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

annotate scripts/sparse/pcg.m @ 20164:df437a52bcaf stable

doc: Update more docstrings to have one sentence summary as first line. Reviewed miscellaneous, sparse, strings in scripts directory. * scripts/miscellaneous/bzip2.m, scripts/miscellaneous/citation.m, scripts/miscellaneous/compare_versions.m, scripts/miscellaneous/computer.m, scripts/miscellaneous/debug.m, scripts/miscellaneous/dir.m, scripts/miscellaneous/edit.m, scripts/miscellaneous/error_ids.m, scripts/miscellaneous/fileattrib.m, scripts/miscellaneous/fullfile.m, scripts/miscellaneous/genvarname.m, scripts/miscellaneous/gzip.m, scripts/miscellaneous/mkoctfile.m, scripts/miscellaneous/news.m, scripts/miscellaneous/open.m, scripts/miscellaneous/parseparams.m, scripts/miscellaneous/recycle.m, scripts/miscellaneous/run.m, scripts/miscellaneous/swapbytes.m, scripts/miscellaneous/tar.m, scripts/miscellaneous/tmpnam.m, scripts/miscellaneous/unpack.m, scripts/miscellaneous/what.m, scripts/sparse/bicg.m, scripts/sparse/bicgstab.m, scripts/sparse/cgs.m, scripts/sparse/colperm.m, scripts/sparse/eigs.m, scripts/sparse/etreeplot.m, scripts/sparse/gmres.m, scripts/sparse/gplot.m, scripts/sparse/ichol.m, scripts/sparse/ilu.m, scripts/sparse/pcg.m, scripts/sparse/pcr.m, scripts/sparse/qmr.m, scripts/sparse/spaugment.m, scripts/sparse/spconvert.m, scripts/sparse/spdiags.m, scripts/sparse/spfun.m, scripts/sparse/spones.m, scripts/sparse/sprandsym.m, scripts/sparse/spstats.m, scripts/sparse/spy.m, scripts/sparse/svds.m, scripts/sparse/treelayout.m, scripts/sparse/treeplot.m, scripts/strings/base2dec.m, scripts/strings/bin2dec.m, scripts/strings/blanks.m, scripts/strings/cstrcat.m, scripts/strings/deblank.m, scripts/strings/dec2base.m, scripts/strings/dec2bin.m, scripts/strings/dec2hex.m, scripts/strings/findstr.m, scripts/strings/hex2dec.m, scripts/strings/index.m, scripts/strings/isletter.m, scripts/strings/isstrprop.m, scripts/strings/mat2str.m, scripts/strings/ostrsplit.m, scripts/strings/regexptranslate.m, scripts/strings/rindex.m, scripts/strings/str2num.m, scripts/strings/strcat.m, scripts/strings/strchr.m, scripts/strings/strjoin.m, scripts/strings/strjust.m, scripts/strings/strmatch.m, scripts/strings/strsplit.m, scripts/strings/strtok.m, scripts/strings/strtrim.m, scripts/strings/strtrunc.m, scripts/strings/substr.m, scripts/strings/untabify.m, scripts/time/datenum.m: Update more docstrings to have one sentence summary as first line.

author	Rik <rik@octave.org>
date	Mon, 04 May 2015 14:22:02 -0700
parents	9fc020886ae9
children

rev	line source
19697 4197fc428c7d maint: Update copyright notices for 2015. John W. Eaton <jwe@octave.org> parents: 19596 diff changeset	1 ## Copyright (C) 2004-2015 Piotr Krzyzanowski
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	2 ##
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	3 ## This file is part of Octave.
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	4 ##
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	5 ## Octave is free software; you can redistribute it and/or modify it
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	6 ## under the terms of the GNU General Public License as published by
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 7007 diff changeset	7 ## the Free Software Foundation; either version 3 of the License, or (at
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 7007 diff changeset	8 ## your option) any later version.
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	9 ##
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	10 ## Octave is distributed in the hope that it will be useful, but
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	13 ## General Public License for more details.
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	14 ##
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	15 ## You should have received a copy of the GNU General Public License
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 7007 diff changeset	16 ## along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 7007 diff changeset	17 ## <http://www.gnu.org/licenses/>.
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	18
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	19 ## -- texinfo --
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10846 diff changeset	20 ## @deftypefn {Function File} {@var{x} =} pcg (@var{A}, @var{b}, @var{tol}, @var{maxit}, @var{m1}, @var{m2}, @var{x0}, @dots{})
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	21 ## @deftypefnx {Function File} {[@var{x}, @var{flag}, @var{relres}, @var{iter}, @var{resvec}, @var{eigest}] =} pcg (@dots{})
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	22 ##
17681 f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	23 ## Solve the linear system of equations @w{@code{@var{A} * @var{x} = @var{b}}}
20164 df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	24 ## by means of the Preconditioned Conjugate Gradient iterative method.
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	25 ##
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	26 ## The input arguments are
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	27 ##
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	28 ## @itemize
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	29 ## @item
17681 f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	30 ## @var{A} can be either a square (preferably sparse) matrix or a function
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	31 ## handle, inline function or string containing the name of a function which
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	32 ## computes @w{@code{@var{A} * @var{x}}}. In principle, @var{A} should be
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	33 ## symmetric and positive definite; if @code{pcg} finds @var{A} not to be
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	34 ## positive definite, a warning is printed and the @var{flag} output will be
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	35 ## set.
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	36 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	37 ## @item
17681 f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	38 ## @var{b} is the right-hand side vector.
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	39 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	40 ## @item
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	41 ## @var{tol} is the required relative tolerance for the residual error,
17681 f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	42 ## @w{@code{@var{b} - @var{A} * @var{x}}}. The iteration stops if
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	43 ## @w{@code{norm (@var{b} - @var{A} * @var{x})} @leq{}
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	44 ## @w{@var{tol} * norm (@var{b})}}.
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	45 ## If @var{tol} is omitted or empty then a tolerance of 1e-6 is used.
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	46 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	47 ## @item
17681 f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	48 ## @var{maxit} is the maximum allowable number of iterations; if @var{maxit}
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	49 ## is omitted or empty then a value of 20 is used.
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	50 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	51 ## @item
10846 a4f482e66b65 Grammarcheck more of the documentation. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	52 ## @var{m} = @var{m1} * @var{m2} is the (left) preconditioning matrix, so that
a4f482e66b65 Grammarcheck more of the documentation. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	53 ## the iteration is (theoretically) equivalent to solving by @code{pcg}
17681 f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	54 ## @w{@code{@var{P} * @var{x} = @var{m} \ @var{b}}}, with
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	55 ## @w{@code{@var{P} = @var{m} \ @var{A}}}.
20164 df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	56 ## Note that a proper choice of the preconditioner may dramatically improve
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	57 ## the overall performance of the method. Instead of matrices @var{m1} and
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	58 ## @var{m2}, the user may pass two functions which return the results of
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	59 ## applying the inverse of @var{m1} and @var{m2} to a vector (usually this is
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	60 ## the preferred way of using the preconditioner). If @var{m1} is omitted or
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	61 ## empty @code{[]} then no preconditioning is applied. If @var{m2} is
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	62 ## omitted, @var{m} = @var{m1} will be used as a preconditioner.
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	63 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	64 ## @item
17681 f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	65 ## @var{x0} is the initial guess. If @var{x0} is omitted or empty then the
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	66 ## function sets @var{x0} to a zero vector by default.
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	67 ## @end itemize
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	68 ##
17681 f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	69 ## The arguments which follow @var{x0} are treated as parameters, and passed in
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	70 ## a proper way to any of the functions (@var{A} or @var{m}) which are passed
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	71 ## to @code{pcg}. See the examples below for further details. The output
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	72 ## arguments are
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	73 ##
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	74 ## @itemize
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	75 ## @item
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	76 ## @var{x} is the computed approximation to the solution of
17681 f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	77 ## @w{@code{@var{A} * @var{x} = @var{b}}}.
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	78 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	79 ## @item
17681 f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	80 ## @var{flag} reports on the convergence. A value of 0 means the solution
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	81 ## converged and the tolerance criterion given by @var{tol} is satisfied.
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	82 ## A value of 1 means that the @var{maxit} limit for the iteration count was
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	83 ## reached. A value of 3 indicates that the (preconditioned) matrix was found
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	84 ## not to be positive definite.
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	85 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	86 ## @item
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	87 ## @var{relres} is the ratio of the final residual to its initial value,
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	88 ## measured in the Euclidean norm.
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	89 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	90 ## @item
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	91 ## @var{iter} is the actual number of iterations performed.
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	92 ##
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	93 ## @item
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	94 ## @var{resvec} describes the convergence history of the method.
17681 f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	95 ## @code{@var{resvec}(i,1)} is the Euclidean norm of the residual, and
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	96 ## @code{@var{resvec}(i,2)} is the preconditioned residual norm, after the
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	97 ## (@var{i}-1)-th iteration, @code{@var{i} = 1, 2, @dots{}, @var{iter}+1}.
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	98 ## The preconditioned residual norm is defined as
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	99 ## @code{norm (@var{r}) ^ 2 = @var{r}' * (@var{m} \ @var{r})} where
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10846 diff changeset	100 ## @code{@var{r} = @var{b} - @var{A} * @var{x}}, see also the
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	101 ## description of @var{m}. If @var{eigest} is not required, only
17681 f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	102 ## @code{@var{resvec}(:,1)} is returned.
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	103 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	104 ## @item
17681 f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	105 ## @var{eigest} returns the estimate for the smallest @code{@var{eigest}(1)}
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	106 ## and largest @code{@var{eigest}(2)} eigenvalues of the preconditioned matrix
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	107 ## @w{@code{@var{P} = @var{m} \ @var{A}}}. In particular, if no
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	108 ## preconditioning is used, the estimates for the extreme eigenvalues of
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	109 ## @var{A} are returned. @code{@var{eigest}(1)} is an overestimate and
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	110 ## @code{@var{eigest}(2)} is an underestimate, so that
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	111 ## @code{@var{eigest}(2) / @var{eigest}(1)} is a lower bound for
19593 446c46af4b42 strip trailing whitespace from most source files John W. Eaton <jwe@octave.org> parents: 17744 diff changeset	112 ## @code{cond (@var{P}, 2)}, which nevertheless in the limit should
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	113 ## theoretically be equal to the actual value of the condition number.
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	114 ## The method which computes @var{eigest} works only for symmetric positive
17681 f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	115 ## definite @var{A} and @var{m}, and the user is responsible for verifying this
f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	116 ## assumption.
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	117 ## @end itemize
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	118 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	119 ## Let us consider a trivial problem with a diagonal matrix (we exploit the
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	120 ## sparsity of A)
c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	121 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	122 ## @example
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	123 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	124 ## n = 10;
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	125 ## A = diag (sparse (1:n));
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	126 ## b = rand (n, 1);
19148 e278c939a419 Deprecate luinc. Rik <rik@octave.org> parents: 19040 diff changeset	127 ## [l, u, p] = ilu (A, struct ("droptol", 1.e-3));
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	128 ## @end group
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	129 ## @end example
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	130 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	131 ## @sc{Example 1:} Simplest use of @code{pcg}
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	132 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	133 ## @example
17681 f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	134 ## x = pcg (A, b)
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	135 ## @end example
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	136 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	137 ## @sc{Example 2:} @code{pcg} with a function which computes
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10846 diff changeset	138 ## @code{@var{A} * @var{x}}
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	139 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	140 ## @example
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	141 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	142 ## function y = apply_a (x)
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	143 ## y = [1:N]' .* x;
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	144 ## endfunction
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	145 ##
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	146 ## x = pcg ("apply_a", b)
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	147 ## @end group
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	148 ## @end example
6747 392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	149 ##
392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	150 ## @sc{Example 3:} @code{pcg} with a preconditioner: @var{l} * @var{u}
392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	151 ##
392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	152 ## @example
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	153 ## x = pcg (A, b, 1.e-6, 500, l*u)
6747 392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	154 ## @end example
392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	155 ##
392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	156 ## @sc{Example 4:} @code{pcg} with a preconditioner: @var{l} * @var{u}.
20164 df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	157 ## Faster than @sc{Example 3} since lower and upper triangular matrices are
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	158 ## easier to invert
6747 392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	159 ##
392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	160 ## @example
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	161 ## x = pcg (A, b, 1.e-6, 500, l, u)
6747 392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	162 ## @end example
392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	163 ##
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	164 ## @sc{Example 5:} Preconditioned iteration, with full diagnostics. The
20164 df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	165 ## preconditioner (quite strange, because even the original matrix @var{A} is
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	166 ## trivial) is defined as a function
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	167 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	168 ## @example
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	169 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	170 ## function y = apply_m (x)
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	171 ## k = floor (length (x) - 2);
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	172 ## y = x;
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	173 ## y(1:k) = x(1:k) ./ [1:k]';
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	174 ## endfunction
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	175 ##
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	176 ## [x, flag, relres, iter, resvec, eigest] = ...
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	177 ## pcg (A, b, [], [], "apply_m");
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	178 ## semilogy (1:iter+1, resvec);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	179 ## @end group
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	180 ## @end example
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	181 ##
20164 df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	182 ## @sc{Example 6:} Finally, a preconditioner which depends on a parameter
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	183 ## @var{k}.
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	184 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	185 ## @example
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	186 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	187 ## function y = apply_M (x, varargin)
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	188 ## K = varargin@{1@};
6547 4fb053f24fd6 [project @ 2007-04-19 21:47:40 by jwe] jwe parents: 6498 diff changeset	189 ## y = x;
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	190 ## y(1:K) = x(1:K) ./ [1:K]';
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	191 ## endfunction
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	192 ##
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	193 ## [x, flag, relres, iter, resvec, eigest] = ...
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	194 ## pcg (A, b, [], [], "apply_m", [], [], 3)
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	195 ## @end group
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	196 ## @end example
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	197 ##
10791 3140cb7a05a1 Add spellchecker scripts for Octave and run spellcheck of documentation Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	198 ## References:
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	199 ##
10793 be55736a0783 Grammarcheck the documentation from m-files. Rik <octave@nomad.inbox5.com> parents: 10791 diff changeset	200 ## @enumerate
be55736a0783 Grammarcheck the documentation from m-files. Rik <octave@nomad.inbox5.com> parents: 10791 diff changeset	201 ## @item
be55736a0783 Grammarcheck the documentation from m-files. Rik <octave@nomad.inbox5.com> parents: 10791 diff changeset	202 ## C.T. Kelley, @cite{Iterative Methods for Linear and Nonlinear Equations},
be55736a0783 Grammarcheck the documentation from m-files. Rik <octave@nomad.inbox5.com> parents: 10791 diff changeset	203 ## SIAM, 1995. (the base PCG algorithm)
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	204 ##
10793 be55736a0783 Grammarcheck the documentation from m-files. Rik <octave@nomad.inbox5.com> parents: 10791 diff changeset	205 ## @item
19596 0e1f5a750d00 maint: Periodic merge of gui-release to default. John W. Eaton <jwe@octave.org> parents: 19148 19593 diff changeset	206 ## @nospell{Y. Saad}, @cite{Iterative Methods for Sparse Linear Systems},
16826 a4969508008e doc: Periodic spellcheck of the documentation. Rik <rik@octave.org> parents: 14872 diff changeset	207 ## @nospell{PWS} 1996. (condition number estimate from PCG)
a4969508008e doc: Periodic spellcheck of the documentation. Rik <rik@octave.org> parents: 14872 diff changeset	208 ## Revised version of this book is available online at
a4969508008e doc: Periodic spellcheck of the documentation. Rik <rik@octave.org> parents: 14872 diff changeset	209 ## @url{http://www-users.cs.umn.edu/~saad/books.html}
10793 be55736a0783 Grammarcheck the documentation from m-files. Rik <octave@nomad.inbox5.com> parents: 10791 diff changeset	210 ## @end enumerate
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	211 ##
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	212 ## @seealso{sparse, pcr}
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	213 ## @end deftypefn
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	214
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	215 ## Author: Piotr Krzyzanowski <piotr.krzyzanowski@mimuw.edu.pl>
6747 392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	216 ## Modified by: Vittoria Rezzonico <vittoria.rezzonico@epfl.ch>
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	217 ## - Add the ability to provide the pre-conditioner as two separate matrices
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	218
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10846 diff changeset	219 function [x, flag, relres, iter, resvec, eigest] = pcg (A, b, tol, maxit, m1, m2, x0, varargin)
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	220
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8506 diff changeset	221 ## M = M1*M2
6747 392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	222
392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	223 if (nargin < 7 \|\| isempty (x0))
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	224 x = zeros (size (b));
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	225 else
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	226 x = x0;
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	227 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	228
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8506 diff changeset	229 if (nargin < 5 \|\| isempty (m1))
cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8506 diff changeset	230 exist_m1 = 0;
cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8506 diff changeset	231 else
cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8506 diff changeset	232 exist_m1 = 1;
cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8506 diff changeset	233 endif
6747 392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	234
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8506 diff changeset	235 if (nargin < 6 \|\| isempty (m2))
cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8506 diff changeset	236 exist_m2 = 0;
cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8506 diff changeset	237 else
cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8506 diff changeset	238 exist_m2 = 1;
cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8506 diff changeset	239 endif
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	240
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	241 if (nargin < 4 \|\| isempty (maxit))
14872 c2dbdeaa25df maint: use rows() and columns() to clarify m-files. Rik <octave@nomad.inbox5.com> parents: 14868 diff changeset	242 maxit = min (rows (b), 20);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	243 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	244
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	245 maxit += 2;
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	246
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	247 if (nargin < 3 \|\| isempty (tol))
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	248 tol = 1e-6;
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	249 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	250
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	251 preconditioned_residual_out = false;
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	252 if (nargout > 5)
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	253 T = zeros (maxit, maxit);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	254 preconditioned_residual_out = true;
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	255 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	256
8506 bc982528de11 comment style fixes John W. Eaton <jwe@octave.org> parents: 7515 diff changeset	257 ## Assume A is positive definite.
bc982528de11 comment style fixes John W. Eaton <jwe@octave.org> parents: 7515 diff changeset	258 matrix_positive_definite = true;
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	259
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	260 p = zeros (size (b));
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	261 oldtau = 1;
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10846 diff changeset	262 if (isnumeric (A))
8506 bc982528de11 comment style fixes John W. Eaton <jwe@octave.org> parents: 7515 diff changeset	263 ## A is a matrix.
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	264 r = b - A*x;
8506 bc982528de11 comment style fixes John W. Eaton <jwe@octave.org> parents: 7515 diff changeset	265 else
bc982528de11 comment style fixes John W. Eaton <jwe@octave.org> parents: 7515 diff changeset	266 ## A should be a function.
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10846 diff changeset	267 r = b - feval (A, x, varargin{:});
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	268 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	269
17681 f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	270 b_norm = norm (b);
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	271 resvec(1,1) = norm (r);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	272 alpha = 1;
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	273 iter = 2;
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	274
17681 f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	275 while (resvec(iter-1,1) > tol * b_norm && iter < maxit)
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8506 diff changeset	276 if (exist_m1)
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	277 if (isnumeric (m1))
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	278 y = m1 \ r;
6747 392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	279 else
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	280 y = feval (m1, r, varargin{:});
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	281 endif
6747 392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	282 else
392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	283 y = r;
392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	284 endif
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8506 diff changeset	285 if (exist_m2)
cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8506 diff changeset	286 if (isnumeric (m2))
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	287 z = m2 \ y;
6747 392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	288 else
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	289 z = feval (m2, y, varargin{:});
6747 392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	290 endif
392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	291 else
392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	292 z = y;
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	293 endif
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	294 tau = z' * r;
17681 f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	295 resvec(iter-1,2) = sqrt (tau);
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	296 beta = tau / oldtau;
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	297 oldtau = tau;
6747 392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	298 p = z + beta * p;
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10846 diff changeset	299 if (isnumeric (A))
8506 bc982528de11 comment style fixes John W. Eaton <jwe@octave.org> parents: 7515 diff changeset	300 ## A is a matrix.
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10846 diff changeset	301 w = A * p;
8506 bc982528de11 comment style fixes John W. Eaton <jwe@octave.org> parents: 7515 diff changeset	302 else
bc982528de11 comment style fixes John W. Eaton <jwe@octave.org> parents: 7515 diff changeset	303 ## A should be a function.
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10846 diff changeset	304 w = feval (A, p, varargin{:});
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	305 endif
8506 bc982528de11 comment style fixes John W. Eaton <jwe@octave.org> parents: 7515 diff changeset	306 ## Needed only for eigest.
bc982528de11 comment style fixes John W. Eaton <jwe@octave.org> parents: 7515 diff changeset	307 oldalpha = alpha;
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	308 alpha = tau / (p'*w);
8506 bc982528de11 comment style fixes John W. Eaton <jwe@octave.org> parents: 7515 diff changeset	309 if (alpha <= 0.0)
bc982528de11 comment style fixes John W. Eaton <jwe@octave.org> parents: 7515 diff changeset	310 ## Negative matrix.
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	311 matrix_positive_definite = false;
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	312 endif
6747 392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	313 x += alpha * p;
392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	314 r -= alpha * w;
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	315 if (nargout > 5 && iter > 2)
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	316 T(iter-1:iter, iter-1:iter) = T(iter-1:iter, iter-1:iter) + ...
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	317 [1 sqrt(beta); sqrt(beta) beta]./oldalpha;
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	318 ## EVS = eig (T(2:iter-1,2:iter-1));
5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	319 ## fprintf (stderr,"PCG condest: %g (iteration: %d)\n", max (EVS)/min (EVS),iter);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	320 endif
17681 f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	321 resvec(iter,1) = norm (r);
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	322 iter++;
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	323 endwhile
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	324
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	325 if (nargout > 5)
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	326 if (matrix_positive_definite)
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	327 if (iter > 3)
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	328 T = T(2:iter-2,2:iter-2);
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	329 l = eig (T);
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	330 eigest = [min(l), max(l)];
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	331 ## fprintf (stderr, "pcg condest: %g\n", eigest(2)/eigest(1));
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	332 else
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	333 eigest = [NaN, NaN];
11588 d5bd2766c640 style fixes for warning and error messages in script files John W. Eaton <jwe@octave.org> parents: 11587 diff changeset	334 warning ("pcg: eigenvalue estimate failed: iteration converged too fast");
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	335 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	336 else
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	337 eigest = [NaN, NaN];
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	338 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	339
8506 bc982528de11 comment style fixes John W. Eaton <jwe@octave.org> parents: 7515 diff changeset	340 ## Apply the preconditioner once more and finish with the precond
bc982528de11 comment style fixes John W. Eaton <jwe@octave.org> parents: 7515 diff changeset	341 ## residual.
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8506 diff changeset	342 if (exist_m1)
cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8506 diff changeset	343 if (isnumeric (m1))
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	344 y = m1 \ r;
6747 392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	345 else
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	346 y = feval (m1, r, varargin{:});
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	347 endif
6747 392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	348 else
392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	349 y = r;
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	350 endif
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8506 diff changeset	351 if (exist_m2)
cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8506 diff changeset	352 if (isnumeric (m2))
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	353 z = m2 \ y;
6747 392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	354 else
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	355 z = feval (m2, y, varargin{:});
6747 392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	356 endif
392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	357 else
392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	358 z = y;
392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	359 endif
392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	360
17681 f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	361 resvec(iter-1,2) = sqrt (r' * z);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	362 else
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	363 resvec = resvec(:,1);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	364 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	365
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	366 flag = 0;
17681 f6fded839513 pcg.m: Change success criterion to match reference text (bug #40057) Rik <rik@octave.org> parents: 17336 diff changeset	367 relres = resvec(iter-1,1) ./ resvec(1,1);
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	368 iter -= 2;
6747 392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	369 if (iter >= maxit - 2)
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	370 flag = 1;
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	371 if (nargout < 2)
6498 2c85044aa63f [project @ 2007-04-05 17:59:47 by jwe] jwe parents: 5838 diff changeset	372 warning ("pcg: maximum number of iterations (%d) reached\n", iter);
6747 392d61107f11 [project @ 2007-06-19 20:30:30 by dbateman] dbateman parents: 6547 diff changeset	373 warning ("the initial residual norm was reduced %g times.\n", ...
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	374 1.0 / relres);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	375 endif
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	376 elseif (nargout < 2)
6498 2c85044aa63f [project @ 2007-04-05 17:59:47 by jwe] jwe parents: 5838 diff changeset	377 fprintf (stderr, "pcg: converged in %d iterations. ", iter);
2c85044aa63f [project @ 2007-04-05 17:59:47 by jwe] jwe parents: 5838 diff changeset	378 fprintf (stderr, "the initial residual norm was reduced %g times.\n",...
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	379 1.0/relres);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	380 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	381
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	382 if (! matrix_positive_definite)
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	383 flag = 3;
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	384 if (nargout < 2)
6498 2c85044aa63f [project @ 2007-04-05 17:59:47 by jwe] jwe parents: 5838 diff changeset	385 warning ("pcg: matrix not positive definite?\n");
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	386 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	387 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	388 endfunction
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	389
14237 11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	390
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	391 %!demo
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	392 %! ## Simplest usage of pcg (see also 'help pcg')
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	393 %!
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	394 %! N = 10;
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	395 %! A = diag ([1:N]); b = rand (N, 1);
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	396 %! y = A \ b; # y is the true solution
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	397 %! x = pcg (A, b);
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	398 %! printf ("The solution relative error is %g\n", norm (x - y) / norm (y));
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	399 %!
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	400 %! ## You shouldn't be afraid if pcg issues some warning messages in this
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	401 %! ## example: watch out in the second example, why it takes N iterations
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	402 %! ## of pcg to converge to (a very accurate, by the way) solution
14237 11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	403
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	404 %!demo
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	405 %! ## Full output from pcg, except for the eigenvalue estimates
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	406 %! ## We use this output to plot the convergence history
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	407 %!
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	408 %! N = 10;
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	409 %! A = diag ([1:N]); b = rand (N, 1);
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	410 %! X = A \ b; # X is the true solution
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	411 %! [x, flag, relres, iter, resvec] = pcg (A, b);
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	412 %! printf ("The solution relative error is %g\n", norm (x - X) / norm (X));
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	413 %! title ("Convergence history");
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	414 %! semilogy ([0:iter], resvec / resvec(1), "o-g");
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	415 %! xlabel ("Iteration"); ylabel ("log(\|\|b-Ax\|\|/\|\|b\|\|)");
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	416 %! legend ("relative residual");
14237 11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	417
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	418 %!demo
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	419 %! ## Full output from pcg, including the eigenvalue estimates
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	420 %! ## Hilbert matrix is extremely ill-conditioned, so pcg WILL have problems
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	421 %!
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	422 %! N = 10;
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	423 %! A = hilb (N); b = rand (N, 1);
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	424 %! X = A \ b; # X is the true solution
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	425 %! [x, flag, relres, iter, resvec, eigest] = pcg (A, b, [], 200);
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	426 %! printf ("The solution relative error is %g\n", norm (x - X) / norm (X));
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	427 %! printf ("Condition number estimate is %g\n", eigest(2) / eigest(1));
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	428 %! printf ("Actual condition number is %g\n", cond (A));
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	429 %! title ("Convergence history");
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	430 %! semilogy ([0:iter], resvec, ["o-g";"+-r"]);
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	431 %! xlabel ("Iteration"); ylabel ("log(\|\|b-Ax\|\|)");
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	432 %! legend ("absolute residual", "absolute preconditioned residual");
14237 11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	433
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	434 %!demo
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	435 %! ## Full output from pcg, including the eigenvalue estimates
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	436 %! ## We use the 1-D Laplacian matrix for A, and cond(A) = O(N^2)
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	437 %! ## and that's the reason we need some preconditioner; here we take
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	438 %! ## a very simple and not powerful Jacobi preconditioner,
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	439 %! ## which is the diagonal of A.
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	440 %!
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	441 %! N = 100;
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	442 %! A = zeros (N, N);
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	443 %! for i = 1 : N - 1 # form 1-D Laplacian matrix
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	444 %! A(i:i+1, i:i+1) = [2 -1; -1 2];
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	445 %! endfor
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	446 %! b = rand (N, 1);
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	447 %! X = A \ b; # X is the true solution
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	448 %! maxit = 80;
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	449 %! printf ("System condition number is %g\n", cond (A));
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	450 %! ## No preconditioner: the convergence is very slow!
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	451 %!
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	452 %! [x, flag, relres, iter, resvec, eigest] = pcg (A, b, [], maxit);
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	453 %! printf ("System condition number estimate is %g\n", eigest(2) / eigest(1));
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	454 %! title ("Convergence history");
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	455 %! semilogy ([0:iter], resvec(:,1), "o-g");
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	456 %! xlabel ("Iteration"); ylabel ("log(\|\|b-Ax\|\|)");
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	457 %! legend ("NO preconditioning: absolute residual");
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	458 %!
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	459 %! pause (1);
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	460 %! ## Test Jacobi preconditioner: it will not help much!!!
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	461 %!
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	462 %! M = diag (diag (A)); # Jacobi preconditioner
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	463 %! [x, flag, relres, iter, resvec, eigest] = pcg (A, b, [], maxit, M);
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	464 %! printf ("JACOBI preconditioned system condition number estimate is %g\n", eigest(2) / eigest(1));
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	465 %! hold on;
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	466 %! semilogy ([0:iter], resvec(:,1), "o-r");
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	467 %! legend ("NO preconditioning: absolute residual", ...
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	468 %! "JACOBI preconditioner: absolute residual");
14237 11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	469 %!
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	470 %! pause (1);
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	471 %! ## Test nonoverlapping block Jacobi preconditioner: it will help much!
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	472 %!
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	473 %! M = zeros (N, N); k = 4;
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	474 %! for i = 1 : k : N # form 1-D Laplacian matrix
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	475 %! M(i:i+k-1, i:i+k-1) = A(i:i+k-1, i:i+k-1);
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	476 %! endfor
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	477 %! [x, flag, relres, iter, resvec, eigest] = pcg (A, b, [], maxit, M);
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	478 %! printf ("BLOCK JACOBI preconditioned system condition number estimate is %g\n", eigest(2) / eigest(1));
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	479 %! semilogy ([0:iter], resvec(:,1), "o-b");
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	480 %! legend ("NO preconditioning: absolute residual", ...
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	481 %! "JACOBI preconditioner: absolute residual", ...
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	482 %! "BLOCK JACOBI preconditioner: absolute residual");
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	483 %! hold off;
14237 11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	484
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	485 %!test
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	486 %! ## solve small diagonal system
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	487 %!
14237 11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	488 %! N = 10;
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	489 %! A = diag ([1:N]); b = rand (N, 1);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	490 %! X = A \ b; # X is the true solution
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	491 %! [x, flag] = pcg (A, b, [], N+1);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	492 %! assert (norm (x - X) / norm (X), 0, 1e-10);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	493 %! assert (flag, 0);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	494
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	495 %!test
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	496 %! ## solve small indefinite diagonal system
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	497 %! ## despite A is indefinite, the iteration continues and converges
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	498 %! ## indefiniteness of A is detected
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	499 %!
14237 11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	500 %! N = 10;
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	501 %! A = diag([1:N] .* (-ones(1, N) .^ 2)); b = rand (N, 1);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	502 %! X = A \ b; # X is the true solution
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	503 %! [x, flag] = pcg (A, b, [], N+1);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	504 %! assert (norm (x - X) / norm (X), 0, 1e-10);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	505 %! assert (flag, 3);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	506
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	507 %!test
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	508 %! ## solve tridiagonal system, do not converge in default 20 iterations
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	509 %!
14237 11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	510 %! N = 100;
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	511 %! A = zeros (N, N);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	512 %! for i = 1 : N - 1 # form 1-D Laplacian matrix
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	513 %! A(i:i+1, i:i+1) = [2 -1; -1 2];
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	514 %! endfor
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	515 %! b = ones (N, 1);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	516 %! X = A \ b; # X is the true solution
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	517 %! [x, flag, relres, iter, resvec, eigest] = pcg (A, b, 1e-12);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	518 %! assert (flag);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	519 %! assert (relres > 1.0);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	520 %! assert (iter, 20); # should perform max allowable default number of iterations
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	521
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	522 %!test
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	523 %! ## solve tridiagonal system with 'perfect' preconditioner
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	524 %! ## which converges in one iteration, so the eigest does not
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16826 diff changeset	525 %! ## work and issues a warning
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	526 %!
14237 11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	527 %! N = 100;
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	528 %! A = zeros (N, N);
19833 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19697 diff changeset	529 %! for i = 1 : N - 1 # form 1-D Laplacian matrix
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19697 diff changeset	530 %! A(i:i+1, i:i+1) = [2 -1; -1 2];
14237 11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	531 %! endfor
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	532 %! b = ones (N, 1);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	533 %! X = A \ b; # X is the true solution
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	534 %! [x, flag, relres, iter, resvec, eigest] = pcg (A, b, [], [], A, [], b);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	535 %! assert (norm (x - X) / norm (X), 0, 1e-6);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	536 %! assert (flag, 0);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	537 %! assert (iter, 1); # should converge in one iteration
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	538 %! assert (isnan (eigest), isnan ([NaN, NaN]));
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	539

Mercurial > octave-antonio

annotate scripts/sparse/pcg.m @ 20164:df437a52bcaf stable