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

annotate scripts/linear-algebra/rank.m @ 20170:af2b7695f1c4 draft default tip @

gallery.m: clean and vectorize part of qmult. * scripts/special-matrix/gallery.m: make qmult() follow Octave guidelines, vectorize last for loop in qmult().

author	Antonio Pino Robles <data.script93@gmail.com>
date	Thu, 28 May 2015 18:32:47 +0200
parents	4197fc428c7d
children	03b9d17a2d95

rev	line source
19697 4197fc428c7d maint: Update copyright notices for 2015. John W. Eaton <jwe@octave.org> parents: 17744 diff changeset	1 ## Copyright (C) 1993-2015 John W. Eaton
2313 5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	2 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	3 ## This file is part of Octave.
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	4 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	5 ## Octave is free software; you can redistribute it and/or modify it
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 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: 6046 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: 6046 diff changeset	8 ## your option) any later version.
2313 5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	9 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	10 ## Octave is distributed in the hope that it will be useful, but
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	13 ## General Public License for more details.
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	14 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 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: 6046 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: 6046 diff changeset	17 ## <http://www.gnu.org/licenses/>.
245 16a24e76d6e0 [project @ 1993-12-03 02:00:15 by jwe] jwe parents: 4 diff changeset	18
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 2847 diff changeset	19 ## -- texinfo --
12584 7ef7e20057fa Improve documentation strings in Linear Algebra chapter. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	20 ## @deftypefn {Function File} {} rank (@var{A})
7ef7e20057fa Improve documentation strings in Linear Algebra chapter. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	21 ## @deftypefnx {Function File} {} rank (@var{A}, @var{tol})
16952 3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	22 ## Compute the rank of matrix @var{A}, using the singular value decomposition.
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	23 ##
11470 eb9e0b597d61 Use common names for variables in documentation and code for a few more m-script files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	24 ## The rank is taken to be the number of singular values of @var{A} that
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 2847 diff changeset	25 ## are greater than the specified tolerance @var{tol}. If the second
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 2847 diff changeset	26 ## argument is omitted, it is taken to be
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3372 diff changeset	27 ##
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 2847 diff changeset	28 ## @example
11470 eb9e0b597d61 Use common names for variables in documentation and code for a few more m-script files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	29 ## tol = max (size (@var{A})) * sigma(1) * eps;
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 2847 diff changeset	30 ## @end example
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3372 diff changeset	31 ##
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 2847 diff changeset	32 ## @noindent
3600 c11d138d654a [project @ 2000-02-24 03:55:32 by jwe] jwe parents: 3426 diff changeset	33 ## where @code{eps} is machine precision and @code{sigma(1)} is the largest
11470 eb9e0b597d61 Use common names for variables in documentation and code for a few more m-script files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	34 ## singular value of @var{A}.
16952 3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	35 ##
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	36 ## The rank of a matrix is the number of linearly independent rows or
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	37 ## columns and determines how many particular solutions exist to a system
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	38 ## of equations. Use @code{null} for finding the remaining homogenous
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	39 ## solutions.
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	40 ##
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	41 ## Example:
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	42 ##
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	43 ## @example
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	44 ## @group
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	45 ## x = [1 2 3
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	46 ## 4 5 6
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	47 ## 7 8 9];
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	48 ## rank (x)
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	49 ## @result{} 2
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	50 ## @end group
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	51 ## @end example
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	52 ##
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	53 ## @noindent
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	54 ## The number of linearly independent rows is only 2 because the final row
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	55 ## is a linear combination of -1row1 + 2row2.
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	56 ##
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	57 ## @seealso{null, sprank, svd}
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 2847 diff changeset	58 ## @end deftypefn
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	59
2314 949ab8eba8bc [project @ 1996-07-12 03:58:02 by jwe] jwe parents: 2313 diff changeset	60 ## Author: jwe
949ab8eba8bc [project @ 1996-07-12 03:58:02 by jwe] jwe parents: 2313 diff changeset	61
2311 2b5788792cad [project @ 1996-07-11 20:18:38 by jwe] jwe parents: 2303 diff changeset	62 function retval = rank (A, tol)
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	63
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	64 if (nargin == 1)
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	65 sigma = svd (A);
4706 2c73119a576a [project @ 2004-01-22 04:36:54 by jwe] jwe parents: 3600 diff changeset	66 if (isempty (sigma))
2c73119a576a [project @ 2004-01-22 04:36:54 by jwe] jwe parents: 3600 diff changeset	67 tolerance = 0;
2c73119a576a [project @ 2004-01-22 04:36:54 by jwe] jwe parents: 3600 diff changeset	68 else
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7017 diff changeset	69 if (isa (A, "single"))
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9245 diff changeset	70 tolerance = max (size (A)) * sigma (1) * eps ("single");
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7017 diff changeset	71 else
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9245 diff changeset	72 tolerance = max (size (A)) * sigma (1) * eps;
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7017 diff changeset	73 endif
4706 2c73119a576a [project @ 2004-01-22 04:36:54 by jwe] jwe parents: 3600 diff changeset	74 endif
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	75 elseif (nargin == 2)
262 5f18dd3a9b61 [project @ 1993-12-29 08:55:02 by jwe] jwe parents: 245 diff changeset	76 sigma = svd (A);
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	77 tolerance = tol;
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	78 else
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5307 diff changeset	79 print_usage ();
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	80 endif
4706 2c73119a576a [project @ 2004-01-22 04:36:54 by jwe] jwe parents: 3600 diff changeset	81
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	82 retval = sum (sigma > tolerance);
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	83
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	84 endfunction
12813 8c4605b4d0c8 codesprint: Wrote 6 tests for rank.m David Wells <drwells@vt.edu> parents: 12584 diff changeset	85
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	86
12813 8c4605b4d0c8 codesprint: Wrote 6 tests for rank.m David Wells <drwells@vt.edu> parents: 12584 diff changeset	87 %!test
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 12813 diff changeset	88 %! A = [1 2 3 4 5 6 7;
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 12813 diff changeset	89 %! 4 5 6 7 8 9 12;
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 12813 diff changeset	90 %! 1 2 3.1 4 5 6 7;
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 12813 diff changeset	91 %! 2 3 4 5 6 7 8;
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 12813 diff changeset	92 %! 3 4 5 6 7 8 9;
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 12813 diff changeset	93 %! 4 5 6 7 8 9 10;
12813 8c4605b4d0c8 codesprint: Wrote 6 tests for rank.m David Wells <drwells@vt.edu> parents: 12584 diff changeset	94 %! 5 6 7 8 9 10 11];
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	95 %! assert (rank (A), 4);
12813 8c4605b4d0c8 codesprint: Wrote 6 tests for rank.m David Wells <drwells@vt.edu> parents: 12584 diff changeset	96
8c4605b4d0c8 codesprint: Wrote 6 tests for rank.m David Wells <drwells@vt.edu> parents: 12584 diff changeset	97 %!test
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 12813 diff changeset	98 %! A = [1 2 3 4 5 6 7;
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 12813 diff changeset	99 %! 4 5 6 7 8 9 12;
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 12813 diff changeset	100 %! 1 2 3.0000001 4 5 6 7;
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 12813 diff changeset	101 %! 4 5 6 7 8 9 12.00001;
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 12813 diff changeset	102 %! 3 4 5 6 7 8 9;
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 12813 diff changeset	103 %! 4 5 6 7 8 9 10;
12813 8c4605b4d0c8 codesprint: Wrote 6 tests for rank.m David Wells <drwells@vt.edu> parents: 12584 diff changeset	104 %! 5 6 7 8 9 10 11];
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	105 %! assert (rank (A), 4);
12813 8c4605b4d0c8 codesprint: Wrote 6 tests for rank.m David Wells <drwells@vt.edu> parents: 12584 diff changeset	106
8c4605b4d0c8 codesprint: Wrote 6 tests for rank.m David Wells <drwells@vt.edu> parents: 12584 diff changeset	107 %!test
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 12813 diff changeset	108 %! A = [1 2 3 4 5 6 7;
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 12813 diff changeset	109 %! 4 5 6 7 8 9 12;
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 12813 diff changeset	110 %! 1 2 3 4 5 6 7;
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 12813 diff changeset	111 %! 4 5 6 7 8 9 12.00001;
12813 8c4605b4d0c8 codesprint: Wrote 6 tests for rank.m David Wells <drwells@vt.edu> parents: 12584 diff changeset	112 %! 3 4 5 6 7 8 9;
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 12813 diff changeset	113 %! 4 5 6 7 8 9 10;
12813 8c4605b4d0c8 codesprint: Wrote 6 tests for rank.m David Wells <drwells@vt.edu> parents: 12584 diff changeset	114 %! 5 6 7 8 9 10 11];
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	115 %! assert (rank (A), 3);
12813 8c4605b4d0c8 codesprint: Wrote 6 tests for rank.m David Wells <drwells@vt.edu> parents: 12584 diff changeset	116
8c4605b4d0c8 codesprint: Wrote 6 tests for rank.m David Wells <drwells@vt.edu> parents: 12584 diff changeset	117 %!test
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 12813 diff changeset	118 %! A = [1 2 3 4 5 6 7;
12813 8c4605b4d0c8 codesprint: Wrote 6 tests for rank.m David Wells <drwells@vt.edu> parents: 12584 diff changeset	119 %! 4 5 6 7 8 9 12;
8c4605b4d0c8 codesprint: Wrote 6 tests for rank.m David Wells <drwells@vt.edu> parents: 12584 diff changeset	120 %! 1 2 3 4 5 6 7;
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 12813 diff changeset	121 %! 4 5 6 7 8 9 12;
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 12813 diff changeset	122 %! 3 4 5 6 7 8 9;
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 12813 diff changeset	123 %! 4 5 6 7 8 9 10;
12813 8c4605b4d0c8 codesprint: Wrote 6 tests for rank.m David Wells <drwells@vt.edu> parents: 12584 diff changeset	124 %! 5 6 7 8 9 10 11];
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	125 %! assert (rank (A), 3);
12813 8c4605b4d0c8 codesprint: Wrote 6 tests for rank.m David Wells <drwells@vt.edu> parents: 12584 diff changeset	126
8c4605b4d0c8 codesprint: Wrote 6 tests for rank.m David Wells <drwells@vt.edu> parents: 12584 diff changeset	127 %!test
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	128 %! A = eye (100);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	129 %! assert (rank (A), 100);
12813 8c4605b4d0c8 codesprint: Wrote 6 tests for rank.m David Wells <drwells@vt.edu> parents: 12584 diff changeset	130
16952 3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	131 %!assert (rank ([]), 0)
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	132 %!assert (rank ([1:9]), 1)
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	133 %!assert (rank ([1:9]'), 1)
3c20fb2aa419 doc: Add example to rank docstring. Rik <rik@octave.org> parents: 14363 diff changeset	134
12813 8c4605b4d0c8 codesprint: Wrote 6 tests for rank.m David Wells <drwells@vt.edu> parents: 12584 diff changeset	135 %!test
8c4605b4d0c8 codesprint: Wrote 6 tests for rank.m David Wells <drwells@vt.edu> parents: 12584 diff changeset	136 %! A = [1, 2, 3; 1, 2.001, 3; 1, 2, 3.0000001];
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	137 %! assert (rank (A), 3);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	138 %! assert (rank (A,0.0009), 1);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	139 %! assert (rank (A,0.0006), 2);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	140 %! assert (rank (A,0.00000002), 3);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	141

Mercurial > octave-antonio

annotate scripts/linear-algebra/rank.m @ 20170:af2b7695f1c4 draft default tip @