octave: libinterp/corefcn/gsvd.cc annotate

annotate libinterp/corefcn/gsvd.cc @ 22235:63b41167ef1e

gsvd: new function imported from Octave-Forge linear-algebra package. * libinterp/corefcn/gsvd.cc: New function to the interpreter. Imported from the linear-algebra package. * CmplxGSVD.cc, CmplxGSVD.h, dbleGSVD.cc, dbleGSVD.h: new classes imported from the linear-algebra package to compute gsvd of Matrix and ComplexMatrix. * liboctave/operators/mx-defs.h, liboctave/operators/mx-ext.h: use new classes. * libinterp/corefcn/module.mk, liboctave/numeric/module.mk: Add to the * scripts/help/__unimplemented__.m: Remove "gsvd" from list. * doc/interpreter/linalg.txi: Add to manual. build system. * NEWS: Add function to list of new functions for 4.2.

author	Barbara Locsi <locsi.barbara@gmail.com>
date	Thu, 04 Aug 2016 07:50:31 +0200
parents
children	065a44375723

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>
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	3 //
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	4 // 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	5 // 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	6 // 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	7 // version.
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	8 //
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	9 // 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	10 // 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	11 // 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	12 // details.
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	13 //
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	14 // 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	15 // 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	16
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	17 #ifdef HAVE_CONFIG_H
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	18 # include <config.h>
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	19 #endif
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	20
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	21 #include "defun.h"
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	22 #include "error.h"
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	23 #include "gripes.h"
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	24 #include "pr-output.h"
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	25 #include "utils.h"
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	26 #include "ovl.h"
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	27
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	28 #include "CmplxGSVD.h"
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	29 #include "dbleGSVD.h"
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	30
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	31 DEFUN (gsvd, args, nargout,
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	32 doc: /* -- texinfo --
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	33 @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	34 @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	35 @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	36 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	37 @iftex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	38 @tex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	39 $$
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	40 U^H A X = [I 0; 0 C] [0 R]
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	41 V^H B X = [0 S; 0 0] [0 R]
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	42 CC + SS = eye(columns(A))
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	43 I and 0 are padding matrices of suitable size
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	44 R is upper triangular
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	45 $$
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	46 @end tex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	47 @end iftex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	48 @ifinfo
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 @example
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	51 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	52 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	53 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	54 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	55 r is upper triangular
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	56 @end example
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	57 @end ifinfo
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	58
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	59 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	60 values
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	61 @iftex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	62 @tex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	63 diag(C)./diag(S).
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	64 @end tex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	65 @end iftex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	66 @ifinfo
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	67 diag(r)./diag(s).
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	68 @end ifinfo
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	69 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	70 @iftex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	71 @tex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	72 $U$, $V$, and $X$.
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	73 @end tex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	74 @end iftex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	75 @ifinfo
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	76 U, V, and X.
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	77 @end ifinfo
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	78 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	79 @iftex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	80 @tex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	81 R,
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	82 @end tex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	83 @end iftex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	84 @ifinfo
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	85 r,
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	86 @end ifinfo
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	87 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	88 define this transformation as the simulatenous diagonalisation of the
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	89 input matrices, this can be achieved by multiplying
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	90 @iftex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	91 @tex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	92 X
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	93 @end tex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	94 @end iftex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	95 @ifinfo
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	96 x
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	97 @end ifinfo
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	98 by the inverse of
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	99 @iftex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	100 @tex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	101 [I 0; 0 R].
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	102 @end tex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	103 @end iftex
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	104 @ifinfo
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	105 [I 0; 0 r].
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	106 @end ifinfo
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	107
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	108 For example,
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	109
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	110 @example
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	111 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	112 @end example
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	113
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	114 @noindent
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	115 returns
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	116
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	117 @example
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	118 ans =
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 0.1055705
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	121 0.0031759
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 and
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 [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	129 @end example
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	130
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	131 @noindent
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	132 returns
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 @example
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	135 u =
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 -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	138 -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	139 -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	140
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	141 v =
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	142
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	143 -0.41974 0.90765
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	144 -0.90765 -0.41974
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	145
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	146 c =
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	147
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	148 0.10499 0.00000
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	149 0.00000 0.00318
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 s =
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	152 0.99447 0.00000
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	153 0.00000 0.99999
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	154 x =
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 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	157 -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	158 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	159
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	160 r =
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	161 -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	162 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	163 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	164
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	165 @end example
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	166
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	167 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	168
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	169 @end deftypefn */)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	170 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	171 octave_value_list retval;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	172
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	173 int nargin = args.length ();
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 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	176 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	177 print_usage ();
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	178 return retval;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	179 }
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 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	182
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	183 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	184 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	185
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	186 // 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	187 octave_idx_type np = argB.columns ();
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	188
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	189 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	190 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	191 if (nargout == 5)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	192 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	193 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	194 identity_matrix (nr, nr));
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	195 else if (nargout == 6)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	196 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	197 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	198 identity_matrix (nr, nr),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	199 identity_matrix (nr, nr));
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	200 else
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	201 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	202 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	203 else
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	204 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	205 if ((nc != np))
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	206 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	207 print_usage ();
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	208 return retval;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	209 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	210
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	211 GSVD::type type = ((nargout == 0 \|\| nargout == 1)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	212 ? GSVD::sigma_only
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	213 : (nargout > 5) ? GSVD::std : GSVD::economy );
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 (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	216 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	217 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	218 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	219
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	220 if (! error_state)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	221 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	222 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	223 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	224 error ("gsvd: cannot take GSVD of matrix containing Inf or NaN values");
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	225 return retval;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	226 }
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 (tmpB.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 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	230 error ("gsvd: cannot take GSVD of matrix containing Inf or NaN values");
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
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	234 GSVD result (tmpA, tmpB, type);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	235
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	236 // 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	237
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	238 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	239 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	240 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	241 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	242 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	243 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	244 retval = ovl (sigA.diag());
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 else
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	247 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	248 if (nargout > 5)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	249 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	250 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	251 result.singular_values_A (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	252 result.singular_values_B (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	253 result.right_singular_matrix (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	254 result.R_matrix ());
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	255 else
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	256 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	257 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	258 result.singular_values_A (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	259 result.singular_values_B (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	260 result.right_singular_matrix ());
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	261 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	262 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	263 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	264 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	265 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	266 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	267 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	268
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	269 if (! error_state)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	270 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	271 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	272 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	273 error ("gsvd: cannot take GSVD of matrix containing Inf or NaN values");
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	274 return retval;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	275 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	276 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	277 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	278 error ("gsvd: cannot take GSVD of matrix containing Inf or NaN values");
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	279 return retval;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	280 }
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 ComplexGSVD result (ctmpA, ctmpB, type);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	283
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	284 // 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	285
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	286 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	287 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	288 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	289 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	290 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	291 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	292 retval = ovl (sigA.diag());
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 else
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	295 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	296 if (nargout > 5)
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	297 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	298 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	299 result.singular_values_A (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	300 result.singular_values_B (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	301 result.right_singular_matrix (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	302 result.R_matrix ());
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	303 else
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	304 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	305 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	306 result.singular_values_A (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	307 result.singular_values_B (),
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	308 result.right_singular_matrix ());
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	309 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	310 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	311 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	312 else
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	313 {
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	314 gripe_wrong_type_arg ("gsvd", argA);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	315 gripe_wrong_type_arg ("gsvd", argB);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	316 return retval;
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 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	319
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	320 return retval;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	321 }
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	322
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 %# 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	325 %!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	326
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	327 %! 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	328 %! A = A0; B = B0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	329 %! # 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	330 %! # 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	331 %! [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	332 %! 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	333 %! D2 = S;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	334 %!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	335 %!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	336 %!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	337
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	338 %! # 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	339 %! B(2, 2) = 0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	340 %! [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	341 %! 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	342 %! 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	343 %!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	344 %!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	345 %!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	346
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	347 %! # 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	348 %! B = B0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	349 %! 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	350 %! [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	351 %! 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	352 %! D2 = S;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	353 %!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	354 %!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	355 %!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	356
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	357 %! # 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	358 %! 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	359 %! [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	360 %! 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	361 %! 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	362 %!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	363 %!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	364 %!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	365
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	366 %! # now, A is 3x5
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	367 %! 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	368 %! # 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	369 %! # 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	370
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	371 %! [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	372 %! D1 = [C zeros(3,2)];
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	373 %! D2 = [S zeros(3,2); zeros(2, 3) eye(2)];
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	374 %!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	375 %!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	376 %!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	377
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	378 %! # 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	379 %! B(2, 2) = 0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	380 %! # 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	381
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	382 %! [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	383 %! 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	384 %! 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	385 %!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	386 %!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	387 %!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	388
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	389 %! # 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	390 %! B = B0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	391 %! 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	392 %! # 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	393 %! [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	394 %! 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	395 %! 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	396 %!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	397 %!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	398 %!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	399
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	400 %! # 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	401 %! A = A0.'; B = B0.';
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	402 %! 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	403 %! 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	404 %! # 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	405 %! [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	406 %! 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	407 %! 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	408 %!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	409 %!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	410 %!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	411
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	412 %! 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	413 %! A = A0; B = B0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	414 %! # 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	415 %! # 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	416 %! [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	417 %! 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	418 %! D2 = S;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	419 %!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	420 %!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	421 %!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	422
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	423 %! # 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	424 %! B(2, 2) = 0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	425 %! # 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	426
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	427 %! [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	428 %! 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	429 %! 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	430 %!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	431 %!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	432 %!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	433
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	434 %! # 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	435 %! B = B0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	436 %! 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	437 %! # 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	438 %! [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	439 %! 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	440 %! D2 = S;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	441 %!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	442 %!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	443 %!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	444
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	445 %! # 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	446 %! 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	447 %! # 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	448 %! [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	449 %! 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	450 %! 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	451 %!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	452 %!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	453 %!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	454
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	455 %! # now, A is 3x5
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	456 %! A = A0.'; B0=diag([1 2 4 8 16])+j*diag([-5 4 -3 2 -1]);
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	457 %! B = B0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	458 %! # 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	459 %! # 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	460 %! [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	461 %! D1 = [C zeros(3,2)];
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	462 %! D2 = [S zeros(3,2); zeros(2, 3) eye(2)];
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	463 %!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	464 %!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	465 %!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	466
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	467 %! # 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	468 %! B(2, 2) = 0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	469 %! # 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	470 %! [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	471 %! 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	472 %! 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	473 %!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	474 %!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	475 %!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	476
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	477 %! # 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	478 %! B = B0;
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	479 %! 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	480 %! # 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	481 %! [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	482 %! 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	483 %! 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	484 %!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	485 %!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	486 %!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	487
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	488 %! # 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	489 %! A = A0.'; B = B0.';
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	490 %! 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	491 %! 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	492 %! # 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	493 %! [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	494 %! 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	495 %! 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	496 %!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	497 %!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	498 %!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	499
63b41167ef1e gsvd: new function imported from Octave-Forge linear-algebra package. Barbara Locsi <locsi.barbara@gmail.com> parents: diff changeset	500 */

Mercurial > octave

annotate libinterp/corefcn/gsvd.cc @ 22235:63b41167ef1e