Mercurial > octave-nkf

annotate scripts/sparse/eigs.m @ 19631:db92e7e28e1f

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
strip trailing whitespace from most source files * NEWS, doc/interpreter/contributors.in, doc/interpreter/func.txi, doc/interpreter/genpropdoc.m, doc/interpreter/octave_logo.eps, doc/interpreter/plot.txi, doc/interpreter/stmt.txi, examples/data/Makefile.am, libinterp/corefcn/data.cc, libinterp/corefcn/debug.cc, libinterp/corefcn/error.cc, libinterp/corefcn/file-io.cc, libinterp/corefcn/gl-render.cc, libinterp/corefcn/graphics.cc, libinterp/corefcn/graphics.in.h, libinterp/corefcn/load-path.cc, libinterp/corefcn/pr-output.cc, libinterp/corefcn/pt-jit.cc, libinterp/corefcn/strfind.cc, libinterp/corefcn/toplev.cc, libinterp/corefcn/toplev.h, libinterp/corefcn/urlwrite.cc, libinterp/corefcn/variables.cc, libinterp/octave-value/ov-classdef.cc, libinterp/octave-value/ov-classdef.h, libinterp/octave.cc, libinterp/parse-tree/lex.h, libinterp/parse-tree/oct-parse.in.yy, libinterp/parse-tree/pt-classdef.h, liboctave/system/file-ops.cc, liboctave/system/oct-env.cc, m4/acinclude.m4, scripts/deprecated/finite.m, scripts/deprecated/fmod.m, scripts/deprecated/fnmatch.m, scripts/deprecated/luinc.m, scripts/deprecated/octave_tmp_file_name.m, scripts/deprecated/syl.m, scripts/deprecated/usage.m, scripts/general/inputParser.m, scripts/general/interp1.m, scripts/general/interp2.m, scripts/general/interp3.m, scripts/general/isequal.m, scripts/general/private/__isequal__.m, scripts/geometry/voronoi.m, scripts/image/image.m, scripts/image/imshow.m, scripts/image/ind2rgb.m, scripts/linear-algebra/bandwidth.m, scripts/linear-algebra/isbanded.m, scripts/miscellaneous/bzip2.m, scripts/miscellaneous/cast.m, scripts/miscellaneous/copyfile.m, scripts/miscellaneous/delete.m, scripts/miscellaneous/fullfile.m, scripts/miscellaneous/getappdata.m, scripts/miscellaneous/gunzip.m, scripts/miscellaneous/isappdata.m, scripts/miscellaneous/ls.m, scripts/miscellaneous/mex.m, scripts/miscellaneous/movefile.m, scripts/miscellaneous/orderfields.m, scripts/miscellaneous/recycle.m, scripts/miscellaneous/rmappdata.m, scripts/miscellaneous/setfield.m, scripts/miscellaneous/symvar.m, scripts/miscellaneous/tar.m, scripts/miscellaneous/tmpnam.m, scripts/miscellaneous/unpack.m, scripts/miscellaneous/ver.m, scripts/miscellaneous/what.m, scripts/miscellaneous/xor.m, scripts/miscellaneous/zip.m, scripts/optimization/fminbnd.m, scripts/optimization/sqp.m, scripts/path/private/getsavepath.m, scripts/path/savepath.m, scripts/pkg/pkg.m, scripts/pkg/private/installed_packages.m, scripts/plot/draw/plotyy.m, scripts/plot/draw/polar.m, scripts/plot/draw/private/__quiver__.m, scripts/plot/draw/private/__scatter__.m, scripts/plot/draw/private/__stem__.m, scripts/plot/draw/surface.m, scripts/plot/draw/surfnorm.m, scripts/plot/util/copyobj.m, scripts/plot/util/hgload.m, scripts/plot/util/hgsave.m, scripts/plot/util/isprop.m, scripts/plot/util/linkprop.m, scripts/plot/util/private/__go_draw_axes__.m, scripts/set/setdiff.m, scripts/set/union.m, scripts/signal/periodogram.m, scripts/sparse/eigs.m, scripts/sparse/ilu.m, scripts/sparse/qmr.m, scripts/sparse/sprand.m, scripts/sparse/sprandn.m, scripts/specfun/beta.m, scripts/specfun/ellipke.m, scripts/specfun/isprime.m, scripts/statistics/base/lscov.m, scripts/testfun/__run_test_suite__.m, scripts/testfun/test.m: Strip trailing whitespace.
author John W. Eaton <jwe@octave.org>
date Tue, 20 Jan 2015 10:29:54 -0500
parents 0e1f5a750d00
children 5d0663bff506
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
17744
d63878346099 maint: Update copyright notices for release.
John W. Eaton <jwe@octave.org>
parents: 17338
diff changeset
1 ## Copyright (C) 2005-2013 David Bateman
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
2 ##
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
3 ## This file is part of Octave.
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
4 ##
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
5 ## Octave is free software; you can redistribute it and/or modify it
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
6 ## under the terms of the GNU General Public License as published by
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
7 ## the Free Software Foundation; either version 3 of the License, or (at
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
8 ## your option) any later version.
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
9 ##
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
10 ## Octave is distributed in the hope that it will be useful, but
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
13 ## General Public License for more details.
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
14 ##
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
15 ## You should have received a copy of the GNU General Public License
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
16 ## along with Octave; see the file COPYING. If not, see
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
17 ## <http://www.gnu.org/licenses/>.
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
18
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
19 ## -*- texinfo -*-
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
20 ## @deftypefn {Function File} {@var{d} =} eigs (@var{A})
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
21 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{A}, @var{k})
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
22 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{A}, @var{k}, @var{sigma})
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
23 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{A}, @var{k}, @var{sigma}, @var{opts})
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
24 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{A}, @var{B})
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
25 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{A}, @var{B}, @var{k})
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
26 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{A}, @var{B}, @var{k}, @var{sigma})
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
27 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{A}, @var{B}, @var{k}, @var{sigma}, @var{opts})
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
28 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{af}, @var{n})
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
29 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{af}, @var{n}, @var{B})
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
30 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{af}, @var{n}, @var{k})
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
31 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{af}, @var{n}, @var{B}, @var{k})
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
32 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{af}, @var{n}, @var{k}, @var{sigma})
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
33 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{af}, @var{n}, @var{B}, @var{k}, @var{sigma})
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
34 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{af}, @var{n}, @var{k}, @var{sigma}, @var{opts})
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
35 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{af}, @var{n}, @var{B}, @var{k}, @var{sigma}, @var{opts})
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
36 ## @deftypefnx {Function File} {[@var{V}, @var{d}] =} eigs (@var{A}, @dots{})
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
37 ## @deftypefnx {Function File} {[@var{V}, @var{d}] =} eigs (@var{af}, @var{n}, @dots{})
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
38 ## @deftypefnx {Function File} {[@var{V}, @var{d}, @var{flag}] =} eigs (@var{A}, @dots{})
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
39 ## @deftypefnx {Function File} {[@var{V}, @var{d}, @var{flag}] =} eigs (@var{af}, @var{n}, @dots{})
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
40 ## Calculate a limited number of eigenvalues and eigenvectors of @var{A},
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
41 ## based on a selection criteria. The number of eigenvalues and eigenvectors to
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
42 ## calculate is given by @var{k} and defaults to 6.
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
43 ##
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
44 ## By default, @code{eigs} solve the equation
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
45 ## @tex
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
46 ## $A \nu = \lambda \nu$,
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
47 ## @end tex
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
48 ## @ifinfo
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
49 ## @code{A * v = lambda * v},
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
50 ## @end ifinfo
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
51 ## where
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
52 ## @tex
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
53 ## $\lambda$ is a scalar representing one of the eigenvalues, and $\nu$
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
54 ## @end tex
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
55 ## @ifinfo
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
56 ## @code{lambda} is a scalar representing one of the eigenvalues, and @code{v}
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
57 ## @end ifinfo
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
58 ## is the corresponding eigenvector. If given the positive definite matrix
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
59 ## @var{B} then @code{eigs} solves the general eigenvalue equation
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
60 ## @tex
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
61 ## $A \nu = \lambda B \nu$.
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
62 ## @end tex
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
63 ## @ifinfo
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
64 ## @code{A * v = lambda * B * v}.
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
65 ## @end ifinfo
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
66 ##
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
67 ## The argument @var{sigma} determines which eigenvalues are returned.
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
68 ## @var{sigma} can be either a scalar or a string. When @var{sigma} is a
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
69 ## scalar, the @var{k} eigenvalues closest to @var{sigma} are returned. If
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
70 ## @var{sigma} is a string, it must have one of the following values.
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
71 ##
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
72 ## @table @asis
17281
bc924baa2c4e doc: Add new @qcode macro for code samples which are quoted.
Rik <rik@octave.org>
parents: 17220
diff changeset
73 ## @item @qcode{"lm"}
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
74 ## Largest Magnitude (default).
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
75 ##
17281
bc924baa2c4e doc: Add new @qcode macro for code samples which are quoted.
Rik <rik@octave.org>
parents: 17220
diff changeset
76 ## @item @qcode{"sm"}
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
77 ## Smallest Magnitude.
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
78 ##
17281
bc924baa2c4e doc: Add new @qcode macro for code samples which are quoted.
Rik <rik@octave.org>
parents: 17220
diff changeset
79 ## @item @qcode{"la"}
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
80 ## Largest Algebraic (valid only for real symmetric problems).
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
81 ##
17281
bc924baa2c4e doc: Add new @qcode macro for code samples which are quoted.
Rik <rik@octave.org>
parents: 17220
diff changeset
82 ## @item @qcode{"sa"}
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
83 ## Smallest Algebraic (valid only for real symmetric problems).
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
84 ##
17281
bc924baa2c4e doc: Add new @qcode macro for code samples which are quoted.
Rik <rik@octave.org>
parents: 17220
diff changeset
85 ## @item @qcode{"be"}
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
86 ## Both Ends, with one more from the high-end if @var{k} is odd (valid only for
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
87 ## real symmetric problems).
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
88 ##
17281
bc924baa2c4e doc: Add new @qcode macro for code samples which are quoted.
Rik <rik@octave.org>
parents: 17220
diff changeset
89 ## @item @qcode{"lr"}
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
90 ## Largest Real part (valid only for complex or unsymmetric problems).
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
91 ##
17281
bc924baa2c4e doc: Add new @qcode macro for code samples which are quoted.
Rik <rik@octave.org>
parents: 17220
diff changeset
92 ## @item @qcode{"sr"}
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
93 ## Smallest Real part (valid only for complex or unsymmetric problems).
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
94 ##
17281
bc924baa2c4e doc: Add new @qcode macro for code samples which are quoted.
Rik <rik@octave.org>
parents: 17220
diff changeset
95 ## @item @qcode{"li"}
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
96 ## Largest Imaginary part (valid only for complex or unsymmetric problems).
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
97 ##
17281
bc924baa2c4e doc: Add new @qcode macro for code samples which are quoted.
Rik <rik@octave.org>
parents: 17220
diff changeset
98 ## @item @qcode{"si"}
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
99 ## Smallest Imaginary part (valid only for complex or unsymmetric problems).
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
100 ## @end table
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
101 ##
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
102 ## If @var{opts} is given, it is a structure defining possible options that
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
103 ## @code{eigs} should use. The fields of the @var{opts} structure are:
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
104 ##
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
105 ## @table @code
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
106 ## @item issym
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
107 ## If @var{af} is given, then flags whether the function @var{af} defines a
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
108 ## symmetric problem. It is ignored if @var{A} is given. The default is false.
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
109 ##
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
110 ## @item isreal
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
111 ## If @var{af} is given, then flags whether the function @var{af} defines a
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
112 ## real problem. It is ignored if @var{A} is given. The default is true.
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
113 ##
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
114 ## @item tol
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
115 ## Defines the required convergence tolerance, calculated as
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
116 ## @code{tol * norm (A)}. The default is @code{eps}.
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
117 ##
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
118 ## @item maxit
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
119 ## The maximum number of iterations. The default is 300.
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
120 ##
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
121 ## @item p
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
122 ## The number of Lanzcos basis vectors to use. More vectors will result in
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
123 ## faster convergence, but a greater use of memory. The optimal value of
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
124 ## @code{p} is problem dependent and should be in the range @var{k} to @var{n}.
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
125 ## The default value is @code{2 * @var{k}}.
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
126 ##
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
127 ## @item v0
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
128 ## The starting vector for the algorithm. An initial vector close to the
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
129 ## final vector will speed up convergence. The default is for @sc{arpack}
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
130 ## to randomly generate a starting vector. If specified, @code{v0} must be
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
131 ## an @var{n}-by-1 vector where @code{@var{n} = rows (@var{A})}
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
132 ##
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
133 ## @item disp
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
134 ## The level of diagnostic printout (0|1|2). If @code{disp} is 0 then
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
135 ## diagnostics are disabled. The default value is 0.
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
136 ##
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
137 ## @item cholB
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
138 ## Flag if @code{chol (@var{B})} is passed rather than @var{B}. The default is
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
139 ## false.
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
140 ##
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
141 ## @item permB
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
142 ## The permutation vector of the Cholesky@tie{}factorization of @var{B} if
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
143 ## @code{cholB} is true. That is @code{chol (@var{B}(permB, permB))}. The
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
144 ## default is @code{1:@var{n}}.
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
145 ##
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
146 ## @end table
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
147 ##
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
148 ## It is also possible to represent @var{A} by a function denoted @var{af}.
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
149 ## @var{af} must be followed by a scalar argument @var{n} defining the length
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
150 ## of the vector argument accepted by @var{af}. @var{af} can be
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
151 ## a function handle, an inline function, or a string. When @var{af} is a
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
152 ## string it holds the name of the function to use.
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
153 ##
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
154 ## @var{af} is a function of the form @code{y = af (x)}
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
155 ## where the required return value of @var{af} is determined by
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
156 ## the value of @var{sigma}. The four possible forms are
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
157 ##
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
158 ## @table @code
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
159 ## @item A * x
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
160 ## if @var{sigma} is not given or is a string other than "sm".
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
161 ##
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
162 ## @item A \ x
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
163 ## if @var{sigma} is 0 or "sm".
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
164 ##
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
165 ## @item (A - sigma * I) \ x
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
166 ## for the standard eigenvalue problem, where @code{I} is the identity matrix of
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
167 ## the same size as @var{A}.
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
168 ##
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
169 ## @item (A - sigma * B) \ x
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
170 ## for the general eigenvalue problem.
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
171 ## @end table
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
172 ##
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
173 ## The return arguments of @code{eigs} depend on the number of return arguments
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
174 ## requested. With a single return argument, a vector @var{d} of length @var{k}
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
175 ## is returned containing the @var{k} eigenvalues that have been found. With
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
176 ## two return arguments, @var{V} is a @var{n}-by-@var{k} matrix whose columns
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
177 ## are the @var{k} eigenvectors corresponding to the returned eigenvalues. The
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
178 ## eigenvalues themselves are returned in @var{d} in the form of a
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
179 ## @var{n}-by-@var{k} matrix, where the elements on the diagonal are the
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
180 ## eigenvalues.
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
181 ##
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
182 ## Given a third return argument @var{flag}, @code{eigs} returns the status
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
183 ## of the convergence. If @var{flag} is 0 then all eigenvalues have converged.
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
184 ## Any other value indicates a failure to converge.
19631
db92e7e28e1f strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 19630
diff changeset
185 ##
19074
0850b5212619 doc: Add @nospell macro around proper names in documentation.
Rik <rik@octave.org>
parents: 18817
diff changeset
186 ## This function is based on the @sc{arpack} package, written by
0850b5212619 doc: Add @nospell macro around proper names in documentation.
Rik <rik@octave.org>
parents: 18817
diff changeset
187 ## @nospell{R. Lehoucq, K. Maschhoff, D. Sorensen, and C. Yang}. For more
0850b5212619 doc: Add @nospell macro around proper names in documentation.
Rik <rik@octave.org>
parents: 18817
diff changeset
188 ## information see @url{http://www.caam.rice.edu/software/ARPACK/}.
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
189 ##
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
190 ## @seealso{eig, svds}
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
191 ## @end deftypefn
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
192
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
193 function varargout = eigs (varargin)
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
194
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
195 ## For compatibility with Matlab, handle small matrix cases here
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
196 ## that ARPACK does not.
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
197
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
198 if (nargin == 0)
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
199 print_usage ();
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
200 endif
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
201
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
202 call_eig = false;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
203 offset = 0;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
204 k = 6;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
205 sigma = "lm";
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
206
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
207 if (isnumeric (varargin{1}) && issquare (varargin{1}))
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
208 a = varargin{1};
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
209 if (nargin > 1 && isnumeric (varargin{2})
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
210 && issquare (varargin{2}) && size_equal (a, varargin{2}))
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
211 b = varargin{2};
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
212 offset = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
213 endif
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
214
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
215 if (rows (a) < 9)
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
216 call_eig = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
217 endif
19627
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 18817
diff changeset
218
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
219 if (nargin > 1 + offset)
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
220 tmp = varargin{2+offset};
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
221 if (isnumeric (tmp) && isscalar (tmp) && isreal (tmp)
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
222 && round (tmp) == tmp)
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
223 k = tmp;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
224
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
225 if (rows (a) - k < 3)
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
226 call_eig = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
227 endif
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
228 else
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
229 call_eig = false;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
230 endif
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
231
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
232 if (nargin > 2 + offset)
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
233 tmp = varargin{3+offset};
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
234 if (ischar (tmp) || (isnumeric (tmp) && isscalar (tmp)))
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
235 sigma = tmp;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
236 else
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
237 call_eig = false;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
238 endif
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
239 endif
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
240 endif
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
241 endif
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
242
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
243 if (call_eig)
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
244 varargout = cell (1, min (2, max (1, nargout)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
245 if (offset)
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
246 real_valued = isreal (a) && isreal (b);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
247 symmetric = issymmetric (a) && issymmetric (b);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
248 [varargout{:}] = eig (a, b);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
249 else
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
250 real_valued = isreal (a);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
251 symmetric = issymmetric (a);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
252 [varargout{:}] = eig (a);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
253 endif
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
254 varargout = select (varargout, k, sigma, real_valued, symmetric);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
255 if (nargout == 3)
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
256 varargout{3} = 0;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
257 endif
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
258 else
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
259 varargout = cell (1, max (1, nargout));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
260 [varargout{:}] = __eigs__ (varargin{:});
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
261 endif
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
262
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
263 endfunction
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
264
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
265 function out = select (args, k, sigma, real_valued, symmetric)
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
266
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
267 if (numel (args) == 1)
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
268 d = args{1};
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
269 else
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
270 d = diag (args{2});
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
271 endif
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
272
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
273 if (ischar (sigma))
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
274 switch (sigma)
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
275 case "lm"
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
276 [~, idx] = sort (abs (d), "descend");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
277
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
278 case "sm"
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
279 [~, idx] = sort (abs (d), "ascend");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
280
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
281 case "la"
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
282 if (real_valued && symmetric)
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
283 [~, idx] = sort (real (d), "descend");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
284 else
17846
42453dcfa95e eigs.m: Fix regression when numeric sigma is used and eig() is called instead of __eigs__.
Rik <rik@octave.org>
parents: 17845
diff changeset
285 error ('sigma = "la" requires real symmetric problem');
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
286 endif
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
287
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
288 case "sa"
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
289 if (real_valued && symmetric)
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
290 [~, idx] = sort (real (d), "ascend");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
291 else
17846
42453dcfa95e eigs.m: Fix regression when numeric sigma is used and eig() is called instead of __eigs__.
Rik <rik@octave.org>
parents: 17845
diff changeset
292 error ('sigma = "sa" requires real symmetric problem');
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
293 endif
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
294
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
295 case "be"
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
296 if (real_valued && symmetric)
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
297 [~, idx] = sort (real (d), "ascend");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
298 else
17846
42453dcfa95e eigs.m: Fix regression when numeric sigma is used and eig() is called instead of __eigs__.
Rik <rik@octave.org>
parents: 17845
diff changeset
299 error ('sigma = "be" requires real symmetric problem');
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
300 endif
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
301
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
302 case "lr"
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
303 if (! (real_valued || symmetric))
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
304 [~, idx] = sort (real (d), "descend");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
305 else
17846
42453dcfa95e eigs.m: Fix regression when numeric sigma is used and eig() is called instead of __eigs__.
Rik <rik@octave.org>
parents: 17845
diff changeset
306 error ('sigma = "lr" requires complex or unsymmetric problem');
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
307 endif
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
308
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
309 case "sr"
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
310 if (! (real_valued || symmetric))
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
311 [~, idx] = sort (real (d), "ascend");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
312 else
17846
42453dcfa95e eigs.m: Fix regression when numeric sigma is used and eig() is called instead of __eigs__.
Rik <rik@octave.org>
parents: 17845
diff changeset
313 error ('sigma = "sr" requires complex or unsymmetric problem');
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
314 endif
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
315
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
316 case "li"
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
317 if (! (real_valued || symmetric))
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
318 [~, idx] = sort (imag (d), "descend");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
319 else
17846
42453dcfa95e eigs.m: Fix regression when numeric sigma is used and eig() is called instead of __eigs__.
Rik <rik@octave.org>
parents: 17845
diff changeset
320 error ('sigma = "li" requires complex or unsymmetric problem');
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
321 endif
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
322
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
323 case "si"
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
324 if (! (real_valued || symmetric))
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
325 [~, idx] = sort (imag (d), "ascend");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
326 else
17846
42453dcfa95e eigs.m: Fix regression when numeric sigma is used and eig() is called instead of __eigs__.
Rik <rik@octave.org>
parents: 17845
diff changeset
327 error ('sigma = "si" requires complex or unsymmetric problem');
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
328 endif
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
329
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
330 otherwise
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
331 error ("unrecognized value for sigma: %s", sigma);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
332 endswitch
17846
42453dcfa95e eigs.m: Fix regression when numeric sigma is used and eig() is called instead of __eigs__.
Rik <rik@octave.org>
parents: 17845
diff changeset
333 else
42453dcfa95e eigs.m: Fix regression when numeric sigma is used and eig() is called instead of __eigs__.
Rik <rik@octave.org>
parents: 17845
diff changeset
334 ## numeric sigma, find k closest values
42453dcfa95e eigs.m: Fix regression when numeric sigma is used and eig() is called instead of __eigs__.
Rik <rik@octave.org>
parents: 17845
diff changeset
335 [~, idx] = sort (abs (d - sigma));
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
336 endif
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
337
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
338 d = d(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
339
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
340 n = numel (d);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
341
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
342 k = min (k, n);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
343
17846
42453dcfa95e eigs.m: Fix regression when numeric sigma is used and eig() is called instead of __eigs__.
Rik <rik@octave.org>
parents: 17845
diff changeset
344 if (strcmp (sigma, "be"))
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
345 tmp = k / 2;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
346 n1 = floor (tmp);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
347 n2 = n - ceil (tmp) + 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
348 selection = [1:floor(k/2), n2:n];
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
349 else
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
350 selection = 1:k;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
351 endif
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
352
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
353 d = d(selection);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
354
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
355 if (numel (args) == 1)
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
356 out{1} = d;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
357 else
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
358 out{2} = diag (d);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
359
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
360 v = args{1};
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
361 v = v(:,idx);
18817
1782f5294fdc eigs: selection columns of V, not rows (bug #41795)
John W. Eaton <jwe@octave.org>
parents: 17846
diff changeset
362 out{1} = v(:,selection);
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
363 endif
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
364
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
365 endfunction
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
366
17338
1c89599167a6 maint: End m-files with 1 blank line.
Rik <rik@octave.org>
parents: 17281
diff changeset
367
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
368 #### SPARSE MATRIX VERSIONS ####
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
369
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
370 ## Real positive definite tests, n must be even
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
371 %!shared n, k, A, d0, d2
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
372 %! n = 20;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
373 %! k = 4;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
374 %! A = sparse ([3:n,1:n,1:(n-2)],[1:(n-2),1:n,3:n],[ones(1,n-2),4*ones(1,n),ones(1,n-2)]);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
375 %! d0 = eig (A);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
376 %! d2 = sort (d0);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
377 %! [~, idx] = sort (abs (d0));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
378 %! d0 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
379 %! rand ("state", 42); # initialize generator to make eigs behavior reproducible
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
380 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
381 %! d1 = eigs (A, k);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
382 %! assert (d1, d0(end:-1:(end-k+1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
383 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
384 %! d1 = eigs (A, k+1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
385 %! assert (d1, d0(end:-1:(end-k)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
386 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
387 %! d1 = eigs (A, k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
388 %! assert (d1, d0(end:-1:(end-k+1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
389 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
390 %! d1 = eigs (A, k, "sm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
391 %! assert (d1, d0(k:-1:1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
392 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
393 %! d1 = eigs (A, k, "la");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
394 %! assert (d1, d2(end:-1:(end-k+1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
395 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
396 %! d1 = eigs (A, k, "sa");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
397 %! assert (d1, d2(1:k), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
398 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
399 %! d1 = eigs (A, k, "be");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
400 %! assert (d1, d2([1:floor(k/2), (end - ceil(k/2) + 1):end]), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
401 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
402 %! d1 = eigs (A, k+1, "be");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
403 %! assert (d1, d2([1:floor((k+1)/2), (end - ceil((k+1)/2) + 1):end]), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
404 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
405 %! d1 = eigs (A, k, 4.1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
406 %! [~, idx0] = sort (abs (d0 - 4.1));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
407 %! [~, idx1] = sort (abs (d1 - 4.1));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
408 %! assert (d1(idx1), d0(idx0(1:k)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
409 %!testif HAVE_ARPACK, HAVE_CHOLMOD
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
410 %! d1 = eigs (A, speye (n), k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
411 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
412 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
413 %! assert (eigs (A, k, 4.1), eigs (A, speye (n), k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
414 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
415 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
416 %! d1 = eigs (A, speye (n), k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
417 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
418 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
419 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
420 %! q = [2:n,1];
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
421 %! opts.permB = q;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
422 %! d1 = eigs (A, speye (n)(q,q), k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
423 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
424 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
425 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
426 %! d1 = eigs (A, speye (n), k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
427 %! assert (abs (d1), eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
428 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
429 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
430 %! q = [2:n,1];
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
431 %! opts.permB = q;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
432 %! d1 = eigs (A, speye (n)(q,q), k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
433 %! assert (abs (d1), eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
434 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
435 %! assert (eigs (A, k, 4.1), eigs (A, speye (n), k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
436 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
437 %! fn = @(x) A * x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
438 %! opts.issym = 1; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
439 %! d1 = eigs (fn, n, k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
440 %! assert (d1, d0(end:-1:(end-k+1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
441 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
442 %! fn = @(x) A \ x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
443 %! opts.issym = 1; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
444 %! d1 = eigs (fn, n, k, "sm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
445 %! assert (d1, d0(k:-1:1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
446 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
447 %! fn = @(x) (A - 4.1 * eye (n)) \ x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
448 %! opts.issym = 1; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
449 %! d1 = eigs (fn, n, k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
450 %! assert (d1, eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
451 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
452 %! AA = speye (10);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
453 %! fn = @(x) AA * x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
454 %! opts.issym = 1; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
455 %! assert (eigs (fn, 10, AA, 3, "lm", opts), [1; 1; 1], 10*eps);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
456 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
457 %! [v1,d1] = eigs (A, k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
458 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
459 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
460 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
461 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
462 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
463 %! [v1,d1] = eigs (A, k, "sm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
464 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
465 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
466 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
467 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
468 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
469 %! [v1,d1] = eigs (A, k, "la");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
470 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
471 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
472 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
473 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
474 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
475 %! [v1,d1] = eigs (A, k, "sa");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
476 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
477 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
478 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
479 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
480 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
481 %! [v1,d1] = eigs (A, k, "be");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
482 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
483 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
484 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
485 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
486
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
487 ## Real unsymmetric tests
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
488 %!shared n, k, A, d0
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
489 %! n = 20;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
490 %! k = 4;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
491 %! A = sparse ([3:n,1:n,1:(n-2)],[1:(n-2),1:n,3:n],[ones(1,n-2),1:n,-ones(1,n-2)]);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
492 %! d0 = eig (A);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
493 %! [~, idx] = sort (abs (d0));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
494 %! d0 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
495 %! rand ("state", 42); % initialize generator to make eigs behavior reproducible
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
496 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
497 %! d1 = eigs (A, k);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
498 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
499 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
500 %! d1 = eigs (A, k+1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
501 %! assert (abs (d1), abs (d0(end:-1:(end-k))),1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
502 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
503 %! d1 = eigs (A, k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
504 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
505 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
506 %! d1 = eigs (A, k, "sm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
507 %! assert (abs (d1), abs (d0(1:k)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
508 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
509 %! d1 = eigs (A, k, "lr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
510 %! [~, idx] = sort (real (d0));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
511 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
512 %! assert (real (d1), real (d2(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
513 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
514 %! d1 = eigs (A, k, "sr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
515 %! [~, idx] = sort (real (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
516 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
517 %! assert (real (d1), real (d2(1:k)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
518 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
519 %! d1 = eigs (A, k, "li");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
520 %! [~, idx] = sort (imag (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
521 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
522 %! assert (sort (imag (d1)), sort (imag (d2(end:-1:(end-k+1)))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
523 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
524 %! d1 = eigs (A, k, "si");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
525 %! [~, idx] = sort (imag (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
526 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
527 %! assert (sort (imag (d1)), sort (imag (d2(1:k))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
528 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
529 %! d1 = eigs (A, k, 4.1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
530 %! [~, idx0] = sort (abs (d0 - 4.1));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
531 %! [~, idx1] = sort (abs (d1 - 4.1));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
532 %! assert (abs (d1(idx1)), abs (d0(idx0(1:k))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
533 %! assert (sort (imag (d1(idx1))), sort (imag (d0(idx0(1:k)))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
534 %!testif HAVE_ARPACK, HAVE_CHOLMOD
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
535 %! d1 = eigs (A, speye (n), k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
536 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
537 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
538 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
539 %! d1 = eigs (A, speye (n), k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
540 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
541 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
542 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
543 %! q = [2:n,1];
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
544 %! opts.permB = q;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
545 %! d1 = eigs (A, speye (n)(q,q), k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
546 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
547 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
548 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
549 %! d1 = eigs (A, speye (n), k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
550 %! assert (abs (d1), eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
551 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
552 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
553 %! q = [2:n,1];
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
554 %! opts.permB = q;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
555 %! d1 = eigs (A, speye (n)(q,q), k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
556 %! assert (abs (d1), eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
557 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
558 %! assert (abs (eigs (A, k, 4.1)), abs (eigs (A, speye (n), k, 4.1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
559 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
560 %! assert (sort (imag (eigs (A, k, 4.1))), sort (imag (eigs (A, speye (n), k, 4.1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
561 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
562 %! fn = @(x) A * x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
563 %! opts.issym = 0; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
564 %! d1 = eigs (fn, n, k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
565 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
566 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
567 %! fn = @(x) A \ x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
568 %! opts.issym = 0; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
569 %! d1 = eigs (fn, n, k, "sm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
570 %! assert (abs (d1), d0(1:k), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
571 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
572 %! fn = @(x) (A - 4.1 * eye (n)) \ x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
573 %! opts.issym = 0; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
574 %! d1 = eigs (fn, n, k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
575 %! assert (abs (d1), eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
576 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
577 %! [v1,d1] = eigs (A, k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
578 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
579 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
580 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
581 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
582 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
583 %! [v1,d1] = eigs (A, k, "sm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
584 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
585 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
586 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
587 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
588 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
589 %! [v1,d1] = eigs (A, k, "lr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
590 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
591 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
592 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
593 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
594 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
595 %! [v1,d1] = eigs (A, k, "sr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
596 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
597 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
598 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
599 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
600 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
601 %! [v1,d1] = eigs (A, k, "li");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
602 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
603 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
604 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
605 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
606 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
607 %! [v1,d1] = eigs (A, k, "si");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
608 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
609 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
610 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
611 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
612
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
613
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
614 ## Complex hermitian tests
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
615 %!shared n, k, A, d0
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
616 %! n = 20;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
617 %! k = 4;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
618 %! A = sparse ([3:n,1:n,1:(n-2)],[1:(n-2),1:n,3:n],[1i*ones(1,n-2),4*ones(1,n),-1i*ones(1,n-2)]);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
619 %! d0 = eig (A);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
620 %! [~, idx] = sort (abs (d0));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
621 %! d0 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
622 %! rand ("state", 42); % initialize generator to make eigs behavior reproducible
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
623 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
624 %! d1 = eigs (A, k);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
625 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
626 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
627 %! d1 = eigs (A, k+1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
628 %! assert (abs (d1), abs (d0(end:-1:(end-k))),1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
629 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
630 %! d1 = eigs (A, k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
631 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
632 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
633 %! d1 = eigs (A, k, "sm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
634 %! assert (abs (d1), abs (d0(1:k)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
635 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
636 %! d1 = eigs (A, k, "lr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
637 %! [~, idx] = sort (real (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
638 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
639 %! assert (real (d1), real (d2(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
640 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
641 %! d1 = eigs (A, k, "sr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
642 %! [~, idx] = sort (real (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
643 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
644 %! assert (real (d1), real (d2(1:k)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
645 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
646 %! d1 = eigs (A, k, "li");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
647 %! [~, idx] = sort (imag (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
648 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
649 %! assert (sort (imag (d1)), sort (imag (d2(end:-1:(end-k+1)))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
650 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
651 %! d1 = eigs (A, k, "si");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
652 %! [~, idx] = sort (imag (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
653 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
654 %! assert (sort (imag (d1)), sort (imag (d2(1:k))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
655 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
656 %! d1 = eigs (A, k, 4.1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
657 %! [~, idx0] = sort (abs (d0 - 4.1));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
658 %! [~, idx1] = sort (abs (d1 - 4.1));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
659 %! assert (abs (d1(idx1)), abs (d0(idx0(1:k))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
660 %! assert (sort (imag (d1(idx1))), sort (imag (d0(idx0(1:k)))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
661 %!testif HAVE_ARPACK, HAVE_CHOLMOD
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
662 %! d1 = eigs (A, speye (n), k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
663 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
664 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
665 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
666 %! d1 = eigs (A, speye (n), k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
667 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
668 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
669 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
670 %! q = [2:n,1];
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
671 %! opts.permB = q;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
672 %! d1 = eigs (A, speye (n)(q,q), k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
673 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
674 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
675 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
676 %! d1 = eigs (A, speye (n), k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
677 %! assert (abs (abs (d1)), abs (eigs (A, k, 4.1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
678 %! assert (sort (imag (abs (d1))), sort (imag (eigs (A, k, 4.1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
679 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
680 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
681 %! q = [2:n,1];
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
682 %! opts.permB = q;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
683 %! d1 = eigs (A, speye (n)(q,q), k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
684 %! assert (abs (abs (d1)), abs (eigs (A, k, 4.1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
685 %! assert (sort (imag (abs (d1))), sort (imag (eigs (A, k, 4.1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
686 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
687 %! assert (abs (eigs (A, k, 4.1)), abs (eigs (A, speye (n), k, 4.1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
688 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
689 %! assert (sort (imag (eigs (A, k, 4.1))), sort (imag (eigs (A, speye (n), k, 4.1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
690 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
691 %! fn = @(x) A * x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
692 %! opts.issym = 0; opts.isreal = 0;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
693 %! d1 = eigs (fn, n, k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
694 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
695 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
696 %! fn = @(x) A \ x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
697 %! opts.issym = 0; opts.isreal = 0;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
698 %! d1 = eigs (fn, n, k, "sm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
699 %! assert (abs (d1), d0(1:k), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
700 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
701 %! fn = @(x) (A - 4.1 * eye (n)) \ x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
702 %! opts.issym = 0; opts.isreal = 0;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
703 %! d1 = eigs (fn, n, k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
704 %! assert (abs (d1), eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
705 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
706 %! [v1,d1] = eigs (A, k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
707 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
708 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
709 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
710 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
711 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
712 %! [v1,d1] = eigs (A, k, "sm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
713 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
714 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
715 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
716 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
717 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
718 %! [v1,d1] = eigs (A, k, "lr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
719 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
720 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
721 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
722 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
723 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
724 %! [v1,d1] = eigs (A, k, "sr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
725 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
726 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
727 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
728 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
729 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
730 %! [v1,d1] = eigs (A, k, "li");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
731 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
732 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
733 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
734 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
735 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
736 %! [v1,d1] = eigs (A, k, "si");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
737 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
738 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
739 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
740 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
741
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
742 #### FULL MATRIX VERSIONS ####
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
743
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
744 ## Real positive definite tests, n must be even
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
745 %!shared n, k, A, d0, d2
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
746 %! n = 20;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
747 %! k = 4;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
748 %! A = full (sparse ([3:n,1:n,1:(n-2)],[1:(n-2),1:n,3:n],[ones(1,n-2),4*ones(1,n),ones(1,n-2)]));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
749 %! d0 = eig (A);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
750 %! d2 = sort (d0);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
751 %! [~, idx] = sort (abs (d0));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
752 %! d0 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
753 %! rand ("state", 42); % initialize generator to make eigs behavior reproducible
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
754 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
755 %! d1 = eigs (A, k);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
756 %! assert (d1, d0(end:-1:(end-k+1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
757 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
758 %! d1 = eigs (A, k+1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
759 %! assert (d1, d0(end:-1:(end-k)),1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
760 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
761 %! d1 = eigs (A, k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
762 %! assert (d1, d0(end:-1:(end-k+1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
763 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
764 %! d1 = eigs (A, k, "sm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
765 %! assert (d1, d0(k:-1:1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
766 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
767 %! d1 = eigs (A, k, "la");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
768 %! assert (d1, d2(end:-1:(end-k+1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
769 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
770 %! d1 = eigs (A, k, "sa");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
771 %! assert (d1, d2(1:k), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
772 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
773 %! d1 = eigs (A, k, "be");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
774 %! assert (d1, d2([1:floor(k/2), (end - ceil(k/2) + 1):end]), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
775 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
776 %! d1 = eigs (A, k+1, "be");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
777 %! assert (d1, d2([1:floor((k+1)/2), (end - ceil((k+1)/2) + 1):end]), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
778 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
779 %! d1 = eigs (A, k, 4.1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
780 %! [~, idx0] = sort (abs (d0 - 4.1));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
781 %! [~, idx1] = sort (abs (d1 - 4.1));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
782 %! assert (d1(idx1), d0(idx0(1:k)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
783 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
784 %! d1 = eigs (A, eye (n), k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
785 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
786 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
787 %! assert (eigs (A, k, 4.1), eigs (A, eye (n), k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
788 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
789 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
790 %! d1 = eigs (A, eye (n), k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
791 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
792 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
793 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
794 %! q = [2:n,1];
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
795 %! opts.permB = q;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
796 %! d1 = eigs (A, eye (n)(q,q), k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
797 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
798 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
799 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
800 %! d1 = eigs (A, eye (n), k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
801 %! assert (abs (d1), eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
802 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
803 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
804 %! q = [2:n,1];
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
805 %! opts.permB = q;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
806 %! d1 = eigs (A, eye (n)(q,q), k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
807 %! assert (abs (d1), eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
808 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
809 %! assert (eigs (A, k, 4.1), eigs (A, eye (n), k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
810 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
811 %! fn = @(x) A * x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
812 %! opts.issym = 1; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
813 %! d1 = eigs (fn, n, k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
814 %! assert (d1, d0(end:-1:(end-k+1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
815 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
816 %! fn = @(x) A \ x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
817 %! opts.issym = 1; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
818 %! d1 = eigs (fn, n, k, "sm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
819 %! assert (d1, d0(k:-1:1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
820 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
821 %! fn = @(x) (A - 4.1 * eye (n)) \ x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
822 %! opts.issym = 1; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
823 %! d1 = eigs (fn, n, k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
824 %! assert (d1, eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
825 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
826 %! [v1,d1] = eigs (A, k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
827 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
828 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
829 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
830 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
831 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
832 %! [v1,d1] = eigs (A, k, "sm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
833 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
834 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
835 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
836 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
837 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
838 %! [v1,d1] = eigs (A, k, "la");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
839 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
840 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
841 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
842 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
843 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
844 %! [v1,d1] = eigs (A, k, "sa");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
845 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
846 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
847 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
848 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
849 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
850 %! [v1,d1] = eigs (A, k, "be");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
851 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
852 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
853 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
854 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
855
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
856 ## Real unsymmetric tests
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
857 %!shared n, k, A, d0
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
858 %! n = 20;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
859 %! k = 4;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
860 %! A = full (sparse ([3:n,1:n,1:(n-2)],[1:(n-2),1:n,3:n],[ones(1,n-2),1:n,-ones(1,n-2)]));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
861 %! d0 = eig (A);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
862 %! [~, idx] = sort (abs (d0));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
863 %! d0 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
864 %! rand ("state", 42); % initialize generator to make eigs behavior reproducible
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
865 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
866 %! d1 = eigs (A, k);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
867 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
868 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
869 %! d1 = eigs (A, k+1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
870 %! assert (abs (d1), abs (d0(end:-1:(end-k))),1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
871 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
872 %! d1 = eigs (A, k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
873 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
874 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
875 %! d1 = eigs (A, k, "sm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
876 %! assert (abs (d1), abs (d0(1:k)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
877 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
878 %! d1 = eigs (A, k, "lr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
879 %! [~, idx] = sort (real (d0));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
880 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
881 %! assert (real (d1), real (d2(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
882 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
883 %! d1 = eigs (A, k, "sr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
884 %! [~, idx] = sort (real (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
885 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
886 %! assert (real (d1), real (d2(1:k)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
887 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
888 %! d1 = eigs (A, k, "li");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
889 %! [~, idx] = sort (imag (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
890 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
891 %! assert (sort (imag (d1)), sort (imag (d2(end:-1:(end-k+1)))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
892 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
893 %! d1 = eigs (A, k, "si");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
894 %! [~, idx] = sort (imag (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
895 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
896 %! assert (sort (imag (d1)), sort (imag (d2(1:k))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
897 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
898 %! d1 = eigs (A, k, 4.1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
899 %! [~, idx0] = sort (abs (d0 - 4.1));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
900 %! [~, idx1] = sort (abs (d1 - 4.1));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
901 %! assert (abs (d1(idx1)), abs (d0(idx0(1:k))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
902 %! assert (sort (imag (d1(idx1))), sort (imag (d0(idx0(1:k)))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
903 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
904 %! d1 = eigs (A, eye (n), k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
905 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
906 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
907 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
908 %! d1 = eigs (A, eye (n), k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
909 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
910 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
911 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
912 %! q = [2:n,1];
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
913 %! opts.permB = q;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
914 %! d1 = eigs (A, eye (n)(q,q), k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
915 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
916 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
917 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
918 %! d1 = eigs (A, eye (n), k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
919 %! assert (abs (d1), eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
920 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
921 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
922 %! q = [2:n,1];
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
923 %! opts.permB = q;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
924 %! d1 = eigs (A, eye (n)(q,q), k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
925 %! assert (abs (d1), eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
926 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
927 %! assert (abs (eigs (A, k, 4.1)), abs (eigs (A, eye (n), k, 4.1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
928 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
929 %! assert (sort (imag (eigs (A, k, 4.1))), sort (imag (eigs (A, eye (n), k, 4.1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
930 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
931 %! fn = @(x) A * x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
932 %! opts.issym = 0; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
933 %! d1 = eigs (fn, n, k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
934 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
935 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
936 %! fn = @(x) A \ x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
937 %! opts.issym = 0; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
938 %! d1 = eigs (fn, n, k, "sm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
939 %! assert (abs (d1), d0(1:k), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
940 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
941 %! fn = @(x) (A - 4.1 * eye (n)) \ x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
942 %! opts.issym = 0; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
943 %! d1 = eigs (fn, n, k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
944 %! assert (abs (d1), eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
945 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
946 %! [v1,d1] = eigs (A, k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
947 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
948 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
949 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
950 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
951 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
952 %! [v1,d1] = eigs (A, k, "sm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
953 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
954 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
955 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
956 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
957 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
958 %! [v1,d1] = eigs (A, k, "lr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
959 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
960 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
961 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
962 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
963 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
964 %! [v1,d1] = eigs (A, k, "sr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
965 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
966 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
967 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
968 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
969 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
970 %! [v1,d1] = eigs (A, k, "li");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
971 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
972 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
973 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
974 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
975 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
976 %! [v1,d1] = eigs (A, k, "si");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
977 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
978 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
979 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
980 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
981
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
982 ## Complex hermitian tests
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
983 %!shared n, k, A, d0
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
984 %! n = 20;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
985 %! k = 4;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
986 %! A = full (sparse ([3:n,1:n,1:(n-2)],[1:(n-2),1:n,3:n],[1i*ones(1,n-2),4*ones(1,n),-1i*ones(1,n-2)]));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
987 %! d0 = eig (A);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
988 %! [~, idx] = sort (abs (d0));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
989 %! d0 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
990 %! rand ("state", 42); % initialize generator to make eigs behavior reproducible
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
991 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
992 %! d1 = eigs (A, k);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
993 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
994 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
995 %! d1 = eigs (A, k+1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
996 %! assert (abs (d1), abs (d0(end:-1:(end-k))),1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
997 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
998 %! d1 = eigs (A, k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
999 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1000 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1001 %! d1 = eigs (A, k, "sm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1002 %! assert (abs (d1), abs (d0(1:k)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1003 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1004 %! d1 = eigs (A, k, "lr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1005 %! [~, idx] = sort (real (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1006 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1007 %! assert (real (d1), real (d2(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1008 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1009 %! d1 = eigs (A, k, "sr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1010 %! [~, idx] = sort (real (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1011 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1012 %! assert (real (d1), real (d2(1:k)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1013 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1014 %! d1 = eigs (A, k, "li");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1015 %! [~, idx] = sort (imag (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1016 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1017 %! assert (sort (imag (d1)), sort (imag (d2(end:-1:(end-k+1)))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1018 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1019 %! d1 = eigs (A, k, "si");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1020 %! [~, idx] = sort (imag (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1021 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1022 %! assert (sort (imag (d1)), sort (imag (d2(1:k))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1023 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1024 %! d1 = eigs (A, k, 4.1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1025 %! [~, idx0] = sort (abs (d0 - 4.1));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1026 %! [~, idx1] = sort (abs (d1 - 4.1));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1027 %! assert (abs (d1(idx1)), abs (d0(idx0(1:k))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1028 %! assert (sort (imag (d1(idx1))), sort (imag (d0(idx0(1:k)))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1029 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1030 %! d1 = eigs (A, eye (n), k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1031 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1032 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1033 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1034 %! d1 = eigs (A, eye (n), k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1035 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1036 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1037 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1038 %! q = [2:n,1];
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1039 %! opts.permB = q;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1040 %! d1 = eigs (A, eye (n)(q,q), k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1041 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1042 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1043 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1044 %! d1 = eigs (A, eye (n), k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1045 %! assert (abs (abs (d1)), abs (eigs (A, k, 4.1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1046 %! assert (sort (imag (abs (d1))), sort (imag (eigs (A, k, 4.1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1047 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1048 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1049 %! q = [2:n,1];
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1050 %! opts.permB = q;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1051 %! d1 = eigs (A, eye (n)(q,q), k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1052 %! assert (abs (abs (d1)), abs (eigs (A, k, 4.1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1053 %! assert (sort (imag (abs (d1))), sort (imag (eigs (A, k, 4.1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1054 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1055 %! assert (abs (eigs (A, k, 4.1)), abs (eigs (A, eye (n), k, 4.1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1056 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1057 %! assert (sort (imag (eigs (A, k, 4.1))), sort (imag (eigs (A, eye (n), k, 4.1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1058 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1059 %! fn = @(x) A * x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1060 %! opts.issym = 0; opts.isreal = 0;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1061 %! d1 = eigs (fn, n, k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1062 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1063 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1064 %! fn = @(x) A \ x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1065 %! opts.issym = 0; opts.isreal = 0;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1066 %! d1 = eigs (fn, n, k, "sm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1067 %! assert (abs (d1), d0(1:k), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1068 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1069 %! fn = @(x) (A - 4.1 * eye (n)) \ x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1070 %! opts.issym = 0; opts.isreal = 0;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1071 %! d1 = eigs (fn, n, k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1072 %! assert (abs (d1), eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1073 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1074 %! [v1,d1] = eigs (A, k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1075 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1076 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1077 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1078 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1079 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1080 %! [v1,d1] = eigs (A, k, "sm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1081 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1082 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1083 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1084 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1085 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1086 %! [v1,d1] = eigs (A, k, "lr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1087 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1088 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1089 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1090 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1091 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1092 %! [v1,d1] = eigs (A, k, "sr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1093 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1094 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1095 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1096 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1097 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1098 %! [v1,d1] = eigs (A, k, "li");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1099 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1100 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1101 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1102 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1103 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1104 %! [v1,d1] = eigs (A, k, "si");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1105 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1106 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1107 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1108 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1109
17845
0f912af348e0 add a test to mark regression in eigs
Carlo de Falco <cdf@users.sourceforge.net>
parents: 17744
diff changeset
1110 %!test
0f912af348e0 add a test to mark regression in eigs
Carlo de Falco <cdf@users.sourceforge.net>
parents: 17744
diff changeset
1111 %! A = 2 * diag (ones (10, 1)) - diag (ones (9, 1), 1) - diag (ones (9, 1), -1);
0f912af348e0 add a test to mark regression in eigs
Carlo de Falco <cdf@users.sourceforge.net>
parents: 17744
diff changeset
1112 %! B = diag (ones (10, 1));
0f912af348e0 add a test to mark regression in eigs
Carlo de Falco <cdf@users.sourceforge.net>
parents: 17744
diff changeset
1113 %! reseig = eig (A, B);
0f912af348e0 add a test to mark regression in eigs
Carlo de Falco <cdf@users.sourceforge.net>
parents: 17744
diff changeset
1114 %! [~, idx] = sort (abs (reseig), "ascend");
0f912af348e0 add a test to mark regression in eigs
Carlo de Falco <cdf@users.sourceforge.net>
parents: 17744
diff changeset
1115 %! assert (eigs (A, B, 10, 0), reseig (idx))
0f912af348e0 add a test to mark regression in eigs
Carlo de Falco <cdf@users.sourceforge.net>
parents: 17744
diff changeset
1116
18817
1782f5294fdc eigs: selection columns of V, not rows (bug #41795)
John W. Eaton <jwe@octave.org>
parents: 17846
diff changeset
1117 %!test
1782f5294fdc eigs: selection columns of V, not rows (bug #41795)
John W. Eaton <jwe@octave.org>
parents: 17846
diff changeset
1118 %! X = [70 47 42 39 50 73 79 23;
1782f5294fdc eigs: selection columns of V, not rows (bug #41795)
John W. Eaton <jwe@octave.org>
parents: 17846
diff changeset
1119 %! 19 52 61 80 36 76 63 68;
1782f5294fdc eigs: selection columns of V, not rows (bug #41795)
John W. Eaton <jwe@octave.org>
parents: 17846
diff changeset
1120 %! 14 34 66 65 29 4 72 9;
1782f5294fdc eigs: selection columns of V, not rows (bug #41795)
John W. Eaton <jwe@octave.org>
parents: 17846
diff changeset
1121 %! 24 8 78 49 58 54 43 33;
1782f5294fdc eigs: selection columns of V, not rows (bug #41795)
John W. Eaton <jwe@octave.org>
parents: 17846
diff changeset
1122 %! 62 69 32 31 40 46 22 28;
1782f5294fdc eigs: selection columns of V, not rows (bug #41795)
John W. Eaton <jwe@octave.org>
parents: 17846
diff changeset
1123 %! 48 12 45 59 10 17 15 25;
1782f5294fdc eigs: selection columns of V, not rows (bug #41795)
John W. Eaton <jwe@octave.org>
parents: 17846
diff changeset
1124 %! 64 67 77 56 13 55 41 74;
1782f5294fdc eigs: selection columns of V, not rows (bug #41795)
John W. Eaton <jwe@octave.org>
parents: 17846
diff changeset
1125 %! 37 38 18 21 11 3 71 7;
1782f5294fdc eigs: selection columns of V, not rows (bug #41795)
John W. Eaton <jwe@octave.org>
parents: 17846
diff changeset
1126 %! 5 35 16 1 51 27 26 44;
1782f5294fdc eigs: selection columns of V, not rows (bug #41795)
John W. Eaton <jwe@octave.org>
parents: 17846
diff changeset
1127 %! 30 57 60 75 2 53 20 6];
1782f5294fdc eigs: selection columns of V, not rows (bug #41795)
John W. Eaton <jwe@octave.org>
parents: 17846
diff changeset
1128 %! Z = X * X';
1782f5294fdc eigs: selection columns of V, not rows (bug #41795)
John W. Eaton <jwe@octave.org>
parents: 17846
diff changeset
1129 %! r = rank (Z);
1782f5294fdc eigs: selection columns of V, not rows (bug #41795)
John W. Eaton <jwe@octave.org>
parents: 17846
diff changeset
1130 %! assert (r, 8);
1782f5294fdc eigs: selection columns of V, not rows (bug #41795)
John W. Eaton <jwe@octave.org>
parents: 17846
diff changeset
1131 %! [V, D] = eigs (Z, r, "lm");
1782f5294fdc eigs: selection columns of V, not rows (bug #41795)
John W. Eaton <jwe@octave.org>
parents: 17846
diff changeset
1132 %! ZZ = V * D * V';
1782f5294fdc eigs: selection columns of V, not rows (bug #41795)
John W. Eaton <jwe@octave.org>
parents: 17846
diff changeset
1133 %! tmp = abs (Z - ZZ);
1782f5294fdc eigs: selection columns of V, not rows (bug #41795)
John W. Eaton <jwe@octave.org>
parents: 17846
diff changeset
1134 %! assert (max (tmp(:)) < 5e-11);
1782f5294fdc eigs: selection columns of V, not rows (bug #41795)
John W. Eaton <jwe@octave.org>
parents: 17846
diff changeset
1135
17220
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1136 %!assert (eigs (diag (1:5), 5, "sa"), [1;2;3;4;5]);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1137 %!assert (eigs (diag (1:5), 5, "la"), [5;4;3;2;1]);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1138 %!assert (eigs (diag (1:5), 3, "be"), [1;4;5]);