octave-antonio: scripts/linear-algebra/rref.m annotate

annotate scripts/linear-algebra/rref.m @ 20160:03b9d17a2d95 stable

doc: Update more docstrings to have one sentence summary as first line. Reviewed io, java, linear-algebra, prefs, and set script directories. * scripts/io/beep.m, scripts/io/dlmwrite.m, scripts/io/importdata.m, scripts/io/strread.m, scripts/io/textread.m, scripts/java/javaArray.m, scripts/java/java_get.m, scripts/java/java_set.m, scripts/java/javaaddpath.m, scripts/java/javachk.m, scripts/java/javaclasspath.m, scripts/java/javamem.m, scripts/java/javarmpath.m, scripts/linear-algebra/bandwidth.m, scripts/linear-algebra/commutation_matrix.m, scripts/linear-algebra/cond.m, scripts/linear-algebra/condest.m, scripts/linear-algebra/cross.m, scripts/linear-algebra/duplication_matrix.m, scripts/linear-algebra/expm.m, scripts/linear-algebra/housh.m, scripts/linear-algebra/isdefinite.m, scripts/linear-algebra/ishermitian.m, scripts/linear-algebra/issymmetric.m, scripts/linear-algebra/istril.m, scripts/linear-algebra/istriu.m, scripts/linear-algebra/krylov.m, scripts/linear-algebra/logm.m, scripts/linear-algebra/normest.m, scripts/linear-algebra/null.m, scripts/linear-algebra/onenormest.m, scripts/linear-algebra/orth.m, scripts/linear-algebra/qzhess.m, scripts/linear-algebra/rank.m, scripts/linear-algebra/rref.m, scripts/linear-algebra/vech.m, scripts/path/matlabroot.m, scripts/prefs/addpref.m, scripts/prefs/getpref.m, scripts/prefs/ispref.m, scripts/prefs/rmpref.m, scripts/prefs/setpref.m, scripts/set/powerset.m, scripts/set/setdiff.m: Update more docstrings to have one sentence summary as first line.

author	Rik <rik@octave.org>
date	Sun, 03 May 2015 15:36:23 -0700
parents	9fc020886ae9
children

rev	line source
19697 4197fc428c7d maint: Update copyright notices for 2015. John W. Eaton <jwe@octave.org> parents: 17744 diff changeset	1 ## Copyright (C) 2000-2015 Paul Kienzle
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	2 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	3 ## This file is part of Octave.
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	4 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	5 ## Octave is free software; you can redistribute it and/or modify it
1fe78adb91bc [project @ 2006-05-22 06:25:14 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: 5827 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: 5827 diff changeset	8 ## your option) any later version.
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	9 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	10 ## Octave is distributed in the hope that it will be useful, but
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	13 ## General Public License for more details.
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	14 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 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: 5827 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: 5827 diff changeset	17 ## <http://www.gnu.org/licenses/>.
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	18
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	19 ## -- texinfo --
12584 7ef7e20057fa Improve documentation strings in Linear Algebra chapter. Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	20 ## @deftypefn {Function File} {} rref (@var{A})
7ef7e20057fa Improve documentation strings in Linear Algebra chapter. Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	21 ## @deftypefnx {Function File} {} rref (@var{A}, @var{tol})
7ef7e20057fa Improve documentation strings in Linear Algebra chapter. Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	22 ## @deftypefnx {Function File} {[@var{r}, @var{k}] =} rref (@dots{})
20160 03b9d17a2d95 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	23 ## Return the reduced row echelon form of @var{A}.
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	24 ##
20160 03b9d17a2d95 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	25 ## @var{tol} defaults to
03b9d17a2d95 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	26 ## @code{eps * max (size (@var{A})) * norm (@var{A}, inf)}.
03b9d17a2d95 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	27 ##
03b9d17a2d95 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	28 ## The optional return argument @var{k} contains the vector of
03b9d17a2d95 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	29 ## "bound variables", which are those columns on which elimination has been
03b9d17a2d95 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	30 ## performed.
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	31 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	32 ## @end deftypefn
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	33
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	34 ## Author: Paul Kienzle <pkienzle@users.sf.net>
11469 c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	35 ## (based on an anonymous source from the public domain)
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	36
11469 c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	37 function [A, k] = rref (A, tol)
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	38
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	39 if (nargin < 1 \|\| nargin > 2)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	40 print_usage ();
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	41 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	42
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	43 if (ndims (A) > 2)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	44 error ("rref: expecting matrix argument");
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	45 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	46
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	47 [rows, cols] = size (A);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	48
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	49 if (nargin < 2)
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7017 diff changeset	50 if (isa (A, "single"))
11469 c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	51 tol = eps ("single") * max (rows, cols) * norm (A, inf ("single"));
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7017 diff changeset	52 else
11469 c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	53 tol = eps * max (rows, cols) * norm (A, inf);
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7017 diff changeset	54 endif
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	55 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	56
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	57 used = zeros (1, cols);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	58 r = 1;
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	59 for c = 1:cols
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	60 ## Find the pivot row
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	61 [m, pivot] = max (abs (A(r:rows,c)));
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	62 pivot = r + pivot - 1;
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	63
11469 c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	64 if (m <= tol)
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	65 ## Skip column c, making sure the approximately zero terms are
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	66 ## actually zero.
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	67 A(r:rows, c) = zeros (rows-r+1, 1);
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	68 else
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	69 ## keep track of bound variables
19833 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19697 diff changeset	70 used(1, c) = 1;
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	71
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	72 ## Swap current row and pivot row
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	73 A([pivot, r], c:cols) = A([r, pivot], c:cols);
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	74
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	75 ## Normalize pivot row
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	76 A(r, c:cols) = A(r, c:cols) / A(r, c);
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	77
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	78 ## Eliminate the current column
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	79 ridx = [1:r-1, r+1:rows];
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	80 A(ridx, c:cols) = A(ridx, c:cols) - A(ridx, c) * A(r, c:cols);
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	81
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	82 ## Check if done
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	83 if (r++ == rows)
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9245 diff changeset	84 break;
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	85 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	86 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	87 endfor
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	88 k = find (used);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	89
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	90 endfunction
13048 c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref Roman Belov <romblv@gmail.com> parents: 12584 diff changeset	91
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	92
13048 c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref Roman Belov <romblv@gmail.com> parents: 12584 diff changeset	93 %!test
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref Roman Belov <romblv@gmail.com> parents: 12584 diff changeset	94 %! a = [1];
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	95 %! [r k] = rref (a);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	96 %! assert (r, [1], 2e-8);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	97 %! assert (k, [1], 2e-8);
13048 c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref Roman Belov <romblv@gmail.com> parents: 12584 diff changeset	98
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref Roman Belov <romblv@gmail.com> parents: 12584 diff changeset	99 %!test
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref Roman Belov <romblv@gmail.com> parents: 12584 diff changeset	100 %! a = [1 3; 4 5];
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	101 %! [r k] = rref (a);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	102 %! assert (rank (a), rank (r), 2e-8);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	103 %! assert (r, eye (2), 2e-8);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	104 %! assert (k == [1, 2] \|\| k == [2, 1]);
13048 c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref Roman Belov <romblv@gmail.com> parents: 12584 diff changeset	105
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref Roman Belov <romblv@gmail.com> parents: 12584 diff changeset	106 %!test
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref Roman Belov <romblv@gmail.com> parents: 12584 diff changeset	107 %! a = [1 3; 4 5; 7 9];
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	108 %! [r k] = rref (a);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	109 %! assert (rank (a), rank (r), 2e-8);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	110 %! assert (r, eye(3)(:,1:2), 2e-8);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	111 %! assert (k, [1 2], 2e-8);
13048 c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref Roman Belov <romblv@gmail.com> parents: 12584 diff changeset	112
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref Roman Belov <romblv@gmail.com> parents: 12584 diff changeset	113 %!test
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref Roman Belov <romblv@gmail.com> parents: 12584 diff changeset	114 %! a = [1 2 3; 2 4 6; 7 2 0];
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	115 %! [r k] = rref (a);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	116 %! assert (rank (a), rank (r), 2e-8);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	117 %! assert (r, [1 0 (3-7/2); 0 1 (7/4); 0 0 0], 2e-8);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	118 %! assert (k, [1 2], 2e-8);
13048 c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref Roman Belov <romblv@gmail.com> parents: 12584 diff changeset	119
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref Roman Belov <romblv@gmail.com> parents: 12584 diff changeset	120 %!test
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref Roman Belov <romblv@gmail.com> parents: 12584 diff changeset	121 %! a = [1 2 1; 2 4 2.01; 2 4 2.1];
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref Roman Belov <romblv@gmail.com> parents: 12584 diff changeset	122 %! tol = 0.02;
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	123 %! [r k] = rref (a, tol);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	124 %! assert (rank (a, tol), rank (r, tol), 2e-8);
13048 c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref Roman Belov <romblv@gmail.com> parents: 12584 diff changeset	125 %! tol = 0.2;
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	126 %! [r k] = rref (a, tol);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	127 %! assert (rank (a, tol), rank (r, tol), 2e-8);
13048 c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref Roman Belov <romblv@gmail.com> parents: 12584 diff changeset	128
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	129 %!error rref ();
13048 c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref Roman Belov <romblv@gmail.com> parents: 12584 diff changeset	130

Mercurial > octave-antonio

annotate scripts/linear-algebra/rref.m @ 20160:03b9d17a2d95 stable