annotate libinterp/corefcn/eig.cc @ 21966:112b20240c87

move docstrings in C++ files out of C strings and into comments * __contourc__.cc, __dispatch__.cc, __dsearchn__.cc, __ichol__.cc, __ilu__.cc, __lin_interpn__.cc, __luinc__.cc, __magick_read__.cc, __pchip_deriv__.cc, __qp__.cc, balance.cc, besselj.cc, betainc.cc, bitfcns.cc, bsxfun.cc, cellfun.cc, colloc.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc, debug.cc, defaults.cc, det.cc, dirfns.cc, dlmread.cc, dot.cc, eig.cc, ellipj.cc, error.cc, fft.cc, fft2.cc, fftn.cc, file-io.cc, filter.cc, find.cc, gammainc.cc, gcd.cc, getgrent.cc, getpwent.cc, getrusage.cc, givens.cc, graphics.cc, hash.cc, help.cc, hess.cc, hex2num.cc, input.cc, inv.cc, kron.cc, load-path.cc, load-save.cc, lookup.cc, ls-oct-text.cc, lsode.cc, lu.cc, mappers.cc, matrix_type.cc, max.cc, mgorth.cc, nproc.cc, oct-hist.cc, octave-link.cc, ordschur.cc, pager.cc, pinv.cc, pr-output.cc, profiler.cc, psi.cc, pt-jit.cc, quad.cc, quadcc.cc, qz.cc, rand.cc, rcond.cc, regexp.cc, schur.cc, sighandlers.cc, sparse.cc, spparms.cc, sqrtm.cc, str2double.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc, sylvester.cc, symtab.cc, syscalls.cc, sysdep.cc, time.cc, toplev.cc, tril.cc, tsearch.cc, typecast.cc, urlwrite.cc, utils.cc, variables.cc, __delaunayn__.cc, __eigs__.cc, __fltk_uigetfile__.cc, __glpk__.cc, __init_fltk__.cc, __init_gnuplot__.cc, __osmesa_print__.cc, __voronoi__.cc, amd.cc, audiodevinfo.cc, audioread.cc, ccolamd.cc, chol.cc, colamd.cc, convhulln.cc, dmperm.cc, fftw.cc, qr.cc, symbfact.cc, symrcm.cc, ov-base.cc, ov-bool-mat.cc, ov-cell.cc, ov-class.cc, ov-classdef.cc, ov-fcn-handle.cc, ov-fcn-inline.cc, ov-flt-re-mat.cc, ov-int16.cc, ov-int32.cc, ov-int64.cc, ov-int8.cc, ov-java.cc, ov-null-mat.cc, ov-oncleanup.cc, ov-range.cc, ov-re-mat.cc, ov-struct.cc, ov-typeinfo.cc, ov-uint16.cc, ov-uint32.cc, ov-uint64.cc, ov-uint8.cc, ov-usr-fcn.cc, ov.cc, octave.cc, pt-arg-list.cc, pt-binop.cc, pt-eval.cc, pt-mat.cc, lex.ll, oct-parse.in.yy: Docstrings are now comments instead of C strings. * build-aux/mk-opts.pl: Emit docstrings as comments instead of C strings. * DASPK-opts.in, LSODE-opts.in: Don't quote " in docstring fragments. * builtins.h: Include builtin-defun-decls.h unconditionally. * defun.h (DEFUN, DEFUNX, DEFCONSTFUN): Simply emit declaration. (DEFALIAS): Always expand to nothing. * defun-dld.h: No special macro expansions for MAKE_BUILTINS. (DEFUN_DLD): Use FORWARD_DECLARE_FUN. (DEFUNX_DLD): Use FORWARD_DECLARE_FUNX. * defun-int.h: No special macro expansions for MAKE_BUILTINS. (FORWARD_DECLARE_FUN, FORWARD_DECLARE_FUNX): New macros. (DEFINE_FUN_INSTALLER_FUN): If compiling an Octave source file, pass "external-doc" to DEFINE_FUNX_INSTALLER_FUN. (DEFUN_INTERNAL, DEFCONSTFUN_INTERNAL, DEFUNX_INTERNAL, DEFALIAS_INTERNAL): Delete. * common.mk (move_if_change_rule): New macro. (simple_move_if_change_rule): Define using move_if_change_rule. * find-defun-files.sh (DEFUN_PATTERN): Update. Don't transform file name extension to ".df". * libinterp/mk-pkg-add, gendoc.pl: Operate directly on source files. * mkbuiltins: New argument, SRCDIR. Operate directly on source files. * mkdefs: Delete. * libinterp/module.mk (BUILT_SOURCES): Update list to contain only files included in other source files. (GENERATED_MAKE_BUILTINS_INCS, DEF_FILES): Delete. (LIBINTERP_BUILT_DISTFILES): Include $(OPT_HANDLERS) here. (LIBINTERP_BUILT_NODISTFILES): Not here. Remove $(ALL_DEF_FILES from the list. (libinterp_EXTRA_DIST): Remove mkdefs from the list. (FOUND_DEFUN_FILES): Rename from SRC_DEF_FILES. (DLDFCN_DEFUN_FILES): Rename from DLDFCN_DEF_FILES. (SRC_DEFUN_FILES): Rename from SRC_DEF_FILES. (ALL_DEFUN_FILES): Rename from ALL_DEF_FILES. (%.df: %.cc): Delete pattern rule. (libinterp/build-env-features.cc, libinterp/builtins.cc, libinterp/dldfcn/PKG_ADD): Use mv instead of move-if-change. (libinterp/builtins.cc, libinterp/builtin-defun-decls.h): Update mkbuiltins command. ($(srcdir)/libinterp/DOCSTRINGS): Update gendoc.pl command. * liboctave/module.mk (BUILT_SOURCES): Don't include liboctave-build-info.cc in the list.
author John W. Eaton <jwe@octave.org>
date Tue, 21 Jun 2016 16:07:51 -0400
parents aba2e6293dd8
children 510886d03ef2
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1 /*
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2
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3 Copyright (C) 1996-2015 John W. Eaton
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4
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5 This file is part of Octave.
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6
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7 Octave is free software; you can redistribute it and/or modify it
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8 under the terms of the GNU General Public License as published by the
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9 Free Software Foundation; either version 3 of the License, or (at your
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10 option) any later version.
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11
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12 Octave is distributed in the hope that it will be useful, but WITHOUT
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13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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15 for more details.
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16
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17 You should have received a copy of the GNU General Public License
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18 along with Octave; see the file COPYING. If not, see
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19 <http://www.gnu.org/licenses/>.
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20
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21 */
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22
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23 #if defined (HAVE_CONFIG_H)
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24 # include "config.h"
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25 #endif
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26
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27 #include "EIG.h"
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28 #include "fEIG.h"
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29
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30 #include "defun.h"
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31 #include "error.h"
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32 #include "errwarn.h"
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33 #include "ovl.h"
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34 #include "utils.h"
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35
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36 DEFUN (eig, args, nargout,
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37 doc: /* -*- texinfo -*-
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38 @deftypefn {} {@var{lambda} =} eig (@var{A})
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39 @deftypefnx {} {@var{lambda} =} eig (@var{A}, @var{B})
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40 @deftypefnx {} {[@var{V}, @var{lambda}] =} eig (@var{A})
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41 @deftypefnx {} {[@var{V}, @var{lambda}] =} eig (@var{A}, @var{B})
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42 Compute the eigenvalues (and optionally the eigenvectors) of a matrix
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43 or a pair of matrices
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44
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45 The algorithm used depends on whether there are one or two input
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46 matrices, if they are real or complex, and if they are symmetric
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47 (Hermitian if complex) or non-symmetric.
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48
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49 The eigenvalues returned by @code{eig} are not ordered.
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50 @seealso{eigs, svd}
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51 @end deftypefn */)
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52 {
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53 int nargin = args.length ();
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54
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55 if (nargin > 2 || nargin == 0)
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56 print_usage ();
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57
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58 octave_value_list retval;
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59
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60 octave_value arg_a, arg_b;
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61
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62 octave_idx_type nr_a, nr_b, nc_a, nc_b;
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63 nr_a = nr_b = nc_a = nc_b = 0;
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64
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65 arg_a = args(0);
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66 nr_a = arg_a.rows ();
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67 nc_a = arg_a.columns ();
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69 int arg_is_empty = empty_arg ("eig", nr_a, nc_a);
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70 if (arg_is_empty < 0)
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71 return retval;
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72 else if (arg_is_empty > 0)
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73 return octave_value_list (2, Matrix ());
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74
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75 if (! arg_a.is_double_type () && ! arg_a.is_single_type ())
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76 err_wrong_type_arg ("eig", arg_a);
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77
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78 if (nargin == 2)
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79 {
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80 arg_b = args(1);
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81 nr_b = arg_b.rows ();
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82 nc_b = arg_b.columns ();
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83
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84 arg_is_empty = empty_arg ("eig", nr_b, nc_b);
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85 if (arg_is_empty < 0)
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86 return retval;
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87 else if (arg_is_empty > 0)
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88 return ovl (2, Matrix ());
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89
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90 if (! arg_b.is_single_type () && ! arg_b.is_double_type ())
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91 err_wrong_type_arg ("eig", arg_b);
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92 }
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93
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94 if (nr_a != nc_a)
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95 err_square_matrix_required ("eig", "A");
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97 if (nargin == 2 && nr_b != nc_b)
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98 err_square_matrix_required ("eig", "B");
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99
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100 Matrix tmp_a, tmp_b;
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101 ComplexMatrix ctmp_a, ctmp_b;
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102 FloatMatrix ftmp_a, ftmp_b;
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103 FloatComplexMatrix fctmp_a, fctmp_b;
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104
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105 if (arg_a.is_single_type ())
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106 {
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107 FloatEIG result;
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108
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109 if (nargin == 1)
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110 {
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111 if (arg_a.is_real_type ())
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112 {
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113 ftmp_a = arg_a.float_matrix_value ();
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114
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115 result = FloatEIG (ftmp_a, nargout > 1);
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116 }
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117 else
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118 {
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119 fctmp_a = arg_a.float_complex_matrix_value ();
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120
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121 result = FloatEIG (fctmp_a, nargout > 1);
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122 }
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123 }
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124 else if (nargin == 2)
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125 {
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126 if (arg_a.is_real_type () && arg_b.is_real_type ())
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127 {
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128 ftmp_a = arg_a.float_matrix_value ();
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129 ftmp_b = arg_b.float_matrix_value ();
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130
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131 result = FloatEIG (ftmp_a, ftmp_b, nargout > 1);
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132 }
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133 else
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134 {
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135 fctmp_a = arg_a.float_complex_matrix_value ();
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136 fctmp_b = arg_b.float_complex_matrix_value ();
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137
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138 result = FloatEIG (fctmp_a, fctmp_b, nargout > 1);
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139 }
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140 }
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141
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142 if (nargout == 0 || nargout == 1)
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143 {
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144 retval = ovl (result.eigenvalues ());
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145 }
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146 else
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147 {
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148 // Blame it on Matlab.
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149 FloatComplexDiagMatrix d (result.eigenvalues ());
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150
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151 retval = ovl (result.eigenvectors (), d);
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152 }
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153 }
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154 else
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155 {
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156 EIG result;
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157
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158 if (nargin == 1)
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159 {
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160 if (arg_a.is_real_type ())
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161 {
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162 tmp_a = arg_a.matrix_value ();
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163
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164 result = EIG (tmp_a, nargout > 1);
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165 }
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166 else
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167 {
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168 ctmp_a = arg_a.complex_matrix_value ();
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169
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170 result = EIG (ctmp_a, nargout > 1);
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171 }
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172 }
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173 else if (nargin == 2)
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174 {
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175 if (arg_a.is_real_type () && arg_b.is_real_type ())
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176 {
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177 tmp_a = arg_a.matrix_value ();
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178 tmp_b = arg_b.matrix_value ();
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179
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180 result = EIG (tmp_a, tmp_b, nargout > 1);
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181 }
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182 else
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183 {
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184 ctmp_a = arg_a.complex_matrix_value ();
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185 ctmp_b = arg_b.complex_matrix_value ();
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186
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187 result = EIG (ctmp_a, ctmp_b, nargout > 1);
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188 }
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189 }
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190
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191 if (nargout == 0 || nargout == 1)
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192 {
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193 retval = ovl (result.eigenvalues ());
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194 }
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195 else
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196 {
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197 // Blame it on Matlab.
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198 ComplexDiagMatrix d (result.eigenvalues ());
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199
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200 retval = ovl (result.eigenvectors (), d);
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201 }
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202 }
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203
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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204 return retval;
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205 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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206
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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207 /*
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208 %!assert (eig ([1, 2; 2, 1]), [-1; 3], sqrt (eps))
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209
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210 %!test
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211 %! [v, d] = eig ([1, 2; 2, 1]);
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212 %! x = 1 / sqrt (2);
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213 %! assert (d, [-1, 0; 0, 3], sqrt (eps));
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214 %! assert (v, [-x, x; x, x], sqrt (eps));
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215
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216 %!assert (eig (single ([1, 2; 2, 1])), single ([-1; 3]), sqrt (eps ("single")))
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217
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218 %!test
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219 %! [v, d] = eig (single ([1, 2; 2, 1]));
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220 %! x = single (1 / sqrt (2));
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221 %! assert (d, single ([-1, 0; 0, 3]), sqrt (eps ("single")));
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222 %! assert (v, [-x, x; x, x], sqrt (eps ("single")));
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223
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224 %!test
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225 %! A = [1, 2; -1, 1]; B = [3, 3; 1, 2];
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226 %! [v, d] = eig (A, B);
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227 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps));
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228 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps));
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229
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230 %!test
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231 %! A = single ([1, 2; -1, 1]); B = single ([3, 3; 1, 2]);
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232 %! [v, d] = eig (A, B);
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233 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps ("single")));
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234 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps ("single")));
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235
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236 %!test
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237 %! A = [1, 2; 2, 1]; B = [3, -2; -2, 3];
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238 %! [v, d] = eig (A, B);
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239 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps));
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240 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps));
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241
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242 %!test
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243 %! A = single ([1, 2; 2, 1]); B = single ([3, -2; -2, 3]);
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244 %! [v, d] = eig (A, B);
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245 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps ("single")));
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246 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps ("single")));
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247
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248 %!test
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249 %! A = [1+3i, 2+i; 2-i, 1+3i]; B = [5+9i, 2+i; 2-i, 5+9i];
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250 %! [v, d] = eig (A, B);
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251 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps));
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252 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps));
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253
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254 %!test
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255 %! A = single ([1+3i, 2+i; 2-i, 1+3i]); B = single ([5+9i, 2+i; 2-i, 5+9i]);
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256 %! [v, d] = eig (A, B);
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257 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps ("single")));
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258 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps ("single")));
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259
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260 %!test
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261 %! A = [1+3i, 2+3i; 3-8i, 8+3i]; B = [8+i, 3+i; 4-9i, 3+i];
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262 %! [v, d] = eig (A, B);
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263 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps));
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264 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps));
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265
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266 %!test
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267 %! A = single ([1+3i, 2+3i; 3-8i, 8+3i]); B = single ([8+i, 3+i; 4-9i, 3+i]);
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268 %! [v, d] = eig (A, B);
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269 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps ("single")));
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270 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps ("single")));
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271
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272 %!test
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273 %! A = [1, 2; 3, 8]; B = [8, 3; 4, 3];
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274 %! [v, d] = eig (A, B);
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275 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps));
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276 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps));
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277
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278 %!test
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279 %! A = [1, 1+i; 1-i, 1]; B = [2, 0; 0, 2];
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280 %! [v, d] = eig (A, B);
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281 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps));
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282 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps));
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283
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284 %!test
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285 %! A = single ([1, 1+i; 1-i, 1]); B = single ([2, 0; 0, 2]);
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286 %! [v, d] = eig (A, B);
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287 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps ("single")));
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288 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps ("single")));
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289
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290 %!error eig ()
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291 %!error eig ([1, 2; 3, 4], [4, 3; 2, 1], 1)
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292 %!error <EIG requires same size matrices> eig ([1, 2; 3, 4], 2)
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293 %!error <must be a square matrix> eig ([1, 2; 3, 4; 5, 6])
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294 %!error <wrong type argument> eig ("abcd")
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295 %!error <wrong type argument> eig ([1 2 ; 2 3], "abcd")
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296 %!error <wrong type argument> eig (false, [1 2 ; 2 3])
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295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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297 */