) THEN -C -C Multiply by inv(L). -C - DO 20 J = 1, N - 1 - JP = IPIV( J ) - T = ZWORK( JP ) - IF( JP.NE.J ) THEN - ZWORK( JP ) = ZWORK( J ) - ZWORK( J ) = T - END IF - ZWORK( J+1 ) = ZWORK( J+1 ) - T * H( J+1, J ) - 20 CONTINUE -C -C Multiply by inv(U). -C - CALL ZLATRS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N, - $ H, LDH, ZWORK, SCALE, DWORK, INFO ) - ELSE -C -C Multiply by inv(U'). -C - CALL ZLATRS( 'Upper', 'Conjugate transpose', 'Non-unit', - $ NORMIN, N, H, LDH, ZWORK, SCALE, DWORK, INFO ) -C -C Multiply by inv(L'). -C - DO 30 J = N - 1, 1, -1 - ZWORK( J ) = ZWORK( J ) - - $ DCONJG( H( J+1, J ) ) * ZWORK( J+1 ) - JP = IPIV( J ) - IF( JP.NE.J ) THEN - T = ZWORK( JP ) - ZWORK( JP ) = ZWORK( J ) - ZWORK( J ) = T - END IF - 30 CONTINUE - END IF -C -C Divide X by 1/SCALE if doing so will not cause overflow. -C - NORMIN = 'Y' - IF( SCALE.NE.ONE ) THEN - IX = IZAMAX( N, ZWORK, 1 ) - IF( SCALE.LT.CABS1( ZWORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO - $ ) GO TO 40 - CALL ZDRSCL( N, SCALE, ZWORK, 1 ) - END IF - GO TO 10 - END IF -C -C Compute the estimate of the reciprocal condition number. -C - IF( HINVNM.NE.ZERO ) - $ RCOND = ( ONE / HINVNM ) / HNORM -C - 40 CONTINUE - RETURN -C *** Last line of MB02TZ *** - END
--- a/extra/control-devel/devel/dksyn/MB03OY.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,388 +0,0 @@ - SUBROUTINE MB03OY( M, N, A, LDA, RCOND, SVLMAX, RANK, SVAL, JPVT, - $ TAU, DWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To compute a rank-revealing QR factorization of a real general -C M-by-N matrix A, which may be rank-deficient, and estimate its -C effective rank using incremental condition estimation. -C -C The routine uses a truncated QR factorization with column pivoting -C [ R11 R12 ] -C A * P = Q * R, where R = [ ], -C [ 0 R22 ] -C with R11 defined as the largest leading upper triangular submatrix -C whose estimated condition number is less than 1/RCOND. The order -C of R11, RANK, is the effective rank of A. Condition estimation is -C performed during the QR factorization process. Matrix R22 is full -C (but of small norm), or empty. -C -C MB03OY does not perform any scaling of the matrix A. -C -C ARGUMENTS -C -C Input/Output Parameters -C -C M (input) INTEGER -C The number of rows of the matrix A. M >= 0. -C -C N (input) INTEGER -C The number of columns of the matrix A. N >= 0. -C -C A (input/output) DOUBLE PRECISION array, dimension -C ( LDA, N ) -C On entry, the leading M-by-N part of this array must -C contain the given matrix A. -C On exit, the leading RANK-by-RANK upper triangular part -C of A contains the triangular factor R11, and the elements -C below the diagonal in the first RANK columns, with the -C array TAU, represent the orthogonal matrix Q as a product -C of RANK elementary reflectors. -C The remaining N-RANK columns contain the result of the -C QR factorization process used. -C -C LDA INTEGER -C The leading dimension of the array A. LDA >= max(1,M). -C -C RCOND (input) DOUBLE PRECISION -C RCOND is used to determine the effective rank of A, which -C is defined as the order of the largest leading triangular -C submatrix R11 in the QR factorization with pivoting of A, -C whose estimated condition number is less than 1/RCOND. -C 0 <= RCOND <= 1. -C NOTE that when SVLMAX > 0, the estimated rank could be -C less than that defined above (see SVLMAX). -C -C SVLMAX (input) DOUBLE PRECISION -C If A is a submatrix of another matrix B, and the rank -C decision should be related to that matrix, then SVLMAX -C should be an estimate of the largest singular value of B -C (for instance, the Frobenius norm of B). If this is not -C the case, the input value SVLMAX = 0 should work. -C SVLMAX >= 0. -C -C RANK (output) INTEGER -C The effective (estimated) rank of A, i.e., the order of -C the submatrix R11. -C -C SVAL (output) DOUBLE PRECISION array, dimension ( 3 ) -C The estimates of some of the singular values of the -C triangular factor R: -C SVAL(1): largest singular value of R(1:RANK,1:RANK); -C SVAL(2): smallest singular value of R(1:RANK,1:RANK); -C SVAL(3): smallest singular value of R(1:RANK+1,1:RANK+1), -C if RANK < MIN( M, N ), or of R(1:RANK,1:RANK), -C otherwise. -C If the triangular factorization is a rank-revealing one -C (which will be the case if the leading columns were well- -C conditioned), then SVAL(1) will also be an estimate for -C the largest singular value of A, and SVAL(2) and SVAL(3) -C will be estimates for the RANK-th and (RANK+1)-st singular -C values of A, respectively. -C By examining these values, one can confirm that the rank -C is well defined with respect to the chosen value of RCOND. -C The ratio SVAL(1)/SVAL(2) is an estimate of the condition -C number of R(1:RANK,1:RANK). -C -C JPVT (output) INTEGER array, dimension ( N ) -C If JPVT(i) = k, then the i-th column of A*P was the k-th -C column of A. -C -C TAU (output) DOUBLE PRECISION array, dimension ( MIN( M, N ) ) -C The leading RANK elements of TAU contain the scalar -C factors of the elementary reflectors. -C -C Workspace -C -C DWORK DOUBLE PRECISION array, dimension ( 3*N-1 ) -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value. -C -C METHOD -C -C The routine computes a truncated QR factorization with column -C pivoting of A, A * P = Q * R, with R defined above, and, -C during this process, finds the largest leading submatrix whose -C estimated condition number is less than 1/RCOND, taking the -C possible positive value of SVLMAX into account. This is performed -C using the LAPACK incremental condition estimation scheme and a -C slightly modified rank decision test. The factorization process -C stops when RANK has been determined. -C -C The matrix Q is represented as a product of elementary reflectors -C -C Q = H(1) H(2) . . . H(k), where k = rank <= min(m,n). -C -C Each H(i) has the form -C -C H = I - tau * v * v' -C -C where tau is a real scalar, and v is a real vector with -C v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in -C A(i+1:m,i), and tau in TAU(i). -C -C The matrix P is represented in jpvt as follows: If -C jpvt(j) = i -C then the jth column of P is the ith canonical unit vector. -C -C REFERENCES -C -C [1] Bischof, C.H. and P. Tang. -C Generalizing Incremental Condition Estimation. -C LAPACK Working Notes 32, Mathematics and Computer Science -C Division, Argonne National Laboratory, UT, CS-91-132, -C May 1991. -C -C [2] Bischof, C.H. and P. Tang. -C Robust Incremental Condition Estimation. -C LAPACK Working Notes 33, Mathematics and Computer Science -C Division, Argonne National Laboratory, UT, CS-91-133, -C May 1991. -C -C NUMERICAL ASPECTS -C -C The algorithm is backward stable. -C -C CONTRIBUTOR -C -C V. Sima, Katholieke Univ. Leuven, Belgium, Feb. 1998. -C -C REVISIONS -C -C V. Sima, Research Institute for Informatics, Bucharest, Jan. 2009. -C V. Sima, Jan. 2010, following Bujanovic and Drmac's suggestion. -C -C KEYWORDS -C -C Eigenvalue problem, matrix operations, orthogonal transformation, -C singular values. -C -C ****************************************************************** -C -C .. Parameters .. - INTEGER IMAX, IMIN - PARAMETER ( IMAX = 1, IMIN = 2 ) - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) -C .. Scalar Arguments .. - INTEGER INFO, LDA, M, N, RANK - DOUBLE PRECISION RCOND, SVLMAX -C .. Array Arguments .. - INTEGER JPVT( * ) - DOUBLE PRECISION A( LDA, * ), DWORK( * ), SVAL( 3 ), TAU( * ) -C .. -C .. Local Scalars .. - INTEGER I, ISMAX, ISMIN, ITEMP, J, MN, PVT - DOUBLE PRECISION AII, C1, C2, S1, S2, SMAX, SMAXPR, SMIN, - $ SMINPR, TEMP, TEMP2, TOLZ -C .. -C .. External Functions .. - INTEGER IDAMAX - DOUBLE PRECISION DLAMCH, DNRM2 - EXTERNAL DLAMCH, DNRM2, IDAMAX -C .. External Subroutines .. - EXTERNAL DLAIC1, DLARF, DLARFG, DSCAL, DSWAP, XERBLA -C .. Intrinsic Functions .. - INTRINSIC ABS, MAX, MIN, SQRT -C .. -C .. Executable Statements .. -C -C Test the input scalar arguments. -C - INFO = 0 - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -4 - ELSE IF( RCOND.LT.ZERO .OR. RCOND.GT.ONE ) THEN - INFO = -5 - ELSE IF( SVLMAX.LT.ZERO ) THEN - INFO = -6 - END IF -C - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'MB03OY', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - MN = MIN( M, N ) - IF( MN.EQ.0 ) THEN - RANK = 0 - SVAL( 1 ) = ZERO - SVAL( 2 ) = ZERO - SVAL( 3 ) = ZERO - RETURN - END IF -C - TOLZ = SQRT( DLAMCH( 'Epsilon' ) ) - ISMIN = 1 - ISMAX = ISMIN + N -C -C Initialize partial column norms and pivoting vector. The first n -C elements of DWORK store the exact column norms. The already used -C leading part is then overwritten by the condition estimator. -C - DO 10 I = 1, N - DWORK( I ) = DNRM2( M, A( 1, I ), 1 ) - DWORK( N+I ) = DWORK( I ) - JPVT( I ) = I - 10 CONTINUE -C -C Compute factorization and determine RANK using incremental -C condition estimation. -C - RANK = 0 -C - 20 CONTINUE - IF( RANK.LT.MN ) THEN - I = RANK + 1 -C -C Determine ith pivot column and swap if necessary. -C - PVT = ( I-1 ) + IDAMAX( N-I+1, DWORK( I ), 1 ) -C - IF( PVT.NE.I ) THEN - CALL DSWAP( M, A( 1, PVT ), 1, A( 1, I ), 1 ) - ITEMP = JPVT( PVT ) - JPVT( PVT ) = JPVT( I ) - JPVT( I ) = ITEMP - DWORK( PVT ) = DWORK( I ) - DWORK( N+PVT ) = DWORK( N+I ) - END IF -C -C Save A(I,I) and generate elementary reflector H(i). -C - IF( I.LT.M ) THEN - AII = A( I, I ) - CALL DLARFG( M-I+1, A( I, I ), A( I+1, I ), 1, TAU( I ) ) - ELSE - TAU( M ) = ZERO - END IF -C - IF( RANK.EQ.0 ) THEN -C -C Initialize; exit if matrix is zero (RANK = 0). -C - SMAX = ABS( A( 1, 1 ) ) - IF ( SMAX.EQ.ZERO ) THEN - SVAL( 1 ) = ZERO - SVAL( 2 ) = ZERO - SVAL( 3 ) = ZERO - RETURN - END IF - SMIN = SMAX - SMAXPR = SMAX - SMINPR = SMIN - C1 = ONE - C2 = ONE - ELSE -C -C One step of incremental condition estimation. -C - CALL DLAIC1( IMIN, RANK, DWORK( ISMIN ), SMIN, A( 1, I ), - $ A( I, I ), SMINPR, S1, C1 ) - CALL DLAIC1( IMAX, RANK, DWORK( ISMAX ), SMAX, A( 1, I ), - $ A( I, I ), SMAXPR, S2, C2 ) - END IF -C - IF( SVLMAX*RCOND.LE.SMAXPR ) THEN - IF( SVLMAX*RCOND.LE.SMINPR ) THEN - IF( SMAXPR*RCOND.LE.SMINPR ) THEN -C -C Continue factorization, as rank is at least RANK. -C - IF( I.LT.N ) THEN -C -C Apply H(i) to A(i:m,i+1:n) from the left. -C - AII = A( I, I ) - A( I, I ) = ONE - CALL DLARF( 'Left', M-I+1, N-I, A( I, I ), 1, - $ TAU( I ), A( I, I+1 ), LDA, - $ DWORK( 2*N+1 ) ) - A( I, I ) = AII - END IF -C -C Update partial column norms. -C - DO 30 J = I + 1, N - IF( DWORK( J ).NE.ZERO ) THEN - TEMP = ABS( A( I, J ) ) / DWORK( J ) - TEMP = MAX( ( ONE + TEMP )*( ONE - TEMP ), ZERO) - TEMP2 = TEMP*( DWORK( J ) / DWORK( N+J ) )**2 - IF( TEMP2.LE.TOLZ ) THEN - IF( M-I.GT.0 ) THEN - DWORK( J ) = DNRM2( M-I, A( I+1, J ), 1 ) - DWORK( N+J ) = DWORK( J ) - ELSE - DWORK( J ) = ZERO - DWORK( N+J ) = ZERO - END IF - ELSE - DWORK( J ) = DWORK( J )*SQRT( TEMP ) - END IF - END IF - 30 CONTINUE -C - DO 40 I = 1, RANK - DWORK( ISMIN+I-1 ) = S1*DWORK( ISMIN+I-1 ) - DWORK( ISMAX+I-1 ) = S2*DWORK( ISMAX+I-1 ) - 40 CONTINUE -C - DWORK( ISMIN+RANK ) = C1 - DWORK( ISMAX+RANK ) = C2 - SMIN = SMINPR - SMAX = SMAXPR - RANK = RANK + 1 - GO TO 20 - END IF - END IF - END IF - END IF -C -C Restore the changed part of the (RANK+1)-th column and set SVAL. -C - IF ( RANK.LT.N ) THEN - IF ( I.LT.M ) THEN - CALL DSCAL( M-I, -A( I, I )*TAU( I ), A( I+1, I ), 1 ) - A( I, I ) = AII - END IF - END IF - IF ( RANK.EQ.0 ) THEN - SMIN = ZERO - SMINPR = ZERO - END IF - SVAL( 1 ) = SMAX - SVAL( 2 ) = SMIN - SVAL( 3 ) = SMINPR -C - RETURN -C *** Last line of MB03OY *** - END
--- a/extra/control-devel/devel/dksyn/MC01PD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,159 +0,0 @@ - SUBROUTINE MC01PD( K, REZ, IMZ, P, DWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To compute the coefficients of a real polynomial P(x) from its -C zeros. -C -C ARGUMENTS -C -C Input/Output Parameters -C -C K (input) INTEGER -C The number of zeros (and hence the degree) of P(x). -C K >= 0. -C -C REZ (input) DOUBLE PRECISION array, dimension (K) -C IMZ (input) DOUBLE PRECISION array, dimension (K) -C The real and imaginary parts of the i-th zero of P(x) -C must be stored in REZ(i) and IMZ(i), respectively, where -C i = 1, 2, ..., K. The zeros may be supplied in any order, -C except that complex conjugate zeros must appear -C consecutively. -C -C P (output) DOUBLE PRECISION array, dimension (K+1) -C This array contains the coefficients of P(x) in increasing -C powers of x. If K = 0, then P(1) is set to one. -C -C Workspace -C -C DWORK DOUBLE PRECISION array, dimension (K+1) -C If K = 0, this array is not referenced. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C > 0: if INFO = i, (REZ(i),IMZ(i)) is a complex zero but -C (REZ(i-1),IMZ(i-1)) is not its conjugate. -C -C METHOD -C -C The routine computes the coefficients of the real K-th degree -C polynomial P(x) as -C -C P(x) = (x - r(1)) * (x - r(2)) * ... * (x - r(K)) -C -C where r(i) = (REZ(i),IMZ(i)). -C -C Note that REZ(i) = REZ(j) and IMZ(i) = -IMZ(j) if r(i) and r(j) -C form a complex conjugate pair (where i <> j), and that IMZ(i) = 0 -C if r(i) is real. -C -C NUMERICAL ASPECTS -C -C None. -C -C CONTRIBUTOR -C -C Release 3.0: V. Sima, Katholieke Univ. Leuven, Belgium, Mar. 1997. -C Supersedes Release 2.0 routine MC01DD by A.J. Geurts. -C -C REVISIONS -C -C V. Sima, May 2002. -C -C KEYWORDS -C -C Elementary polynomial operations, polynomial operations. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) -C .. Scalar Arguments .. - INTEGER INFO, K -C .. Array Arguments .. - DOUBLE PRECISION DWORK(*), IMZ(*), P(*), REZ(*) -C .. Local Scalars .. - INTEGER I - DOUBLE PRECISION U, V -C .. External Subroutines .. - EXTERNAL DAXPY, DCOPY, XERBLA -C .. Executable Statements .. -C -C Test the input scalar arguments. -C - IF( K.LT.0 ) THEN - INFO = -1 -C -C Error return. -C - CALL XERBLA( 'MC01PD', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - INFO = 0 - P(1) = ONE - IF ( K.EQ.0 ) - $ RETURN -C - I = 1 -C WHILE ( I <= K ) DO - 20 IF ( I.LE.K ) THEN - U = REZ(I) - V = IMZ(I) - DWORK(1) = ZERO -C - IF ( V.EQ.ZERO ) THEN - CALL DCOPY( I, P, 1, DWORK(2), 1 ) - CALL DAXPY( I, -U, P, 1, DWORK, 1 ) - I = I + 1 -C - ELSE - IF ( I.EQ.K ) THEN - INFO = K - RETURN - ELSE IF ( ( U.NE.REZ(I+1) ) .OR. ( V.NE.-IMZ(I+1) ) ) THEN - INFO = I + 1 - RETURN - END IF -C - DWORK(2) = ZERO - CALL DCOPY( I, P, 1, DWORK(3), 1 ) - CALL DAXPY( I, -(U + U), P, 1, DWORK(2), 1 ) - CALL DAXPY( I, U**2+V**2, P, 1, DWORK, 1 ) - I = I + 2 - END IF -C - CALL DCOPY( I, DWORK, 1, P, 1 ) - GO TO 20 - END IF -C END WHILE 20 -C - RETURN -C *** Last line of MC01PD *** - END
--- a/extra/control-devel/devel/dksyn/SB02MR.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,75 +0,0 @@ - LOGICAL FUNCTION SB02MR( REIG, IEIG ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To select the unstable eigenvalues for solving the continuous-time -C algebraic Riccati equation. -C -C ARGUMENTS -C -C Input/Output Parameters -C -C REIG (input) DOUBLE PRECISION -C The real part of the current eigenvalue considered. -C -C IEIG (input) DOUBLE PRECISION -C The imaginary part of the current eigenvalue considered. -C -C METHOD -C -C The function value SB02MR is set to .TRUE. for an unstable -C eigenvalue and to .FALSE., otherwise. -C -C REFERENCES -C -C None. -C -C NUMERICAL ASPECTS -C -C None. -C -C CONTRIBUTOR -C -C V. Sima, Katholieke Univ. Leuven, Belgium, Aug. 1997. -C -C REVISIONS -C -C - -C -C KEYWORDS -C -C Algebraic Riccati equation, closed loop system, continuous-time -C system, optimal regulator, Schur form. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO - PARAMETER ( ZERO = 0.0D0 ) -C .. Scalar Arguments .. - DOUBLE PRECISION IEIG, REIG -C .. Executable Statements .. -C - SB02MR = REIG.GE.ZERO -C - RETURN -C *** Last line of SB02MR *** - END
--- a/extra/control-devel/devel/dksyn/SB02MS.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,79 +0,0 @@ - LOGICAL FUNCTION SB02MS( REIG, IEIG ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To select the unstable eigenvalues for solving the discrete-time -C algebraic Riccati equation. -C -C ARGUMENTS -C -C Input/Output Parameters -C -C REIG (input) DOUBLE PRECISION -C The real part of the current eigenvalue considered. -C -C IEIG (input) DOUBLE PRECISION -C The imaginary part of the current eigenvalue considered. -C -C METHOD -C -C The function value SB02MS is set to .TRUE. for an unstable -C eigenvalue (i.e., with modulus greater than or equal to one) and -C to .FALSE., otherwise. -C -C REFERENCES -C -C None. -C -C NUMERICAL ASPECTS -C -C None. -C -C CONTRIBUTOR -C -C V. Sima, Katholieke Univ. Leuven, Belgium, Aug. 1997. -C -C REVISIONS -C -C - -C -C KEYWORDS -C -C Algebraic Riccati equation, closed loop system, discrete-time -C system, optimal regulator, Schur form. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D0 ) -C .. Scalar Arguments .. - DOUBLE PRECISION IEIG, REIG -C .. External Functions .. - DOUBLE PRECISION DLAPY2 - EXTERNAL DLAPY2 -C .. Executable Statements .. -C - SB02MS = DLAPY2( REIG, IEIG ).GE.ONE -C - RETURN -C *** Last line of SB02MS *** - END
--- a/extra/control-devel/devel/dksyn/SB02MV.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,75 +0,0 @@ - LOGICAL FUNCTION SB02MV( REIG, IEIG ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To select the stable eigenvalues for solving the continuous-time -C algebraic Riccati equation. -C -C ARGUMENTS -C -C Input/Output Parameters -C -C REIG (input) DOUBLE PRECISION -C The real part of the current eigenvalue considered. -C -C IEIG (input) DOUBLE PRECISION -C The imaginary part of the current eigenvalue considered. -C -C METHOD -C -C The function value SB02MV is set to .TRUE. for a stable eigenvalue -C and to .FALSE., otherwise. -C -C REFERENCES -C -C None. -C -C NUMERICAL ASPECTS -C -C None. -C -C CONTRIBUTOR -C -C V. Sima, Katholieke Univ. Leuven, Belgium, Aug. 1997. -C -C REVISIONS -C -C - -C -C KEYWORDS -C -C Algebraic Riccati equation, closed loop system, continuous-time -C system, optimal regulator, Schur form. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO - PARAMETER ( ZERO = 0.0D0 ) -C .. Scalar Arguments .. - DOUBLE PRECISION IEIG, REIG -C .. Executable Statements .. -C - SB02MV = REIG.LT.ZERO -C - RETURN -C *** Last line of SB02MV *** - END
--- a/extra/control-devel/devel/dksyn/SB02MW.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,79 +0,0 @@ - LOGICAL FUNCTION SB02MW( REIG, IEIG ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To select the stable eigenvalues for solving the discrete-time -C algebraic Riccati equation. -C -C ARGUMENTS -C -C Input/Output Parameters -C -C REIG (input) DOUBLE PRECISION -C The real part of the current eigenvalue considered. -C -C IEIG (input) DOUBLE PRECISION -C The imaginary part of the current eigenvalue considered. -C -C METHOD -C -C The function value SB02MW is set to .TRUE. for a stable -C eigenvalue (i.e., with modulus less than one) and to .FALSE., -C otherwise. -C -C REFERENCES -C -C None. -C -C NUMERICAL ASPECTS -C -C None. -C -C CONTRIBUTOR -C -C V. Sima, Katholieke Univ. Leuven, Belgium, Aug. 1997. -C -C REVISIONS -C -C - -C -C KEYWORDS -C -C Algebraic Riccati equation, closed loop system, discrete-time -C system, optimal regulator, Schur form. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D0 ) -C .. Scalar Arguments .. - DOUBLE PRECISION IEIG, REIG -C .. External Functions .. - DOUBLE PRECISION DLAPY2 - EXTERNAL DLAPY2 -C .. Executable Statements .. -C - SB02MW = DLAPY2( REIG, IEIG ).LT.ONE -C - RETURN -C *** Last line of SB02MW *** - END
--- a/extra/control-devel/devel/dksyn/SB02QD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,804 +0,0 @@ - SUBROUTINE SB02QD( JOB, FACT, TRANA, UPLO, LYAPUN, N, A, LDA, T, - $ LDT, U, LDU, G, LDG, Q, LDQ, X, LDX, SEP, - $ RCOND, FERR, IWORK, DWORK, LDWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To estimate the conditioning and compute an error bound on the -C solution of the real continuous-time matrix algebraic Riccati -C equation -C -C op(A)'*X + X*op(A) + Q - X*G*X = 0, (1) -C -C where op(A) = A or A' (A**T) and Q, G are symmetric (Q = Q**T, -C G = G**T). The matrices A, Q and G are N-by-N and the solution X -C is N-by-N. -C -C ARGUMENTS -C -C Mode Parameters -C -C JOB CHARACTER*1 -C Specifies the computation to be performed, as follows: -C = 'C': Compute the reciprocal condition number only; -C = 'E': Compute the error bound only; -C = 'B': Compute both the reciprocal condition number and -C the error bound. -C -C FACT CHARACTER*1 -C Specifies whether or not the real Schur factorization of -C the matrix Ac = A - G*X (if TRANA = 'N') or Ac = A - X*G -C (if TRANA = 'T' or 'C') is supplied on entry, as follows: -C = 'F': On entry, T and U (if LYAPUN = 'O') contain the -C factors from the real Schur factorization of the -C matrix Ac; -C = 'N': The Schur factorization of Ac will be computed -C and the factors will be stored in T and U (if -C LYAPUN = 'O'). -C -C TRANA CHARACTER*1 -C Specifies the form of op(A) to be used, as follows: -C = 'N': op(A) = A (No transpose); -C = 'T': op(A) = A**T (Transpose); -C = 'C': op(A) = A**T (Conjugate transpose = Transpose). -C -C UPLO CHARACTER*1 -C Specifies which part of the symmetric matrices Q and G is -C to be used, as follows: -C = 'U': Upper triangular part; -C = 'L': Lower triangular part. -C -C LYAPUN CHARACTER*1 -C Specifies whether or not the original Lyapunov equations -C should be solved in the iterative estimation process, -C as follows: -C = 'O': Solve the original Lyapunov equations, updating -C the right-hand sides and solutions with the -C matrix U, e.g., RHS <-- U'*RHS*U; -C = 'R': Solve reduced Lyapunov equations only, without -C updating the right-hand sides and solutions. -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the matrices A, X, Q, and G. N >= 0. -C -C A (input) DOUBLE PRECISION array, dimension (LDA,N) -C If FACT = 'N' or LYAPUN = 'O', the leading N-by-N part of -C this array must contain the matrix A. -C If FACT = 'F' and LYAPUN = 'R', A is not referenced. -C -C LDA INTEGER -C The leading dimension of the array A. -C LDA >= max(1,N), if FACT = 'N' or LYAPUN = 'O'; -C LDA >= 1, if FACT = 'F' and LYAPUN = 'R'. -C -C T (input or output) DOUBLE PRECISION array, dimension -C (LDT,N) -C If FACT = 'F', then T is an input argument and on entry, -C the leading N-by-N upper Hessenberg part of this array -C must contain the upper quasi-triangular matrix T in Schur -C canonical form from a Schur factorization of Ac (see -C argument FACT). -C If FACT = 'N', then T is an output argument and on exit, -C if INFO = 0 or INFO = N+1, the leading N-by-N upper -C Hessenberg part of this array contains the upper quasi- -C triangular matrix T in Schur canonical form from a Schur -C factorization of Ac (see argument FACT). -C -C LDT INTEGER -C The leading dimension of the array T. LDT >= max(1,N). -C -C U (input or output) DOUBLE PRECISION array, dimension -C (LDU,N) -C If LYAPUN = 'O' and FACT = 'F', then U is an input -C argument and on entry, the leading N-by-N part of this -C array must contain the orthogonal matrix U from a real -C Schur factorization of Ac (see argument FACT). -C If LYAPUN = 'O' and FACT = 'N', then U is an output -C argument and on exit, if INFO = 0 or INFO = N+1, it -C contains the orthogonal N-by-N matrix from a real Schur -C factorization of Ac (see argument FACT). -C If LYAPUN = 'R', the array U is not referenced. -C -C LDU INTEGER -C The leading dimension of the array U. -C LDU >= 1, if LYAPUN = 'R'; -C LDU >= MAX(1,N), if LYAPUN = 'O'. -C -C G (input) DOUBLE PRECISION array, dimension (LDG,N) -C If UPLO = 'U', the leading N-by-N upper triangular part of -C this array must contain the upper triangular part of the -C matrix G. -C If UPLO = 'L', the leading N-by-N lower triangular part of -C this array must contain the lower triangular part of the -C matrix G. _ -C Matrix G should correspond to G in the "reduced" Riccati -C equation (with matrix T, instead of A), if LYAPUN = 'R'. -C See METHOD. -C -C LDG INTEGER -C The leading dimension of the array G. LDG >= max(1,N). -C -C Q (input) DOUBLE PRECISION array, dimension (LDQ,N) -C If UPLO = 'U', the leading N-by-N upper triangular part of -C this array must contain the upper triangular part of the -C matrix Q. -C If UPLO = 'L', the leading N-by-N lower triangular part of -C this array must contain the lower triangular part of the -C matrix Q. _ -C Matrix Q should correspond to Q in the "reduced" Riccati -C equation (with matrix T, instead of A), if LYAPUN = 'R'. -C See METHOD. -C -C LDQ INTEGER -C The leading dimension of the array Q. LDQ >= max(1,N). -C -C X (input) DOUBLE PRECISION array, dimension (LDX,N) -C The leading N-by-N part of this array must contain the -C symmetric solution matrix of the original Riccati -C equation (with matrix A), if LYAPUN = 'O', or of the -C "reduced" Riccati equation (with matrix T), if -C LYAPUN = 'R'. See METHOD. -C -C LDX INTEGER -C The leading dimension of the array X. LDX >= max(1,N). -C -C SEP (output) DOUBLE PRECISION -C If JOB = 'C' or JOB = 'B', the estimated quantity -C sep(op(Ac),-op(Ac)'). -C If N = 0, or X = 0, or JOB = 'E', SEP is not referenced. -C -C RCOND (output) DOUBLE PRECISION -C If JOB = 'C' or JOB = 'B', an estimate of the reciprocal -C condition number of the continuous-time Riccati equation. -C If N = 0 or X = 0, RCOND is set to 1 or 0, respectively. -C If JOB = 'E', RCOND is not referenced. -C -C FERR (output) DOUBLE PRECISION -C If JOB = 'E' or JOB = 'B', an estimated forward error -C bound for the solution X. If XTRUE is the true solution, -C FERR bounds the magnitude of the largest entry in -C (X - XTRUE) divided by the magnitude of the largest entry -C in X. -C If N = 0 or X = 0, FERR is set to 0. -C If JOB = 'C', FERR is not referenced. -C -C Workspace -C -C IWORK INTEGER array, dimension (N*N) -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C On exit, if INFO = 0 or INFO = N+1, DWORK(1) returns the -C optimal value of LDWORK. -C -C LDWORK INTEGER -C The dimension of the array DWORK. -C Let LWA = N*N, if LYAPUN = 'O' and JOB = 'E' or 'B'; -C LWA = 0, otherwise. -C If FACT = 'N', then -C LDWORK = MAX(1, 5*N, 2*N*N), if JOB = 'C'; -C LDWORK = MAX(1, LWA + 5*N, 4*N*N ), if JOB = 'E', 'B'. -C If FACT = 'F', then -C LDWORK = MAX(1, 2*N*N), if JOB = 'C'; -C LDWORK = MAX(1, 4*N*N ), if JOB = 'E' or 'B'. -C For good performance, LDWORK must generally be larger. -C -C Error indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C > 0: if INFO = i, i <= N, the QR algorithm failed to -C complete the reduction of the matrix Ac to Schur -C canonical form (see LAPACK Library routine DGEES); -C on exit, the matrix T(i+1:N,i+1:N) contains the -C partially converged Schur form, and DWORK(i+1:N) and -C DWORK(N+i+1:2*N) contain the real and imaginary -C parts, respectively, of the converged eigenvalues; -C this error is unlikely to appear; -C = N+1: if the matrices T and -T' have common or very -C close eigenvalues; perturbed values were used to -C solve Lyapunov equations, but the matrix T, if given -C (for FACT = 'F'), is unchanged. -C -C METHOD -C -C The condition number of the Riccati equation is estimated as -C -C cond = ( norm(Theta)*norm(A) + norm(inv(Omega))*norm(Q) + -C norm(Pi)*norm(G) ) / norm(X), -C -C where Omega, Theta and Pi are linear operators defined by -C -C Omega(W) = op(Ac)'*W + W*op(Ac), -C Theta(W) = inv(Omega(op(W)'*X + X*op(W))), -C Pi(W) = inv(Omega(X*W*X)), -C -C and Ac = A - G*X (if TRANA = 'N') or Ac = A - X*G (if TRANA = 'T' -C or 'C'). Note that the Riccati equation (1) is equivalent to -C _ _ _ _ _ _ -C op(T)'*X + X*op(T) + Q + X*G*X = 0, (2) -C _ _ _ -C where X = U'*X*U, Q = U'*Q*U, and G = U'*G*U, with U the -C orthogonal matrix reducing Ac to a real Schur form, T = U'*Ac*U. -C -C The routine estimates the quantities -C -C sep(op(Ac),-op(Ac)') = 1 / norm(inv(Omega)), -C -C norm(Theta) and norm(Pi) using 1-norm condition estimator. -C -C The forward error bound is estimated using a practical error bound -C similar to the one proposed in [2]. -C -C REFERENCES -C -C [1] Ghavimi, A.R. and Laub, A.J. -C Backward error, sensitivity, and refinement of computed -C solutions of algebraic Riccati equations. -C Numerical Linear Algebra with Applications, vol. 2, pp. 29-49, -C 1995. -C -C [2] Higham, N.J. -C Perturbation theory and backward error for AX-XB=C. -C BIT, vol. 33, pp. 124-136, 1993. -C -C [3] Petkov, P.Hr., Konstantinov, M.M., and Mehrmann, V. -C DGRSVX and DMSRIC: Fortran 77 subroutines for solving -C continuous-time matrix algebraic Riccati equations with -C condition and accuracy estimates. -C Preprint SFB393/98-16, Fak. f. Mathematik, Tech. Univ. -C Chemnitz, May 1998. -C -C NUMERICAL ASPECTS -C 3 -C The algorithm requires 0(N ) operations. -C The accuracy of the estimates obtained depends on the solution -C accuracy and on the properties of the 1-norm estimator. -C -C FURTHER COMMENTS -C -C The option LYAPUN = 'R' may occasionally produce slightly worse -C or better estimates, and it is much faster than the option 'O'. -C When SEP is computed and it is zero, the routine returns -C immediately, with RCOND and FERR (if requested) set to 0 and 1, -C respectively. In this case, the equation is singular. -C -C CONTRIBUTOR -C -C P.Hr. Petkov, Technical University of Sofia, December 1998. -C V. Sima, Katholieke Univ. Leuven, Belgium, February 1999. -C -C REVISIONS -C -C V. Sima, Research Institute for Informatics, Bucharest, Oct. 2004. -C -C KEYWORDS -C -C Conditioning, error estimates, orthogonal transformation, -C real Schur form, Riccati equation. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE, TWO, FOUR, HALF - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0, - $ FOUR = 4.0D+0, HALF = 0.5D+0 ) -C .. -C .. Scalar Arguments .. - CHARACTER FACT, JOB, LYAPUN, TRANA, UPLO - INTEGER INFO, LDA, LDG, LDQ, LDT, LDU, LDWORK, LDX, N - DOUBLE PRECISION FERR, RCOND, SEP -C .. -C .. Array Arguments .. - INTEGER IWORK( * ) - DOUBLE PRECISION A( LDA, * ), DWORK( * ), G( LDG, * ), - $ Q( LDQ, * ), T( LDT, * ), U( LDU, * ), - $ X( LDX, * ) -C .. -C .. Local Scalars .. - LOGICAL JOBB, JOBC, JOBE, LOWER, NEEDAC, NOFACT, - $ NOTRNA, UPDATE - CHARACTER LOUP, SJOB, TRANAT - INTEGER I, IABS, INFO2, IRES, ITMP, IXBS, J, JJ, JX, - $ KASE, LDW, LWA, NN, SDIM, WRKOPT - DOUBLE PRECISION ANORM, BIGNUM, DENOM, EPS, EPSN, EST, GNORM, - $ PINORM, QNORM, SCALE, SIG, TEMP, THNORM, TMAX, - $ XANORM, XNORM -C .. -C .. Local Arrays .. - LOGICAL BWORK( 1 ) -C .. -C .. External Functions .. - LOGICAL LSAME, SELECT - DOUBLE PRECISION DLAMCH, DLANGE, DLANHS, DLANSY - EXTERNAL DLAMCH, DLANGE, DLANHS, DLANSY, LSAME, SELECT -C .. -C .. External Subroutines .. - EXTERNAL DAXPY, DCOPY, DGEES, DLACON, DLACPY, DSCAL, - $ DSYMM, DSYR2K, MA02ED, MB01RU, MB01UD, SB03MY, - $ SB03QX, SB03QY, XERBLA -C .. -C .. Intrinsic Functions .. - INTRINSIC ABS, DBLE, INT, MAX, MIN -C .. -C .. Executable Statements .. -C -C Decode and Test input parameters. -C - JOBC = LSAME( JOB, 'C' ) - JOBE = LSAME( JOB, 'E' ) - JOBB = LSAME( JOB, 'B' ) - NOFACT = LSAME( FACT, 'N' ) - NOTRNA = LSAME( TRANA, 'N' ) - LOWER = LSAME( UPLO, 'L' ) - UPDATE = LSAME( LYAPUN, 'O' ) -C - NEEDAC = UPDATE .AND. .NOT.JOBC -C - NN = N*N - IF( NEEDAC ) THEN - LWA = NN - ELSE - LWA = 0 - END IF -C - IF( NOFACT ) THEN - IF( JOBC ) THEN - LDW = MAX( 5*N, 2*NN ) - ELSE - LDW = MAX( LWA + 5*N, 4*NN ) - END IF - ELSE - IF( JOBC ) THEN - LDW = 2*NN - ELSE - LDW = 4*NN - END IF - END IF -C - INFO = 0 - IF( .NOT.( JOBB .OR. JOBC .OR. JOBE ) ) THEN - INFO = -1 - ELSE IF( .NOT.( NOFACT .OR. LSAME( FACT, 'F' ) ) ) THEN - INFO = -2 - ELSE IF( .NOT.( NOTRNA .OR. LSAME( TRANA, 'T' ) .OR. - $ LSAME( TRANA, 'C' ) ) ) THEN - INFO = -3 - ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN - INFO = -4 - ELSE IF( .NOT.( UPDATE .OR. LSAME( LYAPUN, 'R' ) ) ) THEN - INFO = -5 - ELSE IF( N.LT.0 ) THEN - INFO = -6 - ELSE IF( LDA.LT.1 .OR. - $ ( LDA.LT.N .AND. ( UPDATE .OR. NOFACT ) ) ) THEN - INFO = -8 - ELSE IF( LDT.LT.MAX( 1, N ) ) THEN - INFO = -10 - ELSE IF( LDU.LT.1 .OR. ( LDU.LT.N .AND. UPDATE ) ) THEN - INFO = -12 - ELSE IF( LDG.LT.MAX( 1, N ) ) THEN - INFO = -14 - ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN - INFO = -16 - ELSE IF( LDX.LT.MAX( 1, N ) ) THEN - INFO = -18 - ELSE IF( LDWORK.LT.MAX( 1, LDW ) ) THEN - INFO = -24 - END IF -C - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'SB02QD', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF( N.EQ.0 ) THEN - IF( .NOT.JOBE ) - $ RCOND = ONE - IF( .NOT.JOBC ) - $ FERR = ZERO - DWORK( 1 ) = ONE - RETURN - END IF -C -C Compute the 1-norm of the matrix X. -C - XNORM = DLANSY( '1-norm', UPLO, N, X, LDX, DWORK ) - IF( XNORM.EQ.ZERO ) THEN -C -C The solution is zero. -C - IF( .NOT.JOBE ) - $ RCOND = ZERO - IF( .NOT.JOBC ) - $ FERR = ZERO - DWORK( 1 ) = DBLE( N ) - RETURN - END IF -C -C Workspace usage. -C - IXBS = 0 - ITMP = IXBS + NN - IABS = ITMP + NN - IRES = IABS + NN -C -C Workspace: LWR, where -C LWR = N*N, if LYAPUN = 'O' and JOB = 'E' or 'B', or -C FACT = 'N', -C LWR = 0, otherwise. -C - IF( NEEDAC .OR. NOFACT ) THEN -C - CALL DLACPY( 'Full', N, N, A, LDA, DWORK, N ) - IF( NOTRNA ) THEN -C -C Compute Ac = A - G*X. -C - CALL DSYMM( 'Left', UPLO, N, N, -ONE, G, LDG, X, LDX, ONE, - $ DWORK, N ) - ELSE -C -C Compute Ac = A - X*G. -C - CALL DSYMM( 'Right', UPLO, N, N, -ONE, G, LDG, X, LDX, ONE, - $ DWORK, N ) - END IF -C - WRKOPT = DBLE( NN ) - IF( NOFACT ) - $ CALL DLACPY( 'Full', N, N, DWORK, N, T, LDT ) - ELSE - WRKOPT = DBLE( N ) - END IF -C - IF( NOFACT ) THEN -C -C Compute the Schur factorization of Ac, Ac = U*T*U'. -C Workspace: need LWA + 5*N; -C prefer larger; -C LWA = N*N, if LYAPUN = 'O' and JOB = 'E' or 'B'; -C LWA = 0, otherwise. -C (Note: Comments in the code beginning "Workspace:" describe the -C minimal amount of real workspace needed at that point in the -C code, as well as the preferred amount for good performance.) -C - IF( UPDATE ) THEN - SJOB = 'V' - ELSE - SJOB = 'N' - END IF - CALL DGEES( SJOB, 'Not ordered', SELECT, N, T, LDT, SDIM, - $ DWORK( LWA+1 ), DWORK( LWA+N+1 ), U, LDU, - $ DWORK( LWA+2*N+1 ), LDWORK-LWA-2*N, BWORK, INFO ) - IF( INFO.GT.0 ) THEN - IF( LWA.GT.0 ) - $ CALL DCOPY( 2*N, DWORK( LWA+1 ), 1, DWORK, 1 ) - RETURN - END IF -C - WRKOPT = MAX( WRKOPT, INT( DWORK( LWA+2*N+1 ) ) + LWA + 2*N ) - END IF - IF( NEEDAC ) - $ CALL DLACPY( 'Full', N, N, DWORK, N, DWORK( IABS+1 ), N ) -C - IF( NOTRNA ) THEN - TRANAT = 'T' - ELSE - TRANAT = 'N' - END IF -C - IF( .NOT.JOBE ) THEN -C -C Estimate sep(op(Ac),-op(Ac)') = sep(op(T),-op(T)') and -C norm(Theta). -C Workspace LWA + 2*N*N. -C - CALL SB03QY( 'Both', TRANA, LYAPUN, N, T, LDT, U, LDU, X, LDX, - $ SEP, THNORM, IWORK, DWORK, LDWORK, INFO ) -C - WRKOPT = MAX( WRKOPT, LWA + 2*NN ) -C -C Return if the equation is singular. -C - IF( SEP.EQ.ZERO ) THEN - RCOND = ZERO - IF( JOBB ) - $ FERR = ONE - DWORK( 1 ) = DBLE( WRKOPT ) - RETURN - END IF -C -C Estimate norm(Pi). -C Workspace LWA + 2*N*N. -C - KASE = 0 -C -C REPEAT - 10 CONTINUE - CALL DLACON( NN, DWORK( ITMP+1 ), DWORK, IWORK, EST, KASE ) - IF( KASE.NE.0 ) THEN -C -C Select the triangular part of symmetric matrix to be used. -C - IF( DLANSY( '1-norm', 'Upper', N, DWORK, N, DWORK( ITMP+1 )) - $ .GE. - $ DLANSY( '1-norm', 'Lower', N, DWORK, N, DWORK( ITMP+1 )) - $ ) THEN - LOUP = 'U' - ELSE - LOUP = 'L' - END IF -C -C Compute RHS = X*W*X. -C - CALL MB01RU( LOUP, 'No Transpose', N, N, ZERO, ONE, DWORK, - $ N, X, LDX, DWORK, N, DWORK( ITMP+1 ), NN, - $ INFO2 ) - CALL DSCAL( N, HALF, DWORK, N+1 ) -C - IF( UPDATE ) THEN -C -C Transform the right-hand side: RHS := U'*RHS*U. -C - CALL MB01RU( LOUP, 'Transpose', N, N, ZERO, ONE, DWORK, - $ N, U, LDU, DWORK, N, DWORK( ITMP+1 ), NN, - $ INFO2 ) - CALL DSCAL( N, HALF, DWORK, N+1 ) - END IF -C -C Fill in the remaining triangle of the symmetric matrix. -C - CALL MA02ED( LOUP, N, DWORK, N ) -C - IF( KASE.EQ.1 ) THEN -C -C Solve op(T)'*Y + Y*op(T) = scale*RHS. -C - CALL SB03MY( TRANA, N, T, LDT, DWORK, N, SCALE, INFO2 ) - ELSE -C -C Solve op(T)*W + W*op(T)' = scale*RHS. -C - CALL SB03MY( TRANAT, N, T, LDT, DWORK, N, SCALE, INFO2 ) - END IF -C - IF( UPDATE ) THEN -C -C Transform back to obtain the solution: Z := U*Z*U', with -C Z = Y or Z = W. -C - CALL MB01RU( LOUP, 'No transpose', N, N, ZERO, ONE, - $ DWORK, N, U, LDU, DWORK, N, DWORK( ITMP+1 ), - $ NN, INFO2 ) - CALL DSCAL( N, HALF, DWORK, N+1 ) -C -C Fill in the remaining triangle of the symmetric matrix. -C - CALL MA02ED( LOUP, N, DWORK, N ) - END IF - GO TO 10 - END IF -C UNTIL KASE = 0 -C - IF( EST.LT.SCALE ) THEN - PINORM = EST / SCALE - ELSE - BIGNUM = ONE / DLAMCH( 'Safe minimum' ) - IF( EST.LT.SCALE*BIGNUM ) THEN - PINORM = EST / SCALE - ELSE - PINORM = BIGNUM - END IF - END IF -C -C Compute the 1-norm of A or T. -C - IF( UPDATE ) THEN - ANORM = DLANGE( '1-norm', N, N, A, LDA, DWORK ) - ELSE - ANORM = DLANHS( '1-norm', N, T, LDT, DWORK ) - END IF -C -C Compute the 1-norms of the matrices Q and G. -C - QNORM = DLANSY( '1-norm', UPLO, N, Q, LDQ, DWORK ) - GNORM = DLANSY( '1-norm', UPLO, N, G, LDG, DWORK ) -C -C Estimate the reciprocal condition number. -C - TMAX = MAX( SEP, XNORM, ANORM, GNORM ) - IF( TMAX.LE.ONE ) THEN - TEMP = SEP*XNORM - DENOM = QNORM + ( SEP*ANORM )*THNORM + - $ ( SEP*GNORM )*PINORM - ELSE - TEMP = ( SEP / TMAX )*( XNORM / TMAX ) - DENOM = ( ( ONE / TMAX )*( QNORM / TMAX ) ) + - $ ( ( SEP / TMAX )*( ANORM / TMAX ) )*THNORM + - $ ( ( SEP / TMAX )*( GNORM / TMAX ) )*PINORM - END IF - IF( TEMP.GE.DENOM ) THEN - RCOND = ONE - ELSE - RCOND = TEMP / DENOM - END IF - END IF -C - IF( .NOT.JOBC ) THEN -C -C Form a triangle of the residual matrix -C R = op(A)'*X + X*op(A) + Q - X*G*X, -C or _ _ _ _ _ _ -C R = op(T)'*X + X*op(T) + Q + X*G*X, -C exploiting the symmetry. -C Workspace 4*N*N. -C - IF( UPDATE ) THEN - CALL DLACPY( UPLO, N, N, Q, LDQ, DWORK( IRES+1 ), N ) - CALL DSYR2K( UPLO, TRANAT, N, N, ONE, A, LDA, X, LDX, ONE, - $ DWORK( IRES+1 ), N ) - SIG = -ONE - ELSE - CALL MB01UD( 'Right', TRANA, N, N, ONE, T, LDT, X, LDX, - $ DWORK( IRES+1 ), N, INFO2 ) - JJ = IRES + 1 - IF( LOWER ) THEN - DO 20 J = 1, N - CALL DAXPY( N-J+1, ONE, DWORK( JJ ), N, DWORK( JJ ), - $ 1 ) - CALL DAXPY( N-J+1, ONE, Q( J, J ), 1, DWORK( JJ ), 1 ) - JJ = JJ + N + 1 - 20 CONTINUE - ELSE - DO 30 J = 1, N - CALL DAXPY( J, ONE, DWORK( IRES+J ), N, DWORK( JJ ), - $ 1 ) - CALL DAXPY( J, ONE, Q( 1, J ), 1, DWORK( JJ ), 1 ) - JJ = JJ + N - 30 CONTINUE - END IF - SIG = ONE - END IF - CALL MB01RU( UPLO, TRANAT, N, N, ONE, SIG, DWORK( IRES+1 ), - $ N, X, LDX, G, LDG, DWORK( ITMP+1 ), NN, INFO2 ) -C -C Get the machine precision. -C - EPS = DLAMCH( 'Epsilon' ) - EPSN = EPS*DBLE( N + 4 ) - TEMP = EPS*FOUR -C -C Add to abs(R) a term that takes account of rounding errors in -C forming R: -C abs(R) := abs(R) + EPS*(4*abs(Q) + (n+4)*(abs(op(Ac))'*abs(X) -C + abs(X)*abs(op(Ac))) + 2*(n+1)*abs(X)*abs(G)*abs(X)), -C or _ _ -C abs(R) := abs(R) + EPS*(4*abs(Q) + (n+4)*(abs(op(T))'*abs(X) -C _ _ _ _ -C + abs(X)*abs(op(T))) + 2*(n+1)*abs(X)*abs(G)*abs(X)), -C where EPS is the machine precision. -C - DO 50 J = 1, N - DO 40 I = 1, N - DWORK( IXBS+(J-1)*N+I ) = ABS( X( I, J ) ) - 40 CONTINUE - 50 CONTINUE -C - IF( LOWER ) THEN - DO 70 J = 1, N - DO 60 I = J, N - DWORK( IRES+(J-1)*N+I ) = TEMP*ABS( Q( I, J ) ) + - $ ABS( DWORK( IRES+(J-1)*N+I ) ) - 60 CONTINUE - 70 CONTINUE - ELSE - DO 90 J = 1, N - DO 80 I = 1, J - DWORK( IRES+(J-1)*N+I ) = TEMP*ABS( Q( I, J ) ) + - $ ABS( DWORK( IRES+(J-1)*N+I ) ) - 80 CONTINUE - 90 CONTINUE - END IF -C - IF( UPDATE ) THEN -C - DO 110 J = 1, N - DO 100 I = 1, N - DWORK( IABS+(J-1)*N+I ) = - $ ABS( DWORK( IABS+(J-1)*N+I ) ) - 100 CONTINUE - 110 CONTINUE -C - CALL DSYR2K( UPLO, TRANAT, N, N, EPSN, DWORK( IABS+1 ), N, - $ DWORK( IXBS+1 ), N, ONE, DWORK( IRES+1 ), N ) - ELSE -C - DO 130 J = 1, N - DO 120 I = 1, MIN( J+1, N ) - DWORK( IABS+(J-1)*N+I ) = ABS( T( I, J ) ) - 120 CONTINUE - 130 CONTINUE -C - CALL MB01UD( 'Left', TRANAT, N, N, EPSN, DWORK( IABS+1 ), N, - $ DWORK( IXBS+1), N, DWORK( ITMP+1 ), N, INFO2 ) - JJ = IRES + 1 - JX = ITMP + 1 - IF( LOWER ) THEN - DO 140 J = 1, N - CALL DAXPY( N-J+1, ONE, DWORK( JX ), N, DWORK( JX ), - $ 1 ) - CALL DAXPY( N-J+1, ONE, DWORK( JX ), 1, DWORK( JJ ), - $ 1 ) - JJ = JJ + N + 1 - JX = JX + N + 1 - 140 CONTINUE - ELSE - DO 150 J = 1, N - CALL DAXPY( J, ONE, DWORK( ITMP+J ), N, DWORK( JX ), - $ 1 ) - CALL DAXPY( J, ONE, DWORK( JX ), 1, DWORK( JJ ), 1 ) - JJ = JJ + N - JX = JX + N - 150 CONTINUE - END IF - END IF -C - IF( LOWER ) THEN - DO 170 J = 1, N - DO 160 I = J, N - DWORK( IABS+(J-1)*N+I ) = ABS( G( I, J ) ) - 160 CONTINUE - 170 CONTINUE - ELSE - DO 190 J = 1, N - DO 180 I = 1, J - DWORK( IABS+(J-1)*N+I ) = ABS( G( I, J ) ) - 180 CONTINUE - 190 CONTINUE - END IF -C - CALL MB01RU( UPLO, TRANA, N, N, ONE, EPS*DBLE( 2*( N + 1 ) ), - $ DWORK( IRES+1 ), N, DWORK( IXBS+1), N, - $ DWORK( IABS+1 ), N, DWORK( ITMP+1 ), NN, INFO2 ) -C - WRKOPT = MAX( WRKOPT, 4*NN ) -C -C Compute forward error bound, using matrix norm estimator. -C Workspace 4*N*N. -C - XANORM = DLANSY( 'Max', UPLO, N, X, LDX, DWORK ) -C - CALL SB03QX( TRANA, UPLO, LYAPUN, N, XANORM, T, LDT, U, LDU, - $ DWORK( IRES+1 ), N, FERR, IWORK, DWORK, IRES, - $ INFO ) - END IF -C - DWORK( 1 ) = DBLE( WRKOPT ) - RETURN -C -C *** Last line of SB02QD *** - END
--- a/extra/control-devel/devel/dksyn/SB02RD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,1133 +0,0 @@ - SUBROUTINE SB02RD( JOB, DICO, HINV, TRANA, UPLO, SCAL, SORT, FACT, - $ LYAPUN, N, A, LDA, T, LDT, V, LDV, G, LDG, Q, - $ LDQ, X, LDX, SEP, RCOND, FERR, WR, WI, S, LDS, - $ IWORK, DWORK, LDWORK, BWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To solve for X either the continuous-time algebraic Riccati -C equation -C -1 -C Q + op(A)'*X + X*op(A) - X*op(B)*R op(B)'*X = 0, (1) -C -C or the discrete-time algebraic Riccati equation -C -1 -C X = op(A)'*X*op(A) - op(A)'*X*op(B)*(R + op(B)'*X*op(B)) * -C op(B)'*X*op(A) + Q, (2) -C -C where op(M) = M or M' (M**T), A, op(B), Q, and R are N-by-N, -C N-by-M, N-by-N, and M-by-M matrices respectively, with Q symmetric -C and R symmetric nonsingular; X is an N-by-N symmetric matrix. -C -1 -C The matrix G = op(B)*R *op(B)' must be provided on input, instead -C of B and R, that is, the continuous-time equation -C -C Q + op(A)'*X + X*op(A) - X*G*X = 0, (3) -C -C or the discrete-time equation -C -1 -C Q + op(A)'*X*(I_n + G*X) *op(A) - X = 0, (4) -C -C are solved, where G is an N-by-N symmetric matrix. SLICOT Library -C routine SB02MT should be used to compute G, given B and R. SB02MT -C also enables to solve Riccati equations corresponding to optimal -C problems with coupling terms. -C -C The routine also returns the computed values of the closed-loop -C spectrum of the optimal system, i.e., the stable eigenvalues -C lambda(1),...,lambda(N) of the corresponding Hamiltonian or -C symplectic matrix associated to the optimal problem. It is assumed -C that the matrices A, G, and Q are such that the associated -C Hamiltonian or symplectic matrix has N stable eigenvalues, i.e., -C with negative real parts, in the continuous-time case, and with -C moduli less than one, in the discrete-time case. -C -C Optionally, estimates of the conditioning and error bound on the -C solution of the Riccati equation (3) or (4) are returned. -C -C ARGUMENTS -C -C Mode Parameters -C -C JOB CHARACTER*1 -C Specifies the computation to be performed, as follows: -C = 'X': Compute the solution only; -C = 'C': Compute the reciprocal condition number only; -C = 'E': Compute the error bound only; -C = 'A': Compute all: the solution, reciprocal condition -C number, and the error bound. -C -C DICO CHARACTER*1 -C Specifies the type of Riccati equation to be solved or -C analyzed, as follows: -C = 'C': Equation (3), continuous-time case; -C = 'D': Equation (4), discrete-time case. -C -C HINV CHARACTER*1 -C If DICO = 'D' and JOB = 'X' or JOB = 'A', specifies which -C symplectic matrix is to be constructed, as follows: -C = 'D': The matrix H in (6) (see METHOD) is constructed; -C = 'I': The inverse of the matrix H in (6) is constructed. -C HINV is not used if DICO = 'C', or JOB = 'C' or 'E'. -C -C TRANA CHARACTER*1 -C Specifies the form of op(A) to be used, as follows: -C = 'N': op(A) = A (No transpose); -C = 'T': op(A) = A**T (Transpose); -C = 'C': op(A) = A**T (Conjugate transpose = Transpose). -C -C UPLO CHARACTER*1 -C Specifies which triangle of the matrices G and Q is -C stored, as follows: -C = 'U': Upper triangle is stored; -C = 'L': Lower triangle is stored. -C -C SCAL CHARACTER*1 -C If JOB = 'X' or JOB = 'A', specifies whether or not a -C scaling strategy should be used, as follows: -C = 'G': General scaling should be used; -C = 'N': No scaling should be used. -C SCAL is not used if JOB = 'C' or 'E'. -C -C SORT CHARACTER*1 -C If JOB = 'X' or JOB = 'A', specifies which eigenvalues -C should be obtained in the top of the Schur form, as -C follows: -C = 'S': Stable eigenvalues come first; -C = 'U': Unstable eigenvalues come first. -C SORT is not used if JOB = 'C' or 'E'. -C -C FACT CHARACTER*1 -C If JOB <> 'X', specifies whether or not a real Schur -C factorization of the closed-loop system matrix Ac is -C supplied on entry, as follows: -C = 'F': On entry, T and V contain the factors from a real -C Schur factorization of the matrix Ac; -C = 'N': A Schur factorization of Ac will be computed -C and the factors will be stored in T and V. -C For a continuous-time system, the matrix Ac is given by -C Ac = A - G*X, if TRANA = 'N', or -C Ac = A - X*G, if TRANA = 'T' or 'C', -C and for a discrete-time system, the matrix Ac is given by -C Ac = inv(I_n + G*X)*A, if TRANA = 'N', or -C Ac = A*inv(I_n + X*G), if TRANA = 'T' or 'C'. -C FACT is not used if JOB = 'X'. -C -C LYAPUN CHARACTER*1 -C If JOB <> 'X', specifies whether or not the original or -C "reduced" Lyapunov equations should be solved for -C estimating reciprocal condition number and/or the error -C bound, as follows: -C = 'O': Solve the original Lyapunov equations, updating -C the right-hand sides and solutions with the -C matrix V, e.g., X <-- V'*X*V; -C = 'R': Solve reduced Lyapunov equations only, without -C updating the right-hand sides and solutions. -C This means that a real Schur form T of Ac appears -C in the equations, instead of Ac. -C LYAPUN is not used if JOB = 'X'. -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the matrices A, Q, G, and X. N >= 0. -C -C A (input) DOUBLE PRECISION array, dimension (LDA,N) -C If JOB = 'X' or JOB = 'A' or FACT = 'N' or LYAPUN = 'O', -C the leading N-by-N part of this array must contain the -C coefficient matrix A of the equation. -C If JOB = 'C' or 'E' and FACT = 'F' and LYAPUN = 'R', A is -C not referenced. -C -C LDA INTEGER -C The leading dimension of the array A. -C LDA >= MAX(1,N), if JOB = 'X' or JOB = 'A' or -C FACT = 'N' or LYAPUN = 'O'. -C LDA >= 1, otherwise. -C -C T (input or output) DOUBLE PRECISION array, dimension -C (LDT,N) -C If JOB <> 'X' and FACT = 'F', then T is an input argument -C and on entry, the leading N-by-N upper Hessenberg part of -C this array must contain the upper quasi-triangular matrix -C T in Schur canonical form from a Schur factorization of Ac -C (see argument FACT). -C If JOB <> 'X' and FACT = 'N', then T is an output argument -C and on exit, if INFO = 0 or INFO = 7, the leading N-by-N -C upper Hessenberg part of this array contains the upper -C quasi-triangular matrix T in Schur canonical form from a -C Schur factorization of Ac (see argument FACT). -C If JOB = 'X', the array T is not referenced. -C -C LDT INTEGER -C The leading dimension of the array T. -C LDT >= 1, if JOB = 'X'; -C LDT >= MAX(1,N), if JOB <> 'X'. -C -C V (input or output) DOUBLE PRECISION array, dimension -C (LDV,N) -C If JOB <> 'X' and FACT = 'F', then V is an input argument -C and on entry, the leading N-by-N part of this array must -C contain the orthogonal matrix V from a real Schur -C factorization of Ac (see argument FACT). -C If JOB <> 'X' and FACT = 'N', then V is an output argument -C and on exit, if INFO = 0 or INFO = 7, the leading N-by-N -C part of this array contains the orthogonal N-by-N matrix -C from a real Schur factorization of Ac (see argument FACT). -C If JOB = 'X', the array V is not referenced. -C -C LDV INTEGER -C The leading dimension of the array V. -C LDV >= 1, if JOB = 'X'; -C LDV >= MAX(1,N), if JOB <> 'X'. -C -C G (input/output) DOUBLE PRECISION array, dimension (LDG,N) -C On entry, the leading N-by-N upper triangular part (if -C UPLO = 'U') or lower triangular part (if UPLO = 'L') of -C this array must contain the upper triangular part or lower -C triangular part, respectively, of the symmetric matrix G. -C On exit, if JOB = 'X' and DICO = 'D', or JOB <> 'X' and -C LYAPUN = 'R', the leading N-by-N part of this array -C contains the symmetric matrix G fully stored. -C If JOB <> 'X' and LYAPUN = 'R', this array is modified -C internally, but restored on exit. -C -C LDG INTEGER -C The leading dimension of the array G. LDG >= MAX(1,N). -C -C Q (input/output) DOUBLE PRECISION array, dimension (LDQ,N) -C On entry, the leading N-by-N upper triangular part (if -C UPLO = 'U') or lower triangular part (if UPLO = 'L') of -C this array must contain the upper triangular part or lower -C triangular part, respectively, of the symmetric matrix Q. -C On exit, if JOB = 'X' and DICO = 'D', or JOB <> 'X' and -C LYAPUN = 'R', the leading N-by-N part of this array -C contains the symmetric matrix Q fully stored. -C If JOB <> 'X' and LYAPUN = 'R', this array is modified -C internally, but restored on exit. -C -C LDQ INTEGER -C The leading dimension of the array Q. LDQ >= MAX(1,N). -C -C X (input or output) DOUBLE PRECISION array, dimension -C (LDX,N) -C If JOB = 'C' or JOB = 'E', then X is an input argument -C and on entry, the leading N-by-N part of this array must -C contain the symmetric solution matrix of the algebraic -C Riccati equation. If LYAPUN = 'R', this array is modified -C internally, but restored on exit; however, it could differ -C from the input matrix at the round-off error level. -C If JOB = 'X' or JOB = 'A', then X is an output argument -C and on exit, if INFO = 0 or INFO >= 6, the leading N-by-N -C part of this array contains the symmetric solution matrix -C X of the algebraic Riccati equation. -C -C LDX INTEGER -C The leading dimension of the array X. LDX >= MAX(1,N). -C -C SEP (output) DOUBLE PRECISION -C If JOB = 'C' or JOB = 'A', and INFO = 0 or INFO = 7, the -C estimated quantity -C sep(op(Ac),-op(Ac)'), if DICO = 'C', or -C sepd(op(Ac),op(Ac)'), if DICO = 'D'. (See METHOD.) -C If JOB = 'C' or JOB = 'A' and X = 0, or JOB = 'E', SEP is -C not referenced. -C If JOB = 'X', and INFO = 0, INFO = 5 or INFO = 7, -C SEP contains the scaling factor used, which should -C multiply the (2,1) submatrix of U to recover X from the -C first N columns of U (see METHOD). If SCAL = 'N', SEP is -C set to 1. -C -C RCOND (output) DOUBLE PRECISION -C If JOB = 'C' or JOB = 'A', and INFO = 0 or INFO = 7, an -C estimate of the reciprocal condition number of the -C algebraic Riccati equation. -C If N = 0 or X = 0, RCOND is set to 1 or 0, respectively. -C If JOB = 'X', or JOB = 'E', RCOND is not referenced. -C -C FERR (output) DOUBLE PRECISION -C If JOB = 'E' or JOB = 'A', and INFO = 0 or INFO = 7, an -C estimated forward error bound for the solution X. If XTRUE -C is the true solution, FERR bounds the magnitude of the -C largest entry in (X - XTRUE) divided by the magnitude of -C the largest entry in X. -C If N = 0 or X = 0, FERR is set to 0. -C If JOB = 'X', or JOB = 'C', FERR is not referenced. -C -C WR (output) DOUBLE PRECISION array, dimension (2*N) -C WI (output) DOUBLE PRECISION array, dimension (2*N) -C If JOB = 'X' or JOB = 'A', and INFO = 0 or INFO >= 5, -C these arrays contain the real and imaginary parts, -C respectively, of the eigenvalues of the 2N-by-2N matrix S, -C ordered as specified by SORT (except for the case -C HINV = 'D', when the order is opposite to that specified -C by SORT). The leading N elements of these arrays contain -C the closed-loop spectrum of the system matrix Ac (see -C argument FACT). Specifically, -C lambda(k) = WR(k) + j*WI(k), for k = 1,2,...,N. -C If JOB = 'C' or JOB = 'E', these arrays are not -C referenced. -C -C S (output) DOUBLE PRECISION array, dimension (LDS,2*N) -C If JOB = 'X' or JOB = 'A', and INFO = 0 or INFO >= 5, the -C leading 2N-by-2N part of this array contains the ordered -C real Schur form S of the (scaled, if SCAL = 'G') -C Hamiltonian or symplectic matrix H. That is, -C -C ( S S ) -C ( 11 12 ) -C S = ( ), -C ( 0 S ) -C ( 22 ) -C -C where S , S and S are N-by-N matrices. -C 11 12 22 -C If JOB = 'C' or JOB = 'E', this array is not referenced. -C -C LDS INTEGER -C The leading dimension of the array S. -C LDS >= MAX(1,2*N), if JOB = 'X' or JOB = 'A'; -C LDS >= 1, if JOB = 'C' or JOB = 'E'. -C -C Workspace -C -C IWORK INTEGER array, dimension (LIWORK) -C LIWORK >= 2*N, if JOB = 'X'; -C LIWORK >= N*N, if JOB = 'C' or JOB = 'E'; -C LIWORK >= MAX(2*N,N*N), if JOB = 'A'. -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C On exit, if INFO = 0, or INFO = 7, DWORK(1) returns the -C optimal value of LDWORK. If INFO = 0, or INFO >= 5, and -C JOB = 'X', or JOB = 'A', then DWORK(2) returns an estimate -C RCONDU of the reciprocal of the condition number (in the -C 1-norm) of the N-th order system of algebraic equations -C from which the solution matrix X is obtained, and DWORK(3) -C returns the reciprocal pivot growth factor for the LU -C factorization of the coefficient matrix of that system -C (see SLICOT Library routine MB02PD); if DWORK(3) is much -C less than 1, then the computed X and RCONDU could be -C unreliable. -C If DICO = 'D', and JOB = 'X', or JOB = 'A', then DWORK(4) -C returns the reciprocal condition number RCONDA of the -C given matrix A, and DWORK(5) returns the reciprocal pivot -C growth factor for A or for its leading columns, if A is -C singular (see SLICOT Library routine MB02PD); if DWORK(5) -C is much less than 1, then the computed S and RCONDA could -C be unreliable. -C On exit, if INFO = 0, or INFO >= 4, and JOB = 'X', the -C elements DWORK(6:5+4*N*N) contain the 2*N-by-2*N -C transformation matrix U which reduced the Hamiltonian or -C symplectic matrix H to the ordered real Schur form S. -C -C LDWORK INTEGER -C The length of the array DWORK. -C LDWORK >= 5+MAX(1,4*N*N+8*N), if JOB = 'X' or JOB = 'A'; -C This may also be used for JOB = 'C' or JOB = 'E', but -C exact bounds are as follows: -C LDWORK >= 5 + MAX(1,LWS,LWE) + LWN, where -C LWS = 0, if FACT = 'F' or LYAPUN = 'R'; -C = 5*N, if FACT = 'N' and LYAPUN = 'O' and -C DICO = 'C' and JOB = 'C'; -C = 5*N+N*N, if FACT = 'N' and LYAPUN = 'O' and -C DICO = 'C' and JOB = 'E'; -C = 5*N+N*N, if FACT = 'N' and LYAPUN = 'O' and -C DICO = 'D'; -C LWE = 2*N*N, if DICO = 'C' and JOB = 'C'; -C = 4*N*N, if DICO = 'C' and JOB = 'E'; -C = MAX(3,2*N*N) + N*N, if DICO = 'D' and JOB = 'C'; -C = MAX(3,2*N*N) + 2*N*N, if DICO = 'D' and JOB = 'E'; -C LWN = 0, if LYAPUN = 'O' or JOB = 'C'; -C = 2*N, if LYAPUN = 'R' and DICO = 'C' and JOB = 'E'; -C = 3*N, if LYAPUN = 'R' and DICO = 'D' and JOB = 'E'. -C For optimum performance LDWORK should sometimes be larger. -C -C BWORK LOGICAL array, dimension (LBWORK) -C LBWORK >= 2*N, if JOB = 'X' or JOB = 'A'; -C LBWORK >= 1, if JOB = 'C' or JOB = 'E', and -C FACT = 'N' and LYAPUN = 'R'; -C LBWORK >= 0, otherwise. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C = 1: if matrix A is (numerically) singular in discrete- -C time case; -C = 2: if the Hamiltonian or symplectic matrix H cannot be -C reduced to real Schur form; -C = 3: if the real Schur form of the Hamiltonian or -C symplectic matrix H cannot be appropriately ordered; -C = 4: if the Hamiltonian or symplectic matrix H has less -C than N stable eigenvalues; -C = 5: if the N-th order system of linear algebraic -C equations, from which the solution matrix X would -C be obtained, is singular to working precision; -C = 6: if the QR algorithm failed to complete the reduction -C of the matrix Ac to Schur canonical form, T; -C = 7: if T and -T' have some almost equal eigenvalues, if -C DICO = 'C', or T has almost reciprocal eigenvalues, -C if DICO = 'D'; perturbed values were used to solve -C Lyapunov equations, but the matrix T, if given (for -C FACT = 'F'), is unchanged. (This is a warning -C indicator.) -C -C METHOD -C -C The method used is the Schur vector approach proposed by Laub [1], -C but with an optional scaling, which enhances the numerical -C stability [6]. It is assumed that [A,B] is a stabilizable pair -C (where for (3) or (4), B is any matrix such that B*B' = G with -C rank(B) = rank(G)), and [E,A] is a detectable pair, where E is any -C matrix such that E*E' = Q with rank(E) = rank(Q). Under these -C assumptions, any of the algebraic Riccati equations (1)-(4) is -C known to have a unique non-negative definite solution. See [2]. -C Now consider the 2N-by-2N Hamiltonian or symplectic matrix -C -C ( op(A) -G ) -C H = ( ), (5) -C ( -Q -op(A)' ), -C -C for continuous-time equation, and -C -1 -1 -C ( op(A) op(A) *G ) -C H = ( -1 -1 ), (6) -C ( Q*op(A) op(A)' + Q*op(A) *G ) -C -C for discrete-time equation, respectively, where -C -1 -C G = op(B)*R *op(B)'. -C The assumptions guarantee that H in (5) has no pure imaginary -C eigenvalues, and H in (6) has no eigenvalues on the unit circle. -C If Y is an N-by-N matrix then there exists an orthogonal matrix U -C such that U'*Y*U is an upper quasi-triangular matrix. Moreover, U -C can be chosen so that the 2-by-2 and 1-by-1 diagonal blocks -C (corresponding to the complex conjugate eigenvalues and real -C eigenvalues respectively) appear in any desired order. This is the -C ordered real Schur form. Thus, we can find an orthogonal -C similarity transformation U which puts (5) or (6) in ordered real -C Schur form -C -C U'*H*U = S = (S(1,1) S(1,2)) -C ( 0 S(2,2)) -C -C where S(i,j) is an N-by-N matrix and the eigenvalues of S(1,1) -C have negative real parts in case of (5), or moduli greater than -C one in case of (6). If U is conformably partitioned into four -C N-by-N blocks -C -C U = (U(1,1) U(1,2)) -C (U(2,1) U(2,2)) -C -C with respect to the assumptions we then have -C (a) U(1,1) is invertible and X = U(2,1)*inv(U(1,1)) solves (1), -C (2), (3), or (4) with X = X' and non-negative definite; -C (b) the eigenvalues of S(1,1) (if DICO = 'C') or S(2,2) (if -C DICO = 'D') are equal to the eigenvalues of optimal system -C (the 'closed-loop' spectrum). -C -C [A,B] is stabilizable if there exists a matrix F such that (A-BF) -C is stable. [E,A] is detectable if [A',E'] is stabilizable. -C -C The condition number of a Riccati equation is estimated as -C -C cond = ( norm(Theta)*norm(A) + norm(inv(Omega))*norm(Q) + -C norm(Pi)*norm(G) ) / norm(X), -C -C where Omega, Theta and Pi are linear operators defined by -C -C Omega(W) = op(Ac)'*W + W*op(Ac), -C Theta(W) = inv(Omega(op(W)'*X + X*op(W))), -C Pi(W) = inv(Omega(X*W*X)), -C -C in the continuous-time case, and -C -C Omega(W) = op(Ac)'*W*op(Ac) - W, -C Theta(W) = inv(Omega(op(W)'*X*op(Ac) + op(Ac)'X*op(W))), -C Pi(W) = inv(Omega(op(Ac)'*X*W*X*op(Ac))), -C -C in the discrete-time case, and Ac has been defined (see argument -C FACT). Details are given in the comments of SLICOT Library -C routines SB02QD and SB02SD. -C -C The routine estimates the quantities -C -C sep(op(Ac),-op(Ac)') = 1 / norm(inv(Omega)), -C sepd(op(Ac),op(Ac)') = 1 / norm(inv(Omega)), -C -C norm(Theta) and norm(Pi) using 1-norm condition estimator. -C -C The forward error bound is estimated using a practical error bound -C similar to the one proposed in [5]. -C -C REFERENCES -C -C [1] Laub, A.J. -C A Schur Method for Solving Algebraic Riccati equations. -C IEEE Trans. Auto. Contr., AC-24, pp. 913-921, 1979. -C -C [2] Wonham, W.M. -C On a matrix Riccati equation of stochastic control. -C SIAM J. Contr., 6, pp. 681-697, 1968. -C -C [3] Sima, V. -C Algorithms for Linear-Quadratic Optimization. -C Pure and Applied Mathematics: A Series of Monographs and -C Textbooks, vol. 200, Marcel Dekker, Inc., New York, 1996. -C -C [4] Ghavimi, A.R. and Laub, A.J. -C Backward error, sensitivity, and refinement of computed -C solutions of algebraic Riccati equations. -C Numerical Linear Algebra with Applications, vol. 2, pp. 29-49, -C 1995. -C -C [5] Higham, N.J. -C Perturbation theory and backward error for AX-XB=C. -C BIT, vol. 33, pp. 124-136, 1993. -C -C [6] Petkov, P.Hr., Konstantinov, M.M., and Mehrmann, V. -C DGRSVX and DMSRIC: Fortran 77 subroutines for solving -C continuous-time matrix algebraic Riccati equations with -C condition and accuracy estimates. -C Preprint SFB393/98-16, Fak. f. Mathematik, Tech. Univ. -C Chemnitz, May 1998. -C -C NUMERICAL ASPECTS -C 3 -C The algorithm requires 0(N ) operations. The solution accuracy -C can be controlled by the output parameter FERR. -C -C FURTHER COMMENTS -C -C To obtain a stabilizing solution of the algebraic Riccati -C equation for DICO = 'D', set SORT = 'U', if HINV = 'D', or set -C SORT = 'S', if HINV = 'I'. -C -C The routine can also compute the anti-stabilizing solutions of -C the algebraic Riccati equations, by specifying -C SORT = 'U' if DICO = 'D' and HINV = 'I', or DICO = 'C', or -C SORT = 'S' if DICO = 'D' and HINV = 'D'. -C -C Usually, the combinations HINV = 'D' and SORT = 'U', or HINV = 'I' -C and SORT = 'U', for stabilizing and anti-stabilizing solutions, -C respectively, will be faster then the other combinations [3]. -C -C The option LYAPUN = 'R' may produce slightly worse or better -C estimates, and it is faster than the option 'O'. -C -C This routine is a functionally extended and more accurate -C version of the SLICOT Library routine SB02MD. Transposed problems -C can be dealt with as well. Iterative refinement is used whenever -C useful to solve linear algebraic systems. Condition numbers and -C error bounds on the solutions are optionally provided. -C -C CONTRIBUTOR -C -C V. Sima, Research Institute for Informatics, Bucharest, Apr. 1999. -C -C REVISIONS -C -C V. Sima, Research Institute for Informatics, Bucharest, Oct. 2001, -C Dec. 2002, Oct. 2004. -C -C KEYWORDS -C -C Algebraic Riccati equation, closed loop system, continuous-time -C system, discrete-time system, optimal regulator, Schur form. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, HALF, ONE - PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0 ) -C .. Scalar Arguments .. - CHARACTER DICO, FACT, HINV, JOB, LYAPUN, SCAL, SORT, - $ TRANA, UPLO - INTEGER INFO, LDA, LDG, LDQ, LDS, LDT, LDV, LDWORK, LDX, - $ N - DOUBLE PRECISION FERR, RCOND, SEP -C .. Array Arguments .. - LOGICAL BWORK(*) - INTEGER IWORK(*) - DOUBLE PRECISION A(LDA,*), DWORK(*), G(LDG,*), Q(LDQ,*), - $ S(LDS,*), T(LDT,*), V(LDV,*), WI(*), WR(*), - $ X(LDX,*) -C .. Local Scalars .. - LOGICAL COLEQU, DISCR, JBXA, JOBA, JOBC, JOBE, JOBX, - $ LHINV, LSCAL, LSCL, LSORT, LUPLO, NOFACT, - $ NOTRNA, ROWEQU, UPDATE - CHARACTER EQUED, JOBS, LOFACT, LOUP, TRANAT - INTEGER I, IERR, IU, IW, IWB, IWC, IWF, IWI, IWR, LDW, - $ LWE, LWN, LWS, N2, NN, NP1, NROT - DOUBLE PRECISION GNORM, QNORM, PIVOTA, PIVOTU, RCONDA, RCONDU, - $ WRKOPT -C .. External Functions .. - LOGICAL LSAME, SB02MR, SB02MS, SB02MV, SB02MW - DOUBLE PRECISION DLAMCH, DLANGE, DLANSY - EXTERNAL DLAMCH, DLANGE, DLANSY, LSAME, SB02MR, SB02MS, - $ SB02MV, SB02MW -C .. External Subroutines .. - EXTERNAL DAXPY, DCOPY, DGEES, DGESV, DLACPY, DLASCL, - $ DLASET, DSCAL, DSWAP, DSYMM, MA02AD, MA02ED, - $ MB01RU, MB01SD, MB02PD, SB02QD, SB02RU, SB02SD, - $ XERBLA -C .. Intrinsic Functions .. - INTRINSIC DBLE, MAX -C .. Executable Statements .. -C -C Decode the input parameters. -C - N2 = N + N - NN = N*N - NP1 = N + 1 - INFO = 0 - JOBA = LSAME( JOB, 'A' ) - JOBC = LSAME( JOB, 'C' ) - JOBE = LSAME( JOB, 'E' ) - JOBX = LSAME( JOB, 'X' ) - NOFACT = LSAME( FACT, 'N' ) - NOTRNA = LSAME( TRANA, 'N' ) - DISCR = LSAME( DICO, 'D' ) - LUPLO = LSAME( UPLO, 'U' ) - LSCAL = LSAME( SCAL, 'G' ) - LSORT = LSAME( SORT, 'S' ) - UPDATE = LSAME( LYAPUN, 'O' ) - JBXA = JOBX .OR. JOBA - LHINV = .FALSE. - IF ( DISCR .AND. JBXA ) - $ LHINV = LSAME( HINV, 'D' ) -C -C Test the input scalar arguments. -C - IF( .NOT.( JBXA .OR. JOBC .OR. JOBE ) ) THEN - INFO = -1 - ELSE IF( .NOT.( DISCR .OR. LSAME( DICO, 'C' ) ) ) THEN - INFO = -2 - ELSE IF( DISCR .AND. JBXA ) THEN - IF( .NOT.( LHINV .OR. LSAME( HINV, 'I' ) ) ) - $ INFO = -3 - END IF - IF( INFO.EQ.0 ) THEN - IF( .NOT.( NOTRNA .OR. LSAME( TRANA, 'T' ) .OR. - $ LSAME( TRANA, 'C' ) ) ) THEN - INFO = -4 - ELSE IF( .NOT.( LUPLO .OR. LSAME( UPLO, 'L' ) ) ) - $ THEN - INFO = -5 - ELSE IF( JBXA ) THEN - IF( .NOT.( LSCAL .OR. LSAME( SCAL, 'N' ) ) ) THEN - INFO = -6 - ELSE IF( .NOT.( LSORT .OR. LSAME( SORT, 'U' ) ) ) THEN - INFO = -7 - END IF - END IF - IF( INFO.EQ.0 .AND. .NOT.JOBX ) THEN - IF( .NOT.( NOFACT .OR. LSAME( FACT, 'F' ) ) ) THEN - INFO = -8 - ELSE IF( .NOT.( UPDATE .OR. LSAME( LYAPUN, 'R' ) ) ) THEN - INFO = -9 - END IF - END IF - IF( INFO.EQ.0 ) THEN - IF( N.LT.0 ) THEN - INFO = -10 - ELSE IF( LDA.LT.1 .OR. ( ( JBXA .OR. NOFACT .OR. UPDATE ) - $ .AND. LDA.LT.N ) ) THEN - INFO = -12 - ELSE IF( LDT.LT.1 .OR. ( .NOT. JOBX .AND. LDT.LT.N ) ) THEN - INFO = -14 - ELSE IF( LDV.LT.1 .OR. ( .NOT. JOBX .AND. LDV.LT.N ) ) THEN - INFO = -16 - ELSE IF( LDG.LT.MAX( 1, N ) ) THEN - INFO = -18 - ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN - INFO = -20 - ELSE IF( LDX.LT.MAX( 1, N ) ) THEN - INFO = -22 - ELSE IF( LDS.LT.1 .OR. ( JBXA .AND. LDS.LT.N2 ) ) THEN - INFO = -29 - ELSE - IF( JBXA ) THEN - IF( LDWORK.LT.5 + MAX( 1, 4*NN + 8*N ) ) - $ INFO = -32 - ELSE - IF( NOFACT .AND. UPDATE ) THEN - IF( .NOT.DISCR .AND. JOBC ) THEN - LWS = 5*N - ELSE - LWS = 5*N + NN - END IF - ELSE - LWS = 0 - END IF - IF( DISCR ) THEN - IF( JOBC ) THEN - LWE = MAX( 3, 2*NN) + NN - ELSE - LWE = MAX( 3, 2*NN) + 2*NN - END IF - ELSE - IF( JOBC ) THEN - LWE = 2*NN - ELSE - LWE = 4*NN - END IF - END IF - IF( UPDATE .OR. JOBC ) THEN - LWN = 0 - ELSE - IF( DISCR ) THEN - LWN = 3*N - ELSE - LWN = 2*N - END IF - END IF - IF( LDWORK.LT.5 + MAX( 1, LWS, LWE ) + LWN ) - $ INFO = -32 - END IF - END IF - END IF - END IF -C - IF ( INFO.NE.0 ) THEN -C -C Error return. -C - CALL XERBLA( 'SB02RD', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF ( N.EQ.0 ) THEN - IF( JOBX ) - $ SEP = ONE - IF( JOBC .OR. JOBA ) - $ RCOND = ONE - IF( JOBE .OR. JOBA ) - $ FERR = ZERO - DWORK(1) = ONE - DWORK(2) = ONE - DWORK(3) = ONE - IF ( DISCR ) THEN - DWORK(4) = ONE - DWORK(5) = ONE - END IF - RETURN - END IF -C - IF ( JBXA ) THEN -C -C Compute the solution matrix X. -C -C Initialise the Hamiltonian or symplectic matrix associated with -C the problem. -C Workspace: need 0 if DICO = 'C'; -C 6*N, if DICO = 'D'. -C - CALL SB02RU( DICO, HINV, TRANA, UPLO, N, A, LDA, G, LDG, Q, - $ LDQ, S, LDS, IWORK, DWORK, LDWORK, IERR ) -C - IF ( IERR.NE.0 ) THEN - INFO = 1 - IF ( DISCR ) THEN - DWORK(4) = DWORK(1) - DWORK(5) = DWORK(2) - END IF - RETURN - END IF -C - IF ( DISCR ) THEN - WRKOPT = 6*N - RCONDA = DWORK(1) - PIVOTA = DWORK(2) - ELSE - WRKOPT = 0 - END IF -C - IF ( LSCAL ) THEN -C -C Scale the Hamiltonian or symplectic matrix S, using the -C square roots of the norms of the matrices Q and G. -C - QNORM = SQRT( DLANSY( '1-norm', UPLO, N, Q, LDQ, DWORK ) ) - GNORM = SQRT( DLANSY( '1-norm', UPLO, N, G, LDG, DWORK ) ) -C - LSCL = QNORM.GT.GNORM .AND. GNORM.GT.ZERO - IF( LSCL ) THEN - CALL DLASCL( 'G', 0, 0, QNORM, GNORM, N, N, S(NP1,1), - $ LDS, IERR ) - CALL DLASCL( 'G', 0, 0, GNORM, QNORM, N, N, S(1,NP1), - $ LDS, IERR ) - END IF - ELSE - LSCL = .FALSE. - END IF -C -C Find the ordered Schur factorization of S, S = U*H*U'. -C Workspace: need 5 + 4*N*N + 6*N; -C prefer larger. -C - IU = 6 - IW = IU + 4*NN - LDW = LDWORK - IW + 1 - IF ( .NOT.DISCR ) THEN - IF ( LSORT ) THEN - CALL DGEES( 'Vectors', 'Sorted', SB02MV, N2, S, LDS, - $ NROT, WR, WI, DWORK(IU), N2, DWORK(IW), LDW, - $ BWORK, IERR ) - ELSE - CALL DGEES( 'Vectors', 'Sorted', SB02MR, N2, S, LDS, - $ NROT, WR, WI, DWORK(IU), N2, DWORK(IW), LDW, - $ BWORK, IERR ) - END IF - ELSE - IF ( LSORT ) THEN - CALL DGEES( 'Vectors', 'Sorted', SB02MW, N2, S, LDS, - $ NROT, WR, WI, DWORK(IU), N2, DWORK(IW), LDW, - $ BWORK, IERR ) - ELSE - CALL DGEES( 'Vectors', 'Sorted', SB02MS, N2, S, LDS, - $ NROT, WR, WI, DWORK(IU), N2, DWORK(IW), LDW, - $ BWORK, IERR ) - END IF - IF ( LHINV ) THEN - CALL DSWAP( N, WR, 1, WR(NP1), 1 ) - CALL DSWAP( N, WI, 1, WI(NP1), 1 ) - END IF - END IF - IF ( IERR.GT.N2 ) THEN - INFO = 3 - ELSE IF ( IERR.GT.0 ) THEN - INFO = 2 - ELSE IF ( NROT.NE.N ) THEN - INFO = 4 - END IF - IF ( INFO.NE.0 ) THEN - IF ( DISCR ) THEN - DWORK(4) = RCONDA - DWORK(5) = PIVOTA - END IF - RETURN - END IF -C - WRKOPT = MAX( WRKOPT, DWORK(IW) + DBLE( IW - 1 ) ) -C -C Compute the solution of X*U(1,1) = U(2,1) using -C LU factorization and iterative refinement. The (2,1) block of S -C is used as a workspace for factoring U(1,1). -C Workspace: need 5 + 4*N*N + 8*N. -C -C First transpose U(2,1) in-situ. -C - DO 20 I = 1, N - 1 - CALL DSWAP( N-I, DWORK(IU+N+I*(N2+1)-1), N2, - $ DWORK(IU+N+(I-1)*(N2+1)+1), 1 ) - 20 CONTINUE -C - IWR = IW - IWC = IWR + N - IWF = IWC + N - IWB = IWF + N - IW = IWB + N -C - CALL MB02PD( 'Equilibrate', 'Transpose', N, N, DWORK(IU), N2, - $ S(NP1,1), LDS, IWORK, EQUED, DWORK(IWR), - $ DWORK(IWC), DWORK(IU+N), N2, X, LDX, RCONDU, - $ DWORK(IWF), DWORK(IWB), IWORK(NP1), DWORK(IW), - $ IERR ) - IF( JOBX ) THEN -C -C Restore U(2,1) back in-situ. -C - DO 40 I = 1, N - 1 - CALL DSWAP( N-I, DWORK(IU+N+I*(N2+1)-1), N2, - $ DWORK(IU+N+(I-1)*(N2+1)+1), 1 ) - 40 CONTINUE -C - IF( .NOT.LSAME( EQUED, 'N' ) ) THEN -C -C Undo the equilibration of U(1,1) and U(2,1). -C - ROWEQU = LSAME( EQUED, 'R' ) .OR. LSAME( EQUED, 'B' ) - COLEQU = LSAME( EQUED, 'C' ) .OR. LSAME( EQUED, 'B' ) -C - IF( ROWEQU ) THEN -C - DO 60 I = 1, N - DWORK(IWR+I-1) = ONE / DWORK(IWR+I-1) - 60 CONTINUE -C - CALL MB01SD( 'Row scaling', N, N, DWORK(IU), N2, - $ DWORK(IWR), DWORK(IWC) ) - END IF -C - IF( COLEQU ) THEN -C - DO 80 I = 1, N - DWORK(IWC+I-1) = ONE / DWORK(IWC+I-1) - 80 CONTINUE -C - CALL MB01SD( 'Column scaling', N, N, DWORK(IU), N2, - $ DWORK(IWR), DWORK(IWC) ) - CALL MB01SD( 'Column scaling', N, N, DWORK(IU+N), N2, - $ DWORK(IWR), DWORK(IWC) ) - END IF - END IF -C -C Set S(2,1) to zero. -C - CALL DLASET( 'Full', N, N, ZERO, ZERO, S(NP1,1), LDS ) - END IF -C - PIVOTU = DWORK(IW) -C - IF ( IERR.GT.0 ) THEN -C -C Singular matrix. Set INFO and DWORK for error return. -C - INFO = 5 - GO TO 160 - END IF -C -C Make sure the solution matrix X is symmetric. -C - DO 100 I = 1, N - 1 - CALL DAXPY( N-I, ONE, X(I,I+1), LDX, X(I+1,I), 1 ) - CALL DSCAL( N-I, HALF, X(I+1,I), 1 ) - CALL DCOPY( N-I, X(I+1,I), 1, X(I,I+1), LDX ) - 100 CONTINUE -C - IF( LSCAL ) THEN -C -C Undo scaling for the solution matrix. -C - IF( LSCL ) - $ CALL DLASCL( 'G', 0, 0, GNORM, QNORM, N, N, X, LDX, - $ IERR ) - END IF - END IF -C - IF ( .NOT.JOBX ) THEN - IF ( .NOT.JOBA ) - $ WRKOPT = 0 -C -C Estimate the conditioning and compute an error bound on the -C solution of the algebraic Riccati equation. -C - IW = 6 - LOFACT = FACT - IF ( NOFACT .AND. .NOT.UPDATE ) THEN -C -C Compute Ac and its Schur factorization. -C - IF ( DISCR ) THEN - CALL DLASET( 'Full', N, N, ZERO, ONE, DWORK(IW), N ) - CALL DSYMM( 'Left', UPLO, N, N, ONE, G, LDG, X, LDX, - $ ONE, DWORK(IW), N ) - IF ( NOTRNA ) THEN -C -C Compute Ac = inv(I_n + G*X)*A. -C - CALL DLACPY( 'Full', N, N, A, LDA, T, LDT ) - CALL DGESV( N, N, DWORK(IW), N, IWORK, T, LDT, IERR ) - ELSE -C -C Compute Ac = A*inv(I_n + X*G). -C - CALL MA02AD( 'Full', N, N, A, LDA, T, LDT ) - CALL DGESV( N, N, DWORK(IW), N, IWORK, T, LDT, IERR ) - DO 120 I = 2, N - CALL DSWAP( I-1, T(1,I), 1, T(I,1), LDT ) - 120 CONTINUE - END IF -C - ELSE -C - CALL DLACPY( 'Full', N, N, A, LDA, T, LDT ) - IF ( NOTRNA ) THEN -C -C Compute Ac = A - G*X. -C - CALL DSYMM( 'Left', UPLO, N, N, -ONE, G, LDG, X, LDX, - $ ONE, T, LDT ) - ELSE -C -C Compute Ac = A - X*G. -C - CALL DSYMM( 'Right', UPLO, N, N, -ONE, G, LDG, X, LDX, - $ ONE, T, LDT ) - END IF - END IF -C -C Compute the Schur factorization of Ac, Ac = V*T*V'. -C Workspace: need 5 + 5*N. -C prefer larger. -C - IWR = IW - IWI = IWR + N - IW = IWI + N - LDW = LDWORK - IW + 1 -C - CALL DGEES( 'Vectors', 'Not ordered', SB02MS, N, T, LDT, - $ NROT, DWORK(IWR), DWORK(IWI), V, LDV, DWORK(IW), - $ LDW, BWORK, IERR ) -C - IF( IERR.NE.0 ) THEN - INFO = 6 - GO TO 160 - END IF -C - WRKOPT = MAX( WRKOPT, DWORK(IW) + DBLE( IW - 1 ) ) - LOFACT = 'F' - IW = 6 - END IF -C - IF ( .NOT.UPDATE ) THEN -C -C Update G, Q, and X using the orthogonal matrix V. -C - TRANAT = 'T' -C -C Save the diagonal elements of G and Q. -C - CALL DCOPY( N, G, LDG+1, DWORK(IW), 1 ) - CALL DCOPY( N, Q, LDQ+1, DWORK(IW+N), 1 ) - IW = IW + N2 -C - IF ( JOBA ) - $ CALL DLACPY( 'Full', N, N, X, LDX, S(NP1,1), LDS ) - CALL MB01RU( UPLO, TRANAT, N, N, ZERO, ONE, X, LDX, V, LDV, - $ X, LDX, DWORK(IW), NN, IERR ) - CALL DSCAL( N, HALF, X, LDX+1 ) - CALL MA02ED( UPLO, N, X, LDX ) - IF( .NOT.DISCR ) THEN - CALL MA02ED( UPLO, N, G, LDG ) - CALL MA02ED( UPLO, N, Q, LDQ ) - END IF - CALL MB01RU( UPLO, TRANAT, N, N, ZERO, ONE, G, LDG, V, LDV, - $ G, LDG, DWORK(IW), NN, IERR ) - CALL DSCAL( N, HALF, G, LDG+1 ) - CALL MB01RU( UPLO, TRANAT, N, N, ZERO, ONE, Q, LDQ, V, LDV, - $ Q, LDQ, DWORK(IW), NN, IERR ) - CALL DSCAL( N, HALF, Q, LDQ+1 ) - END IF -C -C Estimate the conditioning and/or the error bound. -C Workspace: 5 + MAX(1,LWS,LWE) + LWN, where -C -C LWS = 0, if FACT = 'F' or LYAPUN = 'R'; -C = 5*N, if FACT = 'N' and LYAPUN = 'O' and DICO = 'C' -C and JOB = 'C'; -C = 5*N+N*N, if FACT = 'N' and LYAPUN = 'O' and DICO = 'C' -C and (JOB = 'E' or JOB = 'A'); -C = 5*N+N*N, if FACT = 'N' and LYAPUN = 'O' and -C DICO = 'D'; -C LWE = 2*N*N, if DICO = 'C' and JOB = 'C'; -C = 4*N*N, if DICO = 'C' and (JOB = 'E' or -C JOB = 'A'); -C = MAX(3,2*N*N) + N*N, if DICO = 'D' and JOB = 'C'; -C = MAX(3,2*N*N) + 2*N*N, if DICO = 'D' and (JOB = 'E' or -C JOB = 'A'); -C LWN = 0, if LYAPUN = 'O' or JOB = 'C'; -C = 2*N, if LYAPUN = 'R' and DICO = 'C' and (JOB = 'E' or -C JOB = 'A'); -C = 3*N, if LYAPUN = 'R' and DICO = 'D' and (JOB = 'E' or -C JOB = 'A'). -C - LDW = LDWORK - IW + 1 - IF ( JOBA ) THEN - JOBS = 'B' - ELSE - JOBS = JOB - END IF -C - IF ( DISCR ) THEN - CALL SB02SD( JOBS, LOFACT, TRANA, UPLO, LYAPUN, N, A, LDA, - $ T, LDT, V, LDV, G, LDG, Q, LDQ, X, LDX, SEP, - $ RCOND, FERR, IWORK, DWORK(IW), LDW, IERR ) - ELSE - CALL SB02QD( JOBS, LOFACT, TRANA, UPLO, LYAPUN, N, A, LDA, - $ T, LDT, V, LDV, G, LDG, Q, LDQ, X, LDX, SEP, - $ RCOND, FERR, IWORK, DWORK(IW), LDW, IERR ) - END IF -C - WRKOPT = MAX( WRKOPT, DWORK(IW) + DBLE( IW - 1 ) ) - IF( IERR.EQ.NP1 ) THEN - INFO = 7 - ELSE IF( IERR.GT.0 ) THEN - INFO = 6 - GO TO 160 - END IF -C - IF ( .NOT.UPDATE ) THEN -C -C Restore X, G, and Q and set S(2,1) to zero, if needed. -C - IF ( JOBA ) THEN - CALL DLACPY( 'Full', N, N, S(NP1,1), LDS, X, LDX ) - CALL DLASET( 'Full', N, N, ZERO, ZERO, S(NP1,1), LDS ) - ELSE - CALL MB01RU( UPLO, TRANA, N, N, ZERO, ONE, X, LDX, V, - $ LDV, X, LDX, DWORK(IW), NN, IERR ) - CALL DSCAL( N, HALF, X, LDX+1 ) - CALL MA02ED( UPLO, N, X, LDX ) - END IF - IF ( LUPLO ) THEN - LOUP = 'L' - ELSE - LOUP = 'U' - END IF -C - IW = 6 - CALL DCOPY( N, DWORK(IW), 1, G, LDG+1 ) - CALL MA02ED( LOUP, N, G, LDG ) - CALL DCOPY( N, DWORK(IW+N), 1, Q, LDQ+1 ) - CALL MA02ED( LOUP, N, Q, LDQ ) - END IF -C - END IF -C -C Set the optimal workspace and other details. -C - DWORK(1) = WRKOPT - 160 CONTINUE - IF( JBXA ) THEN - DWORK(2) = RCONDU - DWORK(3) = PIVOTU - IF ( DISCR ) THEN - DWORK(4) = RCONDA - DWORK(5) = PIVOTA - END IF - IF( JOBX ) THEN - IF ( LSCL ) THEN - SEP = QNORM / GNORM - ELSE - SEP = ONE - END IF - END IF - END IF -C - RETURN -C *** Last line of SB02RD *** - END
--- a/extra/control-devel/devel/dksyn/SB02RU.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,508 +0,0 @@ - SUBROUTINE SB02RU( DICO, HINV, TRANA, UPLO, N, A, LDA, G, LDG, Q, - $ LDQ, S, LDS, IWORK, DWORK, LDWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To construct the 2n-by-2n Hamiltonian or symplectic matrix S -C associated to the linear-quadratic optimization problem, used to -C solve the continuous- or discrete-time algebraic Riccati equation, -C respectively. -C -C For a continuous-time problem, S is defined by -C -C ( op(A) -G ) -C S = ( ), (1) -C ( -Q -op(A)' ) -C -C and for a discrete-time problem by -C -C -1 -1 -C ( op(A) op(A) *G ) -C S = ( -1 -1 ), (2) -C ( Q*op(A) op(A)' + Q*op(A) *G ) -C -C or -C -T -T -C ( op(A) + G*op(A) *Q -G*op(A) ) -C S = ( -T -T ), (3) -C ( -op(A) *Q op(A) ) -C -C where op(A) = A or A' (A**T), A, G, and Q are n-by-n matrices, -C with G and Q symmetric. Matrix A must be nonsingular in the -C discrete-time case. -C -C ARGUMENTS -C -C Mode Parameters -C -C DICO CHARACTER*1 -C Specifies the type of the system as follows: -C = 'C': Continuous-time system; -C = 'D': Discrete-time system. -C -C HINV CHARACTER*1 -C If DICO = 'D', specifies which of the matrices (2) or (3) -C is constructed, as follows: -C = 'D': The matrix S in (2) is constructed; -C = 'I': The (inverse) matrix S in (3) is constructed. -C HINV is not referenced if DICO = 'C'. -C -C TRANA CHARACTER*1 -C Specifies the form of op(A) to be used, as follows: -C = 'N': op(A) = A (No transpose); -C = 'T': op(A) = A**T (Transpose); -C = 'C': op(A) = A**T (Conjugate transpose = Transpose). -C -C UPLO CHARACTER*1 -C Specifies which triangle of the matrices G and Q is -C stored, as follows: -C = 'U': Upper triangle is stored; -C = 'L': Lower triangle is stored. -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the matrices A, G, and Q. N >= 0. -C -C A (input) DOUBLE PRECISION array, dimension (LDA,N) -C The leading N-by-N part of this array must contain the -C matrix A. -C -C LDA INTEGER -C The leading dimension of the array A. LDA >= MAX(1,N). -C -C G (input/output) DOUBLE PRECISION array, dimension (LDG,N) -C On entry, the leading N-by-N upper triangular part (if -C UPLO = 'U') or lower triangular part (if UPLO = 'L') of -C this array must contain the upper triangular part or lower -C triangular part, respectively, of the symmetric matrix G. -C On exit, if DICO = 'D', the leading N-by-N part of this -C array contains the symmetric matrix G fully stored. -C If DICO = 'C', this array is not modified on exit, and the -C strictly lower triangular part (if UPLO = 'U') or strictly -C upper triangular part (if UPLO = 'L') is not referenced. -C -C LDG INTEGER -C The leading dimension of the array G. LDG >= MAX(1,N). -C -C Q (input/output) DOUBLE PRECISION array, dimension (LDQ,N) -C On entry, the leading N-by-N upper triangular part (if -C UPLO = 'U') or lower triangular part (if UPLO = 'L') of -C this array must contain the upper triangular part or lower -C triangular part, respectively, of the symmetric matrix Q. -C On exit, if DICO = 'D', the leading N-by-N part of this -C array contains the symmetric matrix Q fully stored. -C If DICO = 'C', this array is not modified on exit, and the -C strictly lower triangular part (if UPLO = 'U') or strictly -C upper triangular part (if UPLO = 'L') is not referenced. -C -C LDQ INTEGER -C The leading dimension of the array Q. LDQ >= MAX(1,N). -C -C S (output) DOUBLE PRECISION array, dimension (LDS,2*N) -C If INFO = 0, the leading 2N-by-2N part of this array -C contains the Hamiltonian or symplectic matrix of the -C problem. -C -C LDS INTEGER -C The leading dimension of the array S. LDS >= MAX(1,2*N). -C -C Workspace -C -C IWORK INTEGER array, dimension (LIWORK), where -C LIWORK >= 0, if DICO = 'C'; -C LIWORK >= 2*N, if DICO = 'D'. -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C On exit, if DICO = 'D', DWORK(1) returns the reciprocal -C condition number RCOND of the given matrix A, and -C DWORK(2) returns the reciprocal pivot growth factor -C norm(A)/norm(U) (see SLICOT Library routine MB02PD). -C If DWORK(2) is much less than 1, then the computed S -C and RCOND could be unreliable. If 0 < INFO <= N, then -C DWORK(2) contains the reciprocal pivot growth factor for -C the leading INFO columns of A. -C -C LDWORK INTEGER -C The length of the array DWORK. -C LDWORK >= 0, if DICO = 'C'; -C LDWORK >= MAX(2,6*N), if DICO = 'D'. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C = i: if the leading i-by-i (1 <= i <= N) upper triangular -C submatrix of A is singular in discrete-time case; -C = N+1: if matrix A is numerically singular in discrete- -C time case. -C -C METHOD -C -C For a continuous-time problem, the 2n-by-2n Hamiltonian matrix (1) -C is constructed. -C For a discrete-time problem, the 2n-by-2n symplectic matrix (2) or -C (3) - the inverse of the matrix in (2) - is constructed. -C -C NUMERICAL ASPECTS -C -C The discrete-time case needs the inverse of the matrix A, hence -C the routine should not be used when A is ill-conditioned. -C 3 -C The algorithm requires 0(n ) floating point operations in the -C discrete-time case. -C -C FURTHER COMMENTS -C -C This routine is a functionally extended and with improved accuracy -C version of the SLICOT Library routine SB02MU. Transposed problems -C can be dealt with as well. The LU factorization of op(A) (with -C no equilibration) and iterative refinement are used for solving -C the various linear algebraic systems involved. -C -C CONTRIBUTOR -C -C V. Sima, Research Institute for Informatics, Bucharest, Apr. 1999. -C -C REVISIONS -C -C - -C -C KEYWORDS -C -C Algebraic Riccati equation, closed loop system, continuous-time -C system, discrete-time system, optimal regulator, Schur form. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) -C .. Scalar Arguments .. - CHARACTER DICO, HINV, TRANA, UPLO - INTEGER INFO, LDA, LDG, LDQ, LDS, LDWORK, N -C .. Array Arguments .. - INTEGER IWORK(*) - DOUBLE PRECISION A(LDA,*), DWORK(*), G(LDG,*), Q(LDQ,*), - $ S(LDS,*) -C .. Local Scalars .. - CHARACTER EQUED, TRANAT - LOGICAL DISCR, LHINV, LUPLO, NOTRNA - INTEGER I, J, N2, NJ, NP1 - DOUBLE PRECISION PIVOTG, RCOND, RCONDA, TEMP -C .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -C .. External Subroutines .. - EXTERNAL DCOPY, DGEMM, DLACPY, DLASET, DSWAP, MA02AD, - $ MA02ED, MB02PD, XERBLA -C .. Intrinsic Functions .. - INTRINSIC MAX -C .. Executable Statements .. -C - N2 = N + N - INFO = 0 - DISCR = LSAME( DICO, 'D' ) - LUPLO = LSAME( UPLO, 'U' ) - NOTRNA = LSAME( TRANA, 'N' ) - IF( DISCR ) - $ LHINV = LSAME( HINV, 'D' ) -C -C Test the input scalar arguments. -C - IF( .NOT.DISCR .AND. .NOT.LSAME( DICO, 'C' ) ) THEN - INFO = -1 - ELSE IF( DISCR ) THEN - IF( .NOT.LHINV .AND. .NOT.LSAME( HINV, 'I' ) ) - $ INFO = -2 - ELSE IF( INFO.EQ.0 ) THEN - IF( .NOT.NOTRNA .AND. .NOT.LSAME( TRANA, 'T' ) - $ .AND. .NOT.LSAME( TRANA, 'C' ) ) THEN - INFO = -3 - ELSE IF( .NOT.LUPLO .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -4 - ELSE IF( N.LT.0 ) THEN - INFO = -5 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -7 - ELSE IF( LDG.LT.MAX( 1, N ) ) THEN - INFO = -9 - ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN - INFO = -11 - ELSE IF( LDS.LT.MAX( 1, N2 ) ) THEN - INFO = -13 - ELSE IF( ( LDWORK.LT.0 ) .OR. - $ ( DISCR .AND. LDWORK.LT.MAX( 2, 6*N ) ) ) THEN - INFO = -16 - END IF - END IF -C - IF ( INFO.NE.0 ) THEN -C -C Error return. -C - CALL XERBLA( 'SB02RU', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF ( N.EQ.0 ) THEN - IF ( DISCR ) THEN - DWORK(1) = ONE - DWORK(2) = ONE - END IF - RETURN - END IF -C -C The code tries to exploit data locality as much as possible, -C assuming that LDS is greater than LDA, LDQ, and/or LDG. -C - IF ( .NOT.DISCR ) THEN -C -C Continuous-time case: Construct Hamiltonian matrix column-wise. -C -C Copy op(A) in S(1:N,1:N), and construct full Q -C in S(N+1:2*N,1:N) and change the sign. -C - DO 100 J = 1, N - IF ( NOTRNA ) THEN - CALL DCOPY( N, A(1,J), 1, S(1,J), 1 ) - ELSE - CALL DCOPY( N, A(J,1), LDA, S(1,J), 1 ) - END IF -C - IF ( LUPLO ) THEN -C - DO 20 I = 1, J - S(N+I,J) = -Q(I,J) - 20 CONTINUE -C - DO 40 I = J + 1, N - S(N+I,J) = -Q(J,I) - 40 CONTINUE -C - ELSE -C - DO 60 I = 1, J - 1 - S(N+I,J) = -Q(J,I) - 60 CONTINUE -C - DO 80 I = J, N - S(N+I,J) = -Q(I,J) - 80 CONTINUE -C - END IF - 100 CONTINUE -C -C Construct full G in S(1:N,N+1:2*N) and change the sign, and -C construct -op(A)' in S(N+1:2*N,N+1:2*N). -C - DO 240 J = 1, N - NJ = N + J - IF ( LUPLO ) THEN -C - DO 120 I = 1, J - S(I,NJ) = -G(I,J) - 120 CONTINUE -C - DO 140 I = J + 1, N - S(I,NJ) = -G(J,I) - 140 CONTINUE -C - ELSE -C - DO 160 I = 1, J - 1 - S(I,NJ) = -G(J,I) - 160 CONTINUE -C - DO 180 I = J, N - S(I,NJ) = -G(I,J) - 180 CONTINUE -C - END IF -C - IF ( NOTRNA ) THEN -C - DO 200 I = 1, N - S(N+I,NJ) = -A(J,I) - 200 CONTINUE -C - ELSE -C - DO 220 I = 1, N - S(N+I,NJ) = -A(I,J) - 220 CONTINUE -C - END IF - 240 CONTINUE -C - ELSE -C -C Discrete-time case: Construct the symplectic matrix (2) or (3). -C -C Fill in the remaining triangles of the symmetric matrices Q -C and G. -C - CALL MA02ED( UPLO, N, Q, LDQ ) - CALL MA02ED( UPLO, N, G, LDG ) -C -C Prepare the construction of S in (2) or (3). -C - NP1 = N + 1 - IF ( NOTRNA ) THEN - TRANAT = 'T' - ELSE - TRANAT = 'N' - END IF -C -C Solve op(A)'*X = Q in S(N+1:2*N,1:N), using the LU -C factorization of op(A), obtained in S(1:N,1:N), and -C iterative refinement. No equilibration of A is used. -C Workspace: 6*N. -C - CALL MB02PD( 'No equilibration', TRANAT, N, N, A, LDA, S, - $ LDS, IWORK, EQUED, DWORK, DWORK, Q, LDQ, - $ S(NP1,1), LDS, RCOND, DWORK, DWORK(NP1), - $ IWORK(NP1), DWORK(N2+1), INFO ) -C -C Return if the matrix is exactly singular or singular to -C working precision. -C - IF( INFO.GT.0 ) THEN - DWORK(1) = RCOND - DWORK(2) = DWORK(N2+1) - RETURN - END IF -C - RCONDA = RCOND - PIVOTG = DWORK(N2+1) -C - IF ( LHINV ) THEN -C -C Complete the construction of S in (2). -C -C Transpose X in-situ. -C - DO 260 J = 1, N - 1 - CALL DSWAP( N-J, S(NP1+J,J), 1, S(N+J,J+1), LDS ) - 260 CONTINUE -C -C Solve op(A)*X = I_n in S(N+1:2*N,N+1:2*N), using the LU -C factorization of op(A), computed in S(1:N,1:N), and -C iterative refinement. -C - CALL DLASET( 'Full', N, N, ZERO, ONE, S(1,NP1), LDS ) - CALL MB02PD( 'Factored', TRANA, N, N, A, LDA, S, LDS, IWORK, - $ EQUED, DWORK, DWORK, S(1,NP1), LDS, S(NP1,NP1), - $ LDS, RCOND, DWORK, DWORK(NP1), IWORK(NP1), - $ DWORK(N2+1), INFO ) -C -C Solve op(A)*X = G in S(1:N,N+1:2*N), using the LU -C factorization of op(A), computed in S(1:N,1:N), and -C iterative refinement. -C - CALL MB02PD( 'Factored', TRANA, N, N, A, LDA, S, LDS, IWORK, - $ EQUED, DWORK, DWORK, G, LDG, S(1,NP1), LDS, - $ RCOND, DWORK, DWORK(NP1), IWORK(NP1), - $ DWORK(N2+1), INFO ) -C -C -1 -C Copy op(A) from S(N+1:2*N,N+1:2*N) in S(1:N,1:N). -C - CALL DLACPY( 'Full', N, N, S(NP1,NP1), LDS, S, LDS ) -C -C -1 -C Compute op(A)' + Q*op(A) *G in S(N+1:2*N,N+1:2*N). -C - IF ( NOTRNA ) THEN - CALL MA02AD( 'Full', N, N, A, LDA, S(NP1,NP1), LDS ) - ELSE - CALL DLACPY( 'Full', N, N, A, LDA, S(NP1,NP1), LDS ) - END IF - CALL DGEMM( 'No transpose', 'No transpose', N, N, N, ONE, - $ Q, LDQ, S(1,NP1), LDS, ONE, S(NP1,NP1), LDS ) -C - ELSE -C -C Complete the construction of S in (3). -C -C Change the sign of X. -C - DO 300 J = 1, N -C - DO 280 I = NP1, N2 - S(I,J) = -S(I,J) - 280 CONTINUE -C - 300 CONTINUE -C -C Solve op(A)'*X = I_n in S(N+1:2*N,N+1:2*N), using the LU -C factorization of op(A), computed in S(1:N,1:N), and -C iterative refinement. -C - CALL DLASET( 'Full', N, N, ZERO, ONE, S(1,NP1), LDS ) - CALL MB02PD( 'Factored', TRANAT, N, N, A, LDA, S, LDS, - $ IWORK, EQUED, DWORK, DWORK, S(1,NP1), LDS, - $ S(NP1,NP1), LDS, RCOND, DWORK, DWORK(NP1), - $ IWORK(NP1), DWORK(N2+1), INFO ) -C -C Solve op(A)*X' = -G in S(1:N,N+1:2*N), using the LU -C factorization of op(A), obtained in S(1:N,1:N), and -C iterative refinement. -C - CALL MB02PD( 'Factored', TRANA, N, N, A, LDA, S, LDS, IWORK, - $ EQUED, DWORK, DWORK, G, LDG, S(1,NP1), LDS, - $ RCOND, DWORK, DWORK(NP1), IWORK(NP1), - $ DWORK(N2+1), INFO ) -C -C Change the sign of X and transpose it in-situ. -C - DO 340 J = NP1, N2 -C - DO 320 I = 1, N - TEMP = -S(I,J) - S(I,J) = -S(J-N,I+N) - S(J-N,I+N) = TEMP - 320 CONTINUE -C - 340 CONTINUE -C -T -C Compute op(A) + G*op(A) *Q in S(1:N,1:N). -C - IF ( NOTRNA ) THEN - CALL DLACPY( 'Full', N, N, A, LDA, S, LDS ) - ELSE - CALL MA02AD( 'Full', N, N, A, LDA, S, LDS ) - END IF - CALL DGEMM( 'No transpose', 'No transpose', N, N, N, -ONE, - $ G, LDG, S(NP1,1), LDS, ONE, S, LDS ) -C - END IF - DWORK(1) = RCONDA - DWORK(2) = PIVOTG - END IF - RETURN -C -C *** Last line of SB02RU *** - END
--- a/extra/control-devel/devel/dksyn/SB02SD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,859 +0,0 @@ - SUBROUTINE SB02SD( JOB, FACT, TRANA, UPLO, LYAPUN, N, A, LDA, T, - $ LDT, U, LDU, G, LDG, Q, LDQ, X, LDX, SEPD, - $ RCOND, FERR, IWORK, DWORK, LDWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To estimate the conditioning and compute an error bound on the -C solution of the real discrete-time matrix algebraic Riccati -C equation (see FURTHER COMMENTS) -C -1 -C X = op(A)'*X*(I_n + G*X) *op(A) + Q, (1) -C -C where op(A) = A or A' (A**T) and Q, G are symmetric (Q = Q**T, -C G = G**T). The matrices A, Q and G are N-by-N and the solution X -C is N-by-N. -C -C ARGUMENTS -C -C Mode Parameters -C -C JOB CHARACTER*1 -C Specifies the computation to be performed, as follows: -C = 'C': Compute the reciprocal condition number only; -C = 'E': Compute the error bound only; -C = 'B': Compute both the reciprocal condition number and -C the error bound. -C -C FACT CHARACTER*1 -C Specifies whether or not the real Schur factorization of -C the matrix Ac = inv(I_n + G*X)*A (if TRANA = 'N'), or -C Ac = A*inv(I_n + X*G) (if TRANA = 'T' or 'C'), is supplied -C on entry, as follows: -C = 'F': On entry, T and U (if LYAPUN = 'O') contain the -C factors from the real Schur factorization of the -C matrix Ac; -C = 'N': The Schur factorization of Ac will be computed -C and the factors will be stored in T and U (if -C LYAPUN = 'O'). -C -C TRANA CHARACTER*1 -C Specifies the form of op(A) to be used, as follows: -C = 'N': op(A) = A (No transpose); -C = 'T': op(A) = A**T (Transpose); -C = 'C': op(A) = A**T (Conjugate transpose = Transpose). -C -C UPLO CHARACTER*1 -C Specifies which part of the symmetric matrices Q and G is -C to be used, as follows: -C = 'U': Upper triangular part; -C = 'L': Lower triangular part. -C -C LYAPUN CHARACTER*1 -C Specifies whether or not the original Lyapunov equations -C should be solved in the iterative estimation process, -C as follows: -C = 'O': Solve the original Lyapunov equations, updating -C the right-hand sides and solutions with the -C matrix U, e.g., RHS <-- U'*RHS*U; -C = 'R': Solve reduced Lyapunov equations only, without -C updating the right-hand sides and solutions. -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the matrices A, X, Q, and G. N >= 0. -C -C A (input) DOUBLE PRECISION array, dimension (LDA,N) -C If FACT = 'N' or LYAPUN = 'O', the leading N-by-N part of -C this array must contain the matrix A. -C If FACT = 'F' and LYAPUN = 'R', A is not referenced. -C -C LDA INTEGER -C The leading dimension of the array A. -C LDA >= max(1,N), if FACT = 'N' or LYAPUN = 'O'; -C LDA >= 1, if FACT = 'F' and LYAPUN = 'R'. -C -C T (input or output) DOUBLE PRECISION array, dimension -C (LDT,N) -C If FACT = 'F', then T is an input argument and on entry, -C the leading N-by-N upper Hessenberg part of this array -C must contain the upper quasi-triangular matrix T in Schur -C canonical form from a Schur factorization of Ac (see -C argument FACT). -C If FACT = 'N', then T is an output argument and on exit, -C if INFO = 0 or INFO = N+1, the leading N-by-N upper -C Hessenberg part of this array contains the upper quasi- -C triangular matrix T in Schur canonical form from a Schur -C factorization of Ac (see argument FACT). -C -C LDT INTEGER -C The leading dimension of the array T. LDT >= max(1,N). -C -C U (input or output) DOUBLE PRECISION array, dimension -C (LDU,N) -C If LYAPUN = 'O' and FACT = 'F', then U is an input -C argument and on entry, the leading N-by-N part of this -C array must contain the orthogonal matrix U from a real -C Schur factorization of Ac (see argument FACT). -C If LYAPUN = 'O' and FACT = 'N', then U is an output -C argument and on exit, if INFO = 0 or INFO = N+1, it -C contains the orthogonal N-by-N matrix from a real Schur -C factorization of Ac (see argument FACT). -C If LYAPUN = 'R', the array U is not referenced. -C -C LDU INTEGER -C The leading dimension of the array U. -C LDU >= 1, if LYAPUN = 'R'; -C LDU >= MAX(1,N), if LYAPUN = 'O'. -C -C G (input) DOUBLE PRECISION array, dimension (LDG,N) -C If UPLO = 'U', the leading N-by-N upper triangular part of -C this array must contain the upper triangular part of the -C matrix G. -C If UPLO = 'L', the leading N-by-N lower triangular part of -C this array must contain the lower triangular part of the -C matrix G. _ -C Matrix G should correspond to G in the "reduced" Riccati -C equation (with matrix T, instead of A), if LYAPUN = 'R'. -C See METHOD. -C -C LDG INTEGER -C The leading dimension of the array G. LDG >= max(1,N). -C -C Q (input) DOUBLE PRECISION array, dimension (LDQ,N) -C If UPLO = 'U', the leading N-by-N upper triangular part of -C this array must contain the upper triangular part of the -C matrix Q. -C If UPLO = 'L', the leading N-by-N lower triangular part of -C this array must contain the lower triangular part of the -C matrix Q. _ -C Matrix Q should correspond to Q in the "reduced" Riccati -C equation (with matrix T, instead of A), if LYAPUN = 'R'. -C See METHOD. -C -C LDQ INTEGER -C The leading dimension of the array Q. LDQ >= max(1,N). -C -C X (input) DOUBLE PRECISION array, dimension (LDX,N) -C The leading N-by-N part of this array must contain the -C symmetric solution matrix of the original Riccati -C equation (with matrix A), if LYAPUN = 'O', or of the -C "reduced" Riccati equation (with matrix T), if -C LYAPUN = 'R'. See METHOD. -C -C LDX INTEGER -C The leading dimension of the array X. LDX >= max(1,N). -C -C SEPD (output) DOUBLE PRECISION -C If JOB = 'C' or JOB = 'B', the estimated quantity -C sepd(op(Ac),op(Ac)'). -C If N = 0, or X = 0, or JOB = 'E', SEPD is not referenced. -C -C RCOND (output) DOUBLE PRECISION -C If JOB = 'C' or JOB = 'B', an estimate of the reciprocal -C condition number of the discrete-time Riccati equation. -C If N = 0 or X = 0, RCOND is set to 1 or 0, respectively. -C If JOB = 'E', RCOND is not referenced. -C -C FERR (output) DOUBLE PRECISION -C If JOB = 'E' or JOB = 'B', an estimated forward error -C bound for the solution X. If XTRUE is the true solution, -C FERR bounds the magnitude of the largest entry in -C (X - XTRUE) divided by the magnitude of the largest entry -C in X. -C If N = 0 or X = 0, FERR is set to 0. -C If JOB = 'C', FERR is not referenced. -C -C Workspace -C -C IWORK INTEGER array, dimension (N*N) -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C On exit, if INFO = 0 or INFO = N+1, DWORK(1) returns the -C optimal value of LDWORK. -C -C LDWORK INTEGER -C The dimension of the array DWORK. -C Let LWA = N*N, if LYAPUN = 'O'; -C LWA = 0, otherwise, -C and LWN = N, if LYAPUN = 'R' and JOB = 'E' or 'B'; -C LWN = 0, otherwise. -C If FACT = 'N', then -C LDWORK = MAX(LWA + 5*N, MAX(3,2*N*N) + N*N), -C if JOB = 'C'; -C LDWORK = MAX(LWA + 5*N, MAX(3,2*N*N) + 2*N*N + LWN), -C if JOB = 'E' or 'B'. -C If FACT = 'F', then -C LDWORK = MAX(3,2*N*N) + N*N, if JOB = 'C'; -C LDWORK = MAX(3,2*N*N) + 2*N*N + LWN, -C if JOB = 'E' or 'B'. -C For good performance, LDWORK must generally be larger. -C -C Error indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C > 0: if INFO = i, i <= N, the QR algorithm failed to -C complete the reduction of the matrix Ac to Schur -C canonical form (see LAPACK Library routine DGEES); -C on exit, the matrix T(i+1:N,i+1:N) contains the -C partially converged Schur form, and DWORK(i+1:N) and -C DWORK(N+i+1:2*N) contain the real and imaginary -C parts, respectively, of the converged eigenvalues; -C this error is unlikely to appear; -C = N+1: if T has almost reciprocal eigenvalues; perturbed -C values were used to solve Lyapunov equations, but -C the matrix T, if given (for FACT = 'F'), is -C unchanged. -C -C METHOD -C -C The condition number of the Riccati equation is estimated as -C -C cond = ( norm(Theta)*norm(A) + norm(inv(Omega))*norm(Q) + -C norm(Pi)*norm(G) ) / norm(X), -C -C where Omega, Theta and Pi are linear operators defined by -C -C Omega(W) = op(Ac)'*W*op(Ac) - W, -C Theta(W) = inv(Omega(op(W)'*X*op(Ac) + op(Ac)'X*op(W))), -C Pi(W) = inv(Omega(op(Ac)'*X*W*X*op(Ac))), -C -C and Ac = inv(I_n + G*X)*A (if TRANA = 'N'), or -C Ac = A*inv(I_n + X*G) (if TRANA = 'T' or 'C'). -C -C Note that the Riccati equation (1) is equivalent to -C -C X = op(Ac)'*X*op(Ac) + op(Ac)'*X*G*X*op(Ac) + Q, (2) -C -C and to -C _ _ _ _ _ _ -C X = op(T)'*X*op(T) + op(T)'*X*G*X*op(T) + Q, (3) -C _ _ _ -C where X = U'*X*U, Q = U'*Q*U, and G = U'*G*U, with U the -C orthogonal matrix reducing Ac to a real Schur form, T = U'*Ac*U. -C -C The routine estimates the quantities -C -C sepd(op(Ac),op(Ac)') = 1 / norm(inv(Omega)), -C -C norm(Theta) and norm(Pi) using 1-norm condition estimator. -C -C The forward error bound is estimated using a practical error bound -C similar to the one proposed in [2]. -C -C REFERENCES -C -C [1] Ghavimi, A.R. and Laub, A.J. -C Backward error, sensitivity, and refinement of computed -C solutions of algebraic Riccati equations. -C Numerical Linear Algebra with Applications, vol. 2, pp. 29-49, -C 1995. -C -C [2] Higham, N.J. -C Perturbation theory and backward error for AX-XB=C. -C BIT, vol. 33, pp. 124-136, 1993. -C -C [3] Petkov, P.Hr., Konstantinov, M.M., and Mehrmann, V. -C DGRSVX and DMSRIC: Fortran 77 subroutines for solving -C continuous-time matrix algebraic Riccati equations with -C condition and accuracy estimates. -C Preprint SFB393/98-16, Fak. f. Mathematik, Tech. Univ. -C Chemnitz, May 1998. -C -C NUMERICAL ASPECTS -C 3 -C The algorithm requires 0(N ) operations. -C The accuracy of the estimates obtained depends on the solution -C accuracy and on the properties of the 1-norm estimator. -C -C FURTHER COMMENTS -C -C The option LYAPUN = 'R' may occasionally produce slightly worse -C or better estimates, and it is much faster than the option 'O'. -C When SEPD is computed and it is zero, the routine returns -C immediately, with RCOND and FERR (if requested) set to 0 and 1, -C respectively. In this case, the equation is singular. -C -C Let B be an N-by-M matrix (if TRANA = 'N') or an M-by-N matrix -C (if TRANA = 'T' or 'C'), let R be an M-by-M symmetric positive -C definite matrix (R = R**T), and denote G = op(B)*inv(R)*op(B)'. -C Then, the Riccati equation (1) is equivalent to the standard -C discrete-time matrix algebraic Riccati equation -C -C X = op(A)'*X*op(A) - (4) -C -1 -C op(A)'*X*op(B)*(R + op(B)'*X*op(B)) *op(B)'*X*op(A) + Q. -C -C By symmetry, the equation (1) is also equivalent to -C -1 -C X = op(A)'*(I_n + X*G) *X*op(A) + Q. -C -C CONTRIBUTOR -C -C V. Sima, Research Institute for Informatics, Bucharest, and -C P.Hr. Petkov, Technical University of Sofia, March 1999. -C -C REVISIONS -C -C V. Sima, Research Institute for Informatics, Bucharest, Oct. 2004. -C -C KEYWORDS -C -C Conditioning, error estimates, orthogonal transformation, -C real Schur form, Riccati equation. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE, TWO, FOUR, HALF - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0, - $ FOUR = 4.0D+0, HALF = 0.5D+0 ) -C .. -C .. Scalar Arguments .. - CHARACTER FACT, JOB, LYAPUN, TRANA, UPLO - INTEGER INFO, LDA, LDG, LDQ, LDT, LDU, LDWORK, LDX, N - DOUBLE PRECISION FERR, RCOND, SEPD -C .. -C .. Array Arguments .. - INTEGER IWORK( * ) - DOUBLE PRECISION A( LDA, * ), DWORK( * ), G( LDG, * ), - $ Q( LDQ, * ), T( LDT, * ), U( LDU, * ), - $ X( LDX, * ) -C .. -C .. Local Scalars .. - LOGICAL JOBB, JOBC, JOBE, LOWER, NEEDAC, NOFACT, - $ NOTRNA, UPDATE - CHARACTER LOUP, SJOB, TRANAT - INTEGER I, IABS, INFO2, IRES, IWRK, IXBS, IXMA, J, JJ, - $ KASE, LDW, LWA, LWR, NN, SDIM, WRKOPT - DOUBLE PRECISION ANORM, BIGNUM, DENOM, EPS, EPSN, EPST, EST, - $ GNORM, PINORM, QNORM, SCALE, TEMP, THNORM, - $ TMAX, XANORM, XNORM -C .. -C .. Local Arrays .. - LOGICAL BWORK( 1 ) -C .. -C .. External Functions .. - LOGICAL LSAME, SELECT - DOUBLE PRECISION DLAMCH, DLANGE, DLANHS, DLANSY - EXTERNAL DLAMCH, DLANGE, DLANHS, DLANSY, LSAME, SELECT -C .. -C .. External Subroutines .. - EXTERNAL DAXPY, DCOPY, DGEES, DGEMM, DGESV, DLACON, - $ DLACPY, DLASET, DSCAL, DSWAP, DSYMM, MA02ED, - $ MB01RU, MB01RX, MB01RY, MB01UD, SB03MX, SB03SX, - $ SB03SY, XERBLA -C .. -C .. Intrinsic Functions .. - INTRINSIC ABS, DBLE, INT, MAX, MIN -C .. -C .. Executable Statements .. -C -C Decode and Test input parameters. -C - JOBC = LSAME( JOB, 'C' ) - JOBE = LSAME( JOB, 'E' ) - JOBB = LSAME( JOB, 'B' ) - NOFACT = LSAME( FACT, 'N' ) - NOTRNA = LSAME( TRANA, 'N' ) - LOWER = LSAME( UPLO, 'L' ) - UPDATE = LSAME( LYAPUN, 'O' ) -C - NEEDAC = UPDATE .AND. .NOT.JOBC -C - NN = N*N - IF( UPDATE ) THEN - LWA = NN - ELSE - LWA = 0 - END IF -C - IF( JOBC ) THEN - LDW = MAX( 3, 2*NN ) + NN - ELSE - LDW = MAX( 3, 2*NN ) + 2*NN - IF( .NOT.UPDATE ) - $ LDW = LDW + N - END IF - IF( NOFACT ) - $ LDW = MAX( LWA + 5*N, LDW ) -C - INFO = 0 - IF( .NOT.( JOBB .OR. JOBC .OR. JOBE ) ) THEN - INFO = -1 - ELSE IF( .NOT.( NOFACT .OR. LSAME( FACT, 'F' ) ) ) THEN - INFO = -2 - ELSE IF( .NOT.( NOTRNA .OR. LSAME( TRANA, 'T' ) .OR. - $ LSAME( TRANA, 'C' ) ) ) THEN - INFO = -3 - ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN - INFO = -4 - ELSE IF( .NOT.( UPDATE .OR. LSAME( LYAPUN, 'R' ) ) ) THEN - INFO = -5 - ELSE IF( N.LT.0 ) THEN - INFO = -6 - ELSE IF( LDA.LT.1 .OR. - $ ( LDA.LT.N .AND. ( UPDATE .OR. NOFACT ) ) ) THEN - INFO = -8 - ELSE IF( LDT.LT.MAX( 1, N ) ) THEN - INFO = -10 - ELSE IF( LDU.LT.1 .OR. ( LDU.LT.N .AND. UPDATE ) ) THEN - INFO = -12 - ELSE IF( LDG.LT.MAX( 1, N ) ) THEN - INFO = -14 - ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN - INFO = -16 - ELSE IF( LDX.LT.MAX( 1, N ) ) THEN - INFO = -18 - ELSE IF( LDWORK.LT.LDW ) THEN - INFO = -24 - END IF -C - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'SB02SD', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF( N.EQ.0 ) THEN - IF( .NOT.JOBE ) - $ RCOND = ONE - IF( .NOT.JOBC ) - $ FERR = ZERO - DWORK( 1 ) = ONE - RETURN - END IF -C -C Compute the 1-norm of the matrix X. -C - XNORM = DLANSY( '1-norm', UPLO, N, X, LDX, DWORK ) - IF( XNORM.EQ.ZERO ) THEN -C -C The solution is zero. -C - IF( .NOT.JOBE ) - $ RCOND = ZERO - IF( .NOT.JOBC ) - $ FERR = ZERO - DWORK( 1 ) = DBLE( N ) - RETURN - END IF -C -C Workspace usage. -C - IRES = 0 - IXBS = IRES + NN - IXMA = MAX( 3, 2*NN ) - IABS = IXMA + NN - IWRK = IABS + NN -C -C Workspace: LWK, where -C LWK = 2*N*N, if LYAPUN = 'O', or FACT = 'N', -C LWK = N, otherwise. -C - IF( UPDATE .OR. NOFACT ) THEN -C - CALL DLASET( 'Full', N, N, ZERO, ONE, DWORK( IXBS+1 ), N ) - CALL DSYMM( 'Left', UPLO, N, N, ONE, G, LDG, X, LDX, ONE, - $ DWORK( IXBS+1 ), N ) - IF( NOTRNA ) THEN -C -1 -C Compute Ac = (I_n + G*X) *A. -C - CALL DLACPY( 'Full', N, N, A, LDA, DWORK, N ) - CALL DGESV( N, N, DWORK( IXBS+1 ), N, IWORK, DWORK, N, - $ INFO2 ) - ELSE -C -1 -C Compute Ac = A*(I_n + X*G) . -C - DO 10 J = 1, N - CALL DCOPY( N, A( 1, J ), 1, DWORK( J ), N ) - 10 CONTINUE - CALL DGESV( N, N, DWORK( IXBS+1 ), N, IWORK, DWORK, N, - $ INFO2 ) - DO 20 J = 2, N - CALL DSWAP( J-1, DWORK( (J-1)*N+1 ), 1, DWORK( J ), N ) - 20 CONTINUE - END IF -C - WRKOPT = DBLE( 2*NN ) - IF( NOFACT ) - $ CALL DLACPY( 'Full', N, N, DWORK, N, T, LDT ) - ELSE - WRKOPT = DBLE( N ) - END IF -C - IF( NOFACT ) THEN -C -C Compute the Schur factorization of Ac, Ac = U*T*U'. -C Workspace: need LWA + 5*N; -C prefer larger; -C LWA = N*N, if LYAPUN = 'O'; -C LWA = 0, otherwise. -C (Note: Comments in the code beginning "Workspace:" describe the -C minimal amount of real workspace needed at that point in the -C code, as well as the preferred amount for good performance.) -C - IF( UPDATE ) THEN - SJOB = 'V' - ELSE - SJOB = 'N' - END IF - CALL DGEES( SJOB, 'Not ordered', SELECT, N, T, LDT, SDIM, - $ DWORK( LWA+1 ), DWORK( LWA+N+1 ), U, LDU, - $ DWORK( LWA+2*N+1 ), LDWORK-LWA-2*N, BWORK, INFO ) - IF( INFO.GT.0 ) THEN - IF( LWA.GT.0 ) - $ CALL DCOPY( 2*N, DWORK( LWA+1 ), 1, DWORK, 1 ) - RETURN - END IF -C - WRKOPT = MAX( WRKOPT, INT( DWORK( LWA+2*N+1 ) ) + LWA + 2*N ) - END IF - IF( NEEDAC ) THEN - CALL DLACPY( 'Full', N, N, DWORK, N, DWORK( IABS+1 ), N ) - LWR = NN - ELSE - LWR = 0 - END IF -C - IF( NOTRNA ) THEN - TRANAT = 'T' - ELSE - TRANAT = 'N' - END IF -C _ -C Compute X*op(Ac) or X*op(T). -C - IF( UPDATE ) THEN - CALL DGEMM( 'NoTranspose', TRANA, N, N, N, ONE, X, LDX, DWORK, - $ N, ZERO, DWORK( IXMA+1 ), N ) - ELSE - CALL MB01UD( 'Right', TRANA, N, N, ONE, T, LDT, X, LDX, - $ DWORK( IXMA+1 ), N, INFO2 ) - END IF -C - IF( .NOT.JOBE ) THEN -C -C Estimate sepd(op(Ac),op(Ac)') = sepd(op(T),op(T)') and -C norm(Theta). -C Workspace LWR + MAX(3,2*N*N) + N*N, where -C LWR = N*N, if LYAPUN = 'O' and JOB = 'B', -C LWR = 0, otherwise. -C - CALL SB03SY( 'Both', TRANA, LYAPUN, N, T, LDT, U, LDU, - $ DWORK( IXMA+1 ), N, SEPD, THNORM, IWORK, DWORK, - $ IXMA, INFO ) -C - WRKOPT = MAX( WRKOPT, LWR + MAX( 3, 2*NN ) + NN ) -C -C Return if the equation is singular. -C - IF( SEPD.EQ.ZERO ) THEN - RCOND = ZERO - IF( JOBB ) - $ FERR = ONE - DWORK( 1 ) = DBLE( WRKOPT ) - RETURN - END IF -C -C Estimate norm(Pi). -C Workspace LWR + MAX(3,2*N*N) + N*N. -C - KASE = 0 -C -C REPEAT - 30 CONTINUE - CALL DLACON( NN, DWORK( IXBS+1 ), DWORK, IWORK, EST, KASE ) - IF( KASE.NE.0 ) THEN -C -C Select the triangular part of symmetric matrix to be used. -C - IF( DLANSY( '1-norm', 'Upper', N, DWORK, N, DWORK( IXBS+1 )) - $ .GE. - $ DLANSY( '1-norm', 'Lower', N, DWORK, N, DWORK( IXBS+1 )) - $ ) THEN - LOUP = 'U' - ELSE - LOUP = 'L' - END IF -C _ _ -C Compute RHS = op(Ac)'*X*W*X*op(Ac) or op(T)'*X*W*X*op(T). -C - CALL MB01RU( LOUP, TRANAT, N, N, ZERO, ONE, DWORK, N, - $ DWORK( IXMA+1 ), N, DWORK, N, DWORK( IXBS+1 ), - $ NN, INFO2 ) - CALL DSCAL( N, HALF, DWORK, N+1 ) -C - IF( UPDATE ) THEN -C -C Transform the right-hand side: RHS := U'*RHS*U. -C - CALL MB01RU( LOUP, 'Transpose', N, N, ZERO, ONE, DWORK, - $ N, U, LDU, DWORK, N, DWORK( IXBS+1 ), NN, - $ INFO2 ) - CALL DSCAL( N, HALF, DWORK, N+1 ) - END IF -C -C Fill in the remaining triangle of the symmetric matrix. -C - CALL MA02ED( LOUP, N, DWORK, N ) -C - IF( KASE.EQ.1 ) THEN -C -C Solve op(T)'*Y*op(T) - Y = scale*RHS. -C - CALL SB03MX( TRANA, N, T, LDT, DWORK, N, SCALE, - $ DWORK( IXBS+1 ), INFO2 ) - ELSE -C -C Solve op(T)*W*op(T)' - W = scale*RHS. -C - CALL SB03MX( TRANAT, N, T, LDT, DWORK, N, SCALE, - $ DWORK( IXBS+1 ), INFO2 ) - END IF -C - IF( UPDATE ) THEN -C -C Transform back to obtain the solution: Z := U*Z*U', with -C Z = Y or Z = W. -C - CALL MB01RU( LOUP, 'No transpose', N, N, ZERO, ONE, - $ DWORK, N, U, LDU, DWORK, N, DWORK( IXBS+1 ), - $ NN, INFO2 ) - CALL DSCAL( N, HALF, DWORK, N+1 ) -C -C Fill in the remaining triangle of the symmetric matrix. -C - CALL MA02ED( LOUP, N, DWORK, N ) - END IF - GO TO 30 - END IF -C UNTIL KASE = 0 -C - IF( EST.LT.SCALE ) THEN - PINORM = EST / SCALE - ELSE - BIGNUM = ONE / DLAMCH( 'Safe minimum' ) - IF( EST.LT.SCALE*BIGNUM ) THEN - PINORM = EST / SCALE - ELSE - PINORM = BIGNUM - END IF - END IF -C -C Compute the 1-norm of A or T. -C - IF( UPDATE ) THEN - ANORM = DLANGE( '1-norm', N, N, A, LDA, DWORK ) - ELSE - ANORM = DLANHS( '1-norm', N, T, LDT, DWORK ) - END IF -C -C Compute the 1-norms of the matrices Q and G. -C - QNORM = DLANSY( '1-norm', UPLO, N, Q, LDQ, DWORK ) - GNORM = DLANSY( '1-norm', UPLO, N, G, LDG, DWORK ) -C -C Estimate the reciprocal condition number. -C - TMAX = MAX( SEPD, XNORM, ANORM, GNORM ) - IF( TMAX.LE.ONE ) THEN - TEMP = SEPD*XNORM - DENOM = QNORM + ( SEPD*ANORM )*THNORM + - $ ( SEPD*GNORM )*PINORM - ELSE - TEMP = ( SEPD / TMAX )*( XNORM / TMAX ) - DENOM = ( ( ONE / TMAX )*( QNORM / TMAX ) ) + - $ ( ( SEPD / TMAX )*( ANORM / TMAX ) )*THNORM + - $ ( ( SEPD / TMAX )*( GNORM / TMAX ) )*PINORM - END IF - IF( TEMP.GE.DENOM ) THEN - RCOND = ONE - ELSE - RCOND = TEMP / DENOM - END IF - END IF -C - IF( .NOT.JOBC ) THEN -C -C Form a triangle of the residual matrix -C R = op(Ac)'*X*op(Ac) + op(Ac)'*X*G*X*op(Ac) + Q - X, -C or _ _ _ _ _ _ -C R = op(T)'*X*op(T) + op(T)'*X*G*X*op(T) + Q - X, -C exploiting the symmetry. Actually, the equivalent formula -C R = op(A)'*X*op(Ac) + Q - X -C is used in the first case. -C Workspace MAX(3,2*N*N) + 2*N*N, if LYAPUN = 'O'; -C MAX(3,2*N*N) + 2*N*N + N, if LYAPUN = 'R'. -C - CALL DLACPY( UPLO, N, N, Q, LDQ, DWORK( IRES+1 ), N ) - JJ = IRES + 1 - IF( LOWER ) THEN - DO 40 J = 1, N - CALL DAXPY( N-J+1, -ONE, X( J, J ), 1, DWORK( JJ ), 1 ) - JJ = JJ + N + 1 - 40 CONTINUE - ELSE - DO 50 J = 1, N - CALL DAXPY( J, -ONE, X( 1, J ), 1, DWORK( JJ ), 1 ) - JJ = JJ + N - 50 CONTINUE - END IF -C - IF( UPDATE ) THEN - CALL MB01RX( 'Left', UPLO, TRANAT, N, N, ONE, ONE, - $ DWORK( IRES+1 ), N, A, LDA, DWORK( IXMA+1 ), N, - $ INFO2 ) - ELSE - CALL MB01RY( 'Left', UPLO, TRANAT, N, ONE, ONE, - $ DWORK( IRES+1 ), N, T, LDT, DWORK( IXMA+1 ), N, - $ DWORK( IWRK+1 ), INFO2 ) - CALL DSYMM( 'Left', UPLO, N, N, ONE, G, LDG, - $ DWORK( IXMA+1 ), N, ZERO, DWORK( IXBS+1 ), N ) - CALL MB01RX( 'Left', UPLO, 'Transpose', N, N, ONE, ONE, - $ DWORK( IRES+1 ), N, DWORK( IXMA+1 ), N, - $ DWORK( IXBS+1 ), N, INFO2 ) - END IF -C -C Get the machine precision. -C - EPS = DLAMCH( 'Epsilon' ) - EPSN = EPS*DBLE( N + 4 ) - EPST = EPS*DBLE( 2*( N + 1 ) ) - TEMP = EPS*FOUR -C -C Add to abs(R) a term that takes account of rounding errors in -C forming R: -C abs(R) := abs(R) + EPS*(4*abs(Q) + 4*abs(X) + -C (n+4)*abs(op(Ac))'*abs(X)*abs(op(Ac)) + 2*(n+1)* -C abs(op(Ac))'*abs(X)*abs(G)*abs(X)*abs(op(Ac))), -C or _ _ -C abs(R) := abs(R) + EPS*(4*abs(Q) + 4*abs(X) + -C _ -C (n+4)*abs(op(T))'*abs(X)*abs(op(T)) + -C _ _ _ -C 2*(n+1)*abs(op(T))'*abs(X)*abs(G)*abs(X)*abs(op(T))), -C where EPS is the machine precision. -C - DO 70 J = 1, N - DO 60 I = 1, N - DWORK( IXBS+(J-1)*N+I ) = ABS( X( I, J ) ) - 60 CONTINUE - 70 CONTINUE -C - IF( LOWER ) THEN - DO 90 J = 1, N - DO 80 I = J, N - DWORK( IRES+(J-1)*N+I ) = TEMP*( ABS( Q( I, J ) ) + - $ ABS( X( I, J ) ) ) + - $ ABS( DWORK( IRES+(J-1)*N+I ) ) - 80 CONTINUE - 90 CONTINUE - ELSE - DO 110 J = 1, N - DO 100 I = 1, J - DWORK( IRES+(J-1)*N+I ) = TEMP*( ABS( Q( I, J ) ) + - $ ABS( X( I, J ) ) ) + - $ ABS( DWORK( IRES+(J-1)*N+I ) ) - 100 CONTINUE - 110 CONTINUE - END IF -C - IF( UPDATE ) THEN -C - DO 130 J = 1, N - DO 120 I = 1, N - DWORK( IABS+(J-1)*N+I ) = - $ ABS( DWORK( IABS+(J-1)*N+I ) ) - 120 CONTINUE - 130 CONTINUE -C - CALL DGEMM( 'NoTranspose', TRANA, N, N, N, ONE, - $ DWORK( IXBS+1 ), N, DWORK( IABS+1 ), N, ZERO, - $ DWORK( IXMA+1 ), N ) - CALL MB01RX( 'Left', UPLO, TRANAT, N, N, ONE, EPSN, - $ DWORK( IRES+1 ), N, DWORK( IABS+1 ), N, - $ DWORK( IXMA+1 ), N, INFO2 ) - ELSE -C - DO 150 J = 1, N - DO 140 I = 1, MIN( J+1, N ) - DWORK( IABS+(J-1)*N+I ) = ABS( T( I, J ) ) - 140 CONTINUE - 150 CONTINUE -C - CALL MB01UD( 'Right', TRANA, N, N, ONE, DWORK( IABS+1 ), N, - $ DWORK( IXBS+1 ), N, DWORK( IXMA+1 ), N, INFO2 ) - CALL MB01RY( 'Left', UPLO, TRANAT, N, ONE, EPSN, - $ DWORK( IRES+1 ), N, DWORK( IABS+1 ), N, - $ DWORK( IXMA+1 ), N, DWORK( IWRK+1 ), INFO2 ) - END IF -C - IF( LOWER ) THEN - DO 170 J = 1, N - DO 160 I = J, N - DWORK( IABS+(J-1)*N+I ) = ABS( G( I, J ) ) - 160 CONTINUE - 170 CONTINUE - ELSE - DO 190 J = 1, N - DO 180 I = 1, J - DWORK( IABS+(J-1)*N+I ) = ABS( G( I, J ) ) - 180 CONTINUE - 190 CONTINUE - END IF -C - IF( UPDATE ) THEN - CALL MB01RU( UPLO, TRANAT, N, N, ONE, EPST, DWORK( IRES+1 ), - $ N, DWORK( IXMA+1 ), N, DWORK( IABS+1 ), N, - $ DWORK( IXBS+1 ), NN, INFO2 ) - WRKOPT = MAX( WRKOPT, MAX( 3, 2*NN ) + 2*NN ) - ELSE - CALL DSYMM( 'Left', UPLO, N, N, ONE, DWORK( IABS+1 ), N, - $ DWORK( IXMA+1 ), N, ZERO, DWORK( IXBS+1 ), N ) - CALL MB01RY( 'Left', UPLO, TRANAT, N, ONE, EPST, - $ DWORK( IRES+1 ), N, DWORK( IXMA+1 ), N, - $ DWORK( IXBS+1 ), N, DWORK( IWRK+1 ), INFO2 ) - WRKOPT = MAX( WRKOPT, MAX( 3, 2*NN ) + 2*NN + N ) - END IF -C -C Compute forward error bound, using matrix norm estimator. -C Workspace MAX(3,2*N*N) + N*N. -C - XANORM = DLANSY( 'Max', UPLO, N, X, LDX, DWORK ) -C - CALL SB03SX( TRANA, UPLO, LYAPUN, N, XANORM, T, LDT, U, LDU, - $ DWORK( IRES+1 ), N, FERR, IWORK, DWORK( IXBS+1 ), - $ IXMA, INFO ) - END IF -C - DWORK( 1 ) = DBLE( WRKOPT ) - RETURN -C -C *** Last line of SB02SD *** - END
--- a/extra/control-devel/devel/dksyn/SB03MV.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,295 +0,0 @@ - SUBROUTINE SB03MV( LTRAN, LUPPER, T, LDT, B, LDB, SCALE, X, LDX, - $ XNORM, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To solve for the 2-by-2 symmetric matrix X in -C -C op(T)'*X*op(T) - X = SCALE*B, -C -C where T is 2-by-2, B is symmetric 2-by-2, and op(T) = T or T', -C where T' denotes the transpose of T. -C -C ARGUMENTS -C -C Mode Parameters -C -C LTRAN LOGICAL -C Specifies the form of op(T) to be used, as follows: -C = .FALSE.: op(T) = T, -C = .TRUE. : op(T) = T'. -C -C LUPPER LOGICAL -C Specifies which triangle of the matrix B is used, and -C which triangle of the matrix X is computed, as follows: -C = .TRUE. : The upper triangular part; -C = .FALSE.: The lower triangular part. -C -C Input/Output Parameters -C -C T (input) DOUBLE PRECISION array, dimension (LDT,2) -C The leading 2-by-2 part of this array must contain the -C matrix T. -C -C LDT INTEGER -C The leading dimension of array T. LDT >= 2. -C -C B (input) DOUBLE PRECISION array, dimension (LDB,2) -C On entry with LUPPER = .TRUE., the leading 2-by-2 upper -C triangular part of this array must contain the upper -C triangular part of the symmetric matrix B and the strictly -C lower triangular part of B is not referenced. -C On entry with LUPPER = .FALSE., the leading 2-by-2 lower -C triangular part of this array must contain the lower -C triangular part of the symmetric matrix B and the strictly -C upper triangular part of B is not referenced. -C -C LDB INTEGER -C The leading dimension of array B. LDB >= 2. -C -C SCALE (output) DOUBLE PRECISION -C The scale factor. SCALE is chosen less than or equal to 1 -C to prevent the solution overflowing. -C -C X (output) DOUBLE PRECISION array, dimension (LDX,2) -C On exit with LUPPER = .TRUE., the leading 2-by-2 upper -C triangular part of this array contains the upper -C triangular part of the symmetric solution matrix X and the -C strictly lower triangular part of X is not referenced. -C On exit with LUPPER = .FALSE., the leading 2-by-2 lower -C triangular part of this array contains the lower -C triangular part of the symmetric solution matrix X and the -C strictly upper triangular part of X is not referenced. -C Note that X may be identified with B in the calling -C statement. -C -C LDX INTEGER -C The leading dimension of array X. LDX >= 2. -C -C XNORM (output) DOUBLE PRECISION -C The infinity-norm of the solution. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C = 1: if T has almost reciprocal eigenvalues, so T -C is perturbed to get a nonsingular equation. -C -C NOTE: In the interests of speed, this routine does not -C check the inputs for errors. -C -C METHOD -C -C The equivalent linear algebraic system of equations is formed and -C solved using Gaussian elimination with complete pivoting. -C -C REFERENCES -C -C [1] Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J., -C Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., -C Ostrouchov, S., and Sorensen, D. -C LAPACK Users' Guide: Second Edition. -C SIAM, Philadelphia, 1995. -C -C NUMERICAL ASPECTS -C -C The algorithm is stable and reliable, since Gaussian elimination -C with complete pivoting is used. -C -C CONTRIBUTOR -C -C Release 3.0: V. Sima, Katholieke Univ. Leuven, Belgium, May 1997. -C Based on DLALD2 by P. Petkov, Tech. University of Sofia, September -C 1993. -C -C REVISIONS -C -C - -C -C KEYWORDS -C -C Discrete-time system, Lyapunov equation, matrix algebra. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE, TWO, FOUR - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0, - $ FOUR = 4.0D+0 ) -C .. -C .. Scalar Arguments .. - LOGICAL LTRAN, LUPPER - INTEGER INFO, LDB, LDT, LDX - DOUBLE PRECISION SCALE, XNORM -C .. -C .. Array Arguments .. - DOUBLE PRECISION B( LDB, * ), T( LDT, * ), X( LDX, * ) -C .. -C .. Local Scalars .. - INTEGER I, IP, IPSV, J, JP, JPSV, K - DOUBLE PRECISION EPS, SMIN, SMLNUM, TEMP, XMAX -C .. -C .. Local Arrays .. - INTEGER JPIV( 3 ) - DOUBLE PRECISION BTMP( 3 ), T9( 3, 3 ), TMP( 3 ) -C .. -C .. External Functions .. - DOUBLE PRECISION DLAMCH - EXTERNAL DLAMCH -C .. -C .. External Subroutines .. - EXTERNAL DSWAP -C .. -C .. Intrinsic Functions .. - INTRINSIC ABS, MAX -C .. -C .. Executable Statements .. -C -C Do not check the input parameters for errors. -C - INFO = 0 -C -C Set constants to control overflow. -C - EPS = DLAMCH( 'P' ) - SMLNUM = DLAMCH( 'S' ) / EPS -C -C Solve equivalent 3-by-3 system using complete pivoting. -C Set pivots less than SMIN to SMIN. -C - SMIN = MAX( ABS( T( 1, 1 ) ), ABS( T( 1, 2 ) ), - $ ABS( T( 2, 1 ) ), ABS( T( 2, 2 ) ) ) - SMIN = MAX( EPS*SMIN, SMLNUM ) - T9( 1, 1 ) = T( 1, 1 )*T( 1, 1 ) - ONE - T9( 2, 2 ) = T( 1, 1 )*T( 2, 2 ) + T( 1, 2 )*T( 2, 1 ) - ONE - T9( 3, 3 ) = T( 2, 2 )*T( 2, 2 ) - ONE - IF( LTRAN ) THEN - T9( 1, 2 ) = T( 1, 1 )*T( 1, 2 ) + T( 1, 1 )*T( 1, 2 ) - T9( 1, 3 ) = T( 1, 2 )*T( 1, 2 ) - T9( 2, 1 ) = T( 1, 1 )*T( 2, 1 ) - T9( 2, 3 ) = T( 1, 2 )*T( 2, 2 ) - T9( 3, 1 ) = T( 2, 1 )*T( 2, 1 ) - T9( 3, 2 ) = T( 2, 1 )*T( 2, 2 ) + T( 2, 1 )*T( 2, 2 ) - ELSE - T9( 1, 2 ) = T( 1, 1 )*T( 2, 1 ) + T( 1, 1 )*T( 2, 1 ) - T9( 1, 3 ) = T( 2, 1 )*T( 2, 1 ) - T9( 2, 1 ) = T( 1, 1 )*T( 1, 2 ) - T9( 2, 3 ) = T( 2, 1 )*T( 2, 2 ) - T9( 3, 1 ) = T( 1, 2 )*T( 1, 2 ) - T9( 3, 2 ) = T( 1, 2 )*T( 2, 2 ) + T( 1, 2 )*T( 2, 2 ) - END IF - BTMP( 1 ) = B( 1, 1 ) - IF ( LUPPER ) THEN - BTMP( 2 ) = B( 1, 2 ) - ELSE - BTMP( 2 ) = B( 2, 1 ) - END IF - BTMP( 3 ) = B( 2, 2 ) -C -C Perform elimination. -C - DO 50 I = 1, 2 - XMAX = ZERO -C - DO 20 IP = I, 3 -C - DO 10 JP = I, 3 - IF( ABS( T9( IP, JP ) ).GE.XMAX ) THEN - XMAX = ABS( T9( IP, JP ) ) - IPSV = IP - JPSV = JP - END IF - 10 CONTINUE -C - 20 CONTINUE -C - IF( IPSV.NE.I ) THEN - CALL DSWAP( 3, T9( IPSV, 1 ), 3, T9( I, 1 ), 3 ) - TEMP = BTMP( I ) - BTMP( I ) = BTMP( IPSV ) - BTMP( IPSV ) = TEMP - END IF - IF( JPSV.NE.I ) - $ CALL DSWAP( 3, T9( 1, JPSV ), 1, T9( 1, I ), 1 ) - JPIV( I ) = JPSV - IF( ABS( T9( I, I ) ).LT.SMIN ) THEN - INFO = 1 - T9( I, I ) = SMIN - END IF -C - DO 40 J = I + 1, 3 - T9( J, I ) = T9( J, I ) / T9( I, I ) - BTMP( J ) = BTMP( J ) - T9( J, I )*BTMP( I ) -C - DO 30 K = I + 1, 3 - T9( J, K ) = T9( J, K ) - T9( J, I )*T9( I, K ) - 30 CONTINUE -C - 40 CONTINUE -C - 50 CONTINUE -C - IF( ABS( T9( 3, 3 ) ).LT.SMIN ) - $ T9( 3, 3 ) = SMIN - SCALE = ONE - IF( ( FOUR*SMLNUM )*ABS( BTMP( 1 ) ).GT.ABS( T9( 1, 1 ) ) .OR. - $ ( FOUR*SMLNUM )*ABS( BTMP( 2 ) ).GT.ABS( T9( 2, 2 ) ) .OR. - $ ( FOUR*SMLNUM )*ABS( BTMP( 3 ) ).GT.ABS( T9( 3, 3 ) ) ) THEN - SCALE = ( ONE / FOUR ) / MAX( ABS( BTMP( 1 ) ), - $ ABS( BTMP( 2 ) ), ABS( BTMP( 3 ) ) ) - BTMP( 1 ) = BTMP( 1 )*SCALE - BTMP( 2 ) = BTMP( 2 )*SCALE - BTMP( 3 ) = BTMP( 3 )*SCALE - END IF -C - DO 70 I = 1, 3 - K = 4 - I - TEMP = ONE / T9( K, K ) - TMP( K ) = BTMP( K )*TEMP -C - DO 60 J = K + 1, 3 - TMP( K ) = TMP( K ) - ( TEMP*T9( K, J ) )*TMP( J ) - 60 CONTINUE -C - 70 CONTINUE -C - DO 80 I = 1, 2 - IF( JPIV( 3-I ).NE.3-I ) THEN - TEMP = TMP( 3-I ) - TMP( 3-I ) = TMP( JPIV( 3-I ) ) - TMP( JPIV( 3-I ) ) = TEMP - END IF - 80 CONTINUE -C - X( 1, 1 ) = TMP( 1 ) - IF ( LUPPER ) THEN - X( 1, 2 ) = TMP( 2 ) - ELSE - X( 2, 1 ) = TMP( 2 ) - END IF - X( 2, 2 ) = TMP( 3 ) - XNORM = MAX( ABS( TMP( 1 ) ) + ABS( TMP( 2 ) ), - $ ABS( TMP( 2 ) ) + ABS( TMP( 3 ) ) ) -C - RETURN -C *** Last line of SB03MV *** - END
--- a/extra/control-devel/devel/dksyn/SB03MW.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,293 +0,0 @@ - SUBROUTINE SB03MW( LTRAN, LUPPER, T, LDT, B, LDB, SCALE, X, LDX, - $ XNORM, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To solve for the 2-by-2 symmetric matrix X in -C -C op(T)'*X + X*op(T) = SCALE*B, -C -C where T is 2-by-2, B is symmetric 2-by-2, and op(T) = T or T', -C where T' denotes the transpose of T. -C -C ARGUMENTS -C -C Mode Parameters -C -C LTRAN LOGICAL -C Specifies the form of op(T) to be used, as follows: -C = .FALSE.: op(T) = T, -C = .TRUE. : op(T) = T'. -C -C LUPPER LOGICAL -C Specifies which triangle of the matrix B is used, and -C which triangle of the matrix X is computed, as follows: -C = .TRUE. : The upper triangular part; -C = .FALSE.: The lower triangular part. -C -C Input/Output Parameters -C -C T (input) DOUBLE PRECISION array, dimension (LDT,2) -C The leading 2-by-2 part of this array must contain the -C matrix T. -C -C LDT INTEGER -C The leading dimension of array T. LDT >= 2. -C -C B (input) DOUBLE PRECISION array, dimension (LDB,2) -C On entry with LUPPER = .TRUE., the leading 2-by-2 upper -C triangular part of this array must contain the upper -C triangular part of the symmetric matrix B and the strictly -C lower triangular part of B is not referenced. -C On entry with LUPPER = .FALSE., the leading 2-by-2 lower -C triangular part of this array must contain the lower -C triangular part of the symmetric matrix B and the strictly -C upper triangular part of B is not referenced. -C -C LDB INTEGER -C The leading dimension of array B. LDB >= 2. -C -C SCALE (output) DOUBLE PRECISION -C The scale factor. SCALE is chosen less than or equal to 1 -C to prevent the solution overflowing. -C -C X (output) DOUBLE PRECISION array, dimension (LDX,2) -C On exit with LUPPER = .TRUE., the leading 2-by-2 upper -C triangular part of this array contains the upper -C triangular part of the symmetric solution matrix X and the -C strictly lower triangular part of X is not referenced. -C On exit with LUPPER = .FALSE., the leading 2-by-2 lower -C triangular part of this array contains the lower -C triangular part of the symmetric solution matrix X and the -C strictly upper triangular part of X is not referenced. -C Note that X may be identified with B in the calling -C statement. -C -C LDX INTEGER -C The leading dimension of array X. LDX >= 2. -C -C XNORM (output) DOUBLE PRECISION -C The infinity-norm of the solution. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C = 1: if T and -T have too close eigenvalues, so T -C is perturbed to get a nonsingular equation. -C -C NOTE: In the interests of speed, this routine does not -C check the inputs for errors. -C -C METHOD -C -C The equivalent linear algebraic system of equations is formed and -C solved using Gaussian elimination with complete pivoting. -C -C REFERENCES -C -C [1] Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J., -C Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., -C Ostrouchov, S., and Sorensen, D. -C LAPACK Users' Guide: Second Edition. -C SIAM, Philadelphia, 1995. -C -C NUMERICAL ASPECTS -C -C The algorithm is stable and reliable, since Gaussian elimination -C with complete pivoting is used. -C -C CONTRIBUTOR -C -C Release 3.0: V. Sima, Katholieke Univ. Leuven, Belgium, May 1997. -C Based on DLALY2 by P. Petkov, Tech. University of Sofia, September -C 1993. -C -C REVISIONS -C -C - -C -C KEYWORDS -C -C Continuous-time system, Lyapunov equation, matrix algebra. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE, TWO, FOUR - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0, - $ FOUR = 4.0D+0 ) -C .. -C .. Scalar Arguments .. - LOGICAL LTRAN, LUPPER - INTEGER INFO, LDB, LDT, LDX - DOUBLE PRECISION SCALE, XNORM -C .. -C .. Array Arguments .. - DOUBLE PRECISION B( LDB, * ), T( LDT, * ), X( LDX, * ) -C .. -C .. Local Scalars .. - INTEGER I, IP, IPSV, J, JP, JPSV, K - DOUBLE PRECISION EPS, SMIN, SMLNUM, TEMP, XMAX -C .. -C .. Local Arrays .. - INTEGER JPIV( 3 ) - DOUBLE PRECISION BTMP( 3 ), T9( 3, 3 ), TMP( 3 ) -C .. -C .. External Functions .. - DOUBLE PRECISION DLAMCH - EXTERNAL DLAMCH -C .. -C .. External Subroutines .. - EXTERNAL DSWAP -C .. -C .. Intrinsic Functions .. - INTRINSIC ABS, MAX -C .. -C .. Executable Statements .. -C -C Do not check the input parameters for errors -C - INFO = 0 -C -C Set constants to control overflow -C - EPS = DLAMCH( 'P' ) - SMLNUM = DLAMCH( 'S' ) / EPS -C -C Solve equivalent 3-by-3 system using complete pivoting. -C Set pivots less than SMIN to SMIN. -C - SMIN = MAX( MAX( ABS( T( 1, 1 ) ), ABS( T( 1, 2 ) ), - $ ABS( T( 2, 1 ) ), ABS( T( 2, 2 ) ) )*EPS, - $ SMLNUM ) - T9( 1, 3 ) = ZERO - T9( 3, 1 ) = ZERO - T9( 1, 1 ) = T( 1, 1 ) - T9( 2, 2 ) = T( 1, 1 ) + T( 2, 2 ) - T9( 3, 3 ) = T( 2, 2 ) - IF( LTRAN ) THEN - T9( 1, 2 ) = T( 1, 2 ) - T9( 2, 1 ) = T( 2, 1 ) - T9( 2, 3 ) = T( 1, 2 ) - T9( 3, 2 ) = T( 2, 1 ) - ELSE - T9( 1, 2 ) = T( 2, 1 ) - T9( 2, 1 ) = T( 1, 2 ) - T9( 2, 3 ) = T( 2, 1 ) - T9( 3, 2 ) = T( 1, 2 ) - END IF - BTMP( 1 ) = B( 1, 1 )/TWO - IF ( LUPPER ) THEN - BTMP( 2 ) = B( 1, 2 ) - ELSE - BTMP( 2 ) = B( 2, 1 ) - END IF - BTMP( 3 ) = B( 2, 2 )/TWO -C -C Perform elimination -C - DO 50 I = 1, 2 - XMAX = ZERO -C - DO 20 IP = I, 3 -C - DO 10 JP = I, 3 - IF( ABS( T9( IP, JP ) ).GE.XMAX ) THEN - XMAX = ABS( T9( IP, JP ) ) - IPSV = IP - JPSV = JP - END IF - 10 CONTINUE -C - 20 CONTINUE -C - IF( IPSV.NE.I ) THEN - CALL DSWAP( 3, T9( IPSV, 1 ), 3, T9( I, 1 ), 3 ) - TEMP = BTMP( I ) - BTMP( I ) = BTMP( IPSV ) - BTMP( IPSV ) = TEMP - END IF - IF( JPSV.NE.I ) - $ CALL DSWAP( 3, T9( 1, JPSV ), 1, T9( 1, I ), 1 ) - JPIV( I ) = JPSV - IF( ABS( T9( I, I ) ).LT.SMIN ) THEN - INFO = 1 - T9( I, I ) = SMIN - END IF -C - DO 40 J = I + 1, 3 - T9( J, I ) = T9( J, I ) / T9( I, I ) - BTMP( J ) = BTMP( J ) - T9( J, I )*BTMP( I ) -C - DO 30 K = I + 1, 3 - T9( J, K ) = T9( J, K ) - T9( J, I )*T9( I, K ) - 30 CONTINUE -C - 40 CONTINUE -C - 50 CONTINUE -C - IF( ABS( T9( 3, 3 ) ).LT.SMIN ) - $ T9( 3, 3 ) = SMIN - SCALE = ONE - IF( ( FOUR*SMLNUM )*ABS( BTMP( 1 ) ).GT.ABS( T9( 1, 1 ) ) .OR. - $ ( FOUR*SMLNUM )*ABS( BTMP( 2 ) ).GT.ABS( T9( 2, 2 ) ) .OR. - $ ( FOUR*SMLNUM )*ABS( BTMP( 3 ) ).GT.ABS( T9( 3, 3 ) ) ) THEN - SCALE = ( ONE / FOUR ) / MAX( ABS( BTMP( 1 ) ), - $ ABS( BTMP( 2 ) ), ABS( BTMP( 3 ) ) ) - BTMP( 1 ) = BTMP( 1 )*SCALE - BTMP( 2 ) = BTMP( 2 )*SCALE - BTMP( 3 ) = BTMP( 3 )*SCALE - END IF -C - DO 70 I = 1, 3 - K = 4 - I - TEMP = ONE / T9( K, K ) - TMP( K ) = BTMP( K )*TEMP -C - DO 60 J = K + 1, 3 - TMP( K ) = TMP( K ) - ( TEMP*T9( K, J ) )*TMP( J ) - 60 CONTINUE -C - 70 CONTINUE -C - DO 80 I = 1, 2 - IF( JPIV( 3-I ).NE.3-I ) THEN - TEMP = TMP( 3-I ) - TMP( 3-I ) = TMP( JPIV( 3-I ) ) - TMP( JPIV( 3-I ) ) = TEMP - END IF - 80 CONTINUE -C - X( 1, 1 ) = TMP( 1 ) - IF ( LUPPER ) THEN - X( 1, 2 ) = TMP( 2 ) - ELSE - X( 2, 1 ) = TMP( 2 ) - END IF - X( 2, 2 ) = TMP( 3 ) - XNORM = MAX( ABS( TMP( 1 ) ) + ABS( TMP( 2 ) ), - $ ABS( TMP( 2 ) ) + ABS( TMP( 3 ) ) ) -C - RETURN -C *** Last line of SB03MW *** - END
--- a/extra/control-devel/devel/dksyn/SB03MX.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,711 +0,0 @@ - SUBROUTINE SB03MX( TRANA, N, A, LDA, C, LDC, SCALE, DWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To solve the real discrete Lyapunov matrix equation -C -C op(A)'*X*op(A) - X = scale*C -C -C where op(A) = A or A' (A**T), A is upper quasi-triangular and C is -C symmetric (C = C'). (A' denotes the transpose of the matrix A.) -C A is N-by-N, the right hand side C and the solution X are N-by-N, -C and scale is an output scale factor, set less than or equal to 1 -C to avoid overflow in X. The solution matrix X is overwritten -C onto C. -C -C A must be in Schur canonical form (as returned by LAPACK routines -C DGEES or DHSEQR), that is, block upper triangular with 1-by-1 and -C 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its -C diagonal elements equal and its off-diagonal elements of opposite -C sign. -C -C ARGUMENTS -C -C Mode Parameters -C -C TRANA CHARACTER*1 -C Specifies the form of op(A) to be used, as follows: -C = 'N': op(A) = A (No transpose); -C = 'T': op(A) = A**T (Transpose); -C = 'C': op(A) = A**T (Conjugate transpose = Transpose). -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the matrices A, X, and C. N >= 0. -C -C A (input) DOUBLE PRECISION array, dimension (LDA,N) -C The leading N-by-N part of this array must contain the -C upper quasi-triangular matrix A, in Schur canonical form. -C The part of A below the first sub-diagonal is not -C referenced. -C -C LDA INTEGER -C The leading dimension of array A. LDA >= MAX(1,N). -C -C C (input/output) DOUBLE PRECISION array, dimension (LDC,N) -C On entry, the leading N-by-N part of this array must -C contain the symmetric matrix C. -C On exit, if INFO >= 0, the leading N-by-N part of this -C array contains the symmetric solution matrix X. -C -C LDC INTEGER -C The leading dimension of array C. LDC >= MAX(1,N). -C -C SCALE (output) DOUBLE PRECISION -C The scale factor, scale, set less than or equal to 1 to -C prevent the solution overflowing. -C -C Workspace -C -C DWORK DOUBLE PRECISION array, dimension (2*N) -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C = 1: if A has almost reciprocal eigenvalues; perturbed -C values were used to solve the equation (but the -C matrix A is unchanged). -C -C METHOD -C -C A discrete-time version of the Bartels-Stewart algorithm is used. -C A set of equivalent linear algebraic systems of equations of order -C at most four are formed and solved using Gaussian elimination with -C complete pivoting. -C -C REFERENCES -C -C [1] Barraud, A.Y. T -C A numerical algorithm to solve A XA - X = Q. -C IEEE Trans. Auto. Contr., AC-22, pp. 883-885, 1977. -C -C [2] Bartels, R.H. and Stewart, G.W. T -C Solution of the matrix equation A X + XB = C. -C Comm. A.C.M., 15, pp. 820-826, 1972. -C -C NUMERICAL ASPECTS -C 3 -C The algorithm requires 0(N ) operations. -C -C CONTRIBUTOR -C -C Release 3.0: V. Sima, Katholieke Univ. Leuven, Belgium, May 1997. -C Supersedes Release 2.0 routine SB03AZ by Control Systems Research -C Group, Kingston Polytechnic, United Kingdom, October 1982. -C Based on DTRLPD by P. Petkov, Tech. University of Sofia, September -C 1993. -C -C REVISIONS -C -C V. Sima, Katholieke Univ. Leuven, Belgium, May 1999. -C V. Sima, Research Institute for Informatics, Bucharest, Apr. 2000. -C A. Varga, DLR Oberpfaffenhofen, March 2002. -C -C KEYWORDS -C -C Discrete-time system, Lyapunov equation, matrix algebra, real -C Schur form. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) -C .. -C .. Scalar Arguments .. - CHARACTER TRANA - INTEGER INFO, LDA, LDC, N - DOUBLE PRECISION SCALE -C .. -C .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), C( LDC, * ), DWORK( * ) -C .. -C .. Local Scalars .. - LOGICAL NOTRNA, LUPPER - INTEGER IERR, J, K, K1, K2, KNEXT, L, L1, L2, LNEXT, - $ MINK1N, MINK2N, MINL1N, MINL2N, NP1 - DOUBLE PRECISION A11, BIGNUM, DA11, DB, EPS, P11, P12, P21, P22, - $ SCALOC, SMIN, SMLNUM, XNORM -C .. -C .. Local Arrays .. - DOUBLE PRECISION VEC( 2, 2 ), X( 2, 2 ) -C .. -C .. External Functions .. - LOGICAL LSAME - DOUBLE PRECISION DDOT, DLAMCH, DLANHS - EXTERNAL DDOT, DLAMCH, DLANHS, LSAME -C .. -C .. External Subroutines .. - EXTERNAL DLABAD, DLALN2, DSCAL, DSYMV, SB03MV, SB04PX, - $ XERBLA -C .. -C .. Intrinsic Functions .. - INTRINSIC ABS, DBLE, MAX, MIN -C .. -C .. Executable Statements .. -C -C Decode and Test input parameters. -C - NOTRNA = LSAME( TRANA, 'N' ) - LUPPER = .TRUE. -C - INFO = 0 - IF( .NOT.NOTRNA .AND. .NOT.LSAME( TRANA, 'T' ) .AND. - $ .NOT.LSAME( TRANA, 'C' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -4 - ELSE IF( LDC.LT.MAX( 1, N ) ) THEN - INFO = -6 - END IF -C - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'SB03MX', -INFO ) - RETURN - END IF -C - SCALE = ONE -C -C Quick return if possible. -C - IF( N.EQ.0 ) - $ RETURN -C -C Set constants to control overflow. -C - EPS = DLAMCH( 'P' ) - SMLNUM = DLAMCH( 'S' ) - BIGNUM = ONE / SMLNUM - CALL DLABAD( SMLNUM, BIGNUM ) - SMLNUM = SMLNUM*DBLE( N*N ) / EPS - BIGNUM = ONE / SMLNUM -C - SMIN = MAX( SMLNUM, EPS*DLANHS( 'Max', N, A, LDA, DWORK ) ) - NP1 = N + 1 -C - IF( NOTRNA ) THEN -C -C Solve A'*X*A - X = scale*C. -C -C The (K,L)th block of X is determined starting from -C upper-left corner column by column by -C -C A(K,K)'*X(K,L)*A(L,L) - X(K,L) = C(K,L) - R(K,L), -C -C where -C K L-1 -C R(K,L) = SUM {A(I,K)'*SUM [X(I,J)*A(J,L)]} + -C I=1 J=1 -C -C K-1 -C {SUM [A(I,K)'*X(I,L)]}*A(L,L). -C I=1 -C -C Start column loop (index = L). -C L1 (L2): column index of the first (last) row of X(K,L). -C - LNEXT = 1 -C - DO 60 L = 1, N - IF( L.LT.LNEXT ) - $ GO TO 60 - L1 = L - L2 = L - IF( L.LT.N ) THEN - IF( A( L+1, L ).NE.ZERO ) - $ L2 = L2 + 1 - LNEXT = L2 + 1 - END IF -C -C Start row loop (index = K). -C K1 (K2): row index of the first (last) row of X(K,L). -C - DWORK( L1 ) = ZERO - DWORK( N+L1 ) = ZERO - CALL DSYMV( 'Lower', L1-1, ONE, C, LDC, A( 1, L1 ), 1, ZERO, - $ DWORK, 1 ) - CALL DSYMV( 'Lower', L1-1, ONE, C, LDC, A( 1, L2 ), 1, ZERO, - $ DWORK( NP1 ), 1 ) -C - KNEXT = L -C - DO 50 K = L, N - IF( K.LT.KNEXT ) - $ GO TO 50 - K1 = K - K2 = K - IF( K.LT.N ) THEN - IF( A( K+1, K ).NE.ZERO ) - $ K2 = K2 + 1 - KNEXT = K2 + 1 - END IF -C - IF( L1.EQ.L2 .AND. K1.EQ.K2 ) THEN - DWORK( K1 ) = DDOT( L1-1, C( K1, 1 ), LDC, A( 1, L1 ), - $ 1 ) -C - VEC( 1, 1 ) = C( K1, L1 ) - - $ ( DDOT( K1, A( 1, K1 ), 1, DWORK, 1 ) + A( L1, L1 ) - $ *DDOT( K1-1, A( 1, K1 ), 1, C( 1, L1 ), 1 ) ) - SCALOC = ONE -C - A11 = A( K1, K1 )*A( L1, L1 ) - ONE - DA11 = ABS( A11 ) - IF( DA11.LE.SMIN ) THEN - A11 = SMIN - DA11 = SMIN - INFO = 1 - END IF - DB = ABS( VEC( 1, 1 ) ) - IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN - IF( DB.GT.BIGNUM*DA11 ) - $ SCALOC = ONE / DB - END IF - X( 1, 1 ) = ( VEC( 1, 1 )*SCALOC ) / A11 -C - IF( SCALOC.NE.ONE ) THEN -C - DO 10 J = 1, N - CALL DSCAL( N, SCALOC, C( 1, J ), 1 ) - 10 CONTINUE -C - CALL DSCAL( N, SCALOC, DWORK, 1 ) - SCALE = SCALE*SCALOC - END IF - C( K1, L1 ) = X( 1, 1 ) - IF( K1.NE.L1 ) THEN - C( L1, K1 ) = X( 1, 1 ) - END IF -C - ELSE IF( L1.EQ.L2 .AND. K1.NE.K2 ) THEN -C - DWORK( K1 ) = DDOT( L1-1, C( K1, 1 ), LDC, A( 1, L1 ), - $ 1 ) - DWORK( K2 ) = DDOT( L1-1, C( K2, 1 ), LDC, A( 1, L1 ), - $ 1 ) -C - VEC( 1, 1 ) = C( K1, L1 ) - - $ ( DDOT( K2, A( 1, K1 ), 1, DWORK, 1 ) + A( L1, L1 ) - $ *DDOT( K1-1, A( 1, K1 ), 1, C( 1, L1 ), 1 ) ) -C - VEC( 2, 1 ) = C( K2, L1 ) - - $ ( DDOT( K2, A( 1, K2 ), 1, DWORK, 1 ) + A( L1, L1 ) - $ *DDOT( K1-1, A( 1, K2 ), 1, C( 1, L1 ), 1 ) ) -C - CALL DLALN2( .TRUE., 2, 1, SMIN, A( L1, L1 ), - $ A( K1, K1 ), LDA, ONE, ONE, VEC, 2, ONE, - $ ZERO, X, 2, SCALOC, XNORM, IERR ) - IF( IERR.NE.0 ) - $ INFO = 1 -C - IF( SCALOC.NE.ONE ) THEN -C - DO 20 J = 1, N - CALL DSCAL( N, SCALOC, C( 1, J ), 1 ) - 20 CONTINUE -C - CALL DSCAL( N, SCALOC, DWORK, 1 ) - SCALE = SCALE*SCALOC - END IF - C( K1, L1 ) = X( 1, 1 ) - C( K2, L1 ) = X( 2, 1 ) - C( L1, K1 ) = X( 1, 1 ) - C( L1, K2 ) = X( 2, 1 ) -C - ELSE IF( L1.NE.L2 .AND. K1.EQ.K2 ) THEN -C - DWORK( K1 ) = DDOT( L1-1, C( K1, 1 ), LDC, A( 1, L1 ), - $ 1 ) - DWORK( N+K1 ) = DDOT( L1-1, C( K1, 1 ), LDC, - $ A( 1, L2 ), 1 ) - P11 = DDOT( K1-1, A( 1, K1 ), 1, C( 1, L1 ), 1 ) - P12 = DDOT( K1-1, A( 1, K1 ), 1, C( 1, L2 ), 1 ) -C - VEC( 1, 1 ) = C( K1, L1 ) - - $ ( DDOT( K1, A( 1, K1 ), 1, DWORK, 1 ) + - $ P11*A( L1, L1 ) + P12*A( L2, L1 ) ) -C - VEC( 2, 1 ) = C( K1, L2 ) - - $ ( DDOT( K1, A( 1, K1 ), 1, DWORK( NP1 ), 1 ) + - $ P11*A( L1, L2 ) + P12*A( L2, L2 ) ) -C - CALL DLALN2( .TRUE., 2, 1, SMIN, A( K1, K1 ), - $ A( L1, L1 ), LDA, ONE, ONE, VEC, 2, ONE, - $ ZERO, X, 2, SCALOC, XNORM, IERR ) - IF( IERR.NE.0 ) - $ INFO = 1 -C - IF( SCALOC.NE.ONE ) THEN -C - DO 30 J = 1, N - CALL DSCAL( N, SCALOC, C( 1, J ), 1 ) - 30 CONTINUE -C - CALL DSCAL( N, SCALOC, DWORK, 1 ) - CALL DSCAL( N, SCALOC, DWORK( NP1 ), 1 ) - SCALE = SCALE*SCALOC - END IF - C( K1, L1 ) = X( 1, 1 ) - C( K1, L2 ) = X( 2, 1 ) - C( L1, K1 ) = X( 1, 1 ) - C( L2, K1 ) = X( 2, 1 ) -C - ELSE IF( L1.NE.L2 .AND. K1.NE.K2 ) THEN -C - DWORK( K1 ) = DDOT( L1-1, C( K1, 1 ), LDC, A( 1, L1 ), - $ 1 ) - DWORK( K2 ) = DDOT( L1-1, C( K2, 1 ), LDC, A( 1, L1 ), - $ 1 ) - DWORK( N+K1 ) = DDOT( L1-1, C( K1, 1 ), LDC, - $ A( 1, L2 ), 1 ) - DWORK( N+K2 ) = DDOT( L1-1, C( K2, 1 ), LDC, - $ A( 1, L2 ), 1 ) - P11 = DDOT( K1-1, A( 1, K1 ), 1, C( 1, L1 ), 1 ) - P12 = DDOT( K1-1, A( 1, K1 ), 1, C( 1, L2 ), 1 ) - P21 = DDOT( K1-1, A( 1, K2 ), 1, C( 1, L1 ), 1 ) - P22 = DDOT( K1-1, A( 1, K2 ), 1, C( 1, L2 ), 1 ) -C - VEC( 1, 1 ) = C( K1, L1 ) - - $ ( DDOT( K2, A( 1, K1 ), 1, DWORK, 1 ) + - $ P11*A( L1, L1 ) + P12*A( L2, L1 ) ) -C - VEC( 1, 2 ) = C( K1, L2 ) - - $ ( DDOT( K2, A( 1, K1 ), 1, DWORK( NP1 ), 1 ) + - $ P11*A( L1, L2 ) + P12*A( L2, L2 ) ) -C - VEC( 2, 1 ) = C( K2, L1 ) - - $ ( DDOT( K2, A( 1, K2 ), 1, DWORK, 1 ) + - $ P21*A( L1, L1 ) + P22*A( L2, L1 ) ) -C - VEC( 2, 2 ) = C( K2, L2 ) - - $ ( DDOT( K2, A( 1, K2 ), 1, DWORK( NP1 ), 1 ) + - $ P21*A( L1, L2 ) + P22*A( L2, L2 ) ) -C - IF( K1.EQ.L1 ) THEN - CALL SB03MV( .FALSE., LUPPER, A( K1, K1 ), LDA, - $ VEC, 2, SCALOC, X, 2, XNORM, IERR ) - IF( LUPPER ) THEN - X( 2, 1 ) = X( 1, 2 ) - ELSE - X( 1, 2 ) = X( 2, 1 ) - END IF - ELSE - CALL SB04PX( .TRUE., .FALSE., -1, 2, 2, - $ A( K1, K1 ), LDA, A( L1, L1 ), LDA, - $ VEC, 2, SCALOC, X, 2, XNORM, IERR ) - END IF - IF( IERR.NE.0 ) - $ INFO = 1 -C - IF( SCALOC.NE.ONE ) THEN -C - DO 40 J = 1, N - CALL DSCAL( N, SCALOC, C( 1, J ), 1 ) - 40 CONTINUE -C - CALL DSCAL( N, SCALOC, DWORK, 1 ) - CALL DSCAL( N, SCALOC, DWORK( NP1 ), 1 ) - SCALE = SCALE*SCALOC - END IF - C( K1, L1 ) = X( 1, 1 ) - C( K1, L2 ) = X( 1, 2 ) - C( K2, L1 ) = X( 2, 1 ) - C( K2, L2 ) = X( 2, 2 ) - IF( K1.NE.L1 ) THEN - C( L1, K1 ) = X( 1, 1 ) - C( L2, K1 ) = X( 1, 2 ) - C( L1, K2 ) = X( 2, 1 ) - C( L2, K2 ) = X( 2, 2 ) - END IF - END IF -C - 50 CONTINUE -C - 60 CONTINUE -C - ELSE -C -C Solve A*X*A' - X = scale*C. -C -C The (K,L)th block of X is determined starting from -C bottom-right corner column by column by -C -C A(K,K)*X(K,L)*A(L,L)' - X(K,L) = C(K,L) - R(K,L), -C -C where -C -C N N -C R(K,L) = SUM {A(K,I)* SUM [X(I,J)*A(L,J)']} + -C I=K J=L+1 -C -C N -C { SUM [A(K,J)*X(J,L)]}*A(L,L)' -C J=K+1 -C -C Start column loop (index = L) -C L1 (L2): column index of the first (last) row of X(K,L) -C - LNEXT = N -C - DO 120 L = N, 1, -1 - IF( L.GT.LNEXT ) - $ GO TO 120 - L1 = L - L2 = L - IF( L.GT.1 ) THEN - IF( A( L, L-1 ).NE.ZERO ) THEN - L1 = L1 - 1 - DWORK( L1 ) = ZERO - DWORK( N+L1 ) = ZERO - END IF - LNEXT = L1 - 1 - END IF - MINL1N = MIN( L1+1, N ) - MINL2N = MIN( L2+1, N ) -C -C Start row loop (index = K) -C K1 (K2): row index of the first (last) row of X(K,L) -C - IF( L2.LT.N ) THEN - CALL DSYMV( 'Upper', N-L2, ONE, C( L2+1, L2+1 ), LDC, - $ A( L1, L2+1 ), LDA, ZERO, DWORK( L2+1 ), 1 ) - CALL DSYMV( 'Upper', N-L2, ONE, C( L2+1, L2+1 ), LDC, - $ A( L2, L2+1 ), LDA, ZERO, DWORK( NP1+L2 ), 1) - END IF -C - KNEXT = L -C - DO 110 K = L, 1, -1 - IF( K.GT.KNEXT ) - $ GO TO 110 - K1 = K - K2 = K - IF( K.GT.1 ) THEN - IF( A( K, K-1 ).NE.ZERO ) - $ K1 = K1 - 1 - KNEXT = K1 - 1 - END IF - MINK1N = MIN( K1+1, N ) - MINK2N = MIN( K2+1, N ) -C - IF( L1.EQ.L2 .AND. K1.EQ.K2 ) THEN - DWORK( K1 ) = DDOT( N-L1, C( K1, MINL1N ), LDC, - $ A( L1, MINL1N ), LDA ) -C - VEC( 1, 1 ) = C( K1, L1 ) - - $ ( DDOT( N-K1+1, A( K1, K1 ), LDA, DWORK( K1 ), 1 ) - $ + DDOT( N-K1, A( K1, MINK1N ), LDA, - $ C( MINK1N, L1 ), 1 )*A( L1, L1 ) ) - SCALOC = ONE -C - A11 = A( K1, K1 )*A( L1, L1 ) - ONE - DA11 = ABS( A11 ) - IF( DA11.LE.SMIN ) THEN - A11 = SMIN - DA11 = SMIN - INFO = 1 - END IF - DB = ABS( VEC( 1, 1 ) ) - IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN - IF( DB.GT.BIGNUM*DA11 ) - $ SCALOC = ONE / DB - END IF - X( 1, 1 ) = ( VEC( 1, 1 )*SCALOC ) / A11 -C - IF( SCALOC.NE.ONE ) THEN -C - DO 70 J = 1, N - CALL DSCAL( N, SCALOC, C( 1, J ), 1 ) - 70 CONTINUE -C - CALL DSCAL( N, SCALOC, DWORK, 1 ) - SCALE = SCALE*SCALOC - END IF - C( K1, L1 ) = X( 1, 1 ) - IF( K1.NE.L1 ) THEN - C( L1, K1 ) = X( 1, 1 ) - END IF -C - ELSE IF( L1.EQ.L2 .AND. K1.NE.K2 ) THEN -C - DWORK( K1 ) = DDOT( N-L1, C( K1, MINL1N ), LDC, - $ A( L1, MINL1N ), LDA ) - DWORK( K2 ) = DDOT( N-L1, C( K2, MINL1N ), LDC, - $ A( L1, MINL1N ), LDA ) -C - VEC( 1, 1 ) = C( K1, L1 ) - - $ ( DDOT( NP1-K1, A( K1, K1 ), LDA, DWORK( K1 ), 1 ) - $ + DDOT( N-K2, A( K1, MINK2N ), LDA, - $ C( MINK2N, L1 ), 1 )*A( L1, L1 ) ) -C - VEC( 2, 1 ) = C( K2, L1 ) - - $ ( DDOT( NP1-K1, A( K2, K1 ), LDA, DWORK( K1 ), 1 ) - $ + DDOT( N-K2, A( K2, MINK2N ), LDA, - $ C( MINK2N, L1 ), 1 )*A( L1, L1 ) ) -C - CALL DLALN2( .FALSE., 2, 1, SMIN, A( L1, L1 ), - $ A( K1, K1 ), LDA, ONE, ONE, VEC, 2, ONE, - $ ZERO, X, 2, SCALOC, XNORM, IERR ) - IF( IERR.NE.0 ) - $ INFO = 1 -C - IF( SCALOC.NE.ONE ) THEN -C - DO 80 J = 1, N - CALL DSCAL( N, SCALOC, C( 1, J ), 1 ) - 80 CONTINUE -C - CALL DSCAL( N, SCALOC, DWORK, 1 ) - SCALE = SCALE*SCALOC - END IF - C( K1, L1 ) = X( 1, 1 ) - C( K2, L1 ) = X( 2, 1 ) - C( L1, K1 ) = X( 1, 1 ) - C( L1, K2 ) = X( 2, 1 ) -C - ELSE IF( L1.NE.L2 .AND. K1.EQ.K2 ) THEN -C - DWORK( K1 ) = DDOT( N-L2, C( K1, MINL2N ), LDC, - $ A( L1, MINL2N ), LDA ) - DWORK( N+K1 ) = DDOT( N-L2, C( K1, MINL2N ), LDC, - $ A( L2, MINL2N ), LDA ) - P11 = DDOT( N-K1, A( K1, MINK1N ), LDA, - $ C( MINK1N, L1 ), 1 ) - P12 = DDOT( N-K1, A( K1, MINK1N ), LDA, - $ C( MINK1N, L2 ), 1 ) -C - VEC( 1, 1 ) = C( K1, L1 ) - - $ ( DDOT( NP1-K1, A( K1, K1 ), LDA, DWORK( K1 ), 1 ) - $ + P11*A( L1, L1 ) + P12*A( L1, L2 ) ) -C - VEC( 2, 1 ) = C( K1, L2 ) - - $ ( DDOT( NP1-K1, A( K1, K1 ), LDA, DWORK( N+K1 ), 1) - $ + P11*A( L2, L1 ) + P12*A( L2, L2 ) ) -C - CALL DLALN2( .FALSE., 2, 1, SMIN, A( K1, K1 ), - $ A( L1, L1 ), LDA, ONE, ONE, VEC, 2, ONE, - $ ZERO, X, 2, SCALOC, XNORM, IERR ) - IF( IERR.NE.0 ) - $ INFO = 1 -C - IF( SCALOC.NE.ONE ) THEN -C - DO 90 J = 1, N - CALL DSCAL( N, SCALOC, C( 1, J ), 1 ) - 90 CONTINUE -C - CALL DSCAL( N, SCALOC, DWORK, 1 ) - CALL DSCAL( N, SCALOC, DWORK( NP1 ), 1 ) - SCALE = SCALE*SCALOC - END IF - C( K1, L1 ) = X( 1, 1 ) - C( K1, L2 ) = X( 2, 1 ) - C( L1, K1 ) = X( 1, 1 ) - C( L2, K1 ) = X( 2, 1 ) -C - ELSE IF( L1.NE.L2 .AND. K1.NE.K2 ) THEN -C - DWORK( K1 ) = DDOT( N-L2, C( K1, MINL2N ), LDC, - $ A( L1, MINL2N ), LDA ) - DWORK( K2 ) = DDOT( N-L2, C( K2, MINL2N ), LDC, - $ A( L1, MINL2N ), LDA ) - DWORK( N+K1 ) = DDOT( N-L2, C( K1, MINL2N ), LDC, - $ A( L2, MINL2N ), LDA ) - DWORK( N+K2 ) = DDOT( N-L2, C( K2, MINL2N ), LDC, - $ A( L2, MINL2N ), LDA ) - P11 = DDOT( N-K2, A( K1, MINK2N ), LDA, - $ C( MINK2N, L1 ), 1 ) - P12 = DDOT( N-K2, A( K1, MINK2N ), LDA, - $ C( MINK2N, L2 ), 1 ) - P21 = DDOT( N-K2, A( K2, MINK2N ), LDA, - $ C( MINK2N, L1 ), 1 ) - P22 = DDOT( N-K2, A( K2, MINK2N ), LDA, - $ C( MINK2N, L2 ), 1 ) -C - VEC( 1, 1 ) = C( K1, L1 ) - - $ ( DDOT( NP1-K1, A( K1, K1 ), LDA, DWORK( K1 ), 1 ) - $ + P11*A( L1, L1 ) + P12*A( L1, L2 ) ) -C - VEC( 1, 2 ) = C( K1, L2 ) - - $ ( DDOT( NP1-K1, A( K1, K1 ), LDA, DWORK( N+K1 ), - $ 1) + P11*A( L2, L1 ) + P12*A( L2, L2 ) ) -C - VEC( 2, 1 ) = C( K2, L1 ) - - $ ( DDOT( NP1-K1, A( K2, K1 ), LDA, DWORK( K1 ), - $ 1) + P21*A( L1, L1 ) + P22*A( L1, L2 ) ) -C - VEC( 2, 2 ) = C( K2, L2 ) - - $ ( DDOT( NP1-K1, A( K2, K1 ), LDA, DWORK( N+K1 ), 1) - $ + P21*A( L2, L1 ) + P22*A( L2, L2 ) ) -C - IF( K1.EQ.L1 ) THEN - CALL SB03MV( .TRUE., LUPPER, A( K1, K1 ), LDA, VEC, - $ 2, SCALOC, X, 2, XNORM, IERR ) - IF( LUPPER ) THEN - X( 2, 1 ) = X( 1, 2 ) - ELSE - X( 1, 2 ) = X( 2, 1 ) - END IF - ELSE - CALL SB04PX( .FALSE., .TRUE., -1, 2, 2, - $ A( K1, K1 ), LDA, A( L1, L1 ), LDA, - $ VEC, 2, SCALOC, X, 2, XNORM, IERR ) - END IF - IF( IERR.NE.0 ) - $ INFO = 1 -C - IF( SCALOC.NE.ONE ) THEN -C - DO 100 J = 1, N - CALL DSCAL( N, SCALOC, C( 1, J ), 1 ) - 100 CONTINUE -C - CALL DSCAL( N, SCALOC, DWORK, 1 ) - CALL DSCAL( N, SCALOC, DWORK( NP1 ), 1 ) - SCALE = SCALE*SCALOC - END IF - C( K1, L1 ) = X( 1, 1 ) - C( K1, L2 ) = X( 1, 2 ) - C( K2, L1 ) = X( 2, 1 ) - C( K2, L2 ) = X( 2, 2 ) - IF( K1.NE.L1 ) THEN - C( L1, K1 ) = X( 1, 1 ) - C( L2, K1 ) = X( 1, 2 ) - C( L1, K2 ) = X( 2, 1 ) - C( L2, K2 ) = X( 2, 2 ) - END IF - END IF -C - 110 CONTINUE -C - 120 CONTINUE -C - END IF -C - RETURN -C *** Last line of SB03MX *** - END
--- a/extra/control-devel/devel/dksyn/SB03MY.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,613 +0,0 @@ - SUBROUTINE SB03MY( TRANA, N, A, LDA, C, LDC, SCALE, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To solve the real Lyapunov matrix equation -C -C op(A)'*X + X*op(A) = scale*C -C -C where op(A) = A or A' (A**T), A is upper quasi-triangular and C is -C symmetric (C = C'). (A' denotes the transpose of the matrix A.) -C A is N-by-N, the right hand side C and the solution X are N-by-N, -C and scale is an output scale factor, set less than or equal to 1 -C to avoid overflow in X. The solution matrix X is overwritten -C onto C. -C -C A must be in Schur canonical form (as returned by LAPACK routines -C DGEES or DHSEQR), that is, block upper triangular with 1-by-1 and -C 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its -C diagonal elements equal and its off-diagonal elements of opposite -C sign. -C -C ARGUMENTS -C -C Mode Parameters -C -C TRANA CHARACTER*1 -C Specifies the form of op(A) to be used, as follows: -C = 'N': op(A) = A (No transpose); -C = 'T': op(A) = A**T (Transpose); -C = 'C': op(A) = A**T (Conjugate transpose = Transpose). -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the matrices A, X, and C. N >= 0. -C -C A (input) DOUBLE PRECISION array, dimension (LDA,N) -C The leading N-by-N part of this array must contain the -C upper quasi-triangular matrix A, in Schur canonical form. -C The part of A below the first sub-diagonal is not -C referenced. -C -C LDA INTEGER -C The leading dimension of array A. LDA >= MAX(1,N). -C -C C (input/output) DOUBLE PRECISION array, dimension (LDC,N) -C On entry, the leading N-by-N part of this array must -C contain the symmetric matrix C. -C On exit, if INFO >= 0, the leading N-by-N part of this -C array contains the symmetric solution matrix X. -C -C LDC INTEGER -C The leading dimension of array C. LDC >= MAX(1,N). -C -C SCALE (output) DOUBLE PRECISION -C The scale factor, scale, set less than or equal to 1 to -C prevent the solution overflowing. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C = 1: if A and -A have common or very close eigenvalues; -C perturbed values were used to solve the equation -C (but the matrix A is unchanged). -C -C METHOD -C -C Bartels-Stewart algorithm is used. A set of equivalent linear -C algebraic systems of equations of order at most four are formed -C and solved using Gaussian elimination with complete pivoting. -C -C REFERENCES -C -C [1] Bartels, R.H. and Stewart, G.W. T -C Solution of the matrix equation A X + XB = C. -C Comm. A.C.M., 15, pp. 820-826, 1972. -C -C NUMERICAL ASPECTS -C 3 -C The algorithm requires 0(N ) operations. -C -C CONTRIBUTOR -C -C Release 3.0: V. Sima, Katholieke Univ. Leuven, Belgium, May 1997. -C Supersedes Release 2.0 routine SB03AY by Control Systems Research -C Group, Kingston Polytechnic, United Kingdom, October 1982. -C Based on DTRLYP by P. Petkov, Tech. University of Sofia, September -C 1993. -C -C REVISIONS -C -C V. Sima, Katholieke Univ. Leuven, Belgium, May 1999. -C -C KEYWORDS -C -C Continuous-time system, Lyapunov equation, matrix algebra, real -C Schur form. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) -C .. -C .. Scalar Arguments .. - CHARACTER TRANA - INTEGER INFO, LDA, LDC, N - DOUBLE PRECISION SCALE -C .. -C .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), C( LDC, * ) -C .. -C .. Local Scalars .. - LOGICAL NOTRNA, LUPPER - INTEGER IERR, J, K, K1, K2, KNEXT, L, L1, L2, LNEXT, - $ MINK1N, MINK2N, MINL1N, MINL2N - DOUBLE PRECISION A11, BIGNUM, DA11, DB, EPS, SCALOC, SMIN, - $ SMLNUM, XNORM -C .. -C .. Local Arrays .. - DOUBLE PRECISION DUM( 1 ), VEC( 2, 2 ), X( 2, 2 ) -C .. -C .. External Functions .. - LOGICAL LSAME - DOUBLE PRECISION DDOT, DLAMCH, DLANHS - EXTERNAL DDOT, DLAMCH, DLANHS, LSAME -C .. -C .. External Subroutines .. - EXTERNAL DLABAD, DLALN2, DLASY2, DSCAL, SB03MW, XERBLA -C .. -C .. Intrinsic Functions .. - INTRINSIC ABS, DBLE, MAX, MIN -C .. -C .. Executable Statements .. -C -C Decode and Test input parameters. -C - NOTRNA = LSAME( TRANA, 'N' ) - LUPPER = .TRUE. -C - INFO = 0 - IF( .NOT.NOTRNA .AND. .NOT.LSAME( TRANA, 'T' ) .AND. - $ .NOT.LSAME( TRANA, 'C' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -4 - ELSE IF( LDC.LT.MAX( 1, N ) ) THEN - INFO = -6 - END IF -C - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'SB03MY', -INFO ) - RETURN - END IF -C - SCALE = ONE -C -C Quick return if possible. -C - IF( N.EQ.0 ) - $ RETURN -C -C Set constants to control overflow. -C - EPS = DLAMCH( 'P' ) - SMLNUM = DLAMCH( 'S' ) - BIGNUM = ONE / SMLNUM - CALL DLABAD( SMLNUM, BIGNUM ) - SMLNUM = SMLNUM*DBLE( N*N ) / EPS - BIGNUM = ONE / SMLNUM -C - SMIN = MAX( SMLNUM, EPS*DLANHS( 'Max', N, A, LDA, DUM ) ) -C - IF( NOTRNA ) THEN -C -C Solve A'*X + X*A = scale*C. -C -C The (K,L)th block of X is determined starting from -C upper-left corner column by column by -C -C A(K,K)'*X(K,L) + X(K,L)*A(L,L) = C(K,L) - R(K,L), -C -C where -C K-1 L-1 -C R(K,L) = SUM [A(I,K)'*X(I,L)] + SUM [X(K,J)*A(J,L)]. -C I=1 J=1 -C -C Start column loop (index = L). -C L1 (L2): column index of the first (last) row of X(K,L). -C - LNEXT = 1 -C - DO 60 L = 1, N - IF( L.LT.LNEXT ) - $ GO TO 60 - L1 = L - L2 = L - IF( L.LT.N ) THEN - IF( A( L+1, L ).NE.ZERO ) - $ L2 = L2 + 1 - LNEXT = L2 + 1 - END IF -C -C Start row loop (index = K). -C K1 (K2): row index of the first (last) row of X(K,L). -C - KNEXT = L -C - DO 50 K = L, N - IF( K.LT.KNEXT ) - $ GO TO 50 - K1 = K - K2 = K - IF( K.LT.N ) THEN - IF( A( K+1, K ).NE.ZERO ) - $ K2 = K2 + 1 - KNEXT = K2 + 1 - END IF -C - IF( L1.EQ.L2 .AND. K1.EQ.K2 ) THEN - VEC( 1, 1 ) = C( K1, L1 ) - - $ ( DDOT( K1-1, A( 1, K1 ), 1, C( 1, L1 ), 1 ) + - $ DDOT( L1-1, C( K1, 1 ), LDC, A( 1, L1 ), 1 ) ) - SCALOC = ONE -C - A11 = A( K1, K1 ) + A( L1, L1 ) - DA11 = ABS( A11 ) - IF( DA11.LE.SMIN ) THEN - A11 = SMIN - DA11 = SMIN - INFO = 1 - END IF - DB = ABS( VEC( 1, 1 ) ) - IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN - IF( DB.GT.BIGNUM*DA11 ) - $ SCALOC = ONE / DB - END IF - X( 1, 1 ) = ( VEC( 1, 1 )*SCALOC ) / A11 -C - IF( SCALOC.NE.ONE ) THEN -C - DO 10 J = 1, N - CALL DSCAL( N, SCALOC, C( 1, J ), 1 ) - 10 CONTINUE -C - SCALE = SCALE*SCALOC - END IF - C( K1, L1 ) = X( 1, 1 ) - IF( K1.NE.L1 ) THEN - C( L1, K1 ) = X( 1, 1 ) - END IF -C - ELSE IF( L1.EQ.L2 .AND. K1.NE.K2 ) THEN -C - VEC( 1, 1 ) = C( K1, L1 ) - - $ ( DDOT( K1-1, A( 1, K1 ), 1, C( 1, L1 ), 1 ) + - $ DDOT( L1-1, C( K1, 1 ), LDC, A( 1, L1 ), 1 ) ) -C - VEC( 2, 1 ) = C( K2, L1 ) - - $ ( DDOT( K1-1, A( 1, K2 ), 1, C( 1, L1 ), 1 ) + - $ DDOT( L1-1, C( K2, 1 ), LDC, A( 1, L1 ), 1 ) ) -C - CALL DLALN2( .TRUE., 2, 1, SMIN, ONE, A( K1, K1 ), - $ LDA, ONE, ONE, VEC, 2, -A( L1, L1 ), - $ ZERO, X, 2, SCALOC, XNORM, IERR ) - IF( IERR.NE.0 ) - $ INFO = 1 -C - IF( SCALOC.NE.ONE ) THEN -C - DO 20 J = 1, N - CALL DSCAL( N, SCALOC, C( 1, J ), 1 ) - 20 CONTINUE -C - SCALE = SCALE*SCALOC - END IF - C( K1, L1 ) = X( 1, 1 ) - C( K2, L1 ) = X( 2, 1 ) - C( L1, K1 ) = X( 1, 1 ) - C( L1, K2 ) = X( 2, 1 ) -C - ELSE IF( L1.NE.L2 .AND. K1.EQ.K2 ) THEN -C - VEC( 1, 1 ) = C( K1, L1 ) - - $ ( DDOT( K1-1, A( 1, K1 ), 1, C( 1, L1 ), 1 ) + - $ DDOT( L1-1, C( K1, 1 ), LDC, A( 1, L1 ), 1 ) ) -C - VEC( 2, 1 ) = C( K1, L2 ) - - $ ( DDOT( K1-1, A( 1, K1 ), 1, C( 1, L2 ), 1 ) + - $ DDOT( L1-1, C( K1, 1 ), LDC, A( 1, L2 ), 1 ) ) -C - CALL DLALN2( .TRUE., 2, 1, SMIN, ONE, A( L1, L1 ), - $ LDA, ONE, ONE, VEC, 2, -A( K1, K1 ), - $ ZERO, X, 2, SCALOC, XNORM, IERR ) - IF( IERR.NE.0 ) - $ INFO = 1 -C - IF( SCALOC.NE.ONE ) THEN -C - DO 30 J = 1, N - CALL DSCAL( N, SCALOC, C( 1, J ), 1 ) - 30 CONTINUE -C - SCALE = SCALE*SCALOC - END IF - C( K1, L1 ) = X( 1, 1 ) - C( K1, L2 ) = X( 2, 1 ) - C( L1, K1 ) = X( 1, 1 ) - C( L2, K1 ) = X( 2, 1 ) -C - ELSE IF( L1.NE.L2 .AND. K1.NE.K2 ) THEN -C - VEC( 1, 1 ) = C( K1, L1 ) - - $ ( DDOT( K1-1, A( 1, K1 ), 1, C( 1, L1 ), 1 ) + - $ DDOT( L1-1, C( K1, 1 ), LDC, A( 1, L1 ), 1 ) ) -C - VEC( 1, 2 ) = C( K1, L2 ) - - $ ( DDOT( K1-1, A( 1, K1 ), 1, C( 1, L2 ), 1 ) + - $ DDOT( L1-1, C( K1, 1 ), LDC, A( 1, L2 ), 1 ) ) -C - VEC( 2, 1 ) = C( K2, L1 ) - - $ ( DDOT( K1-1, A( 1, K2 ), 1, C( 1, L1 ), 1 ) + - $ DDOT( L1-1, C( K2, 1 ), LDC, A( 1, L1 ), 1 ) ) -C - VEC( 2, 2 ) = C( K2, L2 ) - - $ ( DDOT( K1-1, A( 1, K2 ), 1, C( 1, L2 ), 1 ) + - $ DDOT( L1-1, C( K2, 1 ), LDC, A( 1, L2 ), 1 ) ) -C - IF( K1.EQ.L1 ) THEN - CALL SB03MW( .FALSE., LUPPER, A( K1, K1 ), LDA, - $ VEC, 2, SCALOC, X, 2, XNORM, IERR ) - IF( LUPPER ) THEN - X( 2, 1 ) = X( 1, 2 ) - ELSE - X( 1, 2 ) = X( 2, 1 ) - END IF - ELSE - CALL DLASY2( .TRUE., .FALSE., 1, 2, 2, A( K1, K1 ), - $ LDA, A( L1, L1 ), LDA, VEC, 2, SCALOC, - $ X, 2, XNORM, IERR ) - END IF - IF( IERR.NE.0 ) - $ INFO = 1 -C - IF( SCALOC.NE.ONE ) THEN -C - DO 40 J = 1, N - CALL DSCAL( N, SCALOC, C( 1, J ), 1 ) - 40 CONTINUE -C - SCALE = SCALE*SCALOC - END IF - C( K1, L1 ) = X( 1, 1 ) - C( K1, L2 ) = X( 1, 2 ) - C( K2, L1 ) = X( 2, 1 ) - C( K2, L2 ) = X( 2, 2 ) - IF( K1.NE.L1 ) THEN - C( L1, K1 ) = X( 1, 1 ) - C( L2, K1 ) = X( 1, 2 ) - C( L1, K2 ) = X( 2, 1 ) - C( L2, K2 ) = X( 2, 2 ) - END IF - END IF -C - 50 CONTINUE -C - 60 CONTINUE -C - ELSE -C -C Solve A*X + X*A' = scale*C. -C -C The (K,L)th block of X is determined starting from -C bottom-right corner column by column by -C -C A(K,K)*X(K,L) + X(K,L)*A(L,L)' = C(K,L) - R(K,L), -C -C where -C N N -C R(K,L) = SUM [A(K,I)*X(I,L)] + SUM [X(K,J)*A(L,J)']. -C I=K+1 J=L+1 -C -C Start column loop (index = L). -C L1 (L2): column index of the first (last) row of X(K,L). -C - LNEXT = N -C - DO 120 L = N, 1, -1 - IF( L.GT.LNEXT ) - $ GO TO 120 - L1 = L - L2 = L - IF( L.GT.1 ) THEN - IF( A( L, L-1 ).NE.ZERO ) - $ L1 = L1 - 1 - LNEXT = L1 - 1 - END IF - MINL1N = MIN( L1+1, N ) - MINL2N = MIN( L2+1, N ) -C -C Start row loop (index = K). -C K1 (K2): row index of the first (last) row of X(K,L). -C - KNEXT = L -C - DO 110 K = L, 1, -1 - IF( K.GT.KNEXT ) - $ GO TO 110 - K1 = K - K2 = K - IF( K.GT.1 ) THEN - IF( A( K, K-1 ).NE.ZERO ) - $ K1 = K1 - 1 - KNEXT = K1 - 1 - END IF - MINK1N = MIN( K1+1, N ) - MINK2N = MIN( K2+1, N ) -C - IF( L1.EQ.L2 .AND. K1.EQ.K2 ) THEN - VEC( 1, 1 ) = C( K1, L1 ) - - $ ( DDOT( N-K1, A( K1, MINK1N ), LDA, - $ C( MINK1N, L1 ), 1 ) + - $ DDOT( N-L1, C( K1, MINL1N ), LDC, - $ A( L1, MINL1N ), LDA ) ) - SCALOC = ONE -C - A11 = A( K1, K1 ) + A( L1, L1 ) - DA11 = ABS( A11 ) - IF( DA11.LE.SMIN ) THEN - A11 = SMIN - DA11 = SMIN - INFO = 1 - END IF - DB = ABS( VEC( 1, 1 ) ) - IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN - IF( DB.GT.BIGNUM*DA11 ) - $ SCALOC = ONE / DB - END IF - X( 1, 1 ) = ( VEC( 1, 1 )*SCALOC ) / A11 -C - IF( SCALOC.NE.ONE ) THEN -C - DO 70 J = 1, N - CALL DSCAL( N, SCALOC, C( 1, J ), 1 ) - 70 CONTINUE -C - SCALE = SCALE*SCALOC - END IF - C( K1, L1 ) = X( 1, 1 ) - IF( K1.NE.L1 ) THEN - C( L1, K1 ) = X( 1, 1 ) - END IF -C - ELSE IF( L1.EQ.L2 .AND. K1.NE.K2 ) THEN -C - VEC( 1, 1 ) = C( K1, L1 ) - - $ ( DDOT( N-K2, A( K1, MINK2N ), LDA, - $ C( MINK2N, L1 ), 1 ) + - $ DDOT( N-L2, C( K1, MINL2N ), LDC, - $ A( L1, MINL2N ), LDA ) ) -C - VEC( 2, 1 ) = C( K2, L1 ) - - $ ( DDOT( N-K2, A( K2, MINK2N ), LDA, - $ C( MINK2N, L1 ), 1 ) + - $ DDOT( N-L2, C( K2, MINL2N ), LDC, - $ A( L1, MINL2N ), LDA ) ) -C - CALL DLALN2( .FALSE., 2, 1, SMIN, ONE, A( K1, K1 ), - $ LDA, ONE, ONE, VEC, 2, -A( L1, L1 ), - $ ZERO, X, 2, SCALOC, XNORM, IERR ) - IF( IERR.NE.0 ) - $ INFO = 1 -C - IF( SCALOC.NE.ONE ) THEN -C - DO 80 J = 1, N - CALL DSCAL( N, SCALOC, C( 1, J ), 1 ) - 80 CONTINUE -C - SCALE = SCALE*SCALOC - END IF - C( K1, L1 ) = X( 1, 1 ) - C( K2, L1 ) = X( 2, 1 ) - C( L1, K1 ) = X( 1, 1 ) - C( L1, K2 ) = X( 2, 1 ) -C - ELSE IF( L1.NE.L2 .AND. K1.EQ.K2 ) THEN -C - VEC( 1, 1 ) = C( K1, L1 ) - - $ ( DDOT( N-K1, A( K1, MINK1N ), LDA, - $ C( MINK1N, L1 ), 1 ) + - $ DDOT( N-L2, C( K1, MINL2N ), LDC, - $ A( L1, MINL2N ), LDA ) ) -C - VEC( 2, 1 ) = C( K1, L2 ) - - $ ( DDOT( N-K1, A( K1, MINK1N ), LDA, - $ C( MINK1N, L2 ), 1 ) + - $ DDOT( N-L2, C( K1, MINL2N ), LDC, - $ A( L2, MINL2N ), LDA ) ) -C - CALL DLALN2( .FALSE., 2, 1, SMIN, ONE, A( L1, L1 ), - $ LDA, ONE, ONE, VEC, 2, -A( K1, K1 ), - $ ZERO, X, 2, SCALOC, XNORM, IERR ) - IF( IERR.NE.0 ) - $ INFO = 1 -C - IF( SCALOC.NE.ONE ) THEN -C - DO 90 J = 1, N - CALL DSCAL( N, SCALOC, C( 1, J ), 1 ) - 90 CONTINUE -C - SCALE = SCALE*SCALOC - END IF - C( K1, L1 ) = X( 1, 1 ) - C( K1, L2 ) = X( 2, 1 ) - C( L1, K1 ) = X( 1, 1 ) - C( L2, K1 ) = X( 2, 1 ) -C - ELSE IF( L1.NE.L2 .AND. K1.NE.K2 ) THEN -C - VEC( 1, 1 ) = C( K1, L1 ) - - $ ( DDOT( N-K2, A( K1, MINK2N ), LDA, - $ C( MINK2N, L1 ), 1 ) + - $ DDOT( N-L2, C( K1, MINL2N ), LDC, - $ A( L1, MINL2N ), LDA ) ) -C - VEC( 1, 2 ) = C( K1, L2 ) - - $ ( DDOT( N-K2, A( K1, MINK2N ), LDA, - $ C( MINK2N, L2 ), 1 ) + - $ DDOT( N-L2, C( K1, MINL2N ), LDC, - $ A( L2, MINL2N ), LDA ) ) -C - VEC( 2, 1 ) = C( K2, L1 ) - - $ ( DDOT( N-K2, A( K2, MINK2N ), LDA, - $ C( MINK2N, L1 ), 1 ) + - $ DDOT( N-L2, C( K2, MINL2N ), LDC, - $ A( L1, MINL2N ), LDA ) ) -C - VEC( 2, 2 ) = C( K2, L2 ) - - $ ( DDOT( N-K2, A( K2, MINK2N ), LDA, - $ C( MINK2N, L2 ), 1 ) + - $ DDOT( N-L2, C( K2, MINL2N ), LDC, - $ A( L2, MINL2N ), LDA ) ) -C - IF( K1.EQ.L1 ) THEN - CALL SB03MW( .TRUE., LUPPER, A( K1, K1 ), LDA, VEC, - $ 2, SCALOC, X, 2, XNORM, IERR ) - IF( LUPPER ) THEN - X( 2, 1 ) = X( 1, 2 ) - ELSE - X( 1, 2 ) = X( 2, 1 ) - END IF - ELSE - CALL DLASY2( .FALSE., .TRUE., 1, 2, 2, A( K1, K1 ), - $ LDA, A( L1, L1 ), LDA, VEC, 2, SCALOC, - $ X, 2, XNORM, IERR ) - END IF - IF( IERR.NE.0 ) - $ INFO = 1 -C - IF( SCALOC.NE.ONE ) THEN -C - DO 100 J = 1, N - CALL DSCAL( N, SCALOC, C( 1, J ), 1 ) - 100 CONTINUE -C - SCALE = SCALE*SCALOC - END IF - C( K1, L1 ) = X( 1, 1 ) - C( K1, L2 ) = X( 1, 2 ) - C( K2, L1 ) = X( 2, 1 ) - C( K2, L2 ) = X( 2, 2 ) - IF( K1.NE.L1 ) THEN - C( L1, K1 ) = X( 1, 1 ) - C( L2, K1 ) = X( 1, 2 ) - C( L1, K2 ) = X( 2, 1 ) - C( L2, K2 ) = X( 2, 2 ) - END IF - END IF -C - 110 CONTINUE -C - 120 CONTINUE -C - END IF -C - RETURN -C *** Last line of SB03MY *** - END
--- a/extra/control-devel/devel/dksyn/SB03QX.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,394 +0,0 @@ - SUBROUTINE SB03QX( TRANA, UPLO, LYAPUN, N, XANORM, T, LDT, U, LDU, - $ R, LDR, FERR, IWORK, DWORK, LDWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To estimate a forward error bound for the solution X of a real -C continuous-time Lyapunov matrix equation, -C -C op(A)'*X + X*op(A) = C, -C -C where op(A) = A or A' (A**T) and C is symmetric (C = C**T). The -C matrix A, the right hand side C, and the solution X are N-by-N. -C An absolute residual matrix, which takes into account the rounding -C errors in forming it, is given in the array R. -C -C ARGUMENTS -C -C Mode Parameters -C -C TRANA CHARACTER*1 -C Specifies the form of op(A) to be used, as follows: -C = 'N': op(A) = A (No transpose); -C = 'T': op(A) = A**T (Transpose); -C = 'C': op(A) = A**T (Conjugate transpose = Transpose). -C -C UPLO CHARACTER*1 -C Specifies which part of the symmetric matrix R is to be -C used, as follows: -C = 'U': Upper triangular part; -C = 'L': Lower triangular part. -C -C LYAPUN CHARACTER*1 -C Specifies whether or not the original Lyapunov equations -C should be solved, as follows: -C = 'O': Solve the original Lyapunov equations, updating -C the right-hand sides and solutions with the -C matrix U, e.g., X <-- U'*X*U; -C = 'R': Solve reduced Lyapunov equations only, without -C updating the right-hand sides and solutions. -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the matrices A and R. N >= 0. -C -C XANORM (input) DOUBLE PRECISION -C The absolute (maximal) norm of the symmetric solution -C matrix X of the Lyapunov equation. XANORM >= 0. -C -C T (input) DOUBLE PRECISION array, dimension (LDT,N) -C The leading N-by-N upper Hessenberg part of this array -C must contain the upper quasi-triangular matrix T in Schur -C canonical form from a Schur factorization of A. -C -C LDT INTEGER -C The leading dimension of array T. LDT >= MAX(1,N). -C -C U (input) DOUBLE PRECISION array, dimension (LDU,N) -C The leading N-by-N part of this array must contain the -C orthogonal matrix U from a real Schur factorization of A. -C If LYAPUN = 'R', the array U is not referenced. -C -C LDU INTEGER -C The leading dimension of array U. -C LDU >= 1, if LYAPUN = 'R'; -C LDU >= MAX(1,N), if LYAPUN = 'O'. -C -C R (input/output) DOUBLE PRECISION array, dimension (LDR,N) -C On entry, if UPLO = 'U', the leading N-by-N upper -C triangular part of this array must contain the upper -C triangular part of the absolute residual matrix R, with -C bounds on rounding errors added. -C On entry, if UPLO = 'L', the leading N-by-N lower -C triangular part of this array must contain the lower -C triangular part of the absolute residual matrix R, with -C bounds on rounding errors added. -C On exit, the leading N-by-N part of this array contains -C the symmetric absolute residual matrix R (with bounds on -C rounding errors added), fully stored. -C -C LDR INTEGER -C The leading dimension of array R. LDR >= MAX(1,N). -C -C FERR (output) DOUBLE PRECISION -C An estimated forward error bound for the solution X. -C If XTRUE is the true solution, FERR bounds the magnitude -C of the largest entry in (X - XTRUE) divided by the -C magnitude of the largest entry in X. -C If N = 0 or XANORM = 0, FERR is set to 0, without any -C calculations. -C -C Workspace -C -C IWORK INTEGER array, dimension (N*N) -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C -C LDWORK INTEGER -C The length of the array DWORK. LDWORK >= 2*N*N. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C = N+1: if the matrices T and -T' have common or very -C close eigenvalues; perturbed values were used to -C solve Lyapunov equations (but the matrix T is -C unchanged). -C -C METHOD -C -C The forward error bound is estimated using a practical error bound -C similar to the one proposed in [1], based on the 1-norm estimator -C in [2]. -C -C REFERENCES -C -C [1] Higham, N.J. -C Perturbation theory and backward error for AX-XB=C. -C BIT, vol. 33, pp. 124-136, 1993. -C -C [2] Higham, N.J. -C FORTRAN codes for estimating the one-norm of a real or -C complex matrix, with applications to condition estimation. -C ACM Trans. Math. Softw., 14, pp. 381-396, 1988. -C -C NUMERICAL ASPECTS -C 3 -C The algorithm requires 0(N ) operations. -C -C FURTHER COMMENTS -C -C The option LYAPUN = 'R' may occasionally produce slightly worse -C or better estimates, and it is much faster than the option 'O'. -C The routine can be also used as a final step in estimating a -C forward error bound for the solution of a continuous-time -C algebraic matrix Riccati equation. -C -C CONTRIBUTOR -C -C V. Sima, Research Institute for Informatics, Bucharest, Romania, -C Oct. 1998. Partly based on DGLSVX (and then SB03QD) by P. Petkov, -C Tech. University of Sofia, March 1998 (and December 1998). -C -C REVISIONS -C -C February 6, 1999, V. Sima, Katholieke Univ. Leuven, Belgium. -C V. Sima, Research Institute for Informatics, Bucharest, Oct. 2004. -C -C KEYWORDS -C -C Lyapunov equation, orthogonal transformation, real Schur form. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE, HALF - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, HALF = 0.5D+0 ) -C .. -C .. Scalar Arguments .. - CHARACTER LYAPUN, TRANA, UPLO - INTEGER INFO, LDR, LDT, LDU, LDWORK, N - DOUBLE PRECISION FERR, XANORM -C .. -C .. Array Arguments .. - INTEGER IWORK( * ) - DOUBLE PRECISION DWORK( * ), R( LDR, * ), T( LDT, * ), - $ U( LDU, * ) -C .. -C .. Local Scalars .. - LOGICAL LOWER, NOTRNA, UPDATE - CHARACTER TRANAT, UPLOW - INTEGER I, IJ, INFO2, ITMP, J, KASE, NN - DOUBLE PRECISION EST, SCALE, TEMP -C .. -C .. External Functions .. - LOGICAL LSAME - DOUBLE PRECISION DLANSY - EXTERNAL DLANSY, LSAME -C .. -C .. External Subroutines .. - EXTERNAL DLACON, DSCAL, MA02ED, MB01RU, SB03MY, XERBLA -C .. -C .. Intrinsic Functions .. - INTRINSIC MAX -C .. -C .. Executable Statements .. -C -C Decode and Test input parameters. -C - NOTRNA = LSAME( TRANA, 'N' ) - UPDATE = LSAME( LYAPUN, 'O' ) -C - NN = N*N - INFO = 0 - IF( .NOT.( NOTRNA .OR. LSAME( TRANA, 'T' ) .OR. - $ LSAME( TRANA, 'C' ) ) ) THEN - INFO = -1 - ELSE IF( .NOT.( LSAME( UPLO, 'L' ) .OR. LSAME( UPLO, 'U' ) ) ) - $ THEN - INFO = -2 - ELSE IF( .NOT.( UPDATE .OR. LSAME( LYAPUN, 'R' ) ) ) THEN - INFO = -3 - ELSE IF( N.LT.0 ) THEN - INFO = -4 - ELSE IF( XANORM.LT.ZERO ) THEN - INFO = -5 - ELSE IF( LDT.LT.MAX( 1, N ) ) THEN - INFO = -7 - ELSE IF( LDU.LT.1 .OR. ( UPDATE .AND. LDU.LT.N ) ) THEN - INFO = -9 - ELSE IF( LDR.LT.MAX( 1, N ) ) THEN - INFO = -11 - ELSE IF( LDWORK.LT.2*NN ) THEN - INFO = -15 - END IF -C - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'SB03QX', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - FERR = ZERO - IF( N.EQ.0 .OR. XANORM.EQ.ZERO ) - $ RETURN -C - ITMP = NN + 1 -C - IF( NOTRNA ) THEN - TRANAT = 'T' - ELSE - TRANAT = 'N' - END IF -C -C Fill in the remaining triangle of the symmetric residual matrix. -C - CALL MA02ED( UPLO, N, R, LDR ) -C - KASE = 0 -C -C REPEAT - 10 CONTINUE - CALL DLACON( NN, DWORK( ITMP ), DWORK, IWORK, EST, KASE ) - IF( KASE.NE.0 ) THEN -C -C Select the triangular part of symmetric matrix to be used. -C - IF( DLANSY( '1-norm', 'Upper', N, DWORK, N, DWORK( ITMP ) ) - $ .GE. - $ DLANSY( '1-norm', 'Lower', N, DWORK, N, DWORK( ITMP ) ) - $ ) THEN - UPLOW = 'U' - LOWER = .FALSE. - ELSE - UPLOW = 'L' - LOWER = .TRUE. - END IF -C - IF( KASE.EQ.2 ) THEN - IJ = 0 - IF( LOWER ) THEN -C -C Scale the lower triangular part of symmetric matrix -C by the residual matrix. -C - DO 30 J = 1, N - DO 20 I = J, N - IJ = IJ + 1 - DWORK( IJ ) = DWORK( IJ )*R( I, J ) - 20 CONTINUE - IJ = IJ + J - 30 CONTINUE - ELSE -C -C Scale the upper triangular part of symmetric matrix -C by the residual matrix. -C - DO 50 J = 1, N - DO 40 I = 1, J - IJ = IJ + 1 - DWORK( IJ ) = DWORK( IJ )*R( I, J ) - 40 CONTINUE - IJ = IJ + N - J - 50 CONTINUE - END IF - END IF -C - IF( UPDATE ) THEN -C -C Transform the right-hand side: RHS := U'*RHS*U. -C - CALL MB01RU( UPLOW, 'Transpose', N, N, ZERO, ONE, DWORK, N, - $ U, LDU, DWORK, N, DWORK( ITMP ), NN, INFO2 ) - CALL DSCAL( N, HALF, DWORK, N+1 ) - END IF - CALL MA02ED( UPLOW, N, DWORK, N ) -C - IF( KASE.EQ.2 ) THEN -C -C Solve op(T)'*Y + Y*op(T) = scale*RHS. -C - CALL SB03MY( TRANA, N, T, LDT, DWORK, N, SCALE, INFO2 ) - ELSE -C -C Solve op(T)*W + W*op(T)' = scale*RHS. -C - CALL SB03MY( TRANAT, N, T, LDT, DWORK, N, SCALE, INFO2 ) - END IF -C - IF( INFO2.GT.0 ) - $ INFO = N + 1 -C - IF( UPDATE ) THEN -C -C Transform back to obtain the solution: Z := U*Z*U', with -C Z = Y or Z = W. -C - CALL MB01RU( UPLOW, 'No transpose', N, N, ZERO, ONE, DWORK, - $ N, U, LDU, DWORK, N, DWORK( ITMP ), NN, INFO2 ) - CALL DSCAL( N, HALF, DWORK, N+1 ) - END IF -C - IF( KASE.EQ.1 ) THEN - IJ = 0 - IF( LOWER ) THEN -C -C Scale the lower triangular part of symmetric matrix -C by the residual matrix. -C - DO 70 J = 1, N - DO 60 I = J, N - IJ = IJ + 1 - DWORK( IJ ) = DWORK( IJ )*R( I, J ) - 60 CONTINUE - IJ = IJ + J - 70 CONTINUE - ELSE -C -C Scale the upper triangular part of symmetric matrix -C by the residual matrix. -C - DO 90 J = 1, N - DO 80 I = 1, J - IJ = IJ + 1 - DWORK( IJ ) = DWORK( IJ )*R( I, J ) - 80 CONTINUE - IJ = IJ + N - J - 90 CONTINUE - END IF - END IF -C -C Fill in the remaining triangle of the symmetric matrix. -C - CALL MA02ED( UPLOW, N, DWORK, N ) - GO TO 10 - END IF -C -C UNTIL KASE = 0 -C -C Compute the estimate of the relative error. -C - TEMP = XANORM*SCALE - IF( TEMP.GT.EST ) THEN - FERR = EST / TEMP - ELSE - FERR = ONE - END IF -C - RETURN -C -C *** Last line of SB03QX *** - END
--- a/extra/control-devel/devel/dksyn/SB03QY.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,443 +0,0 @@ - SUBROUTINE SB03QY( JOB, TRANA, LYAPUN, N, T, LDT, U, LDU, X, LDX, - $ SEP, THNORM, IWORK, DWORK, LDWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To estimate the separation between the matrices op(A) and -op(A)', -C -C sep(op(A),-op(A)') = min norm(op(A)'*X + X*op(A))/norm(X) -C = 1 / norm(inv(Omega)) -C -C and/or the 1-norm of Theta, where op(A) = A or A' (A**T), and -C Omega and Theta are linear operators associated to the real -C continuous-time Lyapunov matrix equation -C -C op(A)'*X + X*op(A) = C, -C -C defined by -C -C Omega(W) = op(A)'*W + W*op(A), -C Theta(W) = inv(Omega(op(W)'*X + X*op(W))). -C -C The 1-norm condition estimators are used. -C -C ARGUMENTS -C -C Mode Parameters -C -C JOB CHARACTER*1 -C Specifies the computation to be performed, as follows: -C = 'S': Compute the separation only; -C = 'T': Compute the norm of Theta only; -C = 'B': Compute both the separation and the norm of Theta. -C -C TRANA CHARACTER*1 -C Specifies the form of op(A) to be used, as follows: -C = 'N': op(A) = A (No transpose); -C = 'T': op(A) = A**T (Transpose); -C = 'C': op(A) = A**T (Conjugate transpose = Transpose). -C -C LYAPUN CHARACTER*1 -C Specifies whether or not the original Lyapunov equations -C should be solved, as follows: -C = 'O': Solve the original Lyapunov equations, updating -C the right-hand sides and solutions with the -C matrix U, e.g., X <-- U'*X*U; -C = 'R': Solve reduced Lyapunov equations only, without -C updating the right-hand sides and solutions. -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the matrices A and X. N >= 0. -C -C T (input) DOUBLE PRECISION array, dimension (LDT,N) -C The leading N-by-N upper Hessenberg part of this array -C must contain the upper quasi-triangular matrix T in Schur -C canonical form from a Schur factorization of A. -C -C LDT INTEGER -C The leading dimension of array T. LDT >= MAX(1,N). -C -C U (input) DOUBLE PRECISION array, dimension (LDU,N) -C The leading N-by-N part of this array must contain the -C orthogonal matrix U from a real Schur factorization of A. -C If LYAPUN = 'R', the array U is not referenced. -C -C LDU INTEGER -C The leading dimension of array U. -C LDU >= 1, if LYAPUN = 'R'; -C LDU >= MAX(1,N), if LYAPUN = 'O'. -C -C X (input) DOUBLE PRECISION array, dimension (LDX,N) -C The leading N-by-N part of this array must contain the -C solution matrix X of the Lyapunov equation (reduced -C Lyapunov equation if LYAPUN = 'R'). -C If JOB = 'S', the array X is not referenced. -C -C LDX INTEGER -C The leading dimension of array X. -C LDX >= 1, if JOB = 'S'; -C LDX >= MAX(1,N), if JOB = 'T' or 'B'. -C -C SEP (output) DOUBLE PRECISION -C If JOB = 'S' or JOB = 'B', and INFO >= 0, SEP contains the -C estimated separation of the matrices op(A) and -op(A)'. -C If JOB = 'T' or N = 0, SEP is not referenced. -C -C THNORM (output) DOUBLE PRECISION -C If JOB = 'T' or JOB = 'B', and INFO >= 0, THNORM contains -C the estimated 1-norm of operator Theta. -C If JOB = 'S' or N = 0, THNORM is not referenced. -C -C Workspace -C -C IWORK INTEGER array, dimension (N*N) -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C -C LDWORK INTEGER -C The length of the array DWORK. LDWORK >= 2*N*N. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C = N+1: if the matrices T and -T' have common or very -C close eigenvalues; perturbed values were used to -C solve Lyapunov equations (but the matrix T is -C unchanged). -C -C METHOD -C -C SEP is defined as the separation of op(A) and -op(A)': -C -C sep( op(A), -op(A)' ) = sigma_min( K ) -C -C where sigma_min(K) is the smallest singular value of the -C N*N-by-N*N matrix -C -C K = kprod( I(N), op(A)' ) + kprod( op(A)', I(N) ). -C -C I(N) is an N-by-N identity matrix, and kprod denotes the Kronecker -C product. The routine estimates sigma_min(K) by the reciprocal of -C an estimate of the 1-norm of inverse(K), computed as suggested in -C [1]. This involves the solution of several continuous-time -C Lyapunov equations, either direct or transposed. The true -C reciprocal 1-norm of inverse(K) cannot differ from sigma_min(K) by -C more than a factor of N. -C The 1-norm of Theta is estimated similarly. -C -C REFERENCES -C -C [1] Higham, N.J. -C FORTRAN codes for estimating the one-norm of a real or -C complex matrix, with applications to condition estimation. -C ACM Trans. Math. Softw., 14, pp. 381-396, 1988. -C -C NUMERICAL ASPECTS -C 3 -C The algorithm requires 0(N ) operations. -C -C FURTHER COMMENTS -C -C When SEP is zero, the routine returns immediately, with THNORM -C (if requested) not set. In this case, the equation is singular. -C The option LYAPUN = 'R' may occasionally produce slightly worse -C or better estimates, and it is much faster than the option 'O'. -C -C CONTRIBUTOR -C -C V. Sima, Research Institute for Informatics, Bucharest, Romania, -C Oct. 1998. Partly based on DGLSVX (and then SB03QD) by P. Petkov, -C Tech. University of Sofia, March 1998 (and December 1998). -C -C REVISIONS -C -C February 13, 1999, V. Sima, Katholieke Univ. Leuven, Belgium. -C V. Sima, Research Institute for Informatics, Bucharest, Oct. 2004. -C -C KEYWORDS -C -C Lyapunov equation, orthogonal transformation, real Schur form. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE, HALF - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, HALF = 0.5D+0 ) -C .. -C .. Scalar Arguments .. - CHARACTER JOB, LYAPUN, TRANA - INTEGER INFO, LDT, LDU, LDWORK, LDX, N - DOUBLE PRECISION SEP, THNORM -C .. -C .. Array Arguments .. - INTEGER IWORK( * ) - DOUBLE PRECISION DWORK( * ), T( LDT, * ), U( LDU, * ), - $ X( LDX, * ) -C .. -C .. Local Scalars .. - LOGICAL NOTRNA, UPDATE, WANTS, WANTT - CHARACTER TRANAT, UPLO - INTEGER INFO2, ITMP, KASE, NN - DOUBLE PRECISION BIGNUM, EST, SCALE -C .. -C .. External Functions .. - LOGICAL LSAME - DOUBLE PRECISION DLAMCH, DLANSY - EXTERNAL DLAMCH, DLANSY, LSAME -C .. -C .. External Subroutines .. - EXTERNAL DLACON, DLACPY, DSCAL, DSYR2K, MA02ED, MB01RU, - $ SB03MY, XERBLA -C .. -C .. Intrinsic Functions .. - INTRINSIC MAX -C .. -C .. Executable Statements .. -C -C Decode and Test input parameters. -C - WANTS = LSAME( JOB, 'S' ) - WANTT = LSAME( JOB, 'T' ) - NOTRNA = LSAME( TRANA, 'N' ) - UPDATE = LSAME( LYAPUN, 'O' ) -C - NN = N*N - INFO = 0 - IF( .NOT. ( WANTS .OR. WANTT .OR. LSAME( JOB, 'B' ) ) ) THEN - INFO = -1 - ELSE IF( .NOT.( NOTRNA .OR. LSAME( TRANA, 'T' ) .OR. - $ LSAME( TRANA, 'C' ) ) ) THEN - INFO = -2 - ELSE IF( .NOT.( UPDATE .OR. LSAME( LYAPUN, 'R' ) ) ) THEN - INFO = -3 - ELSE IF( N.LT.0 ) THEN - INFO = -4 - ELSE IF( LDT.LT.MAX( 1, N ) ) THEN - INFO = -6 - ELSE IF( LDU.LT.1 .OR. ( UPDATE .AND. LDU.LT.N ) ) THEN - INFO = -8 - ELSE IF( LDX.LT.1 .OR. ( .NOT.WANTS .AND. LDX.LT.N ) ) THEN - INFO = -10 - ELSE IF( LDWORK.LT.2*NN ) THEN - INFO = -15 - END IF -C - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'SB03QY', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF( N.EQ.0 ) - $ RETURN -C - ITMP = NN + 1 -C - IF( NOTRNA ) THEN - TRANAT = 'T' - ELSE - TRANAT = 'N' - END IF -C - IF( .NOT.WANTT ) THEN -C -C Estimate sep(op(A),-op(A)'). -C Workspace: 2*N*N. -C - KASE = 0 -C -C REPEAT - 10 CONTINUE - CALL DLACON( NN, DWORK( ITMP ), DWORK, IWORK, EST, KASE ) - IF( KASE.NE.0 ) THEN -C -C Select the triangular part of symmetric matrix to be used. -C - IF( DLANSY( '1-norm', 'Upper', N, DWORK, N, DWORK( ITMP ) ) - $ .GE. - $ DLANSY( '1-norm', 'Lower', N, DWORK, N, DWORK( ITMP ) ) - $ ) THEN - UPLO = 'U' - ELSE - UPLO = 'L' - END IF -C - IF( UPDATE ) THEN -C -C Transform the right-hand side: RHS := U'*RHS*U. -C - CALL MB01RU( UPLO, 'Transpose', N, N, ZERO, ONE, DWORK, - $ N, U, LDU, DWORK, N, DWORK( ITMP ), NN, - $ INFO2 ) - CALL DSCAL( N, HALF, DWORK, N+1 ) - END IF - CALL MA02ED( UPLO, N, DWORK, N ) -C - IF( KASE.EQ.1 ) THEN -C -C Solve op(T)'*Y + Y*op(T) = scale*RHS. -C - CALL SB03MY( TRANA, N, T, LDT, DWORK, N, SCALE, INFO2 ) - ELSE -C -C Solve op(T)*W + W*op(T)' = scale*RHS. -C - CALL SB03MY( TRANAT, N, T, LDT, DWORK, N, SCALE, INFO2 ) - END IF -C - IF( INFO2.GT.0 ) - $ INFO = N + 1 -C - IF( UPDATE ) THEN -C -C Transform back to obtain the solution: Z := U*Z*U', with -C Z = Y or Z = W. -C - CALL MB01RU( UPLO, 'No transpose', N, N, ZERO, ONE, - $ DWORK, N, U, LDU, DWORK, N, DWORK( ITMP ), - $ NN, INFO2 ) - CALL DSCAL( N, HALF, DWORK, N+1 ) -C -C Fill in the remaining triangle of the symmetric matrix. -C - CALL MA02ED( UPLO, N, DWORK, N ) - END IF -C - GO TO 10 - END IF -C UNTIL KASE = 0 -C - IF( EST.GT.SCALE ) THEN - SEP = SCALE / EST - ELSE - BIGNUM = ONE / DLAMCH( 'Safe minimum' ) - IF( SCALE.LT.EST*BIGNUM ) THEN - SEP = SCALE / EST - ELSE - SEP = BIGNUM - END IF - END IF -C -C Return if the equation is singular. -C - IF( SEP.EQ.ZERO ) - $ RETURN - END IF -C - IF( .NOT.WANTS ) THEN -C -C Estimate norm(Theta). -C Workspace: 2*N*N. -C - KASE = 0 -C -C REPEAT - 20 CONTINUE - CALL DLACON( NN, DWORK( ITMP ), DWORK, IWORK, EST, KASE ) - IF( KASE.NE.0 ) THEN -C -C Select the triangular part of symmetric matrix to be used. -C - IF( DLANSY( '1-norm', 'Upper', N, DWORK, N, DWORK( ITMP ) ) - $ .GE. - $ DLANSY( '1-norm', 'Lower', N, DWORK, N, DWORK( ITMP ) ) - $ ) THEN - UPLO = 'U' - ELSE - UPLO = 'L' - END IF -C -C Fill in the remaining triangle of the symmetric matrix. -C - CALL MA02ED( UPLO, N, DWORK, N ) -C -C Compute RHS = op(W)'*X + X*op(W). -C - CALL DSYR2K( UPLO, TRANAT, N, N, ONE, DWORK, N, X, LDX, - $ ZERO, DWORK( ITMP ), N ) - CALL DLACPY( UPLO, N, N, DWORK( ITMP ), N, DWORK, N ) -C - IF( UPDATE ) THEN -C -C Transform the right-hand side: RHS := U'*RHS*U. -C - CALL MB01RU( UPLO, 'Transpose', N, N, ZERO, ONE, DWORK, - $ N, U, LDU, DWORK, N, DWORK( ITMP ), NN, - $ INFO2 ) - CALL DSCAL( N, HALF, DWORK, N+1 ) - END IF - CALL MA02ED( UPLO, N, DWORK, N ) -C - IF( KASE.EQ.1 ) THEN -C -C Solve op(T)'*Y + Y*op(T) = scale*RHS. -C - CALL SB03MY( TRANA, N, T, LDT, DWORK, N, SCALE, INFO2 ) - ELSE -C -C Solve op(T)*W + W*op(T)' = scale*RHS. -C - CALL SB03MY( TRANAT, N, T, LDT, DWORK, N, SCALE, INFO2 ) - END IF -C - IF( INFO2.GT.0 ) - $ INFO = N + 1 -C - IF( UPDATE ) THEN -C -C Transform back to obtain the solution: Z := U*Z*U', with -C Z = Y or Z = W. -C - CALL MB01RU( UPLO, 'No transpose', N, N, ZERO, ONE, - $ DWORK, N, U, LDU, DWORK, N, DWORK( ITMP ), - $ NN, INFO2 ) - CALL DSCAL( N, HALF, DWORK, N+1 ) -C -C Fill in the remaining triangle of the symmetric matrix. -C - CALL MA02ED( UPLO, N, DWORK, N ) - END IF -C - GO TO 20 - END IF -C UNTIL KASE = 0 -C - IF( EST.LT.SCALE ) THEN - THNORM = EST / SCALE - ELSE - BIGNUM = ONE / DLAMCH( 'Safe minimum' ) - IF( EST.LT.SCALE*BIGNUM ) THEN - THNORM = EST / SCALE - ELSE - THNORM = BIGNUM - END IF - END IF - END IF -C - RETURN -C *** Last line of SB03QY *** - END
--- a/extra/control-devel/devel/dksyn/SB03SX.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,398 +0,0 @@ - SUBROUTINE SB03SX( TRANA, UPLO, LYAPUN, N, XANORM, T, LDT, U, LDU, - $ R, LDR, FERR, IWORK, DWORK, LDWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To estimate a forward error bound for the solution X of a real -C discrete-time Lyapunov matrix equation, -C -C op(A)'*X*op(A) - X = C, -C -C where op(A) = A or A' (A**T) and C is symmetric (C = C**T). The -C matrix A, the right hand side C, and the solution X are N-by-N. -C An absolute residual matrix, which takes into account the rounding -C errors in forming it, is given in the array R. -C -C ARGUMENTS -C -C Mode Parameters -C -C TRANA CHARACTER*1 -C Specifies the form of op(A) to be used, as follows: -C = 'N': op(A) = A (No transpose); -C = 'T': op(A) = A**T (Transpose); -C = 'C': op(A) = A**T (Conjugate transpose = Transpose). -C -C UPLO CHARACTER*1 -C Specifies which part of the symmetric matrix R is to be -C used, as follows: -C = 'U': Upper triangular part; -C = 'L': Lower triangular part. -C -C LYAPUN CHARACTER*1 -C Specifies whether or not the original Lyapunov equations -C should be solved, as follows: -C = 'O': Solve the original Lyapunov equations, updating -C the right-hand sides and solutions with the -C matrix U, e.g., X <-- U'*X*U; -C = 'R': Solve reduced Lyapunov equations only, without -C updating the right-hand sides and solutions. -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the matrices A and R. N >= 0. -C -C XANORM (input) DOUBLE PRECISION -C The absolute (maximal) norm of the symmetric solution -C matrix X of the Lyapunov equation. XANORM >= 0. -C -C T (input) DOUBLE PRECISION array, dimension (LDT,N) -C The leading N-by-N upper Hessenberg part of this array -C must contain the upper quasi-triangular matrix T in Schur -C canonical form from a Schur factorization of A. -C -C LDT INTEGER -C The leading dimension of array T. LDT >= MAX(1,N). -C -C U (input) DOUBLE PRECISION array, dimension (LDU,N) -C The leading N-by-N part of this array must contain the -C orthogonal matrix U from a real Schur factorization of A. -C If LYAPUN = 'R', the array U is not referenced. -C -C LDU INTEGER -C The leading dimension of array U. -C LDU >= 1, if LYAPUN = 'R'; -C LDU >= MAX(1,N), if LYAPUN = 'O'. -C -C R (input/output) DOUBLE PRECISION array, dimension (LDR,N) -C On entry, if UPLO = 'U', the leading N-by-N upper -C triangular part of this array must contain the upper -C triangular part of the absolute residual matrix R, with -C bounds on rounding errors added. -C On entry, if UPLO = 'L', the leading N-by-N lower -C triangular part of this array must contain the lower -C triangular part of the absolute residual matrix R, with -C bounds on rounding errors added. -C On exit, the leading N-by-N part of this array contains -C the symmetric absolute residual matrix R (with bounds on -C rounding errors added), fully stored. -C -C LDR INTEGER -C The leading dimension of array R. LDR >= MAX(1,N). -C -C FERR (output) DOUBLE PRECISION -C An estimated forward error bound for the solution X. -C If XTRUE is the true solution, FERR bounds the magnitude -C of the largest entry in (X - XTRUE) divided by the -C magnitude of the largest entry in X. -C If N = 0 or XANORM = 0, FERR is set to 0, without any -C calculations. -C -C Workspace -C -C IWORK INTEGER array, dimension (N*N) -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C -C LDWORK INTEGER -C The length of the array DWORK. -C LDWORK >= 0, if N = 0; -C LDWORK >= MAX(3,2*N*N), if N > 0. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C = N+1: if T has almost reciprocal eigenvalues; perturbed -C values were used to solve Lyapunov equations (but -C the matrix T is unchanged). -C -C METHOD -C -C The forward error bound is estimated using a practical error bound -C similar to the one proposed in [1], based on the 1-norm estimator -C in [2]. -C -C REFERENCES -C -C [1] Higham, N.J. -C Perturbation theory and backward error for AX-XB=C. -C BIT, vol. 33, pp. 124-136, 1993. -C -C [2] Higham, N.J. -C FORTRAN codes for estimating the one-norm of a real or -C complex matrix, with applications to condition estimation. -C ACM Trans. Math. Softw., 14, pp. 381-396, 1988. -C -C NUMERICAL ASPECTS -C 3 -C The algorithm requires 0(N ) operations. -C -C FURTHER COMMENTS -C -C The option LYAPUN = 'R' may occasionally produce slightly worse -C or better estimates, and it is much faster than the option 'O'. -C The routine can be also used as a final step in estimating a -C forward error bound for the solution of a discrete-time algebraic -C matrix Riccati equation. -C -C CONTRIBUTOR -C -C V. Sima, Research Institute for Informatics, Bucharest, Romania, -C Oct. 1998. Partly based on DDLSVX (and then SB03SD) by P. Petkov, -C Tech. University of Sofia, March 1998 (and December 1998). -C -C REVISIONS -C -C February 6, 1999, V. Sima, Katholieke Univ. Leuven, Belgium. -C V. Sima, Research Institute for Informatics, Bucharest, Oct. 2004. -C -C KEYWORDS -C -C Lyapunov equation, orthogonal transformation, real Schur form. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE, HALF - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, HALF = 0.5D+0 ) -C .. -C .. Scalar Arguments .. - CHARACTER LYAPUN, TRANA, UPLO - INTEGER INFO, LDR, LDT, LDU, LDWORK, N - DOUBLE PRECISION FERR, XANORM -C .. -C .. Array Arguments .. - INTEGER IWORK( * ) - DOUBLE PRECISION DWORK( * ), R( LDR, * ), T( LDT, * ), - $ U( LDU, * ) -C .. -C .. Local Scalars .. - LOGICAL LOWER, NOTRNA, UPDATE - CHARACTER TRANAT, UPLOW - INTEGER I, IJ, INFO2, ITMP, J, KASE, NN - DOUBLE PRECISION EST, SCALE, TEMP -C .. -C .. External Functions .. - LOGICAL LSAME - DOUBLE PRECISION DLANSY - EXTERNAL DLANSY, LSAME -C .. -C .. External Subroutines .. - EXTERNAL DLACON, DSCAL, MA02ED, MB01RU, SB03MX, XERBLA -C .. -C .. Intrinsic Functions .. - INTRINSIC MAX -C .. -C .. Executable Statements .. -C -C Decode and Test input parameters. -C - NOTRNA = LSAME( TRANA, 'N' ) - UPDATE = LSAME( LYAPUN, 'O' ) -C - NN = N*N - INFO = 0 - IF( .NOT.( NOTRNA .OR. LSAME( TRANA, 'T' ) .OR. - $ LSAME( TRANA, 'C' ) ) ) THEN - INFO = -1 - ELSE IF( .NOT.( LSAME( UPLO, 'L' ) .OR. LSAME( UPLO, 'U' ) ) ) - $ THEN - INFO = -2 - ELSE IF( .NOT.( UPDATE .OR. LSAME( LYAPUN, 'R' ) ) ) THEN - INFO = -3 - ELSE IF( N.LT.0 ) THEN - INFO = -4 - ELSE IF( XANORM.LT.ZERO ) THEN - INFO = -5 - ELSE IF( LDT.LT.MAX( 1, N ) ) THEN - INFO = -7 - ELSE IF( LDU.LT.1 .OR. ( UPDATE .AND. LDU.LT.N ) ) THEN - INFO = -9 - ELSE IF( LDR.LT.MAX( 1, N ) ) THEN - INFO = -11 - ELSE IF( LDWORK.LT.0 .OR. - $ ( LDWORK.LT.MAX( 3, 2*NN ) .AND. N.GT.0 ) ) THEN - INFO = -15 - END IF -C - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'SB03SX', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - FERR = ZERO - IF( N.EQ.0 .OR. XANORM.EQ.ZERO ) - $ RETURN -C - ITMP = NN + 1 -C - IF( NOTRNA ) THEN - TRANAT = 'T' - ELSE - TRANAT = 'N' - END IF -C -C Fill in the remaining triangle of the symmetric residual matrix. -C - CALL MA02ED( UPLO, N, R, LDR ) -C - KASE = 0 -C -C REPEAT - 10 CONTINUE - CALL DLACON( NN, DWORK( ITMP ), DWORK, IWORK, EST, KASE ) - IF( KASE.NE.0 ) THEN -C -C Select the triangular part of symmetric matrix to be used. -C - IF( DLANSY( '1-norm', 'Upper', N, DWORK, N, DWORK( ITMP ) ) - $ .GE. - $ DLANSY( '1-norm', 'Lower', N, DWORK, N, DWORK( ITMP ) ) - $ ) THEN - UPLOW = 'U' - LOWER = .FALSE. - ELSE - UPLOW = 'L' - LOWER = .TRUE. - END IF -C - IF( KASE.EQ.2 ) THEN - IJ = 0 - IF( LOWER ) THEN -C -C Scale the lower triangular part of symmetric matrix -C by the residual matrix. -C - DO 30 J = 1, N - DO 20 I = J, N - IJ = IJ + 1 - DWORK( IJ ) = DWORK( IJ )*R( I, J ) - 20 CONTINUE - IJ = IJ + J - 30 CONTINUE - ELSE -C -C Scale the upper triangular part of symmetric matrix -C by the residual matrix. -C - DO 50 J = 1, N - DO 40 I = 1, J - IJ = IJ + 1 - DWORK( IJ ) = DWORK( IJ )*R( I, J ) - 40 CONTINUE - IJ = IJ + N - J - 50 CONTINUE - END IF - END IF -C - IF( UPDATE ) THEN -C -C Transform the right-hand side: RHS := U'*RHS*U. -C - CALL MB01RU( UPLOW, 'Transpose', N, N, ZERO, ONE, DWORK, N, - $ U, LDU, DWORK, N, DWORK( ITMP ), NN, INFO2 ) - CALL DSCAL( N, HALF, DWORK, N+1 ) - END IF - CALL MA02ED( UPLOW, N, DWORK, N ) -C - IF( KASE.EQ.2 ) THEN -C -C Solve op(T)'*Y*op(T) - Y = scale*RHS. -C - CALL SB03MX( TRANA, N, T, LDT, DWORK, N, SCALE, - $ DWORK( ITMP ), INFO2 ) - ELSE -C -C Solve op(T)*W*op(T)' - W = scale*RHS. -C - CALL SB03MX( TRANAT, N, T, LDT, DWORK, N, SCALE, - $ DWORK( ITMP ), INFO2 ) - END IF -C - IF( INFO2.GT.0 ) - $ INFO = N + 1 -C - IF( UPDATE ) THEN -C -C Transform back to obtain the solution: Z := U*Z*U', with -C Z = Y or Z = W. -C - CALL MB01RU( UPLOW, 'No transpose', N, N, ZERO, ONE, DWORK, - $ N, U, LDU, DWORK, N, DWORK( ITMP ), NN, INFO2 ) - CALL DSCAL( N, HALF, DWORK, N+1 ) - END IF -C - IF( KASE.EQ.1 ) THEN - IJ = 0 - IF( LOWER ) THEN -C -C Scale the lower triangular part of symmetric matrix -C by the residual matrix. -C - DO 70 J = 1, N - DO 60 I = J, N - IJ = IJ + 1 - DWORK( IJ ) = DWORK( IJ )*R( I, J ) - 60 CONTINUE - IJ = IJ + J - 70 CONTINUE - ELSE -C -C Scale the upper triangular part of symmetric matrix -C by the residual matrix. -C - DO 90 J = 1, N - DO 80 I = 1, J - IJ = IJ + 1 - DWORK( IJ ) = DWORK( IJ )*R( I, J ) - 80 CONTINUE - IJ = IJ + N - J - 90 CONTINUE - END IF - END IF -C -C Fill in the remaining triangle of the symmetric matrix. -C - CALL MA02ED( UPLOW, N, DWORK, N ) - GO TO 10 - END IF -C -C UNTIL KASE = 0 -C -C Compute the estimate of the relative error. -C - TEMP = XANORM*SCALE - IF( TEMP.GT.EST ) THEN - FERR = EST / TEMP - ELSE - FERR = ONE - END IF -C - RETURN -C -C *** Last line of SB03SX *** - END
--- a/extra/control-devel/devel/dksyn/SB03SY.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,451 +0,0 @@ - SUBROUTINE SB03SY( JOB, TRANA, LYAPUN, N, T, LDT, U, LDU, XA, - $ LDXA, SEPD, THNORM, IWORK, DWORK, LDWORK, - $ INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To estimate the "separation" between the matrices op(A) and -C op(A)', -C -C sepd(op(A),op(A)') = min norm(op(A)'*X*op(A) - X)/norm(X) -C = 1 / norm(inv(Omega)) -C -C and/or the 1-norm of Theta, where op(A) = A or A' (A**T), and -C Omega and Theta are linear operators associated to the real -C discrete-time Lyapunov matrix equation -C -C op(A)'*X*op(A) - X = C, -C -C defined by -C -C Omega(W) = op(A)'*W*op(A) - W, -C Theta(W) = inv(Omega(op(W)'*X*op(A) + op(A)'*X*op(W))). -C -C The 1-norm condition estimators are used. -C -C ARGUMENTS -C -C Mode Parameters -C -C JOB CHARACTER*1 -C Specifies the computation to be performed, as follows: -C = 'S': Compute the separation only; -C = 'T': Compute the norm of Theta only; -C = 'B': Compute both the separation and the norm of Theta. -C -C TRANA CHARACTER*1 -C Specifies the form of op(A) to be used, as follows: -C = 'N': op(A) = A (No transpose); -C = 'T': op(A) = A**T (Transpose); -C = 'C': op(A) = A**T (Conjugate transpose = Transpose). -C -C LYAPUN CHARACTER*1 -C Specifies whether or not the original Lyapunov equations -C should be solved, as follows: -C = 'O': Solve the original Lyapunov equations, updating -C the right-hand sides and solutions with the -C matrix U, e.g., X <-- U'*X*U; -C = 'R': Solve reduced Lyapunov equations only, without -C updating the right-hand sides and solutions. -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the matrices A and X. N >= 0. -C -C T (input) DOUBLE PRECISION array, dimension (LDT,N) -C The leading N-by-N upper Hessenberg part of this array -C must contain the upper quasi-triangular matrix T in Schur -C canonical form from a Schur factorization of A. -C -C LDT INTEGER -C The leading dimension of array T. LDT >= MAX(1,N). -C -C U (input) DOUBLE PRECISION array, dimension (LDU,N) -C The leading N-by-N part of this array must contain the -C orthogonal matrix U from a real Schur factorization of A. -C If LYAPUN = 'R', the array U is not referenced. -C -C LDU INTEGER -C The leading dimension of array U. -C LDU >= 1, if LYAPUN = 'R'; -C LDU >= MAX(1,N), if LYAPUN = 'O'. -C -C XA (input) DOUBLE PRECISION array, dimension (LDXA,N) -C The leading N-by-N part of this array must contain the -C matrix product X*op(A), if LYAPUN = 'O', or U'*X*U*op(T), -C if LYAPUN = 'R', in the Lyapunov equation. -C If JOB = 'S', the array XA is not referenced. -C -C LDXA INTEGER -C The leading dimension of array XA. -C LDXA >= 1, if JOB = 'S'; -C LDXA >= MAX(1,N), if JOB = 'T' or 'B'. -C -C SEPD (output) DOUBLE PRECISION -C If JOB = 'S' or JOB = 'B', and INFO >= 0, SEPD contains -C the estimated quantity sepd(op(A),op(A)'). -C If JOB = 'T' or N = 0, SEPD is not referenced. -C -C THNORM (output) DOUBLE PRECISION -C If JOB = 'T' or JOB = 'B', and INFO >= 0, THNORM contains -C the estimated 1-norm of operator Theta. -C If JOB = 'S' or N = 0, THNORM is not referenced. -C -C Workspace -C -C IWORK INTEGER array, dimension (N*N) -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C -C LDWORK INTEGER -C The length of the array DWORK. -C LDWORK >= 0, if N = 0; -C LDWORK >= MAX(3,2*N*N), if N > 0. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C = N+1: if T has (almost) reciprocal eigenvalues; -C perturbed values were used to solve Lyapunov -C equations (but the matrix T is unchanged). -C -C METHOD -C -C SEPD is defined as -C -C sepd( op(A), op(A)' ) = sigma_min( K ) -C -C where sigma_min(K) is the smallest singular value of the -C N*N-by-N*N matrix -C -C K = kprod( op(A)', op(A)' ) - I(N**2). -C -C I(N**2) is an N*N-by-N*N identity matrix, and kprod denotes the -C Kronecker product. The routine estimates sigma_min(K) by the -C reciprocal of an estimate of the 1-norm of inverse(K), computed as -C suggested in [1]. This involves the solution of several discrete- -C time Lyapunov equations, either direct or transposed. The true -C reciprocal 1-norm of inverse(K) cannot differ from sigma_min(K) by -C more than a factor of N. -C The 1-norm of Theta is estimated similarly. -C -C REFERENCES -C -C [1] Higham, N.J. -C FORTRAN codes for estimating the one-norm of a real or -C complex matrix, with applications to condition estimation. -C ACM Trans. Math. Softw., 14, pp. 381-396, 1988. -C -C NUMERICAL ASPECTS -C 3 -C The algorithm requires 0(N ) operations. -C -C FURTHER COMMENTS -C -C When SEPD is zero, the routine returns immediately, with THNORM -C (if requested) not set. In this case, the equation is singular. -C The option LYAPUN = 'R' may occasionally produce slightly worse -C or better estimates, and it is much faster than the option 'O'. -C -C CONTRIBUTOR -C -C V. Sima, Research Institute for Informatics, Bucharest, Romania, -C Oct. 1998. Partly based on DDLSVX (and then SB03SD) by P. Petkov, -C Tech. University of Sofia, March 1998 (and December 1998). -C -C REVISIONS -C -C February 6, 1999, V. Sima, Katholieke Univ. Leuven, Belgium. -C V. Sima, Research Institute for Informatics, Bucharest, Oct. 2004. -C -C KEYWORDS -C -C Lyapunov equation, orthogonal transformation, real Schur form. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE, HALF - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, HALF = 0.5D+0 ) -C .. -C .. Scalar Arguments .. - CHARACTER JOB, LYAPUN, TRANA - INTEGER INFO, LDT, LDU, LDWORK, LDXA, N - DOUBLE PRECISION SEPD, THNORM -C .. -C .. Array Arguments .. - INTEGER IWORK( * ) - DOUBLE PRECISION DWORK( * ), T( LDT, * ), U( LDU, * ), - $ XA( LDXA, * ) -C .. -C .. Local Scalars .. - LOGICAL NOTRNA, UPDATE, WANTS, WANTT - CHARACTER TRANAT, UPLO - INTEGER INFO2, ITMP, KASE, NN - DOUBLE PRECISION BIGNUM, EST, SCALE -C .. -C .. External Functions .. - LOGICAL LSAME - DOUBLE PRECISION DLAMCH, DLANSY - EXTERNAL DLAMCH, DLANSY, LSAME -C .. -C .. External Subroutines .. - EXTERNAL DLACON, DLACPY, DSCAL, DSYR2K, MA02ED, MB01RU, - $ SB03MX, XERBLA -C .. -C .. Intrinsic Functions .. - INTRINSIC MAX -C .. -C .. Executable Statements .. -C -C Decode and Test input parameters. -C - WANTS = LSAME( JOB, 'S' ) - WANTT = LSAME( JOB, 'T' ) - NOTRNA = LSAME( TRANA, 'N' ) - UPDATE = LSAME( LYAPUN, 'O' ) -C - NN = N*N - INFO = 0 - IF( .NOT. ( WANTS .OR. WANTT .OR. LSAME( JOB, 'B' ) ) ) THEN - INFO = -1 - ELSE IF( .NOT.( NOTRNA .OR. LSAME( TRANA, 'T' ) .OR. - $ LSAME( TRANA, 'C' ) ) ) THEN - INFO = -2 - ELSE IF( .NOT.( UPDATE .OR. LSAME( LYAPUN, 'R' ) ) ) THEN - INFO = -3 - ELSE IF( N.LT.0 ) THEN - INFO = -4 - ELSE IF( LDT.LT.MAX( 1, N ) ) THEN - INFO = -6 - ELSE IF( LDU.LT.1 .OR. ( UPDATE .AND. LDU.LT.N ) ) THEN - INFO = -8 - ELSE IF( LDXA.LT.1 .OR. ( .NOT.WANTS .AND. LDXA.LT.N ) ) THEN - INFO = -10 - ELSE IF( LDWORK.LT.0 .OR. - $ ( LDWORK.LT.MAX( 3, 2*NN ) .AND. N.GT.0 ) ) THEN - INFO = -15 - END IF -C - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'SB03SY', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF( N.EQ.0 ) - $ RETURN -C - ITMP = NN + 1 -C - IF( NOTRNA ) THEN - TRANAT = 'T' - ELSE - TRANAT = 'N' - END IF -C - IF( .NOT.WANTT ) THEN -C -C Estimate sepd(op(A),op(A)'). -C Workspace: max(3,2*N*N). -C - KASE = 0 -C -C REPEAT - 10 CONTINUE - CALL DLACON( NN, DWORK( ITMP ), DWORK, IWORK, EST, KASE ) - IF( KASE.NE.0 ) THEN -C -C Select the triangular part of symmetric matrix to be used. -C - IF( DLANSY( '1-norm', 'Upper', N, DWORK, N, DWORK( ITMP ) ) - $ .GE. - $ DLANSY( '1-norm', 'Lower', N, DWORK, N, DWORK( ITMP ) ) - $ ) THEN - UPLO = 'U' - ELSE - UPLO = 'L' - END IF -C - IF( UPDATE ) THEN -C -C Transform the right-hand side: RHS := U'*RHS*U. -C - CALL MB01RU( UPLO, 'Transpose', N, N, ZERO, ONE, DWORK, - $ N, U, LDU, DWORK, N, DWORK( ITMP ), NN, - $ INFO2 ) - CALL DSCAL( N, HALF, DWORK, N+1 ) - END IF - CALL MA02ED( UPLO, N, DWORK, N ) -C - IF( KASE.EQ.1 ) THEN -C -C Solve op(T)'*Y*op(T) - Y = scale*RHS. -C - CALL SB03MX( TRANA, N, T, LDT, DWORK, N, SCALE, - $ DWORK( ITMP ), INFO2 ) - ELSE -C -C Solve op(T)*W*op(T)' - W = scale*RHS. -C - CALL SB03MX( TRANAT, N, T, LDT, DWORK, N, SCALE, - $ DWORK( ITMP ), INFO2 ) - END IF -C - IF( INFO2.GT.0 ) - $ INFO = N + 1 -C - IF( UPDATE ) THEN -C -C Transform back to obtain the solution: Z := U*Z*U', with -C Z = Y or Z = W. -C - CALL MB01RU( UPLO, 'No transpose', N, N, ZERO, ONE, - $ DWORK, N, U, LDU, DWORK, N, DWORK( ITMP ), - $ NN, INFO2 ) - CALL DSCAL( N, HALF, DWORK, N+1 ) -C -C Fill in the remaining triangle of the symmetric matrix. -C - CALL MA02ED( UPLO, N, DWORK, N ) - END IF -C - GO TO 10 - END IF -C UNTIL KASE = 0 -C - IF( EST.GT.SCALE ) THEN - SEPD = SCALE / EST - ELSE - BIGNUM = ONE / DLAMCH( 'Safe minimum' ) - IF( SCALE.LT.EST*BIGNUM ) THEN - SEPD = SCALE / EST - ELSE - SEPD = BIGNUM - END IF - END IF -C -C Return if the equation is singular. -C - IF( SEPD.EQ.ZERO ) - $ RETURN - END IF -C - IF( .NOT.WANTS ) THEN -C -C Estimate norm(Theta). -C Workspace: max(3,2*N*N). -C - KASE = 0 -C -C REPEAT - 20 CONTINUE - CALL DLACON( NN, DWORK( ITMP ), DWORK, IWORK, EST, KASE ) - IF( KASE.NE.0 ) THEN -C -C Select the triangular part of symmetric matrix to be used. -C - IF( DLANSY( '1-norm', 'Upper', N, DWORK, N, DWORK( ITMP ) ) - $ .GE. - $ DLANSY( '1-norm', 'Lower', N, DWORK, N, DWORK( ITMP ) ) - $ ) THEN - UPLO = 'U' - ELSE - UPLO = 'L' - END IF -C -C Fill in the remaining triangle of the symmetric matrix. -C - CALL MA02ED( UPLO, N, DWORK, N ) -C -C Compute RHS = op(W)'*X*op(A) + op(A)'*X*op(W). -C - CALL DSYR2K( UPLO, TRANAT, N, N, ONE, DWORK, N, XA, LDXA, - $ ZERO, DWORK( ITMP ), N ) - CALL DLACPY( UPLO, N, N, DWORK( ITMP ), N, DWORK, N ) -C - IF( UPDATE ) THEN -C -C Transform the right-hand side: RHS := U'*RHS*U. -C - CALL MB01RU( UPLO, 'Transpose', N, N, ZERO, ONE, DWORK, - $ N, U, LDU, DWORK, N, DWORK( ITMP ), NN, - $ INFO2 ) - CALL DSCAL( N, HALF, DWORK, N+1 ) - END IF - CALL MA02ED( UPLO, N, DWORK, N ) -C - IF( KASE.EQ.1 ) THEN -C -C Solve op(T)'*Y*op(T) - Y = scale*RHS. -C - CALL SB03MX( TRANA, N, T, LDT, DWORK, N, SCALE, - $ DWORK( ITMP ), INFO2 ) - ELSE -C -C Solve op(T)*W*op(T)' - W = scale*RHS. -C - CALL SB03MX( TRANAT, N, T, LDT, DWORK, N, SCALE, - $ DWORK( ITMP ), INFO2 ) - END IF -C - IF( INFO2.GT.0 ) - $ INFO = N + 1 -C - IF( UPDATE ) THEN -C -C Transform back to obtain the solution: Z := U*Z*U', with -C Z = Y or Z = W. -C - CALL MB01RU( UPLO, 'No transpose', N, N, ZERO, ONE, - $ DWORK, N, U, LDU, DWORK, N, DWORK( ITMP ), - $ NN, INFO2 ) - CALL DSCAL( N, HALF, DWORK, N+1 ) -C -C Fill in the remaining triangle of the symmetric matrix. -C - CALL MA02ED( UPLO, N, DWORK, N ) - END IF -C - GO TO 20 - END IF -C UNTIL KASE = 0 -C - IF( EST.LT.SCALE ) THEN - THNORM = EST / SCALE - ELSE - BIGNUM = ONE / DLAMCH( 'Safe minimum' ) - IF( EST.LT.SCALE*BIGNUM ) THEN - THNORM = EST / SCALE - ELSE - THNORM = BIGNUM - END IF - END IF - END IF -C - RETURN -C *** Last line of SB03SY *** - END
--- a/extra/control-devel/devel/dksyn/SB04PX.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,468 +0,0 @@ - SUBROUTINE SB04PX( LTRANL, LTRANR, ISGN, N1, N2, TL, LDTL, TR, - $ LDTR, B, LDB, SCALE, X, LDX, XNORM, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To solve for the N1-by-N2 matrix X, 1 <= N1,N2 <= 2, in -C -C op(TL)*X*op(TR) + ISGN*X = SCALE*B, -C -C where TL is N1-by-N1, TR is N2-by-N2, B is N1-by-N2, and ISGN = 1 -C or -1. op(T) = T or T', where T' denotes the transpose of T. -C -C ARGUMENTS -C -C Mode Parameters -C -C LTRANL LOGICAL -C Specifies the form of op(TL) to be used, as follows: -C = .FALSE.: op(TL) = TL, -C = .TRUE. : op(TL) = TL'. -C -C LTRANR LOGICAL -C Specifies the form of op(TR) to be used, as follows: -C = .FALSE.: op(TR) = TR, -C = .TRUE. : op(TR) = TR'. -C -C ISGN INTEGER -C Specifies the sign of the equation as described before. -C ISGN may only be 1 or -1. -C -C Input/Output Parameters -C -C N1 (input) INTEGER -C The order of matrix TL. N1 may only be 0, 1 or 2. -C -C N2 (input) INTEGER -C The order of matrix TR. N2 may only be 0, 1 or 2. -C -C TL (input) DOUBLE PRECISION array, dimension (LDTL,N1) -C The leading N1-by-N1 part of this array must contain the -C matrix TL. -C -C LDTL INTEGER -C The leading dimension of array TL. LDTL >= MAX(1,N1). -C -C TR (input) DOUBLE PRECISION array, dimension (LDTR,N2) -C The leading N2-by-N2 part of this array must contain the -C matrix TR. -C -C LDTR INTEGER -C The leading dimension of array TR. LDTR >= MAX(1,N2). -C -C B (input) DOUBLE PRECISION array, dimension (LDB,N2) -C The leading N1-by-N2 part of this array must contain the -C right-hand side of the equation. -C -C LDB INTEGER -C The leading dimension of array B. LDB >= MAX(1,N1). -C -C SCALE (output) DOUBLE PRECISION -C The scale factor. SCALE is chosen less than or equal to 1 -C to prevent the solution overflowing. -C -C X (output) DOUBLE PRECISION array, dimension (LDX,N2) -C The leading N1-by-N2 part of this array contains the -C solution of the equation. -C Note that X may be identified with B in the calling -C statement. -C -C LDX INTEGER -C The leading dimension of array X. LDX >= MAX(1,N1). -C -C XNORM (output) DOUBLE PRECISION -C The infinity-norm of the solution. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C = 1: if TL and -ISGN*TR have almost reciprocal -C eigenvalues, so TL or TR is perturbed to get a -C nonsingular equation. -C -C NOTE: In the interests of speed, this routine does not -C check the inputs for errors. -C -C METHOD -C -C The equivalent linear algebraic system of equations is formed and -C solved using Gaussian elimination with complete pivoting. -C -C REFERENCES -C -C [1] Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J., -C Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., -C Ostrouchov, S., and Sorensen, D. -C LAPACK Users' Guide: Second Edition. -C SIAM, Philadelphia, 1995. -C -C NUMERICAL ASPECTS -C -C The algorithm is stable and reliable, since Gaussian elimination -C with complete pivoting is used. -C -C CONTRIBUTOR -C -C V. Sima, Katholieke Univ. Leuven, Belgium, May 2000. -C This is a modification and slightly more efficient version of -C SLICOT Library routine SB03MU. -C -C REVISIONS -C -C - -C -C KEYWORDS -C -C Discrete-time system, Sylvester equation, matrix algebra. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE, TWO, HALF, EIGHT - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, - $ TWO = 2.0D+0, HALF = 0.5D+0, EIGHT = 8.0D+0 ) -C .. -C .. Scalar Arguments .. - LOGICAL LTRANL, LTRANR - INTEGER INFO, ISGN, LDB, LDTL, LDTR, LDX, N1, N2 - DOUBLE PRECISION SCALE, XNORM -C .. -C .. Array Arguments .. - DOUBLE PRECISION B( LDB, * ), TL( LDTL, * ), TR( LDTR, * ), - $ X( LDX, * ) -C .. -C .. Local Scalars .. - LOGICAL BSWAP, XSWAP - INTEGER I, IP, IPIV, IPSV, J, JP, JPSV, K - DOUBLE PRECISION BET, EPS, GAM, L21, SGN, SMIN, SMLNUM, TAU1, - $ TEMP, U11, U12, U22, XMAX -C .. -C .. Local Arrays .. - LOGICAL BSWPIV( 4 ), XSWPIV( 4 ) - INTEGER JPIV( 4 ), LOCL21( 4 ), LOCU12( 4 ), - $ LOCU22( 4 ) - DOUBLE PRECISION BTMP( 4 ), T16( 4, 4 ), TMP( 4 ), X2( 2 ) -C .. -C .. External Functions .. - INTEGER IDAMAX - DOUBLE PRECISION DLAMCH - EXTERNAL DLAMCH, IDAMAX -C .. -C .. External Subroutines .. - EXTERNAL DSWAP -C .. -C .. Intrinsic Functions .. - INTRINSIC ABS, MAX -C .. -C .. Data statements .. - DATA LOCU12 / 3, 4, 1, 2 / , LOCL21 / 2, 1, 4, 3 / , - $ LOCU22 / 4, 3, 2, 1 / - DATA XSWPIV / .FALSE., .FALSE., .TRUE., .TRUE. / - DATA BSWPIV / .FALSE., .TRUE., .FALSE., .TRUE. / -C .. -C .. Executable Statements .. -C -C Do not check the input parameters for errors. -C - INFO = 0 - SCALE = ONE -C -C Quick return if possible. -C - IF( N1.EQ.0 .OR. N2.EQ.0 ) THEN - XNORM = ZERO - RETURN - END IF -C -C Set constants to control overflow. -C - EPS = DLAMCH( 'P' ) - SMLNUM = DLAMCH( 'S' ) / EPS - SGN = ISGN -C - K = N1 + N1 + N2 - 2 - GO TO ( 10, 20, 30, 50 )K -C -C 1-by-1: TL11*X*TR11 + ISGN*X = B11. -C - 10 CONTINUE - TAU1 = TL( 1, 1 )*TR( 1, 1 ) + SGN - BET = ABS( TAU1 ) - IF( BET.LE.SMLNUM ) THEN - TAU1 = SMLNUM - BET = SMLNUM - INFO = 1 - END IF -C - GAM = ABS( B( 1, 1 ) ) - IF( SMLNUM*GAM.GT.BET ) - $ SCALE = ONE / GAM -C - X( 1, 1 ) = ( B( 1, 1 )*SCALE ) / TAU1 - XNORM = ABS( X( 1, 1 ) ) - RETURN -C -C 1-by-2: -C TL11*[X11 X12]*op[TR11 TR12] + ISGN*[X11 X12] = [B11 B12]. -C [TR21 TR22] -C - 20 CONTINUE -C - SMIN = MAX( MAX( ABS( TR( 1, 1 ) ), ABS( TR( 1, 2 ) ), - $ ABS( TR( 2, 1 ) ), ABS( TR( 2, 2 ) ) ) - $ *ABS( TL( 1, 1 ) )*EPS, - $ SMLNUM ) - TMP( 1 ) = TL( 1, 1 )*TR( 1, 1 ) + SGN - TMP( 4 ) = TL( 1, 1 )*TR( 2, 2 ) + SGN - IF( LTRANR ) THEN - TMP( 2 ) = TL( 1, 1 )*TR( 2, 1 ) - TMP( 3 ) = TL( 1, 1 )*TR( 1, 2 ) - ELSE - TMP( 2 ) = TL( 1, 1 )*TR( 1, 2 ) - TMP( 3 ) = TL( 1, 1 )*TR( 2, 1 ) - END IF - BTMP( 1 ) = B( 1, 1 ) - BTMP( 2 ) = B( 1, 2 ) - GO TO 40 -C -C 2-by-1: -C op[TL11 TL12]*[X11]*TR11 + ISGN*[X11] = [B11]. -C [TL21 TL22] [X21] [X21] [B21] -C - 30 CONTINUE - SMIN = MAX( MAX( ABS( TL( 1, 1 ) ), ABS( TL( 1, 2 ) ), - $ ABS( TL( 2, 1 ) ), ABS( TL( 2, 2 ) ) ) - $ *ABS( TR( 1, 1 ) )*EPS, - $ SMLNUM ) - TMP( 1 ) = TL( 1, 1 )*TR( 1, 1 ) + SGN - TMP( 4 ) = TL( 2, 2 )*TR( 1, 1 ) + SGN - IF( LTRANL ) THEN - TMP( 2 ) = TL( 1, 2 )*TR( 1, 1 ) - TMP( 3 ) = TL( 2, 1 )*TR( 1, 1 ) - ELSE - TMP( 2 ) = TL( 2, 1 )*TR( 1, 1 ) - TMP( 3 ) = TL( 1, 2 )*TR( 1, 1 ) - END IF - BTMP( 1 ) = B( 1, 1 ) - BTMP( 2 ) = B( 2, 1 ) - 40 CONTINUE -C -C Solve 2-by-2 system using complete pivoting. -C Set pivots less than SMIN to SMIN. -C - IPIV = IDAMAX( 4, TMP, 1 ) - U11 = TMP( IPIV ) - IF( ABS( U11 ).LE.SMIN ) THEN - INFO = 1 - U11 = SMIN - END IF - U12 = TMP( LOCU12( IPIV ) ) - L21 = TMP( LOCL21( IPIV ) ) / U11 - U22 = TMP( LOCU22( IPIV ) ) - U12*L21 - XSWAP = XSWPIV( IPIV ) - BSWAP = BSWPIV( IPIV ) - IF( ABS( U22 ).LE.SMIN ) THEN - INFO = 1 - U22 = SMIN - END IF - IF( BSWAP ) THEN - TEMP = BTMP( 2 ) - BTMP( 2 ) = BTMP( 1 ) - L21*TEMP - BTMP( 1 ) = TEMP - ELSE - BTMP( 2 ) = BTMP( 2 ) - L21*BTMP( 1 ) - END IF - IF( ( TWO*SMLNUM )*ABS( BTMP( 2 ) ).GT.ABS( U22 ) .OR. - $ ( TWO*SMLNUM )*ABS( BTMP( 1 ) ).GT.ABS( U11 ) ) THEN - SCALE = HALF / MAX( ABS( BTMP( 1 ) ), ABS( BTMP( 2 ) ) ) - BTMP( 1 ) = BTMP( 1 )*SCALE - BTMP( 2 ) = BTMP( 2 )*SCALE - END IF - X2( 2 ) = BTMP( 2 ) / U22 - X2( 1 ) = BTMP( 1 ) / U11 - ( U12 / U11 )*X2( 2 ) - IF( XSWAP ) THEN - TEMP = X2( 2 ) - X2( 2 ) = X2( 1 ) - X2( 1 ) = TEMP - END IF - X( 1, 1 ) = X2( 1 ) - IF( N1.EQ.1 ) THEN - X( 1, 2 ) = X2( 2 ) - XNORM = ABS( X2( 1 ) ) + ABS( X2( 2 ) ) - ELSE - X( 2, 1 ) = X2( 2 ) - XNORM = MAX( ABS( X2( 1 ) ), ABS( X2( 2 ) ) ) - END IF - RETURN -C -C 2-by-2: -C op[TL11 TL12]*[X11 X12]*op[TR11 TR12] + ISGN*[X11 X12] = [B11 B12] -C [TL21 TL22] [X21 X22] [TR21 TR22] [X21 X22] [B21 B22] -C -C Solve equivalent 4-by-4 system using complete pivoting. -C Set pivots less than SMIN to SMIN. -C - 50 CONTINUE - SMIN = MAX( ABS( TR( 1, 1 ) ), ABS( TR( 1, 2 ) ), - $ ABS( TR( 2, 1 ) ), ABS( TR( 2, 2 ) ) ) - SMIN = MAX( ABS( TL( 1, 1 ) ), ABS( TL( 1, 2 ) ), - $ ABS( TL( 2, 1 ) ), ABS( TL( 2, 2 ) ) )*SMIN - SMIN = MAX( EPS*SMIN, SMLNUM ) - T16( 1, 1 ) = TL( 1, 1 )*TR( 1, 1 ) + SGN - T16( 2, 2 ) = TL( 2, 2 )*TR( 1, 1 ) + SGN - T16( 3, 3 ) = TL( 1, 1 )*TR( 2, 2 ) + SGN - T16( 4, 4 ) = TL( 2, 2 )*TR( 2, 2 ) + SGN - IF( LTRANL ) THEN - T16( 1, 2 ) = TL( 2, 1 )*TR( 1, 1 ) - T16( 2, 1 ) = TL( 1, 2 )*TR( 1, 1 ) - T16( 3, 4 ) = TL( 2, 1 )*TR( 2, 2 ) - T16( 4, 3 ) = TL( 1, 2 )*TR( 2, 2 ) - ELSE - T16( 1, 2 ) = TL( 1, 2 )*TR( 1, 1 ) - T16( 2, 1 ) = TL( 2, 1 )*TR( 1, 1 ) - T16( 3, 4 ) = TL( 1, 2 )*TR( 2, 2 ) - T16( 4, 3 ) = TL( 2, 1 )*TR( 2, 2 ) - END IF - IF( LTRANR ) THEN - T16( 1, 3 ) = TL( 1, 1 )*TR( 1, 2 ) - T16( 2, 4 ) = TL( 2, 2 )*TR( 1, 2 ) - T16( 3, 1 ) = TL( 1, 1 )*TR( 2, 1 ) - T16( 4, 2 ) = TL( 2, 2 )*TR( 2, 1 ) - ELSE - T16( 1, 3 ) = TL( 1, 1 )*TR( 2, 1 ) - T16( 2, 4 ) = TL( 2, 2 )*TR( 2, 1 ) - T16( 3, 1 ) = TL( 1, 1 )*TR( 1, 2 ) - T16( 4, 2 ) = TL( 2, 2 )*TR( 1, 2 ) - END IF - IF( LTRANL .AND. LTRANR ) THEN - T16( 1, 4 ) = TL( 2, 1 )*TR( 1, 2 ) - T16( 2, 3 ) = TL( 1, 2 )*TR( 1, 2 ) - T16( 3, 2 ) = TL( 2, 1 )*TR( 2, 1 ) - T16( 4, 1 ) = TL( 1, 2 )*TR( 2, 1 ) - ELSE IF( LTRANL .AND. .NOT.LTRANR ) THEN - T16( 1, 4 ) = TL( 2, 1 )*TR( 2, 1 ) - T16( 2, 3 ) = TL( 1, 2 )*TR( 2, 1 ) - T16( 3, 2 ) = TL( 2, 1 )*TR( 1, 2 ) - T16( 4, 1 ) = TL( 1, 2 )*TR( 1, 2 ) - ELSE IF( .NOT.LTRANL .AND. LTRANR ) THEN - T16( 1, 4 ) = TL( 1, 2 )*TR( 1, 2 ) - T16( 2, 3 ) = TL( 2, 1 )*TR( 1, 2 ) - T16( 3, 2 ) = TL( 1, 2 )*TR( 2, 1 ) - T16( 4, 1 ) = TL( 2, 1 )*TR( 2, 1 ) - ELSE - T16( 1, 4 ) = TL( 1, 2 )*TR( 2, 1 ) - T16( 2, 3 ) = TL( 2, 1 )*TR( 2, 1 ) - T16( 3, 2 ) = TL( 1, 2 )*TR( 1, 2 ) - T16( 4, 1 ) = TL( 2, 1 )*TR( 1, 2 ) - END IF - BTMP( 1 ) = B( 1, 1 ) - BTMP( 2 ) = B( 2, 1 ) - BTMP( 3 ) = B( 1, 2 ) - BTMP( 4 ) = B( 2, 2 ) -C -C Perform elimination. -C - DO 100 I = 1, 3 - XMAX = ZERO -C - DO 70 IP = I, 4 -C - DO 60 JP = I, 4 - IF( ABS( T16( IP, JP ) ).GE.XMAX ) THEN - XMAX = ABS( T16( IP, JP ) ) - IPSV = IP - JPSV = JP - END IF - 60 CONTINUE -C - 70 CONTINUE -C - IF( IPSV.NE.I ) THEN - CALL DSWAP( 4, T16( IPSV, 1 ), 4, T16( I, 1 ), 4 ) - TEMP = BTMP( I ) - BTMP( I ) = BTMP( IPSV ) - BTMP( IPSV ) = TEMP - END IF - IF( JPSV.NE.I ) - $ CALL DSWAP( 4, T16( 1, JPSV ), 1, T16( 1, I ), 1 ) - JPIV( I ) = JPSV - IF( ABS( T16( I, I ) ).LT.SMIN ) THEN - INFO = 1 - T16( I, I ) = SMIN - END IF -C - DO 90 J = I + 1, 4 - T16( J, I ) = T16( J, I ) / T16( I, I ) - BTMP( J ) = BTMP( J ) - T16( J, I )*BTMP( I ) -C - DO 80 K = I + 1, 4 - T16( J, K ) = T16( J, K ) - T16( J, I )*T16( I, K ) - 80 CONTINUE -C - 90 CONTINUE -C - 100 CONTINUE -C - IF( ABS( T16( 4, 4 ) ).LT.SMIN ) - $ T16( 4, 4 ) = SMIN - IF( ( EIGHT*SMLNUM )*ABS( BTMP( 1 ) ).GT.ABS( T16( 1, 1 ) ) .OR. - $ ( EIGHT*SMLNUM )*ABS( BTMP( 2 ) ).GT.ABS( T16( 2, 2 ) ) .OR. - $ ( EIGHT*SMLNUM )*ABS( BTMP( 3 ) ).GT.ABS( T16( 3, 3 ) ) .OR. - $ ( EIGHT*SMLNUM )*ABS( BTMP( 4 ) ).GT.ABS( T16( 4, 4 ) ) ) THEN - SCALE = ( ONE / EIGHT ) / MAX( ABS( BTMP( 1 ) ), - $ ABS( BTMP( 2 ) ), ABS( BTMP( 3 ) ), - $ ABS( BTMP( 4 ) ) ) - BTMP( 1 ) = BTMP( 1 )*SCALE - BTMP( 2 ) = BTMP( 2 )*SCALE - BTMP( 3 ) = BTMP( 3 )*SCALE - BTMP( 4 ) = BTMP( 4 )*SCALE - END IF -C - DO 120 I = 1, 4 - K = 5 - I - TEMP = ONE / T16( K, K ) - TMP( K ) = BTMP( K )*TEMP -C - DO 110 J = K + 1, 4 - TMP( K ) = TMP( K ) - ( TEMP*T16( K, J ) )*TMP( J ) - 110 CONTINUE -C - 120 CONTINUE -C - DO 130 I = 1, 3 - IF( JPIV( 4-I ).NE.4-I ) THEN - TEMP = TMP( 4-I ) - TMP( 4-I ) = TMP( JPIV( 4-I ) ) - TMP( JPIV( 4-I ) ) = TEMP - END IF - 130 CONTINUE -C - X( 1, 1 ) = TMP( 1 ) - X( 2, 1 ) = TMP( 2 ) - X( 1, 2 ) = TMP( 3 ) - X( 2, 2 ) = TMP( 4 ) - XNORM = MAX( ABS( TMP( 1 ) ) + ABS( TMP( 3 ) ), - $ ABS( TMP( 2 ) ) + ABS( TMP( 4 ) ) ) -C - RETURN -C *** Last line of SB04PX *** - END
--- a/extra/control-devel/devel/dksyn/SB10AD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,827 +0,0 @@ - SUBROUTINE SB10AD( JOB, N, M, NP, NCON, NMEAS, GAMMA, A, LDA, - $ B, LDB, C, LDC, D, LDD, AK, LDAK, BK, LDBK, CK, - $ LDCK, DK, LDDK, AC, LDAC, BC, LDBC, CC, LDCC, - $ DC, LDDC, RCOND, GTOL, ACTOL, IWORK, LIWORK, - $ DWORK, LDWORK, BWORK, LBWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To compute the matrices of an H-infinity optimal n-state -C controller -C -C | AK | BK | -C K = |----|----|, -C | CK | DK | -C -C using modified Glover's and Doyle's 1988 formulas, for the system -C -C | A | B1 B2 | | A | B | -C P = |----|---------| = |---|---| -C | C1 | D11 D12 | | C | D | -C | C2 | D21 D22 | -C -C and for the estimated minimal possible value of gamma with respect -C to GTOL, where B2 has as column size the number of control inputs -C (NCON) and C2 has as row size the number of measurements (NMEAS) -C being provided to the controller, and then to compute the matrices -C of the closed-loop system -C -C | AC | BC | -C G = |----|----|, -C | CC | DC | -C -C if the stabilizing controller exists. -C -C It is assumed that -C -C (A1) (A,B2) is stabilizable and (C2,A) is detectable, -C -C (A2) D12 is full column rank and D21 is full row rank, -C -C (A3) | A-j*omega*I B2 | has full column rank for all omega, -C | C1 D12 | -C -C (A4) | A-j*omega*I B1 | has full row rank for all omega. -C | C2 D21 | -C -C ARGUMENTS -C -C Input/Output Parameters -C -C JOB (input) INTEGER -C Indicates the strategy for reducing the GAMMA value, as -C follows: -C = 1: Use bisection method for decreasing GAMMA from GAMMA -C to GAMMAMIN until the closed-loop system leaves -C stability. -C = 2: Scan from GAMMA to 0 trying to find the minimal GAMMA -C for which the closed-loop system retains stability. -C = 3: First bisection, then scanning. -C = 4: Find suboptimal controller only. -C -C N (input) INTEGER -C The order of the system. N >= 0. -C -C M (input) INTEGER -C The column size of the matrix B. M >= 0. -C -C NP (input) INTEGER -C The row size of the matrix C. NP >= 0. -C -C NCON (input) INTEGER -C The number of control inputs (M2). M >= NCON >= 0, -C NP-NMEAS >= NCON. -C -C NMEAS (input) INTEGER -C The number of measurements (NP2). NP >= NMEAS >= 0, -C M-NCON >= NMEAS. -C -C GAMMA (input/output) DOUBLE PRECISION -C The initial value of gamma on input. It is assumed that -C gamma is sufficiently large so that the controller is -C admissible. GAMMA >= 0. -C On output it contains the minimal estimated gamma. -C -C A (input) DOUBLE PRECISION array, dimension (LDA,N) -C The leading N-by-N part of this array must contain the -C system state matrix A. -C -C LDA INTEGER -C The leading dimension of the array A. LDA >= max(1,N). -C -C B (input) DOUBLE PRECISION array, dimension (LDB,M) -C The leading N-by-M part of this array must contain the -C system input matrix B. -C -C LDB INTEGER -C The leading dimension of the array B. LDB >= max(1,N). -C -C C (input) DOUBLE PRECISION array, dimension (LDC,N) -C The leading NP-by-N part of this array must contain the -C system output matrix C. -C -C LDC INTEGER -C The leading dimension of the array C. LDC >= max(1,NP). -C -C D (input) DOUBLE PRECISION array, dimension (LDD,M) -C The leading NP-by-M part of this array must contain the -C system input/output matrix D. -C -C LDD INTEGER -C The leading dimension of the array D. LDD >= max(1,NP). -C -C AK (output) DOUBLE PRECISION array, dimension (LDAK,N) -C The leading N-by-N part of this array contains the -C controller state matrix AK. -C -C LDAK INTEGER -C The leading dimension of the array AK. LDAK >= max(1,N). -C -C BK (output) DOUBLE PRECISION array, dimension (LDBK,NMEAS) -C The leading N-by-NMEAS part of this array contains the -C controller input matrix BK. -C -C LDBK INTEGER -C The leading dimension of the array BK. LDBK >= max(1,N). -C -C CK (output) DOUBLE PRECISION array, dimension (LDCK,N) -C The leading NCON-by-N part of this array contains the -C controller output matrix CK. -C -C LDCK INTEGER -C The leading dimension of the array CK. -C LDCK >= max(1,NCON). -C -C DK (output) DOUBLE PRECISION array, dimension (LDDK,NMEAS) -C The leading NCON-by-NMEAS part of this array contains the -C controller input/output matrix DK. -C -C LDDK INTEGER -C The leading dimension of the array DK. -C LDDK >= max(1,NCON). -C -C AC (output) DOUBLE PRECISION array, dimension (LDAC,2*N) -C The leading 2*N-by-2*N part of this array contains the -C closed-loop system state matrix AC. -C -C LDAC INTEGER -C The leading dimension of the array AC. -C LDAC >= max(1,2*N). -C -C BC (output) DOUBLE PRECISION array, dimension (LDBC,M-NCON) -C The leading 2*N-by-(M-NCON) part of this array contains -C the closed-loop system input matrix BC. -C -C LDBC INTEGER -C The leading dimension of the array BC. -C LDBC >= max(1,2*N). -C -C CC (output) DOUBLE PRECISION array, dimension (LDCC,2*N) -C The leading (NP-NMEAS)-by-2*N part of this array contains -C the closed-loop system output matrix CC. -C -C LDCC INTEGER -C The leading dimension of the array CC. -C LDCC >= max(1,NP-NMEAS). -C -C DC (output) DOUBLE PRECISION array, dimension (LDDC,M-NCON) -C The leading (NP-NMEAS)-by-(M-NCON) part of this array -C contains the closed-loop system input/output matrix DC. -C -C LDDC INTEGER -C The leading dimension of the array DC. -C LDDC >= max(1,NP-NMEAS). -C -C RCOND (output) DOUBLE PRECISION array, dimension (4) -C For the last successful step: -C RCOND(1) contains the reciprocal condition number of the -C control transformation matrix; -C RCOND(2) contains the reciprocal condition number of the -C measurement transformation matrix; -C RCOND(3) contains an estimate of the reciprocal condition -C number of the X-Riccati equation; -C RCOND(4) contains an estimate of the reciprocal condition -C number of the Y-Riccati equation. -C -C Tolerances -C -C GTOL DOUBLE PRECISION -C Tolerance used for controlling the accuracy of GAMMA -C and its distance to the estimated minimal possible -C value of GAMMA. -C If GTOL <= 0, then a default value equal to sqrt(EPS) -C is used, where EPS is the relative machine precision. -C -C ACTOL DOUBLE PRECISION -C Upper bound for the poles of the closed-loop system -C used for determining if it is stable. -C ACTOL <= 0 for stable systems. -C -C Workspace -C -C IWORK INTEGER array, dimension (LIWORK) -C -C LIWORK INTEGER -C The dimension of the array IWORK. -C LIWORK >= max(2*max(N,M-NCON,NP-NMEAS,NCON,NMEAS),N*N) -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C On exit, if INFO = 0, DWORK(1) contains the optimal -C value of LDWORK. -C -C LDWORK INTEGER -C The dimension of the array DWORK. -C LDWORK >= LW1 + max(1,LW2,LW3,LW4,LW5 + MAX(LW6,LW7)), -C where -C LW1 = N*M + NP*N + NP*M + M2*M2 + NP2*NP2; -C LW2 = max( ( N + NP1 + 1 )*( N + M2 ) + -C max( 3*( N + M2 ) + N + NP1, 5*( N + M2 ) ), -C ( N + NP2 )*( N + M1 + 1 ) + -C max( 3*( N + NP2 ) + N + M1, 5*( N + NP2 ) ), -C M2 + NP1*NP1 + max( NP1*max( N, M1 ), -C 3*M2 + NP1, 5*M2 ), -C NP2 + M1*M1 + max( max( N, NP1 )*M1, -C 3*NP2 + M1, 5*NP2 ) ); -C LW3 = max( ND1*M1 + max( 4*min( ND1, M1 ) + max( ND1,M1 ), -C 6*min( ND1, M1 ) ), -C NP1*ND2 + max( 4*min( NP1, ND2 ) + -C max( NP1,ND2 ), -C 6*min( NP1, ND2 ) ) ); -C LW4 = 2*M*M + NP*NP + 2*M*N + M*NP + 2*N*NP; -C LW5 = 2*N*N + M*N + N*NP; -C LW6 = max( M*M + max( 2*M1, 3*N*N + -C max( N*M, 10*N*N + 12*N + 5 ) ), -C NP*NP + max( 2*NP1, 3*N*N + -C max( N*NP, 10*N*N + 12*N + 5 ) )); -C LW7 = M2*NP2 + NP2*NP2 + M2*M2 + -C max( ND1*ND1 + max( 2*ND1, ( ND1 + ND2 )*NP2 ), -C ND2*ND2 + max( 2*ND2, ND2*M2 ), 3*N, -C N*( 2*NP2 + M2 ) + -C max( 2*N*M2, M2*NP2 + -C max( M2*M2 + 3*M2, NP2*( 2*NP2 + -C M2 + max( NP2, N ) ) ) ) ); -C M1 = M - M2, NP1 = NP - NP2, -C ND1 = NP1 - M2, ND2 = M1 - NP2. -C For good performance, LDWORK must generally be larger. -C -C BWORK LOGICAL array, dimension (LBWORK) -C -C LBWORK INTEGER -C The dimension of the array BWORK. LBWORK >= 2*N. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C = 1: if the matrix | A-j*omega*I B2 | had not full -C | C1 D12 | -C column rank in respect to the tolerance EPS; -C = 2: if the matrix | A-j*omega*I B1 | had not full row -C | C2 D21 | -C rank in respect to the tolerance EPS; -C = 3: if the matrix D12 had not full column rank in -C respect to the tolerance SQRT(EPS); -C = 4: if the matrix D21 had not full row rank in respect -C to the tolerance SQRT(EPS); -C = 5: if the singular value decomposition (SVD) algorithm -C did not converge (when computing the SVD of one of -C the matrices |A B2 |, |A B1 |, D12 or D21); -C |C1 D12| |C2 D21| -C = 6: if the controller is not admissible (too small value -C of gamma); -C = 7: if the X-Riccati equation was not solved -C successfully (the controller is not admissible or -C there are numerical difficulties); -C = 8: if the Y-Riccati equation was not solved -C successfully (the controller is not admissible or -C there are numerical difficulties); -C = 9: if the determinant of Im2 + Tu*D11HAT*Ty*D22 is -C zero [3]; -C = 10: if there are numerical problems when estimating -C singular values of D1111, D1112, D1111', D1121'; -C = 11: if the matrices Inp2 - D22*DK or Im2 - DK*D22 -C are singular to working precision; -C = 12: if a stabilizing controller cannot be found. -C -C METHOD -C -C The routine implements the Glover's and Doyle's 1988 formulas [1], -C [2], modified to improve the efficiency as described in [3]. -C -C JOB = 1: It tries with a decreasing value of GAMMA, starting with -C the given, and with the newly obtained controller estimates of the -C closed-loop system. If it is stable, (i.e., max(eig(AC)) < ACTOL) -C the iterations can be continued until the given tolerance between -C GAMMA and the estimated GAMMAMIN is reached. Otherwise, in the -C next step GAMMA is increased. The step in the all next iterations -C is step = step/2. The closed-loop system is obtained by the -C formulas given in [2]. -C -C JOB = 2: The same as for JOB = 1, but with non-varying step till -C GAMMA = 0, step = max(0.1, GTOL). -C -C JOB = 3: Combines the JOB = 1 and JOB = 2 cases for a quicker -C procedure. -C -C JOB = 4: Suboptimal controller for current GAMMA only. -C -C REFERENCES -C -C [1] Glover, K. and Doyle, J.C. -C State-space formulae for all stabilizing controllers that -C satisfy an Hinf norm bound and relations to risk sensitivity. -C Systems and Control Letters, vol. 11, pp. 167-172, 1988. -C -C [2] Balas, G.J., Doyle, J.C., Glover, K., Packard, A., and -C Smith, R. -C mu-Analysis and Synthesis Toolbox. -C The MathWorks Inc., Natick, MA, 1995. -C -C [3] Petkov, P.Hr., Gu, D.W., and Konstantinov, M.M. -C Fortran 77 routines for Hinf and H2 design of continuous-time -C linear control systems. -C Rep. 98-14, Department of Engineering, Leicester University, -C Leicester, U.K., 1998. -C -C NUMERICAL ASPECTS -C -C The accuracy of the result depends on the condition numbers of the -C input and output transformations and on the condition numbers of -C the two Riccati equations, as given by the values of RCOND(1), -C RCOND(2), RCOND(3) and RCOND(4), respectively. -C This approach by estimating the closed-loop system and checking -C its poles seems to be reliable. -C -C CONTRIBUTORS -C -C A. Markovski, P.Hr. Petkov, D.W. Gu and M.M. Konstantinov, -C July 2003. -C -C REVISIONS -C -C V. Sima, Research Institute for Informatics, Bucharest, Aug. 2003. -C -C KEYWORDS -C -C Algebraic Riccati equation, H-infinity optimal control, robust -C control. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE, TWO, P1, THOUS - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0, - $ P1 = 0.1D+0, THOUS = 1.0D+3 ) -C .. -C .. Scalar Arguments .. - INTEGER INFO, JOB, LBWORK, LDA, LDAC, LDAK, LDB, LDBC, - $ LDBK, LDC, LDCC, LDCK, LDD, LDDC, LDDK, LDWORK, - $ LIWORK, M, N, NCON, NMEAS, NP - DOUBLE PRECISION ACTOL, GAMMA, GTOL -C .. -C .. Array Arguments .. - LOGICAL BWORK( * ) - INTEGER IWORK( * ) - DOUBLE PRECISION A( LDA, * ), AC( LDAC, * ), AK( LDAK, * ), - $ B( LDB, * ), BC( LDBC, * ), BK( LDBK, * ), - $ C( LDC, * ), CC( LDCC, * ), CK( LDCK, * ), - $ D( LDD, * ), DC( LDDC, * ), DK( LDDK, * ), - $ DWORK( * ), RCOND( 4 ) -C .. -C .. Local Scalars .. - INTEGER I, INF, INFO2, INFO3, IWAC, IWC, IWD, IWD1, - $ IWF, IWH, IWRE, IWRK, IWS1, IWS2, IWTU, IWTY, - $ IWWI, IWWR, IWX, IWY, LW1, LW2, LW3, LW4, LW5, - $ LW6, LW7, LWAMAX, M1, M11, M2, MINWRK, MODE, - $ NP1, NP11, NP2 - DOUBLE PRECISION GAMABS, GAMAMN, GAMAMX, GTOLL, MINEAC, STEPG, - $ TOL2 -C .. -C .. External Functions .. - LOGICAL SELECT - DOUBLE PRECISION DLAMCH - EXTERNAL DLAMCH, SELECT -C .. -C .. External Subroutines .. - EXTERNAL DGEES, DGESVD, DLACPY, SB10LD, SB10PD, SB10QD, - $ SB10RD, XERBLA -C .. -C .. Intrinsic Functions .. - INTRINSIC DBLE, INT, MAX, MIN, SQRT -C .. -C .. Executable Statements .. -C -C Decode and test input parameters. -C - M1 = M - NCON - M2 = NCON - NP1 = NP - NMEAS - NP2 = NMEAS - NP11 = NP1 - M2 - M11 = M1 - NP2 -C - INFO = 0 - IF ( JOB.LT.1 .OR. JOB.GT.4 ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( M.LT.0 ) THEN - INFO = -3 - ELSE IF( NP.LT.0 ) THEN - INFO = -4 - ELSE IF( NCON.LT.0 .OR. M1.LT.0 .OR. M2.GT.NP1 ) THEN - INFO = -5 - ELSE IF( NMEAS.LT.0 .OR. NP1.LT.0 .OR. NP2.GT.M1 ) THEN - INFO = -6 - ELSE IF( GAMMA.LT.ZERO ) THEN - INFO = -7 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -9 - ELSE IF( LDB.LT.MAX( 1, N ) ) THEN - INFO = -11 - ELSE IF( LDC.LT.MAX( 1, NP ) ) THEN - INFO = -13 - ELSE IF( LDD.LT.MAX( 1, NP ) ) THEN - INFO = -15 - ELSE IF( LDAK.LT.MAX( 1, N ) ) THEN - INFO = -17 - ELSE IF( LDBK.LT.MAX( 1, N ) ) THEN - INFO = -19 - ELSE IF( LDCK.LT.MAX( 1, M2 ) ) THEN - INFO = -21 - ELSE IF( LDDK.LT.MAX( 1, M2 ) ) THEN - INFO = -23 - ELSE IF( LDAC.LT.MAX( 1, 2*N ) ) THEN - INFO = -25 - ELSE IF( LDBC.LT.MAX( 1, 2*N ) ) THEN - INFO = -27 - ELSE IF( LDCC.LT.MAX( 1, NP1 ) ) THEN - INFO = -29 - ELSE IF( LDDC.LT.MAX( 1, NP1 ) ) THEN - INFO = -31 - ELSE -C -C Compute workspace. -C - LW1 = N*M + NP*N + NP*M + M2*M2 + NP2*NP2 - LW2 = MAX( ( N + NP1 + 1 )*( N + M2 ) + - $ MAX( 3*( N + M2 ) + N + NP1, 5*( N + M2 ) ), - $ ( N + NP2 )*( N + M1 + 1 ) + - $ MAX( 3*( N + NP2 ) + N + M1, 5*( N + NP2 ) ), - $ M2 + NP1*NP1 + MAX( NP1*MAX( N, M1 ), 3*M2 + NP1, - $ 5*M2 ), - $ NP2 + M1*M1 + MAX( MAX( N, NP1 )*M1, 3*NP2 + M1, - $ 5*NP2 ) ) - LW3 = MAX( NP11*M1 + MAX( 4*MIN( NP11, M1 ) + MAX( NP11, M1 ), - $ 6*MIN( NP11, M1 ) ), - $ NP1*M11 + MAX( 4*MIN( NP1, M11 ) + MAX( NP1, M11 ), - $ 6*MIN( NP1, M11 ) ) ) - LW4 = 2*M*M + NP*NP + 2*M*N + M*NP + 2*N*NP - LW5 = 2*N*N + M*N + N*NP - LW6 = MAX( M*M + MAX( 2*M1, 3*N*N + - $ MAX( N*M, 10*N*N + 12*N + 5 ) ), - $ NP*NP + MAX( 2*NP1, 3*N*N + - $ MAX( N*NP, 10*N*N + 12*N + 5 ) ) ) - LW7 = M2*NP2 + NP2*NP2 + M2*M2 + - $ MAX( NP11*NP11 + MAX( 2*NP11, ( NP11 + M11 )*NP2 ), - $ M11*M11 + MAX( 2*M11, M11*M2 ), 3*N, - $ N*( 2*NP2 + M2 ) + - $ MAX( 2*N*M2, M2*NP2 + - $ MAX( M2*M2 + 3*M2, NP2*( 2*NP2 + - $ M2 + MAX( NP2, N ) ) ) ) ) - MINWRK = LW1 + MAX( 1, LW2, LW3, LW4, LW5 + MAX( LW6, LW7 ) ) - IF( LDWORK.LT.MINWRK ) THEN - INFO = -38 - ELSE IF( LIWORK.LT.MAX( 2*MAX( N, M1, NP1, M2, NP2 ), - $ N*N ) ) THEN - INFO = -36 - ELSE IF( LBWORK.LT.2*N ) THEN - INFO = -40 - END IF - END IF -C - IF ( INFO.NE.0 ) THEN -C -C Error return. -C - CALL XERBLA( 'SB10AD', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF( N.EQ.0 .OR. M.EQ.0 .OR. NP.EQ.0 .OR. M1.EQ.0 .OR. M2.EQ.0 - $ .OR. NP1.EQ.0 .OR. NP2.EQ.0 ) THEN - RCOND( 1 ) = ONE - RCOND( 2 ) = ONE - RCOND( 3 ) = ONE - RCOND( 4 ) = ONE - DWORK( 1 ) = ONE - RETURN - END IF -C - MODE = JOB - IF ( MODE.GT.2 ) - $ MODE = 1 - GTOLL = GTOL - IF( GTOLL.LE.ZERO ) THEN -C -C Set the default value of the tolerance for GAMMA. -C - GTOLL = SQRT( DLAMCH( 'Epsilon' ) ) - END IF -C -C Workspace usage 1. -C - IWC = 1 + N*M - IWD = IWC + NP*N - IWTU = IWD + NP*M - IWTY = IWTU + M2*M2 - IWRK = IWTY + NP2*NP2 -C - CALL DLACPY( 'Full', N, M, B, LDB, DWORK, N ) -C - CALL DLACPY( 'Full', NP, N, C, LDC, DWORK( IWC ), NP ) -C - CALL DLACPY( 'Full', NP, M, D, LDD, DWORK( IWD ), NP ) -C -C Transform the system so that D12 and D21 satisfy the formulas -C in the computation of the Hinf optimal controller. -C Workspace: need LW1 + MAX(1,LWP1,LWP2,LWP3,LWP4), -C prefer larger, -C where -C LW1 = N*M + NP*N + NP*M + M2*M2 + NP2*NP2 -C LWP1 = (N+NP1+1)*(N+M2) + MAX(3*(N+M2)+N+NP1,5*(N+M2)), -C LWP2 = (N+NP2)*(N+M1+1) + MAX(3*(N+NP2)+N+M1,5*(N+NP2)), -C LWP3 = M2 + NP1*NP1 + MAX(NP1*MAX(N,M1),3*M2+NP1,5*M2), -C LWP4 = NP2 + M1*M1 + MAX(MAX(N,NP1)*M1,3*NP2+M1,5*NP2), -C with M1 = M - M2 and NP1 = NP - NP2. -C Denoting Q = MAX(M1,M2,NP1,NP2), an upper bound is -C LW1 + MAX(1,(N+Q)*(N+Q+6),Q*(Q+MAX(N,Q,5)+1). -C - TOL2 = -ONE -C - CALL SB10PD( N, M, NP, NCON, NMEAS, A, LDA, DWORK, N, - $ DWORK( IWC ), NP, DWORK( IWD ), NP, DWORK( IWTU ), - $ M2, DWORK( IWTY ), NP2, RCOND, TOL2, DWORK( IWRK ), - $ LDWORK-IWRK+1, INFO2 ) -C - LWAMAX = INT( DWORK( IWRK ) ) + IWRK - 1 -C - IF ( INFO2.NE.0 ) THEN - INFO = INFO2 - RETURN - END IF -C -C Workspace usage 2. -C - IWD1 = IWRK - IWS1 = IWD1 + NP11*M1 -C -C Check if GAMMA < max(sigma[D1111,D1112],sigma[D1111',D1121']). -C Workspace: need LW1 + MAX(1, LWS1, LWS2), -C prefer larger, -C where -C LWS1 = NP11*M1 + MAX(4*MIN(NP11,M1)+MAX(NP11,M1),6*MIN(NP11,M1)) -C LWS2 = NP1*M11 + MAX(4*MIN(NP1,M11)+MAX(NP1,M11),6*MIN(NP1,M11)) -C - INFO2 = 0 - INFO3 = 0 -C - IF ( NP11.NE.0 .AND. M1.NE.0 ) THEN - IWRK = IWS1 + MIN( NP11, M1 ) - CALL DLACPY( 'Full', NP11, M1, DWORK(IWD), LDD, DWORK(IWD1), - $ NP11 ) - CALL DGESVD( 'N', 'N', NP11, M1, DWORK(IWD1), NP11, - $ DWORK(IWS1), DWORK(IWS1), 1, DWORK(IWS1), 1, - $ DWORK( IWRK ), LDWORK-IWRK+1, INFO2 ) - LWAMAX = MAX( LWAMAX, INT( DWORK( IWRK ) ) + IWRK - 1 ) - ELSE - DWORK(IWS1) = ZERO - END IF -C - IWS2 = IWD1 + NP1*M11 - IF ( NP1.NE.0 .AND. M11.NE.0 ) THEN - IWRK = IWS2 + MIN( NP1, M11 ) - CALL DLACPY( 'Full', NP1, M11, DWORK(IWD), LDD, DWORK(IWD1), - $ NP1 ) - CALL DGESVD( 'N', 'N', NP1, M11, DWORK(IWD1), NP1, DWORK(IWS2), - $ DWORK(IWS2), 1, DWORK(IWS2), 1, DWORK( IWRK ), - $ LDWORK-IWRK+1, INFO3 ) - LWAMAX = MAX( LWAMAX, INT( DWORK( IWRK ) ) + IWRK - 1 ) - ELSE - DWORK(IWS2) = ZERO - END IF -C - GAMAMN = MAX( DWORK(IWS1), DWORK(IWS2) ) -C - IF ( INFO2.GT.0 .OR. INFO3.GT.0 ) THEN - INFO = 10 - RETURN - ELSE IF ( GAMMA.LE.GAMAMN ) THEN - INFO = 6 - RETURN - END IF -C -C Workspace usage 3. -C - IWX = IWD1 - IWY = IWX + N*N - IWF = IWY + N*N - IWH = IWF + M*N - IWRK = IWH + N*NP - IWAC = IWD1 - IWWR = IWAC + 4*N*N - IWWI = IWWR + 2*N - IWRE = IWWI + 2*N -C -C Prepare some auxiliary variables for the gamma iteration. -C - STEPG = GAMMA - GAMAMN - GAMABS = GAMMA - GAMAMX = GAMMA - INF = 0 -C -C ############################################################### -C -C Begin the gamma iteration. -C - 10 CONTINUE - STEPG = STEPG/TWO -C -C Try to compute the state feedback and output injection -C matrices for the current GAMMA. -C - CALL SB10QD( N, M, NP, NCON, NMEAS, GAMMA, A, LDA, DWORK, N, - $ DWORK( IWC ), NP, DWORK( IWD ), NP, DWORK( IWF ), - $ M, DWORK( IWH ), N, DWORK( IWX ), N, DWORK( IWY ), - $ N, RCOND(3), IWORK, DWORK( IWRK ), LDWORK-IWRK+1, - $ BWORK, INFO2 ) -C - IF ( INFO2.NE.0 ) GOTO 30 -C -C Try to compute the Hinf suboptimal (yet) controller. -C - CALL SB10RD( N, M, NP, NCON, NMEAS, GAMMA, A, LDA, DWORK, N, - $ DWORK( IWC ), NP, DWORK( IWD ), NP, DWORK( IWF ), - $ M, DWORK( IWH ), N, DWORK( IWTU ), M2, - $ DWORK( IWTY ), NP2, DWORK( IWX ), N, DWORK( IWY ), - $ N, AK, LDAK, BK, LDBK, CK, LDCK, DK, LDDK, IWORK, - $ DWORK( IWRK ), LDWORK-IWRK+1, INFO2 ) -C - IF ( INFO2.NE.0 ) GOTO 30 -C -C Compute the closed-loop system. -C Workspace: need LW1 + 2*M*M + NP*NP + 2*M*N + M*NP + 2*N*NP; -C prefer larger. -C - CALL SB10LD( N, M, NP, NCON, NMEAS, A, LDA, B, LDB, C, LDC, D, - $ LDD, AK, LDAK, BK, LDBK, CK, LDCK, DK, LDDK, AC, - $ LDAC, BC, LDBC, CC, LDCC, DC, LDDC, IWORK, - $ DWORK( IWD1 ), LDWORK-IWD1+1, INFO2 ) -C - IF ( INFO2.NE.0 ) GOTO 30 -C - LWAMAX = MAX( LWAMAX, INT( DWORK( IWD1 ) ) + IWD1 - 1 ) -C -C Compute the poles of the closed-loop system. -C Workspace: need LW1 + 4*N*N + 4*N + max(1,6*N); -C prefer larger. -C - CALL DLACPY( 'Full', 2*N, 2*N, AC, LDAC, DWORK(IWAC), 2*N ) -C - CALL DGEES( 'N', 'N', SELECT, 2*N, DWORK(IWAC), 2*N, IWORK, - $ DWORK(IWWR), DWORK(IWWI), DWORK(IWRE), 1, - $ DWORK(IWRE), LDWORK-IWRE+1, BWORK, INFO2 ) -C - LWAMAX = MAX( LWAMAX, INT( DWORK( IWRE ) ) + IWRE - 1 ) -C -C Now DWORK(IWWR+I)=Re(Lambda), DWORK(IWWI+I)=Im(Lambda), -C for I=0,2*N-1. -C - MINEAC = -THOUS -C - DO 20 I = 0, 2*N - 1 - MINEAC = MAX( MINEAC, DWORK(IWWR+I) ) - 20 CONTINUE -C -C Check if the closed-loop system is stable. -C - 30 IF ( MODE.EQ.1 ) THEN - IF ( INFO2.EQ.0 .AND. MINEAC.LT.ACTOL ) THEN - GAMABS = GAMMA - GAMMA = GAMMA - STEPG - INF = 1 - ELSE - GAMMA = MIN( GAMMA + STEPG, GAMAMX ) - END IF - ELSE IF ( MODE.EQ.2 ) THEN - IF ( INFO2.EQ.0 .AND. MINEAC.LT.ACTOL ) THEN - GAMABS = GAMMA - INF = 1 - END IF - GAMMA = GAMMA - MAX( P1, GTOLL ) - END IF -C -C More iterations? -C - IF ( MODE.EQ.1 .AND. JOB.EQ.3 .AND. TWO*STEPG.LT.GTOLL ) THEN - MODE = 2 - GAMMA = GAMABS - END IF -C - IF ( JOB.NE.4 .AND. - $ ( MODE.EQ.1 .AND. TWO*STEPG.GE.GTOLL .OR. - $ MODE.EQ.2 .AND. GAMMA.GT.ZERO ) ) THEN - GOTO 10 - END IF -C -C ############################################################### -C -C End of the gamma iteration - Return if no stabilizing controller -C was found. -C - IF ( INF.EQ.0 ) THEN - INFO = 12 - RETURN - END IF -C -C Now compute the state feedback and output injection matrices -C using GAMABS. -C - GAMMA = GAMABS -C -C Integer workspace: need max(2*max(N,M-NCON,NP-NMEAS),N*N). -C Workspace: need LW1P + -C max(1,M*M + max(2*M1,3*N*N + -C max(N*M,10*N*N+12*N+5)), -C NP*NP + max(2*NP1,3*N*N + -C max(N*NP,10*N*N+12*N+5))); -C prefer larger, -C where LW1P = LW1 + 2*N*N + M*N + N*NP. -C An upper bound of the second term after LW1P is -C max(1,4*Q*Q+max(2*Q,3*N*N + max(2*N*Q,10*N*N+12*N+5))). -C - CALL SB10QD( N, M, NP, NCON, NMEAS, GAMMA, A, LDA, DWORK, N, - $ DWORK( IWC ), NP, DWORK( IWD ), NP, DWORK( IWF ), - $ M, DWORK( IWH ), N, DWORK( IWX ), N, DWORK( IWY ), - $ N, RCOND(3), IWORK, DWORK( IWRK ), LDWORK-IWRK+1, - $ BWORK, INFO2 ) -C - LWAMAX = MAX( LWAMAX, INT( DWORK( IWRK ) ) + IWRK - 1 ) -C - IF ( INFO2.GT.0 ) THEN - INFO = INFO2 + 5 - RETURN - END IF -C -C Compute the Hinf optimal controller. -C Integer workspace: need max(2*(max(NP,M)-M2-NP2,M2,N),NP2). -C Workspace: need LW1P + -C max(1, M2*NP2 + NP2*NP2 + M2*M2 + -C max(D1*D1 + max(2*D1, (D1+D2)*NP2), -C D2*D2 + max(2*D2, D2*M2), 3*N, -C N*(2*NP2 + M2) + -C max(2*N*M2, M2*NP2 + -C max(M2*M2+3*M2, NP2*(2*NP2+ -C M2+max(NP2,N)))))) -C where D1 = NP1 - M2 = NP11, D2 = M1 - NP2 = M11; -C prefer larger. -C An upper bound of the second term after LW1P is -C max( 1, Q*(3*Q + 3*N + max(2*N, 4*Q + max(Q, N)))). -C - CALL SB10RD( N, M, NP, NCON, NMEAS, GAMMA, A, LDA, DWORK, N, - $ DWORK( IWC ), NP, DWORK( IWD ), NP, DWORK( IWF ), - $ M, DWORK( IWH ), N, DWORK( IWTU ), M2, DWORK( IWTY ), - $ NP2, DWORK( IWX ), N, DWORK( IWY ), N, AK, LDAK, BK, - $ LDBK, CK, LDCK, DK, LDDK, IWORK, DWORK( IWRK ), - $ LDWORK-IWRK+1, INFO2 ) -C - LWAMAX = MAX( LWAMAX, INT( DWORK( IWRK ) ) + IWRK - 1 ) -C - IF( INFO2.EQ.1 ) THEN - INFO = 6 - RETURN - ELSE IF( INFO2.EQ.2 ) THEN - INFO = 9 - RETURN - END IF -C -C Integer workspace: need 2*max(NCON,NMEAS). -C Workspace: need 2*M*M + NP*NP + 2*M*N + M*NP + 2*N*NP; -C prefer larger. -C - CALL SB10LD( N, M, NP, NCON, NMEAS, A, LDA, B, LDB, C, LDC, D, - $ LDD, AK, LDAK, BK, LDBK, CK, LDCK, DK, LDDK, AC, - $ LDAC, BC, LDBC, CC, LDCC, DC, LDDC, IWORK, DWORK, - $ LDWORK, INFO2 ) -C - IF( INFO2.GT.0 ) THEN - INFO = 11 - RETURN - END IF -C - DWORK( 1 ) = DBLE( LWAMAX ) - RETURN -C *** Last line of SB10AD *** - END
--- a/extra/control-devel/devel/dksyn/SB10LD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,438 +0,0 @@ - SUBROUTINE SB10LD( N, M, NP, NCON, NMEAS, A, LDA, B, LDB, C, LDC, - $ D, LDD, AK, LDAK, BK, LDBK, CK, LDCK, DK, LDDK, - $ AC, LDAC, BC, LDBC, CC, LDCC, DC, LDDC, IWORK, - $ DWORK, LDWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To compute the matrices of the closed-loop system -C -C | AC | BC | -C G = |----|----|, -C | CC | DC | -C -C from the matrices of the open-loop system -C -C | A | B | -C P = |---|---| -C | C | D | -C -C and the matrices of the controller -C -C | AK | BK | -C K = |----|----|. -C | CK | DK | -C -C ARGUMENTS -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the system. N >= 0. -C -C M (input) INTEGER -C The column size of the matrix B. M >= 0. -C -C NP (input) INTEGER -C The row size of the matrix C. NP >= 0. -C -C NCON (input) INTEGER -C The number of control inputs (M2). M >= NCON >= 0. -C NP-NMEAS >= NCON. -C -C NMEAS (input) INTEGER -C The number of measurements (NP2). NP >= NMEAS >= 0. -C M-NCON >= NMEAS. -C -C A (input) DOUBLE PRECISION array, dimension (LDA,N) -C The leading N-by-N part of this array must contain the -C system state matrix A. -C -C LDA INTEGER -C The leading dimension of the array A. LDA >= max(1,N). -C -C B (input) DOUBLE PRECISION array, dimension (LDB,M) -C The leading N-by-M part of this array must contain the -C system input matrix B. -C -C LDB INTEGER -C The leading dimension of the array B. LDB >= max(1,N). -C -C C (input) DOUBLE PRECISION array, dimension (LDC,N) -C The leading NP-by-N part of this array must contain the -C system output matrix C. -C -C LDC INTEGER -C The leading dimension of the array C. LDC >= max(1,NP). -C -C D (input) DOUBLE PRECISION array, dimension (LDD,M) -C The leading NP-by-M part of this array must contain the -C system input/output matrix D. -C -C LDD INTEGER -C The leading dimension of the array D. LDD >= max(1,NP). -C -C AK (input) DOUBLE PRECISION array, dimension (LDAK,N) -C The leading N-by-N part of this array must contain the -C controller state matrix AK. -C -C LDAK INTEGER -C The leading dimension of the array AK. LDAK >= max(1,N). -C -C BK (input) DOUBLE PRECISION array, dimension (LDBK,NMEAS) -C The leading N-by-NMEAS part of this array must contain the -C controller input matrix BK. -C -C LDBK INTEGER -C The leading dimension of the array BK. LDBK >= max(1,N). -C -C CK (input) DOUBLE PRECISION array, dimension (LDCK,N) -C The leading NCON-by-N part of this array must contain the -C controller output matrix CK. -C -C LDCK INTEGER -C The leading dimension of the array CK. -C LDCK >= max(1,NCON). -C -C DK (input) DOUBLE PRECISION array, dimension (LDDK,NMEAS) -C The leading NCON-by-NMEAS part of this array must contain -C the controller input/output matrix DK. -C -C LDDK INTEGER -C The leading dimension of the array DK. -C LDDK >= max(1,NCON). -C -C AC (output) DOUBLE PRECISION array, dimension (LDAC,2*N) -C The leading 2*N-by-2*N part of this array contains the -C closed-loop system state matrix AC. -C -C LDAC INTEGER -C The leading dimension of the array AC. -C LDAC >= max(1,2*N). -C -C BC (output) DOUBLE PRECISION array, dimension (LDBC,M-NCON) -C The leading 2*N-by-(M-NCON) part of this array contains -C the closed-loop system input matrix BC. -C -C LDBC INTEGER -C The leading dimension of the array BC. -C LDBC >= max(1,2*N). -C -C CC (output) DOUBLE PRECISION array, dimension (LDCC,2*N) -C The leading (NP-NMEAS)-by-2*N part of this array contains -C the closed-loop system output matrix CC. -C -C LDCC INTEGER -C The leading dimension of the array CC. -C LDCC >= max(1,NP-NMEAS). -C -C DC (output) DOUBLE PRECISION array, dimension (LDDC,M-NCON) -C The leading (NP-NMEAS)-by-(M-NCON) part of this array -C contains the closed-loop system input/output matrix DC. -C -C LDDC INTEGER -C The leading dimension of the array DC. -C LDDC >= max(1,NP-NMEAS). -C -C Workspace -C -C IWORK INTEGER array, dimension 2*max(NCON,NMEAS) -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C On exit, if INFO = 0, DWORK(1) contains the optimal -C LDWORK. -C -C LDWORK INTEGER -C The dimension of the array DWORK. -C LDWORK >= 2*M*M+NP*NP+2*M*N+M*NP+2*N*NP. -C For good performance, LDWORK must generally be larger. -C -C Error Indicactor -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C = 1: if the matrix Inp2 - D22*DK is singular to working -C precision; -C = 2: if the matrix Im2 - DK*D22 is singular to working -C precision. -C -C METHOD -C -C The routine implements the formulas given in [1]. -C -C REFERENCES -C -C [1] Balas, G.J., Doyle, J.C., Glover, K., Packard, A., and -C Smith, R. -C mu-Analysis and Synthesis Toolbox. -C The MathWorks Inc., Natick, Mass., 1995. -C -C NUMERICAL ASPECTS -C -C The accuracy of the result depends on the condition numbers of the -C matrices Inp2 - D22*DK and Im2 - DK*D22. -C -C CONTRIBUTORS -C -C P.Hr. Petkov, D.W. Gu and M.M. Konstantinov, October 1998. -C -C REVISIONS -C -C V. Sima, Research Institute for Informatics, Bucharest, May 1999. -C A. Markovski, Technical University, Sofia, April, 2003. -C -C KEYWORDS -C -C Closed loop systems, feedback control, robust control. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) -C -C .. Scalar Arguments .. - INTEGER INFO, LDA, LDAC, LDAK, LDB, LDBC, LDBK, LDC, - $ LDCC, LDCK, LDD, LDDC, LDDK, LDWORK, M, N, - $ NCON, NMEAS, NP -C .. -C .. Array Arguments .. - INTEGER IWORK( * ) - DOUBLE PRECISION A( LDA, * ), AC( LDAC, * ), AK( LDAK, * ), - $ B( LDB, * ), BC( LDBC, * ), BK( LDBK, * ), - $ C( LDC, * ), CC( LDCC, * ), CK( LDCK, * ), - $ D( LDD, * ), DC( LDDC, * ), DK( LDDK, * ), - $ DWORK( * ) -C .. -C .. Local Scalars .. - INTEGER INFO2, IW2, IW3, IW4, IW5, IW6, IW7, IW8, IWRK, - $ LWAMAX, M1, M2, MINWRK, N2, NP1, NP2 - DOUBLE PRECISION ANORM, EPS, RCOND -C .. -C .. External Functions .. - DOUBLE PRECISION DLAMCH, DLANGE - EXTERNAL DLAMCH, DLANGE -C .. -C .. External Subroutines .. - EXTERNAL DGECON, DGEMM, DGETRF, DGETRI, DLACPY, DLASET, - $ XERBLA -C .. -C .. Executable Statements .. -C -C Decode and Test input parameters. -C - N2 = 2*N - M1 = M - NCON - M2 = NCON - NP1 = NP - NMEAS - NP2 = NMEAS -C - INFO = 0 - IF( N.LT.0 ) THEN - INFO = -1 - ELSE IF( M.LT.0 ) THEN - INFO = -2 - ELSE IF( NP.LT.0 ) THEN - INFO = -3 - ELSE IF( NCON.LT.0 .OR. M1.LT.0 .OR. M2.GT.NP1 ) THEN - INFO = -4 - ELSE IF( NMEAS.LT.0 .OR. NP1.LT.0 .OR. NP2.GT.M1 ) THEN - INFO = -5 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -7 - ELSE IF( LDB.LT.MAX( 1, N ) ) THEN - INFO = -9 - ELSE IF( LDC.LT.MAX( 1, NP ) ) THEN - INFO = -11 - ELSE IF( LDD.LT.MAX( 1, NP ) ) THEN - INFO = -13 - ELSE IF( LDAK.LT.MAX( 1, N ) ) THEN - INFO = -15 - ELSE IF( LDBK.LT.MAX( 1, N ) ) THEN - INFO = -17 - ELSE IF( LDCK.LT.MAX( 1, M2 ) ) THEN - INFO = -19 - ELSE IF( LDDK.LT.MAX( 1, M2 ) ) THEN - INFO = -21 - ELSE IF( LDAC.LT.MAX( 1, N2 ) ) THEN - INFO = -23 - ELSE IF( LDBC.LT.MAX( 1, N2 ) ) THEN - INFO = -25 - ELSE IF( LDCC.LT.MAX( 1, NP1 ) ) THEN - INFO = -27 - ELSE IF( LDDC.LT.MAX( 1, NP1 ) ) THEN - INFO = -29 - ELSE -C -C Compute workspace. -C - MINWRK = 2*M*M + NP*NP + 2*M*N + M*NP + 2*N*NP - IF( LDWORK.LT.MINWRK ) - $ INFO = -32 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'SB10LD', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF( N.EQ.0 .OR. M.EQ.0 .OR. NP.EQ.0 .OR. M1.EQ.0 .OR. M2.EQ.0 - $ .OR. NP1.EQ.0 .OR. NP2.EQ.0 ) THEN - DWORK( 1 ) = ONE - RETURN - END IF -C -C Get the machine precision. -C - EPS = DLAMCH( 'Epsilon' ) -C -C Workspace usage. -C - IW2 = NP2*NP2 + 1 - IW3 = IW2 + M2*M2 - IW4 = IW3 + NP2*N - IW5 = IW4 + M2*N - IW6 = IW5 + NP2*M1 - IW7 = IW6 + M2*M1 - IW8 = IW7 + M2*N - IWRK = IW8 + NP2*N -C -C Compute inv(Inp2 - D22*DK) . -C - CALL DLASET( 'Full', NP2, NP2, ZERO, ONE, DWORK, NP2 ) - CALL DGEMM( 'N', 'N', NP2, NP2, M2, -ONE, D( NP1+1, M1+1 ), - $ LDD, DK, LDDK, ONE, DWORK, NP2 ) - ANORM = DLANGE( '1', NP2, NP2, DWORK, NP2, DWORK( IWRK ) ) - CALL DGETRF( NP2, NP2, DWORK, NP2, IWORK, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 1 - RETURN - END IF - CALL DGECON( '1', NP2, DWORK, NP2, ANORM, RCOND, DWORK( IWRK ), - $ IWORK( NP2+1 ), INFO ) - LWAMAX = INT( DWORK( IWRK ) ) + IWRK - 1 -C -C Return if the matrix is singular to working precision. -C - IF( RCOND.LT.EPS ) THEN - INFO = 1 - RETURN - END IF - CALL DGETRI( NP2, DWORK, NP2, IWORK, DWORK( IWRK ), LDWORK-IWRK+1, - $ INFO2 ) - LWAMAX = MAX( INT( DWORK( IWRK ) ) + IWRK - 1, LWAMAX ) -C -C Compute inv(Im2 - DK*D22) . -C - CALL DLASET( 'Full', M2, M2, ZERO, ONE, DWORK( IW2 ), M2 ) - CALL DGEMM( 'N', 'N', M2, M2, NP2, -ONE, DK, LDDK, - $ D( NP1+1, M1+1 ), LDD, ONE, DWORK( IW2 ), M2 ) - ANORM = DLANGE( '1', M2, M2, DWORK( IW2 ), M2, DWORK( IWRK ) ) - CALL DGETRF( M2, M2, DWORK( IW2 ), M2, IWORK, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 2 - RETURN - END IF - CALL DGECON( '1', M2, DWORK( IW2 ), M2, ANORM, RCOND, - $ DWORK( IWRK ), IWORK( M2+1 ), INFO ) - LWAMAX = MAX( INT( DWORK( IWRK ) ) + IWRK - 1, LWAMAX ) -C -C Return if the matrix is singular to working precision. -C - IF( RCOND.LT.EPS ) THEN - INFO = 2 - RETURN - END IF - CALL DGETRI( M2, DWORK( IW2 ), M2, IWORK, DWORK( IWRK ), - $ LDWORK-IWRK+1, INFO2 ) - LWAMAX = MAX( INT( DWORK( IWRK ) ) + IWRK - 1, LWAMAX ) -C -C Compute inv(Inp2 - D22*DK)*C2 . -C - CALL DGEMM( 'N', 'N', NP2, N, NP2, ONE, DWORK, NP2, C( NP1+1, 1 ), - $ LDC, ZERO, DWORK( IW3 ), NP2 ) -C -C Compute DK*inv(Inp2 - D22*DK)*C2 . -C - CALL DGEMM( 'N', 'N', M2, N, NP2, ONE, DK, LDDK, DWORK( IW3 ), - $ NP2, ZERO, DWORK( IW4 ), M2 ) -C -C Compute inv(Inp2 - D22*DK)*D21 . -C - CALL DGEMM( 'N', 'N', NP2, M1, NP2, ONE, DWORK, NP2, - $ D( NP1+1, 1 ), LDD, ZERO, DWORK( IW5 ), NP2 ) -C -C Compute DK*inv(Inp2 - D22*DK)*D21 . -C - CALL DGEMM( 'N', 'N', M2, M1, NP2, ONE, DK, LDDK, DWORK( IW5 ), - $ NP2, ZERO, DWORK( IW6 ), M2 ) -C -C Compute inv(Im2 - DK*D22)*CK . -C - CALL DGEMM( 'N', 'N', M2, N, M2, ONE, DWORK( IW2 ), M2, CK, LDCK, - $ ZERO, DWORK( IW7 ), M2 ) -C -C Compute D22*inv(Im2 - DK*D22)*CK . -C - CALL DGEMM( 'N', 'N', NP2, N, M2, ONE, D( NP1+1, M1+1 ), LDD, - $ DWORK( IW7 ), M2, ZERO, DWORK( IW8 ), NP2 ) -C -C Compute AC . -C - CALL DLACPY( 'Full', N, N, A, LDA, AC, LDAC ) - CALL DGEMM( 'N', 'N', N, N, M2, ONE, B( 1, M1+1 ), LDB, - $ DWORK( IW4 ), M2, ONE, AC, LDAC ) - CALL DGEMM( 'N', 'N', N, N, M2, ONE, B( 1, M1+1 ), LDB, - $ DWORK( IW7 ), M2, ZERO, AC( 1, N+1 ), LDAC ) - CALL DGEMM( 'N', 'N', N, N, NP2, ONE, BK, LDBK, DWORK( IW3 ), NP2, - $ ZERO, AC( N+1, 1 ), LDAC ) - CALL DLACPY( 'Full', N, N, AK, LDAK, AC( N+1, N+1 ), LDAC ) - CALL DGEMM( 'N', 'N', N, N, NP2, ONE, BK, LDBK, DWORK( IW8 ), NP2, - $ ONE, AC( N+1, N+1 ), LDAC ) -C -C Compute BC . -C - CALL DLACPY( 'Full', N, M1, B, LDB, BC, LDBC ) - CALL DGEMM( 'N', 'N', N, M1, M2, ONE, B( 1, M1+1 ), LDB, - $ DWORK( IW6 ), M2, ONE, BC, LDBC ) - CALL DGEMM( 'N', 'N', N, M1, NP2, ONE, BK, LDBK, DWORK( IW5 ), - $ NP2, ZERO, BC( N+1, 1 ), LDBC ) -C -C Compute CC . -C - CALL DLACPY( 'Full', NP1, N, C, LDC, CC, LDCC ) - CALL DGEMM( 'N', 'N', NP1, N, M2, ONE, D( 1, M1+1 ), LDD, - $ DWORK( IW4 ), M2, ONE, CC, LDCC ) - CALL DGEMM( 'N', 'N', NP1, N, M2, ONE, D( 1, M1+1 ), LDD, - $ DWORK( IW7 ), M2, ZERO, CC( 1, N+1 ), LDCC ) -C -C Compute DC . -C - CALL DLACPY( 'Full', NP1, M1, D, LDD, DC, LDDC ) - CALL DGEMM( 'N', 'N', NP1, M1, M2, ONE, D( 1, M1+1 ), LDD, - $ DWORK( IW6 ), M2, ONE, DC, LDDC ) -C - RETURN -C *** Last line of SB10LD *** - END
--- a/extra/control-devel/devel/dksyn/SB10MD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,670 +0,0 @@ - SUBROUTINE SB10MD( NC, MP, LENDAT, F, ORD, MNB, NBLOCK, ITYPE, - $ QUTOL, A, LDA, B, LDB, C, LDC, D, LDD, OMEGA, - $ TOTORD, AD, LDAD, BD, LDBD, CD, LDCD, DD, LDDD, - $ MJU, IWORK, LIWORK, DWORK, LDWORK, ZWORK, - $ LZWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To perform the D-step in the D-K iteration. It handles -C continuous-time case. -C -C ARGUMENTS -C -C Input/Output Parameters -C -C NC (input) INTEGER -C The order of the matrix A. NC >= 0. -C -C MP (input) INTEGER -C The order of the matrix D. MP >= 0. -C -C LENDAT (input) INTEGER -C The length of the vector OMEGA. LENDAT >= 2. -C -C F (input) INTEGER -C The number of the measurements and controls, i.e., -C the size of the block I_f in the D-scaling system. -C F >= 0. -C -C ORD (input/output) INTEGER -C The MAX order of EACH block in the fitting procedure. -C ORD <= LENDAT-1. -C On exit, if ORD < 1 then ORD = 1. -C -C MNB (input) INTEGER -C The number of diagonal blocks in the block structure of -C the uncertainty, and the length of the vectors NBLOCK -C and ITYPE. 1 <= MNB <= MP. -C -C NBLOCK (input) INTEGER array, dimension (MNB) -C The vector of length MNB containing the block structure -C of the uncertainty. NBLOCK(I), I = 1:MNB, is the size of -C each block. -C -C ITYPE (input) INTEGER array, dimension (MNB) -C The vector of length MNB indicating the type of each -C block. -C For I = 1 : MNB, -C ITYPE(I) = 1 indicates that the corresponding block is a -C real block. IN THIS CASE ONLY MJU(JW) WILL BE ESTIMATED -C CORRECTLY, BUT NOT D(S)! -C ITYPE(I) = 2 indicates that the corresponding block is a -C complex block. THIS IS THE ONLY ALLOWED VALUE NOW! -C NBLOCK(I) must be equal to 1 if ITYPE(I) is equal to 1. -C -C QUTOL (input) DOUBLE PRECISION -C The acceptable mean relative error between the D(jw) and -C the frequency responce of the estimated block -C [ADi,BDi;CDi,DDi]. When it is reached, the result is -C taken as good enough. -C A good value is QUTOL = 2.0. -C If QUTOL < 0 then only mju(jw) is being estimated, -C not D(s). -C -C A (input/output) DOUBLE PRECISION array, dimension (LDA,NC) -C On entry, the leading NC-by-NC part of this array must -C contain the A matrix of the closed-loop system. -C On exit, if MP > 0, the leading NC-by-NC part of this -C array contains an upper Hessenberg matrix similar to A. -C -C LDA INTEGER -C The leading dimension of the array A. LDA >= MAX(1,NC). -C -C B (input/output) DOUBLE PRECISION array, dimension (LDB,MP) -C On entry, the leading NC-by-MP part of this array must -C contain the B matrix of the closed-loop system. -C On exit, the leading NC-by-MP part of this array contains -C the transformed B matrix corresponding to the Hessenberg -C form of A. -C -C LDB INTEGER -C The leading dimension of the array B. LDB >= MAX(1,NC). -C -C C (input/output) DOUBLE PRECISION array, dimension (LDC,NC) -C On entry, the leading MP-by-NC part of this array must -C contain the C matrix of the closed-loop system. -C On exit, the leading MP-by-NC part of this array contains -C the transformed C matrix corresponding to the Hessenberg -C form of A. -C -C LDC INTEGER -C The leading dimension of the array C. LDC >= MAX(1,MP). -C -C D (input) DOUBLE PRECISION array, dimension (LDD,MP) -C The leading MP-by-MP part of this array must contain the -C D matrix of the closed-loop system. -C -C LDD INTEGER -C The leading dimension of the array D. LDD >= MAX(1,MP). -C -C OMEGA (input) DOUBLE PRECISION array, dimension (LENDAT) -C The vector with the frequencies. -C -C TOTORD (output) INTEGER -C The TOTAL order of the D-scaling system. -C TOTORD is set to zero, if QUTOL < 0. -C -C AD (output) DOUBLE PRECISION array, dimension (LDAD,MP*ORD) -C The leading TOTORD-by-TOTORD part of this array contains -C the A matrix of the D-scaling system. -C Not referenced if QUTOL < 0. -C -C LDAD INTEGER -C The leading dimension of the array AD. -C LDAD >= MAX(1,MP*ORD), if QUTOL >= 0; -C LDAD >= 1, if QUTOL < 0. -C -C BD (output) DOUBLE PRECISION array, dimension (LDBD,MP+F) -C The leading TOTORD-by-(MP+F) part of this array contains -C the B matrix of the D-scaling system. -C Not referenced if QUTOL < 0. -C -C LDBD INTEGER -C The leading dimension of the array BD. -C LDBD >= MAX(1,MP*ORD), if QUTOL >= 0; -C LDBD >= 1, if QUTOL < 0. -C -C CD (output) DOUBLE PRECISION array, dimension (LDCD,MP*ORD) -C The leading (MP+F)-by-TOTORD part of this array contains -C the C matrix of the D-scaling system. -C Not referenced if QUTOL < 0. -C -C LDCD INTEGER -C The leading dimension of the array CD. -C LDCD >= MAX(1,MP+F), if QUTOL >= 0; -C LDCD >= 1, if QUTOL < 0. -C -C DD (output) DOUBLE PRECISION array, dimension (LDDD,MP+F) -C The leading (MP+F)-by-(MP+F) part of this array contains -C the D matrix of the D-scaling system. -C Not referenced if QUTOL < 0. -C -C LDDD INTEGER -C The leading dimension of the array DD. -C LDDD >= MAX(1,MP+F), if QUTOL >= 0; -C LDDD >= 1, if QUTOL < 0. -C -C MJU (output) DOUBLE PRECISION array, dimension (LENDAT) -C The vector with the upper bound of the structured -C singular value (mju) for each frequency in OMEGA. -C -C Workspace -C -C IWORK INTEGER array, dimension (LIWORK) -C -C LIWORK INTEGER -C The length of the array IWORK. -C LIWORK >= MAX( NC, 4*MNB-2, MP, 2*ORD+1 ), if QUTOL >= 0; -C LIWORK >= MAX( NC, 4*MNB-2, MP ), if QUTOL < 0. -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C On exit, if INFO = 0, DWORK(1) returns the optimal value -C of LDWORK, DWORK(2) returns the optimal value of LZWORK, -C and DWORK(3) returns an estimate of the minimum reciprocal -C of the condition numbers (with respect to inversion) of -C the generated Hessenberg matrices. -C -C LDWORK INTEGER -C The length of the array DWORK. -C LDWORK >= MAX( 3, LWM, LWD ), where -C LWM = LWA + MAX( NC + MAX( NC, MP-1 ), -C 2*MP*MP*MNB - MP*MP + 9*MNB*MNB + -C MP*MNB + 11*MP + 33*MNB - 11 ); -C LWD = LWB + MAX( 2, LW1, LW2, LW3, LW4, 2*ORD ), -C if QUTOL >= 0; -C LWD = 0, if QUTOL < 0; -C LWA = MP*LENDAT + 2*MNB + MP - 1; -C LWB = LENDAT*(MP + 2) + ORD*(ORD + 2) + 1; -C LW1 = 2*LENDAT + 4*HNPTS; HNPTS = 2048; -C LW2 = LENDAT + 6*HNPTS; MN = MIN( 2*LENDAT, 2*ORD+1 ); -C LW3 = 2*LENDAT*(2*ORD + 1) + MAX( 2*LENDAT, 2*ORD + 1 ) + -C MAX( MN + 6*ORD + 4, 2*MN + 1 ); -C LW4 = MAX( ORD*ORD + 5*ORD, 6*ORD + 1 + MIN( 1, ORD ) ). -C -C ZWORK COMPLEX*16 array, dimension (LZWORK) -C -C LZWORK INTEGER -C The length of the array ZWORK. -C LZWORK >= MAX( LZM, LZD ), where -C LZM = MAX( MP*MP + NC*MP + NC*NC + 2*NC, -C 6*MP*MP*MNB + 13*MP*MP + 6*MNB + 6*MP - 3 ); -C LZD = MAX( LENDAT*(2*ORD + 3), ORD*ORD + 3*ORD + 1 ), -C if QUTOL >= 0; -C LZD = 0, if QUTOL < 0. -C -C Error indicator -C -C INFO (output) INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C = 1: if one or more values w in OMEGA are (close to -C some) poles of the closed-loop system, i.e., the -C matrix jw*I - A is (numerically) singular; -C = 2: the block sizes must be positive integers; -C = 3: the sum of block sizes must be equal to MP; -C = 4: the size of a real block must be equal to 1; -C = 5: the block type must be either 1 or 2; -C = 6: errors in solving linear equations or in matrix -C inversion; -C = 7: errors in computing eigenvalues or singular values. -C = 1i: INFO on exit from SB10YD is i. (1i means 10 + i.) -C -C METHOD -C -C I. First, W(jw) for the given closed-loop system is being -C estimated. -C II. Now, AB13MD SLICOT subroutine can obtain the D(jw) scaling -C system with respect to NBLOCK and ITYPE, and colaterally, -C mju(jw). -C If QUTOL < 0 then the estimations stop and the routine exits. -C III. Now that we have D(jw), SB10YD subroutine can do block-by- -C block fit. For each block it tries with an increasing order -C of the fit, starting with 1 until the -C (mean quadratic error + max quadratic error)/2 -C between the Dii(jw) and the estimated frequency responce -C of the block becomes less than or equal to the routine -C argument QUTOL, or the order becomes equal to ORD. -C IV. Arrange the obtained blocks in the AD, BD, CD and DD -C matrices and estimate the total order of D(s), TOTORD. -C V. Add the system I_f to the system obtained in IV. -C -C REFERENCES -C -C [1] Balas, G., Doyle, J., Glover, K., Packard, A. and Smith, R. -C Mu-analysis and Synthesis toolbox - User's Guide, -C The Mathworks Inc., Natick, MA, USA, 1998. -C -C CONTRIBUTORS -C -C Asparuh Markovski, Technical University of Sofia, July 2003. -C -C REVISIONS -C -C V. Sima, Research Institute for Informatics, Bucharest, Aug. 2003. -C A. Markovski, V. Sima, October 2003. -C -C KEYWORDS -C -C Frequency response, H-infinity optimal control, robust control, -C structured singular value. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE, TWO, THREE - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0, - $ THREE = 3.0D+0 ) - INTEGER HNPTS - PARAMETER ( HNPTS = 2048 ) -C .. -C .. Scalar Arguments .. - INTEGER F, INFO, LDA, LDAD, LDB, LDBD, LDC, LDCD, LDD, - $ LDDD, LDWORK, LENDAT, LIWORK, LZWORK, MNB, MP, - $ NC, ORD, TOTORD - DOUBLE PRECISION QUTOL -C .. -C .. Array Arguments .. - INTEGER ITYPE(*), IWORK(*), NBLOCK(*) - DOUBLE PRECISION A(LDA, *), AD(LDAD, *), B(LDB, *), BD(LDBD, *), - $ C(LDC, *), CD(LDCD, *), D(LDD, *), DD(LDDD, *), - $ DWORK(*), MJU(*), OMEGA(*) - COMPLEX*16 ZWORK(*) -C .. -C .. Local Scalars .. - CHARACTER BALEIG, INITA - INTEGER CLWMAX, CORD, DLWMAX, I, IC, ICWRK, IDWRK, II, - $ INFO2, IWAD, IWB, IWBD, IWCD, IWDD, IWGJOM, - $ IWIFRD, IWRFRD, IWX, K, LCSIZE, LDSIZE, LORD, - $ LW1, LW2, LW3, LW4, LWA, LWB, MAXCWR, MAXWRK, - $ MN, W - DOUBLE PRECISION MAQE, MEQE, MOD1, MOD2, RCND, RCOND, RQE, TOL, - $ TOLER - COMPLEX*16 FREQ -C .. -C .. External Functions .. - DOUBLE PRECISION DLAMCH - EXTERNAL DLAMCH -C .. -C .. External Subroutines .. - EXTERNAL AB13MD, DCOPY, DLACPY, DLASET, DSCAL, SB10YD, - $ TB05AD, XERBLA -C .. -C .. Intrinsic Functions .. - INTRINSIC ABS, DCMPLX, INT, MAX, MIN, SQRT -C -C Decode and test input parameters. -C -C @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ -C Workspace usage 1. -C -C real -C - IWX = 1 + MP*LENDAT - IWGJOM = IWX + 2*MNB - 1 - IDWRK = IWGJOM + MP - LDSIZE = LDWORK - IDWRK + 1 -C -C complex -C - IWB = MP*MP + 1 - ICWRK = IWB + NC*MP - LCSIZE = LZWORK - ICWRK + 1 -C - INFO = 0 - IF ( NC.LT.0 ) THEN - INFO = -1 - ELSE IF( MP.LT.0 ) THEN - INFO = -2 - ELSE IF( LENDAT.LT.2 ) THEN - INFO = -3 - ELSE IF( F.LT.0 ) THEN - INFO = -4 - ELSE IF( ORD.GT.LENDAT - 1 ) THEN - INFO = -5 - ELSE IF( MNB.LT.1 .OR. MNB.GT.MP ) THEN - INFO = -6 - ELSE IF( LDA.LT.MAX( 1, NC ) ) THEN - INFO = -11 - ELSE IF( LDB.LT.MAX( 1, NC ) ) THEN - INFO = -13 - ELSE IF( LDC.LT.MAX( 1, MP ) ) THEN - INFO = -15 - ELSE IF( LDD.LT.MAX( 1, MP ) ) THEN - INFO = -17 - ELSE IF( LDAD.LT.1 .OR. ( QUTOL.GE.ZERO .AND. LDAD.LT.MP*ORD ) ) - $ THEN - INFO = -21 - ELSE IF( LDBD.LT.1 .OR. ( QUTOL.GE.ZERO .AND. LDBD.LT.MP*ORD ) ) - $ THEN - INFO = -23 - ELSE IF( LDCD.LT.1 .OR. ( QUTOL.GE.ZERO .AND. LDCD.LT.MP + F ) ) - $ THEN - INFO = -25 - ELSE IF( LDDD.LT.1 .OR. ( QUTOL.GE.ZERO .AND. LDDD.LT.MP + F ) ) - $ THEN - INFO = -27 - ELSE -C -C Compute workspace. -C - II = MAX( NC, 4*MNB - 2, MP ) - MN = MIN( 2*LENDAT, 2*ORD + 1 ) - LWA = IDWRK - 1 - LWB = LENDAT*( MP + 2 ) + ORD*( ORD + 2 ) + 1 - LW1 = 2*LENDAT + 4*HNPTS - LW2 = LENDAT + 6*HNPTS - LW3 = 2*LENDAT*( 2*ORD + 1 ) + MAX( 2*LENDAT, 2*ORD + 1 ) + - $ MAX( MN + 6*ORD + 4, 2*MN + 1 ) - LW4 = MAX( ORD*ORD + 5*ORD, 6*ORD + 1 + MIN( 1, ORD ) ) -C - DLWMAX = LWA + MAX( NC + MAX( NC, MP - 1 ), - $ 2*MP*MP*MNB - MP*MP + 9*MNB*MNB + MP*MNB + - $ 11*MP + 33*MNB - 11 ) -C - CLWMAX = MAX( ICWRK - 1 + NC*NC + 2*NC, - $ 6*MP*MP*MNB + 13*MP*MP + 6*MNB + 6*MP - 3 ) -C - IF ( QUTOL.GE.ZERO ) THEN - II = MAX( II, 2*ORD + 1 ) - DLWMAX = MAX( DLWMAX, - $ LWB + MAX( 2, LW1, LW2, LW3, LW4, 2*ORD ) ) - CLWMAX = MAX( CLWMAX, LENDAT*( 2*ORD + 3 ), - $ ORD*( ORD + 3 ) + 1 ) - END IF - IF ( LIWORK.LT.II ) THEN - INFO = -30 - ELSE IF ( LDWORK.LT.MAX( 3, DLWMAX ) ) THEN - INFO = -32 - ELSE IF ( LZWORK.LT.CLWMAX ) THEN - INFO = -34 - END IF - END IF -C - IF ( INFO.NE.0 ) THEN -C -C Error return. -C - CALL XERBLA( 'SB10MD', -INFO ) - RETURN - END IF -C - ORD = MAX( 1, ORD ) - TOTORD = 0 -C -C Quick return if possible. -C - IF( NC.EQ.0 .OR. MP.EQ.0 ) THEN - DWORK(1) = THREE - DWORK(2) = ZERO - DWORK(3) = ONE - RETURN - END IF -C - TOLER = SQRT( DLAMCH( 'Epsilon' ) ) -C - BALEIG = 'C' - RCOND = ONE - MAXCWR = CLWMAX -C -C @@@ 1. Estimate W(jw) for the closed-loop system, @@@ -C @@@ D(jw) and mju(jw) for each frequency. @@@ -C - DO 30 W = 1, LENDAT - FREQ = DCMPLX( ZERO, OMEGA(W) ) - IF ( W.EQ.1 ) THEN - INITA = 'G' - ELSE - INITA = 'H' - END IF -C -C Compute C*inv(jw*I-A)*B. -C Integer workspace: need NC. -C Real workspace: need LWA + NC + MAX(NC,MP-1); -C prefer larger, -C where LWA = MP*LENDAT + 2*MNB + MP - 1. -C Complex workspace: need MP*MP + NC*MP + NC*NC + 2*NC. -C - CALL TB05AD( BALEIG, INITA, NC, MP, MP, FREQ, A, LDA, B, LDB, - $ C, LDC, RCND, ZWORK, MP, DWORK, DWORK, ZWORK(IWB), - $ NC, IWORK, DWORK(IDWRK), LDSIZE, ZWORK(ICWRK), - $ LCSIZE, INFO2 ) -C - IF ( INFO2.GT.0 ) THEN - INFO = 1 - RETURN - END IF -C - RCOND = MIN( RCOND, RCND ) - IF ( W.EQ.1 ) - $ MAXWRK = INT( DWORK(IDWRK) + IDWRK - 1 ) - IC = 0 -C -C D + C*inv(jw*I-A)*B -C - DO 20 K = 1, MP - DO 10 I = 1, MP - IC = IC + 1 - ZWORK(IC) = ZWORK(IC) + DCMPLX ( D(I,K), ZERO ) - 10 CONTINUE - 20 CONTINUE -C -C Estimate D(jw) and mju(jw). -C Integer workspace: need MAX(4*MNB-2,MP). -C Real workspace: need LWA + 2*MP*MP*MNB - MP*MP + 9*MNB*MNB -C + MP*MNB + 11*MP + 33*MNB - 11; -C prefer larger. -C Complex workspace: need 6*MP*MP*MNB + 13*MP*MP + 6*MNB + -C 6*MP - 3. -C - CALL AB13MD( 'N', MP, ZWORK, MP, MNB, NBLOCK, ITYPE, - $ DWORK(IWX), MJU(W), DWORK((W-1)*MP+1), - $ DWORK(IWGJOM), IWORK, DWORK(IDWRK), LDSIZE, - $ ZWORK(IWB), LZWORK-IWB+1, INFO2 ) -C - IF ( INFO2.NE.0 ) THEN - INFO = INFO2 + 1 - RETURN - END IF -C - IF ( W.EQ.1 ) THEN - MAXWRK = MAX( MAXWRK, INT( DWORK(IDWRK) ) + IDWRK - 1 ) - MAXCWR = MAX( MAXCWR, INT( ZWORK(IWB) ) + IWB - 1 ) - END IF -C -C Normalize D(jw) through it's last entry. -C - IF ( DWORK(W*MP).NE.ZERO ) - $ CALL DSCAL( MP, ONE/DWORK(W*MP), DWORK((W-1)*MP+1), 1 ) -C - 30 CONTINUE -C -C Quick return if needed. -C - IF ( QUTOL.LT.ZERO ) THEN - DWORK(1) = MAXWRK - DWORK(2) = MAXCWR - DWORK(3) = RCOND - RETURN - END IF -C -C @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ -C Workspace usage 2. -C -C real -C - IWRFRD = IWX - IWIFRD = IWRFRD + LENDAT - IWAD = IWIFRD + LENDAT - IWBD = IWAD + ORD*ORD - IWCD = IWBD + ORD - IWDD = IWCD + ORD - IDWRK = IWDD + 1 - LDSIZE = LDWORK - IDWRK + 1 -C -C complex -C - ICWRK = ORD + 2 - LCSIZE = LZWORK - ICWRK + 1 - INITA = 'H' -C -C Use default tolerance for SB10YD. -C - TOL = -ONE -C -C @@@ 2. Clear imag parts of D(jw) for SB10YD. @@@ -C - DO 40 I = 1, LENDAT - DWORK(IWIFRD+I-1) = ZERO - 40 CONTINUE -C -C @@@ 3. Clear AD, BD, CD and initialize DD with I_(mp+f). @@@ -C - CALL DLASET( 'Full', MP*ORD, MP*ORD, ZERO, ZERO, AD, LDAD ) - CALL DLASET( 'Full', MP*ORD, MP+F, ZERO, ZERO, BD, LDBD ) - CALL DLASET( 'Full', MP+F, MP*ORD, ZERO, ZERO, CD, LDCD ) - CALL DLASET( 'Full', MP+F, MP+F, ZERO, ONE, DD, LDDD ) -C -C @@@ 4. Block by block frequency identification. @@@ -C - DO 80 II = 1, MP -C - CALL DCOPY( LENDAT, DWORK(II), MP, DWORK(IWRFRD), 1 ) -C -C Increase CORD from 1 to ORD for every block, if needed. -C - CORD = 1 -C - 50 CONTINUE - LORD = CORD -C -C Now, LORD is the desired order. -C Integer workspace: need 2*N+1, where N = LORD. -C Real workspace: need LWB + MAX( 2, LW1, LW2, LW3, LW4), -C where -C LWB = LENDAT*(MP+2) + -C ORD*(ORD+2) + 1, -C HNPTS = 2048, and -C LW1 = 2*LENDAT + 4*HNPTS; -C LW2 = LENDAT + 6*HNPTS; -C MN = min( 2*LENDAT, 2*N+1 ) -C LW3 = 2*LENDAT*(2*N+1) + -C max( 2*LENDAT, 2*N+1 ) + -C max( MN + 6*N + 4, 2*MN+1 ); -C LW4 = max( N*N + 5*N, -C 6*N + 1 + min( 1,N ) ); -C prefer larger. -C Complex workspace: need LENDAT*(2*N+3). -C - CALL SB10YD( 0, 1, LENDAT, DWORK(IWRFRD), DWORK(IWIFRD), - $ OMEGA, LORD, DWORK(IWAD), ORD, DWORK(IWBD), - $ DWORK(IWCD), DWORK(IWDD), TOL, IWORK, - $ DWORK(IDWRK), LDSIZE, ZWORK, LZWORK, INFO2 ) -C -C At this point, LORD is the actual order reached by SB10YD, -C 0 <= LORD <= CORD. -C [ADi,BDi; CDi,DDi] is a minimal realization with ADi in -C upper Hessenberg form. -C The leading LORD-by-LORD part of ORD-by-ORD DWORK(IWAD) -C contains ADi, the leading LORD-by-1 part of ORD-by-1 -C DWORK(IWBD) contains BDi, the leading 1-by-LORD part of -C 1-by-ORD DWORK(IWCD) contains CDi, DWORK(IWDD) contains DDi. -C - IF ( INFO2.NE.0 ) THEN - INFO = 10 + INFO2 - RETURN - END IF -C -C Compare the original D(jw) with the fitted one. -C - MEQE = ZERO - MAQE = ZERO -C - DO 60 W = 1, LENDAT - FREQ = DCMPLX( ZERO, OMEGA(W) ) -C -C Compute CD*inv(jw*I-AD)*BD. -C Integer workspace: need LORD. -C Real workspace: need LWB + 2*LORD; -C prefer larger. -C Complex workspace: need 1 + ORD + LORD*LORD + 2*LORD. -C - CALL TB05AD( BALEIG, INITA, LORD, 1, 1, FREQ, - $ DWORK(IWAD), ORD, DWORK(IWBD), ORD, - $ DWORK(IWCD), 1, RCND, ZWORK, 1, - $ DWORK(IDWRK), DWORK(IDWRK), ZWORK(2), ORD, - $ IWORK, DWORK(IDWRK), LDSIZE, ZWORK(ICWRK), - $ LCSIZE, INFO2 ) -C - IF ( INFO2.GT.0 ) THEN - INFO = 1 - RETURN - END IF -C - RCOND = MIN( RCOND, RCND ) - IF ( W.EQ.1 ) - $ MAXWRK = MAX( MAXWRK, INT( DWORK(IDWRK) ) + IDWRK - 1) -C -C DD + CD*inv(jw*I-AD)*BD -C - ZWORK(1) = ZWORK(1) + DCMPLX( DWORK(IWDD), ZERO ) -C - MOD1 = ABS( DWORK(IWRFRD+W-1) ) - MOD2 = ABS( ZWORK(1) ) - RQE = ABS( ( MOD1 - MOD2 )/( MOD1 + TOLER ) ) - MEQE = MEQE + RQE - MAQE = MAX( MAQE, RQE ) -C - 60 CONTINUE -C - MEQE = MEQE/LENDAT -C - IF ( ( ( MEQE + MAQE )/TWO.LE.QUTOL ) .OR. - $ ( CORD.EQ.ORD ) ) THEN - GOTO 70 - END IF -C - CORD = CORD + 1 - GOTO 50 -C - 70 TOTORD = TOTORD + LORD -C -C Copy ad(ii), bd(ii) and cd(ii) to AD, BD and CD, respectively. -C - CALL DLACPY( 'Full', LORD, LORD, DWORK(IWAD), ORD, - $ AD(TOTORD-LORD+1,TOTORD-LORD+1), LDAD ) - CALL DCOPY( LORD, DWORK(IWBD), 1, BD(TOTORD-LORD+1,II), 1 ) - CALL DCOPY( LORD, DWORK(IWCD), 1, CD(II,TOTORD-LORD+1), LDCD ) -C -C Copy dd(ii) to DD. -C - DD(II,II) = DWORK(IWDD) -C - 80 CONTINUE -C - DWORK(1) = MAXWRK - DWORK(2) = MAXCWR - DWORK(3) = RCOND - RETURN -C -C *** Last line of SB10MD *** - END
--- a/extra/control-devel/devel/dksyn/SB10PD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,505 +0,0 @@ - SUBROUTINE SB10PD( N, M, NP, NCON, NMEAS, A, LDA, B, LDB, C, LDC, - $ D, LDD, TU, LDTU, TY, LDTY, RCOND, TOL, DWORK, - $ LDWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To reduce the matrices D12 and D21 of the linear time-invariant -C system -C -C | A | B1 B2 | | A | B | -C P = |----|---------| = |---|---| -C | C1 | D11 D12 | | C | D | -C | C2 | D21 D22 | -C -C to unit diagonal form, to transform the matrices B, C, and D11 to -C satisfy the formulas in the computation of an H2 and H-infinity -C (sub)optimal controllers and to check the rank conditions. -C -C ARGUMENTS -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the system. N >= 0. -C -C M (input) INTEGER -C The column size of the matrix B. M >= 0. -C -C NP (input) INTEGER -C The row size of the matrix C. NP >= 0. -C -C NCON (input) INTEGER -C The number of control inputs (M2). M >= NCON >= 0, -C NP-NMEAS >= NCON. -C -C NMEAS (input) INTEGER -C The number of measurements (NP2). NP >= NMEAS >= 0, -C M-NCON >= NMEAS. -C -C A (input) DOUBLE PRECISION array, dimension (LDA,N) -C The leading N-by-N part of this array must contain the -C system state matrix A. -C -C LDA INTEGER -C The leading dimension of the array A. LDA >= max(1,N). -C -C B (input/output) DOUBLE PRECISION array, dimension (LDB,M) -C On entry, the leading N-by-M part of this array must -C contain the system input matrix B. -C On exit, the leading N-by-M part of this array contains -C the transformed system input matrix B. -C -C LDB INTEGER -C The leading dimension of the array B. LDB >= max(1,N). -C -C C (input/output) DOUBLE PRECISION array, dimension (LDC,N) -C On entry, the leading NP-by-N part of this array must -C contain the system output matrix C. -C On exit, the leading NP-by-N part of this array contains -C the transformed system output matrix C. -C -C LDC INTEGER -C The leading dimension of the array C. LDC >= max(1,NP). -C -C D (input/output) DOUBLE PRECISION array, dimension (LDD,M) -C On entry, the leading NP-by-M part of this array must -C contain the system input/output matrix D. The -C NMEAS-by-NCON trailing submatrix D22 is not referenced. -C On exit, the leading (NP-NMEAS)-by-(M-NCON) part of this -C array contains the transformed submatrix D11. -C The transformed submatrices D12 = [ 0 Im2 ]' and -C D21 = [ 0 Inp2 ] are not stored. The corresponding part -C of this array contains no useful information. -C -C LDD INTEGER -C The leading dimension of the array D. LDD >= max(1,NP). -C -C TU (output) DOUBLE PRECISION array, dimension (LDTU,M2) -C The leading M2-by-M2 part of this array contains the -C control transformation matrix TU. -C -C LDTU INTEGER -C The leading dimension of the array TU. LDTU >= max(1,M2). -C -C TY (output) DOUBLE PRECISION array, dimension (LDTY,NP2) -C The leading NP2-by-NP2 part of this array contains the -C measurement transformation matrix TY. -C -C LDTY INTEGER -C The leading dimension of the array TY. -C LDTY >= max(1,NP2). -C -C RCOND (output) DOUBLE PRECISION array, dimension (2) -C RCOND(1) contains the reciprocal condition number of the -C control transformation matrix TU; -C RCOND(2) contains the reciprocal condition number of the -C measurement transformation matrix TY. -C RCOND is set even if INFO = 3 or INFO = 4; if INFO = 3, -C then RCOND(2) was not computed, but it is set to 0. -C -C Tolerances -C -C TOL DOUBLE PRECISION -C Tolerance used for controlling the accuracy of the applied -C transformations. Transformation matrices TU and TY whose -C reciprocal condition numbers are less than TOL are not -C allowed. If TOL <= 0, then a default value equal to -C sqrt(EPS) is used, where EPS is the relative machine -C precision. -C -C Workspace -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C On exit, if INFO = 0, DWORK(1) contains the optimal -C LDWORK. -C -C LDWORK INTEGER -C The dimension of the array DWORK. -C LDWORK >= MAX(1,LW1,LW2,LW3,LW4), where -C LW1 = (N+NP1+1)*(N+M2) + MAX(3*(N+M2)+N+NP1,5*(N+M2)), -C LW2 = (N+NP2)*(N+M1+1) + MAX(3*(N+NP2)+N+M1,5*(N+NP2)), -C LW3 = M2 + NP1*NP1 + MAX(NP1*MAX(N,M1),3*M2+NP1,5*M2), -C LW4 = NP2 + M1*M1 + MAX(MAX(N,NP1)*M1,3*NP2+M1,5*NP2), -C with M1 = M - M2 and NP1 = NP - NP2. -C For good performance, LDWORK must generally be larger. -C Denoting Q = MAX(M1,M2,NP1,NP2), an upper bound is -C MAX(1,(N+Q)*(N+Q+6),Q*(Q+MAX(N,Q,5)+1). -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C = 1: if the matrix | A B2 | had not full column rank -C | C1 D12 | -C in respect to the tolerance EPS; -C = 2: if the matrix | A B1 | had not full row rank in -C | C2 D21 | -C respect to the tolerance EPS; -C = 3: if the matrix D12 had not full column rank in -C respect to the tolerance TOL; -C = 4: if the matrix D21 had not full row rank in respect -C to the tolerance TOL; -C = 5: if the singular value decomposition (SVD) algorithm -C did not converge (when computing the SVD of one of -C the matrices |A B2 |, |A B1 |, D12 or D21). -C |C1 D12| |C2 D21| -C -C METHOD -C -C The routine performs the transformations described in [2]. -C -C REFERENCES -C -C [1] Glover, K. and Doyle, J.C. -C State-space formulae for all stabilizing controllers that -C satisfy an Hinf norm bound and relations to risk sensitivity. -C Systems and Control Letters, vol. 11, pp. 167-172, 1988. -C -C [2] Balas, G.J., Doyle, J.C., Glover, K., Packard, A., and -C Smith, R. -C mu-Analysis and Synthesis Toolbox. -C The MathWorks Inc., Natick, Mass., 1995. -C -C NUMERICAL ASPECTS -C -C The precision of the transformations can be controlled by the -C condition numbers of the matrices TU and TY as given by the -C values of RCOND(1) and RCOND(2), respectively. An error return -C with INFO = 3 or INFO = 4 will be obtained if the condition -C number of TU or TY, respectively, would exceed 1/TOL. -C -C CONTRIBUTORS -C -C P.Hr. Petkov, D.W. Gu and M.M. Konstantinov, October 1998. -C -C REVISIONS -C -C V. Sima, Research Institute for Informatics, Bucharest, May 1999, -C Feb. 2000. -C -C KEYWORDS -C -C H-infinity optimal control, robust control, singular value -C decomposition. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) -C .. -C .. Scalar Arguments .. - INTEGER INFO, LDA, LDB, LDC, LDD, LDTU, LDTY, LDWORK, - $ M, N, NCON, NMEAS, NP - DOUBLE PRECISION TOL -C .. -C .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ), - $ D( LDD, * ), DWORK( * ), RCOND( 2 ), - $ TU( LDTU, * ), TY( LDTY, * ) -C .. -C .. Local Scalars .. - INTEGER IEXT, INFO2, IQ, IWRK, J, LWAMAX, M1, M2, - $ MINWRK, ND1, ND2, NP1, NP2 - DOUBLE PRECISION EPS, TOLL -C .. -C .. External Functions .. - DOUBLE PRECISION DLAMCH - EXTERNAL DLAMCH -C .. -C .. External Subroutines .. - EXTERNAL DGEMM, DGESVD, DLACPY, DSCAL, DSWAP, XERBLA -C .. -C .. Intrinsic Functions .. - INTRINSIC DBLE, INT, MAX, SQRT -C .. -C .. Executable Statements .. -C -C Decode and Test input parameters. -C - M1 = M - NCON - M2 = NCON - NP1 = NP - NMEAS - NP2 = NMEAS -C - INFO = 0 - IF( N.LT.0 ) THEN - INFO = -1 - ELSE IF( M.LT.0 ) THEN - INFO = -2 - ELSE IF( NP.LT.0 ) THEN - INFO = -3 - ELSE IF( NCON.LT.0 .OR. M1.LT.0 .OR. M2.GT.NP1 ) THEN - INFO = -4 - ELSE IF( NMEAS.LT.0 .OR. NP1.LT.0 .OR. NP2.GT.M1 ) THEN - INFO = -5 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -7 - ELSE IF( LDB.LT.MAX( 1, N ) ) THEN - INFO = -9 - ELSE IF( LDC.LT.MAX( 1, NP ) ) THEN - INFO = -11 - ELSE IF( LDD.LT.MAX( 1, NP ) ) THEN - INFO = -13 - ELSE IF( LDTU.LT.MAX( 1, M2 ) ) THEN - INFO = -15 - ELSE IF( LDTY.LT.MAX( 1, NP2 ) ) THEN - INFO = -17 - ELSE -C -C Compute workspace. -C - MINWRK = MAX( 1, - $ ( N + NP1 + 1 )*( N + M2 ) + - $ MAX( 3*( N + M2 ) + N + NP1, 5*( N + M2 ) ), - $ ( N + NP2 )*( N + M1 + 1 ) + - $ MAX( 3*( N + NP2 ) + N + M1, 5*( N + NP2 ) ), - $ M2 + NP1*NP1 + MAX( NP1*MAX( N, M1 ), 3*M2 + NP1, - $ 5*M2 ), - $ NP2 + M1*M1 + MAX( MAX( N, NP1 )*M1, 3*NP2 + M1, - $ 5*NP2 ) ) - IF( LDWORK.LT.MINWRK ) - $ INFO = -21 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'SB10PD', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF( N.EQ.0 .OR. M.EQ.0 .OR. NP.EQ.0 .OR. M1.EQ.0 .OR. M2.EQ.0 - $ .OR. NP1.EQ.0 .OR. NP2.EQ.0 ) THEN - RCOND( 1 ) = ONE - RCOND( 2 ) = ONE - DWORK( 1 ) = ONE - RETURN - END IF -C - ND1 = NP1 - M2 - ND2 = M1 - NP2 - EPS = DLAMCH( 'Epsilon' ) - TOLL = TOL - IF( TOLL.LE.ZERO ) THEN -C -C Set the default value of the tolerance for condition tests. -C - TOLL = SQRT( EPS ) - END IF -C -C Determine if |A-jwI B2 | has full column rank at w = 0. -C | C1 D12| -C Workspace: need (N+NP1+1)*(N+M2) + -C max(3*(N+M2)+N+NP1,5*(N+M2)); -C prefer larger. -C - IEXT = N + M2 + 1 - IWRK = IEXT + ( N + NP1 )*( N + M2 ) - CALL DLACPY( 'Full', N, N, A, LDA, DWORK( IEXT ), N+NP1 ) - CALL DLACPY( 'Full', NP1, N, C, LDC, DWORK( IEXT+N ), N+NP1 ) - CALL DLACPY( 'Full', N, M2, B( 1, M1+1 ), LDB, - $ DWORK( IEXT+(N+NP1)*N ), N+NP1 ) - CALL DLACPY( 'Full', NP1, M2, D( 1, M1+1 ), LDD, - $ DWORK( IEXT+(N+NP1)*N+N ), N+NP1 ) - CALL DGESVD( 'N', 'N', N+NP1, N+M2, DWORK( IEXT ), N+NP1, DWORK, - $ TU, LDTU, TY, LDTY, DWORK( IWRK ), LDWORK-IWRK+1, - $ INFO2 ) - IF( INFO2.NE.0 ) THEN - INFO = 5 - RETURN - END IF - IF( DWORK( N+M2 )/DWORK( 1 ).LE.EPS ) THEN - INFO = 1 - RETURN - END IF - LWAMAX = INT( DWORK( IWRK ) ) + IWRK - 1 -C -C Determine if |A-jwI B1 | has full row rank at w = 0. -C | C2 D21| -C Workspace: need (N+NP2)*(N+M1+1) + -C max(3*(N+NP2)+N+M1,5*(N+NP2)); -C prefer larger. -C - IEXT = N + NP2 + 1 - IWRK = IEXT + ( N + NP2 )*( N + M1 ) - CALL DLACPY( 'Full', N, N, A, LDA, DWORK( IEXT ), N+NP2 ) - CALL DLACPY( 'Full', NP2, N, C( NP1+1, 1), LDC, DWORK( IEXT+N ), - $ N+NP2 ) - CALL DLACPY( 'Full', N, M1, B, LDB, DWORK( IEXT+(N+NP2)*N ), - $ N+NP2 ) - CALL DLACPY( 'Full', NP2, M1, D( NP1+1, 1 ), LDD, - $ DWORK( IEXT+(N+NP2)*N+N ), N+NP2 ) - CALL DGESVD( 'N', 'N', N+NP2, N+M1, DWORK( IEXT ), N+NP2, DWORK, - $ TU, LDTU, TY, LDTY, DWORK( IWRK ), LDWORK-IWRK+1, - $ INFO2 ) - IF( INFO2.NE.0 ) THEN - INFO = 5 - RETURN - END IF - IF( DWORK( N+NP2 )/DWORK( 1 ).LE.EPS ) THEN - INFO = 2 - RETURN - END IF - LWAMAX = MAX( INT( DWORK( IWRK ) ) + IWRK - 1, LWAMAX ) -C -C Determine SVD of D12, D12 = U12 S12 V12', and check if D12 has -C full column rank. V12' is stored in TU. -C Workspace: need M2 + NP1*NP1 + max(3*M2+NP1,5*M2); -C prefer larger. -C - IQ = M2 + 1 - IWRK = IQ + NP1*NP1 -C - CALL DGESVD( 'A', 'A', NP1, M2, D( 1, M1+1 ), LDD, DWORK, - $ DWORK( IQ ), NP1, TU, LDTU, DWORK( IWRK ), - $ LDWORK-IWRK+1, INFO2 ) - IF( INFO2.NE.0 ) THEN - INFO = 5 - RETURN - END IF -C - RCOND( 1 ) = DWORK( M2 )/DWORK( 1 ) - IF( RCOND( 1 ).LE.TOLL ) THEN - RCOND( 2 ) = ZERO - INFO = 3 - RETURN - END IF - LWAMAX = MAX( INT( DWORK( IWRK ) ) + IWRK - 1, LWAMAX ) -C -C Determine Q12. -C - IF( ND1.GT.0 ) THEN - CALL DLACPY( 'Full', NP1, M2, DWORK( IQ ), NP1, D( 1, M1+1 ), - $ LDD ) - CALL DLACPY( 'Full', NP1, ND1, DWORK( IQ+NP1*M2 ), NP1, - $ DWORK( IQ ), NP1 ) - CALL DLACPY( 'Full', NP1, M2, D( 1, M1+1 ), LDD, - $ DWORK( IQ+NP1*ND1 ), NP1 ) - END IF -C -C Determine Tu by transposing in-situ and scaling. -C - DO 10 J = 1, M2 - 1 - CALL DSWAP( J, TU( J+1, 1 ), LDTU, TU( 1, J+1 ), 1 ) - 10 CONTINUE -C - DO 20 J = 1, M2 - CALL DSCAL( M2, ONE/DWORK( J ), TU( 1, J ), 1 ) - 20 CONTINUE -C -C Determine C1 =: Q12'*C1. -C Workspace: M2 + NP1*NP1 + NP1*N. -C - CALL DGEMM( 'T', 'N', NP1, N, NP1, ONE, DWORK( IQ ), NP1, C, LDC, - $ ZERO, DWORK( IWRK ), NP1 ) - CALL DLACPY( 'Full', NP1, N, DWORK( IWRK ), NP1, C, LDC ) - LWAMAX = MAX( IWRK + NP1*N - 1, LWAMAX ) -C -C Determine D11 =: Q12'*D11. -C Workspace: M2 + NP1*NP1 + NP1*M1. -C - CALL DGEMM( 'T', 'N', NP1, M1, NP1, ONE, DWORK( IQ ), NP1, D, LDD, - $ ZERO, DWORK( IWRK ), NP1 ) - CALL DLACPY( 'Full', NP1, M1, DWORK( IWRK ), NP1, D, LDD ) - LWAMAX = MAX( IWRK + NP1*M1 - 1, LWAMAX ) -C -C Determine SVD of D21, D21 = U21 S21 V21', and check if D21 has -C full row rank. U21 is stored in TY. -C Workspace: need NP2 + M1*M1 + max(3*NP2+M1,5*NP2); -C prefer larger. -C - IQ = NP2 + 1 - IWRK = IQ + M1*M1 -C - CALL DGESVD( 'A', 'A', NP2, M1, D( NP1+1, 1 ), LDD, DWORK, TY, - $ LDTY, DWORK( IQ ), M1, DWORK( IWRK ), LDWORK-IWRK+1, - $ INFO2 ) - IF( INFO2.NE.0 ) THEN - INFO = 5 - RETURN - END IF -C - RCOND( 2 ) = DWORK( NP2 )/DWORK( 1 ) - IF( RCOND( 2 ).LE.TOLL ) THEN - INFO = 4 - RETURN - END IF - LWAMAX = MAX( INT( DWORK( IWRK ) ) + IWRK - 1, LWAMAX ) -C -C Determine Q21. -C - IF( ND2.GT.0 ) THEN - CALL DLACPY( 'Full', NP2, M1, DWORK( IQ ), M1, D( NP1+1, 1 ), - $ LDD ) - CALL DLACPY( 'Full', ND2, M1, DWORK( IQ+NP2 ), M1, DWORK( IQ ), - $ M1 ) - CALL DLACPY( 'Full', NP2, M1, D( NP1+1, 1 ), LDD, - $ DWORK( IQ+ND2 ), M1 ) - END IF -C -C Determine Ty by scaling and transposing in-situ. -C - DO 30 J = 1, NP2 - CALL DSCAL( NP2, ONE/DWORK( J ), TY( 1, J ), 1 ) - 30 CONTINUE -C - DO 40 J = 1, NP2 - 1 - CALL DSWAP( J, TY( J+1, 1 ), LDTY, TY( 1, J+1 ), 1 ) - 40 CONTINUE -C -C Determine B1 =: B1*Q21'. -C Workspace: NP2 + M1*M1 + N*M1. -C - CALL DGEMM( 'N', 'T', N, M1, M1, ONE, B, LDB, DWORK( IQ ), M1, - $ ZERO, DWORK( IWRK ), N ) - CALL DLACPY( 'Full', N, M1, DWORK( IWRK ), N, B, LDB ) - LWAMAX = MAX( IWRK + N*M1 - 1, LWAMAX ) -C -C Determine D11 =: D11*Q21'. -C Workspace: NP2 + M1*M1 + NP1*M1. -C - CALL DGEMM( 'N', 'T', NP1, M1, M1, ONE, D, LDD, DWORK( IQ ), M1, - $ ZERO, DWORK( IWRK ), NP1 ) - CALL DLACPY( 'Full', NP1, M1, DWORK( IWRK ), NP1, D, LDD ) - LWAMAX = MAX( IWRK + NP1*M1 - 1, LWAMAX ) -C -C Determine B2 =: B2*Tu. -C Workspace: N*M2. -C - CALL DGEMM( 'N', 'N', N, M2, M2, ONE, B( 1, M1+1 ), LDB, TU, LDTU, - $ ZERO, DWORK, N ) - CALL DLACPY( 'Full', N, M2, DWORK, N, B( 1, M1+1 ), LDB ) -C -C Determine C2 =: Ty*C2. -C Workspace: NP2*N. -C - CALL DGEMM( 'N', 'N', NP2, N, NP2, ONE, TY, LDTY, - $ C( NP1+1, 1 ), LDC, ZERO, DWORK, NP2 ) - CALL DLACPY( 'Full', NP2, N, DWORK, NP2, C( NP1+1, 1 ), LDC ) -C - LWAMAX = MAX( N*MAX( M2, NP2 ), LWAMAX ) - DWORK( 1 ) = DBLE( LWAMAX ) - RETURN -C *** Last line of SB10PD *** - END
--- a/extra/control-devel/devel/dksyn/SB10QD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,602 +0,0 @@ - SUBROUTINE SB10QD( N, M, NP, NCON, NMEAS, GAMMA, A, LDA, B, LDB, - $ C, LDC, D, LDD, F, LDF, H, LDH, X, LDX, Y, LDY, - $ XYCOND, IWORK, DWORK, LDWORK, BWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To compute the state feedback and the output injection -C matrices for an H-infinity (sub)optimal n-state controller, -C using Glover's and Doyle's 1988 formulas, for the system -C -C | A | B1 B2 | | A | B | -C P = |----|---------| = |---|---| -C | C1 | D11 D12 | | C | D | -C | C2 | D21 D22 | -C -C and for a given value of gamma, where B2 has as column size the -C number of control inputs (NCON) and C2 has as row size the number -C of measurements (NMEAS) being provided to the controller. -C -C It is assumed that -C -C (A1) (A,B2) is stabilizable and (C2,A) is detectable, -C -C (A2) D12 is full column rank with D12 = | 0 | and D21 is -C | I | -C full row rank with D21 = | 0 I | as obtained by the -C subroutine SB10PD, -C -C (A3) | A-j*omega*I B2 | has full column rank for all omega, -C | C1 D12 | -C -C -C (A4) | A-j*omega*I B1 | has full row rank for all omega. -C | C2 D21 | -C -C -C ARGUMENTS -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the system. N >= 0. -C -C M (input) INTEGER -C The column size of the matrix B. M >= 0. -C -C NP (input) INTEGER -C The row size of the matrix C. NP >= 0. -C -C NCON (input) INTEGER -C The number of control inputs (M2). M >= NCON >= 0, -C NP-NMEAS >= NCON. -C -C NMEAS (input) INTEGER -C The number of measurements (NP2). NP >= NMEAS >= 0, -C M-NCON >= NMEAS. -C -C GAMMA (input) DOUBLE PRECISION -C The value of gamma. It is assumed that gamma is -C sufficiently large so that the controller is admissible. -C GAMMA >= 0. -C -C A (input) DOUBLE PRECISION array, dimension (LDA,N) -C The leading N-by-N part of this array must contain the -C system state matrix A. -C -C LDA INTEGER -C The leading dimension of the array A. LDA >= max(1,N). -C -C B (input) DOUBLE PRECISION array, dimension (LDB,M) -C The leading N-by-M part of this array must contain the -C system input matrix B. -C -C LDB INTEGER -C The leading dimension of the array B. LDB >= max(1,N). -C -C C (input) DOUBLE PRECISION array, dimension (LDC,N) -C The leading NP-by-N part of this array must contain the -C system output matrix C. -C -C LDC INTEGER -C The leading dimension of the array C. LDC >= max(1,NP). -C -C D (input) DOUBLE PRECISION array, dimension (LDD,M) -C The leading NP-by-M part of this array must contain the -C system input/output matrix D. -C -C LDD INTEGER -C The leading dimension of the array D. LDD >= max(1,NP). -C -C F (output) DOUBLE PRECISION array, dimension (LDF,N) -C The leading M-by-N part of this array contains the state -C feedback matrix F. -C -C LDF INTEGER -C The leading dimension of the array F. LDF >= max(1,M). -C -C H (output) DOUBLE PRECISION array, dimension (LDH,NP) -C The leading N-by-NP part of this array contains the output -C injection matrix H. -C -C LDH INTEGER -C The leading dimension of the array H. LDH >= max(1,N). -C -C X (output) DOUBLE PRECISION array, dimension (LDX,N) -C The leading N-by-N part of this array contains the matrix -C X, solution of the X-Riccati equation. -C -C LDX INTEGER -C The leading dimension of the array X. LDX >= max(1,N). -C -C Y (output) DOUBLE PRECISION array, dimension (LDY,N) -C The leading N-by-N part of this array contains the matrix -C Y, solution of the Y-Riccati equation. -C -C LDY INTEGER -C The leading dimension of the array Y. LDY >= max(1,N). -C -C XYCOND (output) DOUBLE PRECISION array, dimension (2) -C XYCOND(1) contains an estimate of the reciprocal condition -C number of the X-Riccati equation; -C XYCOND(2) contains an estimate of the reciprocal condition -C number of the Y-Riccati equation. -C -C Workspace -C -C IWORK INTEGER array, dimension max(2*max(N,M-NCON,NP-NMEAS),N*N) -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C On exit, if INFO = 0, DWORK(1) contains the optimal -C LDWORK. -C -C LDWORK INTEGER -C The dimension of the array DWORK. -C LDWORK >= max(1,M*M + max(2*M1,3*N*N + -C max(N*M,10*N*N+12*N+5)), -C NP*NP + max(2*NP1,3*N*N + -C max(N*NP,10*N*N+12*N+5))), -C where M1 = M - M2 and NP1 = NP - NP2. -C For good performance, LDWORK must generally be larger. -C Denoting Q = MAX(M1,M2,NP1,NP2), an upper bound is -C max(1,4*Q*Q+max(2*Q,3*N*N + max(2*N*Q,10*N*N+12*N+5))). -C -C BWORK LOGICAL array, dimension (2*N) -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C = 1: if the controller is not admissible (too small value -C of gamma); -C = 2: if the X-Riccati equation was not solved -C successfully (the controller is not admissible or -C there are numerical difficulties); -C = 3: if the Y-Riccati equation was not solved -C successfully (the controller is not admissible or -C there are numerical difficulties). -C -C METHOD -C -C The routine implements the Glover's and Doyle's formulas [1],[2] -C modified as described in [3]. The X- and Y-Riccati equations -C are solved with condition and accuracy estimates [4]. -C -C REFERENCES -C -C [1] Glover, K. and Doyle, J.C. -C State-space formulae for all stabilizing controllers that -C satisfy an Hinf norm bound and relations to risk sensitivity. -C Systems and Control Letters, vol. 11, pp. 167-172, 1988. -C -C [2] Balas, G.J., Doyle, J.C., Glover, K., Packard, A., and -C Smith, R. -C mu-Analysis and Synthesis Toolbox. -C The MathWorks Inc., Natick, Mass., 1995. -C -C [3] Petkov, P.Hr., Gu, D.W., and Konstantinov, M.M. -C Fortran 77 routines for Hinf and H2 design of continuous-time -C linear control systems. -C Rep. 98-14, Department of Engineering, Leicester University, -C Leicester, U.K., 1998. -C -C [4] Petkov, P.Hr., Konstantinov, M.M., and Mehrmann, V. -C DGRSVX and DMSRIC: Fortan 77 subroutines for solving -C continuous-time matrix algebraic Riccati equations with -C condition and accuracy estimates. -C Preprint SFB393/98-16, Fak. f. Mathematik, Tech. Univ. -C Chemnitz, May 1998. -C -C NUMERICAL ASPECTS -C -C The precision of the solution of the matrix Riccati equations -C can be controlled by the values of the condition numbers -C XYCOND(1) and XYCOND(2) of these equations. -C -C FURTHER COMMENTS -C -C The Riccati equations are solved by the Schur approach -C implementing condition and accuracy estimates. -C -C CONTRIBUTORS -C -C P.Hr. Petkov, D.W. Gu and M.M. Konstantinov, October 1998. -C -C REVISIONS -C -C V. Sima, Research Institute for Informatics, Bucharest, May 1999, -C Sept. 1999. -C -C KEYWORDS -C -C Algebraic Riccati equation, H-infinity optimal control, robust -C control. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) -C -C .. Scalar Arguments .. - INTEGER INFO, LDA, LDB, LDC, LDD, LDF, LDH, LDWORK, - $ LDX, LDY, M, N, NCON, NMEAS, NP - DOUBLE PRECISION GAMMA -C .. -C .. Array Arguments .. - INTEGER IWORK( * ) - DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ), - $ D( LDD, * ), DWORK( * ), F( LDF, * ), - $ H( LDH, * ), X( LDX, * ), XYCOND( 2 ), - $ Y( LDY, * ) - LOGICAL BWORK( * ) -C -C .. -C .. Local Scalars .. - INTEGER INFO2, IW2, IWA, IWG, IWI, IWQ, IWR, IWRK, IWS, - $ IWT, IWV, LWAMAX, M1, M2, MINWRK, N2, ND1, ND2, - $ NN, NP1, NP2 - DOUBLE PRECISION ANORM, EPS, FERR, RCOND, SEP -C .. -C .. External Functions .. -C - DOUBLE PRECISION DLAMCH, DLANSY - EXTERNAL DLAMCH, DLANSY -C .. -C .. External Subroutines .. - EXTERNAL DGEMM, DLACPY, DLASET, DSYCON, DSYMM, DSYRK, - $ DSYTRF, DSYTRI, MB01RU, MB01RX, SB02RD, XERBLA -C .. -C .. Intrinsic Functions .. - INTRINSIC DBLE, INT, MAX -C .. -C .. Executable Statements .. -C -C Decode and Test input parameters. -C - M1 = M - NCON - M2 = NCON - NP1 = NP - NMEAS - NP2 = NMEAS - NN = N*N -C - INFO = 0 - IF( N.LT.0 ) THEN - INFO = -1 - ELSE IF( M.LT.0 ) THEN - INFO = -2 - ELSE IF( NP.LT.0 ) THEN - INFO = -3 - ELSE IF( NCON.LT.0 .OR. M1.LT.0 .OR. M2.GT.NP1 ) THEN - INFO = -4 - ELSE IF( NMEAS.LT.0 .OR. NP1.LT.0 .OR. NP2.GT.M1 ) THEN - INFO = -5 - ELSE IF( GAMMA.LT.ZERO ) THEN - INFO = -6 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -8 - ELSE IF( LDB.LT.MAX( 1, N ) ) THEN - INFO = -10 - ELSE IF( LDC.LT.MAX( 1, NP ) ) THEN - INFO = -12 - ELSE IF( LDD.LT.MAX( 1, NP ) ) THEN - INFO = -14 - ELSE IF( LDF.LT.MAX( 1, M ) ) THEN - INFO = -16 - ELSE IF( LDH.LT.MAX( 1, N ) ) THEN - INFO = -18 - ELSE IF( LDX.LT.MAX( 1, N ) ) THEN - INFO = -20 - ELSE IF( LDY.LT.MAX( 1, N ) ) THEN - INFO = -22 - ELSE -C -C Compute workspace. -C - MINWRK = MAX( 1, M*M + MAX( 2*M1, 3*NN + - $ MAX( N*M, 10*NN + 12*N + 5 ) ), - $ NP*NP + MAX( 2*NP1, 3*NN + - $ MAX( N*NP, 10*NN + 12*N + 5 ) ) ) - IF( LDWORK.LT.MINWRK ) - $ INFO = -26 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'SB10QD', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF( N.EQ.0 .OR. M.EQ.0 .OR. NP.EQ.0 .OR. M1.EQ.0 .OR. M2.EQ.0 - $ .OR. NP1.EQ.0 .OR. NP2.EQ.0 ) THEN - XYCOND( 1 ) = ONE - XYCOND( 2 ) = ONE - DWORK( 1 ) = ONE - RETURN - END IF - ND1 = NP1 - M2 - ND2 = M1 - NP2 - N2 = 2*N -C -C Get the machine precision. -C - EPS = DLAMCH( 'Epsilon' ) -C -C Workspace usage. -C - IWA = M*M + 1 - IWQ = IWA + NN - IWG = IWQ + NN - IW2 = IWG + NN -C -C Compute |D1111'||D1111 D1112| - gamma^2*Im1 . -C |D1112'| -C - CALL DLASET( 'L', M1, M1, ZERO, -GAMMA*GAMMA, DWORK, M ) - IF( ND1.GT.0 ) - $ CALL DSYRK( 'L', 'T', M1, ND1, ONE, D, LDD, ONE, DWORK, M ) -C -C Compute inv(|D1111'|*|D1111 D1112| - gamma^2*Im1) . -C |D1112'| -C - IWRK = IWA - ANORM = DLANSY( 'I', 'L', M1, DWORK, M, DWORK( IWRK ) ) - CALL DSYTRF( 'L', M1, DWORK, M, IWORK, DWORK( IWRK ), - $ LDWORK-IWRK+1, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 1 - RETURN - END IF -C - LWAMAX = INT( DWORK( IWRK ) ) + IWRK - 1 - CALL DSYCON( 'L', M1, DWORK, M, IWORK, ANORM, RCOND, - $ DWORK( IWRK ), IWORK( M1+1 ), INFO2 ) - IF( RCOND.LT.EPS ) THEN - INFO = 1 - RETURN - END IF -C -C Compute inv(R) block by block. -C - CALL DSYTRI( 'L', M1, DWORK, M, IWORK, DWORK( IWRK ), INFO2 ) -C -C Compute -|D1121 D1122|*inv(|D1111'|*|D1111 D1112| - gamma^2*Im1) . -C |D1112'| -C - CALL DSYMM( 'R', 'L', M2, M1, -ONE, DWORK, M, D( ND1+1, 1 ), LDD, - $ ZERO, DWORK( M1+1 ), M ) -C -C Compute |D1121 D1122|*inv(|D1111'|*|D1111 D1112| - -C |D1112'| -C -C gamma^2*Im1)*|D1121'| + Im2 . -C |D1122'| -C - CALL DLASET( 'Lower', M2, M2, ZERO, ONE, DWORK( M1*(M+1)+1 ), M ) - CALL MB01RX( 'Right', 'Lower', 'Transpose', M2, M1, ONE, -ONE, - $ DWORK( M1*(M+1)+1 ), M, D( ND1+1, 1 ), LDD, - $ DWORK( M1+1 ), M, INFO2 ) -C -C Compute D11'*C1 . -C - CALL DGEMM( 'T', 'N', M1, N, NP1, ONE, D, LDD, C, LDC, ZERO, - $ DWORK( IW2 ), M ) -C -C Compute D1D'*C1 . -C - CALL DLACPY( 'Full', M2, N, C( ND1+1, 1 ), LDC, DWORK( IW2+M1 ), - $ M ) -C -C Compute inv(R)*D1D'*C1 in F . -C - CALL DSYMM( 'L', 'L', M, N, ONE, DWORK, M, DWORK( IW2 ), M, ZERO, - $ F, LDF ) -C -C Compute Ax = A - B*inv(R)*D1D'*C1 . -C - CALL DLACPY( 'Full', N, N, A, LDA, DWORK( IWA ), N ) - CALL DGEMM( 'N', 'N', N, N, M, -ONE, B, LDB, F, LDF, ONE, - $ DWORK( IWA ), N ) -C -C Compute Cx = C1'*C1 - C1'*D1D*inv(R)*D1D'*C1 . -C - IF( ND1.EQ.0 ) THEN - CALL DLASET( 'L', N, N, ZERO, ZERO, DWORK( IWQ ), N ) - ELSE - CALL DSYRK( 'L', 'T', N, NP1, ONE, C, LDC, ZERO, - $ DWORK( IWQ ), N ) - CALL MB01RX( 'Left', 'Lower', 'Transpose', N, M, ONE, -ONE, - $ DWORK( IWQ ), N, DWORK( IW2 ), M, F, LDF, INFO2 ) - END IF -C -C Compute Dx = B*inv(R)*B' . -C - IWRK = IW2 - CALL MB01RU( 'Lower', 'NoTranspose', N, M, ZERO, ONE, - $ DWORK( IWG ), N, B, LDB, DWORK, M, DWORK( IWRK ), - $ M*N, INFO2 ) -C -C Solution of the Riccati equation Ax'*X + X*Ax + Cx - X*Dx*X = 0 . -C Workspace: need M*M + 13*N*N + 12*N + 5; -C prefer larger. -C - IWT = IW2 - IWV = IWT + NN - IWR = IWV + NN - IWI = IWR + N2 - IWS = IWI + N2 - IWRK = IWS + 4*NN -C - CALL SB02RD( 'All', 'Continuous', 'NotUsed', 'NoTranspose', - $ 'Lower', 'GeneralScaling', 'Stable', 'NotFactored', - $ 'Original', N, DWORK( IWA ), N, DWORK( IWT ), N, - $ DWORK( IWV ), N, DWORK( IWG ), N, DWORK( IWQ ), N, - $ X, LDX, SEP, XYCOND( 1 ), FERR, DWORK( IWR ), - $ DWORK( IWI ), DWORK( IWS ), N2, IWORK, DWORK( IWRK ), - $ LDWORK-IWRK+1, BWORK, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 2 - RETURN - END IF -C - LWAMAX = MAX( INT( DWORK( IWRK ) ) + IWRK - 1, LWAMAX ) -C -C Compute F = -inv(R)*|D1D'*C1 + B'*X| . -C - IWRK = IW2 - CALL DGEMM( 'T', 'N', M, N, N, ONE, B, LDB, X, LDX, ZERO, - $ DWORK( IWRK ), M ) - CALL DSYMM( 'L', 'L', M, N, -ONE, DWORK, M, DWORK( IWRK ), M, - $ -ONE, F, LDF ) -C -C Workspace usage. -C - IWA = NP*NP + 1 - IWQ = IWA + NN - IWG = IWQ + NN - IW2 = IWG + NN -C -C Compute |D1111|*|D1111' D1121'| - gamma^2*Inp1 . -C |D1121| -C - CALL DLASET( 'U', NP1, NP1, ZERO, -GAMMA*GAMMA, DWORK, NP ) - IF( ND2.GT.0 ) - $ CALL DSYRK( 'U', 'N', NP1, ND2, ONE, D, LDD, ONE, DWORK, NP ) -C -C Compute inv(|D1111|*|D1111' D1121'| - gamma^2*Inp1) . -C |D1121| -C - IWRK = IWA - ANORM = DLANSY( 'I', 'U', NP1, DWORK, NP, DWORK( IWRK ) ) - CALL DSYTRF( 'U', NP1, DWORK, NP, IWORK, DWORK( IWRK ), - $ LDWORK-IWRK+1, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 1 - RETURN - END IF -C - LWAMAX = MAX( INT( DWORK( IWRK ) ) + IWRK - 1, LWAMAX ) - CALL DSYCON( 'U', NP1, DWORK, NP, IWORK, ANORM, RCOND, - $ DWORK( IWRK ), IWORK( NP1+1 ), INFO2 ) - IF( RCOND.LT.EPS ) THEN - INFO = 1 - RETURN - END IF -C -C Compute inv(RT) . -C - CALL DSYTRI( 'U', NP1, DWORK, NP, IWORK, DWORK( IWRK ), INFO2 ) -C -C Compute -inv(|D1111||D1111' D1121'| - gamma^2*Inp1)*|D1112| . -C |D1121| |D1122| -C - CALL DSYMM( 'L', 'U', NP1, NP2, -ONE, DWORK, NP, D( 1, ND2+1 ), - $ LDD, ZERO, DWORK( NP1*NP+1 ), NP ) -C -C Compute [D1112' D1122']*inv(|D1111||D1111' D1121'| - -C |D1121| -C -C gamma^2*Inp1)*|D1112| + Inp2 . -C |D1122| -C - CALL DLASET( 'Full', NP2, NP2, ZERO, ONE, DWORK( NP1*(NP+1)+1 ), - $ NP ) - CALL MB01RX( 'Left', 'Upper', 'Transpose', NP2, NP1, ONE, -ONE, - $ DWORK( NP1*(NP+1)+1 ), NP, D( 1, ND2+1 ), LDD, - $ DWORK( NP1*NP+1 ), NP, INFO2 ) -C -C Compute B1*D11' . -C - CALL DGEMM( 'N', 'T', N, NP1, M1, ONE, B, LDB, D, LDD, ZERO, - $ DWORK( IW2 ), N ) -C -C Compute B1*DD1' . -C - CALL DLACPY( 'Full', N, NP2, B( 1, ND2+1 ), LDB, - $ DWORK( IW2+NP1*N ), N ) -C -C Compute B1*DD1'*inv(RT) in H . -C - CALL DSYMM( 'R', 'U', N, NP, ONE, DWORK, NP, DWORK( IW2 ), N, - $ ZERO, H, LDH ) -C -C Compute Ay = A - B1*DD1'*inv(RT)*C . -C - CALL DLACPY( 'Full', N, N, A, LDA, DWORK( IWA ), N ) - CALL DGEMM( 'N', 'N', N, N, NP, -ONE, H, LDH, C, LDC, ONE, - $ DWORK( IWA ), N ) -C -C Compute Cy = B1*B1' - B1*DD1'*inv(RT)*DD1*B1' . -C - IF( ND2.EQ.0 ) THEN - CALL DLASET( 'U', N, N, ZERO, ZERO, DWORK( IWQ ), N ) - ELSE - CALL DSYRK( 'U', 'N', N, M1, ONE, B, LDB, ZERO, DWORK( IWQ ), - $ N ) - CALL MB01RX( 'Right', 'Upper', 'Transpose', N, NP, ONE, -ONE, - $ DWORK( IWQ ), N, H, LDH, DWORK( IW2 ), N, INFO2 ) - END IF -C -C Compute Dy = C'*inv(RT)*C . -C - IWRK = IW2 - CALL MB01RU( 'Upper', 'Transpose', N, NP, ZERO, ONE, DWORK( IWG ), - $ N, C, LDC, DWORK, NP, DWORK( IWRK), N*NP, INFO2 ) -C -C Solution of the Riccati equation Ay*Y + Y*Ay' + Cy - Y*Dy*Y = 0 . -C Workspace: need NP*NP + 13*N*N + 12*N + 5; -C prefer larger. -C - IWT = IW2 - IWV = IWT + NN - IWR = IWV + NN - IWI = IWR + N2 - IWS = IWI + N2 - IWRK = IWS + 4*NN -C - CALL SB02RD( 'All', 'Continuous', 'NotUsed', 'Transpose', - $ 'Upper', 'GeneralScaling', 'Stable', 'NotFactored', - $ 'Original', N, DWORK( IWA ), N, DWORK( IWT ), N, - $ DWORK( IWV ), N, DWORK( IWG ), N, DWORK( IWQ ), N, - $ Y, LDY, SEP, XYCOND( 2 ), FERR, DWORK( IWR ), - $ DWORK( IWI ), DWORK( IWS ), N2, IWORK, DWORK( IWRK ), - $ LDWORK-IWRK+1, BWORK, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 3 - RETURN - END IF -C - LWAMAX = MAX( INT( DWORK( IWRK ) ) + IWRK - 1, LWAMAX ) -C -C Compute H = -|B1*DD1' + Y*C'|*inv(RT) . -C - IWRK = IW2 - CALL DGEMM( 'N', 'T', N, NP, N, ONE, Y, LDY, C, LDC, ZERO, - $ DWORK( IWRK ), N ) - CALL DSYMM( 'R', 'U', N, NP, -ONE, DWORK, NP, DWORK( IWRK ), N, - $ -ONE, H, LDH ) -C - DWORK( 1 ) = DBLE( LWAMAX ) - RETURN -C *** Last line of SB10QD *** - END
--- a/extra/control-devel/devel/dksyn/SB10RD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,706 +0,0 @@ - SUBROUTINE SB10RD( N, M, NP, NCON, NMEAS, GAMMA, A, LDA, B, LDB, - $ C, LDC, D, LDD, F, LDF, H, LDH, TU, LDTU, TY, - $ LDTY, X, LDX, Y, LDY, AK, LDAK, BK, LDBK, CK, - $ LDCK, DK, LDDK, IWORK, DWORK, LDWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To compute the matrices of an H-infinity (sub)optimal controller -C -C | AK | BK | -C K = |----|----|, -C | CK | DK | -C -C from the state feedback matrix F and output injection matrix H as -C determined by the SLICOT Library routine SB10QD. -C -C ARGUMENTS -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the system. N >= 0. -C -C M (input) INTEGER -C The column size of the matrix B. M >= 0. -C -C NP (input) INTEGER -C The row size of the matrix C. NP >= 0. -C -C NCON (input) INTEGER -C The number of control inputs (M2). M >= NCON >= 0. -C NP-NMEAS >= NCON. -C -C NMEAS (input) INTEGER -C The number of measurements (NP2). NP >= NMEAS >= 0. -C M-NCON >= NMEAS. -C -C GAMMA (input) DOUBLE PRECISION -C The value of gamma. It is assumed that gamma is -C sufficiently large so that the controller is admissible. -C GAMMA >= 0. -C -C A (input) DOUBLE PRECISION array, dimension (LDA,N) -C The leading N-by-N part of this array must contain the -C system state matrix A. -C -C LDA INTEGER -C The leading dimension of the array A. LDA >= max(1,N). -C -C B (input) DOUBLE PRECISION array, dimension (LDB,M) -C The leading N-by-M part of this array must contain the -C system input matrix B. -C -C LDB INTEGER -C The leading dimension of the array B. LDB >= max(1,N). -C -C C (input) DOUBLE PRECISION array, dimension (LDC,N) -C The leading NP-by-N part of this array must contain the -C system output matrix C. -C -C LDC INTEGER -C The leading dimension of the array C. LDC >= max(1,NP). -C -C D (input) DOUBLE PRECISION array, dimension (LDD,M) -C The leading NP-by-M part of this array must contain the -C system input/output matrix D. -C -C LDD INTEGER -C The leading dimension of the array D. LDD >= max(1,NP). -C -C F (input) DOUBLE PRECISION array, dimension (LDF,N) -C The leading M-by-N part of this array must contain the -C state feedback matrix F. -C -C LDF INTEGER -C The leading dimension of the array F. LDF >= max(1,M). -C -C H (input) DOUBLE PRECISION array, dimension (LDH,NP) -C The leading N-by-NP part of this array must contain the -C output injection matrix H. -C -C LDH INTEGER -C The leading dimension of the array H. LDH >= max(1,N). -C -C TU (input) DOUBLE PRECISION array, dimension (LDTU,M2) -C The leading M2-by-M2 part of this array must contain the -C control transformation matrix TU, as obtained by the -C SLICOT Library routine SB10PD. -C -C LDTU INTEGER -C The leading dimension of the array TU. LDTU >= max(1,M2). -C -C TY (input) DOUBLE PRECISION array, dimension (LDTY,NP2) -C The leading NP2-by-NP2 part of this array must contain the -C measurement transformation matrix TY, as obtained by the -C SLICOT Library routine SB10PD. -C -C LDTY INTEGER -C The leading dimension of the array TY. -C LDTY >= max(1,NP2). -C -C X (input) DOUBLE PRECISION array, dimension (LDX,N) -C The leading N-by-N part of this array must contain the -C matrix X, solution of the X-Riccati equation, as obtained -C by the SLICOT Library routine SB10QD. -C -C LDX INTEGER -C The leading dimension of the array X. LDX >= max(1,N). -C -C Y (input) DOUBLE PRECISION array, dimension (LDY,N) -C The leading N-by-N part of this array must contain the -C matrix Y, solution of the Y-Riccati equation, as obtained -C by the SLICOT Library routine SB10QD. -C -C LDY INTEGER -C The leading dimension of the array Y. LDY >= max(1,N). -C -C AK (output) DOUBLE PRECISION array, dimension (LDAK,N) -C The leading N-by-N part of this array contains the -C controller state matrix AK. -C -C LDAK INTEGER -C The leading dimension of the array AK. LDAK >= max(1,N). -C -C BK (output) DOUBLE PRECISION array, dimension (LDBK,NMEAS) -C The leading N-by-NMEAS part of this array contains the -C controller input matrix BK. -C -C LDBK INTEGER -C The leading dimension of the array BK. LDBK >= max(1,N). -C -C CK (output) DOUBLE PRECISION array, dimension (LDCK,N) -C The leading NCON-by-N part of this array contains the -C controller output matrix CK. -C -C LDCK INTEGER -C The leading dimension of the array CK. -C LDCK >= max(1,NCON). -C -C DK (output) DOUBLE PRECISION array, dimension (LDDK,NMEAS) -C The leading NCON-by-NMEAS part of this array contains the -C controller input/output matrix DK. -C -C LDDK INTEGER -C The leading dimension of the array DK. -C LDDK >= max(1,NCON). -C -C Workspace -C -C IWORK INTEGER array, dimension (LIWORK), where -C LIWORK = max(2*(max(NP,M)-M2-NP2,M2,N),NP2) -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C On exit, if INFO = 0, DWORK(1) contains the optimal -C LDWORK. -C -C LDWORK INTEGER -C The dimension of the array DWORK. -C LDWORK >= max(1, M2*NP2 + NP2*NP2 + M2*M2 + -C max(D1*D1 + max(2*D1, (D1+D2)*NP2), -C D2*D2 + max(2*D2, D2*M2), 3*N, -C N*(2*NP2 + M2) + -C max(2*N*M2, M2*NP2 + -C max(M2*M2+3*M2, NP2*(2*NP2+ -C M2+max(NP2,N)))))) -C where D1 = NP1 - M2, D2 = M1 - NP2, -C NP1 = NP - NP2, M1 = M - M2. -C For good performance, LDWORK must generally be larger. -C Denoting Q = max(M1,M2,NP1,NP2), an upper bound is -C max( 1, Q*(3*Q + 3*N + max(2*N, 4*Q + max(Q, N)))). -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C = 1: if the controller is not admissible (too small value -C of gamma); -C = 2: if the determinant of Im2 + Tu*D11HAT*Ty*D22 is zero. -C -C METHOD -C -C The routine implements the Glover's and Doyle's formulas [1],[2]. -C -C REFERENCES -C -C [1] Glover, K. and Doyle, J.C. -C State-space formulae for all stabilizing controllers that -C satisfy an Hinf norm bound and relations to risk sensitivity. -C Systems and Control Letters, vol. 11, pp. 167-172, 1988. -C -C [2] Balas, G.J., Doyle, J.C., Glover, K., Packard, A., and -C Smith, R. -C mu-Analysis and Synthesis Toolbox. -C The MathWorks Inc., Natick, Mass., 1995. -C -C NUMERICAL ASPECTS -C -C The accuracy of the result depends on the condition numbers of the -C input and output transformations. -C -C CONTRIBUTORS -C -C P.Hr. Petkov, D.W. Gu and M.M. Konstantinov, October 1998. -C -C REVISIONS -C -C V. Sima, Research Institute for Informatics, Bucharest, May 1999, -C Sept. 1999, Oct. 2001. -C -C KEYWORDS -C -C Algebraic Riccati equation, H-infinity optimal control, robust -C control. -C -C ********************************************************************* -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) -C .. -C .. Scalar Arguments .. - INTEGER INFO, LDA, LDAK, LDB, LDBK, LDC, LDCK, LDD, - $ LDDK, LDF, LDH, LDTU, LDTY, LDWORK, LDX, LDY, - $ M, N, NCON, NMEAS, NP - DOUBLE PRECISION GAMMA -C .. -C .. Array Arguments .. - INTEGER IWORK( * ) - DOUBLE PRECISION A( LDA, * ), AK( LDAK, * ), B( LDB, * ), - $ BK( LDBK, * ), C( LDC, * ), CK( LDCK, * ), - $ D( LDD, * ), DK( LDDK, * ), DWORK( * ), - $ F( LDF, * ), H( LDH, * ), TU( LDTU, * ), - $ TY( LDTY, * ), X( LDX, * ), Y( LDY, * ) -C .. -C .. Local Scalars .. - INTEGER I, ID11, ID12, ID21, IJ, INFO2, IW1, IW2, IW3, - $ IW4, IWB, IWC, IWRK, J, LWAMAX, M1, M2, MINWRK, - $ ND1, ND2, NP1, NP2 - DOUBLE PRECISION ANORM, EPS, RCOND -C .. -C .. External Functions .. - DOUBLE PRECISION DLAMCH, DLANGE, DLANSY - EXTERNAL DLAMCH, DLANGE, DLANSY -C .. -C .. External Subroutines .. - EXTERNAL DGECON, DGEMM, DGETRF, DGETRI, DGETRS, DLACPY, - $ DLASET, DPOTRF, DSYCON, DSYRK, DSYTRF, DSYTRS, - $ DTRMM, MA02AD, MB01RX, XERBLA -C .. -C .. Intrinsic Functions .. - INTRINSIC DBLE, INT, MAX -C .. -C .. Executable Statements .. -C -C Decode and Test input parameters. -C - M1 = M - NCON - M2 = NCON - NP1 = NP - NMEAS - NP2 = NMEAS -C - INFO = 0 - IF( N.LT.0 ) THEN - INFO = -1 - ELSE IF( M.LT.0 ) THEN - INFO = -2 - ELSE IF( NP.LT.0 ) THEN - INFO = -3 - ELSE IF( NCON.LT.0 .OR. M1.LT.0 .OR. M2.GT.NP1 ) THEN - INFO = -4 - ELSE IF( NMEAS.LT.0 .OR. NP1.LT.0 .OR. NP2.GT.M1 ) THEN - INFO = -5 - ELSE IF( GAMMA.LT.ZERO ) THEN - INFO = -6 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -8 - ELSE IF( LDB.LT.MAX( 1, N ) ) THEN - INFO = -10 - ELSE IF( LDC.LT.MAX( 1, NP ) ) THEN - INFO = -12 - ELSE IF( LDD.LT.MAX( 1, NP ) ) THEN - INFO = -14 - ELSE IF( LDF.LT.MAX( 1, M ) ) THEN - INFO = -16 - ELSE IF( LDH.LT.MAX( 1, N ) ) THEN - INFO = -18 - ELSE IF( LDTU.LT.MAX( 1, M2 ) ) THEN - INFO = -20 - ELSE IF( LDTY.LT.MAX( 1, NP2 ) ) THEN - INFO = -22 - ELSE IF( LDX.LT.MAX( 1, N ) ) THEN - INFO = -24 - ELSE IF( LDY.LT.MAX( 1, N ) ) THEN - INFO = -26 - ELSE IF( LDAK.LT.MAX( 1, N ) ) THEN - INFO = -28 - ELSE IF( LDBK.LT.MAX( 1, N ) ) THEN - INFO = -30 - ELSE IF( LDCK.LT.MAX( 1, M2 ) ) THEN - INFO = -32 - ELSE IF( LDDK.LT.MAX( 1, M2 ) ) THEN - INFO = -34 - ELSE -C -C Compute workspace. -C - ND1 = NP1 - M2 - ND2 = M1 - NP2 - MINWRK = MAX( 1, M2*NP2 + NP2*NP2 + M2*M2 + - $ MAX( ND1*ND1 + MAX( 2*ND1, ( ND1 + ND2 )*NP2 ), - $ ND2*ND2 + MAX( 2*ND2, ND2*M2 ), 3*N, - $ N*( 2*NP2 + M2 ) + - $ MAX( 2*N*M2, M2*NP2 + - $ MAX( M2*M2 + 3*M2, NP2*( 2*NP2 + - $ M2 + MAX( NP2, N ) ) ) ) ) ) - IF( LDWORK.LT.MINWRK ) - $ INFO = -37 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'SB10RD', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF( N.EQ.0 .OR. M.EQ.0 .OR. NP.EQ.0 .OR. M1.EQ.0 .OR. M2.EQ.0 - $ .OR. NP1.EQ.0 .OR. NP2.EQ.0 ) THEN - DWORK( 1 ) = ONE - RETURN - END IF -C -C Get the machine precision. -C - EPS = DLAMCH( 'Epsilon' ) -C -C Workspace usage. -C - ID11 = 1 - ID21 = ID11 + M2*NP2 - ID12 = ID21 + NP2*NP2 - IW1 = ID12 + M2*M2 - IW2 = IW1 + ND1*ND1 - IW3 = IW2 + ND1*NP2 - IWRK = IW2 -C -C Set D11HAT := -D1122 . -C - IJ = ID11 - DO 20 J = 1, NP2 - DO 10 I = 1, M2 - DWORK( IJ ) = -D( ND1+I, ND2+J ) - IJ = IJ + 1 - 10 CONTINUE - 20 CONTINUE -C -C Set D21HAT := Inp2 . -C - CALL DLASET( 'Upper', NP2, NP2, ZERO, ONE, DWORK( ID21 ), NP2 ) -C -C Set D12HAT := Im2 . -C - CALL DLASET( 'Lower', M2, M2, ZERO, ONE, DWORK( ID12 ), M2 ) -C -C Compute D11HAT, D21HAT, D12HAT . -C - LWAMAX = 0 - IF( ND1.GT.0 ) THEN - IF( ND2.EQ.0 ) THEN -C -C Compute D21HAT'*D21HAT = Inp2 - D1112'*D1112/gamma^2 . -C - CALL DSYRK( 'U', 'T', NP2, ND1, -ONE/GAMMA**2, D, LDD, ONE, - $ DWORK( ID21 ), NP2 ) - ELSE -C -C Compute gdum = gamma^2*Ind1 - D1111*D1111' . -C - CALL DLASET( 'U', ND1, ND1, ZERO, GAMMA**2, DWORK( IW1 ), - $ ND1 ) - CALL DSYRK( 'U', 'N', ND1, ND2, -ONE, D, LDD, ONE, - $ DWORK( IW1 ), ND1 ) - ANORM = DLANSY( 'I', 'U', ND1, DWORK( IW1 ), ND1, - $ DWORK( IWRK ) ) - CALL DSYTRF( 'U', ND1, DWORK( IW1 ), ND1, IWORK, - $ DWORK( IWRK ), LDWORK-IWRK+1, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 1 - RETURN - END IF - LWAMAX = INT( DWORK( IWRK ) ) + IWRK - 1 - CALL DSYCON( 'U', ND1, DWORK( IW1 ), ND1, IWORK, ANORM, - $ RCOND, DWORK( IWRK ), IWORK( ND1+1 ), INFO2 ) -C -C Return if the matrix is singular to working precision. -C - IF( RCOND.LT.EPS ) THEN - INFO = 1 - RETURN - END IF -C -C Compute inv(gdum)*D1112 . -C - CALL DLACPY( 'Full', ND1, NP2, D( 1, ND2+1 ), LDD, - $ DWORK( IW2 ), ND1 ) - CALL DSYTRS( 'U', ND1, NP2, DWORK( IW1 ), ND1, IWORK, - $ DWORK( IW2 ), ND1, INFO2 ) -C -C Compute D11HAT = -D1121*D1111'*inv(gdum)*D1112 - D1122 . -C - CALL DGEMM( 'T', 'N', ND2, NP2, ND1, ONE, D, LDD, - $ DWORK( IW2 ), ND1, ZERO, DWORK( IW3 ), ND2 ) - CALL DGEMM( 'N', 'N', M2, NP2, ND2, -ONE, D( ND1+1, 1 ), - $ LDD, DWORK( IW3 ), ND2, ONE, DWORK( ID11 ), M2 ) -C -C Compute D21HAT'*D21HAT = Inp2 - D1112'*inv(gdum)*D1112 . -C - CALL MB01RX( 'Left', 'Upper', 'Transpose', NP2, ND1, ONE, - $ -ONE, DWORK( ID21 ), NP2, D( 1, ND2+1 ), LDD, - $ DWORK( IW2 ), ND1, INFO2 ) -C - IW2 = IW1 + ND2*ND2 - IWRK = IW2 -C -C Compute gdum = gamma^2*Ind2 - D1111'*D1111 . -C - CALL DLASET( 'L', ND2, ND2, ZERO, GAMMA**2, DWORK( IW1 ), - $ ND2 ) - CALL DSYRK( 'L', 'T', ND2, ND1, -ONE, D, LDD, ONE, - $ DWORK( IW1 ), ND2 ) - ANORM = DLANSY( 'I', 'L', ND2, DWORK( IW1 ), ND2, - $ DWORK( IWRK ) ) - CALL DSYTRF( 'L', ND2, DWORK( IW1 ), ND2, IWORK, - $ DWORK( IWRK ), LDWORK-IWRK+1, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 1 - RETURN - END IF - LWAMAX = MAX( INT( DWORK( IWRK ) ) + IWRK - 1, LWAMAX ) - CALL DSYCON( 'L', ND2, DWORK( IW1 ), ND2, IWORK, ANORM, - $ RCOND, DWORK( IWRK ), IWORK( ND2+1 ), INFO2 ) -C -C Return if the matrix is singular to working precision. -C - IF( RCOND.LT.EPS ) THEN - INFO = 1 - RETURN - END IF -C -C Compute inv(gdum)*D1121' . -C - CALL MA02AD( 'Full', M2, ND2, D( ND1+1, 1 ), LDD, - $ DWORK( IW2 ), ND2 ) - CALL DSYTRS( 'L', ND2, M2, DWORK( IW1 ), ND2, IWORK, - $ DWORK( IW2 ), ND2, INFO2 ) -C -C Compute D12HAT*D12HAT' = Im2 - D1121*inv(gdum)*D1121' . -C - CALL MB01RX( 'Left', 'Lower', 'NoTranspose', M2, ND2, ONE, - $ -ONE, DWORK( ID12 ), M2, D( ND1+1, 1 ), LDD, - $ DWORK( IW2 ), ND2, INFO2 ) - END IF - ELSE - IF( ND2.GT.0 ) THEN -C -C Compute D12HAT*D12HAT' = Im2 - D1121*D1121'/gamma^2 . -C - CALL DSYRK( 'L', 'N', M2, ND2, -ONE/GAMMA**2, D, LDD, ONE, - $ DWORK( ID12 ), M2 ) - END IF - END IF -C -C Compute D21HAT using Cholesky decomposition. -C - CALL DPOTRF( 'U', NP2, DWORK( ID21 ), NP2, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 1 - RETURN - END IF -C -C Compute D12HAT using Cholesky decomposition. -C - CALL DPOTRF( 'L', M2, DWORK( ID12 ), M2, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 1 - RETURN - END IF -C _ -C Compute Z = In - Y*X/gamma^2 and its LU factorization in AK . -C - IWRK = IW1 - CALL DLASET( 'Full', N, N, ZERO, ONE, AK, LDAK ) - CALL DGEMM( 'N', 'N', N, N, N, -ONE/GAMMA**2, Y, LDY, X, LDX, - $ ONE, AK, LDAK ) - ANORM = DLANGE( '1', N, N, AK, LDAK, DWORK( IWRK ) ) - CALL DGETRF( N, N, AK, LDAK, IWORK, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 1 - RETURN - END IF - CALL DGECON( '1', N, AK, LDAK, ANORM, RCOND, DWORK( IWRK ), - $ IWORK( N+1 ), INFO ) -C -C Return if the matrix is singular to working precision. -C - IF( RCOND.LT.EPS ) THEN - INFO = 1 - RETURN - END IF -C - IWB = IW1 - IWC = IWB + N*NP2 - IW1 = IWC + ( M2 + NP2 )*N - IW2 = IW1 + N*M2 -C -C Compute C2' + F12' in BK . -C - DO 40 J = 1, N - DO 30 I = 1, NP2 - BK( J, I ) = C( NP1 + I, J ) + F( ND2 + I, J ) - 30 CONTINUE - 40 CONTINUE -C _ -C Compute the transpose of (C2 + F12)*Z , with Z = inv(Z) . -C - CALL DGETRS( 'Transpose', N, NP2, AK, LDAK, IWORK, BK, LDBK, - $ INFO2 ) -C -C Compute the transpose of F2*Z . -C - CALL MA02AD( 'Full', M2, N, F( M1+1, 1 ), LDF, DWORK( IW1 ), N ) - CALL DGETRS( 'Transpose', N, M2, AK, LDAK, IWORK, DWORK( IW1 ), N, - $ INFO2 ) -C -C Compute the transpose of C1HAT = F2*Z - D11HAT*(C2 + F12)*Z . -C - CALL DGEMM( 'N', 'T', N, M2, NP2, -ONE, BK, LDBK, DWORK( ID11 ), - $ M2, ONE, DWORK( IW1 ), N ) -C -C Compute CHAT . -C - CALL DGEMM( 'N', 'T', M2, N, M2, ONE, TU, LDTU, DWORK( IW1 ), N, - $ ZERO, DWORK( IWC ), M2+NP2 ) - CALL MA02AD( 'Full', N, NP2, BK, LDBK, DWORK( IWC+M2 ), M2+NP2 ) - CALL DTRMM( 'L', 'U', 'N', 'N', NP2, N, -ONE, DWORK( ID21 ), NP2, - $ DWORK( IWC+M2 ), M2+NP2 ) -C -C Compute B2 + H12 . -C - IJ = IW2 - DO 60 J = 1, M2 - DO 50 I = 1, N - DWORK( IJ ) = B( I, M1 + J ) + H( I, ND1 + J ) - IJ = IJ + 1 - 50 CONTINUE - 60 CONTINUE -C -C Compute A + HC in AK . -C - CALL DLACPY( 'Full', N, N, A, LDA, AK, LDAK ) - CALL DGEMM( 'N', 'N', N, N, NP, ONE, H, LDH, C, LDC, ONE, AK, - $ LDAK ) -C -C Compute AHAT = A + HC + (B2 + H12)*C1HAT in AK . -C - CALL DGEMM( 'N', 'T', N, N, M2, ONE, DWORK( IW2 ), N, - $ DWORK( IW1 ), N, ONE, AK, LDAK ) -C -C Compute B1HAT = -H2 + (B2 + H12)*D11HAT in BK . -C - CALL DLACPY( 'Full', N, NP2, H( 1, NP1+1 ), LDH, BK, LDBK ) - CALL DGEMM( 'N', 'N', N, NP2, M2, ONE, DWORK( IW2 ), N, - $ DWORK( ID11 ), M2, -ONE, BK, LDBK ) -C -C Compute the first block of BHAT, BHAT1 . -C - CALL DGEMM( 'N', 'N', N, NP2, NP2, ONE, BK, LDBK, TY, LDTY, ZERO, - $ DWORK( IWB ), N ) -C -C Compute Tu*D11HAT . -C - CALL DGEMM( 'N', 'N', M2, NP2, M2, ONE, TU, LDTU, DWORK( ID11 ), - $ M2, ZERO, DWORK( IW1 ), M2 ) -C -C Compute Tu*D11HAT*Ty in DK . -C - CALL DGEMM( 'N', 'N', M2, NP2, NP2, ONE, DWORK( IW1 ), M2, TY, - $ LDTY, ZERO, DK, LDDK ) -C -C Compute P = Im2 + Tu*D11HAT*Ty*D22 and its condition. -C - IW2 = IW1 + M2*NP2 - IWRK = IW2 + M2*M2 - CALL DLASET( 'Full', M2, M2, ZERO, ONE, DWORK( IW2 ), M2 ) - CALL DGEMM( 'N', 'N', M2, M2, NP2, ONE, DK, LDDK, - $ D( NP1+1, M1+1 ), LDD, ONE, DWORK( IW2 ), M2 ) - ANORM = DLANGE( '1', M2, M2, DWORK( IW2 ), M2, DWORK( IWRK ) ) - CALL DGETRF( M2, M2, DWORK( IW2 ), M2, IWORK, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 2 - RETURN - END IF - CALL DGECON( '1', M2, DWORK( IW2 ), M2, ANORM, RCOND, - $ DWORK( IWRK ), IWORK( M2+1 ), INFO2 ) -C -C Return if the matrix is singular to working precision. -C - IF( RCOND.LT.EPS ) THEN - INFO = 2 - RETURN - END IF -C -C Find the controller matrix CK, CK = inv(P)*CHAT(1:M2,:) . -C - CALL DLACPY( 'Full', M2, N, DWORK( IWC ), M2+NP2, CK, LDCK ) - CALL DGETRS( 'NoTranspose', M2, N, DWORK( IW2 ), M2, IWORK, CK, - $ LDCK, INFO2 ) -C -C Find the controller matrices AK, BK, and DK, exploiting the -C special structure of the relations. -C -C Compute Q = Inp2 + D22*Tu*D11HAT*Ty and its LU factorization. -C - IW3 = IW2 + NP2*NP2 - IW4 = IW3 + NP2*M2 - IWRK = IW4 + NP2*NP2 - CALL DLASET( 'Full', NP2, NP2, ZERO, ONE, DWORK( IW2 ), NP2 ) - CALL DGEMM( 'N', 'N', NP2, NP2, M2, ONE, D( NP1+1, M1+1 ), LDD, - $ DK, LDDK, ONE, DWORK( IW2 ), NP2 ) - CALL DGETRF( NP2, NP2, DWORK( IW2 ), NP2, IWORK, INFO2 ) - IF( INFO2.GT.0 ) THEN - INFO = 2 - RETURN - END IF -C -C Compute A1 = inv(Q)*D22 and inv(Q) . -C - CALL DLACPY( 'Full', NP2, M2, D( NP1+1, M1+1 ), LDD, DWORK( IW3 ), - $ NP2 ) - CALL DGETRS( 'NoTranspose', NP2, M2, DWORK( IW2 ), NP2, IWORK, - $ DWORK( IW3 ), NP2, INFO2 ) - CALL DGETRI( NP2, DWORK( IW2 ), NP2, IWORK, DWORK( IWRK ), - $ LDWORK-IWRK+1, INFO2 ) - LWAMAX = MAX( INT( DWORK( IWRK ) ) + IWRK - 1, LWAMAX ) -C -C Compute A2 = ( inv(Ty) - inv(Q)*inv(Ty) - -C A1*Tu*D11HAT )*inv(D21HAT) . -C - CALL DLACPY( 'Full', NP2, NP2, TY, LDTY, DWORK( IW4 ), NP2 ) - CALL DGETRF( NP2, NP2, DWORK( IW4 ), NP2, IWORK, INFO2 ) - CALL DGETRI( NP2, DWORK( IW4 ), NP2, IWORK, DWORK( IWRK ), - $ LDWORK-IWRK+1, INFO2 ) -C - CALL DLACPY( 'Full', NP2, NP2, DWORK( IW4 ), NP2, DWORK( IWRK ), - $ NP2 ) - CALL DGEMM( 'N', 'N', NP2, NP2, NP2, -ONE, DWORK( IW2), NP2, - $ DWORK( IWRK ), NP2, ONE, DWORK( IW4 ), NP2 ) - CALL DGEMM( 'N', 'N', NP2, NP2, M2, -ONE, DWORK( IW3), NP2, - $ DWORK( IW1 ), M2, ONE, DWORK( IW4 ), NP2 ) - CALL DTRMM( 'R', 'U', 'N', 'N', NP2, NP2, ONE, DWORK( ID21 ), NP2, - $ DWORK( IW4 ), NP2 ) -C -C Compute [ A1 A2 ]*CHAT . -C - CALL DGEMM( 'N', 'N', NP2, N, M2+NP2, ONE, DWORK( IW3 ), NP2, - $ DWORK( IWC ), M2+NP2, ZERO, DWORK( IWRK ), NP2 ) -C -C Compute AK := AHAT - BHAT1*[ A1 A2 ]*CHAT . -C - CALL DGEMM( 'N', 'N', N, N, NP2, -ONE, DWORK( IWB ), N, - $ DWORK( IWRK ), NP2, ONE, AK, LDAK ) -C -C Compute BK := BHAT1*inv(Q) . -C - CALL DGEMM( 'N', 'N', N, NP2, NP2, ONE, DWORK( IWB ), N, - $ DWORK( IW2 ), NP2, ZERO, BK, LDBK ) -C -C Compute DK := Tu*D11HAT*Ty*inv(Q) . -C - CALL DGEMM( 'N', 'N', M2, NP2, NP2, ONE, DK, LDDK, DWORK( IW2 ), - $ NP2, ZERO, DWORK( IW3 ), M2 ) - CALL DLACPY( 'Full', M2, NP2, DWORK( IW3 ), M2, DK, LDDK ) -C - DWORK( 1 ) = DBLE( LWAMAX ) - RETURN -C *** Last line of SB10RD *** - END
--- a/extra/control-devel/devel/dksyn/SB10YD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,689 +0,0 @@ - SUBROUTINE SB10YD( DISCFL, FLAG, LENDAT, RFRDAT, IFRDAT, OMEGA, N, - $ A, LDA, B, C, D, TOL, IWORK, DWORK, LDWORK, - $ ZWORK, LZWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To fit a supplied frequency response data with a stable, minimum -C phase SISO (single-input single-output) system represented by its -C matrices A, B, C, D. It handles both discrete- and continuous-time -C cases. -C -C ARGUMENTS -C -C Input/Output parameters -C -C DISCFL (input) INTEGER -C Indicates the type of the system, as follows: -C = 0: continuous-time system; -C = 1: discrete-time system. -C -C FLAG (input) INTEGER -C If FLAG = 0, then the system zeros and poles are not -C constrained. -C If FLAG = 1, then the system zeros and poles will have -C negative real parts in the continuous-time case, or moduli -C less than 1 in the discrete-time case. Consequently, FLAG -C must be equal to 1 in mu-synthesis routines. -C -C LENDAT (input) INTEGER -C The length of the vectors RFRDAT, IFRDAT and OMEGA. -C LENDAT >= 2. -C -C RFRDAT (input) DOUBLE PRECISION array, dimension (LENDAT) -C The real part of the frequency data to be fitted. -C -C IFRDAT (input) DOUBLE PRECISION array, dimension (LENDAT) -C The imaginary part of the frequency data to be fitted. -C -C OMEGA (input) DOUBLE PRECISION array, dimension (LENDAT) -C The frequencies corresponding to RFRDAT and IFRDAT. -C These values must be nonnegative and monotonically -C increasing. Additionally, for discrete-time systems -C they must be between 0 and PI. -C -C N (input/output) INTEGER -C On entry, the desired order of the system to be fitted. -C N <= LENDAT-1. -C On exit, the order of the obtained system. The value of N -C could only be modified if N > 0 and FLAG = 1. -C -C A (output) DOUBLE PRECISION array, dimension (LDA,N) -C The leading N-by-N part of this array contains the -C matrix A. If FLAG = 1, then A is in an upper Hessenberg -C form, and corresponds to a minimal realization. -C -C LDA INTEGER -C The leading dimension of the array A. LDA >= MAX(1,N). -C -C B (output) DOUBLE PRECISION array, dimension (N) -C The computed vector B. -C -C C (output) DOUBLE PRECISION array, dimension (N) -C The computed vector C. If FLAG = 1, the first N-1 elements -C are zero (for the exit value of N). -C -C D (output) DOUBLE PRECISION array, dimension (1) -C The computed scalar D. -C -C Tolerances -C -C TOL DOUBLE PRECISION -C The tolerance to be used for determining the effective -C rank of matrices. If the user sets TOL > 0, then the given -C value of TOL is used as a lower bound for the reciprocal -C condition number; a (sub)matrix whose estimated condition -C number is less than 1/TOL is considered to be of full -C rank. If the user sets TOL <= 0, then an implicitly -C computed, default tolerance, defined by TOLDEF = SIZE*EPS, -C is used instead, where SIZE is the product of the matrix -C dimensions, and EPS is the machine precision (see LAPACK -C Library routine DLAMCH). -C -C Workspace -C -C IWORK INTEGER array, dimension max(2,2*N+1) -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C On exit, if INFO = 0, DWORK(1) returns the optimal value -C of LDWORK and DWORK(2) contains the optimal value of -C LZWORK. -C -C LDWORK INTEGER -C The length of the array DWORK. -C LDWORK = max( 2, LW1, LW2, LW3, LW4 ), where -C LW1 = 2*LENDAT + 4*HNPTS; HNPTS = 2048; -C LW2 = LENDAT + 6*HNPTS; -C MN = min( 2*LENDAT, 2*N+1 ) -C LW3 = 2*LENDAT*(2*N+1) + max( 2*LENDAT, 2*N+1 ) + -C max( MN + 6*N + 4, 2*MN + 1 ), if N > 0; -C LW3 = 4*LENDAT + 5 , if N = 0; -C LW4 = max( N*N + 5*N, 6*N + 1 + min( 1,N ) ), if FLAG = 1; -C LW4 = 0, if FLAG = 0. -C For optimum performance LDWORK should be larger. -C -C ZWORK COMPLEX*16 array, dimension (LZWORK) -C -C LZWORK INTEGER -C The length of the array ZWORK. -C LZWORK = LENDAT*(2*N+3), if N > 0; -C LZWORK = LENDAT, if N = 0. -C -C Error indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C = 1: if the discrete --> continuous transformation cannot -C be made; -C = 2: if the system poles cannot be found; -C = 3: if the inverse system cannot be found, i.e., D is -C (close to) zero; -C = 4: if the system zeros cannot be found; -C = 5: if the state-space representation of the new -C transfer function T(s) cannot be found; -C = 6: if the continuous --> discrete transformation cannot -C be made. -C -C METHOD -C -C First, if the given frequency data are corresponding to a -C continuous-time system, they are changed to a discrete-time -C system using a bilinear transformation with a scaled alpha. -C Then, the magnitude is obtained from the supplied data. -C Then, the frequency data are linearly interpolated around -C the unit-disc. -C Then, Oppenheim and Schafer complex cepstrum method is applied -C to get frequency data corresponding to a stable, minimum- -C phase system. This is done in the following steps: -C - Obtain LOG (magnitude) -C - Obtain IFFT of the result (DG01MD SLICOT subroutine); -C - halve the data at 0; -C - Obtain FFT of the halved data (DG01MD SLICOT subroutine); -C - Obtain EXP of the result. -C Then, the new frequency data are interpolated back to the -C original frequency. -C Then, based on these newly obtained data, the system matrices -C A, B, C, D are constructed; the very identification is -C performed by Least Squares Method using DGELSY LAPACK subroutine. -C If needed, a discrete-to-continuous time transformation is -C applied on the system matrices by AB04MD SLICOT subroutine. -C Finally, if requested, the poles and zeros of the system are -C checked. If some of them have positive real parts in the -C continuous-time case (or are not inside the unit disk in the -C complex plane in the discrete-time case), they are exchanged with -C their negatives (or reciprocals, respectively), to preserve the -C frequency response, while getting a minimum phase and stable -C system. This is done by SB10ZP SLICOT subroutine. -C -C REFERENCES -C -C [1] Oppenheim, A.V. and Schafer, R.W. -C Discrete-Time Signal Processing. -C Prentice-Hall Signal Processing Series, 1989. -C -C [2] Balas, G., Doyle, J., Glover, K., Packard, A., and Smith, R. -C Mu-analysis and Synthesis toolbox - User's Guide, -C The Mathworks Inc., Natick, MA, USA, 1998. -C -C CONTRIBUTORS -C -C Asparuh Markovski, Technical University of Sofia, July 2003. -C -C REVISIONS -C -C V. Sima, Research Institute for Informatics, Bucharest, Aug. 2003. -C A. Markovski, Technical University of Sofia, October 2003. -C -C KEYWORDS -C -C Bilinear transformation, frequency response, least-squares -C approximation, stability. -C -C ****************************************************************** -C -C .. Parameters .. - COMPLEX*16 ZZERO, ZONE - PARAMETER ( ZZERO = ( 0.0D+0, 0.0D+0 ), - $ ZONE = ( 1.0D+0, 0.0D+0 ) ) - DOUBLE PRECISION ZERO, ONE, TWO, FOUR, TEN - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0, - $ FOUR = 4.0D+0, TEN = 1.0D+1 ) - INTEGER HNPTS - PARAMETER ( HNPTS = 2048 ) -C .. -C .. Scalar Arguments .. - INTEGER DISCFL, FLAG, INFO, LDA, LDWORK, LENDAT, - $ LZWORK, N - DOUBLE PRECISION TOL -C .. -C .. Array Arguments .. - INTEGER IWORK(*) - DOUBLE PRECISION A(LDA, *), B(*), C(*), D(*), DWORK(*), - $ IFRDAT(*), OMEGA(*), RFRDAT(*) - COMPLEX*16 ZWORK(*) -C .. -C .. Local Scalars .. - INTEGER CLWMAX, DLWMAX, I, II, INFO2, IP1, IP2, ISTART, - $ ISTOP, IWA0, IWAB, IWBMAT, IWBP, IWBX, IWDME, - $ IWDOMO, IWMAG, IWS, IWVAR, IWXI, IWXR, IWYMAG, - $ K, LW1, LW2, LW3, LW4, MN, N1, N2, P, RANK - DOUBLE PRECISION P1, P2, PI, PW, RAT, TOLB, TOLL - COMPLEX*16 XHAT(HNPTS/2) -C .. -C .. External Functions .. - DOUBLE PRECISION DLAMCH, DLAPY2 - EXTERNAL DLAMCH, DLAPY2 -C .. -C .. External Subroutines .. - EXTERNAL AB04MD, DCOPY, DG01MD, DGELSY, DLASET, DSCAL, - $ SB10ZP, XERBLA -C .. -C .. Intrinsic Functions .. - INTRINSIC ACOS, ATAN, COS, DBLE, DCMPLX, DIMAG, EXP, LOG, - $ MAX, MIN, SIN, SQRT -C -C Test input parameters and workspace. -C - PI = FOUR*ATAN( ONE ) - PW = OMEGA(1) - N1 = N + 1 - N2 = N + N1 -C - INFO = 0 - IF( DISCFL.NE.0 .AND. DISCFL.NE.1 ) THEN - INFO = -1 - ELSE IF( FLAG.NE.0 .AND. FLAG.NE.1 ) THEN - INFO = -2 - ELSE IF ( LENDAT.LT.2 ) THEN - INFO = -3 - ELSE IF ( PW.LT.ZERO ) THEN - INFO = -6 - ELSE IF( N.GT.LENDAT - 1 ) THEN - INFO = -7 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -9 - ELSE -C - DO 10 K = 2, LENDAT - IF ( OMEGA(K).LT.PW ) - $ INFO = -6 - PW = OMEGA(K) - 10 CONTINUE -C - IF ( DISCFL.EQ.1 .AND. OMEGA(LENDAT).GT.PI ) - $ INFO = -6 - END IF -C - IF ( INFO.EQ.0 ) THEN -C -C Workspace. -C - LW1 = 2*LENDAT + 4*HNPTS - LW2 = LENDAT + 6*HNPTS - MN = MIN( 2*LENDAT, N2 ) -C - IF ( N.GT.0 ) THEN - LW3 = 2*LENDAT*N2 + MAX( 2*LENDAT, N2 ) + - $ MAX( MN + 6*N + 4, 2*MN + 1 ) - ELSE - LW3 = 4*LENDAT + 5 - END IF -C - IF ( FLAG.EQ.0 ) THEN - LW4 = 0 - ELSE - LW4 = MAX( N*N + 5*N, 6*N + 1 + MIN ( 1, N ) ) - END IF -C - DLWMAX = MAX( 2, LW1, LW2, LW3, LW4 ) -C - IF ( N.GT.0 ) THEN - CLWMAX = LENDAT*( N2 + 2 ) - ELSE - CLWMAX = LENDAT - END IF -C - IF ( LDWORK.LT.DLWMAX ) THEN - INFO = -16 - ELSE IF ( LZWORK.LT.CLWMAX ) THEN - INFO = -18 - END IF - END IF -C - IF ( INFO.NE.0 ) THEN -C -C Error return. -C - CALL XERBLA( 'SB10YD', -INFO ) - RETURN - END IF -C -C Set tolerances. -C - TOLB = DLAMCH( 'Epsilon' ) - TOLL = TOL - IF ( TOLL.LE.ZERO ) - $ TOLL = FOUR*DBLE( LENDAT*N )*TOLB -C -C @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ -C -C Workspace usage 1. -C Workspace: need 2*LENDAT + 4*HNPTS. -C - IWDOMO = 1 - IWDME = IWDOMO + LENDAT - IWYMAG = IWDME + 2*HNPTS - IWMAG = IWYMAG + 2*HNPTS -C -C Bilinear transformation. -C - IF ( DISCFL.EQ.0 ) THEN - PW = SQRT( OMEGA(1)*OMEGA(LENDAT) + SQRT( TOLB ) ) -C - DO 20 K = 1, LENDAT - DWORK(IWDME+K-1) = ( OMEGA(K)/PW )**2 - DWORK(IWDOMO+K-1) = - $ ACOS( ( ONE - DWORK(IWDME+K-1) )/ - $ ( ONE + DWORK(IWDME+K-1) ) ) - 20 CONTINUE -C - ELSE - CALL DCOPY( LENDAT, OMEGA, 1, DWORK(IWDOMO), 1 ) - END IF -C -C Linear interpolation. -C - DO 30 K = 1, LENDAT - DWORK(IWMAG+K-1) = DLAPY2( RFRDAT(K), IFRDAT(K) ) - DWORK(IWMAG+K-1) = ( ONE/LOG( TEN ) ) * LOG( DWORK(IWMAG+K-1) ) - 30 CONTINUE -C - DO 40 K = 1, HNPTS - DWORK(IWDME+K-1) = ( K - 1 )*PI/HNPTS - DWORK(IWYMAG+K-1) = ZERO -C - IF ( DWORK(IWDME+K-1).LT.DWORK(IWDOMO) ) THEN - DWORK(IWYMAG+K-1) = DWORK(IWMAG) - ELSE IF ( DWORK(IWDME+K-1).GE.DWORK(IWDOMO+LENDAT-1) ) THEN - DWORK(IWYMAG+K-1) = DWORK(IWMAG+LENDAT-1) - END IF -C - 40 CONTINUE -C - DO 60 I = 2, LENDAT - P1 = HNPTS*DWORK(IWDOMO+I-2)/PI + ONE -C - IP1 = INT( P1 ) - IF ( DBLE( IP1 ).NE.P1 ) - $ IP1 = IP1 + 1 -C - P2 = HNPTS*DWORK(IWDOMO+I-1)/PI + ONE -C - IP2 = INT( P2 ) - IF ( DBLE( IP2 ).NE.P2 ) - $ IP2 = IP2 + 1 -C - DO 50 P = IP1, IP2 - 1 - RAT = DWORK(IWDME+P-1) - DWORK(IWDOMO+I-2) - RAT = RAT/( DWORK(IWDOMO+I-1) - DWORK(IWDOMO+I-2) ) - DWORK(IWYMAG+P-1) = ( ONE - RAT )*DWORK(IWMAG+I-2) + - $ RAT*DWORK(IWMAG+I-1) - 50 CONTINUE -C - 60 CONTINUE -C - DO 70 K = 1, HNPTS - DWORK(IWYMAG+K-1) = EXP( LOG( TEN )*DWORK(IWYMAG+K-1) ) - 70 CONTINUE -C -C Duplicate data around disc. -C - DO 80 K = 1, HNPTS - DWORK(IWDME+HNPTS+K-1) = TWO*PI - DWORK(IWDME+HNPTS-K) - DWORK(IWYMAG+HNPTS+K-1) = DWORK(IWYMAG+HNPTS-K) - 80 CONTINUE -C -C Complex cepstrum to get min phase: -C LOG (Magnitude) -C - DO 90 K = 1, 2*HNPTS - DWORK(IWYMAG+K-1) = TWO*LOG( DWORK(IWYMAG+K-1) ) - 90 CONTINUE -C -C @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ -C -C Workspace usage 2. -C Workspace: need LENDAT + 6*HNPTS. -C - IWXR = IWYMAG - IWXI = IWMAG -C - DO 100 K = 1, 2*HNPTS - DWORK(IWXI+K-1) = ZERO - 100 CONTINUE -C -C IFFT -C - CALL DG01MD( 'I', 2*HNPTS, DWORK(IWXR), DWORK(IWXI), INFO2 ) -C -C Rescale, because DG01MD doesn't do it. -C - CALL DSCAL( HNPTS, ONE/( TWO*HNPTS ), DWORK(IWXR), 1 ) - CALL DSCAL( HNPTS, ONE/( TWO*HNPTS ), DWORK(IWXI), 1 ) -C -C Halve the result at 0. -C - DWORK(IWXR) = DWORK(IWXR)/TWO - DWORK(IWXI) = DWORK(IWXI)/TWO -C -C FFT -C - CALL DG01MD( 'D', HNPTS, DWORK(IWXR), DWORK(IWXI), INFO2 ) -C -C Get the EXP of the result. -C - DO 110 K = 1, HNPTS/2 - XHAT(K) = EXP( DWORK(IWXR+K-1) )* - $ DCMPLX ( COS( DWORK(IWXI+K-1)), SIN( DWORK(IWXI+K-1) ) ) - DWORK(IWDME+K-1) = DWORK(IWDME+2*K-2) - 110 CONTINUE -C -C Interpolate back to original frequency data. -C - ISTART = 1 - ISTOP = LENDAT -C - DO 120 I = 1, LENDAT - ZWORK(I) = ZZERO - IF ( DWORK(IWDOMO+I-1).LE.DWORK(IWDME) ) THEN - ZWORK(I) = XHAT(1) - ISTART = I + 1 - ELSE IF ( DWORK(IWDOMO+I-1).GE.DWORK(IWDME+HNPTS/2-1) ) - $ THEN - ZWORK(I) = XHAT(HNPTS/2) - ISTOP = ISTOP - 1 - END IF - 120 CONTINUE -C - DO 140 I = ISTART, ISTOP - II = HNPTS/2 - 130 CONTINUE - IF ( DWORK(IWDME+II-1).GE.DWORK(IWDOMO+I-1) ) - $ P = II - II = II - 1 - IF ( II.GT.0 ) - $ GOTO 130 - RAT = ( DWORK(IWDOMO+I-1) - DWORK(IWDME+P-2) )/ - $ ( DWORK(IWDME+P-1) - DWORK(IWDME+P-2) ) - ZWORK(I) = RAT*XHAT(P) + ( ONE - RAT )*XHAT(P-1) - 140 CONTINUE -C -C CASE N > 0. -C This is the only allowed case in mu-synthesis subroutines. -C - IF ( N.GT.0 ) THEN -C -C Preparation for frequency identification. -C -C @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ -C -C Complex workspace usage 1. -C Complex workspace: need 2*LENDAT + LENDAT*(N+1). -C - IWA0 = 1 + LENDAT - IWVAR = IWA0 + LENDAT*N1 -C - DO 150 K = 1, LENDAT - IF ( DISCFL.EQ.0 ) THEN - ZWORK(IWVAR+K-1) = DCMPLX( COS( DWORK(IWDOMO+K-1) ), - $ SIN( DWORK(IWDOMO+K-1) ) ) - ELSE - ZWORK(IWVAR+K-1) = DCMPLX( COS( OMEGA(K) ), - $ SIN( OMEGA(K) ) ) - END IF - 150 CONTINUE -C -C Array for DGELSY. -C - DO 160 K = 1, N2 - IWORK(K) = 0 - 160 CONTINUE -C -C Constructing A0. -C - DO 170 K = 1, LENDAT - ZWORK(IWA0+N*LENDAT+K-1) = ZONE - 170 CONTINUE -C - DO 190 I = 1, N - DO 180 K = 1, LENDAT - ZWORK(IWA0+(N-I)*LENDAT+K-1) = - $ ZWORK(IWA0+(N1-I)*LENDAT+K-1)*ZWORK(IWVAR+K-1) - 180 CONTINUE - 190 CONTINUE -C -C @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ -C -C Complex workspace usage 2. -C Complex workspace: need 2*LENDAT + LENDAT*(2*N+1). -C - IWBP = IWVAR - IWAB = IWBP + LENDAT -C -C Constructing BP. -C - DO 200 K = 1, LENDAT - ZWORK(IWBP+K-1) = ZWORK(IWA0+K-1)*ZWORK(K) - 200 CONTINUE -C -C Constructing AB. -C - DO 220 I = 1, N - DO 210 K = 1, LENDAT - ZWORK(IWAB+(I-1)*LENDAT+K-1) = -ZWORK(K)* - $ ZWORK(IWA0+I*LENDAT+K-1) - 210 CONTINUE - 220 CONTINUE -C -C @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ -C -C Workspace usage 3. -C Workspace: need LW3 = 2*LENDAT*(2*N+1) + max(2*LENDAT,2*N+1). -C - IWBX = 1 + 2*LENDAT*N2 - IWS = IWBX + MAX( 2*LENDAT, N2 ) -C -C Constructing AX. -C - DO 240 I = 1, N1 - DO 230 K = 1, LENDAT - DWORK(2*(I-1)*LENDAT+K) = - $ DBLE( ZWORK(IWA0+(I-1)*LENDAT+K-1) ) - DWORK((2*I-1)*LENDAT+K) = - $ DIMAG( ZWORK(IWA0+(I-1)*LENDAT+K-1) ) - 230 CONTINUE - 240 CONTINUE -C - DO 260 I = 1, N - DO 250 K = 1, LENDAT - DWORK(2*N1*LENDAT+2*(I-1)*LENDAT+K) = - $ DBLE( ZWORK(IWAB+(I-1)*LENDAT+K-1) ) - DWORK(2*N1*LENDAT+(2*I-1)*LENDAT+K) = - $ DIMAG( ZWORK(IWAB+(I-1)*LENDAT+K-1) ) - 250 CONTINUE - 260 CONTINUE -C -C Constructing BX. -C - DO 270 K = 1, LENDAT - DWORK(IWBX+K-1) = DBLE( ZWORK(IWBP+K-1) ) - DWORK(IWBX+LENDAT+K-1) = DIMAG( ZWORK(IWBP+K-1) ) - 270 CONTINUE -C -C Estimating X. -C Workspace: need LW3 + max( MN+3*(2*N+1)+1, 2*MN+1 ), -C where MN = min( 2*LENDAT, 2*N+1 ); -C prefer larger. -C - CALL DGELSY( 2*LENDAT, N2, 1, DWORK, 2*LENDAT, DWORK(IWBX), - $ MAX( 2*LENDAT, N2 ), IWORK, TOLL, RANK, - $ DWORK(IWS), LDWORK-IWS+1, INFO2 ) - DLWMAX = MAX( DLWMAX, INT( DWORK(IWS) + IWS - 1 ) ) -C -C Constructing A matrix. -C - DO 280 K = 1, N - A(K,1) = -DWORK(IWBX+N1+K-1) - 280 CONTINUE -C - IF ( N.GT.1 ) - $ CALL DLASET( 'Full', N, N-1, ZERO, ONE, A(1,2), LDA ) -C -C Constructing B matrix. -C - DO 290 K = 1, N - B(K) = DWORK(IWBX+N1+K-1)*DWORK(IWBX) - DWORK(IWBX+K) - 290 CONTINUE -C -C Constructing C matrix. -C - C(1) = -ONE -C - DO 300 K = 2, N - C(K) = ZERO - 300 CONTINUE -C -C Constructing D matrix. -C - D(1) = DWORK(IWBX) -C -C Transform to continuous-time case, if needed. -C Workspace: need max(1,N); -C prefer larger. -C - IF ( DISCFL.EQ.0 ) THEN - CALL AB04MD( 'D', N, 1, 1, ONE, PW, A, LDA, B, LDA, C, 1, - $ D, 1, IWORK, DWORK, LDWORK, INFO2 ) - IF ( INFO2.NE.0 ) THEN - INFO = 1 - RETURN - END IF - DLWMAX = MAX( DLWMAX, INT( DWORK(1) ) ) - END IF -C -C Make all the real parts of the poles and the zeros negative. -C - IF ( FLAG.EQ.1 ) THEN -C -C Workspace: need max(N*N + 5*N, 6*N + 1 + min(1,N)); -C prefer larger. - CALL SB10ZP( DISCFL, N, A, LDA, B, C, D, IWORK, DWORK, - $ LDWORK, INFO ) - IF ( INFO.NE.0 ) - $ RETURN - DLWMAX = MAX( DLWMAX, INT( DWORK(1) ) ) - END IF -C - ELSE -C -C CASE N = 0. -C -C @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ -C -C Workspace usage 4. -C Workspace: need 4*LENDAT. -C - IWBMAT = 1 + 2*LENDAT - IWS = IWBMAT + 2*LENDAT -C -C Constructing AMAT and BMAT. -C - DO 310 K = 1, LENDAT - DWORK(K) = ONE - DWORK(K+LENDAT) = ZERO - DWORK(IWBMAT+K-1) = DBLE( ZWORK(K) ) - DWORK(IWBMAT+LENDAT+K-1) = DIMAG( ZWORK(K) ) - 310 CONTINUE -C -C Estimating D matrix. -C Workspace: need 4*LENDAT + 5; -C prefer larger. -C - IWORK(1) = 0 - CALL DGELSY( 2*LENDAT, 1, 1, DWORK, 2*LENDAT, DWORK(IWBMAT), - $ 2*LENDAT, IWORK, TOLL, RANK, DWORK(IWS), - $ LDWORK-IWS+1, INFO2 ) - DLWMAX = MAX( DLWMAX, INT( DWORK(IWS) + IWS - 1 ) ) -C - D(1) = DWORK(IWBMAT) -C - END IF -C -C @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ -C - DWORK(1) = DLWMAX - DWORK(2) = CLWMAX - RETURN -C -C *** Last line of SB10YD *** - END
--- a/extra/control-devel/devel/dksyn/SB10ZP.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,339 +0,0 @@ - SUBROUTINE SB10ZP( DISCFL, N, A, LDA, B, C, D, IWORK, DWORK, - $ LDWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To transform a SISO (single-input single-output) system [A,B;C,D] -C by mirroring its unstable poles and zeros in the boundary of the -C stability domain, thus preserving the frequency response of the -C system, but making it stable and minimum phase. Specifically, for -C a continuous-time system, the positive real parts of its poles -C and zeros are exchanged with their negatives. Discrete-time -C systems are first converted to continuous-time systems using a -C bilinear transformation, and finally converted back. -C -C ARGUMENTS -C -C Input/Output parameters -C -C DISCFL (input) INTEGER -C Indicates the type of the system, as follows: -C = 0: continuous-time system; -C = 1: discrete-time system. -C -C N (input/output) INTEGER -C On entry, the order of the original system. N >= 0. -C On exit, the order of the transformed, minimal system. -C -C A (input/output) DOUBLE PRECISION array, dimension (LDA,N) -C On entry, the leading N-by-N part of this array must -C contain the original system matrix A. -C On exit, the leading N-by-N part of this array contains -C the transformed matrix A, in an upper Hessenberg form. -C -C LDA INTEGER -C The leading dimension of the array A. LDA >= MAX(1,N). -C -C B (input/output) DOUBLE PRECISION array, dimension (N) -C On entry, this array must contain the original system -C vector B. -C On exit, this array contains the transformed vector B. -C -C C (input/output) DOUBLE PRECISION array, dimension (N) -C On entry, this array must contain the original system -C vector C. -C On exit, this array contains the transformed vector C. -C The first N-1 elements are zero (for the exit value of N). -C -C D (input/output) DOUBLE PRECISION array, dimension (1) -C On entry, this array must contain the original system -C scalar D. -C On exit, this array contains the transformed scalar D. -C -C Workspace -C -C IWORK INTEGER array, dimension max(2,N+1) -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C On exit, if INFO = 0, DWORK(1) returns the optimal value -C of LDWORK. -C -C LDWORK INTEGER -C The length of the array DWORK. -C LDWORK >= max(N*N + 5*N, 6*N + 1 + min(1,N)). -C For optimum performance LDWORK should be larger. -C -C Error indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C = 1: if the discrete --> continuous transformation cannot -C be made; -C = 2: if the system poles cannot be found; -C = 3: if the inverse system cannot be found, i.e., D is -C (close to) zero; -C = 4: if the system zeros cannot be found; -C = 5: if the state-space representation of the new -C transfer function T(s) cannot be found; -C = 6: if the continuous --> discrete transformation cannot -C be made. -C -C METHOD -C -C First, if the system is discrete-time, it is transformed to -C continuous-time using alpha = beta = 1 in the bilinear -C transformation implemented in the SLICOT routine AB04MD. -C Then the eigenvalues of A, i.e., the system poles, are found. -C Then, the inverse of the original system is found and its poles, -C i.e., the system zeros, are evaluated. -C The obtained system poles Pi and zeros Zi are checked and if a -C positive real part is detected, it is exchanged by -Pi or -Zi. -C Then the polynomial coefficients of the transfer function -C T(s) = Q(s)/P(s) are found. -C The state-space representation of T(s) is then obtained. -C The system matrices B, C, D are scaled so that the transformed -C system has the same system gain as the original system. -C If the original system is discrete-time, then the result (which is -C continuous-time) is converted back to discrete-time. -C -C CONTRIBUTORS -C -C Asparuh Markovski, Technical University of Sofia, July 2003. -C -C REVISIONS -C -C V. Sima, Research Institute for Informatics, Bucharest, Aug. 2003. -C -C KEYWORDS -C -C Bilinear transformation, stability, state-space representation. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) -C .. -C .. Scalar Arguments .. - INTEGER DISCFL, INFO, LDA, LDWORK, N -C .. -C .. Array Arguments .. - INTEGER IWORK( * ) - DOUBLE PRECISION A( LDA, * ), B( * ), C( * ), D( * ), DWORK( * ) -C .. -C .. Local Scalars .. - INTEGER I, IDW1, IDW2, IDW3, IMP, IMZ, INFO2, IWA, IWP, - $ IWPS, IWQ, IWQS, LDW1, MAXWRK, REP, REZ - DOUBLE PRECISION RCOND, SCALB, SCALC, SCALD -C .. -C .. Local Arrays .. - INTEGER INDEX(1) -C .. -C .. External Subroutines .. - EXTERNAL AB04MD, AB07ND, DCOPY, DGEEV, DLACPY, DSCAL, - $ MC01PD, TD04AD, XERBLA -C .. -C .. Intrinsic Functions .. - INTRINSIC ABS, INT, MAX, MIN, SIGN, SQRT -C -C Test input parameters and workspace. -C - INFO = 0 - IF ( DISCFL.NE.0 .AND. DISCFL.NE.1 ) THEN - INFO = -1 - ELSE IF ( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -4 - ELSE IF ( LDWORK.LT.MAX( N*N + 5*N, 6*N + 1 + MIN( 1, N ) ) ) THEN - INFO = -10 - END IF -C - IF ( INFO.NE.0 ) THEN -C -C Error return. -C - CALL XERBLA( 'SB10ZP', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF( N.EQ.0 ) THEN - DWORK(1) = ONE - RETURN - END IF -C -C Workspace usage 1. -C - REP = 1 - IMP = REP + N - REZ = IMP + N - IMZ = REZ + N - IWA = REZ - IDW1 = IWA + N*N - LDW1 = LDWORK - IDW1 + 1 -C -C 1. Discrete --> continuous transformation if needed. -C - IF ( DISCFL.EQ.1 ) THEN -C -C Workspace: need max(1,N); -C prefer larger. -C - CALL AB04MD( 'D', N, 1, 1, ONE, ONE, A, LDA, B, LDA, C, 1, - $ D, 1, IWORK, DWORK, LDWORK, INFO2 ) - IF ( INFO2.NE.0 ) THEN - INFO = 1 - RETURN - END IF - MAXWRK = INT( DWORK(1) ) - ELSE - MAXWRK = 0 - END IF -C -C 2. Determine the factors for restoring system gain. -C - SCALD = D(1) - SCALC = SQRT( ABS( SCALD ) ) - SCALB = SIGN( SCALC, SCALD ) -C -C 3. Find the system poles, i.e., the eigenvalues of A. -C Workspace: need N*N + 2*N + 3*N; -C prefer larger. -C - CALL DLACPY( 'Full', N, N, A, LDA, DWORK(IWA), N ) -C - CALL DGEEV( 'N', 'N', N, DWORK(IWA), N, DWORK(REP), DWORK(IMP), - $ DWORK(IDW1), 1, DWORK(IDW1), 1, DWORK(IDW1), LDW1, - $ INFO2 ) - IF ( INFO2.NE.0 ) THEN - INFO = 2 - RETURN - END IF - MAXWRK = MAX( MAXWRK, INT( DWORK(IDW1) + IDW1 - 1 ) ) -C -C 4. Compute the inverse system [Ai, Bi; Ci, Di]. -C Workspace: need N*N + 2*N + 4; -C prefer larger. -C - CALL AB07ND( N, 1, A, LDA, B, LDA, C, 1, D, 1, RCOND, IWORK, - $ DWORK(IDW1), LDW1, INFO2 ) - IF ( INFO2.NE.0 ) THEN - INFO = 3 - RETURN - END IF - MAXWRK = MAX( MAXWRK, INT( DWORK(IDW1) + IDW1 - 1 ) ) -C -C 5. Find the system zeros, i.e., the eigenvalues of Ai. -C Workspace: need 4*N + 3*N; -C prefer larger. -C - IDW1 = IMZ + N - LDW1 = LDWORK - IDW1 + 1 -C - CALL DGEEV( 'N', 'N', N, A, LDA, DWORK(REZ), DWORK(IMZ), - $ DWORK(IDW1), 1, DWORK(IDW1), 1, DWORK(IDW1), LDW1, - $ INFO2 ) - IF ( INFO2.NE.0 ) THEN - INFO = 4 - RETURN - END IF - MAXWRK = MAX( MAXWRK, INT( DWORK(IDW1) + IDW1 - 1 ) ) -C -C 6. Exchange the zeros and the poles with positive real parts with -C their negatives. -C - DO 10 I = 0, N - 1 - IF ( DWORK(REP+I).GT.ZERO ) - $ DWORK(REP+I) = -DWORK(REP+I) - IF ( DWORK(REZ+I).GT.ZERO ) - $ DWORK(REZ+I) = -DWORK(REZ+I) - 10 CONTINUE -C -C Workspace usage 2. -C - IWP = IDW1 - IDW2 = IWP + N + 1 - IWPS = 1 -C -C 7. Construct the nominator and the denominator -C of the system transfer function T( s ) = Q( s )/P( s ). -C 8. Rearrange the coefficients in Q(s) and P(s) because -C MC01PD subroutine produces them in increasing powers of s. -C Workspace: need 6*N + 2. -C - CALL MC01PD( N, DWORK(REP), DWORK(IMP), DWORK(IWP), DWORK(IDW2), - $ INFO2 ) - CALL DCOPY( N+1, DWORK(IWP), -1, DWORK(IWPS), 1 ) -C -C Workspace usage 3. -C - IWQ = IDW1 - IWQS = IWPS + N + 1 - IDW3 = IWQS + N + 1 -C - CALL MC01PD( N, DWORK(REZ), DWORK(IMZ), DWORK(IWQ), DWORK(IDW2), - $ INFO2 ) - CALL DCOPY( N+1, DWORK(IWQ), -1, DWORK(IWQS), 1 ) -C -C 9. Make the conversion T(s) --> [A, B; C, D]. -C Workspace: need 2*N + 2 + N + max(N,3); -C prefer larger. -C - INDEX(1) = N - CALL TD04AD( 'R', 1, 1, INDEX, DWORK(IWPS), 1, DWORK(IWQS), 1, 1, - $ N, A, LDA, B, LDA, C, 1, D, 1, -ONE, IWORK, - $ DWORK(IDW3), LDWORK-IDW3+1, INFO2 ) - IF ( INFO2.NE.0 ) THEN - INFO = 5 - RETURN - END IF - MAXWRK = MAX( MAXWRK, INT( DWORK(IDW3) + IDW3 - 1 ) ) -C -C 10. Scale the transformed system to the previous gain. -C - IF ( N.GT.0 ) THEN - CALL DSCAL( N, SCALB, B, 1 ) - C(N) = SCALC*C(N) - END IF -C - D(1) = SCALD -C -C 11. Continuous --> discrete transformation if needed. -C - IF ( DISCFL.EQ.1 ) THEN - CALL AB04MD( 'C', N, 1, 1, ONE, ONE, A, LDA, B, LDA, C, 1, - $ D, 1, IWORK, DWORK, LDWORK, INFO2 ) - - IF ( INFO2.NE.0 ) THEN - INFO = 6 - RETURN - END IF - END IF -C - DWORK(1) = MAXWRK - RETURN -C -C *** Last line of SB10ZP *** - END
--- a/extra/control-devel/devel/dksyn/TB01ID.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,402 +0,0 @@ - SUBROUTINE TB01ID( JOB, N, M, P, MAXRED, A, LDA, B, LDB, C, LDC, - $ SCALE, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To reduce the 1-norm of a system matrix -C -C S = ( A B ) -C ( C 0 ) -C -C corresponding to the triple (A,B,C), by balancing. This involves -C a diagonal similarity transformation inv(D)*A*D applied -C iteratively to A to make the rows and columns of -C -1 -C diag(D,I) * S * diag(D,I) -C -C as close in norm as possible. -C -C The balancing can be performed optionally on the following -C particular system matrices -C -C S = A, S = ( A B ) or S = ( A ) -C ( C ) -C -C ARGUMENTS -C -C Mode Parameters -C -C JOB CHARACTER*1 -C Indicates which matrices are involved in balancing, as -C follows: -C = 'A': All matrices are involved in balancing; -C = 'B': B and A matrices are involved in balancing; -C = 'C': C and A matrices are involved in balancing; -C = 'N': B and C matrices are not involved in balancing. -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the matrix A, the number of rows of matrix B -C and the number of columns of matrix C. -C N represents the dimension of the state vector. N >= 0. -C -C M (input) INTEGER. -C The number of columns of matrix B. -C M represents the dimension of input vector. M >= 0. -C -C P (input) INTEGER. -C The number of rows of matrix C. -C P represents the dimension of output vector. P >= 0. -C -C MAXRED (input/output) DOUBLE PRECISION -C On entry, the maximum allowed reduction in the 1-norm of -C S (in an iteration) if zero rows or columns are -C encountered. -C If MAXRED > 0.0, MAXRED must be larger than one (to enable -C the norm reduction). -C If MAXRED <= 0.0, then the value 10.0 for MAXRED is -C used. -C On exit, if the 1-norm of the given matrix S is non-zero, -C the ratio between the 1-norm of the given matrix and the -C 1-norm of the balanced matrix. -C -C A (input/output) DOUBLE PRECISION array, dimension (LDA,N) -C On entry, the leading N-by-N part of this array must -C contain the system state matrix A. -C On exit, the leading N-by-N part of this array contains -C the balanced matrix inv(D)*A*D. -C -C LDA INTEGER -C The leading dimension of the array A. LDA >= max(1,N). -C -C B (input/output) DOUBLE PRECISION array, dimension (LDB,M) -C On entry, if M > 0, the leading N-by-M part of this array -C must contain the system input matrix B. -C On exit, if M > 0, the leading N-by-M part of this array -C contains the balanced matrix inv(D)*B. -C The array B is not referenced if M = 0. -C -C LDB INTEGER -C The leading dimension of the array B. -C LDB >= MAX(1,N) if M > 0. -C LDB >= 1 if M = 0. -C -C C (input/output) DOUBLE PRECISION array, dimension (LDC,N) -C On entry, if P > 0, the leading P-by-N part of this array -C must contain the system output matrix C. -C On exit, if P > 0, the leading P-by-N part of this array -C contains the balanced matrix C*D. -C The array C is not referenced if P = 0. -C -C LDC INTEGER -C The leading dimension of the array C. LDC >= MAX(1,P). -C -C SCALE (output) DOUBLE PRECISION array, dimension (N) -C The scaling factors applied to S. If D(j) is the scaling -C factor applied to row and column j, then SCALE(j) = D(j), -C for j = 1,...,N. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit. -C < 0: if INFO = -i, the i-th argument had an illegal -C value. -C -C METHOD -C -C Balancing consists of applying a diagonal similarity -C transformation -C -1 -C diag(D,I) * S * diag(D,I) -C -C to make the 1-norms of each row of the first N rows of S and its -C corresponding column nearly equal. -C -C Information about the diagonal matrix D is returned in the vector -C SCALE. -C -C REFERENCES -C -C [1] Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J., -C Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., -C Ostrouchov, S., and Sorensen, D. -C LAPACK Users' Guide: Second Edition. -C SIAM, Philadelphia, 1995. -C -C NUMERICAL ASPECTS -C -C None. -C -C CONTRIBUTOR -C -C Release 3.0: V. Sima, Katholieke Univ. Leuven, Belgium, Jan. 1998. -C This subroutine is based on LAPACK routine DGEBAL, and routine -C BALABC (A. Varga, German Aerospace Research Establishment, DLR). -C -C REVISIONS -C -C - -C -C KEYWORDS -C -C Balancing, eigenvalue, matrix algebra, matrix operations, -C similarity transformation. -C -C ********************************************************************* -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) - DOUBLE PRECISION SCLFAC - PARAMETER ( SCLFAC = 1.0D+1 ) - DOUBLE PRECISION FACTOR, MAXR - PARAMETER ( FACTOR = 0.95D+0, MAXR = 10.0D+0 ) -C .. -C .. Scalar Arguments .. - CHARACTER JOB - INTEGER INFO, LDA, LDB, LDC, M, N, P - DOUBLE PRECISION MAXRED -C .. -C .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ), - $ SCALE( * ) -C .. -C .. Local Scalars .. - LOGICAL NOCONV, WITHB, WITHC - INTEGER I, ICA, IRA, J - DOUBLE PRECISION CA, CO, F, G, MAXNRM, RA, RO, S, SFMAX1, - $ SFMAX2, SFMIN1, SFMIN2, SNORM, SRED -C .. -C .. External Functions .. - LOGICAL LSAME - INTEGER IDAMAX - DOUBLE PRECISION DASUM, DLAMCH - EXTERNAL DASUM, DLAMCH, IDAMAX, LSAME -C .. -C .. External Subroutines .. - EXTERNAL DSCAL, XERBLA -C .. -C .. Intrinsic Functions .. - INTRINSIC ABS, MAX, MIN -C .. -C .. Executable Statements .. -C -C Test the scalar input arguments. -C - INFO = 0 - WITHB = LSAME( JOB, 'A' ) .OR. LSAME( JOB, 'B' ) - WITHC = LSAME( JOB, 'A' ) .OR. LSAME( JOB, 'C' ) -C - IF( .NOT.WITHB .AND. .NOT.WITHC .AND. .NOT.LSAME( JOB, 'N' ) ) - $ THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( M.LT.0 ) THEN - INFO = -3 - ELSE IF( P.LT.0 ) THEN - INFO = -4 - ELSE IF( MAXRED.GT.ZERO .AND. MAXRED.LT.ONE ) THEN - INFO = -5 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -7 - ELSE IF( ( M.GT.0 .AND. LDB.LT.MAX( 1, N ) ) .OR. - $ ( M.EQ.0 .AND. LDB.LT.1 ) ) THEN - INFO = -9 - ELSE IF( LDC.LT.MAX( 1, P ) ) THEN - INFO = -11 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'TB01ID', -INFO ) - RETURN - END IF -C - IF( N.EQ.0 ) - $ RETURN -C -C Compute the 1-norm of the required part of matrix S and exit if -C it is zero. -C - SNORM = ZERO -C - DO 10 J = 1, N - SCALE( J ) = ONE - CO = DASUM( N, A( 1, J ), 1 ) - IF( WITHC .AND. P.GT.0 ) - $ CO = CO + DASUM( P, C( 1, J ), 1 ) - SNORM = MAX( SNORM, CO ) - 10 CONTINUE -C - IF( WITHB ) THEN -C - DO 20 J = 1, M - SNORM = MAX( SNORM, DASUM( N, B( 1, J ), 1 ) ) - 20 CONTINUE -C - END IF -C - IF( SNORM.EQ.ZERO ) - $ RETURN -C -C Set some machine parameters and the maximum reduction in the -C 1-norm of S if zero rows or columns are encountered. -C - SFMIN1 = DLAMCH( 'S' ) / DLAMCH( 'P' ) - SFMAX1 = ONE / SFMIN1 - SFMIN2 = SFMIN1*SCLFAC - SFMAX2 = ONE / SFMIN2 -C - SRED = MAXRED - IF( SRED.LE.ZERO ) SRED = MAXR -C - MAXNRM = MAX( SNORM/SRED, SFMIN1 ) -C -C Balance the matrix. -C -C Iterative loop for norm reduction. -C - 30 CONTINUE - NOCONV = .FALSE. -C - DO 90 I = 1, N - CO = ZERO - RO = ZERO -C - DO 40 J = 1, N - IF( J.EQ.I ) - $ GO TO 40 - CO = CO + ABS( A( J, I ) ) - RO = RO + ABS( A( I, J ) ) - 40 CONTINUE -C - ICA = IDAMAX( N, A( 1, I ), 1 ) - CA = ABS( A( ICA, I ) ) - IRA = IDAMAX( N, A( I, 1 ), LDA ) - RA = ABS( A( I, IRA ) ) -C - IF( WITHC .AND. P.GT.0 ) THEN - CO = CO + DASUM( P, C( 1, I ), 1 ) - ICA = IDAMAX( P, C( 1, I ), 1 ) - CA = MAX( CA, ABS( C( ICA, I ) ) ) - END IF -C - IF( WITHB .AND. M.GT.0 ) THEN - RO = RO + DASUM( M, B( I, 1 ), LDB ) - IRA = IDAMAX( M, B( I, 1 ), LDB ) - RA = MAX( RA, ABS( B( I, IRA ) ) ) - END IF -C -C Special case of zero CO and/or RO. -C - IF( CO.EQ.ZERO .AND. RO.EQ.ZERO ) - $ GO TO 90 - IF( CO.EQ.ZERO ) THEN - IF( RO.LE.MAXNRM ) - $ GO TO 90 - CO = MAXNRM - END IF - IF( RO.EQ.ZERO ) THEN - IF( CO.LE.MAXNRM ) - $ GO TO 90 - RO = MAXNRM - END IF -C -C Guard against zero CO or RO due to underflow. -C - G = RO / SCLFAC - F = ONE - S = CO + RO - 50 CONTINUE - IF( CO.GE.G .OR. MAX( F, CO, CA ).GE.SFMAX2 .OR. - $ MIN( RO, G, RA ).LE.SFMIN2 )GO TO 60 - F = F*SCLFAC - CO = CO*SCLFAC - CA = CA*SCLFAC - G = G / SCLFAC - RO = RO / SCLFAC - RA = RA / SCLFAC - GO TO 50 -C - 60 CONTINUE - G = CO / SCLFAC - 70 CONTINUE - IF( G.LT.RO .OR. MAX( RO, RA ).GE.SFMAX2 .OR. - $ MIN( F, CO, G, CA ).LE.SFMIN2 )GO TO 80 - F = F / SCLFAC - CO = CO / SCLFAC - CA = CA / SCLFAC - G = G / SCLFAC - RO = RO*SCLFAC - RA = RA*SCLFAC - GO TO 70 -C -C Now balance. -C - 80 CONTINUE - IF( ( CO+RO ).GE.FACTOR*S ) - $ GO TO 90 - IF( F.LT.ONE .AND. SCALE( I ).LT.ONE ) THEN - IF( F*SCALE( I ).LE.SFMIN1 ) - $ GO TO 90 - END IF - IF( F.GT.ONE .AND. SCALE( I ).GT.ONE ) THEN - IF( SCALE( I ).GE.SFMAX1 / F ) - $ GO TO 90 - END IF - G = ONE / F - SCALE( I ) = SCALE( I )*F - NOCONV = .TRUE. -C - CALL DSCAL( N, G, A( I, 1 ), LDA ) - CALL DSCAL( N, F, A( 1, I ), 1 ) - IF( M.GT.0 ) CALL DSCAL( M, G, B( I, 1 ), LDB ) - IF( P.GT.0 ) CALL DSCAL( P, F, C( 1, I ), 1 ) -C - 90 CONTINUE -C - IF( NOCONV ) - $ GO TO 30 -C -C Set the norm reduction parameter. -C - MAXRED = SNORM - SNORM = ZERO -C - DO 100 J = 1, N - CO = DASUM( N, A( 1, J ), 1 ) - IF( WITHC .AND. P.GT.0 ) - $ CO = CO + DASUM( P, C( 1, J ), 1 ) - SNORM = MAX( SNORM, CO ) - 100 CONTINUE -C - IF( WITHB ) THEN -C - DO 110 J = 1, M - SNORM = MAX( SNORM, DASUM( N, B( 1, J ), 1 ) ) - 110 CONTINUE -C - END IF - MAXRED = MAXRED/SNORM - RETURN -C *** Last line of TB01ID *** - END
--- a/extra/control-devel/devel/dksyn/TB01PD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,352 +0,0 @@ - SUBROUTINE TB01PD( JOB, EQUIL, N, M, P, A, LDA, B, LDB, C, LDC, - $ NR, TOL, IWORK, DWORK, LDWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To find a reduced (controllable, observable, or minimal) state- -C space representation (Ar,Br,Cr) for any original state-space -C representation (A,B,C). The matrix Ar is in upper block -C Hessenberg form. -C -C ARGUMENTS -C -C Mode Parameters -C -C JOB CHARACTER*1 -C Indicates whether the user wishes to remove the -C uncontrollable and/or unobservable parts as follows: -C = 'M': Remove both the uncontrollable and unobservable -C parts to get a minimal state-space representation; -C = 'C': Remove the uncontrollable part only to get a -C controllable state-space representation; -C = 'O': Remove the unobservable part only to get an -C observable state-space representation. -C -C EQUIL CHARACTER*1 -C Specifies whether the user wishes to preliminarily balance -C the triplet (A,B,C) as follows: -C = 'S': Perform balancing (scaling); -C = 'N': Do not perform balancing. -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the original state-space representation, i.e. -C the order of the matrix A. N >= 0. -C -C M (input) INTEGER -C The number of system inputs. M >= 0. -C -C P (input) INTEGER -C The number of system outputs. P >= 0. -C -C A (input/output) DOUBLE PRECISION array, dimension (LDA,N) -C On entry, the leading N-by-N part of this array must -C contain the original state dynamics matrix A. -C On exit, the leading NR-by-NR part of this array contains -C the upper block Hessenberg state dynamics matrix Ar of a -C minimal, controllable, or observable realization for the -C original system, depending on the value of JOB, JOB = 'M', -C JOB = 'C', or JOB = 'O', respectively. -C -C LDA INTEGER -C The leading dimension of array A. LDA >= MAX(1,N). -C -C B (input/output) DOUBLE PRECISION array, dimension (LDB,M), -C if JOB = 'C', or (LDB,MAX(M,P)), otherwise. -C On entry, the leading N-by-M part of this array must -C contain the original input/state matrix B; if JOB = 'M', -C or JOB = 'O', the remainder of the leading N-by-MAX(M,P) -C part is used as internal workspace. -C On exit, the leading NR-by-M part of this array contains -C the transformed input/state matrix Br of a minimal, -C controllable, or observable realization for the original -C system, depending on the value of JOB, JOB = 'M', -C JOB = 'C', or JOB = 'O', respectively. -C If JOB = 'C', only the first IWORK(1) rows of B are -C nonzero. -C -C LDB INTEGER -C The leading dimension of array B. LDB >= MAX(1,N). -C -C C (input/output) DOUBLE PRECISION array, dimension (LDC,N) -C On entry, the leading P-by-N part of this array must -C contain the original state/output matrix C; if JOB = 'M', -C or JOB = 'O', the remainder of the leading MAX(M,P)-by-N -C part is used as internal workspace. -C On exit, the leading P-by-NR part of this array contains -C the transformed state/output matrix Cr of a minimal, -C controllable, or observable realization for the original -C system, depending on the value of JOB, JOB = 'M', -C JOB = 'C', or JOB = 'O', respectively. -C If JOB = 'M', or JOB = 'O', only the last IWORK(1) columns -C (in the first NR columns) of C are nonzero. -C -C LDC INTEGER -C The leading dimension of array C. -C LDC >= MAX(1,M,P) if N > 0. -C LDC >= 1 if N = 0. -C -C NR (output) INTEGER -C The order of the reduced state-space representation -C (Ar,Br,Cr) of a minimal, controllable, or observable -C realization for the original system, depending on -C JOB = 'M', JOB = 'C', or JOB = 'O'. -C -C Tolerances -C -C TOL DOUBLE PRECISION -C The tolerance to be used in rank determination when -C transforming (A, B, C). If the user sets TOL > 0, then -C the given value of TOL is used as a lower bound for the -C reciprocal condition number (see the description of the -C argument RCOND in the SLICOT routine MB03OD); a -C (sub)matrix whose estimated condition number is less than -C 1/TOL is considered to be of full rank. If the user sets -C TOL <= 0, then an implicitly computed, default tolerance -C (determined by the SLICOT routine TB01UD) is used instead. -C -C Workspace -C -C IWORK INTEGER array, dimension (N+MAX(M,P)) -C On exit, if INFO = 0, the first nonzero elements of -C IWORK(1:N) return the orders of the diagonal blocks of A. -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C On exit, if INFO = 0, DWORK(1) returns the optimal value -C of LDWORK. -C -C LDWORK INTEGER -C The length of the array DWORK. -C LDWORK >= MAX(1, N + MAX(N, 3*M, 3*P)). -C For optimum performance LDWORK should be larger. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value. -C -C METHOD -C -C If JOB = 'M', the matrices A and B are operated on by orthogonal -C similarity transformations (made up of products of Householder -C transformations) so as to produce an upper block Hessenberg matrix -C A1 and a matrix B1 with all but its first rank(B) rows zero; this -C separates out the controllable part of the original system. -C Applying the same algorithm to the dual of this subsystem, -C therefore separates out the controllable and observable (i.e. -C minimal) part of the original system representation, with the -C final Ar upper block Hessenberg (after using pertransposition). -C If JOB = 'C', or JOB = 'O', only the corresponding part of the -C above procedure is applied. -C -C REFERENCES -C -C [1] Van Dooren, P. -C The Generalized Eigenstructure Problem in Linear System -C Theory. (Algorithm 1) -C IEEE Trans. Auto. Contr., AC-26, pp. 111-129, 1981. -C -C NUMERICAL ASPECTS -C 3 -C The algorithm requires 0(N ) operations and is backward stable. -C -C CONTRIBUTOR -C -C V. Sima, Katholieke Univ. Leuven, Belgium, Feb. 1998. -C -C REVISIONS -C -C A. Varga, DLR Oberpfaffenhofen, July 1998. -C A. Varga, DLR Oberpfaffenhofen, April 28, 1999. -C V. Sima, Research Institute for Informatics, Bucharest, Mar. 2004. -C -C KEYWORDS -C -C Hessenberg form, minimal realization, multivariable system, -C orthogonal transformation, state-space model, state-space -C representation. -C -C ****************************************************************** -C -C .. Parameters .. - INTEGER LDIZ - PARAMETER ( LDIZ = 1 ) - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) -C .. Scalar Arguments .. - CHARACTER EQUIL, JOB - INTEGER INFO, LDA, LDB, LDC, LDWORK, M, N, NR, P - DOUBLE PRECISION TOL -C .. Array Arguments .. - INTEGER IWORK(*) - DOUBLE PRECISION A(LDA,*), B(LDB,*), C(LDC,*), DWORK(*) -C .. Local Scalars .. - LOGICAL LEQUIL, LNJOBC, LNJOBO - INTEGER I, INDCON, ITAU, IZ, JWORK, KL, MAXMP, NCONT, - $ WRKOPT - DOUBLE PRECISION MAXRED -C .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -C .. External Subroutines .. - EXTERNAL AB07MD, TB01ID, TB01UD, TB01XD, XERBLA -C .. Intrinsic Functions .. - INTRINSIC INT, MAX, MIN -C .. Executable Statements .. -C - INFO = 0 - MAXMP = MAX( M, P ) - LNJOBC = .NOT.LSAME( JOB, 'C' ) - LNJOBO = .NOT.LSAME( JOB, 'O' ) - LEQUIL = LSAME( EQUIL, 'S' ) -C -C Test the input scalar arguments. -C - IF( LNJOBC .AND. LNJOBO .AND. .NOT.LSAME( JOB, 'M' ) ) THEN - INFO = -1 - ELSE IF( .NOT.LEQUIL .AND. .NOT.LSAME( EQUIL, 'N' ) ) THEN - INFO = -2 - ELSE IF( N.LT.0 ) THEN - INFO = -3 - ELSE IF( M.LT.0 ) THEN - INFO = -4 - ELSE IF( P.LT.0 ) THEN - INFO = -5 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -7 - ELSE IF( LDB.LT.MAX( 1, N ) ) THEN - INFO = -9 - ELSE IF( LDC.LT.1 .OR. ( N.GT.0 .AND. LDC.LT.MAXMP ) ) THEN - INFO = -11 - ELSE IF( LDWORK.LT.MAX( 1, N + MAX( N, 3*MAXMP ) ) ) THEN - INFO = -16 - END IF -C - IF ( INFO.NE.0 ) THEN -C -C Error return. -C - CALL XERBLA( 'TB01PD', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF ( N.EQ.0 .OR. ( LNJOBC .AND. MIN( N, P ).EQ.0 ) .OR. - $ ( LNJOBO .AND. MIN( N, M ).EQ.0 ) ) THEN - NR = 0 -C - DO 5 I = 1, N - IWORK(I) = 0 - 5 CONTINUE -C - DWORK(1) = ONE - RETURN - END IF -C -C If required, balance the triplet (A,B,C) (default MAXRED). -C Workspace: need N. -C -C (Note: Comments in the code beginning "Workspace:" describe the -C minimal amount of real workspace needed at that point in the code, -C as well as the preferred amount for good performance.) -C - IF ( LEQUIL ) THEN - MAXRED = ZERO - CALL TB01ID( 'A', N, M, P, MAXRED, A, LDA, B, LDB, C, LDC, - $ DWORK, INFO ) - WRKOPT = N - ELSE - WRKOPT = 1 - END IF -C - IZ = 1 - ITAU = 1 - JWORK = ITAU + N - IF ( LNJOBO ) THEN -C -C Separate out controllable subsystem (of order NCONT): -C A <-- Z'*A*Z, B <-- Z'*B, C <-- C*Z. -C -C Workspace: need N + MAX(N, 3*M, P). -C prefer larger. -C - CALL TB01UD( 'No Z', N, M, P, A, LDA, B, LDB, C, LDC, NCONT, - $ INDCON, IWORK, DWORK(IZ), LDIZ, DWORK(ITAU), TOL, - $ IWORK(N+1), DWORK(JWORK), LDWORK-JWORK+1, INFO ) -C - WRKOPT = INT( DWORK(JWORK) ) + JWORK - 1 - ELSE - NCONT = N - END IF -C - IF ( LNJOBC ) THEN -C -C Separate out the observable subsystem (of order NR): -C Form the dual of the subsystem of order NCONT (which is -C controllable, if JOB = 'M'), leaving rest as it is. -C - CALL AB07MD( 'Z', NCONT, M, P, A, LDA, B, LDB, C, LDC, DWORK, - $ 1, INFO ) -C -C And separate out the controllable part of this dual subsystem. -C -C Workspace: need NCONT + MAX(NCONT, 3*P, M). -C prefer larger. -C - CALL TB01UD( 'No Z', NCONT, P, M, A, LDA, B, LDB, C, LDC, NR, - $ INDCON, IWORK, DWORK(IZ), LDIZ, DWORK(ITAU), TOL, - $ IWORK(N+1), DWORK(JWORK), LDWORK-JWORK+1, INFO ) -C - WRKOPT = MAX( WRKOPT, INT( DWORK(JWORK) )+JWORK-1 ) -C -C Transpose and reorder (to get a block upper Hessenberg -C matrix A), giving, for JOB = 'M', the controllable and -C observable (i.e., minimal) part of original system. -C - IF( INDCON.GT.0 ) THEN - KL = IWORK(1) - 1 - IF ( INDCON.GE.2 ) - $ KL = KL + IWORK(2) - ELSE - KL = 0 - END IF - CALL TB01XD( 'Zero D', NR, P, M, KL, MAX( 0, NR-1 ), A, LDA, - $ B, LDB, C, LDC, DWORK, 1, INFO ) - ELSE - NR = NCONT - END IF -C -C Annihilate the trailing components of IWORK(1:N). -C - DO 10 I = INDCON + 1, N - IWORK(I) = 0 - 10 CONTINUE -C -C Set optimal workspace dimension. -C - DWORK(1) = WRKOPT - RETURN -C *** Last line of TB01PD *** - END
--- a/extra/control-devel/devel/dksyn/TB01UD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,491 +0,0 @@ - SUBROUTINE TB01UD( JOBZ, N, M, P, A, LDA, B, LDB, C, LDC, NCONT, - $ INDCON, NBLK, Z, LDZ, TAU, TOL, IWORK, DWORK, - $ LDWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To find a controllable realization for the linear time-invariant -C multi-input system -C -C dX/dt = A * X + B * U, -C Y = C * X, -C -C where A, B, and C are N-by-N, N-by-M, and P-by-N matrices, -C respectively, and A and B are reduced by this routine to -C orthogonal canonical form using (and optionally accumulating) -C orthogonal similarity transformations, which are also applied -C to C. Specifically, the system (A, B, C) is reduced to the -C triplet (Ac, Bc, Cc), where Ac = Z' * A * Z, Bc = Z' * B, -C Cc = C * Z, with -C -C [ Acont * ] [ Bcont ] -C Ac = [ ], Bc = [ ], -C [ 0 Auncont ] [ 0 ] -C -C and -C -C [ A11 A12 . . . A1,p-1 A1p ] [ B1 ] -C [ A21 A22 . . . A2,p-1 A2p ] [ 0 ] -C [ 0 A32 . . . A3,p-1 A3p ] [ 0 ] -C Acont = [ . . . . . . . ], Bc = [ . ], -C [ . . . . . . ] [ . ] -C [ . . . . . ] [ . ] -C [ 0 0 . . . Ap,p-1 App ] [ 0 ] -C -C where the blocks B1, A21, ..., Ap,p-1 have full row ranks and -C p is the controllability index of the pair. The size of the -C block Auncont is equal to the dimension of the uncontrollable -C subspace of the pair (A, B). -C -C ARGUMENTS -C -C Mode Parameters -C -C JOBZ CHARACTER*1 -C Indicates whether the user wishes to accumulate in a -C matrix Z the orthogonal similarity transformations for -C reducing the system, as follows: -C = 'N': Do not form Z and do not store the orthogonal -C transformations; -C = 'F': Do not form Z, but store the orthogonal -C transformations in the factored form; -C = 'I': Z is initialized to the unit matrix and the -C orthogonal transformation matrix Z is returned. -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the original state-space representation, -C i.e. the order of the matrix A. N >= 0. -C -C M (input) INTEGER -C The number of system inputs, or of columns of B. M >= 0. -C -C P (input) INTEGER -C The number of system outputs, or of rows of C. P >= 0. -C -C A (input/output) DOUBLE PRECISION array, dimension (LDA,N) -C On entry, the leading N-by-N part of this array must -C contain the original state dynamics matrix A. -C On exit, the leading NCONT-by-NCONT part contains the -C upper block Hessenberg state dynamics matrix Acont in Ac, -C given by Z' * A * Z, of a controllable realization for -C the original system. The elements below the first block- -C subdiagonal are set to zero. The leading N-by-N part -C contains the matrix Ac. -C -C LDA INTEGER -C The leading dimension of array A. LDA >= MAX(1,N). -C -C B (input/output) DOUBLE PRECISION array, dimension (LDB,M) -C On entry, the leading N-by-M part of this array must -C contain the input matrix B. -C On exit, the leading NCONT-by-M part of this array -C contains the transformed input matrix Bcont in Bc, given -C by Z' * B, with all elements but the first block set to -C zero. The leading N-by-M part contains the matrix Bc. -C -C LDB INTEGER -C The leading dimension of array B. LDB >= MAX(1,N). -C -C C (input/output) DOUBLE PRECISION array, dimension (LDC,N) -C On entry, the leading P-by-N part of this array must -C contain the output matrix C. -C On exit, the leading P-by-N part of this array contains -C the transformed output matrix Cc, given by C * Z. -C -C LDC INTEGER -C The leading dimension of array C. LDC >= MAX(1,P). -C -C NCONT (output) INTEGER -C The order of the controllable state-space representation. -C -C INDCON (output) INTEGER -C The controllability index of the controllable part of the -C system representation. -C -C NBLK (output) INTEGER array, dimension (N) -C The leading INDCON elements of this array contain the -C the orders of the diagonal blocks of Acont. -C -C Z (output) DOUBLE PRECISION array, dimension (LDZ,N) -C If JOBZ = 'I', then the leading N-by-N part of this -C array contains the matrix of accumulated orthogonal -C similarity transformations which reduces the given system -C to orthogonal canonical form. -C If JOBZ = 'F', the elements below the diagonal, with the -C array TAU, represent the orthogonal transformation matrix -C as a product of elementary reflectors. The transformation -C matrix can then be obtained by calling the LAPACK Library -C routine DORGQR. -C If JOBZ = 'N', the array Z is not referenced and can be -C supplied as a dummy array (i.e. set parameter LDZ = 1 and -C declare this array to be Z(1,1) in the calling program). -C -C LDZ INTEGER -C The leading dimension of array Z. If JOBZ = 'I' or -C JOBZ = 'F', LDZ >= MAX(1,N); if JOBZ = 'N', LDZ >= 1. -C -C TAU (output) DOUBLE PRECISION array, dimension (N) -C The elements of TAU contain the scalar factors of the -C elementary reflectors used in the reduction of B and A. -C -C Tolerances -C -C TOL DOUBLE PRECISION -C The tolerance to be used in rank determination when -C transforming (A, B). If the user sets TOL > 0, then -C the given value of TOL is used as a lower bound for the -C reciprocal condition number (see the description of the -C argument RCOND in the SLICOT routine MB03OD); a -C (sub)matrix whose estimated condition number is less than -C 1/TOL is considered to be of full rank. If the user sets -C TOL <= 0, then an implicitly computed, default tolerance, -C defined by TOLDEF = N*N*EPS, is used instead, where EPS -C is the machine precision (see LAPACK Library routine -C DLAMCH). -C -C Workspace -C -C IWORK INTEGER array, dimension (M) -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C On exit, if INFO = 0, DWORK(1) returns the optimal value -C of LDWORK. -C -C LDWORK INTEGER -C The length of the array DWORK. -C LDWORK >= MAX(1, N, 3*M, P). -C For optimum performance LDWORK should be larger. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value. -C -C METHOD -C -C Matrix B is first QR-decomposed and the appropriate orthogonal -C similarity transformation applied to the matrix A. Leaving the -C first rank(B) states unchanged, the remaining lower left block -C of A is then QR-decomposed and the new orthogonal matrix, Q1, -C is also applied to the right of A to complete the similarity -C transformation. By continuing in this manner, a completely -C controllable state-space pair (Acont, Bcont) is found for the -C given (A, B), where Acont is upper block Hessenberg with each -C subdiagonal block of full row rank, and Bcont is zero apart from -C its (independent) first rank(B) rows. -C All orthogonal transformations determined in this process are also -C applied to the matrix C, from the right. -C NOTE that the system controllability indices are easily -C calculated from the dimensions of the blocks of Acont. -C -C REFERENCES -C -C [1] Konstantinov, M.M., Petkov, P.Hr. and Christov, N.D. -C Orthogonal Invariants and Canonical Forms for Linear -C Controllable Systems. -C Proc. 8th IFAC World Congress, Kyoto, 1, pp. 49-54, 1981. -C -C [2] Paige, C.C. -C Properties of numerical algorithms related to computing -C controllablity. -C IEEE Trans. Auto. Contr., AC-26, pp. 130-138, 1981. -C -C [3] Petkov, P.Hr., Konstantinov, M.M., Gu, D.W. and -C Postlethwaite, I. -C Optimal Pole Assignment Design of Linear Multi-Input Systems. -C Leicester University, Report 99-11, May 1996. -C -C NUMERICAL ASPECTS -C 3 -C The algorithm requires 0(N ) operations and is backward stable. -C -C FURTHER COMMENTS -C -C If the system matrices A and B are badly scaled, it would be -C useful to scale them with SLICOT routine TB01ID, before calling -C the routine. -C -C CONTRIBUTOR -C -C V. Sima, Katholieke Univ. Leuven, Belgium, Feb. 1998. -C -C REVISIONS -C -C V. Sima, Katholieke Univ. Leuven, Belgium, May 1999, Nov. 2003. -C A. Varga, DLR Oberpfaffenhofen, March 2002, Nov. 2003. -C -C KEYWORDS -C -C Controllability, minimal realization, orthogonal canonical form, -C orthogonal transformation. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) -C .. Scalar Arguments .. - CHARACTER JOBZ - INTEGER INDCON, INFO, LDA, LDB, LDC, LDWORK, LDZ, M, N, - $ NCONT, P - DOUBLE PRECISION TOL -C .. Array Arguments .. - DOUBLE PRECISION A(LDA,*), B(LDB,*), C(LDC,*), DWORK(*), TAU(*), - $ Z(LDZ,*) - INTEGER IWORK(*), NBLK(*) -C .. Local Scalars .. - LOGICAL LJOBF, LJOBI, LJOBZ - INTEGER IQR, ITAU, J, MCRT, NBL, NCRT, NI, NJ, RANK, - $ WRKOPT - DOUBLE PRECISION ANORM, BNORM, FNRM, TOLDEF -C .. Local Arrays .. - DOUBLE PRECISION SVAL(3) -C .. External Functions .. - LOGICAL LSAME - DOUBLE PRECISION DLAMCH, DLANGE, DLAPY2 - EXTERNAL DLAMCH, DLANGE, DLAPY2, LSAME -C .. External Subroutines .. - EXTERNAL DCOPY, DLACPY, DLAPMT, DLASET, DORGQR, DORMQR, - $ MB01PD, MB03OY, XERBLA -C .. Intrinsic Functions .. - INTRINSIC DBLE, INT, MAX, MIN -C .. -C .. Executable Statements .. -C - INFO = 0 - LJOBF = LSAME( JOBZ, 'F' ) - LJOBI = LSAME( JOBZ, 'I' ) - LJOBZ = LJOBF.OR.LJOBI -C -C Test the input scalar arguments. -C - IF( .NOT.LJOBZ .AND. .NOT.LSAME( JOBZ, 'N' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( M.LT.0 ) THEN - INFO = -3 - ELSE IF( P.LT.0 ) THEN - INFO = -4 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -6 - ELSE IF( LDB.LT.MAX( 1, N ) ) THEN - INFO = -8 - ELSE IF( LDC.LT.MAX( 1, P ) ) THEN - INFO = -10 - ELSE IF( .NOT.LJOBZ .AND. LDZ.LT.1 .OR. - $ LJOBZ .AND. LDZ.LT.MAX( 1, N ) ) THEN - INFO = -15 - ELSE IF( LDWORK.LT.MAX( 1, N, 3*M, P ) ) THEN - INFO = -20 - END IF -C - IF ( INFO.NE.0 ) THEN -C -C Error return. -C - CALL XERBLA( 'TB01UD', -INFO ) - RETURN - END IF -C - NCONT = 0 - INDCON = 0 -C -C Calculate the absolute norms of A and B (used for scaling). -C - ANORM = DLANGE( 'M', N, N, A, LDA, DWORK ) - BNORM = DLANGE( 'M', N, M, B, LDB, DWORK ) -C -C Quick return if possible. -C - IF ( MIN( N, M ).EQ.0 .OR. BNORM.EQ.ZERO ) THEN - IF( N.GT.0 ) THEN - IF ( LJOBI ) THEN - CALL DLASET( 'Full', N, N, ZERO, ONE, Z, LDZ ) - ELSE IF ( LJOBF ) THEN - CALL DLASET( 'Full', N, N, ZERO, ZERO, Z, LDZ ) - CALL DLASET( 'Full', N, 1, ZERO, ZERO, TAU, N ) - END IF - END IF - DWORK(1) = ONE - RETURN - END IF -C -C Scale (if needed) the matrices A and B. -C - CALL MB01PD( 'S', 'G', N, N, 0, 0, ANORM, 0, NBLK, A, LDA, INFO ) - CALL MB01PD( 'S', 'G', N, M, 0, 0, BNORM, 0, NBLK, B, LDB, INFO ) -C -C Compute the Frobenius norm of [ B A ] (used for rank estimation). -C - FNRM = DLAPY2( DLANGE( 'F', N, M, B, LDB, DWORK ), - $ DLANGE( 'F', N, N, A, LDA, DWORK ) ) -C - TOLDEF = TOL - IF ( TOLDEF.LE.ZERO ) THEN -C -C Use the default tolerance in controllability determination. -C - TOLDEF = DBLE( N*N )*DLAMCH( 'EPSILON' ) - END IF -C - IF ( FNRM.LT.TOLDEF ) - $ FNRM = ONE -C - WRKOPT = 1 - NI = 0 - ITAU = 1 - NCRT = N - MCRT = M - IQR = 1 -C -C (Note: Comments in the code beginning "Workspace:" describe the -C minimal amount of real workspace needed at that point in the -C code, as well as the preferred amount for good performance. -C NB refers to the optimal block size for the immediately -C following subroutine, as returned by ILAENV.) -C - 10 CONTINUE -C -C Rank-revealing QR decomposition with column pivoting. -C The calculation is performed in NCRT rows of B starting from -C the row IQR (initialized to 1 and then set to rank(B)+1). -C Workspace: 3*MCRT. -C - CALL MB03OY( NCRT, MCRT, B(IQR,1), LDB, TOLDEF, FNRM, RANK, - $ SVAL, IWORK, TAU(ITAU), DWORK, INFO ) -C - IF ( RANK.NE.0 ) THEN - NJ = NI - NI = NCONT - NCONT = NCONT + RANK - INDCON = INDCON + 1 - NBLK(INDCON) = RANK -C -C Premultiply and postmultiply the appropriate block row -C and block column of A by Q' and Q, respectively. -C Workspace: need NCRT; -C prefer NCRT*NB. -C - CALL DORMQR( 'Left', 'Transpose', NCRT, NCRT, RANK, - $ B(IQR,1), LDB, TAU(ITAU), A(NI+1,NI+1), LDA, - $ DWORK, LDWORK, INFO ) - WRKOPT = MAX( WRKOPT, INT( DWORK(1) ) ) -C -C Workspace: need N; -C prefer N*NB. -C - CALL DORMQR( 'Right', 'No transpose', N, NCRT, RANK, - $ B(IQR,1), LDB, TAU(ITAU), A(1,NI+1), LDA, - $ DWORK, LDWORK, INFO ) - WRKOPT = MAX( WRKOPT, INT( DWORK(1) ) ) -C -C Postmultiply the appropriate block column of C by Q. -C Workspace: need P; -C prefer P*NB. -C - CALL DORMQR( 'Right', 'No transpose', P, NCRT, RANK, - $ B(IQR,1), LDB, TAU(ITAU), C(1,NI+1), LDC, - $ DWORK, LDWORK, INFO ) - WRKOPT = MAX( WRKOPT, INT( DWORK(1) ) ) -C -C If required, save transformations. -C - IF ( LJOBZ.AND.NCRT.GT.1 ) THEN - CALL DLACPY( 'L', NCRT-1, MIN( RANK, NCRT-1 ), - $ B(IQR+1,1), LDB, Z(NI+2,ITAU), LDZ ) - END IF -C -C Zero the subdiagonal elements of the current matrix. -C - IF ( RANK.GT.1 ) - $ CALL DLASET( 'L', RANK-1, RANK-1, ZERO, ZERO, B(IQR+1,1), - $ LDB ) -C -C Backward permutation of the columns of B or A. -C - IF ( INDCON.EQ.1 ) THEN - CALL DLAPMT( .FALSE., RANK, M, B(IQR,1), LDB, IWORK ) - IQR = RANK + 1 - ELSE - DO 20 J = 1, MCRT - CALL DCOPY( RANK, B(IQR,J), 1, A(NI+1,NJ+IWORK(J)), - $ 1 ) - 20 CONTINUE - END IF -C - ITAU = ITAU + RANK - IF ( RANK.NE.NCRT ) THEN - MCRT = RANK - NCRT = NCRT - RANK - CALL DLACPY( 'G', NCRT, MCRT, A(NCONT+1,NI+1), LDA, - $ B(IQR,1), LDB ) - CALL DLASET( 'G', NCRT, MCRT, ZERO, ZERO, - $ A(NCONT+1,NI+1), LDA ) - GO TO 10 - END IF - END IF -C -C If required, accumulate transformations. -C Workspace: need N; prefer N*NB. -C - IF ( LJOBI ) THEN - CALL DORGQR( N, N, ITAU-1, Z, LDZ, TAU, DWORK, - $ LDWORK, INFO ) - WRKOPT = MAX( WRKOPT, INT( DWORK(1) ) ) - END IF -C -C Annihilate the trailing blocks of B. -C - IF( IQR.LE.N ) - $ CALL DLASET( 'G', N-IQR+1, M, ZERO, ZERO, B(IQR,1), LDB ) -C -C Annihilate the trailing elements of TAU, if JOBZ = 'F'. -C - IF ( LJOBF ) THEN - DO 30 J = ITAU, N - TAU(J) = ZERO - 30 CONTINUE - END IF -C -C Undo scaling of A and B. -C - IF ( INDCON.LT.N ) THEN - NBL = INDCON + 1 - NBLK(NBL) = N - NCONT - ELSE - NBL = 0 - END IF - CALL MB01PD( 'U', 'H', N, N, 0, 0, ANORM, NBL, NBLK, A, LDA, - $ INFO ) - CALL MB01PD( 'U', 'G', NBLK(1), M, 0, 0, BNORM, 0, NBLK, B, LDB, - $ INFO ) -C -C Set optimal workspace dimension. -C - DWORK(1) = WRKOPT - RETURN -C *** Last line of TB01UD *** - END
--- a/extra/control-devel/devel/dksyn/TB01XD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,284 +0,0 @@ - SUBROUTINE TB01XD( JOBD, N, M, P, KL, KU, A, LDA, B, LDB, C, LDC, - $ D, LDD, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To apply a special transformation to a system given as a triple -C (A,B,C), -C -C A <-- P * A' * P, B <-- P * C', C <-- B' * P, -C -C where P is a matrix with 1 on the secondary diagonal, and with 0 -C in the other entries. Matrix A can be specified as a band matrix. -C Optionally, matrix D of the system can be transposed. This -C transformation is actually a special similarity transformation of -C the dual system. -C -C ARGUMENTS -C -C Mode Parameters -C -C JOBD CHARACTER*1 -C Specifies whether or not a non-zero matrix D appears in -C the given state space model: -C = 'D': D is present; -C = 'Z': D is assumed a zero matrix. -C -C Input/Output Parameters -C -C N (input) INTEGER -C The order of the matrix A, the number of rows of matrix B -C and the number of columns of matrix C. -C N represents the dimension of the state vector. N >= 0. -C -C M (input) INTEGER. -C The number of columns of matrix B. -C M represents the dimension of input vector. M >= 0. -C -C P (input) INTEGER. -C The number of rows of matrix C. -C P represents the dimension of output vector. P >= 0. -C -C KL (input) INTEGER -C The number of subdiagonals of A to be transformed. -C MAX( 0, N-1 ) >= KL >= 0. -C -C KU (input) INTEGER -C The number of superdiagonals of A to be transformed. -C MAX( 0, N-1 ) >= KU >= 0. -C -C A (input/output) DOUBLE PRECISION array, dimension (LDA,N) -C On entry, the leading N-by-N part of this array must -C contain the system state matrix A. -C On exit, the leading N-by-N part of this array contains -C the transformed (pertransposed) matrix P*A'*P. -C -C LDA INTEGER -C The leading dimension of the array A. LDA >= MAX(1,N). -C -C B (input/output) DOUBLE PRECISION array, dimension -C (LDB,MAX(M,P)) -C On entry, the leading N-by-M part of this array must -C contain the original input/state matrix B. -C On exit, the leading N-by-P part of this array contains -C the dual input/state matrix P*C'. -C -C LDB INTEGER -C The leading dimension of the array B. -C LDB >= MAX(1,N) if M > 0 or P > 0. -C LDB >= 1 if M = 0 and P = 0. -C -C C (input/output) DOUBLE PRECISION array, dimension (LDC,N) -C On entry, the leading P-by-N part of this array must -C contain the original state/output matrix C. -C On exit, the leading M-by-N part of this array contains -C the dual state/output matrix B'*P. -C -C LDC INTEGER -C The leading dimension of array C. -C LDC >= MAX(1,M,P) if N > 0. -C LDC >= 1 if N = 0. -C -C D (input/output) DOUBLE PRECISION array, dimension -C (LDD,MAX(M,P)) -C On entry, if JOBD = 'D', the leading P-by-M part of this -C array must contain the original direct transmission -C matrix D. -C On exit, if JOBD = 'D', the leading M-by-P part of this -C array contains the transposed direct transmission matrix -C D'. The array D is not referenced if JOBD = 'Z'. -C -C LDD INTEGER -C The leading dimension of array D. -C LDD >= MAX(1,M,P) if JOBD = 'D'. -C LDD >= 1 if JOBD = 'Z'. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit. -C < 0: if INFO = -i, the i-th argument had an illegal -C value. -C -C METHOD -C -C The rows and/or columns of the matrices of the triplet (A,B,C) -C and, optionally, of the matrix D are swapped in a special way. -C -C NUMERICAL ASPECTS -C -C None. -C -C CONTRIBUTOR -C -C V. Sima, Katholieke Univ. Leuven, Belgium, Feb. 1998. -C Partly based on routine DMPTR (A. Varga, German Aerospace -C Research Establishment, DLR, Aug. 1992). -C -C -C REVISIONS -C -C 07-31-1998, 04-25-1999, A. Varga. -C 03-16-2004, V. Sima. -C -C KEYWORDS -C -C Matrix algebra, matrix operations, similarity transformation. -C -C ********************************************************************* -C -C .. -C .. Scalar Arguments .. - CHARACTER JOBD - INTEGER INFO, KL, KU, LDA, LDB, LDC, LDD, M, N, P -C .. -C .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ), - $ D( LDD, * ) -C .. -C .. Local Scalars .. - LOGICAL LJOBD - INTEGER J, J1, LDA1, MAXMP, MINMP, NM1 -C .. -C .. External functions .. - LOGICAL LSAME - EXTERNAL LSAME -C .. -C .. External Subroutines .. - EXTERNAL DCOPY, DSWAP, XERBLA -C .. -C .. Intrinsic Functions .. - INTRINSIC MAX, MIN -C .. -C .. Executable Statements .. -C -C Test the scalar input arguments. -C - INFO = 0 - LJOBD = LSAME( JOBD, 'D' ) - MAXMP = MAX( M, P ) - MINMP = MIN( M, P ) - NM1 = N - 1 -C - IF( .NOT.LJOBD .AND. .NOT.LSAME( JOBD, 'Z' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( M.LT.0 ) THEN - INFO = -3 - ELSE IF( P.LT.0 ) THEN - INFO = -4 - ELSE IF( KL.LT.0 .OR. KL.GT.MAX( 0, NM1 ) ) THEN - INFO = -5 - ELSE IF( KU.LT.0 .OR. KU.GT.MAX( 0, NM1 ) ) THEN - INFO = -6 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -8 - ELSE IF( ( MAXMP.GT.0 .AND. LDB.LT.MAX( 1, N ) ) .OR. - $ ( MINMP.EQ.0 .AND. LDB.LT.1 ) ) THEN - INFO = -10 - ELSE IF( LDC.LT.1 .OR. ( N.GT.0 .AND. LDC.LT.MAXMP ) ) THEN - INFO = -12 - ELSE IF( LDD.LT.1 .OR. ( LJOBD .AND. LDD.LT.MAXMP ) ) THEN - INFO = -14 - END IF -C - IF( INFO.NE.0 ) THEN -C -C Error return. -C - CALL XERBLA( 'TB01XD', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF ( LJOBD ) THEN -C -C Replace D by D', if non-scalar. -C - DO 5 J = 1, MAXMP - IF ( J.LT.MINMP ) THEN - CALL DSWAP( MINMP-J, D(J+1,J), 1, D(J,J+1), LDD ) - ELSE IF ( J.GT.P ) THEN - CALL DCOPY( P, D(1,J), 1, D(J,1), LDD ) - ELSE IF ( J.GT.M ) THEN - CALL DCOPY( M, D(J,1), LDD, D(1,J), 1 ) - END IF - 5 CONTINUE -C - END IF -C - IF( N.EQ.0 ) - $ RETURN -C -C Replace matrix A by P*A'*P. -C - IF ( KL.EQ.NM1 .AND. KU.EQ.NM1 ) THEN -C -C Full matrix A. -C - DO 10 J = 1, NM1 - CALL DSWAP( N-J, A( 1, J ), 1, A( N-J+1, J+1 ), -LDA ) - 10 CONTINUE -C - ELSE -C -C Band matrix A. -C - LDA1 = LDA + 1 -C -C Pertranspose the KL subdiagonals. -C - DO 20 J = 1, MIN( KL, N-2 ) - J1 = ( N - J )/2 - CALL DSWAP( J1, A(J+1,1), LDA1, A(N-J1+1,N-J1+1-J), -LDA1 ) - 20 CONTINUE -C -C Pertranspose the KU superdiagonals. -C - DO 30 J = 1, MIN( KU, N-2 ) - J1 = ( N - J )/2 - CALL DSWAP( J1, A(1,J+1), LDA1, A(N-J1+1-J,N-J1+1), -LDA1 ) - 30 CONTINUE -C -C Pertranspose the diagonal. -C - J1 = N/2 - CALL DSWAP( J1, A(1,1), LDA1, A(N-J1+1,N-J1+1), -LDA1 ) -C - END IF -C -C Replace matrix B by P*C' and matrix C by B'*P. -C - DO 40 J = 1, MAXMP - IF ( J.LE.MINMP ) THEN - CALL DSWAP( N, B(1,J), 1, C(J,1), -LDC ) - ELSE IF ( J.GT.P ) THEN - CALL DCOPY( N, B(1,J), 1, C(J,1), -LDC ) - ELSE - CALL DCOPY( N, C(J,1), -LDC, B(1,J), 1 ) - END IF - 40 CONTINUE -C - RETURN -C *** Last line of TB01XD *** - END
--- a/extra/control-devel/devel/dksyn/TB05AD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,545 +0,0 @@ - SUBROUTINE TB05AD( BALEIG, INITA, N, M, P, FREQ, A, LDA, B, LDB, - $ C, LDC, RCOND, G, LDG, EVRE, EVIM, HINVB, - $ LDHINV, IWORK, DWORK, LDWORK, ZWORK, LZWORK, - $ INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To find the complex frequency response matrix (transfer matrix) -C G(freq) of the state-space representation (A,B,C) given by -C -1 -C G(freq) = C * ((freq*I - A) ) * B -C -C where A, B and C are real N-by-N, N-by-M and P-by-N matrices -C respectively and freq is a complex scalar. -C -C ARGUMENTS -C -C Mode Parameters -C -C BALEIG CHARACTER*1 -C Determines whether the user wishes to balance matrix A -C and/or compute its eigenvalues and/or estimate the -C condition number of the problem as follows: -C = 'N': The matrix A should not be balanced and neither -C the eigenvalues of A nor the condition number -C estimate of the problem are to be calculated; -C = 'C': The matrix A should not be balanced and only an -C estimate of the condition number of the problem -C is to be calculated; -C = 'B' or 'E' and INITA = 'G': The matrix A is to be -C balanced and its eigenvalues calculated; -C = 'A' and INITA = 'G': The matrix A is to be balanced, -C and its eigenvalues and an estimate of the -C condition number of the problem are to be -C calculated. -C -C INITA CHARACTER*1 -C Specifies whether or not the matrix A is already in upper -C Hessenberg form as follows: -C = 'G': The matrix A is a general matrix; -C = 'H': The matrix A is in upper Hessenberg form and -C neither balancing nor the eigenvalues of A are -C required. -C INITA must be set to 'G' for the first call to the -C routine, unless the matrix A is already in upper -C Hessenberg form and neither balancing nor the eigenvalues -C of A are required. Thereafter, it must be set to 'H' for -C all subsequent calls. -C -C Input/Output Parameters -C -C N (input) INTEGER -C The number of states, i.e. the order of the state -C transition matrix A. N >= 0. -C -C M (input) INTEGER -C The number of inputs, i.e. the number of columns in the -C matrix B. M >= 0. -C -C P (input) INTEGER -C The number of outputs, i.e. the number of rows in the -C matrix C. P >= 0. -C -C FREQ (input) COMPLEX*16 -C The frequency freq at which the frequency response matrix -C (transfer matrix) is to be evaluated. -C -C A (input/output) DOUBLE PRECISION array, dimension (LDA,N) -C On entry, the leading N-by-N part of this array must -C contain the state transition matrix A. -C If INITA = 'G', then, on exit, the leading N-by-N part of -C this array contains an upper Hessenberg matrix similar to -C (via an orthogonal matrix consisting of a sequence of -C Householder transformations) the original state transition -C matrix A. -C -C LDA INTEGER -C The leading dimension of array A. LDA >= MAX(1,N). -C -C B (input/output) DOUBLE PRECISION array, dimension (LDB,M) -C On entry, the leading N-by-M part of this array must -C contain the input/state matrix B. -C If INITA = 'G', then, on exit, the leading N-by-M part of -C this array contains the product of the transpose of the -C orthogonal transformation matrix used to reduce A to upper -C Hessenberg form and the original input/state matrix B. -C -C LDB INTEGER -C The leading dimension of array B. LDB >= MAX(1,N). -C -C C (input/output) DOUBLE PRECISION array, dimension (LDC,N) -C On entry, the leading P-by-N part of this array must -C contain the state/output matrix C. -C If INITA = 'G', then, on exit, the leading P-by-N part of -C this array contains the product of the original output/ -C state matrix C and the orthogonal transformation matrix -C used to reduce A to upper Hessenberg form. -C -C LDC INTEGER -C The leading dimension of array C. LDC >= MAX(1,P). -C -C RCOND (output) DOUBLE PRECISION -C If BALEIG = 'C' or BALEIG = 'A', then RCOND contains an -C estimate of the reciprocal of the condition number of -C matrix H with respect to inversion (see METHOD). -C -C G (output) COMPLEX*16 array, dimension (LDG,M) -C The leading P-by-M part of this array contains the -C frequency response matrix G(freq). -C -C LDG INTEGER -C The leading dimension of array G. LDG >= MAX(1,P). -C -C EVRE, (output) DOUBLE PRECISION arrays, dimension (N) -C EVIM If INITA = 'G' and BALEIG = 'B' or 'E' or BALEIG = 'A', -C then these arrays contain the real and imaginary parts, -C respectively, of the eigenvalues of the matrix A. -C Otherwise, these arrays are not referenced. -C -C HINVB (output) COMPLEX*16 array, dimension (LDHINV,M) -C The leading N-by-M part of this array contains the -C -1 -C product H B. -C -C LDHINV INTEGER -C The leading dimension of array HINVB. LDHINV >= MAX(1,N). -C -C Workspace -C -C IWORK INTEGER array, dimension (N) -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C On exit, if INFO = 0, DWORK(1) returns the optimal value -C of LDWORK. -C -C LDWORK INTEGER -C The length of the array DWORK. -C LDWORK >= MAX(1, N - 1 + MAX(N,M,P)), -C if INITA = 'G' and BALEIG = 'N', or 'B', or 'E'; -C LDWORK >= MAX(1, N + MAX(N,M-1,P-1)), -C if INITA = 'G' and BALEIG = 'C', or 'A'; -C LDWORK >= MAX(1, 2*N), -C if INITA = 'H' and BALEIG = 'C', or 'A'; -C LDWORK >= 1, otherwise. -C For optimum performance when INITA = 'G' LDWORK should be -C larger. -C -C ZWORK COMPLEX*16 array, dimension (LZWORK) -C -C LZWORK INTEGER -C The length of the array ZWORK. -C LZWORK >= MAX(1,N*N+2*N), if BALEIG = 'C', or 'A'; -C LZWORK >= MAX(1,N*N), otherwise. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C = 1: if more than 30*N iterations are required to -C isolate all the eigenvalues of the matrix A; the -C computations are continued; -C = 2: if either FREQ is too near to an eigenvalue of the -C matrix A, or RCOND is less than EPS, where EPS is -C the machine precision (see LAPACK Library routine -C DLAMCH). -C -C METHOD -C -C The matrix A is first balanced (if BALEIG = 'B' or 'E', or -C BALEIG = 'A') and then reduced to upper Hessenberg form; the same -C transformations are applied to the matrix B and the matrix C. -C The complex Hessenberg matrix H = (freq*I - A) is then used -C -1 -C to solve for C * H * B. -C -C Depending on the input values of parameters BALEIG and INITA, -C the eigenvalues of matrix A and the condition number of -C matrix H with respect to inversion are also calculated. -C -C REFERENCES -C -C [1] Laub, A.J. -C Efficient Calculation of Frequency Response Matrices from -C State-Space Models. -C ACM TOMS, 12, pp. 26-33, 1986. -C -C NUMERICAL ASPECTS -C 3 -C The algorithm requires 0(N ) operations. -C -C CONTRIBUTOR -C -C Release 3.0: V. Sima, Katholieke Univ. Leuven, Belgium, Dec. 1996. -C Supersedes Release 2.0 routine TB01FD by A.J.Laub, University of -C Southern California, Los Angeles, CA 90089, United States of -C America, June 1982. -C -C REVISIONS -C -C V. Sima, February 22, 1998 (changed the name of TB01RD). -C V. Sima, February 12, 1999, August 7, 2003. -C A. Markovski, Technical University of Sofia, September 30, 2003. -C V. Sima, October 1, 2003. -C -C KEYWORDS -C -C Frequency response, Hessenberg form, matrix algebra, input output -C description, multivariable system, orthogonal transformation, -C similarity transformation, state-space representation, transfer -C matrix. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) - COMPLEX*16 CZERO - PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ) ) -C .. Scalar Arguments .. - CHARACTER BALEIG, INITA - INTEGER INFO, LDA, LDB, LDC, LDG, LDHINV, LDWORK, - $ LZWORK, M, N, P - DOUBLE PRECISION RCOND - COMPLEX*16 FREQ -C .. Array Arguments .. - INTEGER IWORK(*) - DOUBLE PRECISION A(LDA,*), B(LDB,*), C(LDC,*), DWORK(*), EVIM(*), - $ EVRE(*) - COMPLEX*16 ZWORK(*), G(LDG,*), HINVB(LDHINV,*) -C .. Local Scalars .. - CHARACTER BALANC - LOGICAL LBALBA, LBALEA, LBALEB, LBALEC, LINITA - INTEGER I, IGH, IJ, ITAU, J, JJ, JP, JWORK, K, LOW, - $ WRKOPT - DOUBLE PRECISION HNORM, T -C .. External Functions .. - LOGICAL LSAME - DOUBLE PRECISION DASUM, DLAMCH - EXTERNAL DASUM, DLAMCH, LSAME -C .. External Subroutines .. - EXTERNAL DGEBAL, DGEHRD, DHSEQR, DORMHR, DSCAL, DSWAP, - $ MB02RZ, MB02SZ, MB02TZ, XERBLA, ZLASET -C .. Intrinsic Functions .. - INTRINSIC DBLE, DCMPLX, INT, MAX, MIN -C .. Executable Statements .. -C - INFO = 0 - LBALEC = LSAME( BALEIG, 'C' ) - LBALEB = LSAME( BALEIG, 'B' ) .OR. LSAME( BALEIG, 'E' ) - LBALEA = LSAME( BALEIG, 'A' ) - LBALBA = LBALEB.OR.LBALEA - LINITA = LSAME( INITA, 'G' ) -C -C Test the input scalar arguments. -C - IF( .NOT.LBALEC .AND. .NOT.LBALBA .AND. - $ .NOT.LSAME( BALEIG, 'N' ) ) THEN - INFO = -1 - ELSE IF( .NOT.LINITA .AND. .NOT.LSAME( INITA, 'H' ) ) THEN - INFO = -2 - ELSE IF( N.LT.0 ) THEN - INFO = -3 - ELSE IF( M.LT.0 ) THEN - INFO = -4 - ELSE IF( P.LT.0 ) THEN - INFO = -5 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -8 - ELSE IF( LDB.LT.MAX( 1, N ) ) THEN - INFO = -10 - ELSE IF( LDC.LT.MAX( 1, P ) ) THEN - INFO = -12 - ELSE IF( LDG.LT.MAX( 1, P ) ) THEN - INFO = -15 - ELSE IF( LDHINV.LT.MAX( 1, N ) ) THEN - INFO = -19 - ELSE IF( ( LINITA .AND. .NOT.LBALEC .AND. .NOT.LBALEA .AND. - $ LDWORK.LT.N - 1 + MAX( N, M, P ) ) .OR. - $ ( LINITA .AND. ( LBALEC .OR. LBALEA ) .AND. - $ LDWORK.LT.N + MAX( N, M-1, P-1 ) ) .OR. - $ ( .NOT.LINITA .AND. ( LBALEC .OR. LBALEA ) .AND. - $ LDWORK.LT.2*N ) .OR. ( LDWORK.LT.1 ) ) THEN - INFO = -22 - ELSE IF( ( ( LBALEC .OR. LBALEA ) .AND. LZWORK.LT.N*( N + 2 ) ) - $ .OR. ( LZWORK.LT.MAX( 1, N*N ) ) ) THEN - INFO = -24 - END IF -C - IF ( INFO.NE.0 ) THEN -C -C Error return -C - CALL XERBLA( 'TB05AD', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF ( N.EQ.0 ) THEN - IF ( MIN( M, P ).GT.0 ) - $ CALL ZLASET( 'Full', P, M, CZERO, CZERO, G, LDG ) - RCOND = ONE - DWORK(1) = ONE - RETURN - END IF -C -C (Note: Comments in the code beginning "Workspace:" describe the -C minimal amount of real workspace needed at that point in the -C code, as well as the preferred amount for good performance. -C NB refers to the optimal block size for the immediately -C following subroutine, as returned by ILAENV.) -C - WRKOPT = 1 -C - IF ( LINITA ) THEN - BALANC = 'N' - IF ( LBALBA ) BALANC = 'B' -C -C Workspace: need N. -C - CALL DGEBAL( BALANC, N, A, LDA, LOW, IGH, DWORK, INFO ) - IF ( LBALBA ) THEN -C -C Adjust B and C matrices based on information in the -C vector DWORK which describes the balancing of A and is -C defined in the subroutine DGEBAL. -C - DO 10 J = 1, N - JJ = J - IF ( JJ.LT.LOW .OR. JJ.GT.IGH ) THEN - IF ( JJ.LT.LOW ) JJ = LOW - JJ - JP = DWORK(JJ) - IF ( JP.NE.JJ ) THEN -C -C Permute rows of B. -C - IF ( M.GT.0 ) - $ CALL DSWAP( M, B(JJ,1), LDB, B(JP,1), LDB ) -C -C Permute columns of C. -C - IF ( P.GT.0 ) - $ CALL DSWAP( P, C(1,JJ), 1, C(1,JP), 1 ) - END IF - END IF - 10 CONTINUE -C - IF ( IGH.NE.LOW ) THEN -C - DO 20 J = LOW, IGH - T = DWORK(J) -C -C Scale rows of permuted B. -C - IF ( M.GT.0 ) - $ CALL DSCAL( M, ONE/T, B(J,1), LDB ) -C -C Scale columns of permuted C. -C - IF ( P.GT.0 ) - $ CALL DSCAL( P, T, C(1,J), 1 ) - 20 CONTINUE -C - END IF - END IF -C -C Reduce A to Hessenberg form by orthogonal similarities and -C accumulate the orthogonal transformations into B and C. -C Workspace: need 2*N - 1; prefer N - 1 + N*NB. -C - ITAU = 1 - JWORK = ITAU + N - 1 - CALL DGEHRD( N, LOW, IGH, A, LDA, DWORK(ITAU), DWORK(JWORK), - $ LDWORK-JWORK+1, INFO ) - WRKOPT = MAX( WRKOPT, INT( DWORK(JWORK) )+JWORK-1 ) -C -C Workspace: need N - 1 + M; prefer N - 1 + M*NB. -C - CALL DORMHR( 'Left', 'Transpose', N, M, LOW, IGH, A, LDA, - $ DWORK(ITAU), B, LDB, DWORK(JWORK), LDWORK-JWORK+1, - $ INFO ) - WRKOPT = MAX( WRKOPT, INT( DWORK(JWORK) )+JWORK-1 ) -C -C Workspace: need N - 1 + P; prefer N - 1 + P*NB. -C - CALL DORMHR( 'Right', 'No transpose', P, N, LOW, IGH, A, LDA, - $ DWORK(ITAU), C, LDC, DWORK(JWORK), LDWORK-JWORK+1, - $ INFO ) - WRKOPT = MAX( WRKOPT, INT( DWORK(JWORK) )+JWORK-1 ) - IF ( LBALBA ) THEN -C -C Temporarily store Hessenberg form of A in array ZWORK. -C - IJ = 0 - DO 40 J = 1, N -C - DO 30 I = 1, N - IJ = IJ + 1 - ZWORK(IJ) = DCMPLX( A(I,J), ZERO ) - 30 CONTINUE -C - 40 CONTINUE -C -C Compute the eigenvalues of A if that option is requested. -C Workspace: need N. -C - CALL DHSEQR( 'Eigenvalues', 'No Schur', N, LOW, IGH, A, LDA, - $ EVRE, EVIM, DWORK, 1, DWORK, LDWORK, INFO ) -C -C Restore upper Hessenberg form of A. -C - IJ = 0 - DO 60 J = 1, N -C - DO 50 I = 1, N - IJ = IJ + 1 - A(I,J) = DBLE( ZWORK(IJ) ) - 50 CONTINUE -C - 60 CONTINUE -C - IF ( INFO.GT.0 ) THEN -C -C DHSEQR could not evaluate the eigenvalues of A. -C - INFO = 1 - END IF - END IF - END IF -C -C Update H := (FREQ * I) - A with appropriate value of FREQ. -C - IJ = 0 - JJ = 1 - DO 80 J = 1, N -C - DO 70 I = 1, N - IJ = IJ + 1 - ZWORK(IJ) = -DCMPLX( A(I,J), ZERO ) - 70 CONTINUE -C - ZWORK(JJ) = FREQ + ZWORK(JJ) - JJ = JJ + N + 1 - 80 CONTINUE -C - IF ( LBALEC .OR. LBALEA ) THEN -C -C Efficiently compute the 1-norm of the matrix for condition -C estimation. -C - HNORM = ZERO - JJ = 1 -C - DO 90 J = 1, N - T = ABS( ZWORK(JJ) ) + DASUM( J-1, A(1,J), 1 ) - IF ( J.LT.N ) T = T + ABS( A(J+1,J) ) - HNORM = MAX( HNORM, T ) - JJ = JJ + N + 1 - 90 CONTINUE -C - END IF -C -C Factor the complex Hessenberg matrix. -C - CALL MB02SZ( N, ZWORK, N, IWORK, INFO ) - IF ( INFO.NE.0 ) INFO = 2 -C - IF ( LBALEC .OR. LBALEA ) THEN -C -C Estimate the condition of the matrix. -C -C Workspace: need 2*N. -C - CALL MB02TZ( '1-norm', N, HNORM, ZWORK, N, IWORK, RCOND, DWORK, - $ ZWORK(N*N+1), INFO ) - WRKOPT = MAX( WRKOPT, 2*N ) - IF ( RCOND.LT.DLAMCH( 'Epsilon' ) ) INFO = 2 - END IF -C - IF ( INFO.NE.0 ) THEN -C -C Error return: Linear system is numerically or exactly singular. -C - RETURN - END IF -C -C Compute (H-INVERSE)*B. -C - DO 110 J = 1, M -C - DO 100 I = 1, N - HINVB(I,J) = DCMPLX( B(I,J), ZERO ) - 100 CONTINUE -C - 110 CONTINUE -C - CALL MB02RZ( 'No transpose', N, M, ZWORK, N, IWORK, HINVB, LDHINV, - $ INFO ) -C -C Compute C*(H-INVERSE)*B. -C - DO 150 J = 1, M -C - DO 120 I = 1, P - G(I,J) = CZERO - 120 CONTINUE -C - DO 140 K = 1, N -C - DO 130 I = 1, P - G(I,J) = G(I,J) + DCMPLX( C(I,K), ZERO )*HINVB(K,J) - 130 CONTINUE -C - 140 CONTINUE -C - 150 CONTINUE -C -C G now contains the desired frequency response matrix. -C Set the optimal workspace. -C - DWORK(1) = WRKOPT -C - RETURN -C *** Last line of TB05AD *** - END
--- a/extra/control-devel/devel/dksyn/TD03AY.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,171 +0,0 @@ - SUBROUTINE TD03AY( MWORK, PWORK, INDEX, DCOEFF, LDDCOE, UCOEFF, - $ LDUCO1, LDUCO2, N, A, LDA, B, LDB, C, LDC, D, - $ LDD, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C Calculates a state-space representation for a (PWORK x MWORK) -C transfer matrix given in the form of polynomial row vectors over -C common denominators (not necessarily lcd's). Such a description -C is simply the polynomial matrix representation -C -C T(s) = inv(D(s)) * U(s), -C -C where D(s) is diagonal with (I,I)-th element D:I(s) of degree -C INDEX(I); applying Wolovich's Observable Structure Theorem to -C this left matrix fraction then yields an equivalent state-space -C representation in observable companion form, of order -C N = sum(INDEX(I)). As D(s) is diagonal, the PWORK ordered -C 'non-trivial' columns of C and A are very simply calculated, these -C submatrices being diagonal and (INDEX(I) x 1) - block diagonal, -C respectively: finding B and D is also somewhat simpler than for -C general P(s) as dealt with in TC04AD. Finally, the state-space -C representation obtained here is not necessarily controllable -C (as D(s) and U(s) are not necessarily relatively left prime), but -C it is theoretically completely observable: however, its -C observability matrix may be poorly conditioned, so it is safer -C not to assume observability either. -C -C REVISIONS -C -C May 13, 1998. -C -C KEYWORDS -C -C Coprime matrix fraction, elementary polynomial operations, -C polynomial matrix, state-space representation, transfer matrix. -C -C ****************************************************************** -C - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) -C .. Scalar Arguments .. - INTEGER INFO, LDA, LDB, LDC, LDD, LDDCOE, LDUCO1, - $ LDUCO2, MWORK, N, PWORK -C .. Array Arguments .. - INTEGER INDEX(*) - DOUBLE PRECISION A(LDA,*), B(LDB,*), C(LDC,*), D(LDD,*), - $ DCOEFF(LDDCOE,*), UCOEFF(LDUCO1,LDUCO2,*) -C .. Local Scalars .. - INTEGER I, IA, IBIAS, INDCUR, JA, JMAX1, K - DOUBLE PRECISION ABSDIA, ABSDMX, BIGNUM, DIAG, SMLNUM, UMAX1, - $ TEMP -C .. External Functions .. - INTEGER IDAMAX - DOUBLE PRECISION DLAMCH - EXTERNAL DLAMCH, IDAMAX -C .. External Subroutines .. - EXTERNAL DAXPY, DCOPY, DLASET, DSCAL -C .. Intrinsic Functions .. - INTRINSIC ABS -C .. Executable Statements .. -C - INFO = 0 -C -C Initialize A and C to be zero, apart from 1's on the subdiagonal -C of A. -C - CALL DLASET( 'Upper', N, N, ZERO, ZERO, A, LDA ) - IF ( N.GT.1 ) CALL DLASET( 'Lower', N-1, N-1, ZERO, ONE, A(2,1), - $ LDA ) -C - CALL DLASET( 'Full', PWORK, N, ZERO, ZERO, C, LDC ) -C -C Calculate B and D, as well as 'non-trivial' elements of A and C. -C Check if any leading coefficient of D(s) nearly zero: if so, exit. -C Caution is taken to avoid overflow. -C - SMLNUM = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' ) - BIGNUM = ONE / SMLNUM -C - IBIAS = 2 - JA = 0 -C - DO 20 I = 1, PWORK - ABSDIA = ABS( DCOEFF(I,1) ) - JMAX1 = IDAMAX( MWORK, UCOEFF(I,1,1), LDUCO1 ) - UMAX1 = ABS( UCOEFF(I,JMAX1,1) ) - IF ( ( ABSDIA.LT.SMLNUM ) .OR. - $ ( ABSDIA.LT.ONE .AND. UMAX1.GT.ABSDIA*BIGNUM ) ) THEN -C -C Error return. -C - INFO = I - RETURN - END IF - DIAG = ONE/DCOEFF(I,1) - INDCUR = INDEX(I) - IF ( INDCUR.NE.0 ) THEN - IBIAS = IBIAS + INDCUR - JA = JA + INDCUR - IF ( INDCUR.GE.1 ) THEN - JMAX1 = IDAMAX( INDCUR, DCOEFF(I,2), LDDCOE ) - ABSDMX = ABS( DCOEFF(I,JMAX1) ) - IF ( ABSDIA.GE.ONE ) THEN - IF ( UMAX1.GT.ONE ) THEN - IF ( ( ABSDMX/ABSDIA ).GT.( BIGNUM/UMAX1 ) ) THEN -C -C Error return. -C - INFO = I - RETURN - END IF - END IF - ELSE - IF ( UMAX1.GT.ONE ) THEN - IF ( ABSDMX.GT.( BIGNUM*ABSDIA )/UMAX1 ) THEN -C -C Error return. -C - INFO = I - RETURN - END IF - END IF - END IF - END IF -C -C I-th 'non-trivial' sub-vector of A given from coefficients -C of D:I(s), while I-th row block of B given from this and -C row I of U(s). -C - DO 10 K = 2, INDCUR + 1 - IA = IBIAS - K - TEMP = -DIAG*DCOEFF(I,K) - A(IA,JA) = TEMP -C - CALL DCOPY( MWORK, UCOEFF(I,1,K), LDUCO1, B(IA,1), LDB ) - CALL DAXPY( MWORK, TEMP, UCOEFF(I,1,1), LDUCO1, B(IA,1), - $ LDB ) - 10 CONTINUE -C - IF ( JA.LT.N ) A(JA+1,JA) = ZERO -C -C Finally, I-th 'non-trivial' entry of C and row of D obtained -C also. -C - C(I,JA) = DIAG - END IF -C - CALL DCOPY( MWORK, UCOEFF(I,1,1), LDUCO1, D(I,1), LDD ) - CALL DSCAL( MWORK, DIAG, D(I,1), LDD ) - 20 CONTINUE -C - RETURN -C *** Last line of TD03AY *** - END
--- a/extra/control-devel/devel/dksyn/TD04AD.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,425 +0,0 @@ - SUBROUTINE TD04AD( ROWCOL, M, P, INDEX, DCOEFF, LDDCOE, UCOEFF, - $ LDUCO1, LDUCO2, NR, A, LDA, B, LDB, C, LDC, D, - $ LDD, TOL, IWORK, DWORK, LDWORK, INFO ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C PURPOSE -C -C To find a minimal state-space representation (A,B,C,D) for a -C proper transfer matrix T(s) given as either row or column -C polynomial vectors over denominator polynomials, possibly with -C uncancelled common terms. -C -C ARGUMENTS -C -C Mode Parameters -C -C ROWCOL CHARACTER*1 -C Indicates whether the transfer matrix T(s) is given as -C rows or columns over common denominators as follows: -C = 'R': T(s) is given as rows over common denominators; -C = 'C': T(s) is given as columns over common denominators. -C -C Input/Output Parameters -C -C M (input) INTEGER -C The number of system inputs. M >= 0. -C -C P (input) INTEGER -C The number of system outputs. P >= 0. -C -C INDEX (input) INTEGER array, dimension (porm), where porm = P, -C if ROWCOL = 'R', and porm = M, if ROWCOL = 'C'. -C This array must contain the degrees of the denominator -C polynomials in D(s). -C -C DCOEFF (input) DOUBLE PRECISION array, dimension (LDDCOE,kdcoef), -C where kdcoef = MAX(INDEX(I)) + 1. -C The leading porm-by-kdcoef part of this array must contain -C the coefficients of each denominator polynomial. -C DCOEFF(I,K) is the coefficient in s**(INDEX(I)-K+1) of the -C I-th denominator polynomial in D(s), where -C K = 1,2,...,kdcoef. -C -C LDDCOE INTEGER -C The leading dimension of array DCOEFF. -C LDDCOE >= MAX(1,P) if ROWCOL = 'R'; -C LDDCOE >= MAX(1,M) if ROWCOL = 'C'. -C -C UCOEFF (input) DOUBLE PRECISION array, dimension -C (LDUCO1,LDUCO2,kdcoef) -C The leading P-by-M-by-kdcoef part of this array must -C contain the numerator matrix U(s); if ROWCOL = 'C', this -C array is modified internally but restored on exit, and the -C remainder of the leading MAX(M,P)-by-MAX(M,P)-by-kdcoef -C part is used as internal workspace. -C UCOEFF(I,J,K) is the coefficient in s**(INDEX(iorj)-K+1) -C of polynomial (I,J) of U(s), where K = 1,2,...,kdcoef; -C if ROWCOL = 'R' then iorj = I, otherwise iorj = J. -C Thus for ROWCOL = 'R', U(s) = -C diag(s**INDEX(I))*(UCOEFF(.,.,1)+UCOEFF(.,.,2)/s+...). -C -C LDUCO1 INTEGER -C The leading dimension of array UCOEFF. -C LDUCO1 >= MAX(1,P) if ROWCOL = 'R'; -C LDUCO1 >= MAX(1,M,P) if ROWCOL = 'C'. -C -C LDUCO2 INTEGER -C The second dimension of array UCOEFF. -C LDUCO2 >= MAX(1,M) if ROWCOL = 'R'; -C LDUCO2 >= MAX(1,M,P) if ROWCOL = 'C'. -C -C NR (output) INTEGER -C The order of the resulting minimal realization, i.e. the -C order of the state dynamics matrix A. -C -C A (output) DOUBLE PRECISION array, dimension (LDA,N), -C porm -C where N = SUM INDEX(I). -C I=1 -C The leading NR-by-NR part of this array contains the upper -C block Hessenberg state dynamics matrix A of a minimal -C realization. -C -C LDA INTEGER -C The leading dimension of array A. LDA >= MAX(1,N). -C -C B (output) DOUBLE PRECISION array, dimension (LDB,MAX(M,P)) -C The leading NR-by-M part of this array contains the -C input/state matrix B of a minimal realization; the -C remainder of the leading N-by-MAX(M,P) part is used as -C internal workspace. -C -C LDB INTEGER -C The leading dimension of array B. LDB >= MAX(1,N). -C -C C (output) DOUBLE PRECISION array, dimension (LDC,N) -C The leading P-by-NR part of this array contains the -C state/output matrix C of a minimal realization; the -C remainder of the leading MAX(M,P)-by-N part is used as -C internal workspace. -C -C LDC INTEGER -C The leading dimension of array C. LDC >= MAX(1,M,P). -C -C D (output) DOUBLE PRECISION array, dimension (LDD,M), -C if ROWCOL = 'R', and (LDD,MAX(M,P)) if ROWCOL = 'C'. -C The leading P-by-M part of this array contains the direct -C transmission matrix D; if ROWCOL = 'C', the remainder of -C the leading MAX(M,P)-by-MAX(M,P) part is used as internal -C workspace. -C -C LDD INTEGER -C The leading dimension of array D. -C LDD >= MAX(1,P) if ROWCOL = 'R'; -C LDD >= MAX(1,M,P) if ROWCOL = 'C'. -C -C Tolerances -C -C TOL DOUBLE PRECISION -C The tolerance to be used in rank determination when -C transforming (A, B, C). If the user sets TOL > 0, then -C the given value of TOL is used as a lower bound for the -C reciprocal condition number (see the description of the -C argument RCOND in the SLICOT routine MB03OD); a -C (sub)matrix whose estimated condition number is less than -C 1/TOL is considered to be of full rank. If the user sets -C TOL <= 0, then an implicitly computed, default tolerance -C (determined by the SLICOT routine TB01UD) is used instead. -C -C Workspace -C -C IWORK INTEGER array, dimension (N+MAX(M,P)) -C On exit, if INFO = 0, the first nonzero elements of -C IWORK(1:N) return the orders of the diagonal blocks of A. -C -C DWORK DOUBLE PRECISION array, dimension (LDWORK) -C On exit, if INFO = 0, DWORK(1) returns the optimal value -C of LDWORK. -C -C LDWORK INTEGER -C The length of the array DWORK. -C LDWORK >= MAX(1, N + MAX(N, 3*M, 3*P)). -C For optimum performance LDWORK should be larger. -C -C Error Indicator -C -C INFO INTEGER -C = 0: successful exit; -C < 0: if INFO = -i, the i-th argument had an illegal -C value; -C > 0: if INFO = i, then i is the first integer for which -C ABS( DCOEFF(I,1) ) is so small that the calculations -C would overflow (see SLICOT Library routine TD03AY); -C that is, the leading coefficient of a polynomial is -C nearly zero; no state-space representation is -C calculated. -C -C METHOD -C -C The method for transfer matrices factorized by rows will be -C described here: T(s) factorized by columns is dealt with by -C operating on the dual T'(s). This description for T(s) is -C actually the left polynomial matrix representation -C -C T(s) = inv(D(s))*U(s), -C -C where D(s) is diagonal with its (I,I)-th polynomial element of -C degree INDEX(I). The first step is to check whether the leading -C coefficient of any polynomial element of D(s) is approximately -C zero; if so the routine returns with INFO > 0. Otherwise, -C Wolovich's Observable Structure Theorem is used to construct a -C state-space representation in observable companion form which -C is equivalent to the above polynomial matrix representation. -C The method is particularly easy here due to the diagonal form -C of D(s). This state-space representation is not necessarily -C controllable (as D(s) and U(s) are not necessarily relatively -C left prime), but it is in theory completely observable; however, -C its observability matrix may be poorly conditioned, so it is -C treated as a general state-space representation and SLICOT -C Library routine TB01PD is then called to separate out a minimal -C realization from this general state-space representation by means -C of orthogonal similarity transformations. -C -C REFERENCES -C -C [1] Patel, R.V. -C Computation of Minimal-Order State-Space Realizations and -C Observability Indices using Orthogonal Transformations. -C Int. J. Control, 33, pp. 227-246, 1981. -C -C [2] Wolovich, W.A. -C Linear Multivariable Systems, (Theorem 4.3.3). -C Springer-Verlag, 1974. -C -C NUMERICAL ASPECTS -C 3 -C The algorithm requires 0(N ) operations. -C -C CONTRIBUTOR -C -C V. Sima, Katholieke Univ. Leuven, Belgium, March 1998. -C Supersedes Release 3.0 routine TD01OD. -C -C REVISIONS -C -C - -C -C KEYWORDS -C -C Controllability, elementary polynomial operations, minimal -C realization, polynomial matrix, state-space representation, -C transfer matrix. -C -C ****************************************************************** -C -C .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) -C .. Scalar Arguments .. - CHARACTER ROWCOL - INTEGER INFO, LDA, LDB, LDC, LDD, LDDCOE, LDUCO1, - $ LDUCO2, LDWORK, M, NR, P - DOUBLE PRECISION TOL -C .. Array Arguments .. - INTEGER INDEX(*), IWORK(*) - DOUBLE PRECISION A(LDA,*), B(LDB,*), C(LDC,*), D(LDD,*), - $ DCOEFF(LDDCOE,*), DWORK(*), - $ UCOEFF(LDUCO1,LDUCO2,*) -C .. Local Scalars .. - LOGICAL LROCOC, LROCOR - INTEGER I, J, JSTOP, K, KDCOEF, MPLIM, MWORK, N, PWORK -C .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -C .. External Subroutines .. - EXTERNAL DLASET, DSWAP, TB01PD, TB01XD, TD03AY, XERBLA -C .. Intrinsic Functions .. - INTRINSIC MAX -C .. Executable Statements .. -C - INFO = 0 - LROCOR = LSAME( ROWCOL, 'R' ) - LROCOC = LSAME( ROWCOL, 'C' ) - MPLIM = MAX( 1, M, P ) -C -C Test the input scalar arguments. -C - IF( .NOT.LROCOR .AND. .NOT.LROCOC ) THEN - INFO = -1 - ELSE IF( M.LT.0 ) THEN - INFO = -2 - ELSE IF( P.LT.0 ) THEN - INFO = -3 - ELSE IF( ( LROCOR .AND. LDDCOE.LT.MAX( 1, P ) ) .OR. - $ ( LROCOC .AND. LDDCOE.LT.MAX( 1, M ) ) ) THEN - INFO = -6 - ELSE IF( ( LROCOR .AND. LDUCO1.LT.MAX( 1, P ) ) .OR. - $ ( LROCOC .AND. LDUCO1.LT.MPLIM ) ) THEN - INFO = -8 - ELSE IF( ( LROCOR .AND. LDUCO2.LT.MAX( 1, M ) ) .OR. - $ ( LROCOC .AND. LDUCO2.LT.MPLIM ) ) THEN - INFO = -9 - END IF -C - N = 0 - IF ( INFO.EQ.0 ) THEN - IF ( LROCOR ) THEN -C -C Initialization for T(s) given as rows over common -C denominators. -C - PWORK = P - MWORK = M - ELSE -C -C Initialization for T(s) given as columns over common -C denominators. -C - PWORK = M - MWORK = P - END IF -C -C Calculate N, the order of the resulting state-space -C representation. -C - KDCOEF = 0 -C - DO 10 I = 1, PWORK - KDCOEF = MAX( KDCOEF, INDEX(I) ) - N = N + INDEX(I) - 10 CONTINUE -C - KDCOEF = KDCOEF + 1 -C - IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -12 - ELSE IF( LDB.LT.MAX( 1, N ) ) THEN - INFO = -14 - ELSE IF( LDC.LT.MPLIM ) THEN - INFO = -16 - ELSE IF( ( LROCOR .AND. LDD.LT.MAX( 1, P ) ) .OR. - $ ( LROCOC .AND. LDD.LT.MPLIM ) ) THEN - INFO = -18 - ELSE IF( LDWORK.LT.MAX( 1, N + MAX( N, 3*M, 3*P ) ) ) THEN - INFO = -22 - END IF - END IF -C - IF ( INFO.NE.0 ) THEN -C -C Error return. -C - CALL XERBLA( 'TD04AD', -INFO ) - RETURN - END IF -C -C Quick return if possible. -C - IF ( MAX( N, M, P ).EQ.0 ) THEN - NR = 0 - DWORK(1) = ONE - RETURN - END IF -C - IF ( LROCOC ) THEN -C -C Initialize the remainder of the leading -C MPLIM-by-MPLIM-by-KDCOEF part of U(s) to zero. -C - IF ( P.LT.M ) THEN -C - DO 20 K = 1, KDCOEF - CALL DLASET( 'Full', M-P, MPLIM, ZERO, ZERO, - $ UCOEFF(P+1,1,K), LDUCO1 ) - 20 CONTINUE -C - ELSE IF ( P.GT.M ) THEN -C - DO 30 K = 1, KDCOEF - CALL DLASET( 'Full', MPLIM, P-M, ZERO, ZERO, - $ UCOEFF(1,M+1,K), LDUCO1 ) - 30 CONTINUE -C - END IF -C - IF ( MPLIM.NE.1 ) THEN -C -C Non-scalar T(s) factorized by columns: transpose it (i.e. -C U(s)). -C - JSTOP = MPLIM - 1 -C - DO 50 K = 1, KDCOEF -C - DO 40 J = 1, JSTOP - CALL DSWAP( MPLIM-J, UCOEFF(J+1,J,K), 1, - $ UCOEFF(J,J+1,K), LDUCO1 ) - 40 CONTINUE -C - 50 CONTINUE -C - END IF - END IF -C -C Construct non-minimal state-space representation (by Wolovich's -C Structure Theorem) which has transfer matrix T(s) or T'(s) as -C appropriate ... -C - CALL TD03AY( MWORK, PWORK, INDEX, DCOEFF, LDDCOE, UCOEFF, LDUCO1, - $ LDUCO2, N, A, LDA, B, LDB, C, LDC, D, LDD, INFO ) - IF ( INFO.GT.0 ) - $ RETURN -C -C and then separate out a minimal realization from this. -C -C Workspace: need N + MAX(N, 3*MWORK, 3*PWORK). -C - CALL TB01PD( 'Minimal', 'Scale', N, MWORK, PWORK, A, LDA, B, LDB, - $ C, LDC, NR, TOL, IWORK, DWORK, LDWORK, INFO ) -C - IF ( LROCOC ) THEN -C -C If T(s) originally factorized by columns, find dual of minimal -C state-space representation, and reorder the rows and columns -C to get an upper block Hessenberg state dynamics matrix. -C - K = IWORK(1)+IWORK(2)-1 - CALL TB01XD( 'D', NR, MWORK, PWORK, K, NR-1, A, LDA, B, LDB, - $ C, LDC, D, LDD, INFO ) - IF ( MPLIM.NE.1 ) THEN -C -C Also, retranspose U(s) if this is non-scalar. -C - DO 70 K = 1, KDCOEF -C - DO 60 J = 1, JSTOP - CALL DSWAP( MPLIM-J, UCOEFF(J+1,J,K), 1, - $ UCOEFF(J,J+1,K), LDUCO1 ) - 60 CONTINUE -C - 70 CONTINUE -C - END IF - END IF -C - RETURN -C *** Last line of TD04AD *** - END
--- a/extra/control-devel/devel/dksyn/makefile_dksyn.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,15 +0,0 @@ -mex muHopt.f \ - SB10AD.f SB10MD.f AB05MD.f AB07ND.f AB04MD.f \ - SB10PD.f SB10QD.f SB10RD.f SB10LD.f select.f \ - TB05AD.f AB13MD.f SB10YD.f MB01RX.f MB01RU.f \ - SB02RD.f MA02AD.f MB02SZ.f MB02TZ.f MB02RZ.f \ - DG01MD.f SB10ZP.f SB02MS.f MA02ED.f SB02RU.f \ - SB02SD.f SB02QD.f SB02MV.f SB02MW.f SB02MR.f \ - MB02PD.f MB01SD.f MC01PD.f TD04AD.f MB01UD.f \ - SB03SY.f SB03MX.f SB03SX.f MB01RY.f SB03QY.f \ - SB03QX.f SB03MY.f TD03AY.f TB01PD.f TB01XD.f \ - SB04PX.f SB03MV.f SB03MW.f AB07MD.f TB01UD.f \ - TB01ID.f MB01PD.f MB03OY.f MB01QD.f \ - "$(mkoctfile -p LAPACK_LIBS)" \ - "$(mkoctfile -p BLAS_LIBS)" \ - "$(mkoctfile -p FLIBS)"
--- a/extra/control-devel/devel/dksyn/muHopt.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,882 +0,0 @@ -C MUHOPT.f - Gateway function to compute the mu optimal or H_inf -C controller using SLICOT routines SB10AD, SB10MD, AB04MD, -C AB05MD, and AB07ND. -C -C RELEASE 2.0 of SLICOT Robust Control Toolbox. -C Based on SLICOT RELEASE 5.0, Copyright (c) 2004-2010 NICONET e.V. -C -C Matlab call: -C If mu optimal controller is desired (job > 0): -C -C [AK,BK,CK,DK(,mju,RCOND)] = muHopt(job,discr,A,B,C,D,ncon,nmeas, -C gamma,omega,nblock,itype,ord(,qutol(,gtol(,actol)))) -C -C If H_inf optimal controller is only desired (job <= 0): -C -C [AK,BK,CK,DK(,gammin,RCOND)] = muHopt(job,discr,A,B,C,D,ncon, -C nmeas,gamma(,gtol(,actol))) -C -C Purpose: -C To compute the matrices of the mu optimal or H_inf optimal -C controller given the model in a state space. It also outputs the -C mu norm of the closed loop system, if mu optimal controller is -C desired, or the value of gamma reached in the H_inf synthesis -C problem, if H_inf controller is only desired. -C The discrete-time systems are handled via bilinear transformation -C to continuous-time and then the controller obtained is discretised. -C For the K step the SB10AD subroutine is employed, and the SB10MD -C subroutine performs the D step. -C -C Input parameters: -C job - indicates the type of the controller as well as the strategy -C for reducing the gamma value: -C > 0 : mu optimal controller is desired; -C <= 0 : H_inf optimal controller only is desired. -C Specifically, job -C = 0 : find suboptimal controller only; -C and abs(job) specifies the strategy for reducing gamma: -C = 1 : use bisection method for decreasing gamma from gamma -C to gammin until the closed-loop system leaves -C stability; -C = 2 : scan from gamma to 0 trying to find the minimal gamma -C for which the closed-loop system retains stability; -C = 3 : first bisection, then scanning. -C discr - indicates the type of the system, as follows: -C = 0 : continuous-time system; -C = 1 : discrete-time system. -C A - the n-by-n system state matrix A of the plant. -C B - the n-by-m system input matrix B of the plant. -C C - the p-by-n system output matrix C of the plant. -C D - the p-by-m system input/output matrix D of the plant. -C ncon - the number of control inputs. -C p-nmeas >= ncon >= 0. -C nmeas - the number of measurements. -C p-nmeas = m-ncon >= nmeas >= 0. -C gamma - the initial value of gamma on input. It is assumed that -C gamma is sufficiently large so that the controller is -C admissible. gamma >= 0. -C omega - the vector of length lendat >= 2 with the frequencies. -C They must be nonnegative, in increasing order, and -C for discrete-time systems between 0 and pi. -C nblock - the vector with the block structure of the uncertainty. -C nblock(I) is the size of each block. -C itype - the vector of the same length as nblock indicating -C the type of each block. -C itype(I) = 1 indicates that the corresponding block is a -C real block. THIS OPTION IS NOT SUPPORTED NOW. -C itype(I) = 2 indicates that the corresponding block is a -C complex block. THIS IS THE ONLY ALLOWED VALUE NOW! -C ord - the maximum order of each block in the D-fitting procedure. -C 1 <= ord <= lendat-1. -C qutol - (optional) the acceptable mean relative error between -C the D(jw) and the frequency response of the estimated block -C [ADi,BDi;CDi,DDi]. When it is reached, the result is -C taken as good enough. -C Default: qutol = 2. -C gtol - (optional) tolerance used for controlling the accuracy -C of gamma and its distance to the estimated minimal possible -C value of gamma. -C If gtol <= 0, then sqrt(EPS) is used, where EPS is the -C relative machine precision. -C Default: gtol = 0.01. -C actol - (optional) upper bound for the poles of the closed-loop -C system used for determining if it is stable. -C actol <= 0 for stable systems. -C Default: actol = 0. -C -C Output parameters: -C AK - the n-by-n controller state matrix AK. -C BK - the n-by-nmeas controller input matrix BK. -C CK - the ncon-by-n controller output matrix CK. -C DK - the ncon-by-nmeas controller input/output matrix DK. -C mju - (optional) the vector with the estimated upper bound of -C the structured singular value for each frequency in omega -C for the closed-loop system. -C gammin - (optional) the estimated minimal admissible gamma. -C RCOND - (optional) for each successful J-th K step: -C RCOND(J) contains the reciprocal condition number of the -C control transformation matrix; -C RCOND(J+1) contains the reciprocal condition number of the -C measurement transformation matrix; -C RCOND(J+2) contains an estimate of the reciprocal condition -C number of the X-Riccati equation; -C RCOND(J+3) contains an estimate of the reciprocal condition -C number of the Y-Riccati equation. -C If job = 0, only RCOND(1:4) are set by the first K step. -C -C Contributor: -C A. Markovski, Technical University of Sofia, October 2003. -C -C Revisions: -C V. Sima, April 2004, Sept. 2004, Mar. 2005, Apr. 2009. -C -C*********************************************************************** -C - SUBROUTINE MEXFUNCTION( NLHS, PLHS, NRHS, PRHS ) -C -C .. Parameters .. - INTEGER MAXIT, HNPTS - PARAMETER ( MAXIT = 15, HNPTS = 2048 ) - DOUBLE PRECISION ZERO, ONE, TWO, P01 - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0, - $ P01 = 0.01D0 ) -C -C .. Mex-file interface parameters .. - INTEGER NLHS, PLHS(*), NRHS, PRHS(*) -C -C .. Mex-file integer functions .. - INTEGER mxCreateDoubleMatrix, mxGetPr, mxGetM, mxGetN - $ mxIsNumeric, mxIsComplex -C -C .. Parameters used by SLICOT subroutines .. - INTEGER F, INFO, JOB, LBWORK, LDA, LDAC, LDAD, LDAE, - $ LDAK, LDB, LDBC, LDBD, LDBE, LDBK, LDC, LDCC, - $ LDCD, LDCE, LDCK, LDD, LDDC, LDDD, LDDE, LDDK, - $ LDWORK, LENDAT, LIWORK, LZWORK, M, M2, MNB, N, - $ N2E, NE, NEB, NP, NP1, NP2, NTEMP, ORD, TOTORD - DOUBLE PRECISION ACTOL, GAMMA, GTOL, QUTOL, TEMP - DOUBLE PRECISION RCOND(4*MAXIT) -C -C .. Allocatable arrays .. -C !Fortran 90/95 (Fixed dimensions should be used with Fortran 77.) - LOGICAL, ALLOCATABLE :: BWORK(:) - INTEGER, ALLOCATABLE :: ITYPE(:), IWORK(:), NBLOCK(:) - DOUBLE PRECISION, ALLOCATABLE :: A(:), AC(:), AD(:), AE(:), AK(:), - $ AKB(:), B(:), BC(:), BD(:), - $ BE(:), BK(:), BKB(:), C(:), - $ CC(:), CD(:), CE(:), CK(:), - $ CKB(:), D(:), DC(:), DD(:), - $ DE(:), DK(:), DKB(:), DWORK(:), - $ MJU(:), OMEGA(:), PMJU(:), - $ RITYPE(:), RNBLCK(:) - COMPLEX*16, ALLOCATABLE :: ZWORK(:) -C -C .. Local variables and constant dimension arrays .. - CHARACTER CONJOB - CHARACTER*120 TEXT - INTEGER DISCR, I, IP, ITER, ITERB, LD1, LD2, LD3, LD4, - $ LI1, LI2, LI3, LI4, LW1, LW2, LW3, LW4, LW5, - $ LW6, LW7, LWA, LWB, LZD, LZM, M1, M11, MD, MIT, - $ MN, NA, NB, NC, ND, NIT, NNB, NP11 - DOUBLE PRECISION PMPEAK, MUPEAK, TOL -C -C .. External functions .. - DOUBLE PRECISION DLAMCH - EXTERNAL DLAMCH -C -C .. External subroutines .. - EXTERNAL AB04MD, AB05MD, AB07ND, DCOPY, SB10AD, SB10MD -C -C ..Intrinsic functions.. - INTRINSIC ABS, COS, INT, MAX, MIN, SQRT -C -C Check for proper number of arguments. -C - IF ( NRHS.EQ.0 ) THEN - CALL mexErrMsgTxt( 'Matlab call: [AK,BK,CK,DK,MJU,RCOND]='// - $ 'MUHOPT(JOB,DISCR,A,B,C,D,NCON,NMEAS,GAMMA,OMEGA,NBLOCK,ITYPE,'// - $ 'ORD[,QUTOL[,GTOL[,ACTOL]]]) or [AK,BK,CK,DK,GAMMIN,RCOND]='// - $ 'MUHOPT(JOB,DISCR,A,B,C,D,NCON,NMEAS,GAMMA[,GTOL[,ACTOL]])') - ELSE IF ( NRHS.LT.9 ) THEN - CALL mexErrMsgTxt - $ ( 'MUHOPT requires at least 9 input arguments' ) - ELSE IF ( NRHS.GT.16 ) THEN - CALL mexErrMsgTxt - $ ( 'MUHOPT requires at most 16 input arguments' ) - ELSE IF ( NLHS.LT.4 ) THEN - CALL mexErrMsgTxt - $ ( 'MUHOPT requires at least 4 output arguments' ) - END IF -C -C job -C - IF ( mxGetM( PRHS(1) ).NE.1 .OR. mxGetN( PRHS(1) ).NE.1 ) THEN - CALL mexErrMsgTxt( 'JOB must be a scalar' ) - ELSE IF ( mxIsNumeric( PRHS(1) ).EQ.0 .OR. - $ mxIsComplex( PRHS(1) ).EQ.1 ) THEN - CALL mexErrMsgTxt( 'JOB must be an integer scalar' ) - END IF -C - CALL mxCopyPtrToReal8( mxGetPr( PRHS(1) ), TEMP, 1 ) - JOB = INT( TEMP ) -C - IF ( ABS( JOB ).GT.3 ) THEN - CALL mexErrMsgTxt( 'JOB has -3, -2, -1, 0, 1, 2, or 3 '// - $ 'the only admissible values' ) - END IF -C -C Determine the job. -C - IF ( JOB.GT.0 ) THEN -C mu controller desired. - CONJOB = 'M' - ELSE -C H_inf controller desired. - CONJOB = 'H' - IF ( JOB.EQ.0 ) THEN - JOB = 4 - ELSE - JOB = ABS( JOB ) - END IF - END IF -C -C Recheck for proper number of arguments. -C - IF ( CONJOB.EQ.'M' .AND. NRHS.LT.13 ) THEN - CALL mexErrMsgTxt( 'MUHOPT requires at least 13 input '// - $ 'arguments if mu optimal controller is desired') - ELSE IF ( CONJOB.EQ.'H' .AND. NRHS.GT.11 ) THEN - CALL mexErrMsgTxt( 'MUHOPT requires at most 11 input '// - $ 'arguments if H_inf optimal controller is desired') - END IF -C -C discr -C - IF ( mxGetM( PRHS(2) ).NE.1 .OR. mxGetN( PRHS(2) ).NE.1 ) THEN - CALL mexErrMsgTxt( 'DISCR must be a scalar' ) - ELSE IF ( mxIsNumeric( PRHS(2) ).EQ.0 .OR. - $ mxIsComplex( PRHS(2) ).EQ.1 ) THEN - CALL mexErrMsgTxt( 'DISCR must be an integer scalar' ) - END IF -C - CALL mxCopyPtrToReal8( mxGetPr( PRHS(2) ), TEMP, 1 ) - DISCR = INT( TEMP ) -C - IF ( DISCR.LT.0 .OR. DISCR.GT.1 ) THEN - CALL mexErrMsgTxt( 'DISCR must be 0 or 1' ) - END IF -C -C A, B, C, D -C - IF ( mxIsNumeric( PRHS(3) ).EQ.0 .OR. - $ mxIsComplex( PRHS(3) ).EQ.1 ) THEN - CALL mexErrMsgTxt( 'A must be a numeric matrix' ) - END IF -C - N = mxGetM( PRHS(3) ) - NA = mxGetN( PRHS(3) ) -C - IF ( NA.NE.N ) THEN - CALL mexErrMsgTxt( 'A must be a square matrix' ) - END IF -C - IF ( mxIsNumeric( PRHS(4) ).EQ.0 .OR. - $ mxIsComplex( PRHS(4) ).EQ.1 ) THEN - CALL mexErrMsgTxt( 'B must be a numeric matrix' ) - END IF -C - NB = mxGetM( PRHS(4) ) - M = mxGetN( PRHS(4) ) -C - IF ( NB.NE.N ) THEN - CALL mexErrMsgTxt( 'B must have the same row dimension as A' ) - END IF -C - IF ( mxIsNumeric( PRHS(5) ).EQ.0 .OR. - $ mxIsComplex( PRHS(5) ).EQ.1 ) THEN - CALL mexErrMsgTxt( 'C must be a numeric matrix' ) - END IF -C - NP = mxGetM( PRHS(5) ) - NC = mxGetN( PRHS(5) ) -C - IF ( NC.NE.N ) THEN - CALL mexErrMsgTxt - $ ( 'C must have the same column dimension as A' ) - END IF -C - IF ( mxIsNumeric( PRHS(6) ).EQ.0 .OR. - $ mxIsComplex( PRHS(6) ).EQ.1 ) THEN - CALL mexErrMsgTxt( 'D must be a numeric matrix' ) - END IF -C - ND = mxGetM( PRHS(6) ) - MD = mxGetN( PRHS(6) ) -C - IF ( ND.NE.NP ) THEN - CALL mexErrMsgTxt( 'D must have the same row dimension as C' ) - ELSE IF ( MD.NE.M ) THEN - CALL mexErrMsgTxt - $ ( 'D must have the same column dimension as B' ) - END IF -C -C ncon (M2), nmeas (NP2) -C - IF ( mxGetM( PRHS(7) ).NE.1 .OR. mxGetN( PRHS(7) ).NE.1 ) THEN - CALL mexErrMsgTxt( 'NCON must be a scalar' ) - ELSE IF ( mxIsNumeric( PRHS(7) ).EQ.0 .OR. - $ mxIsComplex( PRHS(7) ).EQ.1 ) THEN - CALL mexErrMsgTxt( 'NCON must be an integer scalar' ) - END IF -C - CALL mxCopyPtrToReal8( mxGetPr( PRHS(7) ), TEMP, 1 ) - M2 = INT( TEMP ) -C - IF ( mxGetM( PRHS(8) ).NE.1 .OR. mxGetN( PRHS(8) ).NE.1 ) THEN - CALL mexErrMsgTxt( 'NMEAS must be a scalar' ) - ELSE IF ( mxIsNumeric( PRHS(8) ).EQ.0 .OR. - $ mxIsComplex( PRHS(8) ).EQ.1 ) THEN - CALL mexErrMsgTxt( 'NMEAS must be an integer scalar' ) - END IF -C - CALL mxCopyPtrToReal8( mxGetPr( PRHS(8) ), TEMP, 1 ) - NP2 = INT( TEMP ) - M1 = M - M2 - NP1 = NP - NP2 -C - IF ( M1.NE.NP1 ) THEN - CALL mexErrMsgTxt( 'M - NCON must be equal to P - NMEAS' ) - END IF -C -C gamma -C - IF ( mxGetM( PRHS(9) ).NE.1 .OR. mxGetN( PRHS(9) ).NE.1 ) THEN - CALL mexErrMsgTxt( 'GAMMA must be a scalar' ) - ELSE IF ( mxIsNumeric( PRHS(9) ).EQ.0 .OR. - $ mxIsComplex( PRHS(9) ).EQ.1 ) THEN - CALL mexErrMsgTxt( 'GAMMA must be a real scalar' ) - END IF -C - CALL mxCopyPtrToReal8( mxGetPr( PRHS(9) ), GAMMA, 1 ) -C - IF ( CONJOB.EQ.'M' ) THEN -C -C The mu controller case. -C -C omega -C - IF ( mxIsNumeric( PRHS(10) ).EQ.0 .OR. - $ mxIsComplex( PRHS(10) ).EQ.1 ) THEN - CALL mexErrMsgTxt( 'OMEGA must be a numeric vector' ) - ELSE IF ( MIN( mxGetM( PRHS(10) ), mxGetN( PRHS(10) ) ).NE.1 ) - $ THEN - CALL mexErrMsgTxt( 'OMEGA must be a vector' ) - END IF -C - LENDAT = mxGetM( PRHS(10) )*mxGetN( PRHS(10) ) - IF ( LENDAT.LE.1 ) THEN - CALL mexErrMsgTxt( 'OMEGA must have at least 2 elements' ) - END IF -C -C nblock -C - IF ( mxIsNumeric( PRHS(11) ).EQ.0 .OR. - $ mxIsComplex( PRHS(11) ).EQ.1 ) THEN - CALL mexErrMsgTxt( 'NBLOCK must be a numeric vector' ) - END IF -C - MNB = mxGetM( PRHS(11) ) - NNB = mxGetN( PRHS(11) ) - MN = MIN( MNB, NNB ) - MNB = MAX( MNB, NNB ) - NNB = MN - IF ( NNB.NE.1 ) THEN - CALL mexErrMsgTxt( 'NBLOCK must be a vector' ) - END IF -C -C itype -C - IF ( mxIsNumeric( PRHS(12) ).EQ.0 .OR. - $ mxIsComplex( PRHS(12) ).EQ.1 ) THEN - CALL mexErrMsgTxt( 'ITYPE must be a numeric vector' ) - END IF -C - MIT = mxGetM( PRHS(12) ) - NIT = mxGetN( PRHS(12) ) - MN = MIN( MIT, NIT ) - MIT = MAX( MIT, NIT ) - NIT = MN -C - IF ( NIT.NE.1 ) THEN - CALL mexErrMsgTxt( 'ITYPE must be a vector' ) - ELSE IF ( MNB.NE.MIT ) THEN - CALL mexErrMsgTxt - $ ( 'ITYPE must have the same size as NBLOCK' ) - END IF -C -C ord -C - IF ( mxGetM( PRHS(13) ).NE.1 .OR. - $ mxGetN( PRHS(13) ).NE.1 ) THEN - CALL mexErrMsgTxt( 'ORD must be a scalar' ) - ELSE IF ( mxIsNumeric( PRHS(13) ).EQ.0 .OR. - $ mxIsComplex( PRHS(13) ).EQ.1 ) THEN - CALL mexErrMsgTxt( 'ORD must be an integer scalar' ) - END IF -C - CALL mxCopyPtrToReal8( mxGetPr( PRHS(13) ), TEMP, 1 ) - ORD = INT( TEMP ) -C - IF ( ORD.LT.1 ) THEN - CALL mexErrMsgTxt( 'ORD must be at least 1' ) - ELSE IF ( ORD.GE.LENDAT ) THEN - WRITE( TEXT, '(''ORD must be less than LENDAT - 1 = '', - $ I7)' ) LENDAT - 1 - CALL mexErrMsgTxt( TEXT ) - END IF -C -C qutol -C - IF ( NRHS.GE.14 ) THEN - IF ( mxGetM( PRHS(14) ).NE.1 .OR. - $ mxGetN( PRHS(14) ).NE.1 ) THEN - CALL mexErrMsgTxt( 'QUTOL must be a scalar' ) - ELSE IF ( mxIsNumeric( PRHS(14) ).EQ.0 .OR. - $ mxIsComplex( PRHS(14) ).EQ.1 ) THEN - CALL mexErrMsgTxt( 'QUTOL must be a real scalar' ) - END IF - CALL mxCopyPtrToReal8( mxGetPr( PRHS(14) ), QUTOL, 1 ) - ELSE - QUTOL = TWO - END IF - IP = 15 - ELSE - IP = 10 - END IF -C -C gtol -C - IF ( NRHS.GE.IP ) THEN - IF ( mxGetM( PRHS(IP) ).NE.1 .OR. - $ mxGetN( PRHS(IP) ).NE.1 ) THEN - CALL mexErrMsgTxt( 'GTOL must be a scalar' ) - ELSE IF ( mxIsNumeric( PRHS(IP) ).EQ.0 .OR. - $ mxIsComplex( PRHS(IP) ).EQ.1 ) THEN - CALL mexErrMsgTxt( 'GTOL must be a real scalar' ) - END IF - CALL mxCopyPtrToReal8( mxGetPr( PRHS(IP) ), GTOL, 1 ) - IP = IP + 1 - ELSE - GTOL = P01 - END IF -C -C actol -C - IF ( NRHS.EQ.IP ) THEN - IF ( mxGetM( PRHS(IP) ).NE.1 .OR. - $ mxGetN( PRHS(IP) ).NE.1 ) THEN - CALL mexErrMsgTxt( 'ACTOL must be a scalar' ) - ELSE IF ( mxIsNumeric( PRHS(IP) ).EQ.0 .OR. - $ mxIsComplex( PRHS(IP) ).EQ.1 ) THEN - CALL mexErrMsgTxt( 'ACTOL must be a real scalar' ) - END IF - CALL mxCopyPtrToReal8( mxGetPr(PRHS(IP) ), ACTOL, 1 ) - ELSE - ACTOL = ZERO - END IF -C -C Set the default tolerance. -C - TOL = SQRT( DLAMCH( 'Epsilon' ) ) -C -C Determine the lenghts of working arrays. -C -C The original system. -C - LDA = MAX( 1, N ) - LDB = LDA - LDC = MAX( 1, NP ) - LDD = LDC -C - IF ( CONJOB.EQ.'M' ) THEN -C -C The scaling system. -C - TOTORD = NP1*ORD -C - F = MAX( M2, NP2 ) - LDAD = MAX( 1, TOTORD ) - LDBD = LDAD - LDCD = MAX( 1, NP1 + F ) - LDDD = LDCD -C -C The extended system. -C - NE = N + 2*TOTORD - LDAE = MAX( 1, NE ) - LDBE = LDAE - LDCE = LDCD - LDDE = LDCE - ELSE - NE = N - LDAE = LDA - END IF -C -C The closed-loop system. -C - N2E = 2*NE - LDAC = MAX( 1, N2E ) - LDBC = LDAC - LDCC = MAX( 1, NP1 ) - LDDC = LDCC -C -C The controller. -C - LDAK = LDAE - LDBK = LDAK - LDCK = MAX( 1, M2 ) - LDDK = LDCK -C -C LBWORK -C -C ..SB10AD.. - LBWORK = N2E -C -C LIWORK -C -C ..SB10AD.. - LI1 = MAX( 2*MAX( NE, M - M2, NP - NP2, M2, NP2 ), NE*NE ) -C - IF ( CONJOB.EQ.'M' ) THEN -C ..SB10MD.. - LI2 = MAX( N2E, 4*MNB - 2, NP1 ) - IF ( QUTOL.GE.ZERO ) - $ LI2 = MAX( LI2, 2*ORD + 1 ) -C ..AB07ND.. - LI3 = 2*M - ELSE - LI2 = 0 - LI3 = 0 - END IF -C -C ..AB04MD.. - LI4 = NE -C - LIWORK = MAX( LI1, LI2, LI3, LI4 ) -C -C LDWORK -C -C ..AB04MD.. - LD1 = LDAK -C -C ..SB10AD.. - NP11 = NP1 - M2 - M11 = M1 - NP2 - LW1 = NE*M + NP*NE + NP*M + M2*M2 + NP2*NP2 - LW2 = MAX( ( NE + NP1 + 1 )*( NE + M2 ) + - $ MAX( 3*( NE + M2 ) + NE + NP1, 5*( NE + M2 ) ), - $ ( NE + NP2 )*( NE + M1 + 1 ) + - $ MAX( 3*( NE + NP2 ) + NE + M1, 5*( NE + NP2 ) ), - $ M2 + NP1*NP1 + MAX( NP1*MAX( NE, M1 ), 3*M2 + NP1, - $ 5*M2 ), - $ NP2 + M1*M1 + MAX( MAX( NE, NP1 )*M1, 3*NP2 + M1, - $ 5*NP2 ) ) - LW3 = MAX( NP11*M1 + MAX( 4*MIN( NP11, M1 ) + MAX( NP11, M1 ), - $ 6*MIN( NP11, M1 ) ), - $ NP1*M11 + MAX( 4*MIN( NP1, M11 ) + MAX( NP1, M11 ), - $ 6*MIN( NP1, M11 ) ) ) - LW4 = 2*M*M + NP*NP + 2*M*NE + M*NP + 2*NE*NP - LW5 = 2*NE*NE + M*NE + NE*NP - LW6 = MAX( M*M + MAX( 2*M1, 3*NE*NE + - $ MAX( NE*M, 10*NE*NE + 12*NE + 5 ) ), - $ NP*NP + MAX( 2*NP1, 3*NE*NE + - $ MAX( NE*NP, 10*NE*NE + 12*NE + 5 ) ) ) - LW7 = M2*NP2 + NP2*NP2 + M2*M2 + - $ MAX( NP11*NP11 + MAX( 2*NP11, ( NP11 + M11 )*NP2 ), - $ M11*M11 + MAX( 2*M11, M11*M2 ), 3*NE, - $ NE*( 2*NP2 + M2 ) + - $ MAX( 2*NE*M2, M2*NP2 + - $ MAX( M2*M2 + 3*M2, NP2*( 2*NP2 + - $ M2 + MAX( NP2, NE ) ) ) ) ) - LD2 = LW1 + MAX( 1, LW2, LW3, LW4, LW5 + MAX( LW6, LW7 ) ) -C - IF ( CONJOB.EQ.'M' ) THEN -C -C ..SB10MD.. - MN = MIN( 2*LENDAT, 2*ORD + 1 ) - LWA = NP1*LENDAT + 2*MNB + NP1 - 1 - LWB = LENDAT*( NP1 + 2 ) + ORD*( ORD + 2 ) + 1 - LW1 = 2*LENDAT + 4*HNPTS - LW2 = LENDAT + 6*HNPTS - LW3 = 2*LENDAT*( 2*ORD + 1 ) + MAX( 2*LENDAT, 2*ORD + 1 ) + - $ MAX( MN + 6*ORD + 4, 2*MN + 1 ) - LW4 = MAX( ORD*ORD + 5*ORD, 6*ORD + 1 + MIN( 1, ORD ) ) -C - LD3 = LWA + MAX( N2E + MAX( N2E, NP1 - 1 ), - $ 2*NP1*NP1*MNB - NP1*NP1 + 9*MNB*MNB + - $ NP1*MNB + 11*NP1 + 33*MNB - 11 ) - IF ( QUTOL.GE.ZERO ) THEN - LD4 = LWB + MAX( LW1, LW2, LW3, LW4 ) - ELSE - LD4 = 0 - END IF -C .. AB05MD.. - LD4 = MAX( LD4, MAX( M, NP )*MAX( N + TOTORD, M, NP ) ) -C .. AB07ND.. - LD4 = MAX( LD4, 4*M ) - ELSE - LD3 = 0 - LD4 = 0 - END IF -C - LDWORK = MAX( LD1, LD2, LD3, LD4 ) -C -C LZWORK -C - IF ( CONJOB.EQ.'M' ) THEN -C ..SB10MD.. - LZM = MAX( NP1*NP1 + N2E*NP1 + N2E*N2E + 2*N2E, - $ 6*NP1*NP1*MNB + 13*NP1*NP1 + 6*MNB + 6*NP1 - 3 ) - IF ( QUTOL.GE.ZERO ) THEN - LZD = MAX( LENDAT*( 2*ORD + 3 ), ORD*ORD + 3*ORD + 1 ) - ELSE - LZD = 0 - END IF - LZWORK = MAX( LZM, LZD ) - END IF -C -C Allocate variable dimension local arrays. -C !Fortran 90/95 -C - ALLOCATE ( A(LDA*N), AC(LDAC*N2E), AK(LDAK*NE), - $ B(LDB*M), BC(LDBC*M1), BK(LDBK*NP2), BWORK(LBWORK), - $ C(LDC*N), CC(LDCC*N2E), CK(LDCK*NE), - $ D(LDD*M), DC(LDDC*M1), DK(LDDK*NP2), DWORK(LDWORK), - $ IWORK(LIWORK) ) -C - IF ( CONJOB.EQ.'M' ) THEN - ALLOCATE ( AD(LDAD*TOTORD), AE(LDAE*NE), AKB(LDAK*NE), - $ BD(LDBD*(M1+F)), BE(LDBE*(M1+F)), BKB(LDBK*NP2), - $ CD(LDCD*TOTORD), CE(LDCE*NE), CKB(LDCK*NE), - $ DD(LDDD*(M1+F)), DE(LDDE*(M1+F)), DKB(LDDK*NP2), - $ ITYPE(MNB), MJU(LENDAT), NBLOCK(MNB), OMEGA(LENDAT), - $ PMJU(LENDAT), RITYPE(MNB), RNBLCK(MNB), - $ ZWORK(LZWORK) ) - END IF -C -C Copy right hand side arguments to local arrays. -C - CALL mxCopyPtrToReal8( mxGetPr( PRHS(3) ), A, N*N ) - CALL mxCopyPtrToReal8( mxGetPr( PRHS(4) ), B, N*M ) - CALL mxCopyPtrToReal8( mxGetPr( PRHS(5) ), C, NP*N ) - CALL mxCopyPtrToReal8( mxGetPr( PRHS(6) ), D, NP*M ) -C - IF ( CONJOB.EQ.'M' ) THEN - CALL mxCopyPtrToReal8( mxGetPr( PRHS(10) ), OMEGA, LENDAT ) - CALL mxCopyPtrToReal8( mxGetPr( PRHS(11) ), RNBLCK, MNB ) - CALL mxCopyPtrToReal8( mxGetPr( PRHS(12) ), RITYPE, MNB ) -C - DO 10 I = 1, MNB - NBLOCK(I) = INT( RNBLCK(I) ) - ITYPE(I) = INT( RITYPE(I) ) - 10 CONTINUE - END IF -C -C Do the actual computations. -C -C Transform to continuous-case, if needed. -C - IF ( DISCR.EQ.1 ) THEN - CALL AB04MD( 'D', N, M, NP, ONE, ONE, A, LDA, B, LDB, C, LDC, - $ D, LDD, IWORK, DWORK, LDWORK, INFO ) -C - IF ( INFO.NE.0 ) THEN - WRITE( TEXT, '('' INFO = '',I4,'' ON EXIT FROM AB04MD'')' ) - $ INFO - GOTO 60 - END IF -C - IF ( CONJOB.EQ.'M' ) THEN -C - DO 20 I = 1, LENDAT - OMEGA(I) = SQRT( ( ONE - COS( OMEGA(I) ) ) / - $ ( ONE + COS( OMEGA(I) ) + TOL ) ) - 20 CONTINUE -C - END IF -C - END IF -C -C Set parameters for the first K step. -C - N2E = 2*N - NE = N - NEB = N - ITER = 1 -C -C First K step - makes use of the original system. -C - CALL SB10AD( JOB, N, M, NP, M2, NP2, GAMMA, A, LDA, B, LDB, C, - $ LDC, D, LDD, AK, LDA, BK, LDB, CK, LDCK, DK, LDDK, - $ AC, LDAC, BC, LDBC, CC, LDCC, DC, LDDC, RCOND, GTOL, - $ ACTOL, IWORK, LIWORK, DWORK, LDWORK, BWORK, LBWORK, - $ INFO ) -C - IF ( INFO.NE.0 ) THEN - WRITE( TEXT, '('' INFO = '',I4,'' ON EXIT FROM SB10AD'')' ) - $ INFO - GOTO 60 - END IF -C -C Skip the D step if H_inf controller only desired. -C - IF ( CONJOB.EQ.'H' ) - $ GOTO 50 -C - PMPEAK = GAMMA + P01 -C -C Start the iteration process -C --------- D step ------------------------------------------------- -C - 30 CONTINUE -C - CALL SB10MD( N2E, NP1, LENDAT, F, ORD, MNB, NBLOCK, ITYPE, - $ QUTOL, AC, LDAC, BC, LDBC, CC, LDCC, DC, LDDC, - $ OMEGA, TOTORD, AD, LDAD, BD, LDBD, CD, LDCD, DD, - $ LDDD, MJU, IWORK, LIWORK, DWORK, LDWORK, ZWORK, - $ LZWORK, INFO ) -C - IF ( INFO.NE.0 ) THEN - WRITE( TEXT, '('' INFO = '',I4,'' ON EXIT FROM SB10MD'')' ) - $ INFO - GOTO 60 - END IF -C -C Check mu. -C - MUPEAK = ZERO -C - DO 40 I = 1, LENDAT - MUPEAK = MAX( MUPEAK, MJU(I) ) - 40 CONTINUE -C - IF ( MUPEAK.GT.PMPEAK ) THEN - IF ( ITER.NE.1 ) - $ CALL DCOPY( LENDAT, PMJU, 1, MJU, 1 ) - GOTO 50 - ELSE -C -C Save the best controller. -C - PMPEAK = MUPEAK - ITERB = ITER - NEB = NE -C - CALL DCOPY( LENDAT, MJU, 1, PMJU, 1 ) - IF ( ITER.NE.1 ) THEN - CALL DCOPY( NE*NE, AKB, 1, AK, 1 ) - CALL DCOPY( NE*NP2, BKB, 1, BK, 1 ) - CALL DCOPY( M2*NE, CKB, 1, CK, 1 ) - CALL DCOPY( M2*NP2, DKB, 1, DK, 1 ) - END IF - END IF -C - ITER = ITER + 1 - IF ( ITER.GT.MAXIT ) - $ GOTO 50 -C -C Dl*P. -C - CALL AB05MD( 'U', 'N', N, M, NP, TOTORD, NP, A, LDA, B, LDB, - $ C, LDC, D, LDD, AD, LDAD, BD, LDBD, CD, LDCD, DD, - $ LDDD, NTEMP, AE, LDAE, BE, LDBE, CE, LDCE, DE, - $ LDDE, DWORK, LDWORK, INFO ) -C -C inv(Dr). -C - CALL AB07ND( TOTORD, M, AD, LDAD, BD, LDBD, CD, LDCD, DD, LDDD, - $ TEMP, IWORK, DWORK, LDWORK, INFO ) -C - IF ( INFO.NE.0 ) THEN - WRITE( TEXT, '('' INFO = '',I4,'' ON EXIT FROM AB07ND'')' ) - $ INFO - GOTO 60 - END IF -C -C Dl*P*inv(Dr). -C - CALL AB05MD( 'U', 'O', TOTORD, M, M, NTEMP, NP, AD, LDAD, BD, - $ LDBD, CD, LDCD, DD, LDDD, AE, LDAE, BE, LDBE, - $ CE, LDCE, DE, LDDE, NE, AE, LDAE, BE, LDBE, CE, - $ LDCE, DE, LDDE, DWORK, LDWORK, INFO ) - N2E = 2*NE - LDAK = MAX( 1, NE ) - LDBK = LDAK -C -C --------- K step ---------------------------------------------- -C - CALL SB10AD( JOB, NE, M, NP, M2, NP2, GAMMA, AE, LDAE, BE, - $ LDBE, CE, LDCE, DE, LDDE, AKB, LDAK, BKB, LDBK, - $ CKB, LDCK, DKB, LDDK, AC, LDAC, BC, LDBC, CC, - $ LDCC, DC, LDDC, RCOND( 4*ITER-3 ), GTOL, ACTOL, - $ IWORK, LIWORK, DWORK, LDWORK, BWORK, LBWORK, - $ INFO ) -C - IF ( INFO.NE.0 ) THEN - INFO = 0 - GOTO 50 - END IF -C - GOTO 30 -C -C ---- End of the mu synthesis ------------------------------------- -C - 50 CONTINUE -C -C Transform back to discrete time if needed. -C - IF ( DISCR.EQ.1 ) THEN - CALL AB04MD( 'C', NEB, NP2, M2, ONE, ONE, AK, LDAK, BK, LDBK, - $ CK, LDCK, DK, LDDK, IWORK, DWORK, LDWORK, INFO ) -C - IF ( INFO.NE.0 ) THEN - WRITE( TEXT, '('' INFO = '',I4,'' ON EXIT FROM AB04MD'')' ) - $ INFO - GOTO 60 - END IF - END IF -C -C Copy output to MATLAB workspace. -C - PLHS(1) = mxCreateDoubleMatrix( NEB, NEB, 0 ) - PLHS(2) = mxCreateDoubleMatrix( NEB, NP2, 0 ) - PLHS(3) = mxCreateDoubleMatrix( M2, NEB, 0 ) - PLHS(4) = mxCreateDoubleMatrix( M2, NP2, 0 ) - CALL mxCopyReal8ToPtr( AK, mxGetPr( PLHS(1) ), NEB*NEB ) - CALL mxCopyReal8ToPtr( BK, mxGetPr( PLHS(2) ), NEB*NP2 ) - CALL mxCopyReal8ToPtr( CK, mxGetPr( PLHS(3) ), M2*NEB ) - CALL mxCopyReal8ToPtr( DK, mxGetPr( PLHS(4) ), M2*NP2 ) -C - IF ( NLHS.GE.5 ) THEN - IF ( CONJOB.EQ.'M' ) THEN -C mu - PLHS(5) = mxCreateDoubleMatrix( LENDAT, 1, 0 ) - CALL mxCopyReal8ToPtr( MJU, mxGetPr( PLHS(5) ), LENDAT ) - IF ( NLHS.GE.6 ) THEN - PLHS(6) = mxCreateDoubleMatrix( ITERB*4, 1, 0 ) - CALL mxCopyReal8ToPtr( RCOND, mxGetPr( PLHS(6) ), - $ ITERB*4 ) - END IF - ELSE -C H_inf - PLHS(5) = mxCreateDoubleMatrix( 1, 1, 0 ) - CALL mxCopyReal8ToPtr( GAMMA, mxGetPr( PLHS(5) ), 1 ) - IF ( NLHS.GE.6 ) THEN - PLHS(6) = mxCreateDoubleMatrix( 4, 1, 0 ) - CALL mxCopyReal8ToPtr( RCOND, mxGetPr( PLHS(6) ), 4 ) - END IF - END IF - END IF -C -C Deallocate local arrays. -C !Fortran 90/95 -C - 60 CONTINUE -C - DEALLOCATE ( A, AC, AK, B, BC, BK, BWORK, C, CC, CK, D, DC, DK, - $ DWORK, IWORK ) -C - IF ( CONJOB.EQ.'M' ) - $ DEALLOCATE ( AD, AE, AKB, BD, BE, BKB, CD, CE, CKB, DD, DE, - $ DKB, ITYPE, MJU, NBLOCK, OMEGA, PMJU, RITYPE, - $ RNBLCK, ZWORK ) -C -C Error and warning handling .. -C - IF ( INFO.NE.0 ) - $ CALL mexErrMsgTxt( TEXT ) -C - RETURN -C -C *** Last line of MUHOPT *** - END
--- a/extra/control-devel/devel/dksyn/select.f Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,27 +0,0 @@ - LOGICAL FUNCTION SELECT( PAR1, PAR2 ) -C -C SLICOT RELEASE 5.0. -C -C Copyright (c) 2002-2010 NICONET e.V. -C -C This program is free software: you can redistribute it and/or -C modify it under the terms of the GNU General Public License as -C published by the Free Software Foundation, either version 2 of -C the License, or (at your option) any later version. -C -C This program is distributed in the hope that it will be useful, -C but WITHOUT ANY WARRANTY; without even the implied warranty of -C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -C GNU General Public License for more details. -C -C You should have received a copy of the GNU General Public License -C along with this program. If not, see -C <http://www.gnu.org/licenses/>. -C -C Void logical function for DGEES. -C - DOUBLE PRECISION PAR1, PAR2 -C - SELECT = .TRUE. - RETURN - END
--- a/extra/control-devel/devel/erie.dat Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,57 +0,0 @@ - 1.0000000e+00 3.7000000e+00 5.9000000e+02 1.4700000e+02 9.3000000e-01 2.6900000e+02 3.1145000e+00 5.8163000e+02 1.4701000e+02 9.5210000e-01 2.6958000e+02 2.5289000e+00 5.7326000e+02 1.4703000e+02 9.7420000e-01 2.7017000e+02 1.9434000e+00 5.6489000e+02 1.4704000e+02 9.9630000e-01 2.7075000e+02 1.5100000e+01 1.1001000e+04 1.5103000e+01 1.0820000e+04 1.5105000e+01 1.0638000e+04 1.5108000e+01 1.0457000e+04 - 2.0000000e+00 1.0300000e+01 3.5000000e+02 1.3600000e+02 8.9000000e-01 2.3700000e+02 9.0367000e+00 3.5832000e+02 1.3538000e+02 8.5518000e-01 2.3520000e+02 7.7735000e+00 3.6664000e+02 1.3476000e+02 8.2036000e-01 2.3340000e+02 6.5102000e+00 3.7496000e+02 1.3413000e+02 7.8554000e-01 2.3160000e+02 1.1700000e+01 6.8380000e+03 1.1908000e+01 6.6498000e+03 1.2116000e+01 6.4615000e+03 1.2324000e+01 6.2733000e+03 - 3.0000000e+00 1.2000000e+01 3.5400000e+02 1.3400000e+02 4.2000000e-01 2.3100000e+02 1.2261000e+01 3.4871000e+02 1.3458000e+02 4.7440000e-01 2.3327000e+02 1.2521000e+01 3.4342000e+02 1.3516000e+02 5.2880000e-01 2.3553000e+02 1.2782000e+01 3.3813000e+02 1.3574000e+02 5.8320000e-01 2.3780000e+02 9.2000000e+00 3.8830000e+03 9.3272000e+00 3.8519000e+03 9.4545000e+00 3.8208000e+03 9.5817000e+00 3.7897000e+03 - 4.0000000e+00 1.9300000e+01 3.3000000e+02 1.3900000e+02 5.3000000e-01 2.1700000e+02 1.6955000e+01 3.4008000e+02 1.3859000e+02 5.7118000e-01 2.1643000e+02 1.4609000e+01 3.5017000e+02 1.3817000e+02 6.1236000e-01 2.1586000e+02 1.2264000e+01 3.6025000e+02 1.3776000e+02 6.5354000e-01 2.1530000e+02 7.1821000e+00 4.2750000e+03 7.0040000e+00 4.4064000e+03 6.8260000e+00 4.5378000e+03 6.6480000e+00 4.6692000e+03 - 5.0000000e+00 2.2300000e+01 3.1200000e+02 9.9000000e+01 5.3000000e-01 1.4400000e+02 2.3995000e+01 3.1678000e+02 9.9816000e+01 5.7336000e-01 1.4049000e+02 2.5690000e+01 3.2156000e+02 1.0063000e+02 6.1673000e-01 1.3698000e+02 2.7385000e+01 3.2634000e+02 1.0145000e+02 6.6009000e-01 1.3347000e+02 6.3618000e+00 1.6240000e+03 6.1731000e+00 1.9356000e+03 5.9845000e+00 2.2472000e+03 5.7959000e+00 2.5588000e+03 - 6.0000000e+00 2.3900000e+01 3.0000000e+02 9.2000000e+01 1.9000000e-01 1.2600000e+02 2.3104000e+01 2.9823000e+02 8.8809000e+01 2.2017000e-01 1.2541000e+02 2.2309000e+01 2.9646000e+02 8.5617000e+01 2.5034000e-01 1.2482000e+02 2.1513000e+01 2.9469000e+02 8.2426000e+01 2.8051000e-01 1.2424000e+02 6.8801000e+00 2.2483000e+03 6.4963000e+00 1.9822000e+03 6.1125000e+00 1.7161000e+03 5.7287000e+00 1.4500000e+03 - 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--- a/extra/control-devel/devel/fixtest.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,34 +0,0 @@ -% Extract FFT -for N = 1:500 - - if (rem (N, 2)) % odd - n1 = (N+1)/2; - else % even - n1 = N/2+1; - endif - - n2 = fix (N/2) + 1; - - if (n1 != n2) - warning ("FFT %d: n1=%d, n2=%d", N, n1, n2); - endif - -endfor - - -% Frequency Vector -for N = 1:500 - - if (rem (N, 2)) % odd - n1 = (N-1)/2; - else % even - n1 = N/2; - endif - - n2 = fix (N/2); - - if (n1 != n2) - warning ("W %d: n1=%d, n2=%d", N, n1, n2); - endif - -endfor
--- a/extra/control-devel/devel/generate_devel_pdf.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,12 +0,0 @@ -homedir = pwd (); -develdir = fileparts (which ("generate_devel_pdf")); -pdfdir = [develdir, "/pdfdoc"]; -cd (pdfdir); - -collect_texinfo_strings - -for i = 1:5 - system ("pdftex -interaction batchmode control-devel.tex"); -endfor - -cd (homedir);
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1564.00 6.000 121.756 - 1566.00 6.000 121.268 - 1568.00 6.000 121.268 - 1570.00 6.000 121.268 - 1572.00 6.000 121.024 - 1574.00 6.000 120.780 - 1576.00 6.000 120.780 - 1578.00 6.000 120.536 - 1580.00 6.000 120.780 - 1582.00 6.000 120.780 - 1584.00 6.000 121.024 - 1586.00 6.000 121.024 - 1588.00 6.000 121.268 - 1590.00 6.000 121.268 - 1592.00 6.000 120.780 - 1594.00 6.000 120.780 - 1596.00 6.000 120.536 - 1598.00 6.000 120.536 - 1600.00 6.000 120.536
--- a/extra/control-devel/devel/iddata_merge.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,14 +0,0 @@ -%u = iddata ({(1:10).', (21:30).'}, {(41:50).', (61:70).'}); -%v = iddata ({(11:20).', (31:40).'}, {(51:60).', (71:80).'}); - -oy = ones (200, 5); -ou = ones (200, 4); -y = repmat ({oy}, 6, 1); -u = repmat ({ou}, 6, 1); - -u = iddata (y, u) -v = u - -a = [u, v] -b = [u; v] -c = merge (u, v) \ No newline at end of file
--- a/extra/control-devel/devel/identVS.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,66 +0,0 @@ -function [sys, x0] = identVS (dat, s = [], nn = []) - -n=nn; - - %nobr = 15; - meth = 3-1; %1-1; - alg = 1-1; - jobd = 2-1; - batch = 4-1; - conct = 2-1; - %ctrl = 0; - rcond = 0.0; - tol = -1.0; - - [ns, l, m, e] = size (dat); - - if (isempty (s) && isempty (n)) - nsmp = ns(1); - nobr = fix ((nsmp+1)/(2*(m+l+1))); - ctrl = 0; # confirm system order estimate - n = 0; - % nsmp >= 2*(m+l+1)*nobr - 1 - % nobr <= (nsmp+1)/(2*(m+l+1)) - elseif (isempty (s)) - s = min (2*n, n+10); - nsmp = ns(1); - nobr = fix ((nsmp+1)/(2*(m+l+1))); - nobr = min (nobr, s); - ctrl = 1; # no confirmation - elseif (isempty (n)) - nobr = s; - ctrl = 0; # confirm system order estimate - n = 0; - else # s & n non-empty - nsmp = ns(1); - nobr = fix ((nsmp+1)/(2*(m+l+1))); - if (s > nobr) - error ("ident: s > nobr"); - endif - nobr = s; - ctrl = 1; - ## TODO: specify n for IB01BD - endif - -nobr - %nsmp = ns(1) - %nobr = fix ((nsmp+1)/(2*(m+l+1))) - % nsmp >= 2*(m+l+1)*nobr - 1 - % nobr <= (nsmp+1)/(2*(m+l+1)) -%nobr = 10 - [r, sv, n] = slident_a (dat.y{1}, dat.u{1}, nobr, n, meth, alg, jobd, batch, conct, ctrl, rcond, tol); - -%r -sv - -n -n = nn; - [a, b, c, d, q, ry, s, k] = slident_b (dat.y{1}, dat.u{1}, nobr, n, meth, alg, jobd, batch, conct, ctrl, rcond, tol, \ - r, sv, n); - - x0 = slident_c (dat.y{1}, dat.u{1}, nobr, n, meth, alg, jobd, batch, conct, ctrl, rcond, tol, \ - a, b, c, d); - - sys = ss (a, b, c, d, -1); - -endfunction
--- a/extra/control-devel/devel/ident_combinations.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,51 +0,0 @@ -function [sys, x0] = ident_combinations (dat, s = [], n = [], meth, alg) - - - - %nobr = 15; -% meth = 1; % 2 % geht: meth/alg 1/1, -% alg = 2; % 0 % geht nicht: meth/alg 0/1 - conct = 1; - ctrl = 0; %1; - rcond = 0.0; - tol = -1.0; % 0; - - [ns, l, m, e] = size (dat); - - if (isempty (s) && isempty (n)) - nsmp = ns(1); - nobr = fix ((nsmp+1)/(2*(m+l+1))); - ctrl = 0; # confirm system order estimate - n = 0; - % nsmp >= 2*(m+l+1)*nobr - 1 - % nobr <= (nsmp+1)/(2*(m+l+1)) - elseif (isempty (s)) - s = min (2*n, n+10); - nsmp = ns(1); - nobr = fix ((nsmp+1)/(2*(m+l+1))); - nobr = min (nobr, s); - ctrl = 1; # no confirmation - elseif (isempty (n)) - nobr = s; - ctrl = 0; # confirm system order estimate - n = 0; - else # s & n non-empty - nsmp = ns(1); - nobr = fix ((nsmp+1)/(2*(m+l+1))); - if (s > nobr) - error ("ident: s > nobr"); - endif - nobr = s; - ctrl = 1; - ## TODO: specify n for IB01BD - endif - - [a, b, c, d, q, ry, s, k, x0] = slident (dat.y, dat.u, nobr, n, meth, alg, conct, ctrl, rcond, tol); - - sys = ss (a, b, c, d, dat.tsam{1}); - - if (numel (x0) == 1) - x0 = x0{1}; - endif - -endfunction
--- a/extra/control-devel/devel/makefile_devel.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,21 +0,0 @@ -## ============================================================================== -## Developer Makefile for OCT-files -## ============================================================================== -## USAGE: * fetch control-devel from Octave-Forge by svn -## * add control-devel/inst, control-devel/src and control-devel/devel -## to your Octave path (by an .octaverc file) -## * run makefile_devel -## ============================================================================== - -homedir = pwd (); -develdir = fileparts (which ("makefile_devel")); -srcdir = [develdir, "/../src"]; -cd (srcdir); - -## system ("make realclean"); # recompile slicotlibrary.a -system ("make clean"); -system ("make -j1 all"); -system ("rm *.o"); -system ("rm *.d"); - -cd (homedir); \ No newline at end of file
--- a/extra/control-devel/devel/pH.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,68 +0,0 @@ -%{ -Contributed by: - Jairo Espinosa - K.U.Leuven ESAT-SISTA - K.Mercierlaan 94 - B3001 Heverlee - Jairo.Espinosa@esat.kuleuven.ac.be - -Description: - Simulation data of a pH neutralization process in a constant volume - stirring tank. - Volume of the tank 1100 liters - Concentration of the acid solution (HAC) 0.0032 Mol/l - Concentration of the base solution (NaOH) 0,05 Mol/l -Sampling: - 10 sec -Number: - 2001 -Inputs: - u1: Acid solution flow in liters - u2: Base solution flow in liters - -Outputs: - y: pH of the solution in the tank - -References: - T.J. Mc Avoy, E.Hsu and S.Lowenthal, Dynamics of pH in controlled - stirred tank reactor, Ind.Eng.Chem.Process Des.Develop.11(1972) - 71-78 - -Properties: - Highly non-linear system. - -Columns: - Column 1: time-steps - Column 2: input u1 - Column 3: input u2 - Column 4: output y - -Category: - Process industry systems - -%} - -clear all, close all, clc - -load pHdata.dat -U=pHdata(:,2:3); -Y=pHdata(:,4); - - -dat = iddata (Y, U) - -[sys, x0] = moen4 (dat, 's', 15, 'n', 6, 'noise', 'k') % s=15, n=6 - - -[y, t] = lsim (sys, [U, Y], [], x0); - -err = norm (Y - y, 1) / norm (Y, 1) -st = isstable (sys) - -figure (1) -plot (t, Y(:,1), 'b', t, y(:,1), 'r') -ylim ([0, 15]) -title ('DaISy [96-014]: pH neutralization process in a stirring tank - highly non-linear') -legend ('y measured', 'y simulated', 'location', 'southeast') - -
--- a/extra/control-devel/devel/pH2.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,74 +0,0 @@ -%{ -Contributed by: - Jairo Espinosa - K.U.Leuven ESAT-SISTA - K.Mercierlaan 94 - B3001 Heverlee - Jairo.Espinosa@esat.kuleuven.ac.be - -Description: - Simulation data of a pH neutralization process in a constant volume - stirring tank. - Volume of the tank 1100 liters - Concentration of the acid solution (HAC) 0.0032 Mol/l - Concentration of the base solution (NaOH) 0,05 Mol/l -Sampling: - 10 sec -Number: - 2001 -Inputs: - u1: Acid solution flow in liters - u2: Base solution flow in liters - -Outputs: - y: pH of the solution in the tank - -References: - T.J. Mc Avoy, E.Hsu and S.Lowenthal, Dynamics of pH in controlled - stirred tank reactor, Ind.Eng.Chem.Process Des.Develop.11(1972) - 71-78 - -Properties: - Highly non-linear system. - -Columns: - Column 1: time-steps - Column 2: input u1 - Column 3: input u2 - Column 4: output y - -Category: - Process industry systems - -%} - -clear all, close all, clc - -load pHdata.dat -U=pHdata(:,2:3); -Y=pHdata(:,4); - - -dat = iddata (Y, U) - -[sys, x0, info] = moen4 (dat, 's', 15, 'n', 6) % s=15, n=6 - -l = lqe (sys, info.Q, 100*info.Ry) - -[a, b, c, d] = ssdata (sys); - -sys = ss ([a-l*c], [b-l*d, l], c, [d, 0], -1) - - -[y, t] = lsim (sys, [U, Y], [], x0); - -err = norm (Y - y, 1) / norm (Y, 1) -st = isstable (sys) - -figure (1) -plot (t, Y(:,1), 'b', t, y(:,1), 'r') -ylim ([0, 15]) -title ('DaISy [96-014]: pH neutralization process in a stirring tank - highly non-linear') -legend ('y measured', 'y simulated', 'location', 'southeast') - -
--- a/extra/control-devel/devel/pHarx.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,69 +0,0 @@ -%{ -Contributed by: - Jairo Espinosa - K.U.Leuven ESAT-SISTA - K.Mercierlaan 94 - B3001 Heverlee - Jairo.Espinosa@esat.kuleuven.ac.be - -Description: - Simulation data of a pH neutralization process in a constant volume - stirring tank. - Volume of the tank 1100 liters - Concentration of the acid solution (HAC) 0.0032 Mol/l - Concentration of the base solution (NaOH) 0,05 Mol/l -Sampling: - 10 sec -Number: - 2001 -Inputs: - u1: Acid solution flow in liters - u2: Base solution flow in liters - -Outputs: - y: pH of the solution in the tank - -References: - T.J. Mc Avoy, E.Hsu and S.Lowenthal, Dynamics of pH in controlled - stirred tank reactor, Ind.Eng.Chem.Process Des.Develop.11(1972) - 71-78 - -Properties: - Highly non-linear system. - -Columns: - Column 1: time-steps - Column 2: input u1 - Column 3: input u2 - Column 4: output y - -Category: - Process industry systems - -%} - -clear all, close all, clc - -load pHdata.dat -U=pHdata(:,2:3); -Y=pHdata(:,4); - - -dat = iddata (Y, U) - -% [sys, x0] = ident (dat, 15, 6) % s=15, n=6 -% sys = arx (dat, 6) % normally na = nb -[sys, x0] = arx (dat, 6) % normally na = nb - - -% [y, t] = lsim (sys, U, [], x0); -% [y, t] = lsim (sys(:, 1:2), U); -[y, t] = lsim (sys, U, [], x0); - -err = norm (Y - y, 1) / norm (Y, 1) - -figure (1) -plot (t, Y(:,1), 'b', t, y(:,1), 'r') - - -
--- a/extra/control-devel/devel/pHdata.dat Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,2001 +0,0 @@ - 1.0000000e+00 8.8758367e+00 1.0000000e+00 6.9129087e+00 - 2.0000000e+00 1.1025642e+01 1.0000000e+00 1.0839350e+01 - 3.0000000e+00 9.4613547e+00 1.0000000e+00 1.0894930e+01 - 4.0000000e+00 1.1930201e+01 1.0000000e+00 1.0955416e+01 - 5.0000000e+00 1.0890642e+01 1.0000000e+00 1.0969890e+01 - 6.0000000e+00 1.1013423e+01 1.0000000e+00 1.0984813e+01 - 7.0000000e+00 1.0606074e+01 1.0000000e+00 1.0999915e+01 - 8.0000000e+00 1.0526539e+01 1.0000000e+00 1.1016242e+01 - 9.0000000e+00 1.1538829e+01 1.0000000e+00 1.1029860e+01 - 1.0000000e+01 9.0908399e+00 1.0000000e+00 1.1042747e+01 - 1.1000000e+01 1.1065979e+01 1.0000000e+00 1.1070374e+01 - 1.2000000e+01 9.9109271e+00 1.0000000e+00 1.1077190e+01 - 1.3000000e+01 9.0996274e+00 1.0000000e+00 1.1094999e+01 - 1.4000000e+01 9.4370599e+00 1.0000000e+00 1.1117991e+01 - 1.5000000e+01 8.6660288e+00 1.0000000e+00 1.1135708e+01 - 1.6000000e+01 9.9460695e+00 1.0000000e+00 1.1154470e+01 - 1.7000000e+01 1.1590625e+01 1.0000000e+00 1.1149743e+01 - 1.8000000e+01 1.1636832e+01 1.0000000e+00 1.1136811e+01 - 1.9000000e+01 8.2422573e+00 1.0000000e+00 1.1144831e+01 - 2.0000000e+01 1.0018092e+01 1.0000000e+00 1.1152625e+01 - 2.1000000e+01 1.0065168e+01 1.0000000e+00 1.1158187e+01 - 2.2000000e+01 9.2761318e+00 1.0000000e+00 1.1165849e+01 - 2.3000000e+01 1.1946568e+01 1.0000000e+00 1.1154987e+01 - 2.4000000e+01 9.0645780e+00 1.0000000e+00 1.1145798e+01 - 2.5000000e+01 8.3629316e+00 1.0000000e+00 1.1164855e+01 - 2.6000000e+01 1.1791057e+01 1.0000000e+00 1.1176835e+01 - 2.7000000e+01 1.0002828e+01 0.0000000e+00 1.1059178e+01 - 2.8000000e+01 9.1083272e+00 0.0000000e+00 1.0894936e+01 - 2.9000000e+01 1.1655270e+01 0.0000000e+00 1.0614993e+01 - 3.0000000e+01 1.0118990e+01 0.0000000e+00 9.8317104e+00 - 3.1000000e+01 9.8577833e+00 0.0000000e+00 6.0060516e+00 - 3.2000000e+01 1.1763920e+01 0.0000000e+00 5.6246623e+00 - 3.3000000e+01 8.2003359e+00 0.0000000e+00 5.4052386e+00 - 3.4000000e+01 1.1080818e+01 0.0000000e+00 5.2496791e+00 - 3.5000000e+01 1.1311269e+01 0.0000000e+00 5.1168385e+00 - 3.6000000e+01 8.5014615e+00 0.0000000e+00 5.0215846e+00 - 3.7000000e+01 1.0753821e+01 0.0000000e+00 4.9428188e+00 - 3.8000000e+01 1.1472989e+01 0.0000000e+00 4.8527575e+00 - 3.9000000e+01 1.0944898e+01 0.0000000e+00 4.7739873e+00 - 4.0000000e+01 1.0901648e+01 0.0000000e+00 4.7034443e+00 - 4.1000000e+01 1.1997832e+01 0.0000000e+00 4.6344089e+00 - 4.2000000e+01 8.9327795e+00 0.0000000e+00 4.5666470e+00 - 4.3000000e+01 1.0000000e+01 0.0000000e+00 4.5131990e+00 - 4.4000000e+01 1.0000000e+01 0.0000000e+00 4.4607910e+00 - 4.5000000e+01 1.0000000e+01 0.0000000e+00 4.4106846e+00 - 4.6000000e+01 1.0000000e+01 0.0000000e+00 4.3628042e+00 - 4.7000000e+01 1.0000000e+01 0.0000000e+00 4.3169213e+00 - 4.8000000e+01 1.0000000e+01 0.0000000e+00 4.2729752e+00 - 4.9000000e+01 1.0000000e+01 0.0000000e+00 4.2308931e+00 - 5.0000000e+01 1.0000000e+01 0.0000000e+00 4.1905193e+00 - 5.1000000e+01 1.0000000e+01 0.0000000e+00 4.1525114e+00 - 5.2000000e+01 1.0000000e+01 2.0000000e+00 4.6163761e+00 - 5.3000000e+01 1.0000000e+01 2.0000000e+00 5.0180717e+00 - 5.4000000e+01 1.0000000e+01 2.0000000e+00 5.5388985e+00 - 5.5000000e+01 1.0000000e+01 2.0000000e+00 1.0240425e+01 - 5.6000000e+01 1.0000000e+01 2.0000000e+00 1.0864526e+01 - 5.7000000e+01 1.0000000e+01 2.0000000e+00 1.1091120e+01 - 5.8000000e+01 1.0000000e+01 2.0000000e+00 1.1226228e+01 - 5.9000000e+01 1.0000000e+01 2.0000000e+00 1.1319712e+01 - 6.0000000e+01 1.0000000e+01 2.0000000e+00 1.1389335e+01 - 6.1000000e+01 1.0000000e+01 2.0000000e+00 1.1443597e+01 - 6.2000000e+01 1.0000000e+01 2.0000000e+00 1.1487179e+01 - 6.3000000e+01 1.0000000e+01 2.0000000e+00 1.1522900e+01 - 6.4000000e+01 1.0000000e+01 2.0000000e+00 1.1552685e+01 - 6.5000000e+01 1.0000000e+01 2.0000000e+00 1.1577810e+01 - 6.6000000e+01 1.0000000e+01 2.0000000e+00 1.1599224e+01 - 6.7000000e+01 1.0000000e+01 2.0000000e+00 1.1617614e+01 - 6.8000000e+01 1.0000000e+01 2.0000000e+00 1.1633520e+01 - 6.9000000e+01 1.0000000e+01 2.0000000e+00 1.1647344e+01 - 7.0000000e+01 1.0000000e+01 2.0000000e+00 1.1659397e+01 - 7.1000000e+01 1.1967972e+01 2.0000000e+00 1.1669950e+01 - 7.2000000e+01 1.1958446e+01 2.0000000e+00 1.1671852e+01 - 7.3000000e+01 8.4544710e+00 2.0000000e+00 1.1680913e+01 - 7.4000000e+01 8.5539305e+00 2.0000000e+00 1.1697474e+01 - 7.5000000e+01 8.6615203e+00 2.0000000e+00 1.1711431e+01 - 7.6000000e+01 1.1876000e+01 2.0000000e+00 1.1707143e+01 - 7.7000000e+01 9.8496978e+00 0.0000000e+00 1.1631787e+01 - 7.8000000e+01 1.1577324e+01 0.0000000e+00 1.1566760e+01 - 7.9000000e+01 1.1767325e+01 0.0000000e+00 1.1481169e+01 - 8.0000000e+01 1.1903341e+01 0.0000000e+00 1.1380073e+01 - 8.1000000e+01 8.4980255e+00 0.0000000e+00 1.1286743e+01 - 8.2000000e+01 9.4398900e+00 0.0000000e+00 1.1170642e+01 - 8.3000000e+01 8.9842068e+00 0.0000000e+00 1.1046493e+01 - 8.4000000e+01 1.1926760e+01 0.0000000e+00 1.0849682e+01 - 8.5000000e+01 1.1654656e+01 0.0000000e+00 1.0495365e+01 - 8.6000000e+01 1.1209312e+01 0.0000000e+00 6.7484067e+00 - 8.7000000e+01 8.0646077e+00 0.0000000e+00 5.7285667e+00 - 8.8000000e+01 1.1870577e+01 0.0000000e+00 5.4585866e+00 - 8.9000000e+01 1.1999824e+01 0.0000000e+00 5.2251051e+00 - 9.0000000e+01 1.1851125e+01 0.0000000e+00 5.0601054e+00 - 9.1000000e+01 1.1445149e+01 0.0000000e+00 4.9330044e+00 - 9.2000000e+01 1.0838319e+01 0.0000000e+00 4.8299847e+00 - 9.3000000e+01 1.0114975e+01 0.0000000e+00 4.7442184e+00 - 9.4000000e+01 9.3756515e+00 0.0000000e+00 4.6714920e+00 - 9.5000000e+01 8.7231029e+00 0.0000000e+00 4.6087369e+00 - 9.6000000e+01 8.2480236e+00 0.0000000e+00 4.5536973e+00 - 9.7000000e+01 8.0164423e+00 0.0000000e+00 4.5041161e+00 - 9.8000000e+01 8.0605453e+00 0.0000000e+00 4.4579115e+00 - 9.9000000e+01 8.3742029e+00 0.0000000e+00 4.4129517e+00 - 1.0000000e+02 8.9138215e+00 0.0000000e+00 4.3678861e+00 - 1.0100000e+02 9.6044024e+00 0.0000000e+00 4.3225636e+00 - 1.0200000e+02 1.0349965e+01 1.0000000e+00 4.5292892e+00 - 1.0300000e+02 1.1046888e+01 1.0000000e+00 4.7084388e+00 - 1.0400000e+02 1.1598310e+01 1.0000000e+00 4.8637019e+00 - 1.0500000e+02 1.1927591e+01 1.0000000e+00 5.0065395e+00 - 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--- a/extra/control-devel/devel/pdfdoc/collect_texinfo_strings.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,41 +0,0 @@ -% pack_name = "generate_html" -% pack_name = "control" -% pack_name = "quaternion" -pack_name = "control-devel" - -% Load Packages -pkg load "generate_html" -pkg ("load", pack_name); - -% Get list of functions -list = pkg ("describe", pack_name); - -%list - -% Open output file -fid = fopen ("functions.texi", "w"); - -for k = 1:numel (list {1}.provides) - - group = list {1}.provides{k}; - functions = group.functions; - - % fprintf (fid, '@section %s\n', group.category); - fprintf (fid, '@chapter %s\n', group.category); - - for k=1:numel(functions) - [TEXT, FORMAT] = get_help_text (functions(k)); - fun = functions{k}; - if (fun(1) == "@") - % fprintf (fid, '@subsection @%s\n', fun); - fprintf (fid, '@section @%s\n', fun); - else - % fprintf (fid, '@subsection %s\n', fun); - fprintf (fid, '@section %s\n', fun); - endif - fprintf (fid,TEXT); - end - -end - -fclose(fid);
--- a/extra/control-devel/devel/pdfdoc/control-devel.tex Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,104 +0,0 @@ -\input texinfo @c -*-texinfo-*- -@c %**start of header -@setfilename control-devel.info -@settitle Octave Control Systems Package -@afourpaper -@set VERSION 0.2.0 -@finalout -@c @afourwide -@c %**end of header - - -@c The following macro is used for the on-line help system, but we don't -@c want lots of `See also: foo, bar, and baz' strings cluttering the -@c printed manual (that information should be in the supporting text for -@c each group of functions and variables). - -@macro seealso {args} -@iftex -@vskip 2pt -@end iftex -@ifnottex -@c Texinfo @sp should work but in practice produces ugly results for HTML. -@c A simple blank line produces the correct behavior. -@c @sp 1 - -@end ifnottex -@noindent -@strong{See also:} \args\. -@end macro - - -@c %*** Start of TITLEPAGE -@titlepage -@title control-devel @value{VERSION} -@subtitle Control Systems Package for GNU Octave -@author Lukas F. Reichlin -@page -@vskip 0pt plus 1filll -Copyright @copyright{} 2009-2012, Lukas F. Reichlin @email{lukas.reichlin@@gmail.com} - -This manual is generated automatically from the texinfo help strings -of the package's functions. - -Permission is granted to make and distribute verbatim copies of -this manual provided the copyright notice and this permission notice -are preserved on all copies. - -Permission is granted to copy and distribute modified versions of this -manual under the conditions for verbatim copying, provided that the entire -resulting derived work is distributed under the terms of a permission -notice identical to this one. - -Permission is granted to copy and distribute translations of this manual -into another language, under the same conditions as for modified versions. -@page -@chapheading Preface -The @acronym{GNU} Octave control package from version 2 onwards was -developed by Lukas F. Reichlin and is based on the proven open-source -library @acronym{SLICOT}. This new package is intended as a replacement -for control-1.0.11 by A. Scottedward Hodel and his students. -Its main features are: -@itemize -@item Reliable solvers for Lyapunov, Sylvester and algebraic Riccati equations. -@item Pole placement techniques as well as @tex $ H_2 $ @end tex -and @tex $ H_{\infty} $ @end tex -synthesis methods. -@item Frequency-weighted model and controller reduction. -@item Overloaded operators due to the use of classes introduced with Octave 3.2. -@item Support for descriptor state-space models and non-proper transfer functions. -@item Improved @acronym{MATLAB} compatibility. -@end itemize - -@sp 5 -@subheading Acknowledgments -The author is indebted to several people and institutions who helped -him to achieve his goals. I am particularly grateful to Luca Favatella -who introduced me to Octave development as well as discussed and revised -my early draft code with great patience. My continued support from the -@acronym{FHNW} University of Applied Sciences of Northwestern Switzerland, -where I could work on the control package as a semester project, has also -been important. Furthermore, I thank the @acronym{SLICOT} authors -Peter Benner, Vasile Sima and Andras Varga for their advice. - - -@sp 5 -@subheading Using the help function -Some functions of the control package are listed with a leading @code{@@lti/}. -This is only needed to view the help text of the function, e.g. @w{@code{help norm}} -shows the built-in function while @w{@code{help @@lti/norm}} shows the overloaded -function for @acronym{LTI} systems. Note that there are @acronym{LTI} functions -like @code{pole} that have no built-in equivalent. - -When just using the function, the leading @code{@@lti/} must @strong{not} be typed. -Octave selects the right function automatically. So one can type @w{@code{norm (sys, inf)}} -and @w{@code{norm (matrix, inf)}} regardless of the class of the argument. -@end titlepage -@c %*** End of TITLEPAGE - -@contents -@c @chapter Function Reference -@include functions.texi - -@end -@bye
--- a/extra/control-devel/devel/pdfdoc/info_generate_manual.txt Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,13 +0,0 @@ -* Check that "pkg list" lists the packages generate_html and control-devel. -* Run collect_texinfo_strings within Octave. This script collects the Texinfo strings from all - functions listed in the package's INDEX file and writes them to the file functions.texi. - Don't edit the file functions.texi since your changes will be lost by the next run. -* Adapt version number in control-devel.tex -* Run control-devel.tex - - -pdftex control-devel.tex -q - -Alternatively: -Run generate_devel_pdf
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1.7400000e+02 1.6400000e+02 5.7200000e+02 1.3640000e+03 -1.6490000e+03 2.5700000e+02 -4.0000000e+01 1.7800000e+02 3.5600000e+02 -2.8437000e+02 -5.3105000e+02 -4.9061000e+02 - 1.7500000e+02 1.6300000e+02 5.8700000e+02 1.3430000e+03 -1.6500000e+03 2.4600000e+02 -1.5000000e+01 1.8500000e+02 3.5300000e+02 -2.6933000e+02 -5.2618000e+02 -4.7915000e+02 - 1.7600000e+02 1.6100000e+02 6.8300000e+02 1.3530000e+03 -1.6580000e+03 2.6100000e+02 -2.7000000e+01 1.7000000e+02 3.5900000e+02 -2.8677000e+02 -5.2909000e+02 -4.8587000e+02 - 1.7700000e+02 1.6000000e+02 5.7200000e+02 1.3590000e+03 -1.6540000e+03 2.6100000e+02 1.5000000e+01 1.7300000e+02 3.5100000e+02 -2.6299000e+02 -5.3393000e+02 -5.0195000e+02 - 1.7800000e+02 1.6000000e+02 6.0700000e+02 1.3550000e+03 -1.6510000e+03 2.6700000e+02 2.3000000e+01 1.7500000e+02 3.5600000e+02 -2.6303000e+02 -5.3557000e+02 -5.0135000e+02 - 1.7900000e+02 1.5800000e+02 5.8000000e+02 1.3490000e+03 -1.6550000e+03 2.7300000e+02 4.4000000e+01 1.7800000e+02 3.3800000e+02 -2.5204000e+02 -5.3960000e+02 -5.0662000e+02 - 1.8000000e+02 1.6100000e+02 6.3100000e+02 1.3620000e+03 -1.6520000e+03 2.7200000e+02 4.7000000e+01 1.7100000e+02 3.2300000e+02 -2.6356000e+02 -5.4610000e+02 -5.1190000e+02 - 1.8100000e+02 1.6000000e+02 7.0600000e+02 1.3820000e+03 -1.6570000e+03 2.9800000e+02 4.0000000e+00 1.5300000e+02 2.9400000e+02 -2.9576000e+02 -5.5968000e+02 -5.2427000e+02 - 1.8200000e+02 1.6100000e+02 6.0100000e+02 1.3560000e+03 -1.6540000e+03 2.7700000e+02 2.3000000e+01 1.4100000e+02 2.9500000e+02 -2.8718000e+02 -5.6851000e+02 -5.3400000e+02 - 1.8300000e+02 1.5900000e+02 5.7000000e+02 1.3540000e+03 -1.6530000e+03 2.7400000e+02 3.9000000e+01 1.4100000e+02 3.0600000e+02 -2.7639000e+02 -5.6855000e+02 -5.2629000e+02 - 1.8400000e+02 1.5800000e+02 5.4700000e+02 1.3470000e+03 -1.6570000e+03 2.6100000e+02 5.2000000e+01 1.3900000e+02 3.1300000e+02 -2.5927000e+02 -5.6399000e+02 -5.2010000e+02 - 1.8500000e+02 1.5800000e+02 5.8200000e+02 1.3320000e+03 -1.6570000e+03 2.5700000e+02 5.3000000e+01 1.4200000e+02 3.1300000e+02 -2.5785000e+02 -5.5747000e+02 -5.2015000e+02 - 1.8600000e+02 1.5700000e+02 5.7000000e+02 1.3400000e+03 -1.6570000e+03 2.6700000e+02 6.9000000e+01 1.4200000e+02 3.1200000e+02 -2.5199000e+02 -5.5578000e+02 -5.2904000e+02 - 1.8700000e+02 1.5400000e+02 5.5600000e+02 1.3430000e+03 -1.6570000e+03 2.6800000e+02 7.4000000e+01 1.3600000e+02 3.0600000e+02 -2.4545000e+02 -5.5582000e+02 -5.3401000e+02 - 1.8800000e+02 1.5700000e+02 5.3700000e+02 1.3450000e+03 -1.6570000e+03 -4.2500000e+02 1.9600000e+02 1.6400000e+02 2.7700000e+02 -2.8011000e+02 -5.4967000e+02 -5.7073000e+02 - 1.8900000e+02 1.5800000e+02 5.5500000e+02 1.3310000e+03 -1.6530000e+03 -5.8100000e+02 3.4700000e+02 2.0800000e+02 1.3300000e+02 -3.1995000e+02 -4.9697000e+02 -6.1617000e+02 - 1.9000000e+02 1.5800000e+02 5.5100000e+02 1.3150000e+03 -1.6540000e+03 -6.4300000e+02 4.6100000e+02 2.3000000e+02 -5.8000000e+01 -3.2126000e+02 -4.1269000e+02 -6.4590000e+02 - 1.9100000e+02 1.5900000e+02 5.9000000e+02 1.3220000e+03 -1.6560000e+03 -6.8700000e+02 5.2600000e+02 2.0400000e+02 -2.5100000e+02 -3.1328000e+02 -3.0600000e+02 -6.5649000e+02 - 1.9200000e+02 1.6000000e+02 5.6600000e+02 1.3150000e+03 -1.6570000e+03 -7.3700000e+02 5.8100000e+02 1.6100000e+02 -3.8500000e+02 -2.7765000e+02 -1.9647000e+02 -6.5015000e+02 - 1.9300000e+02 1.6000000e+02 5.5300000e+02 1.3150000e+03 -1.6530000e+03 -7.6700000e+02 5.8800000e+02 1.1900000e+02 -4.5800000e+02 -2.2465000e+02 -9.2677000e+01 -6.1837000e+02 - 1.9400000e+02 1.6100000e+02 6.4400000e+02 1.3270000e+03 -1.3960000e+03 -7.3100000e+02 5.4900000e+02 6.3000000e+01 -5.2800000e+02 -1.8456000e+02 -2.2277000e+00 -5.7001000e+02 - 1.9500000e+02 1.5900000e+02 6.4000000e+02 1.3350000e+03 -5.7700000e+02 -6.3900000e+02 4.9700000e+02 5.0000000e+00 -5.5000000e+02 -1.1778000e+02 7.2004000e+01 -5.0293000e+02 - 1.9600000e+02 1.6100000e+02 7.2600000e+02 1.3340000e+03 -5.7700000e+02 -7.3000000e+02 4.2000000e+02 -2.0000000e+01 -4.9800000e+02 -9.6611000e+01 1.2077000e+02 -3.9313000e+02 - 1.9700000e+02 1.7500000e+02 7.2900000e+02 1.3100000e+03 -5.7300000e+02 -7.1100000e+02 3.2700000e+02 -4.9000000e+01 -4.6400000e+02 -6.9050000e+01 1.5983000e+02 -2.8852000e+02 - 1.9800000e+02 1.7500000e+02 8.5400000e+02 1.3300000e+03 -5.7600000e+02 -6.9000000e+02 1.9800000e+02 -7.8000000e+01 -4.3800000e+02 -7.2970000e+01 1.8176000e+02 -1.9352000e+02 - 1.9900000e+02 1.6100000e+02 7.2900000e+02 1.3130000e+03 -5.7300000e+02 -6.3600000e+02 1.5400000e+02 -8.0000000e+01 -4.0900000e+02 -1.7599000e+01 2.0261000e+02 -1.1462000e+02 - 2.0000000e+02 1.7600000e+02 7.0600000e+02 1.3140000e+03 -5.8300000e+02 -7.4500000e+02 1.3000000e+02 -6.0000000e+01 -3.7700000e+02 2.7441000e+01 2.2371000e+02 -4.0925000e+01
--- a/extra/control-devel/devel/rarx.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,202 +0,0 @@ -## Copyright (C) 2012 Lukas F. Reichlin -## -## This file is part of LTI Syncope. -## -## LTI Syncope is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## LTI Syncope is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with LTI Syncope. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{sys} =} arx (@var{dat}, @var{na}, @var{nb}) -## ARX -## @end deftypefn - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: April 2012 -## Version: 0.1 - -function [sys, varargout] = rarx (dat, na, nb) - - ## TODO: delays - - if (nargin != 3) - print_usage (); - endif - - if (! isa (dat, "iddata")) - error ("arx: first argument must be an iddata dataset"); - endif - - ## p: outputs, m: inputs, ex: experiments - [~, p, m, ex] = size (dat); - - ## extract data - Y = dat.y; - U = dat.u; - tsam = dat.tsam; - - ## multi-experiment data requires equal sampling times - if (ex > 1 && ! isequal (tsam{:})) - error ("arx: require equally sampled experiments"); - else - tsam = tsam{1}; - endif - - - if (is_real_scalar (na, nb)) - na = repmat (na, p, 1); # na(p-by-1) - nb = repmat (nb, p, m); # nb(p-by-m) - elseif (! (is_real_vector (na) && is_real_matrix (nb) \ - && rows (na) == p && rows (nb) == p && columns (nb) == m)) - error ("arx: require na(%dx1) instead of (%dx%d) and nb(%dx%d) instead of (%dx%d)", \ - p, rows (na), columns (na), p, m, rows (nb), columns (nb)); - endif - - max_nb = max (nb, [], 2); # one maximum for each row/output, max_nb(p-by-1) - n = max (na, max_nb); # n(p-by-1) - - ## create empty cells for numerator and denominator polynomials - num = cell (p, m+p); - den = cell (p, m+p); - - ## MIMO (p-by-m) models are identified as p MISO (1-by-m) models - ## For multi-experiment data, minimize the trace of the error - for i = 1 : p # for every output - Phi = cell (ex, 1); # one regression matrix per experiment - for e = 1 : ex # for every experiment - ## avoid warning: toeplitz: column wins anti-diagonal conflict - ## therefore set first row element equal to y(1) - PhiY = toeplitz (Y{e}(1:end-1, i), [Y{e}(1, i); zeros(na(i)-1, 1)]); - ## create MISO Phi for every experiment - PhiU = arrayfun (@(x) toeplitz (U{e}(1:end-1, x), [U{e}(1, x); zeros(nb(i,x)-1, 1)]), 1:m, "uniformoutput", false); - Phi{e} = (horzcat (-PhiY, PhiU{:}))(n(i):end, :); - endfor - - ## compute parameter vector Theta - Theta = __theta__ (Phi, Y, i, n); - - ## extract polynomial matrices A and B from Theta - ## A is a scalar polynomial for output i, i=1:p - ## B is polynomial row vector (1-by-m) for output i - A = [1; Theta(1:na(i))]; # a0 = 1, a1 = Theta(1), an = Theta(n) - ThetaB = Theta(na(i)+1:end); # all polynomials from B are in one column vector - B = mat2cell (ThetaB, nb(i,:)); # now separate the polynomials, one for each input - B = reshape (B, 1, []); # make B a row cell (1-by-m) - B = cellfun (@(x) [0; x], B, "uniformoutput", false); # b0 = 0 (leading zero required by filt) - - ## add error inputs - Be = repmat ({0}, 1, p); # there are as many error inputs as system outputs (p) - Be(i) = 1; # inputs m+1:m+p are zero, except m+i which is one - num(i, :) = [B, Be]; # numerator polynomials for output i, individual for each input - den(i, :) = repmat ({A}, 1, m+p); # in a row (output i), all inputs have the same denominator polynomial - endfor - - ## A(q) y(t) = B(q) u(t) + e(t) - ## there is only one A per row - ## B(z) and A(z) are a Matrix Fraction Description (MFD) - ## y = A^-1(q) B(q) u(t) + A^-1(q) e(t) - ## since A(q) is a diagonal polynomial matrix, its inverse is trivial: - ## the corresponding transfer function has common row denominators. - - sys = filt (num, den, tsam); # filt creates a transfer function in z^-1 - - ## compute initial state vector x0 if requested - ## this makes only sense for state-space models, therefore convert TF to SS - if (nargout > 1) - sys = prescale (ss (sys(:,1:m))); - x0 = slib01cd (Y, U, sys.a, sys.b, sys.c, sys.d, 0.0); - ## return x0 as vector for single-experiment data - ## instead of a cell containing one vector - if (numel (x0) == 1) - x0 = x0{1}; - endif - varargout{1} = x0; - endif - -endfunction - - -%function theta = __theta__ (phi, y, i, n) -function Theta = __theta__ (Phi, Y, i, n) - - - if (numel (Phi) == 1) # single-experiment dataset - % recursive least-squares with efficient matrix inversion - [pr, pc] = size (Phi{1}); - lambda = 1; % default 1 - Theta = zeros (pc, 1); - P = 10 * eye (pc); - for t = 1 : pr - phi = Phi{1}(t,:); # note that my phi is Ljung's phi.' - y = Y{1}(t+n(i), :); - den = lambda + phi*P*phi.'; - L = P * phi.' / den; - P = (P - (P * phi.' * phi * P) / den) / lambda; - Theta += L * (y - phi*Theta); - endfor -%{ - ## use "square-root algorithm" - A = horzcat (phi{1}, y{1}(n(i)+1:end, i)); # [Phi, Y] - R0 = triu (qr (A, 0)); # 0 for economy-size R (without zero rows) - R1 = R0(1:end-1, 1:end-1); # R1 is triangular - can we exploit this in R1\R2? - R2 = R0(1:end-1, end); - theta = __ls_svd__ (R1, R2); # R1 \ R2 - - ## Theta = Phi \ Y(n+1:end, :); # naive formula - ## theta = __ls_svd__ (phi{1}, y{1}(n(i)+1:end, i)); -%} - else # multi-experiment dataset - ## TODO: find more sophisticated formula than - ## Theta = (Phi1' Phi + Phi2' Phi2 + ...) \ (Phi1' Y1 + Phi2' Y2 + ...) - - ## covariance matrix C = (Phi1' Phi + Phi2' Phi2 + ...) - tmp = cellfun (@(Phi) Phi.' * Phi, phi, "uniformoutput", false); - rc = cellfun (@rcond, tmp); # C auch noch testen? QR oder SVD? - C = plus (tmp{:}); - - ## PhiTY = (Phi1' Y1 + Phi2' Y2 + ...) - tmp = cellfun (@(Phi, Y) Phi.' * Y(n(i)+1:end, i), phi, y, "uniformoutput", false); - PhiTY = plus (tmp{:}); - - ## pseudoinverse Theta = C \ Phi'Y - theta = __ls_svd__ (C, PhiTY); - endif - -endfunction - - -function x = __ls_svd__ (A, b) - - ## solve the problem Ax=b - ## x = A\b would also work, - ## but this way we have better control and warnings - - ## solve linear least squares problem by pseudoinverse - ## the pseudoinverse is computed by singular value decomposition - ## M = U S V* ---> M+ = V S+ U* - ## Th = Ph \ Y = Ph+ Y - ## Th = V S+ U* Y, S+ = 1 ./ diag (S) - - [U, S, V] = svd (A, 0); # 0 for "economy size" decomposition - S = diag (S); # extract main diagonal - r = sum (S > eps*S(1)); - if (r < length (S)) - warning ("arx: rank-deficient coefficient matrix"); - warning ("sampling time too small"); - warning ("persistence of excitation"); - endif - V = V(:, 1:r); - S = S(1:r); - U = U(:, 1:r); - x = V * (S .\ (U' * b)); # U' is the conjugate transpose - -endfunction
--- a/extra/control-devel/devel/subsref_problem.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,10 +0,0 @@ -DestillationME - -tsam = dat.tsam -tsam{:} - - -dat.tsam -dat.tsam{:} % only 1 times -1 instead of 4 - -a(1:4) = tsam{:} \ No newline at end of file
--- a/extra/control-devel/devel/test_arx.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,10 +0,0 @@ -u = [ 0; 0.5; 1; 1; 1; 1; 1 ]; -y = [ 0; 0; 0.25; 0.62; 0.81; 0.90; 0.95 ]; - -dat = iddata (y, u) - -sys = arx (dat, 1, 1) - - -ysim = lsim (sys(1,1), u); -
--- a/extra/control-devel/devel/test_fitfrd.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,6 +0,0 @@ -sys = ss (-1, 1, 1, 0); -n = 1; - -ret0 = fitfrd (sys, n) - -ret1 = fitfrd (sys, n, 1) \ No newline at end of file
--- a/extra/control-devel/devel/test_frd2iddata.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,15 +0,0 @@ -sys = ss (-2,3,4,5) - -H = idfrd (sys) - -H.frequency -H.responsedata - - -dat = iddata (H) -dat.y -H.responsedata - -dat.u % alles 1! -dat.frequency -H.frequency \ No newline at end of file
--- a/extra/control-devel/devel/test_iddata.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,55 +0,0 @@ -dat = iddata ((1:10).', (21:30).') - -a = iddata ({(1:10).', (21:30).'}, {(31:40).', (41:50).'}) - -b = iddata ({(1:10).', (21:30).'}, []) - -c = iddata ({(1:10).', (21:40).'}, {(31:40).', (41:60).'}) - -x = c; -%x.y = {} - -%x.u = [] -x.u = x.y - -d = iddata ({(1:10).', (21:25).'}, {(31:40).', (41:45).'}) - -e = iddata ({(1:10).', (21:25).', (21:125).'}, {(31:40).', (41:45).', (41:145).'}) - - -oy = ones (200, 5); -ou = ones (200, 4); -y = repmat ({oy}, 6, 1); -u = repmat ({ou}, 6, 1); - -f = iddata (y, u) -%{ -f.expname = strseq ("experiment", 1:6) -f.expname(2) = "value 1" -f.expname{2} = "value 2" -%} - -%cat (4, f, f, f) - -%cat (1, f, f) - -u = iddata ({(1:10).', (21:30).'}, {(41:50).', (61:70).'}); -v = iddata ({(11:20).', (31:40).'}, {(51:60).', (71:80).'}); - - -w = cat (1, u, v) - -cat (3, d, e) - -%cat (1, b, 4) - - -un = iddata ({(1:10).', (21:30).'}, {(41:50).', (61:70).'}, [], "expname", strseq ("alpha", 1:2)); -vn = iddata ({(11:20).', (31:40).'}, {(51:60).', (71:80).'}, [], "expname", strseq ("beta", 1:2)); -n = [un; vn] -cat (1, un) - -cat (1, un, un, vn, vn, vn) - -%dat = iddata (ones (100, 3)); -%dat2 = cat (1, dat, zeros (4, 3), dat)
--- a/extra/control-devel/inst/test_devel.m Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,48 +0,0 @@ -## Copyright (C) 2012 Lukas F. Reichlin -## -## This file is part of LTI Syncope. -## -## LTI Syncope is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## LTI Syncope is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with LTI Syncope. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Script File} {} test_devel -## Execute all available tests at once. -## The Octave control-devel package is based on the @uref{http://www.slicot.org, SLICOT} library. -## SLICOT needs a LAPACK library which is also a prerequisite for Octave itself. -## In case of failing test, it is highly recommended to use -## @uref{http://www.netlib.org/lapack/, Netlib's reference LAPACK} -## for building Octave. Using ATLAS may lead to sign changes -## in some entries in the state-space matrices. -## In general, these sign changes are not 'wrong' and can be regarded as -## the result of state transformations. Such state transformations -## (but not input/output transformations) have no influence on the -## input-output behaviour of the system. For better numerics, -## the control package uses such transformations by default when -## calculating the frequency responses and a few other things. -## However, arguments like the Hankel singular Values (HSV) must not change. -## Differing HSVs and failing algorithms are known for using Framework Accelerate -## from Mac OS X 10.7. -## @end deftypefn - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -## identification -test @iddata/iddata -test @iddata/cat -test @iddata/detrend -test @iddata/fft - -test moen4 \ No newline at end of file
--- a/extra/control-devel/src/Makefile Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,34 +0,0 @@ -MKOCTFILE ?= mkoctfile - -ifndef LAPACK_LIBS -LAPACK_LIBS := $(shell $(MKOCTFILE) -p LAPACK_LIBS) -endif -ifndef BLAS_LIBS -BLAS_LIBS := $(shell $(MKOCTFILE) -p BLAS_LIBS) -endif -ifndef FLIBS -FLIBS := $(shell $(MKOCTFILE) -p FLIBS) -endif -LFLAGS := $(shell $(MKOCTFILE) -p LFLAGS) $(LAPACK_LIBS) $(BLAS_LIBS) $(FLIBS) - -all: devel_slicot_functions.oct - -# unpack and compile SLICOT library -slicotlibrary.a: slicot.tar.gz - tar -xzf slicot.tar.gz - mv slicot/src/*.f . - mv slicot/src_aux/*.f . - $(MKOCTFILE) -c *.f - ar -rc slicotlibrary.a *.o - rm -rf *.o *.f slicot - -# slicot functions -devel_slicot_functions.oct: devel_slicot_functions.cc slicotlibrary.a - LFLAGS="$(LFLAGS)" \ - $(MKOCTFILE) devel_slicot_functions.cc common.cc slicotlibrary.a - -clean: - rm -rf *.o core octave-core *.oct *~ *.f slicot - -realclean: clean - rm -rf *.a \ No newline at end of file
--- a/extra/control-devel/src/common.cc Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,97 +0,0 @@ -/* - -Copyright (C) 2010, 2011 Lukas F. Reichlin - -This file is part of LTI Syncope. - -LTI Syncope is free software: you can redistribute it and/or modify -it under the terms of the GNU General Public License as published by -the Free Software Foundation, either version 3 of the License, or -(at your option) any later version. - -LTI Syncope is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -GNU General Public License for more details. - -You should have received a copy of the GNU General Public License -along with LTI Syncope. If not, see <http://www.gnu.org/licenses/>. - -Common code for oct-files. - -Author: Lukas Reichlin <lukas.reichlin@gmail.com> -Created: April 2010 -Version: 0.3 - -*/ - - -#include <octave/oct.h> - -int max (int a, int b) -{ - if (a > b) - return a; - else - return b; -} - -int max (int a, int b, int c) -{ - return max (max (a, b), c); -} - -int max (int a, int b, int c, int d) -{ - return max (max (a, b), max (c, d)); -} - -int max (int a, int b, int c, int d, int e) -{ - return max (max (a, b, c, d), e); -} - -int min (int a, int b) -{ - if (a < b) - return a; - else - return b; -} - -void error_msg (const char name[], int index, int max, const char* msg[]) -{ - if (index == 0) - return; - - if (index < 0) - error ("%s: the %d-th argument had an invalid value", name, index); - else if (index <= max) - error ("%s: %s", name, msg[index]); - else - error ("%s: unknown error, info = %d", name, index); -} - -void warning_msg (const char name[], int index, int max, const char* msg[]) -{ - if (index == 0) - return; - - if (index > 0 && index <= max) - warning ("%s: %s", name, msg[index]); - else - warning ("%s: unknown warning, iwarn = %d", name, index); -} - -void warning_msg (const char name[], int index, int max, const char* msg[], int offset) -{ - if (index == 0) - return; - - if (index > 0 && index <= max) - warning ("%s: %s", name, msg[index]); - else if (index > offset) - warning ("%s: %d+%d: %d %s", name, offset, index-offset, index-offset, msg[max+1]); - else - warning ("%s: unknown warning, iwarn = %d", name, index); -}
--- a/extra/control-devel/src/common.h Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,40 +0,0 @@ -/* - -Copyright (C) 2012 Lukas F. Reichlin - -This file is part of LTI Syncope. - -LTI Syncope is free software: you can redistribute it and/or modify -it under the terms of the GNU General Public License as published by -the Free Software Foundation, either version 3 of the License, or -(at your option) any later version. - -LTI Syncope is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -GNU General Public License for more details. - -You should have received a copy of the GNU General Public License -along with LTI Syncope. If not, see <http://www.gnu.org/licenses/>. - -Common code for oct-files. - -Author: Lukas Reichlin <lukas.reichlin@gmail.com> -Created: February 2012 -Version: 0.1 - -*/ - -#ifndef COMMON_H -#define COMMON_H - -int max (int a, int b); -int max (int a, int b, int c); -int max (int a, int b, int c, int d); -int max (int a, int b, int c, int d, int e); -int min (int a, int b); -void error_msg (const char name[], int index, int max, const char* msg[]); -void warning_msg (const char name[], int index, int max, const char* msg[]); -void warning_msg (const char name[], int index, int max, const char* msg[], int offset); - -#endif
--- a/extra/control-devel/src/devel_slicot_functions.cc Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,3 +0,0 @@ -#include "slident_a.cc" -#include "slident_b.cc" -#include "slident_c.cc" \ No newline at end of file
--- a/extra/control-devel/src/readme Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,69 +0,0 @@ -SLICOT Library Root Directory ------------------------------ - -SLICOT - Subroutine Library In COntrol Theory - is a general purpose basic -mathematical library for control theoretical computations. The library -provides tools to perform essential system analysis and synthesis tasks. -The main emphasis in SLICOT is on numerical reliability of implemented -algorithms and the numerical robustness and efficiency of routines. -Providing algorithmic flexibility and the use of rigorous implementation -and documentation standards are other SLICOT features. - -The SLICOT Library is available as standard Fortran 77 code in double -precision. Each user-callable subroutine for control computations is -accompanied by an example program which illustrates the use of the -subroutine and can act as a template for the user's own routines. - -The SLICOT Library is organized by chapters, sections and subsections. -The following chapters are currently included: - -A : Analysis Routines -B : Benchmark and Test Problems -D : Data Analysis -F : Filtering -I : Identification -M : Mathematical Routines -N : Nonlinear Systems - (not yet available, except for some auxiliary routines for Wiener systems) -S : Synthesis Routines -T : Transformation Routines -U : Utility Routines - -SLICOT Library Root Directory contains few, basic files for the SLICOT Library -distribution and generation. When distributed, SLICOT software comes with -several filled-in subdirectories (benchmark_data, doc, examples, examples77, -src, and src_aux), and five files in this root -directory: -- this file, readme, -- the file Installation.txt, describing the SLICOT software installation, -- the main SLICOT Library documentation index, libindex.html, and -- two template files for building the object library and executable programs, - make.inc and makefile, -- GNU GENERAL PUBLIC LICENSE Version 2 text file. -The last two files might need few changes for being adapted to the specific -platform used. Details about installing/updating the SLICOT software are -given in the file Installation.txt. - -After software installation, this directory will also contain the library -file slicot.a or slicot.lib, for Unix or Windows platforms, respectively. -The library file could then be linked in applications programs, as usual. -Specific examples are contained in the directories examples and examples77. -The on-line documentation of the SLICOT user's callable routines is -accessible via the main SLICOT Library documentation index, libindex.html. -This file also contains a link to the documentation of the lower-level, -support routines. - -The SLICOT Library is built on LAPACK (Linear Algebra PACKage) and BLAS -(Basic Linear Algebra Subprograms) collections. Therefore, these -packages should be available on the platform used. - -Basic References: - -1. P. Benner, V. Mehrmann, V. Sima, S. Van Huffel, and A. Varga, - "SLICOT - A Subroutine Library in Systems and Control Theory", - Applied and Computational Control, Signals, and Circuits - (Birkhauser), Vol. 1, Ch. 10, pp. 505-546, 1999. - -2. S. Van Huffel, V. Sima, A. Varga, S. Hammarling, and F. Delebecque, - "Development of High Performance Numerical Software for Control", - IEEE Control Systems Magazine, Vol. 24, Nr. 1, Feb., pp. 60-76, 2004.
--- a/extra/control-devel/src/slident_a.cc Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,422 +0,0 @@ -/* - -Copyright (C) 2012 Lukas F. Reichlin - -This file is part of LTI Syncope. - -LTI Syncope is free software: you can redistribute it and/or modify -it under the terms of the GNU General Public License as published by -the Free Software Foundation, either version 3 of the License, or -(at your option) any later version. - -LTI Syncope is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -GNU General Public License for more details. - -You should have received a copy of the GNU General Public License -along with LTI Syncope. If not, see <http://www.gnu.org/licenses/>. - -SLICOT system identification -Uses SLICOT IB01AD, IB01BD and IB01CD by courtesy of NICONET e.V. -<http://www.slicot.org> - -Author: Lukas Reichlin <lukas.reichlin@gmail.com> -Created: March 2012 -Version: 0.1 - -*/ - -#include <octave/oct.h> -#include <f77-fcn.h> -#include "common.h" - -extern "C" -{ - int F77_FUNC (ib01ad, IB01AD) - (char& METH, char& ALG, char& JOBD, - char& BATCH, char& CONCT, char& CTRL, - int& NOBR, int& M, int& L, - int& NSMP, - double* U, int& LDU, - double* Y, int& LDY, - int& N, - double* R, int& LDR, - double* SV, - double& RCOND, double& TOL, - int* IWORK, - double* DWORK, int& LDWORK, - int& IWARN, int& INFO); - - int F77_FUNC (ib01bd, IB01BD) - (char& METH, char& JOB, char& JOBCK, - int& NOBR, int& N, int& M, int& L, - int& NSMPL, - double* R, int& LDR, - double* A, int& LDA, - double* C, int& LDC, - double* B, int& LDB, - double* D, int& LDD, - double* Q, int& LDQ, - double* RY, int& LDRY, - double* S, int& LDS, - double* K, int& LDK, - double& TOL, - int* IWORK, - double* DWORK, int& LDWORK, - bool* BWORK, - int& IWARN, int& INFO); - - int F77_FUNC (ib01cd, IB01CD) - (char& JOBX0, char& COMUSE, char& JOB, - int& N, int& M, int& L, - int& NSMP, - double* A, int& LDA, - double* B, int& LDB, - double* C, int& LDC, - double* D, int& LDD, - double* U, int& LDU, - double* Y, int& LDY, - double* X0, - double* V, int& LDV, - double& TOL, - int* IWORK, - double* DWORK, int& LDWORK, - int& IWARN, int& INFO); -} - -// PKG_ADD: autoload ("slident_a", "devel_slicot_functions.oct"); -DEFUN_DLD (slident_a, args, nargout, - "-*- texinfo -*-\n\ -Slicot IB01AD Release 5.0\n\ -No argument checking.\n\ -For internal use only.") -{ - int nargin = args.length (); - octave_value_list retval; - - if (nargin != 12) - { - print_usage (); - } - else - { -//////////////////////////////////////////////////////////////////////////////////// -// SLICOT IB01AD - preprocess the input-output data // -//////////////////////////////////////////////////////////////////////////////////// - - // arguments in - char meth; - char alg; - char jobd; - char batch; - char conct; - char ctrl; - char metha; - char jobda; // ??? unused - - Matrix y = args(0).matrix_value (); - Matrix u = args(1).matrix_value (); - int nobr = args(2).int_value (); - int nuser = args(3).int_value (); - - const int imeth = args(4).int_value (); - const int ialg = args(5).int_value (); - const int ijobd = args(6).int_value (); - const int ibatch = args(7).int_value (); - const int iconct = args(8).int_value (); - const int ictrl = args(9).int_value (); - - double rcond = args(10).double_value (); - double tol = args(11).double_value (); - double tolb = args(10).double_value (); // tolb = rcond - - - switch (imeth) - { - case 0: - meth = 'M'; - metha = 'M'; - break; - case 1: - meth = 'N'; - metha = 'N'; - break; - case 2: - meth = 'C'; - metha = 'N'; // no typo here - break; - default: - error ("slib01ad: argument 'meth' invalid"); - } - - switch (ialg) - { - case 0: - alg = 'C'; - break; - case 1: - alg = 'F'; - break; - case 2: - alg = 'Q'; - break; - default: - error ("slib01ad: argument 'alg' invalid"); - } - - if (meth == 'C') - jobd = 'N'; - else if (ijobd == 0) - jobd = 'M'; - else - jobd = 'N'; - - switch (ibatch) - { - case 0: - batch = 'F'; - break; - case 1: - batch = 'I'; - break; - case 2: - batch = 'L'; - break; - case 3: - batch = 'O'; - break; - default: - error ("slib01ad: argument 'batch' invalid"); - } - - if (iconct == 0) - conct = 'C'; - else - conct = 'N'; - - if (ictrl == 0) - ctrl = 'C'; - else - ctrl = 'N'; - - - int m = u.columns (); // m: number of inputs - int l = y.columns (); // l: number of outputs - int nsmp = y.rows (); // nsmp: number of samples - // y.rows == u.rows is checked by iddata class - // TODO: check minimal nsmp size - - if (batch == 'O') - { - if (nsmp < 2*(m+l+1)*nobr - 1) - error ("slident: require NSMP >= 2*(M+L+1)*NOBR - 1"); - } - else - { - if (nsmp < 2*nobr) - error ("slident: require NSMP >= 2*NOBR"); - } - - int ldu; - - if (m == 0) - ldu = 1; - else // m > 0 - ldu = nsmp; - - int ldy = nsmp; - - // arguments out - int n; - int ldr; - - if (metha == 'M' && jobd == 'M') - ldr = max (2*(m+l)*nobr, 3*m*nobr); - else if (metha == 'N' || (metha == 'M' && jobd == 'N')) - ldr = 2*(m+l)*nobr; - else - error ("slib01ad: could not handle 'ldr' case"); - - Matrix r (ldr, 2*(m+l)*nobr); - ColumnVector sv (l*nobr); - - // workspace - int liwork; - - if (metha == 'N') // if METH = 'N' - liwork = (m+l)*nobr; - else if (alg == 'F') // if METH = 'M' and ALG = 'F' - liwork = m+l; - else // if METH = 'M' and ALG = 'C' or 'Q' - liwork = 0; - - // TODO: Handle 'k' for DWORK - - int ldwork; - int ns = nsmp - 2*nobr + 1; - - if (alg == 'C') - { - if (batch == 'F' || batch == 'I') - { - if (conct == 'C') - ldwork = (4*nobr-2)*(m+l); - else // (conct == 'N') - ldwork = 1; - } - else if (metha == 'M') // && (batch == 'L' || batch == 'O') - { - if (conct == 'C' && batch == 'L') - ldwork = max ((4*nobr-2)*(m+l), 5*l*nobr); - else if (jobd == 'M') - ldwork = max ((2*m-1)*nobr, (m+l)*nobr, 5*l*nobr); - else // (jobd == 'N') - ldwork = 5*l*nobr; - } - else // meth == 'N' && (batch == 'L' || batch == 'O') - { - ldwork = 5*(m+l)*nobr + 1; - } - } - else if (alg == 'F') - { - if (batch != 'O' && conct == 'C') - ldwork = (m+l)*2*nobr*(m+l+3); - else if (batch == 'F' || batch == 'I') // && conct == 'N' - ldwork = (m+l)*2*nobr*(m+l+1); - else // (batch == 'L' || '0' && conct == 'N') - ldwork = (m+l)*4*nobr*(m+l+1)+(m+l)*2*nobr; - } - else // (alg == 'Q') - { - // int ns = nsmp - 2*nobr + 1; - - if (ldr >= ns && batch == 'F') - { - ldwork = 4*(m+l)*nobr; - } - else if (ldr >= ns && batch == 'O') - { - if (metha == 'M') - ldwork = max (4*(m+l)*nobr, 5*l*nobr); - else // (meth == 'N') - ldwork = 5*(m+l)*nobr + 1; - } - else if (conct == 'C' && (batch == 'I' || batch == 'L')) - { - ldwork = 4*(nobr+1)*(m+l)*nobr; - } - else // if ALG = 'Q', (BATCH = 'F' or 'O', and LDR < NS), or (BATCH = 'I' or 'L' and CONCT = 'N') - { - ldwork = 6*(m+l)*nobr; - } - } - -/* -IB01AD.f Lines 438-445 -C FURTHER COMMENTS -C -C For ALG = 'Q', BATCH = 'O' and LDR < NS, or BATCH <> 'O', the -C calculations could be rather inefficient if only minimal workspace -C (see argument LDWORK) is provided. It is advisable to provide as -C much workspace as possible. Almost optimal efficiency can be -C obtained for LDWORK = (NS+2)*(2*(M+L)*NOBR), assuming that the -C cache size is large enough to accommodate R, U, Y, and DWORK. -*/ - -// warning ("==================== ldwork before: %d =====================", ldwork); -// ldwork = (ns+2)*(2*(m+l)*nobr); -ldwork = max (ldwork, (ns+2)*(2*(m+l)*nobr)); -// ldwork *= 3; -// warning ("==================== ldwork after: %d =====================", ldwork); - - -/* -IB01AD.f Lines 291-195: -c the workspace used for alg = 'q' is -c ldrwrk*2*(m+l)*nobr + 4*(m+l)*nobr, -c where ldrwrk = ldwork/(2*(m+l)*nobr) - 2; recommended -c value ldrwrk = ns, assuming a large enough cache size. -c for good performance, ldwork should be larger. - -somehow ldrwrk and ldwork must have been mixed up here - -*/ - - - OCTAVE_LOCAL_BUFFER (int, iwork, liwork); - OCTAVE_LOCAL_BUFFER (double, dwork, ldwork); - - // error indicators - int iwarn = 0; - int info = 0; - - - // SLICOT routine IB01AD - F77_XFCN (ib01ad, IB01AD, - (metha, alg, jobd, - batch, conct, ctrl, - nobr, m, l, - nsmp, - u.fortran_vec (), ldu, - y.fortran_vec (), ldy, - n, - r.fortran_vec (), ldr, - sv.fortran_vec (), - rcond, tol, - iwork, - dwork, ldwork, - iwarn, info)); - - - if (f77_exception_encountered) - error ("ident: exception in SLICOT subroutine IB01AD"); - - static const char* err_msg[] = { - "0: OK", - "1: a fast algorithm was requested (ALG = 'C', or 'F') " - "in sequential data processing, but it failed; the " - "routine can be repeatedly called again using the " - "standard QR algorithm", - "2: the singular value decomposition (SVD) algorithm did " - "not converge"}; - - static const char* warn_msg[] = { - "0: OK", - "1: the number of 100 cycles in sequential data " - "processing has been exhausted without signaling " - "that the last block of data was get; the cycle " - "counter was reinitialized", - "2: a fast algorithm was requested (ALG = 'C' or 'F'), " - "but it failed, and the QR algorithm was then used " - "(non-sequential data processing)", - "3: all singular values were exactly zero, hence N = 0 " - "(both input and output were identically zero)", - "4: the least squares problems with coefficient matrix " - "U_f, used for computing the weighted oblique " - "projection (for METH = 'N'), have a rank-deficient " - "coefficient matrix", - "5: the least squares problem with coefficient matrix " - "r_1 [6], used for computing the weighted oblique " - "projection (for METH = 'N'), has a rank-deficient " - "coefficient matrix"}; - - - error_msg ("ident", info, 2, err_msg); - warning_msg ("ident", iwarn, 5, warn_msg); - - - // resize - int rs = 2*(m+l)*nobr; - r.resize (rs, rs); - - - // return values - retval(0) = r; - retval(1) = sv; - retval(2) = octave_value (n); - } - - return retval; -}
--- a/extra/control-devel/src/slident_b.cc Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,669 +0,0 @@ -/* - -Copyright (C) 2012 Lukas F. Reichlin - -This file is part of LTI Syncope. - -LTI Syncope is free software: you can redistribute it and/or modify -it under the terms of the GNU General Public License as published by -the Free Software Foundation, either version 3 of the License, or -(at your option) any later version. - -LTI Syncope is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -GNU General Public License for more details. - -You should have received a copy of the GNU General Public License -along with LTI Syncope. If not, see <http://www.gnu.org/licenses/>. - -SLICOT system identification -Uses SLICOT IB01AD, IB01BD and IB01CD by courtesy of NICONET e.V. -<http://www.slicot.org> - -Author: Lukas Reichlin <lukas.reichlin@gmail.com> -Created: March 2012 -Version: 0.1 - -*/ - -#include <octave/oct.h> -#include <f77-fcn.h> -#include "common.h" - -extern "C" -{ - int F77_FUNC (ib01ad, IB01AD) - (char& METH, char& ALG, char& JOBD, - char& BATCH, char& CONCT, char& CTRL, - int& NOBR, int& M, int& L, - int& NSMP, - double* U, int& LDU, - double* Y, int& LDY, - int& N, - double* R, int& LDR, - double* SV, - double& RCOND, double& TOL, - int* IWORK, - double* DWORK, int& LDWORK, - int& IWARN, int& INFO); - - int F77_FUNC (ib01bd, IB01BD) - (char& METH, char& JOB, char& JOBCK, - int& NOBR, int& N, int& M, int& L, - int& NSMPL, - double* R, int& LDR, - double* A, int& LDA, - double* C, int& LDC, - double* B, int& LDB, - double* D, int& LDD, - double* Q, int& LDQ, - double* RY, int& LDRY, - double* S, int& LDS, - double* K, int& LDK, - double& TOL, - int* IWORK, - double* DWORK, int& LDWORK, - bool* BWORK, - int& IWARN, int& INFO); - - int F77_FUNC (ib01cd, IB01CD) - (char& JOBX0, char& COMUSE, char& JOB, - int& N, int& M, int& L, - int& NSMP, - double* A, int& LDA, - double* B, int& LDB, - double* C, int& LDC, - double* D, int& LDD, - double* U, int& LDU, - double* Y, int& LDY, - double* X0, - double* V, int& LDV, - double& TOL, - int* IWORK, - double* DWORK, int& LDWORK, - int& IWARN, int& INFO); -} - -// PKG_ADD: autoload ("slident_b", "devel_slicot_functions.oct"); -DEFUN_DLD (slident_b, args, nargout, - "-*- texinfo -*-\n\ -Slicot IB01AD Release 5.0\n\ -No argument checking.\n\ -For internal use only.") -{ - int nargin = args.length (); - octave_value_list retval; - - if (nargin != 15) - { - print_usage (); - } - else - { -//////////////////////////////////////////////////////////////////////////////////// -// SLICOT IB01AD - preprocess the input-output data // -//////////////////////////////////////////////////////////////////////////////////// - - // arguments in - char meth; - char alg; - char jobd; - char batch; - char conct; - char ctrl; - char metha; - char jobda; // ??? unused - - Matrix y = args(0).matrix_value (); - Matrix u = args(1).matrix_value (); - int nobr = args(2).int_value (); - int nuser = args(3).int_value (); - - const int imeth = args(4).int_value (); - const int ialg = args(5).int_value (); - const int ijobd = args(6).int_value (); - const int ibatch = args(7).int_value (); - const int iconct = args(8).int_value (); - const int ictrl = args(9).int_value (); - - double rcond = args(10).double_value (); - double tol = args(11).double_value (); - double tolb = args(10).double_value (); // tolb = rcond - - Matrix r = args(12).matrix_value (); - Matrix sv = args(13).matrix_value (); - int n = args(14).int_value (); - - - switch (imeth) - { - case 0: - meth = 'M'; - metha = 'M'; - break; - case 1: - meth = 'N'; - metha = 'N'; - break; - case 2: - meth = 'C'; - metha = 'N'; // no typo here - break; - default: - error ("slib01ad: argument 'meth' invalid"); - } - - switch (ialg) - { - case 0: - alg = 'C'; - break; - case 1: - alg = 'F'; - break; - case 2: - alg = 'Q'; - break; - default: - error ("slib01ad: argument 'alg' invalid"); - } - - if (meth == 'C') - jobd = 'N'; - else if (ijobd == 0) - jobd = 'M'; - else - jobd = 'N'; - - switch (ibatch) - { - case 0: - batch = 'F'; - break; - case 1: - batch = 'I'; - break; - case 2: - batch = 'L'; - break; - case 3: - batch = 'O'; - break; - default: - error ("slib01ad: argument 'batch' invalid"); - } - - if (iconct == 0) - conct = 'C'; - else - conct = 'N'; - - if (ictrl == 0) - ctrl = 'C'; - else - ctrl = 'N'; - - - int m = u.columns (); // m: number of inputs - int l = y.columns (); // l: number of outputs - int nsmp = y.rows (); // nsmp: number of samples - // y.rows == u.rows is checked by iddata class - // TODO: check minimal nsmp size - - if (batch == 'O') - { - if (nsmp < 2*(m+l+1)*nobr - 1) - error ("slident: require NSMP >= 2*(M+L+1)*NOBR - 1"); - } - else - { - if (nsmp < 2*nobr) - error ("slident: require NSMP >= 2*NOBR"); - } - - int ldu; - - if (m == 0) - ldu = 1; - else // m > 0 - ldu = nsmp; - - int ldy = nsmp; - - // arguments out - //int n; - int ldr; - - if (metha == 'M' && jobd == 'M') - ldr = max (2*(m+l)*nobr, 3*m*nobr); - else if (metha == 'N' || (metha == 'M' && jobd == 'N')) - ldr = 2*(m+l)*nobr; - else - error ("slib01ad: could not handle 'ldr' case"); - - //Matrix r (ldr, 2*(m+l)*nobr); - //ColumnVector sv (l*nobr); - - // workspace - int liwork; - - if (metha == 'N') // if METH = 'N' - liwork = (m+l)*nobr; - else if (alg == 'F') // if METH = 'M' and ALG = 'F' - liwork = m+l; - else // if METH = 'M' and ALG = 'C' or 'Q' - liwork = 0; - - // TODO: Handle 'k' for DWORK - - int ldwork; - int ns = nsmp - 2*nobr + 1; - - if (alg == 'C') - { - if (batch == 'F' || batch == 'I') - { - if (conct == 'C') - ldwork = (4*nobr-2)*(m+l); - else // (conct == 'N') - ldwork = 1; - } - else if (metha == 'M') // && (batch == 'L' || batch == 'O') - { - if (conct == 'C' && batch == 'L') - ldwork = max ((4*nobr-2)*(m+l), 5*l*nobr); - else if (jobd == 'M') - ldwork = max ((2*m-1)*nobr, (m+l)*nobr, 5*l*nobr); - else // (jobd == 'N') - ldwork = 5*l*nobr; - } - else // meth == 'N' && (batch == 'L' || batch == 'O') - { - ldwork = 5*(m+l)*nobr + 1; - } - } - else if (alg == 'F') - { - if (batch != 'O' && conct == 'C') - ldwork = (m+l)*2*nobr*(m+l+3); - else if (batch == 'F' || batch == 'I') // && conct == 'N' - ldwork = (m+l)*2*nobr*(m+l+1); - else // (batch == 'L' || '0' && conct == 'N') - ldwork = (m+l)*4*nobr*(m+l+1)+(m+l)*2*nobr; - } - else // (alg == 'Q') - { - // int ns = nsmp - 2*nobr + 1; - - if (ldr >= ns && batch == 'F') - { - ldwork = 4*(m+l)*nobr; - } - else if (ldr >= ns && batch == 'O') - { - if (metha == 'M') - ldwork = max (4*(m+l)*nobr, 5*l*nobr); - else // (meth == 'N') - ldwork = 5*(m+l)*nobr + 1; - } - else if (conct == 'C' && (batch == 'I' || batch == 'L')) - { - ldwork = 4*(nobr+1)*(m+l)*nobr; - } - else // if ALG = 'Q', (BATCH = 'F' or 'O', and LDR < NS), or (BATCH = 'I' or 'L' and CONCT = 'N') - { - ldwork = 6*(m+l)*nobr; - } - } - -/* -IB01AD.f Lines 438-445 -C FURTHER COMMENTS -C -C For ALG = 'Q', BATCH = 'O' and LDR < NS, or BATCH <> 'O', the -C calculations could be rather inefficient if only minimal workspace -C (see argument LDWORK) is provided. It is advisable to provide as -C much workspace as possible. Almost optimal efficiency can be -C obtained for LDWORK = (NS+2)*(2*(M+L)*NOBR), assuming that the -C cache size is large enough to accommodate R, U, Y, and DWORK. -*/ - -// warning ("==================== ldwork before: %d =====================", ldwork); -// ldwork = (ns+2)*(2*(m+l)*nobr); -ldwork = max (ldwork, (ns+2)*(2*(m+l)*nobr)); -// ldwork *= 3; -// warning ("==================== ldwork after: %d =====================", ldwork); - - -/* -IB01AD.f Lines 291-195: -c the workspace used for alg = 'q' is -c ldrwrk*2*(m+l)*nobr + 4*(m+l)*nobr, -c where ldrwrk = ldwork/(2*(m+l)*nobr) - 2; recommended -c value ldrwrk = ns, assuming a large enough cache size. -c for good performance, ldwork should be larger. - -somehow ldrwrk and ldwork must have been mixed up here - -*/ - -#if 0 - OCTAVE_LOCAL_BUFFER (int, iwork, liwork); - OCTAVE_LOCAL_BUFFER (double, dwork, ldwork); - - // error indicators - int iwarn = 0; - int info = 0; - - - // SLICOT routine IB01AD - F77_XFCN (ib01ad, IB01AD, - (metha, alg, jobd, - batch, conct, ctrl, - nobr, m, l, - nsmp, - u.fortran_vec (), ldu, - y.fortran_vec (), ldy, - n, - r.fortran_vec (), ldr, - sv.fortran_vec (), - rcond, tol, - iwork, - dwork, ldwork, - iwarn, info)); - - - if (f77_exception_encountered) - error ("ident: exception in SLICOT subroutine IB01AD"); - - static const char* err_msg[] = { - "0: OK", - "1: a fast algorithm was requested (ALG = 'C', or 'F') " - "in sequential data processing, but it failed; the " - "routine can be repeatedly called again using the " - "standard QR algorithm", - "2: the singular value decomposition (SVD) algorithm did " - "not converge"}; - - static const char* warn_msg[] = { - "0: OK", - "1: the number of 100 cycles in sequential data " - "processing has been exhausted without signaling " - "that the last block of data was get; the cycle " - "counter was reinitialized", - "2: a fast algorithm was requested (ALG = 'C' or 'F'), " - "but it failed, and the QR algorithm was then used " - "(non-sequential data processing)", - "3: all singular values were exactly zero, hence N = 0 " - "(both input and output were identically zero)", - "4: the least squares problems with coefficient matrix " - "U_f, used for computing the weighted oblique " - "projection (for METH = 'N'), have a rank-deficient " - "coefficient matrix", - "5: the least squares problem with coefficient matrix " - "r_1 [6], used for computing the weighted oblique " - "projection (for METH = 'N'), has a rank-deficient " - "coefficient matrix"}; - - - error_msg ("ident", info, 2, err_msg); - warning_msg ("ident", iwarn, 5, warn_msg); - - - // resize - int rs = 2*(m+l)*nobr; - r.resize (rs, rs); - - if (nuser > 0) - { - if (nuser < nobr) - { - n = nuser; - // warning ("ident: nuser (%d) < nobr (%d), n = nuser", nuser, nobr); - } - else - error ("ident: 'nuser' invalid"); - } -#endif -//////////////////////////////////////////////////////////////////////////////////// -// SLICOT IB01BD - estimating system matrices, Kalman gain, and covariances // -//////////////////////////////////////////////////////////////////////////////////// - - // arguments in - char job = 'A'; - char jobck = 'K'; - - // TODO: if meth == 'C', which meth should be taken for IB01AD.f, 'M' or 'N'? - - int nsmpl = nsmp; - - if (nsmpl < 2*(m+l)*nobr) - error ("slident: nsmpl (%d) < 2*(m+l)*nobr (%d)", nsmpl, nobr); - - // arguments out - int lda = max (1, n); - int ldc = max (1, l); - int ldb = max (1, n); - int ldd = max (1, l); - int ldq = n; // if JOBCK = 'C' or 'K' - int ldry = l; // if JOBCK = 'C' or 'K' - int lds = n; // if JOBCK = 'C' or 'K' - int ldk = n; // if JOBCK = 'K' - - Matrix a (lda, n); - Matrix c (ldc, n); - Matrix b (ldb, m); - Matrix d (ldd, m); - - Matrix q (ldq, n); - Matrix ry (ldry, l); - Matrix s (lds, l); - Matrix k (ldk, l); - - // workspace - int liwork_b; - int liw1; - int liw2; - - liw1 = max (n, m*nobr+n, l*nobr, m*(n+l)); - liw2 = n*n; // if JOBCK = 'K' - liwork_b = max (liw1, liw2); - - int ldwork_b; - int ldw1; - int ldw2; - int ldw3; -/* - if (meth == 'M') - { - int ldw1a = max (2*(l*nobr-l)*n+2*n, (l*nobr-l)*n+n*n+7*n); - int ldw1b = max (2*(l*nobr-l)*n+n*n+7*n, - (l*nobr-l)*n+n+6*m*nobr, - (l*nobr-l)*n+n+max (l+m*nobr, l*nobr + max (3*l*nobr+1, m))); - ldw1 = max (ldw1a, ldw1b); - - int aw; - - if (m == 0 || job == 'C') - aw = n + n*n; - else - aw = 0; - - ldw2 = l*nobr*n + max ((l*nobr-l)*n+aw+2*n+max(5*n,(2*m+l)*nobr+l), 4*(m*nobr+n)+1, m*nobr+2*n+l ); - } - else if (meth == 'N') - { - ldw1 = l*nobr*n + max ((l*nobr-l)*n+2*n+(2*m+l)*nobr+l, - 2*(l*nobr-l)*n+n*n+8*n, - n+4*(m*nobr+n)+1, - m*nobr+3*n+l); - - if (m == 0 || job == 'C') - ldw2 = 0; - else - ldw2 = l*nobr*n+m*nobr*(n+l)*(m*(n+l)+1)+ max ((n+l)*(n+l), 4*m*(n+l)+1); - - } - else // (meth == 'C') - { - int ldw1a = max (2*(l*nobr-l)*n+2*n, (l*nobr-l)*n+n*n+7*n); - int ldw1b = l*nobr*n + max ((l*nobr-l)*n+2*n+(2*m+l)*nobr+l, - 2*(l*nobr-l)*n+n*n+8*n, - n+4*(m*nobr+n)+1, - m*nobr+3*n+l); - - ldw1 = max (ldw1a, ldw1b); - - ldw2 = l*nobr*n+m*nobr*(n+l)*(m*(n+l)+1)+ max ((n+l)*(n+l), 4*m*(n+l)+1); - - } -*/ - - int ldw1ax = max (2*(l*nobr-l)*n+2*n, (l*nobr-l)*n+n*n+7*n); - int ldw1bx = max (2*(l*nobr-l)*n+n*n+7*n, - (l*nobr-l)*n+n+6*m*nobr, - (l*nobr-l)*n+n+max (l+m*nobr, l*nobr + max (3*l*nobr+1, m))); - int ldw1x = max (ldw1ax, ldw1bx); - - int aw; - - if (m == 0 || job == 'C') - aw = n + n*n; - else - aw = 0; - - int ldw2x = l*nobr*n + max ((l*nobr-l)*n+aw+2*n+max(5*n,(2*m+l)*nobr+l), 4*(m*nobr+n)+1, m*nobr+2*n+l ); - - - - int ldw1y = l*nobr*n + max ((l*nobr-l)*n+2*n+(2*m+l)*nobr+l, - 2*(l*nobr-l)*n+n*n+8*n, - n+4*(m*nobr+n)+1, - m*nobr+3*n+l); - int ldw2y; - if (m == 0 || job == 'C') - int ldw2y = 0; - else - int ldw2y = l*nobr*n+m*nobr*(n+l)*(m*(n+l)+1)+ max ((n+l)*(n+l), 4*m*(n+l)+1); - - - int ldw1az = max (2*(l*nobr-l)*n+2*n, (l*nobr-l)*n+n*n+7*n); - int ldw1bz = l*nobr*n + max ((l*nobr-l)*n+2*n+(2*m+l)*nobr+l, - 2*(l*nobr-l)*n+n*n+8*n, - n+4*(m*nobr+n)+1, - m*nobr+3*n+l); - - int ldw1z = max (ldw1az, ldw1bz); - - int ldw2z = l*nobr*n+m*nobr*(n+l)*(m*(n+l)+1)+ max ((n+l)*(n+l), 4*m*(n+l)+1); - - - ldw1 = max (ldw1x, ldw1y, ldw1z); - ldw2 = max (ldw2x, ldw2y, ldw2z); - - - - ldw3 = max(4*n*n + 2*n*l + l*l + max (3*l, n*l), 14*n*n + 12*n + 5); - ldwork_b = max (ldw1, ldw2, ldw3); - - // - ldwork_b *= 3; - - OCTAVE_LOCAL_BUFFER (int, iwork_b, liwork_b); - OCTAVE_LOCAL_BUFFER (double, dwork_b, ldwork_b); - OCTAVE_LOCAL_BUFFER (bool, bwork, 2*n); - - - // error indicators - int iwarn_b = 0; - int info_b = 0; - - - // SLICOT routine IB01BD - F77_XFCN (ib01bd, IB01BD, - (meth, job, jobck, - nobr, n, m, l, - nsmpl, - r.fortran_vec (), ldr, - a.fortran_vec (), lda, - c.fortran_vec (), ldc, - b.fortran_vec (), ldb, - d.fortran_vec (), ldd, - q.fortran_vec (), ldq, - ry.fortran_vec (), ldry, - s.fortran_vec (), lds, - k.fortran_vec (), ldk, - tolb, - iwork_b, - dwork_b, ldwork_b, - bwork, - iwarn_b, info_b)); - - - if (f77_exception_encountered) - error ("ident: exception in SLICOT subroutine IB01BD"); - - static const char* err_msg_b[] = { - "0: OK", - "1: error message not specified", - "2: the singular value decomposition (SVD) algorithm did " - "not converge", - "3: a singular upper triangular matrix was found", - "4: matrix A is (numerically) singular in discrete-" - "time case", - "5: the Hamiltonian or symplectic matrix H cannot be " - "reduced to real Schur form", - "6: the real Schur form of the Hamiltonian or " - "symplectic matrix H cannot be appropriately ordered", - "7: the Hamiltonian or symplectic matrix H has less " - "than N stable eigenvalues", - "8: the N-th order system of linear algebraic " - "equations, from which the solution matrix X would " - "be obtained, is singular to working precision", - "9: the QR algorithm failed to complete the reduction " - "of the matrix Ac to Schur canonical form, T", - "10: the QR algorithm did not converge"}; - - static const char* warn_msg_b[] = { - "0: OK", - "1: warning message not specified", - "2: warning message not specified", - "3: warning message not specified", - "4: a least squares problem to be solved has a " - "rank-deficient coefficient matrix", - "5: the computed covariance matrices are too small. " - "The problem seems to be a deterministic one; the " - "gain matrix is set to zero"}; - - - error_msg ("ident", info_b, 10, err_msg_b); - warning_msg ("ident", iwarn_b, 5, warn_msg_b); - - // resize - a.resize (n, n); - c.resize (l, n); - b.resize (n, m); - d.resize (l, m); - - q.resize (n, n); - ry.resize (l, l); - s.resize (n, l); - k.resize (n, l); - - - - // return values - retval(0) = a; - retval(1) = b; - retval(2) = c; - retval(3) = d; - - retval(4) = q; - retval(5) = ry; - retval(6) = s; - retval(7) = k; - } - - return retval; -}
--- a/extra/control-devel/src/slident_c.cc Sat Mar 09 19:12:03 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,473 +0,0 @@ -/* - -Copyright (C) 2012 Lukas F. Reichlin - -This file is part of LTI Syncope. - -LTI Syncope is free software: you can redistribute it and/or modify -it under the terms of the GNU General Public License as published by -the Free Software Foundation, either version 3 of the License, or -(at your option) any later version. - -LTI Syncope is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -GNU General Public License for more details. - -You should have received a copy of the GNU General Public License -along with LTI Syncope. If not, see <http://www.gnu.org/licenses/>. - -SLICOT system identification -Uses SLICOT IB01AD, IB01BD and IB01CD by courtesy of NICONET e.V. -<http://www.slicot.org> - -Author: Lukas Reichlin <lukas.reichlin@gmail.com> -Created: March 2012 -Version: 0.1 - -*/ - -#include <octave/oct.h> -#include <f77-fcn.h> -#include "common.h" - -extern "C" -{ - int F77_FUNC (ib01ad, IB01AD) - (char& METH, char& ALG, char& JOBD, - char& BATCH, char& CONCT, char& CTRL, - int& NOBR, int& M, int& L, - int& NSMP, - double* U, int& LDU, - double* Y, int& LDY, - int& N, - double* R, int& LDR, - double* SV, - double& RCOND, double& TOL, - int* IWORK, - double* DWORK, int& LDWORK, - int& IWARN, int& INFO); - - int F77_FUNC (ib01bd, IB01BD) - (char& METH, char& JOB, char& JOBCK, - int& NOBR, int& N, int& M, int& L, - int& NSMPL, - double* R, int& LDR, - double* A, int& LDA, - double* C, int& LDC, - double* B, int& LDB, - double* D, int& LDD, - double* Q, int& LDQ, - double* RY, int& LDRY, - double* S, int& LDS, - double* K, int& LDK, - double& TOL, - int* IWORK, - double* DWORK, int& LDWORK, - bool* BWORK, - int& IWARN, int& INFO); - - int F77_FUNC (ib01cd, IB01CD) - (char& JOBX0, char& COMUSE, char& JOB, - int& N, int& M, int& L, - int& NSMP, - double* A, int& LDA, - double* B, int& LDB, - double* C, int& LDC, - double* D, int& LDD, - double* U, int& LDU, - double* Y, int& LDY, - double* X0, - double* V, int& LDV, - double& TOL, - int* IWORK, - double* DWORK, int& LDWORK, - int& IWARN, int& INFO); -} - -// PKG_ADD: autoload ("slident_c", "devel_slicot_functions.oct"); -DEFUN_DLD (slident_c, args, nargout, - "-*- texinfo -*-\n\ -Slicot IB01AD Release 5.0\n\ -No argument checking.\n\ -For internal use only.") -{ - int nargin = args.length (); - octave_value_list retval; - - if (nargin != 16) - { - print_usage (); - } - else - { -//////////////////////////////////////////////////////////////////////////////////// -// SLICOT IB01AD - preprocess the input-output data // -//////////////////////////////////////////////////////////////////////////////////// - - // arguments in - char meth; - char alg; - char jobd; - char batch; - char conct; - char ctrl; - char metha; - char jobda; // ??? unused - - Matrix y = args(0).matrix_value (); - Matrix u = args(1).matrix_value (); - int nobr = args(2).int_value (); - int nuser = args(3).int_value (); - - const int imeth = args(4).int_value (); - const int ialg = args(5).int_value (); - const int ijobd = args(6).int_value (); - const int ibatch = args(7).int_value (); - const int iconct = args(8).int_value (); - const int ictrl = args(9).int_value (); - - double rcond = args(10).double_value (); - double tol = args(11).double_value (); - double tolb = args(10).double_value (); // tolb = rcond - - Matrix a = args(12).matrix_value (); - Matrix b = args(13).matrix_value (); - Matrix c = args(14).matrix_value (); - Matrix d = args(15).matrix_value (); - - - switch (imeth) - { - case 0: - meth = 'M'; - metha = 'M'; - break; - case 1: - meth = 'N'; - metha = 'N'; - break; - case 2: - meth = 'C'; - metha = 'N'; // no typo here - break; - default: - error ("slib01ad: argument 'meth' invalid"); - } - - switch (ialg) - { - case 0: - alg = 'C'; - break; - case 1: - alg = 'F'; - break; - case 2: - alg = 'Q'; - break; - default: - error ("slib01ad: argument 'alg' invalid"); - } - - if (meth == 'C') - jobd = 'N'; - else if (ijobd == 0) - jobd = 'M'; - else - jobd = 'N'; - - switch (ibatch) - { - case 0: - batch = 'F'; - break; - case 1: - batch = 'I'; - break; - case 2: - batch = 'L'; - break; - case 3: - batch = 'O'; - break; - default: - error ("slib01ad: argument 'batch' invalid"); - } - - if (iconct == 0) - conct = 'C'; - else - conct = 'N'; - - if (ictrl == 0) - ctrl = 'C'; - else - ctrl = 'N'; - - - int m = u.columns (); // m: number of inputs - int l = y.columns (); // l: number of outputs - int nsmp = y.rows (); // nsmp: number of samples - // y.rows == u.rows is checked by iddata class - // TODO: check minimal nsmp size - - if (batch == 'O') - { - if (nsmp < 2*(m+l+1)*nobr - 1) - error ("slident: require NSMP >= 2*(M+L+1)*NOBR - 1"); - } - else - { - if (nsmp < 2*nobr) - error ("slident: require NSMP >= 2*NOBR"); - } - - int ldu; - - if (m == 0) - ldu = 1; - else // m > 0 - ldu = nsmp; - - int ldy = nsmp; - - // arguments out - int n; - int ldr; - - if (metha == 'M' && jobd == 'M') - ldr = max (2*(m+l)*nobr, 3*m*nobr); - else if (metha == 'N' || (metha == 'M' && jobd == 'N')) - ldr = 2*(m+l)*nobr; - else - error ("slib01ad: could not handle 'ldr' case"); - - Matrix r (ldr, 2*(m+l)*nobr); - ColumnVector sv (l*nobr); - - // workspace - int liwork; - - if (metha == 'N') // if METH = 'N' - liwork = (m+l)*nobr; - else if (alg == 'F') // if METH = 'M' and ALG = 'F' - liwork = m+l; - else // if METH = 'M' and ALG = 'C' or 'Q' - liwork = 0; - - // TODO: Handle 'k' for DWORK - - int ldwork; - int ns = nsmp - 2*nobr + 1; - - if (alg == 'C') - { - if (batch == 'F' || batch == 'I') - { - if (conct == 'C') - ldwork = (4*nobr-2)*(m+l); - else // (conct == 'N') - ldwork = 1; - } - else if (metha == 'M') // && (batch == 'L' || batch == 'O') - { - if (conct == 'C' && batch == 'L') - ldwork = max ((4*nobr-2)*(m+l), 5*l*nobr); - else if (jobd == 'M') - ldwork = max ((2*m-1)*nobr, (m+l)*nobr, 5*l*nobr); - else // (jobd == 'N') - ldwork = 5*l*nobr; - } - else // meth == 'N' && (batch == 'L' || batch == 'O') - { - ldwork = 5*(m+l)*nobr + 1; - } - } - else if (alg == 'F') - { - if (batch != 'O' && conct == 'C') - ldwork = (m+l)*2*nobr*(m+l+3); - else if (batch == 'F' || batch == 'I') // && conct == 'N' - ldwork = (m+l)*2*nobr*(m+l+1); - else // (batch == 'L' || '0' && conct == 'N') - ldwork = (m+l)*4*nobr*(m+l+1)+(m+l)*2*nobr; - } - else // (alg == 'Q') - { - // int ns = nsmp - 2*nobr + 1; - - if (ldr >= ns && batch == 'F') - { - ldwork = 4*(m+l)*nobr; - } - else if (ldr >= ns && batch == 'O') - { - if (metha == 'M') - ldwork = max (4*(m+l)*nobr, 5*l*nobr); - else // (meth == 'N') - ldwork = 5*(m+l)*nobr + 1; - } - else if (conct == 'C' && (batch == 'I' || batch == 'L')) - { - ldwork = 4*(nobr+1)*(m+l)*nobr; - } - else // if ALG = 'Q', (BATCH = 'F' or 'O', and LDR < NS), or (BATCH = 'I' or 'L' and CONCT = 'N') - { - ldwork = 6*(m+l)*nobr; - } - } - -/* -IB01AD.f Lines 438-445 -C FURTHER COMMENTS -C -C For ALG = 'Q', BATCH = 'O' and LDR < NS, or BATCH <> 'O', the -C calculations could be rather inefficient if only minimal workspace -C (see argument LDWORK) is provided. It is advisable to provide as -C much workspace as possible. Almost optimal efficiency can be -C obtained for LDWORK = (NS+2)*(2*(M+L)*NOBR), assuming that the -C cache size is large enough to accommodate R, U, Y, and DWORK. -*/ - -// warning ("==================== ldwork before: %d =====================", ldwork); -// ldwork = (ns+2)*(2*(m+l)*nobr); -ldwork = max (ldwork, (ns+2)*(2*(m+l)*nobr)); -// ldwork *= 3; -// warning ("==================== ldwork after: %d =====================", ldwork); - - -/* -IB01AD.f Lines 291-195: -c the workspace used for alg = 'q' is -c ldrwrk*2*(m+l)*nobr + 4*(m+l)*nobr, -c where ldrwrk = ldwork/(2*(m+l)*nobr) - 2; recommended -c value ldrwrk = ns, assuming a large enough cache size. -c for good performance, ldwork should be larger. - -somehow ldrwrk and ldwork must have been mixed up here - -*/ - - -//////////////////////////////////////////////////////////////////////////////////// -// SLICOT IB01BD - estimating system matrices, Kalman gain, and covariances // -//////////////////////////////////////////////////////////////////////////////////// - - // arguments in - char job = 'A'; - char jobck = 'K'; - - // TODO: if meth == 'C', which meth should be taken for IB01AD.f, 'M' or 'N'? - n = nuser; - - - int nsmpl = nsmp; - - if (nsmpl < 2*(m+l)*nobr) - error ("slident: nsmpl (%d) < 2*(m+l)*nobr (%d)", nsmpl, nobr); - - // arguments out - int lda = max (1, n); - int ldc = max (1, l); - int ldb = max (1, n); - int ldd = max (1, l); - int ldq = n; // if JOBCK = 'C' or 'K' - int ldry = l; // if JOBCK = 'C' or 'K' - int lds = n; // if JOBCK = 'C' or 'K' - int ldk = n; // if JOBCK = 'K' - -//////////////////////////////////////////////////////////////////////////////////// -// SLICOT IB01CD - estimating the initial state // -//////////////////////////////////////////////////////////////////////////////////// - -// TODO: use only one iwork and dwork for all three slicot routines -// ldwork = max (ldwork_a, ldwork_b, ldwork_c) - - - // arguments in - char jobx0 = 'X'; - char comuse = 'U'; - char jobbd = 'D'; - - // arguments out - int ldv = max (1, n); - - ColumnVector x0 (n); - Matrix v (ldv, n); - - // workspace - int liwork_c = n; // if JOBX0 = 'X' and COMUSE <> 'C' - int ldwork_c; - int t = nsmp; - - int ldw1_c = 2; - int ldw2_c = t*l*(n + 1) + 2*n + max (2*n*n, 4*n); - int ldw3_c = n*(n + 1) + 2*n + max (n*l*(n + 1) + 2*n*n + l*n, 4*n); - - ldwork_c = ldw1_c + n*( n + m + l ) + max (5*n, ldw1_c, min (ldw2_c, ldw3_c)); - - OCTAVE_LOCAL_BUFFER (int, iwork_c, liwork_c); - OCTAVE_LOCAL_BUFFER (double, dwork_c, ldwork_c); - - // error indicators - int iwarn_c = 0; - int info_c = 0; - - - // SLICOT routine IB01CD - F77_XFCN (ib01cd, IB01CD, - (jobx0, comuse, jobbd, - n, m, l, - nsmp, - a.fortran_vec (), lda, - b.fortran_vec (), ldb, - c.fortran_vec (), ldc, - d.fortran_vec (), ldd, - u.fortran_vec (), ldu, - y.fortran_vec (), ldy, - x0.fortran_vec (), - v.fortran_vec (), ldv, - tolb, - iwork_c, - dwork_c, ldwork_c, - iwarn_c, info_c)); - - - if (f77_exception_encountered) - error ("ident: exception in SLICOT subroutine IB01CD"); - - static const char* err_msg_c[] = { - "0: OK", - "1: the QR algorithm failed to compute all the " - "eigenvalues of the matrix A (see LAPACK Library " - "routine DGEES); the locations DWORK(i), for " - "i = g+1:g+N*N, contain the partially converged " - "Schur form", - "2: the singular value decomposition (SVD) algorithm did " - "not converge"}; - - static const char* warn_msg_c[] = { - "0: OK", - "1: warning message not specified", - "2: warning message not specified", - "3: warning message not specified", - "4: the least squares problem to be solved has a " - "rank-deficient coefficient matrix", - "5: warning message not specified", - "6: the matrix A is unstable; the estimated x(0) " - "and/or B and D could be inaccurate"}; - - - error_msg ("ident", info_c, 2, err_msg_c); - warning_msg ("ident", iwarn_c, 6, warn_msg_c); - - - // return values - - - retval(0) = x0; - } - - return retval; -}