octave: libinterp/corefcn/gsvd.cc annotate

annotate libinterp/corefcn/gsvd.cc @ 22237:867b177af1fe

gsvd: replace deprecated gripe_wrong_type_arg with err_wrong_type_arg.

author	Carnë Draug <carandraug@octave.org>
date	Tue, 09 Aug 2016 21:34:53 +0100
parents	065a44375723
children	dfb49a84c0e4

rev	line source
22235 63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	1 // Copyright (C) 1996, 1997 John W. Eaton
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	2 // Copyright (C) 2006, 2010 Pascal Dupuis <Pascal.Dupuis@uclouvain.be>
22236 065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	3 // Copyright (C) 2016 Barbara Lócsi
22235 63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	4 //
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	5 // This program is free software; you can redistribute it and/or modify it under
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	6 // the terms of the GNU General Public License as published by the Free Software
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	7 // Foundation; either version 3 of the License, or (at your option) any later
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	8 // version.
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	9 //
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	10 // This program is distributed in the hope that it will be useful, but WITHOUT
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	11 // ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	12 // FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	13 // details.
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	14 //
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	15 // You should have received a copy of the GNU General Public License along with
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	16 // this program; if not, see <http://www.gnu.org/licenses/>.
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	17
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	18 #ifdef HAVE_CONFIG_H
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	19 # include <config.h>
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	20 #endif
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	21
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	22 #include "defun.h"
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	23 #include "error.h"
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	24 #include "gripes.h"
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	25 #include "pr-output.h"
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	26 #include "utils.h"
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	27 #include "ovl.h"
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	28
22236 065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	29 #include "gsvd.h"
065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	30
065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	31 template <typename T>
065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	32 static typename gsvd<T>::Type
065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	33 gsvd_type (int nargout)
065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	34 {
065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	35 return ((nargout == 0 \|\| nargout == 1)
065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	36 ? gsvd<T>::Type::sigma_only
065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	37 : (nargout > 5) ? gsvd<T>::Type::std : gsvd<T>::Type::economy);
065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	38 }
065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	39
22235 63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	40
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	41 DEFUN (gsvd, args, nargout,
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	42 doc: /* -- texinfo --
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	43 @deftypefn {Loadable Function} {@var{s} =} gsvd (@var{a}, @var{b})
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	44 @deftypefnx {Loadable Function} {[@var{u}, @var{v}, @var{c}, @var{s}, @var{x} [, @var{r}]] =} gsvd (@var{a}, @var{b})
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	45 @cindex generalised singular value decomposition
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	46 Compute the generalised singular value decomposition of (@var{a}, @var{b}):
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	47 @iftex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	48 @tex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	49 $$
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	50 U^H A X = [I 0; 0 C] [0 R]
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	51 V^H B X = [0 S; 0 0] [0 R]
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	52 CC + SS = eye(columns(A))
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	53 I and 0 are padding matrices of suitable size
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	54 R is upper triangular
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	55 $$
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	56 @end tex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	57 @end iftex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	58 @ifinfo
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	59
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	60 @example
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	61 u' * a * x = [I 0; 0 c] * [0 r]
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	62 v' * b * x = [0 s; 0 0] * [0 r]
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	63 c * c + s * s = eye(columns(a))
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	64 I and 0 are padding matrices of suitable size
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	65 r is upper triangular
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	66 @end example
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	67 @end ifinfo
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	68
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	69 The function @code{gsvd} normally returns the vector of generalised singular
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	70 values
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	71 @iftex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	72 @tex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	73 diag(C)./diag(S).
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	74 @end tex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	75 @end iftex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	76 @ifinfo
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	77 diag(r)./diag(s).
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	78 @end ifinfo
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	79 If asked for five return values, it computes
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	80 @iftex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	81 @tex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	82 $U$, $V$, and $X$.
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	83 @end tex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	84 @end iftex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	85 @ifinfo
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	86 U, V, and X.
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	87 @end ifinfo
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	88 With a sixth output argument, it also returns
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	89 @iftex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	90 @tex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	91 R,
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	92 @end tex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	93 @end iftex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	94 @ifinfo
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	95 r,
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	96 @end ifinfo
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	97 The common upper triangular right term. Other authors, like S. Van Huffel,
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	98 define this transformation as the simulatenous diagonalisation of the
22236 065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	99 input matrices, this can be achieved by multiplying
22235 63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	100 @iftex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	101 @tex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	102 X
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	103 @end tex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	104 @end iftex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	105 @ifinfo
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	106 x
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	107 @end ifinfo
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	108 by the inverse of
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	109 @iftex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	110 @tex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	111 [I 0; 0 R].
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	112 @end tex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	113 @end iftex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	114 @ifinfo
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	115 [I 0; 0 r].
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	116 @end ifinfo
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	117
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	118 For example,
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	119
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	120 @example
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	121 gsvd (hilb (3), [1 2 3; 3 2 1])
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	122 @end example
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	123
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	124 @noindent
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	125 returns
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	126
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	127 @example
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	128 ans =
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	129
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	130 0.1055705
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	131 0.0031759
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	132 @end example
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	133
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	134 @noindent
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	135 and
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	136
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	137 @example
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	138 [u, v, c, s, x, r] = gsvd (hilb (3), [1 2 3; 3 2 1])
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	139 @end example
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	140
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	141 @noindent
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	142 returns
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	143
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	144 @example
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	145 u =
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	146
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	147 -0.965609 0.240893 0.097825
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	148 -0.241402 -0.690927 -0.681429
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	149 -0.096561 -0.681609 0.725317
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	150
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	151 v =
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	152
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	153 -0.41974 0.90765
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	154 -0.90765 -0.41974
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	155
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	156 c =
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	157
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	158 0.10499 0.00000
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	159 0.00000 0.00318
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	160
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	161 s =
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	162 0.99447 0.00000
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	163 0.00000 0.99999
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	164 x =
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	165
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	166 0.408248 0.902199 0.139179
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	167 -0.816497 0.429063 -0.386314
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	168 0.408248 -0.044073 -0.911806
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	169
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	170 r =
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	171 -0.14093 -1.24345 0.43737
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	172 0.00000 -3.90043 2.57818
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	173 0.00000 0.00000 -2.52599
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	174
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	175 @end example
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	176
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	177 The code is a wrapper to the corresponding Lapack dggsvd and zggsvd routines.
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	178
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	179 @end deftypefn */)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	180 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	181 octave_value_list retval;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	182
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	183 int nargin = args.length ();
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	184
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	185 if (nargin < 2 \|\| nargin > 2 \|\| (nargout > 1 && (nargout < 5 \|\| nargout > 6)))
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	186 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	187 print_usage ();
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	188 return retval;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	189 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	190
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	191 octave_value argA = args(0), argB = args(1);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	192
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	193 octave_idx_type nr = argA.rows ();
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	194 octave_idx_type nc = argA.columns ();
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	195
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	196 // octave_idx_type nn = argB.rows ();
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	197 octave_idx_type np = argB.columns ();
22236 065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	198
22235 63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	199 if (nr == 0 \|\| nc == 0)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	200 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	201 if (nargout == 5)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	202 retval = ovl (identity_matrix (nc, nc), identity_matrix (nc, nc),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	203 Matrix (nr, nc), identity_matrix (nr, nr),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	204 identity_matrix (nr, nr));
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	205 else if (nargout == 6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	206 retval = ovl (identity_matrix (nc, nc), identity_matrix (nc, nc),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	207 Matrix (nr, nc), identity_matrix (nr, nr),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	208 identity_matrix (nr, nr),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	209 identity_matrix (nr, nr));
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	210 else
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	211 retval = ovl (Matrix (0, 1));
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	212 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	213 else
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	214 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	215 if ((nc != np))
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	216 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	217 print_usage ();
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	218 return retval;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	219 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	220
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	221 if (argA.is_real_type () && argB.is_real_type ())
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	222 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	223 Matrix tmpA = argA.matrix_value ();
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	224 Matrix tmpB = argB.matrix_value ();
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	225
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	226 if (! error_state)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	227 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	228 if (tmpA.any_element_is_inf_or_nan ())
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	229 {
22236 065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	230 error ("gsvd: cannot take gsvd of matrix containing Inf or NaN values");
22235 63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	231 return retval;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	232 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	233
22236 065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	234 if (tmpB.any_element_is_inf_or_nan ())
065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	235 {
065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	236 error ("gsvd: cannot take gsvd of matrix containing Inf or NaN values");
065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	237 return retval;
065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	238 }
065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	239
065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	240 gsvd<Matrix> result (tmpA, tmpB, gsvd_type<Matrix> (nargout));
22235 63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	241
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	242 // DiagMatrix sigma = result.singular_values ();
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	243
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	244 if (nargout == 0 \|\| nargout == 1)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	245 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	246 DiagMatrix sigA = result.singular_values_A ();
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	247 DiagMatrix sigB = result.singular_values_B ();
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	248 for (int i = sigA.rows() - 1; i >=0; i--)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	249 sigA.dgxelem(i) /= sigB.dgxelem(i);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	250 retval = ovl (sigA.diag());
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	251 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	252 else
22236 065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	253 {
22235 63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	254 if (nargout > 5)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	255 retval = ovl (result.left_singular_matrix_A (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	256 result.left_singular_matrix_B (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	257 result.singular_values_A (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	258 result.singular_values_B (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	259 result.right_singular_matrix (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	260 result.R_matrix ());
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	261 else
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	262 retval = ovl (result.left_singular_matrix_A (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	263 result.left_singular_matrix_B (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	264 result.singular_values_A (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	265 result.singular_values_B (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	266 result.right_singular_matrix ());
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	267 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	268 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	269 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	270 else if (argA.is_complex_type () \|\| argB.is_complex_type ())
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	271 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	272 ComplexMatrix ctmpA = argA.complex_matrix_value ();
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	273 ComplexMatrix ctmpB = argB.complex_matrix_value ();
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	274
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	275 if (! error_state)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	276 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	277 if (ctmpA.any_element_is_inf_or_nan ())
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	278 {
22236 065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	279 error ("gsvd: cannot take gsvd of matrix containing Inf or NaN values");
22235 63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	280 return retval;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	281 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	282 if (ctmpB.any_element_is_inf_or_nan ())
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	283 {
22236 065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	284 error ("gsvd: cannot take gsvd of matrix containing Inf or NaN values");
22235 63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	285 return retval;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	286 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	287
22236 065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	288 gsvd<ComplexMatrix> result (ctmpA, ctmpB, gsvd_type<ComplexMatrix> (nargout));
22235 63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	289
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	290 // DiagMatrix sigma = result.singular_values ();
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	291
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	292 if (nargout == 0 \|\| nargout == 1)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	293 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	294 DiagMatrix sigA = result.singular_values_A ();
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	295 DiagMatrix sigB = result.singular_values_B ();
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	296 for (int i = sigA.rows() - 1; i >=0; i--)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	297 sigA.dgxelem(i) /= sigB.dgxelem(i);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	298 retval = ovl (sigA.diag());
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	299 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	300 else
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	301 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	302 if (nargout > 5)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	303 retval = ovl (result.left_singular_matrix_A (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	304 result.left_singular_matrix_B (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	305 result.singular_values_A (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	306 result.singular_values_B (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	307 result.right_singular_matrix (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	308 result.R_matrix ());
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	309 else
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	310 retval = ovl (result.left_singular_matrix_A (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	311 result.left_singular_matrix_B (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	312 result.singular_values_A (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	313 result.singular_values_B (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	314 result.right_singular_matrix ());
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	315 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	316 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	317 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	318 else
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	319 {
22237 867b177af1fe gsvd: replace deprecated gripe_wrong_type_arg with err_wrong_type_arg. Carnë Draug <carandraug@octave.org> parents: 22236 diff changeset	320 err_wrong_type_arg ("gsvd", argA);
867b177af1fe gsvd: replace deprecated gripe_wrong_type_arg with err_wrong_type_arg. Carnë Draug <carandraug@octave.org> parents: 22236 diff changeset	321 err_wrong_type_arg ("gsvd", argB);
22235 63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	322 return retval;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	323 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	324 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	325
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	326 return retval;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	327 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	328
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	329 /*
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	330 %# a few tests for gsvd.m
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	331 %!shared A, A0, B, B0, U, V, C, S, X, R, D1, D2
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	332
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	333 %! A0=randn(5, 3); B0=diag([1 2 4]);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	334 %! A = A0; B = B0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	335 %! # disp('Full rank, 5x3 by 3x3 matrices');
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	336 %! # disp([rank(A) rank(B) rank([A' B'])]);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	337 %! [U, V, C, S, X, R] = gsvd(A, B);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	338 %! D1 = zeros(5, 3); D1(1:3, 1:3) = C;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	339 %! D2 = S;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	340 %!assert(norm(diag(C).^2+diag(S).^2 - ones(3, 1)) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	341 %!assert(norm((U'AX)-D1*R) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	342 %!assert(norm((V'BX)-D2*R) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	343
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	344 %! # disp('A 5x3 full rank, B 3x3 rank deficient');
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	345 %! B(2, 2) = 0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	346 %! [U, V, C, S, X, R] = gsvd(A, B);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	347 %! D1 = zeros(5, 3); D1(1, 1) = 1; D1(2:3, 2:3) = C;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	348 %! D2 = [zeros(2, 1) S; zeros(1, 3)];
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	349 %!assert(norm(diag(C).^2+diag(S).^2 - ones(2, 1)) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	350 %!assert(norm((U'AX)-D1*R) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	351 %!assert(norm((V'BX)-D2*R) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	352
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	353 %! # disp('A 5x3 rank deficient, B 3x3 full rank');
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	354 %! B = B0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	355 %! A(:, 3) = 2*A(:, 1) - A(:, 2);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	356 %! [U, V, C, S, X, R] = gsvd(A, B);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	357 %! D1 = zeros(5, 3); D1(1:3, 1:3) = C;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	358 %! D2 = S;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	359 %!assert(norm(diag(C).^2+diag(S).^2 - ones(3, 1)) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	360 %!assert(norm((U'AX)-D1*R) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	361 %!assert(norm((V'BX)-D2*R) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	362
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	363 %! # disp("A 5x3, B 3x3, [A' B'] rank deficient");
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	364 %! B(:, 3) = 2*B(:, 1) - B(:, 2);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	365 %! [U, V, C, S, X, R] = gsvd(A, B);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	366 %! D1 = zeros(5, 2); D1(1:2, 1:2) = C;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	367 %! D2 = [S; zeros(1, 2)];
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	368 %!assert(norm(diag(C).^2+diag(S).^2 - ones(2, 1)) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	369 %!assert(norm((U'AX)-D1*[zeros(2, 1) R]) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	370 %!assert(norm((V'BX)-D2*[zeros(2, 1) R]) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	371
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	372 %! # now, A is 3x5
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	373 %! A = A0.'; B0=diag([1 2 4 8 16]); B = B0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	374 %! # disp('Full rank, 3x5 by 5x5 matrices');
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	375 %! # disp([rank(A) rank(B) rank([A' B'])]);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	376
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	377 %! [U, V, C, S, X, R] = gsvd(A, B);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	378 %! D1 = [C zeros(3,2)];
22236 065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	379 %! D2 = [S zeros(3,2); zeros(2, 3) eye(2)];
22235 63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	380 %!assert(norm(diag(C).^2+diag(S).^2 - ones(3, 1)) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	381 %!assert(norm((U'AX)-D1*R) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	382 %!assert(norm((V'BX)-D2*R) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	383
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	384 %! # disp('A 5x3 full rank, B 5x5 rank deficient');
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	385 %! B(2, 2) = 0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	386 %! # disp([rank(A) rank(B) rank([A' B'])]);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	387
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	388 %! [U, V, C, S, X, R] = gsvd(A, B);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	389 %! D1 = zeros(3, 5); D1(1, 1) = 1; D1(2:3, 2:3) = C;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	390 %! D2 = zeros(5, 5); D2(1:2, 2:3) = S; D2(3:4, 4:5) = eye(2);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	391 %!assert(norm(diag(C).^2+diag(S).^2 - ones(2, 1)) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	392 %!assert(norm((U'AX)-D1*R) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	393 %!assert(norm((V'BX)-D2*R) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	394
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	395 %! # disp('A 3x5 rank deficient, B 5x5 full rank');
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	396 %! B = B0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	397 %! A(3, :) = 2*A(1, :) - A(2, :);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	398 %! # disp([rank(A) rank(B) rank([A' B'])]);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	399 %! [U, V, C, S, X, R] = gsvd(A, B);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	400 %! D1 = zeros(3, 5); D1(1:3, 1:3) = C;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	401 %! D2 = zeros(5, 5); D2(1:3, 1:3) = S; D2(4:5, 4:5) = eye(2);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	402 %!assert(norm(diag(C).^2+diag(S).^2 - ones(3, 1)) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	403 %!assert(norm((U'AX)-D1*R) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	404 %!assert(norm((V'BX)-D2*R) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	405
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	406 %! # disp("A 5x3, B 5x5, [A' B'] rank deficient");
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	407 %! A = A0.'; B = B0.';
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	408 %! A(:, 3) = 2*A(:, 1) - A(:, 2);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	409 %! B(:, 3) = 2*B(:, 1) - B(:, 2);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	410 %! # disp([rank(A) rank(B) rank([A' B'])]);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	411 %! [U, V, C, S, X, R]=gsvd(A, B);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	412 %! D1 = zeros(3, 4); D1(1:3, 1:3) = C;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	413 %! D2 = eye(4); D2(1:3, 1:3) = S; D2(5,:) = 0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	414 %!assert(norm(diag(C).^2+diag(S).^2 - ones(3, 1)) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	415 %!assert(norm((U'AX)-D1*[zeros(4, 1) R]) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	416 %!assert(norm((V'BX)-D2*[zeros(4, 1) R]) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	417
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	418 %! A0 = A0 +j * randn(5, 3); B0 = B0=diag([1 2 4]) + j*diag([4 -2 -1]);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	419 %! A = A0; B = B0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	420 %! # disp('Complex: Full rank, 5x3 by 3x3 matrices');
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	421 %! # disp([rank(A) rank(B) rank([A' B'])]);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	422 %! [U, V, C, S, X, R] = gsvd(A, B);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	423 %! D1 = zeros(5, 3); D1(1:3, 1:3) = C;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	424 %! D2 = S;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	425 %!assert(norm(diag(C).^2+diag(S).^2 - ones(3, 1)) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	426 %!assert(norm((U'AX)-D1*R) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	427 %!assert(norm((V'BX)-D2*R) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	428
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	429 %! # disp('Complex: A 5x3 full rank, B 3x3 rank deficient');
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	430 %! B(2, 2) = 0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	431 %! # disp([rank(A) rank(B) rank([A' B'])]);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	432
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	433 %! [U, V, C, S, X, R] = gsvd(A, B);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	434 %! D1 = zeros(5, 3); D1(1, 1) = 1; D1(2:3, 2:3) = C;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	435 %! D2 = [zeros(2, 1) S; zeros(1, 3)];
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	436 %!assert(norm(diag(C).^2+diag(S).^2 - ones(2, 1)) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	437 %!assert(norm((U'AX)-D1*R) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	438 %!assert(norm((V'BX)-D2*R) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	439
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	440 %! # disp('Complex: A 5x3 rank deficient, B 3x3 full rank');
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	441 %! B = B0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	442 %! A(:, 3) = 2*A(:, 1) - A(:, 2);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	443 %! # disp([rank(A) rank(B) rank([A' B'])]);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	444 %! [U, V, C, S, X, R] = gsvd(A, B);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	445 %! D1 = zeros(5, 3); D1(1:3, 1:3) = C;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	446 %! D2 = S;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	447 %!assert(norm(diag(C).^2+diag(S).^2 - ones(3, 1)) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	448 %!assert(norm((U'AX)-D1*R) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	449 %!assert(norm((V'BX)-D2*R) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	450
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	451 %! # disp("Complex: A 5x3, B 3x3, [A' B'] rank deficient");
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	452 %! B(:, 3) = 2*B(:, 1) - B(:, 2);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	453 %! # disp([rank(A) rank(B) rank([A' B'])]);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	454 %! [U, V, C, S, X, R] = gsvd(A, B);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	455 %! D1 = zeros(5, 2); D1(1:2, 1:2) = C;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	456 %! D2 = [S; zeros(1, 2)];
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	457 %!assert(norm(diag(C).^2+diag(S).^2 - ones(2, 1)) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	458 %!assert(norm((U'AX)-D1*[zeros(2, 1) R]) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	459 %!assert(norm((V'BX)-D2*[zeros(2, 1) R]) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	460
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	461 %! # now, A is 3x5
22236 065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	462 %! A = A0.'; B0=diag([1 2 4 8 16])+j*diag([-5 4 -3 2 -1]);
22235 63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	463 %! B = B0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	464 %! # disp('Complex: Full rank, 3x5 by 5x5 matrices');
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	465 %! # disp([rank(A) rank(B) rank([A' B'])]);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	466 %! [U, V, C, S, X, R] = gsvd(A, B);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	467 %! D1 = [C zeros(3,2)];
22236 065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	468 %! D2 = [S zeros(3,2); zeros(2, 3) eye(2)];
22235 63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	469 %!assert(norm(diag(C).^2+diag(S).^2 - ones(3, 1)) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	470 %!assert(norm((U'AX)-D1*R) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	471 %!assert(norm((V'BX)-D2*R) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	472
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	473 %! # disp('Complex: A 5x3 full rank, B 5x5 rank deficient');
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	474 %! B(2, 2) = 0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	475 %! # disp([rank(A) rank(B) rank([A' B'])]);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	476 %! [U, V, C, S, X, R] = gsvd(A, B);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	477 %! D1 = zeros(3, 5); D1(1, 1) = 1; D1(2:3, 2:3) = C;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	478 %! D2 = zeros(5,5); D2(1:2, 2:3) = S; D2(3:4, 4:5) = eye(2);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	479 %!assert(norm(diag(C).^2+diag(S).^2 - ones(2, 1)) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	480 %!assert(norm((U'AX)-D1*R) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	481 %!assert(norm((V'BX)-D2*R) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	482
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	483 %! # disp('Complex: A 3x5 rank deficient, B 5x5 full rank');
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	484 %! B = B0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	485 %! A(3, :) = 2*A(1, :) - A(2, :);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	486 %! # disp([rank(A) rank(B) rank([A' B'])]);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	487 %! [U, V, C, S, X, R] = gsvd(A, B);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	488 %! D1 = zeros(3, 5); D1(1:3, 1:3) = C;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	489 %! D2 = zeros(5,5); D2(1:3, 1:3) = S; D2(4:5, 4:5) = eye(2);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	490 %!assert(norm(diag(C).^2+diag(S).^2 - ones(3, 1)) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	491 %!assert(norm((U'AX)-D1*R) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	492 %!assert(norm((V'BX)-D2*R) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	493
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	494 %! # disp("Complex: A 5x3, B 5x5, [A' B'] rank deficient");
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	495 %! A = A0.'; B = B0.';
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	496 %! A(:, 3) = 2*A(:, 1) - A(:, 2);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	497 %! B(:, 3) = 2*B(:, 1) - B(:, 2);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	498 %! # disp([rank(A) rank(B) rank([A' B'])]);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	499 %! [U, V, C, S, X, R]=gsvd(A, B);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	500 %! D1 = zeros(3, 4); D1(1:3, 1:3) = C;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	501 %! D2 = eye(4); D2(1:3, 1:3) = S; D2(5,:) = 0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	502 %!assert(norm(diag(C).^2+diag(S).^2 - ones(3, 1)) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	503 %!assert(norm((U'AX)-D1*[zeros(4, 1) R]) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	504 %!assert(norm((V'BX)-D2*[zeros(4, 1) R]) <= 1e-6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	505
22236 065a44375723 gsvd: reduce code duplication with templates. Barbara Locsi <locsi.barbara@gmail.com> parents: 22235 diff changeset	506 */

Mercurial > octave

annotate libinterp/corefcn/gsvd.cc @ 22237:867b177af1fe