octave: scripts/sparse/bicg.m annotate

annotate scripts/sparse/bicg.m @ 30893:e1788b1a315f

maint: Use "fcn" as preferred abbreviation for "function" in m-files. * accumarray.m, accumdim.m, quadl.m, quadv.m, randi.m, structfun.m, __is_function__.m, uigetfile.m, uimenu.m, uiputfile.m, doc_cache_create.m, colorspace_conversion_input_check.m, imageIO.m, argnames.m, vectorize.m, vectorize.m, normest1.m, inputname.m, nthargout.m, display_info_file.m, decic.m, ode15i.m, ode15s.m, ode23.m, ode23s.m, ode45.m, odeset.m, check_default_input.m, integrate_adaptive.m, ode_event_handler.m, runge_kutta_23.m, runge_kutta_23s.m, runge_kutta_45_dorpri.m, runge_kutta_interpolate.m, starting_stepsize.m, __all_opts__.m, fminbnd.m, fminsearch.m, fminunc.m, fsolve.m, fzero.m, sqp.m, fplot.m, plotyy.m, __bar__.m, __ezplot__.m, flat_entry.html, profexport.m, movfun.m, bicg.m, bicgstab.m, cgs.m, eigs.m, gmres.m, pcg.m, __alltohandles__.m, __sprand__.m, qmr.m, tfqmr.m, dump_demos.m: Replace "func", "fun", "fn" in documentation and variable names with "fcn".

author	Rik <rik@octave.org>
date	Mon, 04 Apr 2022 18:14:56 -0700
parents	796f54d4ddbf
children	597f3ee61a48

rev	line source
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	1 ########################################################################
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	2 ##
30564 796f54d4ddbf update Octave Project Developers copyright for the new year John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	3 ## Copyright (C) 2006-2022 The Octave Project Developers
27918 b442ec6dda5c use centralized file for copyright info for individual contributors John W. Eaton <jwe@octave.org> parents: 27356 diff changeset	4 ##
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	5 ## See the file COPYRIGHT.md in the top-level directory of this
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	6 ## distribution or <https://octave.org/copyright/>.
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	7 ##
17795 0a8c35ae5ce1 maint: Fix various problems with GPL copyright statements. Rik <rik@octave.org> parents: 17744 diff changeset	8 ## This file is part of Octave.
0a8c35ae5ce1 maint: Fix various problems with GPL copyright statements. Rik <rik@octave.org> parents: 17744 diff changeset	9 ##
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23084 diff changeset	10 ## Octave is free software: you can redistribute it and/or modify it
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	11 ## under the terms of the GNU General Public License as published by
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23084 diff changeset	12 ## the Free Software Foundation, either version 3 of the License, or
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	13 ## (at your option) any later version.
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	14 ##
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	15 ## Octave is distributed in the hope that it will be useful, but
3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	18 ## GNU General Public License for more details.
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	19 ##
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	20 ## You should have received a copy of the GNU General Public License
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	21 ## along with Octave; see the file COPYING. If not, see
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23084 diff changeset	22 ## <https://www.gnu.org/licenses/>.
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	23 ##
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	24 ########################################################################
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	25
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	26 ## -- texinfo --
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	27 ## @deftypefn {} {@var{x} =} bicg (@var{A}, @var{b})
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	28 ## @deftypefnx {} {@var{x} =} bicg (@var{A}, @var{b}, @var{tol})
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	29 ## @deftypefnx {} {@var{x} =} bicg (@var{A}, @var{b}, @var{tol}, @var{maxit})
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	30 ## @deftypefnx {} {@var{x} =} bicg (@var{A}, @var{b}, @var{tol}, @var{maxit}, @var{M})
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	31 ## @deftypefnx {} {@var{x} =} bicg (@var{A}, @var{b}, @var{tol}, @var{maxit}, @var{M1}, @var{M2})
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	32 ## @deftypefnx {} {@var{x} =} bicg (@var{A}, @var{b}, @var{tol}, @var{maxit}, @var{M}, [], @var{x0})
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	33 ## @deftypefnx {} {@var{x} =} bicg (@var{A}, @var{b}, @var{tol}, @var{maxit}, @var{M1}, @var{M2}, @var{x0})
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	34 ## @deftypefnx {} {@var{x} =} bicg (@var{A}, @var{b}, @var{tol}, @var{maxit}, @var{M}, [], @var{x0}, @dots{})
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	35 ## @deftypefnx {} {@var{x} =} bicg (@var{A}, @var{b}, @var{tol}, @var{maxit}, @var{M1}, @var{M2}, @var{x0}, @dots{})
20852 516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20711 diff changeset	36 ## @deftypefnx {} {[@var{x}, @var{flag}, @var{relres}, @var{iter}, @var{resvec}] =} bicg (@var{A}, @var{b}, @dots{})
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	37 ## Solve the linear system of equations @w{@code{@var{A} * @var{x} = @var{b}}}
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	38 ## by means of the Bi-Conjugate Gradient iterative method.
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	39 ##
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	40 ## The input arguments are:
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	41 ##
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	42 ## @itemize
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	43 ##
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	44 ## @item @var{A} is the matrix of the linear system and it must be square.
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	45 ## @var{A} can be passed as a matrix, function handle, or inline function
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	46 ## @code{Afcn} such that @w{@code{Afcn (x, "notransp") = A * x}} and
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	47 ## @w{@code{Afcn (x, "transp") = A' * x}}. Additional parameters to
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	48 ## @code{Afcn} may be passed after @var{x0}.
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	49 ##
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	50 ## @item @var{b} is the right-hand side vector. It must be a column vector
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	51 ## with the same number of rows as @var{A}.
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	52 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	53 ## @item
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	54 ## @var{tol} is the required relative tolerance for the residual error,
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	55 ## @w{@code{@var{b} - @var{A} * @var{x}}}. The iteration stops if
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	56 ## @w{@code{norm (@var{b} - @var{A} * @var{x})} @leq{}
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	57 ## @w{@code{@var{tol} * norm (@var{b})}}}.
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	58 ## If @var{tol} is omitted or empty, then a tolerance of 1e-6 is used.
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13796 diff changeset	59 ##
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	60 ## @item
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	61 ## @var{maxit} is the maximum allowed number of iterations; if @var{maxit}
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	62 ## is omitted or empty then a value of 20 is used.
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13796 diff changeset	63 ##
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	64 ## @item
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	65 ## @var{M1}, @var{M2} are the preconditioners. The preconditioner @var{M} is
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	66 ## given as @code{@var{M} = @var{M1} * @var{M2}}. Both @var{M1} and @var{M2}
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	67 ## can be passed as a matrix or as a function handle or inline function
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	68 ## @code{g} such that @w{@code{g (@var{x}, "notransp") = @var{M1} \ @var{x}}}
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	69 ## or @w{@code{g (@var{x}, "notransp") = @var{M2} \ @var{x}}} and
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	70 ## @w{@code{g (@var{x}, "transp") = @var{M1}' \ @var{x}}} or
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	71 ## @w{@code{g (@var{x}, "transp") = @var{M2}' \ @var{x}}}.
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	72 ## If @var{M1} is omitted or empty, then preconditioning is not applied.
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	73 ## The preconditioned system is theoretically equivalent to applying the
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	74 ## @code{bicg} method to the linear system
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	75 ## @code{inv (@var{M1}) * A * inv (@var{M2}) * @var{y} = inv
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	76 ## (@var{M1}) * @var{b}} and
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	77 ## @code{inv (@var{M2'}) * A' * inv (@var{M1'}) * @var{z} =
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	78 ## inv (@var{M2'}) * @var{b}} and then setting
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	79 ## @code{@var{x} = inv (@var{M2}) * @var{y}}.
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	80 ##
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	81 ## @item
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	82 ## @var{x0} is the initial guess. If @var{x0} is omitted or empty then the
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	83 ## function sets @var{x0} to a zero vector by default.
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	84 ## @end itemize
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	85 ##
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	86 ## Any arguments which follow @var{x0} are treated as parameters, and passed in
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	87 ## an appropriate manner to any of the functions (@var{Afcn} or @var{Mfcn}) or
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	88 ## that have been given to @code{bicg}.
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	89 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	90 ## The output parameters are:
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	91 ##
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	92 ## @itemize
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	93 ##
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	94 ## @item
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	95 ## @var{x} is the computed approximation to the solution of
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	96 ## @w{@code{@var{A} * @var{x} = @var{b}}}. If the algorithm did not converge,
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	97 ## then @var{x} is the iteration which has the minimum residual.
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	98 ##
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	99 ## @item
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	100 ## @var{flag} indicates the exit status:
14853 72b8b39e12be doc: Periodic grammarcheck of documentation. Rik <octave@nomad.inbox5.com> parents: 14609 diff changeset	101 ##
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	102 ## @itemize
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	103 ## @item 0: The algorithm converged to within the prescribed tolerance.
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13796 diff changeset	104 ##
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	105 ## @item 1: The algorithm did not converge and it reached the maximum number of
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	106 ## iterations.
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13796 diff changeset	107 ##
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	108 ## @item 2: The preconditioner matrix is singular.
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	109 ##
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	110 ## @item 3: The algorithm stagnated, i.e., the absolute value of the
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	111 ## difference between the current iteration @var{x} and the previous is less
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	112 ## than @code{eps * norm (@var{x},2)}.
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	113 ##
25200 b3ee0179d7b0 bicg.m: Check for denominators much smaller than numerators bicg.m (bug #53589). Marco Caliari <marco.caliari@univr.it> parents: 25166 diff changeset	114 ## @item 4: The algorithm could not continue because intermediate values
b3ee0179d7b0 bicg.m: Check for denominators much smaller than numerators bicg.m (bug #53589). Marco Caliari <marco.caliari@univr.it> parents: 25166 diff changeset	115 ## became too small or too large for reliable computation.
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	116 ## @end itemize
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	117 ##
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	118 ## @item
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	119 ## @var{relres} is the ratio of the final residual to its initial value,
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	120 ## measured in the Euclidean norm.
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	121 ##
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	122 ## @item
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	123 ## @var{iter} is the iteration which @var{x} is computed.
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	124 ##
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	125 ## @item
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	126 ## @var{resvec} is a vector containing the residual at each iteration.
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	127 ## The total number of iterations performed is given by
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	128 ## @code{length (@var{resvec}) - 1}.
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	129 ## @end itemize
16816 12005245b645 doc: Periodic grammarcheck of documentation. Rik <rik@octave.org> parents: 16768 diff changeset	130 ##
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	131 ## Consider a trivial problem with a tridiagonal matrix
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13796 diff changeset	132 ##
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	133 ## @example
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	134 ## @group
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	135 ## n = 20;
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	136 ## A = toeplitz (sparse ([1, 1], [1, 2], [2, 1] * n ^ 2, 1, n)) + ...
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	137 ## toeplitz (sparse (1, 2, -1, 1, n) * n / 2, ...
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	138 ## sparse (1, 2, 1, 1, n) * n / 2);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	139 ## b = A * ones (n, 1);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	140 ## restart = 5;
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	141 ## [M1, M2] = ilu (A); # in this tridiag case, it corresponds to lu (A)
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	142 ## M = M1 * M2;
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	143 ## Afcn = @@(x, string) strcmp (string, "notransp") * (A * x) + ...
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	144 ## strcmp (string, "transp") * (A' * x);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	145 ## Mfcn = @@(x, string) strcmp (string, "notransp") * (M \ x) + ...
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	146 ## strcmp (string, "transp") * (M' \ x);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	147 ## M1fcn = @@(x, string) strcmp (string, "notransp") * (M1 \ x) + ...
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	148 ## strcmp (string, "transp") * (M1' \ x);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	149 ## M2fcn = @@(x, string) strcmp (string, "notransp") * (M2 \ x) + ...
25579 07c2c42f457e doc: Miscellaneous documentation fixes all over the manual (bug #54288). Rik <rik@octave.org> parents: 25200 diff changeset	150 ## strcmp (string, "transp") * (M2' \ x);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	151 ## @end group
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	152 ## @end example
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13796 diff changeset	153 ##
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	154 ## @sc{Example 1:} simplest usage of @code{bicg}
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	155 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	156 ## @example
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	157 ## x = bicg (A, b)
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	158 ## @end example
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	159 ##
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	160 ## @sc{Example 2:} @code{bicg} with a function that computes
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	161 ## @code{@var{A}@var{x}} and @code{@var{A'}@var{x}}
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	162 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	163 ## @example
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	164 ## x = bicg (Afcn, b, [], n)
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	165 ## @end example
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	166 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	167 ## @sc{Example 3:} @code{bicg} with a preconditioner matrix @var{M}
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	168 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	169 ## @example
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	170 ## x = bicg (A, b, 1e-6, n, M)
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	171 ## @end example
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	172 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	173 ## @sc{Example 4:} @code{bicg} with a function as preconditioner
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13796 diff changeset	174 ##
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	175 ## @example
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	176 ## x = bicg (Afcn, b, 1e-6, n, Mfcn)
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	177 ## @end example
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	178 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	179 ## @sc{Example 5:} @code{bicg} with preconditioner matrices @var{M1}
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	180 ## and @var{M2}
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	181 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	182 ## @example
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	183 ## x = bicg (A, b, 1e-6, n, M1, M2)
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	184 ## @end example
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	185 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	186 ## @sc{Example 6:} @code{bicg} with functions as preconditioners
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	187 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	188 ## @example
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	189 ## x = bicg (Afcn, b, 1e-6, n, M1fcn, M2fcn)
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	190 ## @end example
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	191 ##
24992 3d5a39077708 avoid some warnings from old versions of makeinfo (bug #53479) Guillaume Flandin parents: 24985 diff changeset	192 ## @sc{Example 7:} @code{bicg} with as input a function requiring an argument
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	193 ##
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	194 ## @example
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	195 ## @group
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	196 ## function y = Ap (A, x, string, z)
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	197 ## ## compute A^z * x or (A^z)' * x
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	198 ## y = x;
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	199 ## if (strcmp (string, "notransp"))
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	200 ## for i = 1:z
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	201 ## y = A * y;
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	202 ## endfor
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	203 ## elseif (strcmp (string, "transp"))
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	204 ## for i = 1:z
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	205 ## y = A' * y;
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	206 ## endfor
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	207 ## endif
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	208 ## endfunction
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	209 ##
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	210 ## Apfcn = @@(x, string, p) Ap (A, x, string, p);
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	211 ## x = bicg (Apfcn, b, [], [], [], [], [], 2);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	212 ## @end group
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	213 ## @end example
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	214 ##
27984 b09432b20a84 maint: Remove special cases of old version control keywords in code base. Rik <rik@octave.org> parents: 27923 diff changeset	215 ## Reference:
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	216 ##
27984 b09432b20a84 maint: Remove special cases of old version control keywords in code base. Rik <rik@octave.org> parents: 27923 diff changeset	217 ## @nospell{Y. Saad}, @cite{Iterative Methods for Sparse Linear Systems},
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	218 ## Second edition, 2003, SIAM.
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	219 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	220 ## @seealso{bicgstab, cgs, gmres, pcg, qmr, tfqmr}
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	221 ## @end deftypefn
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	222
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	223 function [x_min, flag, relres, iter_min, resvec] = ...
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	224 bicg (A, b, tol = [], maxit = [], M1 = [], M2 = [], x0 = [], varargin)
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	225
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	226 [Afcn, M1fcn, M2fcn] = __alltohandles__ (A, b, M1, M2, "bicg");
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	227
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	228 [tol, maxit, x0] = __default__input__ ({1e-06, min(rows(b), 20), ...
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	229 zeros(rows (b),1)}, tol, maxit, x0);
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	230
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	231 if (columns (b) == 2)
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	232 c = b(:,2);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	233 b = b(:,1);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	234 else
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	235 c = b;
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	236 endif
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	237 norm_b = norm (b, 2);
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	238
28912 0de38a6ef693 maint: Use Octave convention of space after function name in scripts dir. Rik <rik@octave.org> parents: 27984 diff changeset	239 if (norm_b == 0) # the only (only iff det (A) == 0) solution is x = 0
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	240 if (nargout < 2)
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	241 printf ("The right hand side vector is all zero so bicg\n")
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	242 printf ("returned an all zero solution without iterating.\n")
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	243 endif
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	244 x_min = zeros (numel (b), 1);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	245 flag = 0;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	246 relres = 0;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	247 iter_min = 0;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	248 resvec = 0;
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	249 return;
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	250 endif
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	251
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	252 x = x_min = x_pr = x0;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	253 iter = iter_min = 0;
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	254 flag = 1; # Default flag is "maximum number of iterations reached"
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	255 resvec = zeros (maxit + 1, 1);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	256 r0 = b - Afcn (x, "notransp", varargin{:}); # Residual of the system
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	257 s0 = c - Afcn (x, "transp", varargin{:}); # Res. of the "dual system"
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	258 resvec(1) = norm (r0, 2);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	259
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	260 try
28928 ae7ce8358953 maint: Add semicolon to end of all warning() and error() invocations. Rik <rik@octave.org> parents: 28917 diff changeset	261 warning ("error", "Octave:singular-matrix", "local");
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	262 prec_r0 = M1fcn (r0, "notransp", varargin{:}); # r0 preconditioned
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	263 prec_s0 = s0;
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	264 prec_r0 = M2fcn (prec_r0, "notransp", varargin{:});
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	265 prec_s0 = M2fcn (prec_s0, "transp", varargin{:});
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	266 prec_s0 = M1fcn (prec_s0, "transp", varargin{:}); # s0 preconditioned
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	267 p = prec_r0; # Direction of the system
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	268 q = prec_s0; # Direction of the "dual system"
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	269 catch
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	270 flag = 2;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	271 end_try_catch
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	272
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	273 while ((flag != 2) && (iter < maxit) && (resvec(iter+1) >= norm_b * tol))
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	274 v = Afcn (p, "notransp", varargin{:});
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	275 prod_qv = q' * v;
25200 b3ee0179d7b0 bicg.m: Check for denominators much smaller than numerators bicg.m (bug #53589). Marco Caliari <marco.caliari@univr.it> parents: 25166 diff changeset	276 alpha = (s0' * prec_r0);
b3ee0179d7b0 bicg.m: Check for denominators much smaller than numerators bicg.m (bug #53589). Marco Caliari <marco.caliari@univr.it> parents: 25166 diff changeset	277 if (abs (prod_qv) <= eps * abs (alpha))
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	278 flag = 4;
28917 72d57dbcc305 maint: Add semicolon after break and return keywords. Rik <rik@octave.org> parents: 28912 diff changeset	279 break;
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	280 endif
25200 b3ee0179d7b0 bicg.m: Check for denominators much smaller than numerators bicg.m (bug #53589). Marco Caliari <marco.caliari@univr.it> parents: 25166 diff changeset	281 alpha ./= prod_qv;
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	282 x += alpha * p;
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	283 prod_rs = (s0' * prec_r0); # Product between r0 and s0
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	284 r0 -= alpha * v;
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	285 s0 -= conj (alpha) * Afcn (q, "transp", varargin{:});
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	286 prec_r0 = M1fcn (r0, "notransp", varargin{:});
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	287 prec_s0 = s0;
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	288 prec_r0 = M2fcn (prec_r0, "notransp", varargin{:});
25200 b3ee0179d7b0 bicg.m: Check for denominators much smaller than numerators bicg.m (bug #53589). Marco Caliari <marco.caliari@univr.it> parents: 25166 diff changeset	289 beta = s0' * prec_r0;
b3ee0179d7b0 bicg.m: Check for denominators much smaller than numerators bicg.m (bug #53589). Marco Caliari <marco.caliari@univr.it> parents: 25166 diff changeset	290 if (abs (prod_rs) <= abs (beta))
b3ee0179d7b0 bicg.m: Check for denominators much smaller than numerators bicg.m (bug #53589). Marco Caliari <marco.caliari@univr.it> parents: 25166 diff changeset	291 flag = 4;
b3ee0179d7b0 bicg.m: Check for denominators much smaller than numerators bicg.m (bug #53589). Marco Caliari <marco.caliari@univr.it> parents: 25166 diff changeset	292 break;
b3ee0179d7b0 bicg.m: Check for denominators much smaller than numerators bicg.m (bug #53589). Marco Caliari <marco.caliari@univr.it> parents: 25166 diff changeset	293 endif
b3ee0179d7b0 bicg.m: Check for denominators much smaller than numerators bicg.m (bug #53589). Marco Caliari <marco.caliari@univr.it> parents: 25166 diff changeset	294 beta ./= prod_rs;
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	295 prec_s0 = M2fcn (prec_s0, "transp", varargin{:});
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	296 prec_s0 = M1fcn (prec_s0, "transp", varargin{:});
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	297 iter += 1;
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	298 resvec(iter+1) = norm (r0);
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	299 if (resvec(iter+1) <= resvec(iter_min+1))
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	300 x_min = x;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	301 iter_min = iter;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	302 endif
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	303 if (norm (x - x_pr) <= norm (x) * eps)
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	304 flag = 3;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	305 break;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	306 endif
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	307 p = prec_r0 + beta*p;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	308 q = prec_s0 + conj (beta) * q;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	309 endwhile
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	310 resvec = resvec(1:iter+1,1);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	311
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	312 if (flag == 2)
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	313 relres = 1;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	314 else
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	315 relres = resvec(iter_min+1) / norm_b;
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	316 endif
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	317
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	318 if ((flag == 1) && (relres <= tol))
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	319 flag = 0;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	320 endif
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	321
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	322 if (nargout < 2)
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	323 switch (flag)
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	324 case 0
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	325 printf ("bicg converged at iteration %i ", iter_min);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	326 printf ("to a solution with relative residual %e\n", relres);
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	327 case 1
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	328 printf ("bicg stopped at iteration %i ", iter);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	329 printf ("without converging to the desired tolerance %e\n", tol);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	330 printf ("because the maximum number of iterations was reached. ");
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	331 printf ("The iterate returned (number %i) has ", iter_min);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	332 printf ("relative residual %e\n", relres);
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	333 case 2
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	334 printf ("bicg stopped at iteration %i ", iter);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	335 printf ("without converging to the desired tolerance %e\n", tol);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	336 printf ("because the preconditioner matrix is singular.\n");
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	337 printf ("The iterate returned (number %i) ", iter_min);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	338 printf ("has relative residual %e\n", relres);
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	339 case 3
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	340 printf ("bicg stopped at iteration %i ", iter);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	341 printf ("without converging to the desired tolerance %e\n", tol);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	342 printf ("because the method stagnated.\n");
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	343 printf ("The iterate returned (number %i) ", iter_min);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	344 printf ("has relative residual %e\n", relres);
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	345 case 4
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	346 printf ("bicg stopped at iteration %i ", iter);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	347 printf ("without converging to the desired tolerance %e\n", tol);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	348 printf ("because the method can't continue.\n");
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	349 printf ("The iterate returned (number %i) ", iter_min);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	350 printf ("has relative residual %e\n", relres);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	351 endswitch
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	352 endif
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	353
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	354 endfunction
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	355
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	356
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	357 %!demo
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	358 %! ## simplest use case
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	359 %! n = 20;
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	360 %! A = toeplitz (sparse ([1, 1], [1, 2], [2, 1] * n ^ 2, 1, n)) + ...
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	361 %! toeplitz (sparse (1, 2, -1, 1, n) * n / 2, ...
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	362 %! sparse (1, 2, 1, 1, n) * n / 2);
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	363 %! b = A * ones (n, 1);
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	364 %! [M1, M2] = ilu (A + 0.1 * eye (n));
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	365 %! M = M1 * M2;
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	366 %! x = bicg (A, b, [], n);
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	367 %! function y = Ap (A, x, string, z)
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	368 %! ## compute A^z * x or (A^z)' * x
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	369 %! y = x;
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	370 %! if (strcmp (string, "notransp"))
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	371 %! for i = 1:z
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	372 %! y = A * y;
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	373 %! endfor
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	374 %! elseif (strcmp (string, "transp"))
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	375 %! for i = 1:z
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	376 %! y = A' * y;
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	377 %! endfor
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	378 %! endif
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	379 %! endfunction
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	380 %!
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	381 %! Afcn = @(x, string) Ap (A, x, string, 1);
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	382 %! x = bicg (Afcn, b, [], n);
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	383 %! x = bicg (A, b, 1e-6, n, M);
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	384 %! x = bicg (A, b, 1e-6, n, M1, M2);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	385 %! function y = Mfcn (M, x, string)
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	386 %! if (strcmp (string, "notransp"))
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	387 %! y = M \ x;
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	388 %! else
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	389 %! y = M' \ x;
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	390 %! endif
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	391 %! endfunction
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	392 %!
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	393 %! M1fcn = @(x, string) Mfcn (M, x, string);
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	394 %! x = bicg (Afcn, b, 1e-6, n, M1fcn);
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	395 %! M1fcn = @(x, string) Mfcn (M1, x, string);
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	396 %! M2fcn = @(x, string) Mfcn (M2, x, string);
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	397 %! x = bicg (Afcn, b, 1e-6, n, M1fcn, M2fcn);
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	398 %! Afcn = @(x, string, p) Ap (A, x, string, p);
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	399 %! ## Solution of A^2 * x = b
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	400 %! x = bicg (Afcn, b, [], 2*n, [], [], [], 2);
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	401
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	402 %!test
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	403 %! ## Check that all type of inputs work
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	404 %! A = sparse (toeplitz ([2, 1, 0, 0, 0], [2, -1, 0, 0, 0]));
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	405 %! b = A * ones (5, 1);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	406 %! M1 = diag (sqrt (diag (A)));
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	407 %! M2 = M1;
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	408 %! Afcn = @(z, string) strcmp (string, "notransp") * (A * z) + ...
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	409 %! strcmp (string, "transp") * (A' * z);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	410 %! M1_fcn = @(z, string) strcmp (string,"notransp") * (M1 \ z) + ...
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	411 %! strcmp (string, "transp") * (M1' \ z);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	412 %! M2_fcn = @(z, string) strcmp (string, "notransp") * (M2 \ z) + ...
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	413 %! strcmp (string, "transp") * (M2' \ z);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	414 %! [x, flag] = bicg (A, b);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	415 %! assert (flag, 0);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	416 %! [x, flag] = bicg (A, b, [], [], M1, M2);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	417 %! assert (flag, 0);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	418 %! [x, flag] = bicg (A, b, [], [], M1_fcn, M2_fcn);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	419 %! assert (flag, 0);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	420 %! [x, flag] = bicg (A, b,[], [], M1_fcn, M2);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	421 %! assert (flag, 0);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	422 %! [x, flag] = bicg (A, b,[], [], M1, M2_fcn);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	423 %! assert (flag, 0);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	424 %! [x, flag] = bicg (Afcn, b);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	425 %! assert (flag, 0);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	426 %! [x, flag] = bicg (Afcn, b,[], [], M1, M2);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	427 %! assert (flag, 0);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	428 %! [x, flag] = bicg (Afcn, b,[], [], M1_fcn, M2);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	429 %! assert (flag, 0);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	430 %! [x, flag] = bicg (Afcn, b,[], [], M1, M2_fcn);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	431 %! assert (flag, 0);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	432 %! [x, flag] = bicg (Afcn, b,[], [], M1_fcn, M2_fcn);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	433 %! assert (flag, 0);
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	434
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	435 %!test
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	436 %! n = 100;
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	437 %! A = spdiags ([-2ones(n,1) 4ones(n,1) -ones(n,1)], -1:1, n, n);
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	438 %! b = sum (A, 2);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	439 %! tol = 1e-8;
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	440 %! maxit = 15;
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	441 %! M1 = spdiags ([ones(n,1)/(-2) ones(n,1)],-1:0, n, n);
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	442 %! M2 = spdiags ([4*ones(n,1) -ones(n,1)], 0:1, n, n);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	443 %! [x, flag, relres, iter, resvec] = bicg (A, b, tol, maxit, M1, M2);
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	444 %! assert (norm (b - A*x) / norm (b), 0, tol);
13796 53674ceb9133 maint: fix function definition in test John W. Eaton <jwe@octave.org> parents: 13141 diff changeset	445
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	446 %!function y = afcn (x, t, a)
16933 e39f00a32dc7 maint: Use parentheses around condition for switch(),while(),if() statements. Rik <rik@octave.org> parents: 16816 diff changeset	447 %! switch (t)
17174 c3c1ebfaa7dc maint: Use common indentation for switch statement. Rik <rik@octave.org> parents: 16933 diff changeset	448 %! case "notransp"
c3c1ebfaa7dc maint: Use common indentation for switch statement. Rik <rik@octave.org> parents: 16933 diff changeset	449 %! y = a * x;
c3c1ebfaa7dc maint: Use common indentation for switch statement. Rik <rik@octave.org> parents: 16933 diff changeset	450 %! case "transp"
c3c1ebfaa7dc maint: Use common indentation for switch statement. Rik <rik@octave.org> parents: 16933 diff changeset	451 %! y = a' * x;
13796 53674ceb9133 maint: fix function definition in test John W. Eaton <jwe@octave.org> parents: 13141 diff changeset	452 %! endswitch
53674ceb9133 maint: fix function definition in test John W. Eaton <jwe@octave.org> parents: 13141 diff changeset	453 %!endfunction
53674ceb9133 maint: fix function definition in test John W. Eaton <jwe@octave.org> parents: 13141 diff changeset	454 %!
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	455 %!test
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	456 %! n = 100;
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	457 %! A = spdiags ([-2ones(n,1) 4ones(n,1) -ones(n,1)], -1:1, n, n);
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	458 %! b = sum (A, 2);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	459 %! tol = 1e-8;
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	460 %! maxit = 15;
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	461 %! M1 = spdiags ([ones(n,1)/(-2) ones(n,1)],-1:0, n, n);
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	462 %! M2 = spdiags ([4*ones(n,1) -ones(n,1)], 0:1, n, n);
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	463 %!
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	464 %! [x, flag, relres, iter, resvec] = bicg (@(x, t) afcn (x, t, A),
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	465 %! b, tol, maxit, M1, M2);
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	466 %! assert (x, ones (size (b)), 1e-7);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	467
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	468 %!test
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	469 %! n = 100;
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	470 %! tol = 1e-8;
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	471 %! a = sprand (n, n, .1);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	472 %! A = a' * a + 100 * eye (n);
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	473 %! b = sum (A, 2);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	474 %! [x, flag, relres, iter, resvec] = bicg (A, b, tol, [], diag (diag (A)));
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	475 %! assert (x, ones (size (b)), 1e-7);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	476
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	477 %!test
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	478 %! ## Check that if the preconditioner is singular, the method doesn't work
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	479 %! A = sparse (toeplitz ([2, 1, 0, 0, 0], [2, -1, 0, 0, 0]));
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	480 %! b = ones (5,1);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	481 %! M = ones (5);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	482 %! [x, flag] = bicg (A, b, [], [], M);
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	483 %! assert (flag, 2);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	484
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	485 %!test
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	486 %! ## If A singular, the algorithm doesn't work due to division by zero
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	487 %! A = ones (5);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	488 %! b = [1:5]';
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	489 %! [x, flag] = bicg (A, b);
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	490 %! assert (flag, 4);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	491
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	492 %!test
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	493 %! ## test for a complex linear system
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	494 %! A = sparse (toeplitz ([2, 1, 0, 0, 0], [2, -1, 0, 0, 0]) + ...
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	495 %! 1i * toeplitz ([2, 1, 0, 0, 0], [2, -1, 0, 0, 0]));
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	496 %! b = sum (A, 2);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	497 %! [x, flag] = bicg (A, b);
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	498 %! assert (flag, 0);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	499
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	500 %!test
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	501 %! A = single (1);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	502 %! b = 1;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	503 %! [x, flag] = bicg (A, b);
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	504 %! assert (class (x), "single");
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	505
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	506 %!test
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	507 %! A = 1;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	508 %! b = single (1);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	509 %! [x, flag] = bicg (A, b);
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	510 %! assert (class (x), "single");
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	511
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	512 %!test
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	513 %! A = single (1);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	514 %! b = single (1);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	515 %! [x, flag] = bicg (A, b);
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	516 %! assert (class (x), "single");
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	517
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	518 %!test
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	519 %!function y = Afcn (x, trans)
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	520 %! A = sparse (toeplitz ([2, 1, 0, 0], [2, -1, 0, 0]));
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	521 %! if (strcmp (trans, "notransp"))
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	522 %! y = A * x;
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	523 %! else
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	524 %! y = A' * x;
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	525 %! endif
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	526 %!endfunction
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	527 %!
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	528 %! [x, flag] = bicg ("Afcn", [1; 2; 2; 3]);
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	529 %! assert (x, ones (4, 1), 1e-6);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	530
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	531 %!test
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	532 %! ## unpreconditioned residual
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	533 %! A = sparse (toeplitz ([2, 1, 0, 0, 0], [2, -1, 0, 0, 0]));
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	534 %! b = sum (A, 2);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	535 %! M = magic (5);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	536 %! [x, flag, relres] = bicg (A, b, [], 2, M);
26160 b9debf4436aa bicg.m: Relax BIST test by 1eps to pass on some systems (bug #55132). Rik <rik@octave.org> parents: 25579 diff changeset	537 %! assert (norm (b - A * x) / norm (b), 0, relres + eps);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	538
24863 009ed89dd0fa test: make bicg and pcg tests conditional on CHOLMOD and UMFPACK Mike Miller <mtmiller@octave.org> parents: 24860 diff changeset	539 ## Preconditioned technique
009ed89dd0fa test: make bicg and pcg tests conditional on CHOLMOD and UMFPACK Mike Miller <mtmiller@octave.org> parents: 24860 diff changeset	540 %!testif HAVE_UMFPACK
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	541 %! A = sparse (toeplitz ([2, 1, 0, 0, 0], [2, -1, 0, 0, 0]));
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	542 %! b = sum (A, 2);
25159 b8279dd83664 Turn off warning about sparse lu factorization in bicg BIST test (bug #53390). Marco Caliari <marco.caliari@univr.it> parents: 25152 diff changeset	543 %! warning ("off", "Octave:lu:sparse_input", "local");
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	544 %! [M1, M2] = lu (A + eye (5));
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	545 %! [x, flag] = bicg (A, b, [], 1, M1, M2);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	546 %! ## b has two columns!
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	547 %! [y, flag] = bicg (M1 \ A / M2, [M1 \ b, M2' \ b], [], 1);
25152 ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions. Rik <rik@octave.org> parents: 25054 diff changeset	548 %! assert (x, M2 \ y, 8 * eps);