octave-antonio: scripts/sparse/bicg.m annotate

annotate scripts/sparse/bicg.m @ 14359:7277fe922e99

doc: Use Octave preference for double quote in docstrings in scripts/ * interp1.m, interp2.m, interp3.m, interpn.m, profexplore.m, profile.m, profshow.m, quadgk.m, lookfor.m, imagesc.m, bzip2.m, gzip.m, parseparams.m, pkg.m, ancestor.m, caxis.m, ezmesh.m, ezmeshc.m, ezsurf.m, ezsurfc.m, hidden.m, hold.m, patch.m, pie.m, pie3.m, quiver.m, quiver3.m, scatter3.m, uicontextmenu.m, uicontrol.m, uipanel.m, uipushtool.m, uitoggletool.m, uitoolbar.m, xlim.m, ylim.m, zlim.m, ismember.m, setxor.m, filter2.m, bicg.m, demo.m, example.m, fail.m, test.m: Use Octave preference for double quote in docstrings in scripts/ directory.

author	Rik <octave@nomad.inbox5.com>
date	Mon, 13 Feb 2012 07:38:23 -0800
parents	72c96de7a403
children	f3d52523cde1

rev	line source
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	1 ## Copyright (C) 2006 Sylvain Pelissier <sylvain.pelissier@gmail.com>
14138 72c96de7a403 maint: update copyright notices for 2012 John W. Eaton <jwe@octave.org> parents: 13931 diff changeset	2 ## Copyright (C) 2012 Carlo de Falco
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	3 ##
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	4 ## This program is free software; you can redistribute it and/or modify
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	5 ## it under the terms of the GNU General Public License as published by
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	6 ## the Free Software Foundation; either version 2 of the License, or
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	7 ## (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	8 ##
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	9 ## This program is distributed in the hope that it will be useful,
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	10 ## but WITHOUT ANY WARRANTY; without even the implied warranty of
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	11 ## 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	12 ## 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	13 ##
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	14 ## You should have received a copy of the GNU General Public License
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	15 ## along with this program; If not, see <http://www.gnu.org/licenses/>.
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	16
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	17 ## -- texinfo --
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	18 ##
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13796 diff changeset	19 ## @deftypefn {Function File} {@var{x} =} bicg (@var{A}, @var{b}, @var{rtol}, @var{maxit}, @var{M1}, @var{M2}, @var{x0})
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	20 ## @deftypefnx {Function File} {@var{x} =} bicg (@var{A}, @var{b}, @var{rtol}, @var{maxit}, @var{P})
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13796 diff changeset	21 ## @deftypefnx {Function File} {[@var{x}, @var{flag}, @var{relres}, @var{iter}, @var{resvec}] =} bicg (@var{A}, @var{b}, @dots{})
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	22 ## Solve @code{A x = b} using the Bi-conjugate gradient iterative method.
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	23 ##
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	24 ## @itemize @minus
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	25 ## @item @var{rtol} is the relative tolerance, if not given
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	26 ## or set to [] the default value 1e-6 is used.
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13796 diff changeset	27 ##
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	28 ## @item @var{maxit} the maximum number of outer iterations,
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	29 ## if not given or set to [] the default value
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	30 ## @code{min (20, numel (b))} is used.
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13796 diff changeset	31 ##
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	32 ## @item @var{x0} the initial guess, if not given or set to []
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	33 ## the default value @code{zeros (size (b))} is used.
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	34 ## @end itemize
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	35 ##
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	36 ## @var{A} can be passed as a matrix or as a function handle or
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	37 ## inline function @code{f} such that @code{f(x, "notransp") = A*x}
e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	38 ## and @code{f(x, "transp") = A'*x}.
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	39 ##
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	40 ## The preconditioner @var{P} is given as @code{P = M1 * M2}.
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	41 ## Both @var{M1} and @var{M2} can be passed as a matrix or as
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	42 ## a function handle or inline function @code{g} such that
14359 7277fe922e99 doc: Use Octave preference for double quote in docstrings in scripts/ Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	43 ## @code{g(x, "notransp") = M1 \ x} or @code{g(x, "notransp") = M2 \ x} and
7277fe922e99 doc: Use Octave preference for double quote in docstrings in scripts/ Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	44 ## @code{g(x, "transp") = M1' \ x} or @code{g(x, "transp") = M2' \ x}.
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	45 ##
13931 9de488c6c59c doc: Spellcheck documentation before 3.6.0 release Rik <octave@nomad.inbox5.com> parents: 13929 diff changeset	46 ## If called with more than one output parameter
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	47 ##
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	48 ## @itemize @minus
e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	49 ## @item @var{flag} indicates the exit status:
e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	50 ## @itemize @minus
e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	51 ## @item 0: iteration converged to the within the chosen tolerance
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13796 diff changeset	52 ##
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	53 ## @item 1: the maximum number of iterations was reached before convergence
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13796 diff changeset	54 ##
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	55 ## @item 3: the algorithm reached stagnation
e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	56 ## @end itemize
e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	57 ## (the value 2 is unused but skipped for compatibility).
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13796 diff changeset	58 ##
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	59 ## @item @var{relres} is the final value of the relative residual.
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13796 diff changeset	60 ##
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	61 ## @item @var{iter} is the number of iterations performed.
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13796 diff changeset	62 ##
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	63 ## @item @var{resvec} is a vector containing the relative residual at each iteration.
e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	64 ## @end itemize
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	65 ##
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13796 diff changeset	66 ## @seealso{bicgstab, cgs, gmres, pcg}
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	67 ##
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	68 ## @end deftypefn
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	69
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	70
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	71 function [x, flag, res1, k, resvec] = bicg (A, b, tol, maxit, M1, M2, x0)
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	72
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	73 if (nargin >= 2 && isvector (full (b)))
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	74
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	75 if (ischar (A))
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	76 fun = str2func (A);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	77 Ax = @(x) feval (fun, x, "notransp");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	78 Atx = @(x) feval (fun, x, "transp");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	79 elseif (ismatrix (A))
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	80 Ax = @(x) A * x;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	81 Atx = @(x) A' * x;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	82 elseif (isa (A, "function_handle"))
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	83 Ax = @(x) feval (A, x, "notransp");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	84 Atx = @(x) feval (A, x, "transp");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	85 else
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	86 error (["bicg: first argument is expected to " ...
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	87 "be a function or a square matrix"]);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	88 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	89
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	90 if (nargin < 3 \|\| isempty (tol))
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	91 tol = 1e-6;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	92 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	93
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	94 if (nargin < 4 \|\| isempty (maxit))
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	95 maxit = min (rows (b), 20);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	96 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	97
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	98 if (nargin < 5 \|\| isempty (M1))
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	99 M1m1x = @(x, ignore) x;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	100 M1tm1x = M1m1x;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	101 elseif (ischar (M1))
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	102 fun = str2func (M1);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	103 M1m1x = @(x) feval (fun, x, "notransp");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	104 M1tm1x = @(x) feval (fun, x, "transp");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	105 elseif (ismatrix (M1))
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	106 M1m1x = @(x) M1 \ x;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	107 M1tm1x = @(x) M1' \ x;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	108 elseif (isa (M1, "function_handle"))
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	109 M1m1x = @(x) feval (M1, x, "notransp");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	110 M1tm1x = @(x) feval (M1, x, "transp");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	111 else
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	112 error (["bicg: preconditioner is expected to " ...
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	113 "be a function or matrix"]);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	114 endif
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	115
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	116 if (nargin < 6 \|\| isempty (M2))
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	117 M2m1x = @(x, ignore) x;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	118 M2tm1x = M2m1x;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	119 elseif (ischar (M2))
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	120 fun = str2func (M2);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	121 M2m1x = @(x) feval (fun, x, "notransp");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	122 M2tm1x = @(x) feval (fun, x, "transp");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	123 elseif (ismatrix (M2))
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	124 M2m1x = @(x) M2 \ x;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	125 M2tm1x = @(x) M2' \ x;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	126 elseif (isa (M2, "function_handle"))
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	127 M2m1x = @(x) feval (M2, x, "notransp");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	128 M2tm1x = @(x) feval (M2, x, "transp");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	129 else
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	130 error (["bicg: preconditioner is expected to " ...
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	131 "be a function or matrix"]);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	132 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	133
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	134 Pm1x = @(x) M2m1x (M1m1x (x));
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	135 Ptm1x = @(x) M1tm1x (M2tm1x (x));
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	136
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13073 diff changeset	137 if (nargin < 7 \|\| isempty (x0))
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	138 x0 = zeros (size (b));
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	139 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	140
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	141 y = x = x0;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	142 c = b;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	143
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	144 r0 = b - Ax (x);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	145 s0 = c - Atx (y);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	146
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	147 d = Pm1x (r0);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	148 f = Ptm1x (s0);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	149
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	150 bnorm = norm (b);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	151 res0 = Inf;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	152
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	153 if (any (r0 != 0))
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	154
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	155 for k = 1:maxit
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	156
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	157 a = (s0' * Pm1x (r0)) ./ (f' * Ax (d));
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	158
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	159 x += a * d;
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	160 y += conj (a) * f;
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	161
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	162 r1 = r0 - a * Ax (d);
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	163 s1 = s0 - conj (a) * Atx (f);
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	164
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	165 beta = (s1' * Pm1x (r1)) ./ (s0' * Pm1x (r0));
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	166
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	167 d = Pm1x (r1) + beta * d;
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	168 f = Ptm1x (s1) + conj (beta) * f;
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	169
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	170 r0 = r1;
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	171 s0 = s1;
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	172
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	173 res1 = norm (b - Ax (x)) / bnorm;
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	174 if (res1 < tol)
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	175 flag = 0;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	176 if (nargout < 2)
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	177 printf ("bicg converged at iteration %i ", k);
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	178 printf ("to a solution with relative residual %e\n", res1);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	179 endif
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	180 break;
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	181 endif
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	182
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	183 if (res0 <= res1)
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	184 flag = 3;
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	185 printf ("bicg stopped at iteration %i ", k);
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	186 printf ("without converging to the desired tolerance %e\n", tol);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	187 printf ("because the method stagnated.\n");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	188 printf ("The iterate returned (number %i) ", k-1);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	189 printf ("has relative residual %e\n", res0);
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	190 break
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	191 endif
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	192 res0 = res1;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	193 if (nargout > 4)
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	194 resvec(k) = res0;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	195 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	196 endfor
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	197
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	198 if (k == maxit)
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	199 flag = 1;
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	200 printf ("bicg stopped at iteration %i ", maxit);
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	201 printf ("without converging to the desired tolerance %e\n", tol);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	202 printf ("because the maximum number of iterations was reached. ");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	203 printf ("The iterate returned (number %i) has ", maxit);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	204 printf ("relative residual %e\n", res1);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	205 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	206
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	207 else
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	208 flag = 0;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	209 if (nargout < 2)
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	210 printf ("bicg converged after 0 interations\n");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	211 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	212 endif
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	213
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	214 else
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	215 print_usage ();
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	216 endif
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	217
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	218 endfunction;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	219
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	220
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	221 %!test
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	222 %! n = 100;
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	223 %! 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	224 %! b = sum (A, 2);
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	225 %! tol = 1e-8;
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	226 %! maxit = 15;
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	227 %! 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	228 %! 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	229 %! [x, flag, relres, iter, resvec] = bicg (A, b, tol, maxit, M1, M2);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	230 %! 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	231 %!
13796 53674ceb9133 maint: fix function definition in test John W. Eaton <jwe@octave.org> parents: 13141 diff changeset	232
53674ceb9133 maint: fix function definition in test John W. Eaton <jwe@octave.org> parents: 13141 diff changeset	233 %!function y = afun (x, t, a)
53674ceb9133 maint: fix function definition in test John W. Eaton <jwe@octave.org> parents: 13141 diff changeset	234 %! switch t
53674ceb9133 maint: fix function definition in test John W. Eaton <jwe@octave.org> parents: 13141 diff changeset	235 %! case "notransp"
53674ceb9133 maint: fix function definition in test John W. Eaton <jwe@octave.org> parents: 13141 diff changeset	236 %! y = a * x;
53674ceb9133 maint: fix function definition in test John W. Eaton <jwe@octave.org> parents: 13141 diff changeset	237 %! case "transp"
53674ceb9133 maint: fix function definition in test John W. Eaton <jwe@octave.org> parents: 13141 diff changeset	238 %! y = a' * x;
53674ceb9133 maint: fix function definition in test John W. Eaton <jwe@octave.org> parents: 13141 diff changeset	239 %! endswitch
53674ceb9133 maint: fix function definition in test John W. Eaton <jwe@octave.org> parents: 13141 diff changeset	240 %!endfunction
53674ceb9133 maint: fix function definition in test John W. Eaton <jwe@octave.org> parents: 13141 diff changeset	241 %!
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	242 %!test
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	243 %! n = 100;
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	244 %! 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	245 %! b = sum (A, 2);
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	246 %! tol = 1e-8;
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	247 %! maxit = 15;
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	248 %! 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	249 %! 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	250 %!
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	251 %! [x, flag, relres, iter, resvec] = bicg (@(x, t) afun (x, t, A),
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	252 %! b, tol, maxit, M1, M2);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	253 %! 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	254
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	255 %!test
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	256 %! n = 100;
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	257 %! tol = 1e-8;
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	258 %! a = sprand (n, n, .1);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	259 %! 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	260 %! b = sum (A, 2);
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	261 %! [x, flag, relres, iter, resvec] = bicg (A, b, tol, [], diag (diag (A)));
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: diff changeset	262 %! assert (x, ones (size (b)), 1e-7);