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annotate libinterp/corefcn/pinv.cc @ 20940:48b2ad5ee801

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maint: Rename oct-obj.[cc|h] to ovl.[cc|h] for clarity. * libinterp/corefcn/oct-obj.h: Replaced. Contains a #warning issued if used in compilation and includes "ovl.h" instead. Original file renamed to libinterp/octave-value/ovl.h * libinterp/corefcn/oct-obj.cc: Renamed to libinterp/octave-value/ovl.cc. * oct-obj.cc (ovl ()): Added new function to return empty octave_value_list. * libinterp/corefcn/module.mk: Remove oct-obj.cc from build system. * libinterp/octave-value/module.mk: Add ovl.h and ovl.cc to build system. * mk-opts.pl, annotation-dialog.h, Cell.cc, __contourc__.cc, __dsearchn__.cc, __lin_interpn__.cc, __pchip_deriv__.cc, __qp__.cc, balance.cc, besselj.cc, betainc.cc, colloc.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc, debug.cc, defaults.cc, defun.cc, det.cc, dirfns.cc, dlmread.cc, eig.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, gripes.cc, help.cc, hess.cc, hex2num.cc, hook-fcn.h, input.cc, input.h, inv.cc, kron.cc, load-save.cc, lookup.cc, ls-hdf5.cc, ls-mat-ascii.cc, ls-mat4.cc, ls-mat5.cc, ls-oct-binary.cc, ls-oct-text.cc, lsode.cc, lu.cc, luinc.cc, max.cc, mex.cc, oct-hist.cc, oct-lvalue.cc, oct-lvalue.h, oct-map.h, oct-stream.cc, oct.h, ordschur.cc, pager.cc, pinv.cc, pr-output.cc, quad.cc, quadcc.cc, qz.cc, rand.cc, rcond.cc, regexp.cc, schur.cc, sparse-xpow.cc, strfns.cc, sub2ind.cc, svd.cc, sylvester.cc, symtab.h, syscalls.cc, sysdep.cc, time.cc, toplev.cc, tril.cc, tsearch.cc, typecast.cc, urlwrite.cc, utils.cc, variables.cc, xpow.cc, __delaunayn__.cc, __glpk__.cc, __voronoi__.cc, audiodevinfo.cc, audioread.cc, chol.cc, convhulln.cc, dmperm.cc, qr.cc, symbfact.cc, mkbuiltins, ov-base-diag.h, ov-base-int.cc, ov-base-mat.cc, ov-base-mat.h, ov-base-scalar.cc, ov-base-sparse.cc, ov-base-sparse.h, ov-base.cc, ov-bool-mat.cc, ov-bool.cc, ov-builtin.cc, ov-cell.cc, ov-colon.cc, ov-complex.cc, ov-cs-list.h, ov-cx-mat.cc, ov-dld-fcn.cc, ov-fcn.cc, ov-fcn.h, ov-float.cc, ov-flt-complex.cc, ov-flt-cx-mat.cc, ov-flt-re-mat.cc, ov-int16.cc, ov-int32.cc, ov-int64.cc, ov-int8.cc, ov-java.h, ov-mex-fcn.cc, ov-perm.h, ov-range.cc, ov-re-mat.cc, ov-scalar.cc, ov-str-mat.cc, ov-uint16.cc, ov-uint32.cc, ov-uint64.cc, ov-uint8.cc, ov-usr-fcn.cc, ov-usr-fcn.h, ov.cc, octave.cc, op-b-b.cc, op-b-bm.cc, op-b-sbm.cc, op-bm-b.cc, op-bm-bm.cc, op-bm-sbm.cc, op-cdm-cdm.cc, op-cell.cc, op-chm.cc, op-class.cc, op-cm-cm.cc, op-cm-cs.cc, op-cm-m.cc, op-cm-s.cc, op-cm-scm.cc, op-cm-sm.cc, op-cs-cm.cc, op-cs-cs.cc, op-cs-m.cc, op-cs-s.cc, op-cs-scm.cc, op-cs-sm.cc, op-dm-dm.cc, op-dm-scm.cc, op-dm-sm.cc, op-double-conv.cc, op-fcdm-fcdm.cc, op-fcdm-fdm.cc, op-fcm-fcm.cc, op-fcm-fcs.cc, op-fcm-fm.cc, op-fcm-fs.cc, op-fcn.cc, op-fcs-fcm.cc, op-fcs-fcs.cc, op-fcs-fm.cc, op-fcs-fs.cc, op-fdm-fdm.cc, op-float-conv.cc, op-fm-fcm.cc, op-fm-fcs.cc, op-fm-fm.cc, op-fm-fs.cc, op-fs-fcm.cc, op-fs-fcs.cc, op-fs-fm.cc, op-fs-fs.cc, op-i16-i16.cc, op-i32-i32.cc, op-i64-i64.cc, op-i8-i8.cc, op-int-concat.cc, op-int-conv.cc, op-m-cm.cc, op-m-cs.cc, op-m-m.cc, op-m-s.cc, op-m-scm.cc, op-m-sm.cc, op-pm-pm.cc, op-pm-scm.cc, op-pm-sm.cc, op-range.cc, op-s-cm.cc, op-s-cs.cc, op-s-m.cc, op-s-s.cc, op-s-scm.cc, op-s-sm.cc, op-sbm-b.cc, op-sbm-bm.cc, op-sbm-sbm.cc, op-scm-cm.cc, op-scm-cs.cc, op-scm-m.cc, op-scm-s.cc, op-scm-scm.cc, op-scm-sm.cc, op-sm-cm.cc, op-sm-cs.cc, op-sm-m.cc, op-sm-s.cc, op-sm-scm.cc, op-sm-sm.cc, op-str-m.cc, op-str-s.cc, op-str-str.cc, op-struct.cc, op-ui16-ui16.cc, op-ui32-ui32.cc, op-ui64-ui64.cc, op-ui8-ui8.cc, parse.h, pt-arg-list.cc, pt-assign.cc, pt-binop.cc, pt-cbinop.cc, pt-cell.cc, pt-colon.cc, pt-const.cc, pt-eval.h, pt-fcn-handle.cc, pt-funcall.h, pt-id.cc, pt-idx.cc, pt-jump.cc, pt-mat.cc, pt-select.cc, pt-unop.cc, token.cc, Array-sym.cc: replace '#include "oct-obj.h"' with '#include "ovl.h"'.
author Rik <rik@octave.org>
date Fri, 18 Dec 2015 16:04:56 -0800
parents b17fda023ca6
children a4f5da7c5463
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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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23 #ifdef 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 "defun.h"
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28 #include "error.h"
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29 #include "gripes.h"
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30 #include "ovl.h"
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31 #include "utils.h"
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32 #include "ops.h"
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33 #include "ov-re-diag.h"
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34 #include "ov-cx-diag.h"
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35 #include "ov-flt-re-diag.h"
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36 #include "ov-flt-cx-diag.h"
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37 #include "ov-perm.h"
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38
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39 DEFUN (pinv, args, ,
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40 "-*- texinfo -*-\n\
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41 @deftypefn {} {} pinv (@var{x})\n\
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42 @deftypefnx {} {} pinv (@var{x}, @var{tol})\n\
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43 Return the pseudoinverse of @var{x}.\n\
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44 \n\
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45 Singular values less than @var{tol} are ignored.\n\
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46 \n\
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47 If the second argument is omitted, it is taken to be\n\
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48 \n\
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49 @example\n\
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50 tol = max (size (@var{x})) * sigma_max (@var{x}) * eps,\n\
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51 @end example\n\
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52 \n\
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53 @noindent\n\
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54 where @code{sigma_max (@var{x})} is the maximal singular value of @var{x}.\n\
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55 @end deftypefn")
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56 {
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57 int nargin = args.length ();
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58
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59 if (nargin < 1 || nargin > 2)
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60 print_usage ();
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61
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62 octave_value arg = args(0);
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63
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64 int arg_is_empty = empty_arg ("pinv", arg.rows (), arg.columns ());
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65
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66 if (arg_is_empty < 0)
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67 return octave_value_list ();
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68 else if (arg_is_empty > 0)
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69 return octave_value (Matrix ());
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70
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71 octave_value retval;
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72
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73 bool isfloat = arg.is_single_type ();
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74
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75 if (arg.is_diag_matrix ())
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76 {
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77 if (isfloat)
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78 {
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79 float tol = 0.0;
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80 if (nargin == 2)
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81 tol = args(1).float_value ();
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82
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83 if (tol < 0.0)
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84 error ("pinv: TOL must be greater than zero");
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85
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86 if (arg.is_real_type ())
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87 retval = arg.float_diag_matrix_value ().pseudo_inverse (tol);
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88 else
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89 retval = arg.float_complex_diag_matrix_value ().pseudo_inverse (tol);
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90 }
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91 else
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92 {
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93 double tol = 0.0;
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94 if (nargin == 2)
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95 tol = args(1).double_value ();
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96
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97 if (tol < 0.0)
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98 error ("pinv: TOL must be greater than zero");
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99
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100 if (arg.is_real_type ())
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101 retval = arg.diag_matrix_value ().pseudo_inverse (tol);
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102 else
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103 retval = arg.complex_diag_matrix_value ().pseudo_inverse (tol);
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104 }
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105 }
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106 else if (arg.is_perm_matrix ())
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107 {
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108 retval = arg.perm_matrix_value ().inverse ();
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109 }
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110 else if (isfloat)
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111 {
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112 float tol = 0.0;
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113 if (nargin == 2)
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114 tol = args(1).float_value ();
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115
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116 if (tol < 0.0)
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117 error ("pinv: TOL must be greater than zero");
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118
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119 if (arg.is_real_type ())
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120 {
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121 FloatMatrix m = arg.float_matrix_value ();
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122
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123 retval = m.pseudo_inverse (tol);
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124 }
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125 else if (arg.is_complex_type ())
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126 {
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127 FloatComplexMatrix m = arg.float_complex_matrix_value ();
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128
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129 retval = m.pseudo_inverse (tol);
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130 }
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131 else
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132 gripe_wrong_type_arg ("pinv", arg);
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133 }
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134 else
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135 {
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136 double tol = 0.0;
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137 if (nargin == 2)
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138 tol = args(1).double_value ();
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139
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140 if (tol < 0.0)
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141 error ("pinv: TOL must be greater than zero");
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142
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143 if (arg.is_real_type ())
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144 {
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145 Matrix m = arg.matrix_value ();
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146
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147 retval = m.pseudo_inverse (tol);
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148 }
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149 else if (arg.is_complex_type ())
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150 {
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151 ComplexMatrix m = arg.complex_matrix_value ();
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152
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153 retval = m.pseudo_inverse (tol);
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154 }
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155 else
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156 gripe_wrong_type_arg ("pinv", arg);
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157 }
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158
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159 return retval;
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160 }
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161
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162 /*
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163 %!shared a, b, tol, hitol, d, u, x, y
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164 %! a = reshape (rand*[1:16], 4, 4); # Rank 2 matrix
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165 %! b = pinv (a);
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166 %! tol = 4e-14;
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167 %! hitol = 40*sqrt (eps);
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168 %! d = diag ([rand, rand, hitol, hitol]);
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169 %! u = rand (4); # Could be singular by freak accident
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170 %! x = inv (u)*d*u;
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171 %! y = pinv (x, sqrt (eps));
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172 %!
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173 %!assert (a*b*a, a, tol)
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174 %!assert (b*a*b, b, tol)
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175 %!assert ((b*a)', b*a, tol)
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176 %!assert ((a*b)', a*b, tol)
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177 %!assert (x*y*x, x, -hitol)
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178 %!assert (y*x*y, y, -hitol)
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179 %!assert ((x*y)', x*y, hitol)
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180 %!assert ((y*x)', y*x, hitol)
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181
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182 ## Clear shared variables
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183 %!shared
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184
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185 ## Test pinv for Diagonal matrices
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186 %!test
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187 %! x = diag ([3 2 1 0 -0.5]);
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188 %! y = pinv (x);
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189 %! assert (typeinfo (y)(1:8), "diagonal");
1fa5bba16218 [mq]: pinv
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190 %! assert (isa (y, "double"));
1fa5bba16218 [mq]: pinv
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191 %! assert (diag (y), [1/3, 1/2, 1, 0 1/-0.5]');
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192 %! y = pinv (x, 1);
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193 %! assert (diag (y), [1/3 1/2 1 0 0]');
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194 %! y = pinv (x, 2);
1fa5bba16218 [mq]: pinv
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195 %! assert (diag (y), [1/3 1/2 0 0 0]');
1fa5bba16218 [mq]: pinv
Rik <rik@octave.org>
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diff changeset
196
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diff changeset
197 */