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

annotate scripts/sparse/pcr.m @ 19697:4197fc428c7d

maint: Update copyright notices for 2015.

author	John W. Eaton <jwe@octave.org>
date	Wed, 11 Feb 2015 14:19:08 -0500
parents	0850b5212619
children	df437a52bcaf

rev	line source
19697 4197fc428c7d maint: Update copyright notices for 2015. John W. Eaton <jwe@octave.org> parents: 19040 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: 7001 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: 7001 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: 7001 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: 7001 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: 10793 diff changeset	20 ## @deftypefn {Function File} {@var{x} =} pcr (@var{A}, @var{b}, @var{tol}, @var{maxit}, @var{m}, @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}] =} pcr (@dots{})
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	22 ##
14093 050bc580cb60 doc: Various docstring improvements before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	23 ## Solve the linear system of equations @code{@var{A} * @var{x} = @var{b}}
11563 3c6e8aaa9555 Grammarcheck m-files before 3.4 release. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	24 ## by means of the Preconditioned Conjugate Residuals iterative
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	25 ## method. The input arguments are
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	26 ##
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	27 ## @itemize
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	28 ## @item
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	29 ## @var{A} can be either a square (preferably sparse) matrix or a
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	30 ## function handle, inline function or string containing the name
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	31 ## of a function which computes @code{@var{A} * @var{x}}. In principle
994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	32 ## @var{A} should be symmetric and non-singular; if @code{pcr}
994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	33 ## finds @var{A} to be numerically singular, you will get a warning
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	34 ## message and the @var{flag} output parameter will be set.
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	35 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	36 ## @item
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	37 ## @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	38 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	39 ## @item
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	40 ## @var{tol} is the required relative tolerance for the residual error,
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	41 ## @code{@var{b} - @var{A} * @var{x}}. The iteration stops if
c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	42 ## @code{norm (@var{b} - @var{A} * @var{x}) <=
11563 3c6e8aaa9555 Grammarcheck m-files before 3.4 release. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	43 ## @var{tol} * norm (@var{b} - @var{A} * @var{x0})}.
3c6e8aaa9555 Grammarcheck m-files before 3.4 release. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	44 ## If @var{tol} is empty or is omitted, the function sets
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	45 ## @code{@var{tol} = 1e-6} by default.
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
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	48 ## @var{maxit} is the maximum allowable number of iterations; if
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	49 ## @code{[]} is supplied for @code{maxit}, or @code{pcr} has less
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	50 ## arguments, a default value equal to 20 is used.
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	51 ##
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	52 ## @item
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	53 ## @var{m} is the (left) preconditioning matrix, so that the iteration is
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	54 ## (theoretically) equivalent to solving by @code{pcr} @code{@var{P} *
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	55 ## @var{x} = @var{m} \ @var{b}}, with @code{@var{P} = @var{m} \ @var{A}}.
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	56 ## Note that a proper choice of the preconditioner may dramatically
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	57 ## improve the overall performance of the method. Instead of matrix
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	58 ## @var{m}, the user may pass a function which returns the results of
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	59 ## applying the inverse of @var{m} to a vector (usually this is the
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	60 ## preferred way of using the preconditioner). If @code{[]} is supplied
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	61 ## for @var{m}, or @var{m} is omitted, no preconditioning is applied.
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	62 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	63 ## @item
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	64 ## @var{x0} is the initial guess. If @var{x0} is empty or omitted, the
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	65 ## function sets @var{x0} to a zero vector by default.
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	66 ## @end itemize
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	67 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	68 ## The arguments which follow @var{x0} are treated as parameters, and
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	69 ## passed in a proper way to any of the functions (@var{A} or @var{m})
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	70 ## which are passed to @code{pcr}. See the examples below for further
1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	71 ## details. The output arguments are
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	72 ##
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	73 ## @itemize
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	74 ## @item
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	75 ## @var{x} is the computed approximation to the solution of
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	76 ## @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	77 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	78 ## @item
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	79 ## @var{flag} reports on the convergence. @code{@var{flag} = 0} means
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	80 ## the solution converged and the tolerance criterion given by @var{tol}
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	81 ## is satisfied. @code{@var{flag} = 1} means that the @var{maxit} limit
1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	82 ## for the iteration count was reached. @code{@var{flag} = 3} reports t
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	83 ## @code{pcr} breakdown, see [1] for details.
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	84 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	85 ## @item
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	86 ## @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	87 ## 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	88 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	89 ## @item
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	90 ## @var{iter} is the actual number of iterations performed.
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	91 ##
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	92 ## @item
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	93 ## @var{resvec} describes the convergence history of the method,
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	94 ## so that @code{@var{resvec} (i)} contains the Euclidean norms of the
7001 8b0cfeb06365 [project @ 2007-10-10 18:02:59 by jwe] jwe parents: 6498 diff changeset	95 ## residual after the (@var{i}-1)-th iteration, @code{@var{i} =
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	96 ## 1,2, @dots{}, @var{iter}+1}.
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	97 ## @end itemize
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	98 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	99 ## 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	100 ## sparsity of A)
c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	101 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	102 ## @example
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	103 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	104 ## n = 10;
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	105 ## A = sparse (diag (1:n));
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	106 ## b = rand (N, 1);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	107 ## @end group
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	108 ## @end example
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	109 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	110 ## @sc{Example 1:} Simplest use of @code{pcr}
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	111 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	112 ## @example
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	113 ## x = pcr (A, b)
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	114 ## @end example
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	115 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	116 ## @sc{Example 2:} @code{pcr} with a function which computes
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	117 ## @code{@var{A} * @var{x}}.
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	118 ##
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	119 ## @example
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	120 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	121 ## 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	122 ## y = [1:10]' .* x;
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	123 ## endfunction
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	124 ##
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	125 ## x = pcr ("apply_a", b)
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	126 ## @end group
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	127 ## @end example
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	128 ##
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	129 ## @sc{Example 3:} Preconditioned iteration, with full diagnostics. The
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	130 ## preconditioner (quite strange, because even the original matrix
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	131 ## @var{A} is 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	132 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	133 ## @example
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	134 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	135 ## 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	136 ## 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	137 ## y = x;
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	138 ## 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	139 ## endfunction
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	140 ##
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	141 ## [x, flag, relres, iter, resvec] = ...
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	142 ## pcr (A, b, [], [], "apply_m")
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	143 ## semilogy ([1:iter+1], resvec);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	144 ## @end group
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	145 ## @end example
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	146 ##
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	147 ## @sc{Example 4:} Finally, a preconditioner which depends on a
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	148 ## parameter @var{k}.
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	149 ##
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	150 ## @example
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	151 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	152 ## function y = apply_m (x, varargin)
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	153 ## k = varargin@{1@};
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	154 ## y = x;
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	155 ## 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	156 ## endfunction
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	157 ##
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	158 ## [x, flag, relres, iter, resvec] = ...
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	159 ## pcr (A, b, [], [], "apply_m"', [], 3)
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	160 ## @end group
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	161 ## @end example
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	162 ##
10791 3140cb7a05a1 Add spellchecker scripts for Octave and run spellcheck of documentation Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	163 ## References:
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	164 ##
19040 0850b5212619 doc: Add @nospell macro around proper names in documentation. Rik <rik@octave.org> parents: 17744 diff changeset	165 ## [1] @nospell{W. Hackbusch}, @cite{Iterative Solution of Large Sparse
0850b5212619 doc: Add @nospell macro around proper names in documentation. Rik <rik@octave.org> parents: 17744 diff changeset	166 ## Systems of Equations}, section 9.5.4; Springer, 1994
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	167 ##
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	168 ## @seealso{sparse, pcg}
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	169 ## @end deftypefn
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	170
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	171 ## Author: Piotr Krzyzanowski <piotr.krzyzanowski@mimuw.edu.pl>
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	172
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	173 function [x, flag, relres, iter, resvec] = pcr (A, b, tol, maxit, m, x0, varargin)
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	174
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	175 breakdown = false;
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	176
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	177 if (nargin < 6 \|\| isempty (x0))
376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	178 x = zeros (size (b));
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	179 else
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	180 x = x0;
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	181 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	182
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	183 if (nargin < 5)
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 7031 diff changeset	184 m = [];
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	185 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	186
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	187 if (nargin < 4 \|\| isempty (maxit))
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	188 maxit = 20;
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	189 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	190
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	191 maxit += 2;
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	192
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	193 if (nargin < 3 \|\| isempty (tol))
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	194 tol = 1e-6;
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	195 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	196
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	197 if (nargin < 2)
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	198 print_usage ();
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	199 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	200
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	201 ## init
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	202 if (isnumeric (A)) # is A a matrix?
994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	203 r = b - A*x;
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	204 else # then A should be a function!
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	205 r = b - feval (A, x, varargin{:});
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	206 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	207
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	208 if (isnumeric (m)) # is M a matrix?
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	209 if (isempty (m)) # if M is empty, use no precond
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	210 p = r;
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	211 else # otherwise, apply the precond
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 7031 diff changeset	212 p = m \ r;
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	213 endif
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	214 else # then M should be a function!
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 7031 diff changeset	215 p = feval (m, r, varargin{:});
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	216 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	217
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	218 iter = 2;
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	219
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	220 b_bot_old = 1;
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	221 q_old = p_old = s_old = zeros (size (x));
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	222
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	223 if (isnumeric (A)) # is A a matrix?
994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	224 q = A * p;
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	225 else # then A should be a function!
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	226 q = feval (A, p, varargin{:});
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	227 endif
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	228
c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	229 resvec(1) = abs (norm (r));
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	230
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	231 ## iteration
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	232 while (resvec(iter-1) > tol*resvec(1) && iter < maxit)
376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	233
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	234 if (isnumeric (m)) # is M a matrix?
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	235 if (isempty (m)) # if M is empty, use no precond
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	236 s = q;
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	237 else # otherwise, apply the precond
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	238 s = m \ q;
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	239 endif
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	240 else # then M should be a function!
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 7031 diff changeset	241 s = feval (m, q, varargin{:});
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	242 endif
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	243 b_top = r' * s;
376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	244 b_bot = q' * s;
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	245
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	246 if (b_bot == 0.0)
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	247 breakdown = true;
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	248 break;
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	249 endif
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	250 lambda = b_top / b_bot;
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	251
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	252 x += lambda*p;
376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	253 r -= lambda*q;
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	254
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	255 if (isnumeric (A)) # is A a matrix?
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	256 t = A*s;
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	257 else # then A should be a function!
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	258 t = feval (A, s, varargin{:});
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	259 endif
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	260
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	261 alpha0 = (t'*s) / b_bot;
376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	262 alpha1 = (t'*s_old) / b_bot_old;
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	263
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	264 p_temp = p;
376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	265 q_temp = q;
376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	266
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	267 p = s - alpha0p - alpha1p_old;
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	268 q = t - alpha0q - alpha1q_old;
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	269
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	270 s_old = s;
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	271 p_old = p_temp;
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	272 q_old = q_temp;
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	273 b_bot_old = b_bot;
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	274
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	275 resvec(iter) = abs (norm (r));
376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	276 iter++;
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	277 endwhile
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	278
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	279 flag = 0;
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	280 relres = resvec(iter-1) ./ resvec(1);
376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	281 iter -= 2;
376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	282 if (iter >= maxit-2)
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	283 flag = 1;
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	284 if (nargout < 2)
6498 2c85044aa63f [project @ 2007-04-05 17:59:47 by jwe] jwe parents: 5838 diff changeset	285 warning ("pcr: maximum number of iterations (%d) reached\n", iter);
2c85044aa63f [project @ 2007-04-05 17:59:47 by jwe] jwe parents: 5838 diff changeset	286 warning ("the initial residual norm was reduced %g times.\n", 1.0/relres);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	287 endif
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	288 elseif (nargout < 2 && ! breakdown)
6498 2c85044aa63f [project @ 2007-04-05 17:59:47 by jwe] jwe parents: 5838 diff changeset	289 fprintf (stderr, "pcr: converged in %d iterations. \n", iter);
2c85044aa63f [project @ 2007-04-05 17:59:47 by jwe] jwe parents: 5838 diff changeset	290 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	291 1.0 / relres);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	292 endif
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	293
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	294 if (breakdown)
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	295 flag = 3;
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	296 if (nargout < 2)
7001 8b0cfeb06365 [project @ 2007-10-10 18:02:59 by jwe] jwe parents: 6498 diff changeset	297 warning ("pcr: breakdown occurred:\n");
6498 2c85044aa63f [project @ 2007-04-05 17:59:47 by jwe] jwe parents: 5838 diff changeset	298 warning ("system matrix singular or preconditioner indefinite?\n");
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	299 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	300 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	301
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	302 endfunction
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	303
14237 11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	304
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	305 %!demo
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	306 %! ## Simplest usage of PCR (see also 'help pcr')
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	307 %!
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	308 %! N = 20;
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	309 %! A = diag (linspace (-3.1,3,N)); b = rand (N,1);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	310 %! y = A \ b; # y is the true solution
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	311 %! x = pcr (A,b);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	312 %! printf ("The solution relative error is %g\n", norm (x-y) / norm (y));
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	313 %!
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	314 %! ## You shouldn't be afraid if PCR issues some warning messages in this
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	315 %! ## 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: 14868 diff changeset	316 %! ## of PCR 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	317
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	318 %!demo
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	319 %! ## Full output from PCR
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	320 %! ## We use this output to plot the convergence history
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	321 %!
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	322 %! N = 20;
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	323 %! A = diag (linspace (-3.1,30,N)); b = rand (N,1);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	324 %! X = A \ b; # X is the true solution
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	325 %! [x, flag, relres, iter, resvec] = pcr (A,b);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	326 %! printf ("The solution relative error is %g\n", norm (x-X) / norm (X));
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	327 %! clf;
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	328 %! title ("Convergence history");
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	329 %! xlabel ("Iteration"); ylabel ("log(\|\|b-Ax\|\|/\|\|b\|\|)");
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	330 %! semilogy ([0:iter], resvec/resvec(1), "o-g;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	331
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	332 %!demo
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	333 %! ## Full output from PCR
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	334 %! ## We use indefinite matrix based on the Hilbert matrix, with one
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	335 %! ## strongly negative eigenvalue
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	336 %! ## Hilbert matrix is extremely ill conditioned, so is ours,
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	337 %! ## and that's why PCR WILL have problems
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	338 %!
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	339 %! N = 10;
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	340 %! A = hilb (N); A(1,1) = -A(1,1); b = rand (N,1);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	341 %! X = A \ b; # X is the true solution
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	342 %! printf ("Condition number of A is %g\n", cond (A));
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	343 %! [x, flag, relres, iter, resvec] = pcr (A,b,[],200);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	344 %! if (flag == 3)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	345 %! printf ("PCR breakdown. System matrix is [close to] singular\n");
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	346 %! end
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	347 %! clf;
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	348 %! title ("Convergence history");
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	349 %! xlabel ("Iteration"); ylabel ("log(\|\|b-Ax\|\|)");
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	350 %! semilogy ([0:iter], resvec, "o-g;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	351
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	352 %!demo
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	353 %! ## Full output from PCR
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	354 %! ## We use an indefinite matrix based on the 1-D Laplacian matrix for A,
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	355 %! ## and here we have cond(A) = O(N^2)
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	356 %! ## 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: 14868 diff changeset	357 %! ## a very simple and not powerful Jacobi preconditioner,
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	358 %! ## which is the diagonal of A.
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	359 %!
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	360 %! ## Note that we use here indefinite preconditioners!
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	361 %!
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	362 %! N = 100;
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	363 %! A = zeros (N,N);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	364 %! for i=1:N-1 # form 1-D Laplacian matrix
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	365 %! A(i:i+1,i:i+1) = [2 -1; -1 2];
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	366 %! endfor
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	367 %! A = [A, zeros(size(A)); zeros(size(A)), -A];
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	368 %! b = rand (2*N,1);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	369 %! X = A \ b; # X is the true solution
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	370 %! maxit = 80;
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	371 %! printf ("System condition number is %g\n", cond (A));
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	372 %! ## No preconditioner: the convergence is very slow!
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	373 %!
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	374 %! [x, flag, relres, iter, resvec] = pcr (A,b,[],maxit);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	375 %! clf;
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	376 %! title ("Convergence history");
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	377 %! xlabel ("Iteration"); ylabel ("log(\|\|b-Ax\|\|)");
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	378 %! semilogy ([0:iter], resvec, "o-g;NO preconditioning: absolute residual;");
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	379 %!
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	380 %! pause (1);
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	381 %! ## Test Jacobi preconditioner: it will not help much!!!
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	382 %!
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	383 %! M = diag (diag (A)); # Jacobi preconditioner
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	384 %! [x, flag, relres, iter, resvec] = pcr (A,b,[],maxit,M);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	385 %! hold on;
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	386 %! semilogy ([0:iter],resvec,"o-r;JACOBI preconditioner: absolute residual;");
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	387 %!
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	388 %! pause (1);
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	389 %! ## Test nonoverlapping block Jacobi preconditioner: this one should give
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	390 %! ## some convergence speedup!
14237 11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	391 %!
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	392 %! M = zeros (N,N); k = 4;
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	393 %! for i=1:k:N # get k x k diagonal blocks of A
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	394 %! M(i:i+k-1,i:i+k-1) = A(i:i+k-1,i:i+k-1);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	395 %! endfor
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	396 %! M = [M, zeros(size (M)); zeros(size(M)), -M];
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	397 %! [x, flag, relres, iter, resvec] = pcr (A,b,[],maxit,M);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	398 %! semilogy ([0:iter], resvec, "o-b;BLOCK JACOBI preconditioner: absolute residual;");
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14335 diff changeset	399 %! 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	400
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	401 %!test
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	402 %! ## solve small indefinite diagonal system
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	403 %!
14237 11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	404 %! 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	405 %! A = diag (linspace (-10.1,10,N)); 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	406 %! 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	407 %! [x, flag] = pcr (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	408 %! assert (norm (x-X) / norm (X) < 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	409 %! 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	410
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	411 %!test
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	412 %! ## solve tridiagonal system, do not converge in default 20 iterations
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	413 %! ## should perform max allowable default number of iterations
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	414 %!
14237 11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	415 %! 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	416 %! 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	417 %! 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	418 %! 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	419 %! endfor
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	420 %! 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	421 %! 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	422 %! [x, flag, relres, iter, resvec] = pcr (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	423 %! assert (flag, 1);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	424 %! assert (relres > 0.6);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	425 %! assert (iter, 20);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	426
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	427 %!test
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	428 %! ## solve tridiagonal system with "perfect" preconditioner
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	429 %! ## converges in one iteration
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	430 %!
14237 11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	431 %! 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	432 %! 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	433 %! 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	434 %! 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	435 %! endfor
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	436 %! 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	437 %! 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	438 %! [x, flag, relres, iter] = pcr (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	439 %! assert (norm (x-X) / norm(X) < 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	440 %! assert (relres < 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	441 %! 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	442 %! 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	443

Mercurial > octave-antonio

annotate scripts/sparse/pcr.m @ 19697:4197fc428c7d