Mercurial > octave-nkf
view scripts/optimization/glpk.m @ 17281:bc924baa2c4e
doc: Add new @qcode macro for code samples which are quoted.
Macro handles options ("on") or properties ("position") more elegantly
than @code{"text"}.
* doc/interpreter/macros.texi: Add new @qcode macro.
* doc/interpreter/tips.txi: Add documentation about @qcode macro.
* doc/interpreter/basics.txi, doc/interpreter/container.txi,
doc/interpreter/emacs.txi, doc/interpreter/errors.txi,
doc/interpreter/eval.txi, doc/interpreter/expr.txi,
doc/interpreter/external.txi, doc/interpreter/func.txi,
doc/interpreter/grammar.txi, doc/interpreter/image.txi,
doc/interpreter/install.txi, doc/interpreter/interp.txi,
doc/interpreter/io.txi, doc/interpreter/matrix.txi,
doc/interpreter/numbers.txi, doc/interpreter/oop.txi,
doc/interpreter/package.txi, doc/interpreter/plot.txi,
doc/interpreter/quad.txi, doc/interpreter/sparse.txi,
doc/interpreter/strings.txi, doc/interpreter/system.txi,
doc/interpreter/vectorize.txi, libinterp/corefcn/balance.cc,
libinterp/corefcn/bitfcns.cc, libinterp/corefcn/cellfun.cc,
libinterp/corefcn/conv2.cc, libinterp/corefcn/data.cc,
libinterp/corefcn/debug.cc, libinterp/corefcn/defaults.cc,
libinterp/corefcn/dirfns.cc, libinterp/corefcn/dlmread.cc,
libinterp/corefcn/error.cc, libinterp/corefcn/file-io.cc,
libinterp/corefcn/find.cc, libinterp/corefcn/gammainc.cc,
libinterp/corefcn/graphics.cc, libinterp/corefcn/help.cc,
libinterp/corefcn/hex2num.cc, libinterp/corefcn/input.cc,
libinterp/corefcn/load-path.cc, libinterp/corefcn/load-save.cc,
libinterp/corefcn/ls-oct-ascii.cc, libinterp/corefcn/lu.cc,
libinterp/corefcn/luinc.cc, libinterp/corefcn/matrix_type.cc,
libinterp/corefcn/oct-hist.cc, libinterp/corefcn/pager.cc,
libinterp/corefcn/pr-output.cc, libinterp/corefcn/pt-jit.cc,
libinterp/corefcn/qz.cc, libinterp/corefcn/rand.cc,
libinterp/corefcn/regexp.cc, libinterp/corefcn/schur.cc,
libinterp/corefcn/sighandlers.cc, libinterp/corefcn/sparse.cc,
libinterp/corefcn/spparms.cc, libinterp/corefcn/str2double.cc,
libinterp/corefcn/svd.cc, libinterp/corefcn/symtab.cc,
libinterp/corefcn/syscalls.cc, libinterp/corefcn/toplev.cc,
libinterp/corefcn/tril.cc, libinterp/corefcn/typecast.cc,
libinterp/corefcn/utils.cc, libinterp/corefcn/variables.cc,
libinterp/dldfcn/__init_fltk__.cc, libinterp/dldfcn/chol.cc,
libinterp/dldfcn/colamd.cc, libinterp/dldfcn/fftw.cc, libinterp/dldfcn/qr.cc,
libinterp/dldfcn/symbfact.cc, libinterp/octave-value/ov-base.cc,
libinterp/octave-value/ov-fcn-handle.cc,
libinterp/octave-value/ov-fcn-inline.cc, libinterp/octave-value/ov-java.cc,
libinterp/octave-value/ov-range.cc, libinterp/octave-value/ov-struct.cc,
libinterp/octave-value/ov-usr-fcn.cc, libinterp/parse-tree/oct-parse.in.yy,
libinterp/parse-tree/pt-binop.cc, libinterp/parse-tree/pt-eval.cc,
libinterp/parse-tree/pt-mat.cc, scripts/@ftp/ftp.m,
scripts/deprecated/java_convert_matrix.m, scripts/deprecated/java_debug.m,
scripts/deprecated/java_unsigned_conversion.m, scripts/deprecated/shell_cmd.m,
scripts/general/dblquad.m, scripts/general/display.m,
scripts/general/genvarname.m, scripts/general/idivide.m,
scripts/general/interp1.m, scripts/general/interp2.m,
scripts/general/interp3.m, scripts/general/interpn.m, scripts/general/isa.m,
scripts/general/profexplore.m, scripts/general/profile.m,
scripts/general/quadgk.m, scripts/general/randi.m, scripts/general/structfun.m,
scripts/general/subsindex.m, scripts/general/triplequad.m,
scripts/geometry/griddata.m, scripts/geometry/griddata3.m,
scripts/geometry/griddatan.m, scripts/geometry/voronoi.m, scripts/help/help.m,
scripts/help/lookfor.m, scripts/image/cmpermute.m, scripts/image/colormap.m,
scripts/image/image.m, scripts/image/imagesc.m, scripts/image/imfinfo.m,
scripts/image/imformats.m, scripts/image/imread.m, scripts/image/imshow.m,
scripts/image/imwrite.m, scripts/image/ind2gray.m, scripts/image/lines.m,
scripts/image/rgb2ind.m, scripts/image/spinmap.m, scripts/io/dlmwrite.m,
scripts/io/strread.m, scripts/io/textread.m, scripts/io/textscan.m,
scripts/java/javaclasspath.m, scripts/java/usejava.m,
scripts/miscellaneous/bzip2.m, scripts/miscellaneous/computer.m,
scripts/miscellaneous/copyfile.m, scripts/miscellaneous/debug.m,
scripts/miscellaneous/dos.m, scripts/miscellaneous/edit.m,
scripts/miscellaneous/gzip.m, scripts/miscellaneous/license.m,
scripts/miscellaneous/mkoctfile.m, scripts/miscellaneous/movefile.m,
scripts/miscellaneous/parseparams.m, scripts/miscellaneous/unix.m,
scripts/optimization/fminbnd.m, scripts/optimization/fminsearch.m,
scripts/optimization/fminunc.m, scripts/optimization/fsolve.m,
scripts/optimization/fzero.m, scripts/optimization/glpk.m,
scripts/optimization/lsqnonneg.m, scripts/optimization/optimset.m,
scripts/optimization/pqpnonneg.m, scripts/pkg/pkg.m, scripts/plot/allchild.m,
scripts/plot/ancestor.m, scripts/plot/area.m, scripts/plot/axis.m,
scripts/plot/bar.m, scripts/plot/barh.m, scripts/plot/box.m,
scripts/plot/caxis.m, scripts/plot/cla.m, scripts/plot/clabel.m,
scripts/plot/clf.m, scripts/plot/close.m, scripts/plot/colorbar.m,
scripts/plot/daspect.m, scripts/plot/ezmesh.m, scripts/plot/ezmeshc.m,
scripts/plot/ezsurf.m, scripts/plot/ezsurfc.m, scripts/plot/findall.m,
scripts/plot/findobj.m, scripts/plot/gcbo.m, scripts/plot/gcf.m,
scripts/plot/gco.m, scripts/plot/grid.m, scripts/plot/guihandles.m,
scripts/plot/hdl2struct.m, scripts/plot/hidden.m, scripts/plot/hold.m,
scripts/plot/isonormals.m, scripts/plot/isosurface.m, scripts/plot/legend.m,
scripts/plot/mesh.m, scripts/plot/meshc.m, scripts/plot/meshz.m,
scripts/plot/newplot.m, scripts/plot/orient.m, scripts/plot/pareto.m,
scripts/plot/patch.m, scripts/plot/pbaspect.m, scripts/plot/pcolor.m,
scripts/plot/plot.m, scripts/plot/print.m,
scripts/plot/private/__add_default_menu__.m, scripts/plot/quiver.m,
scripts/plot/quiver3.m, scripts/plot/refreshdata.m, scripts/plot/saveas.m,
scripts/plot/scatter.m, scripts/plot/scatter3.m, scripts/plot/shading.m,
scripts/plot/shrinkfaces.m, scripts/plot/slice.m, scripts/plot/stem.m,
scripts/plot/stem3.m, scripts/plot/struct2hdl.m, scripts/plot/subplot.m,
scripts/plot/surf.m, scripts/plot/surfc.m, scripts/plot/surfl.m,
scripts/plot/tetramesh.m, scripts/plot/uigetfile.m, scripts/plot/uimenu.m,
scripts/plot/uiputfile.m, scripts/plot/waterfall.m, scripts/plot/whitebg.m,
scripts/plot/xlim.m, scripts/plot/ylim.m, scripts/plot/zlim.m,
scripts/polynomial/conv.m, scripts/polynomial/polyout.m,
scripts/polynomial/splinefit.m, scripts/set/ismember.m, scripts/set/powerset.m,
scripts/set/setdiff.m, scripts/set/union.m, scripts/set/unique.m,
scripts/signal/detrend.m, scripts/signal/filter2.m, scripts/signal/freqz.m,
scripts/signal/periodogram.m, scripts/signal/spectral_adf.m,
scripts/signal/spectral_xdf.m, scripts/sparse/eigs.m, scripts/sparse/svds.m,
scripts/specfun/legendre.m, scripts/special-matrix/gallery.m,
scripts/statistics/base/mean.m, scripts/statistics/base/moment.m,
scripts/statistics/tests/cor_test.m,
scripts/statistics/tests/kolmogorov_smirnov_test.m,
scripts/statistics/tests/kolmogorov_smirnov_test_2.m,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/statistics/tests/prop_test_2.m, scripts/statistics/tests/sign_test.m,
scripts/statistics/tests/t_test.m, scripts/statistics/tests/t_test_2.m,
scripts/statistics/tests/t_test_regression.m,
scripts/statistics/tests/u_test.m, scripts/statistics/tests/var_test.m,
scripts/statistics/tests/welch_test.m,
scripts/statistics/tests/wilcoxon_test.m, scripts/statistics/tests/z_test.m,
scripts/statistics/tests/z_test_2.m, scripts/strings/base2dec.m,
scripts/strings/index.m, scripts/strings/isstrprop.m,
scripts/strings/mat2str.m, scripts/strings/regexptranslate.m,
scripts/strings/rindex.m, scripts/strings/str2num.m, scripts/strings/strcat.m,
scripts/strings/strjust.m, scripts/strings/strmatch.m,
scripts/strings/validatestring.m, scripts/testfun/demo.m,
scripts/testfun/example.m, scripts/testfun/test.m, scripts/time/addtodate.m,
scripts/time/asctime.m, scripts/time/datestr.m, scripts/time/datetick.m,
scripts/time/weekday.m, scripts/ui/errordlg.m, scripts/ui/helpdlg.m,
scripts/ui/inputdlg.m, scripts/ui/listdlg.m, scripts/ui/msgbox.m,
scripts/ui/questdlg.m, scripts/ui/warndlg.m: Use new @qcode macro.
author | Rik <rik@octave.org> |
---|---|
date | Mon, 19 Aug 2013 20:46:38 -0700 |
parents | 54e251e699bb |
children | 17be601bc783 |
line wrap: on
line source
## Copyright (C) 2005-2012 Nicolo' Giorgetti ## Copyright (C) 2013 Sébastien Villemot <sebastien@debian.org> ## ## This file is part of Octave. ## ## Octave 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. ## ## Octave 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 Octave; see the file COPYING. If not, see ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{xopt}, @var{fmin}, @var{errnum}, @var{extra}] =} glpk (@var{c}, @var{A}, @var{b}, @var{lb}, @var{ub}, @var{ctype}, @var{vartype}, @var{sense}, @var{param}) ## Solve a linear program using the GNU @sc{glpk} library. Given three ## arguments, @code{glpk} solves the following standard LP: ## @tex ## $$ ## \min_x C^T x ## $$ ## @end tex ## @ifnottex ## ## @example ## min C'*x ## @end example ## ## @end ifnottex ## subject to ## @tex ## $$ ## Ax = b \qquad x \geq 0 ## $$ ## @end tex ## @ifnottex ## ## @example ## @group ## A*x = b ## x >= 0 ## @end group ## @end example ## ## @end ifnottex ## but may also solve problems of the form ## @tex ## $$ ## [ \min_x | \max_x ] C^T x ## $$ ## @end tex ## @ifnottex ## ## @example ## [ min | max ] C'*x ## @end example ## ## @end ifnottex ## subject to ## @tex ## $$ ## Ax [ = | \leq | \geq ] b \qquad LB \leq x \leq UB ## $$ ## @end tex ## @ifnottex ## ## @example ## @group ## A*x [ "=" | "<=" | ">=" ] b ## x >= LB ## x <= UB ## @end group ## @end example ## ## @end ifnottex ## ## Input arguments: ## ## @table @var ## @item c ## A column array containing the objective function coefficients. ## ## @item A ## A matrix containing the constraints coefficients. ## ## @item b ## A column array containing the right-hand side value for each constraint ## in the constraint matrix. ## ## @item lb ## An array containing the lower bound on each of the variables. If ## @var{lb} is not supplied, the default lower bound for the variables is ## zero. ## ## @item ub ## An array containing the upper bound on each of the variables. If ## @var{ub} is not supplied, the default upper bound is assumed to be ## infinite. ## ## @item ctype ## An array of characters containing the sense of each constraint in the ## constraint matrix. Each element of the array may be one of the ## following values ## ## @table @asis ## @item @qcode{"F"} ## A free (unbounded) constraint (the constraint is ignored). ## ## @item @qcode{"U"} ## An inequality constraint with an upper bound (@code{A(i,:)*x <= b(i)}). ## ## @item @qcode{"S"} ## An equality constraint (@code{A(i,:)*x = b(i)}). ## ## @item @qcode{"L"} ## An inequality with a lower bound (@code{A(i,:)*x >= b(i)}). ## ## @item @qcode{"D"} ## An inequality constraint with both upper and lower bounds ## (@code{A(i,:)*x >= -b(i)} @emph{and} (@code{A(i,:)*x <= b(i)}). ## @end table ## ## @item vartype ## A column array containing the types of the variables. ## ## @table @asis ## @item @qcode{"C"} ## A continuous variable. ## ## @item @qcode{"I"} ## An integer variable. ## @end table ## ## @item sense ## If @var{sense} is 1, the problem is a minimization. If @var{sense} is ## -1, the problem is a maximization. The default value is 1. ## ## @item param ## A structure containing the following parameters used to define the ## behavior of solver. Missing elements in the structure take on default ## values, so you only need to set the elements that you wish to change ## from the default. ## ## Integer parameters: ## ## @table @code ## @item msglev (default: 1) ## Level of messages output by solver routines: ## ## @table @asis ## @item 0 (@w{@code{GLP_MSG_OFF}}) ## No output. ## ## @item 1 (@w{@code{GLP_MSG_ERR}}) ## Error and warning messages only. ## ## @item 2 (@w{@code{GLP_MSG_ON}}) ## Normal output. ## ## @item 3 (@w{@code{GLP_MSG_ALL}}) ## Full output (includes informational messages). ## @end table ## ## @item scale (default: 16) ## Scaling option. The values can be combined with the bitwise OR operator and ## may be the following: ## ## @table @asis ## @item 1 (@w{@code{GLP_SF_GM}}) ## Geometric mean scaling. ## ## @item 16 (@w{@code{GLP_SF_EQ}}) ## Equilibration scaling. ## ## @item 32 (@w{@code{GLP_SF_2N}}) ## Round scale factors to power of two. ## ## @item 64 (@w{@code{GLP_SF_SKIP}}) ## Skip if problem is well scaled. ## @end table ## ## Alternatively, a value of 128 (@w{@env{GLP_SF_AUTO}}) may be also ## specified, in which case the routine chooses the scaling options ## automatically. ## ## @item dual (default: 1) ## Simplex method option: ## ## @table @asis ## @item 1 (@w{@code{GLP_PRIMAL}}) ## Use two-phase primal simplex. ## ## @item 2 (@w{@code{GLP_DUALP}}) ## Use two-phase dual simplex, and if it fails, switch to the primal simplex. ## ## @item 3 (@w{@code{GLP_DUAL}}) ## Use two-phase dual simplex. ## @end table ## ## @item price (default: 34) ## Pricing option (for both primal and dual simplex): ## ## @table @asis ## @item 17 (@w{@code{GLP_PT_STD}}) ## Textbook pricing. ## ## @item 34 (@w{@code{GLP_PT_PSE}}) ## Steepest edge pricing. ## @end table ## ## @item itlim (default: intmax) ## Simplex iterations limit. It is decreased by one each time when one simplex ## iteration has been performed, and reaching zero value signals the solver to ## stop the search. ## ## @item outfrq (default: 200) ## Output frequency, in iterations. This parameter specifies how ## frequently the solver sends information about the solution to the ## standard output. ## ## @item branch (default: 4) ## Branching technique option (for MIP only): ## ## @table @asis ## @item 1 (@w{@code{GLP_BR_FFV}}) ## First fractional variable. ## ## @item 2 (@w{@code{GLP_BR_LFV}}) ## Last fractional variable. ## ## @item 3 (@w{@code{GLP_BR_MFV}}) ## Most fractional variable. ## ## @item 4 (@w{@code{GLP_BR_DTH}}) ## Heuristic by Driebeck and Tomlin. ## ## @item 5 (@w{@code{GLP_BR_PCH}}) ## Hybrid pseudocost heuristic. ## @end table ## ## @item btrack (default: 4) ## Backtracking technique option (for MIP only): ## ## @table @asis ## @item 1 (@w{@code{GLP_BT_DFS}}) ## Depth first search. ## ## @item 2 (@w{@code{GLP_BT_BFS}}) ## Breadth first search. ## ## @item 3 (@w{@code{GLP_BT_BLB}}) ## Best local bound. ## ## @item 4 (@w{@code{GLP_BT_BPH}}) ## Best projection heuristic. ## @end table ## ## @item presol (default: 1) ## If this flag is set, the simplex solver uses the built-in LP presolver. ## Otherwise the LP presolver is not used. ## ## @item lpsolver (default: 1) ## Select which solver to use. If the problem is a MIP problem this flag ## will be ignored. ## ## @table @asis ## @item 1 ## Revised simplex method. ## ## @item 2 ## Interior point method. ## @end table ## ## @item rtest (default: 34) ## Ratio test technique: ## ## @table @asis ## @item 17 (@w{@code{GLP_RT_STD}}) ## Standard ("textbook"). ## ## @item 34 (@w{@code{GLP_RT_HAR}}) ## Harris' two-pass ratio test. ## @end table ## ## @item tmlim (default: intmax) ## Searching time limit, in milliseconds. ## ## @item outdly (default: 0) ## Output delay, in seconds. This parameter specifies how long the solver ## should delay sending information about the solution to the standard ## output. ## ## @item save (default: 0) ## If this parameter is nonzero, save a copy of the problem in ## CPLEX LP format to the file @file{"outpb.lp"}. There is currently no ## way to change the name of the output file. ## @end table ## ## Real parameters: ## ## @table @code ## @item tolbnd (default: 1e-7) ## Relative tolerance used to check if the current basic solution is primal ## feasible. It is not recommended that you change this parameter unless you ## have a detailed understanding of its purpose. ## ## @item toldj (default: 1e-7) ## Absolute tolerance used to check if the current basic solution is dual ## feasible. It is not recommended that you change this parameter unless you ## have a detailed understanding of its purpose. ## ## @item tolpiv (default: 1e-10) ## Relative tolerance used to choose eligible pivotal elements of the ## simplex table. It is not recommended that you change this parameter unless ## you have a detailed understanding of its purpose. ## ## @item objll (default: -DBL_MAX) ## Lower limit of the objective function. If the objective ## function reaches this limit and continues decreasing, the solver stops ## the search. This parameter is used in the dual simplex method only. ## ## @item objul (default: +DBL_MAX) ## Upper limit of the objective function. If the objective ## function reaches this limit and continues increasing, the solver stops ## the search. This parameter is used in the dual simplex only. ## ## @item tolint (default: 1e-5) ## Relative tolerance used to check if the current basic solution is integer ## feasible. It is not recommended that you change this parameter unless ## you have a detailed understanding of its purpose. ## ## @item tolobj (default: 1e-7) ## Relative tolerance used to check if the value of the objective function ## is not better than in the best known integer feasible solution. It is ## not recommended that you change this parameter unless you have a ## detailed understanding of its purpose. ## @end table ## @end table ## ## Output values: ## ## @table @var ## @item xopt ## The optimizer (the value of the decision variables at the optimum). ## ## @item fopt ## The optimum value of the objective function. ## ## @item errnum ## Error code. ## ## @table @asis ## @item 0 ## No error. ## ## @item 1 (@w{@code{GLP_EBADB}}) ## Invalid basis. ## ## @item 2 (@w{@code{GLP_ESING}}) ## Singular matrix. ## ## @item 3 (@w{@code{GLP_ECOND}}) ## Ill-conditioned matrix. ## ## @item 4 (@w{@code{GLP_EBOUND}}) ## Invalid bounds. ## ## @item 5 (@w{@code{GLP_EFAIL}}) ## Solver failed. ## ## @item 6 (@w{@code{GLP_EOBJLL}}) ## Objective function lower limit reached. ## ## @item 7 (@w{@code{GLP_EOBJUL}}) ## Objective function upper limit reached. ## ## @item 8 (@w{@code{GLP_EITLIM}}) ## Iterations limit exhausted. ## ## @item 9 (@w{@code{GLP_ETMLIM}}) ## Time limit exhausted. ## ## @item 10 (@w{@code{GLP_ENOPFS}}) ## No primal feasible solution. ## ## @item 11 (@w{@code{GLP_ENODFS}}) ## No dual feasible solution. ## ## @item 12 (@w{@code{GLP_EROOT}}) ## Root LP optimum not provided. ## ## @item 13 (@w{@code{GLP_ESTOP}}) ## Search terminated by application. ## ## @item 14 (@w{@code{GLP_EMIPGAP}}) ## Relative MIP gap tolerance reached. ## ## @item 15 (@w{@code{GLP_ENOFEAS}}) ## No primal/dual feasible solution. ## ## @item 16 (@w{@code{GLP_ENOCVG}}) ## No convergence. ## ## @item 17 (@w{@code{GLP_EINSTAB}}) ## Numerical instability. ## ## @item 18 (@w{@code{GLP_EDATA}}) ## Invalid data. ## ## @item 19 (@w{@code{GLP_ERANGE}}) ## Result out of range. ## @end table ## ## @item extra ## A data structure containing the following fields: ## ## @table @code ## @item lambda ## Dual variables. ## ## @item redcosts ## Reduced Costs. ## ## @item time ## Time (in seconds) used for solving LP/MIP problem. ## ## @item status ## Status of the optimization. ## ## @table @asis ## @item 1 (@w{@code{GLP_UNDEF}}) ## Solution status is undefined. ## ## @item 2 (@w{@code{GLP_FEAS}}) ## Solution is feasible. ## ## @item 3 (@w{@code{GLP_INFEAS}}) ## Solution is infeasible. ## ## @item 4 (@w{@code{GLP_NOFEAS}}) ## Problem has no feasible solution. ## ## @item 5 (@w{@code{GLP_OPT}}) ## Solution is optimal. ## ## @item 6 (@w{@code{GLP_UNBND}}) ## Problem has no unbounded solution. ## @end table ## @end table ## @end table ## ## Example: ## ## @example ## @group ## c = [10, 6, 4]'; ## A = [ 1, 1, 1; ## 10, 4, 5; ## 2, 2, 6]; ## b = [100, 600, 300]'; ## lb = [0, 0, 0]'; ## ub = []; ## ctype = "UUU"; ## vartype = "CCC"; ## s = -1; ## ## param.msglev = 1; ## param.itlim = 100; ## ## [xmin, fmin, status, extra] = ... ## glpk (c, A, b, lb, ub, ctype, vartype, s, param); ## @end group ## @end example ## @end deftypefn ## Author: Nicolo' Giorgetti <giorgetti@dii.unisi.it> ## Adapted-by: jwe function [xopt, fmin, errnum, extra] = glpk (c, A, b, lb, ub, ctype, vartype, sense, param) ## If there is no input output the version and syntax if (nargin < 3 || nargin > 9) print_usage (); return; endif if (all (size (c) > 1) || iscomplex (c) || ischar (c)) error ("glpk:C must be a real vector"); return; endif nx = length (c); ## Force column vector. c = c(:); ## 2) Matrix constraint if (isempty (A)) error ("glpk: A cannot be an empty matrix"); return; endif [nc, nxa] = size (A); if (! isreal (A) || nxa != nx) error ("glpk: A must be a real valued %d by %d matrix", nc, nx); return; endif ## 3) RHS if (isempty (b)) error ("glpk: B cannot be an empty vector"); return; endif if (! isreal (b) || length (b) != nc) error ("glpk: B must be a real valued %d by 1 vector", nc); return; endif ## 4) Vector with the lower bound of each variable if (nargin > 3) if (isempty (lb)) lb = zeros (nx, 1); elseif (! isreal (lb) || all (size (lb) > 1) || length (lb) != nx) error ("glpk: LB must be a real valued %d by 1 column vector", nx); return; endif else lb = zeros (nx, 1); endif ## 5) Vector with the upper bound of each variable if (nargin > 4) if (isempty (ub)) ub = Inf (nx, 1); elseif (! isreal (ub) || all (size (ub) > 1) || length (ub) != nx) error ("glpk: UB must be a real valued %d by 1 column vector", nx); return; endif else ub = Inf (nx, 1); endif ## 6) Sense of each constraint if (nargin > 5) if (isempty (ctype)) ctype = repmat ("S", nc, 1); elseif (! ischar (ctype) || all (size (ctype) > 1) || length (ctype) != nc) error ("glpk: CTYPE must be a char valued vector of length %d", nc); return; elseif (! all (ctype == "F" | ctype == "U" | ctype == "S" | ctype == "L" | ctype == "D")) error ("glpk: CTYPE must contain only F, U, S, L, or D"); return; endif else ctype = repmat ("S", nc, 1); endif ## 7) Vector with the type of variables if (nargin > 6) if (isempty (vartype)) vartype = repmat ("C", nx, 1); elseif (! ischar (vartype) || all (size (vartype) > 1) || length (vartype) != nx) error ("glpk: VARTYPE must be a char valued vector of length %d", nx); return; elseif (! all (vartype == "C" | vartype == "I")) error ("glpk: VARTYPE must contain only C or I"); return; endif else ## As default we consider continuous vars vartype = repmat ("C", nx, 1); endif ## 8) Sense of optimization if (nargin > 7) if (isempty (sense)) sense = 1; elseif (ischar (sense) || all (size (sense) > 1) || ! isreal (sense)) error ("glpk: SENSE must be an integer value"); elseif (sense >= 0) sense = 1; else sense = -1; endif else sense = 1; endif ## 9) Parameters vector if (nargin > 8) if (! isstruct (param)) error ("glpk: PARAM must be a structure"); return; endif else param = struct (); endif [xopt, fmin, errnum, extra] = ... __glpk__ (c, A, b, lb, ub, ctype, vartype, sense, param); endfunction