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maint: merge stable to default.
author John W. Eaton <jwe@octave.org>
date Wed, 10 Feb 2021 10:10:40 -0500
parents 06c8e0877864 0a5b15007766
children 32c3a5805893
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1 ////////////////////////////////////////////////////////////////////////
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2 //
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3 // Copyright (C) 1996-2021 The Octave Project Developers
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4 //
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5 // See the file COPYRIGHT.md in the top-level directory of this
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6 // distribution or <https://octave.org/copyright/>.
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7 //
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8 // This file is part of Octave.
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9 //
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10 // Octave is free software: you can redistribute it and/or modify it
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11 // under the terms of the GNU General Public License as published by
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12 // the Free Software Foundation, either version 3 of the License, or
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13 // (at your option) any later version.
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14 //
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15 // Octave is distributed in the hope that it will be useful, but
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16 // WITHOUT ANY WARRANTY; without even the implied warranty of
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17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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18 // GNU General Public License for more details.
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19 //
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20 // You should have received a copy of the GNU General Public License
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21 // along with Octave; see the file COPYING. If not, see
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22 // <https://www.gnu.org/licenses/>.
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23 //
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24 ////////////////////////////////////////////////////////////////////////
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25
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26 #if defined (HAVE_CONFIG_H)
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27 # include "config.h"
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28 #endif
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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 "ops.h"
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35 #include "ov-re-diag.h"
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36 #include "ov-cx-diag.h"
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37 #include "ov-flt-re-diag.h"
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38 #include "ov-flt-cx-diag.h"
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39 #include "ov-perm.h"
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40
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41 DEFUN (inv, args, nargout,
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42 doc: /* -*- texinfo -*-
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43 @deftypefn {} {@var{x} =} inv (@var{A})
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44 @deftypefnx {} {[@var{x}, @var{rcond}] =} inv (@var{A})
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45 @deftypefnx {} {[@dots{}] =} inverse (@dots{})
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46 Compute the inverse of the square matrix @var{A}.
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47
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48 Return an estimate of the reciprocal condition number if requested,
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49 otherwise warn of an ill-conditioned matrix if the reciprocal condition
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50 number is small.
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51
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52 In general it is best to avoid calculating the inverse of a matrix directly.
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53 For example, it is both faster and more accurate to solve systems of
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54 equations (@var{A}*@math{x} = @math{b}) with
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55 @code{@var{y} = @var{A} \ @math{b}}, rather than
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56 @code{@var{y} = inv (@var{A}) * @math{b}}.
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57
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58 If called with a sparse matrix, then in general @var{x} will be a full
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59 matrix requiring significantly more storage. Avoid forming the inverse of a
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60 sparse matrix if possible.
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61
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62 @code{inverse} is an alias and may be used identically in place of @code{inv}.
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63 @seealso{ldivide, rdivide, pinv}
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64 @end deftypefn */)
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65 {
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66 if (args.length () != 1)
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67 print_usage ();
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68
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69 octave_value arg = args(0);
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70
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71 if (arg.isempty ())
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72 return ovl (Matrix ());
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73
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74 if (arg.rows () != arg.columns ())
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75 err_square_matrix_required ("inverse", "A");
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76
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77 octave_value result;
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78 octave_idx_type info;
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79 double rcond = 0.0;
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80 float frcond = 0.0;
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81 bool isfloat = arg.is_single_type ();
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82
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83 if (arg.is_diag_matrix ())
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84 {
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85 rcond = 1.0;
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86 frcond = 1.0f;
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87 if (arg.iscomplex ())
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88 {
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89 if (isfloat)
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90 {
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91 result = arg.float_complex_diag_matrix_value ().inverse (info);
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92 if (info == -1)
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93 frcond = 0.0f;
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94 else if (nargout > 1)
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95 frcond = arg.float_complex_diag_matrix_value ().rcond ();
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96 }
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97 else
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98 {
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99 result = arg.complex_diag_matrix_value ().inverse (info);
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100 if (info == -1)
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101 rcond = 0.0;
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102 else if (nargout > 1)
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103 rcond = arg.complex_diag_matrix_value ().rcond ();
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104 }
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105 }
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106 else
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107 {
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108 if (isfloat)
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109 {
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110 result = arg.float_diag_matrix_value ().inverse (info);
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111 if (info == -1)
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112 frcond = 0.0f;
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113 else if (nargout > 1)
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114 frcond = arg.float_diag_matrix_value ().rcond ();
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115 }
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116 else
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117 {
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118 result = arg.diag_matrix_value ().inverse (info);
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119 if (info == -1)
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120 rcond = 0.0;
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121 else if (nargout > 1)
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122 rcond = arg.diag_matrix_value ().rcond ();
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123 }
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124 }
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125 }
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126 else if (arg.is_perm_matrix ())
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127 {
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128 rcond = 1.0;
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129 info = 0;
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130 result = arg.perm_matrix_value ().inverse ();
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131 }
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132 else if (isfloat)
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133 {
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134 if (arg.isreal ())
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135 {
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136 FloatMatrix m = arg.float_matrix_value ();
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137
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138 MatrixType mattyp = args(0).matrix_type ();
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139 result = m.inverse (mattyp, info, frcond, 1);
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140 args(0).matrix_type (mattyp);
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141 }
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142 else if (arg.iscomplex ())
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143 {
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144 FloatComplexMatrix m = arg.float_complex_matrix_value ();
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145
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146 MatrixType mattyp = args(0).matrix_type ();
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147 result = m.inverse (mattyp, info, frcond, 1);
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148 args(0).matrix_type (mattyp);
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149 }
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150 }
7789
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David Bateman <dbateman@free.fr>
parents: 7650
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151 else
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jwe
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152 {
23582
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153 if (arg.isreal ())
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154 {
23583
b7747a2c88b2 maint: Deprecate is_sparse_type and replace with issparse.
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155 if (arg.issparse ())
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156 {
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157 SparseMatrix m = arg.sparse_matrix_value ();
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158
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159 MatrixType mattyp = args(0).matrix_type ();
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160 result = m.inverse (mattyp, info, rcond, 1);
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161 args(0).matrix_type (mattyp);
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162 }
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163 else
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164 {
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165 Matrix m = arg.matrix_value ();
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166
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167 MatrixType mattyp = args(0).matrix_type ();
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168 result = m.inverse (mattyp, info, rcond, 1);
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169 args(0).matrix_type (mattyp);
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170 }
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171 }
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172 else if (arg.iscomplex ())
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173 {
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174 if (arg.issparse ())
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175 {
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176 SparseComplexMatrix m = arg.sparse_complex_matrix_value ();
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177
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178 MatrixType mattyp = args(0).matrix_type ();
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179 result = m.inverse (mattyp, info, rcond, 1);
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180 args(0).matrix_type (mattyp);
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181 }
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182 else
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183 {
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184 ComplexMatrix m = arg.complex_matrix_value ();
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185
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186 MatrixType mattyp = args(0).matrix_type ();
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187 result = m.inverse (mattyp, info, rcond, 1);
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188 args(0).matrix_type (mattyp);
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189 }
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190 }
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191 else
21100
e39e05d90788 Switch gripe_XXX to either err_XXX or warn_XXX naming scheme.
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192 err_wrong_type_arg ("inv", arg);
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193 }
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194
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195 octave_value_list retval (nargout > 1 ? 2 : 1);
8da80da1ac37 maint: Use ovl() more places in the code.
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196
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197 retval(0) = result;
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198 if (nargout > 1)
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199 retval(1) = (isfloat ? octave_value (frcond) : octave_value (rcond));
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200
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201 bool rcond_plus_one_eq_one = false;
18243
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202
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203 if (isfloat)
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204 {
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205 volatile float xrcond = frcond;
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206 rcond_plus_one_eq_one = xrcond + 1.0f == 1.0f;
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207 }
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208 else
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209 {
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210 volatile double xrcond = rcond;
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211 rcond_plus_one_eq_one = xrcond + 1.0 == 1.0;
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212 }
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213
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214 if (nargout < 2 && (info == -1 || rcond_plus_one_eq_one))
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215 octave::warn_singular_matrix (isfloat ? frcond : rcond);
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216
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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217 return retval;
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diff changeset
218 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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219
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220 /*
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221 %!assert (inv ([1, 2; 3, 4]), [-2, 1; 1.5, -0.5], sqrt (eps))
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222 %!assert (inv (single ([1, 2; 3, 4])), single ([-2, 1; 1.5, -0.5]), sqrt (eps ("single")))
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223
22849
1d242ae72240 Return 0 for special case of scalar Inf input to inverse (bug #49690).
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diff changeset
224 ## Test special inputs
1d242ae72240 Return 0 for special case of scalar Inf input to inverse (bug #49690).
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225 %!assert (inv (zeros (2,0)), [])
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226 %!warning <matrix singular> assert (inv (Inf), 0)
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227 %!warning <matrix singular> assert (inv (-Inf), -0)
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228 %!warning <matrix singular> assert (inv (single (Inf)), single (0))
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229 %!warning <matrix singular> assert (inv (complex (1, Inf)), 0)
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230 %!warning <matrix singular> assert (inv (single (complex (1,Inf))), single (0))
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diff changeset
231
1d242ae72240 Return 0 for special case of scalar Inf input to inverse (bug #49690).
Rik <rik@octave.org>
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diff changeset
232 %!test
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233 %! [xinv, rcond] = inv (single ([1,2;3,4]));
1d242ae72240 Return 0 for special case of scalar Inf input to inverse (bug #49690).
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234 %! assert (isa (xinv, "single"));
1d242ae72240 Return 0 for special case of scalar Inf input to inverse (bug #49690).
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235 %! assert (isa (rcond, "single"));
1d242ae72240 Return 0 for special case of scalar Inf input to inverse (bug #49690).
Rik <rik@octave.org>
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diff changeset
236
1d242ae72240 Return 0 for special case of scalar Inf input to inverse (bug #49690).
Rik <rik@octave.org>
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diff changeset
237 %!test
1d242ae72240 Return 0 for special case of scalar Inf input to inverse (bug #49690).
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238 %! [xinv, rcond] = inv ([1,2;3,4]);
1d242ae72240 Return 0 for special case of scalar Inf input to inverse (bug #49690).
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diff changeset
239 %! assert (isa (xinv, "double"));
1d242ae72240 Return 0 for special case of scalar Inf input to inverse (bug #49690).
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diff changeset
240 %! assert (isa (rcond, "double"));
1d242ae72240 Return 0 for special case of scalar Inf input to inverse (bug #49690).
Rik <rik@octave.org>
parents: 22755
diff changeset
241
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242 %!testif HAVE_UMFPACK <*56232>
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243 %! fail ("A = inv (sparse ([1, 2;0 ,0]))", "warning", "matrix singular");
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244 %! assert (A, sparse ([Inf, Inf; 0, 0]));
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diff changeset
245
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246 %!testif HAVE_UMFPACK <*56232>
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247 %! fail ("A = inv (sparse ([1i, 2;0 ,0]))", "warning", "matrix singular");
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248 %! assert (A, sparse ([Inf, Inf; 0, 0]));
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249
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marco.caliari@univr.it
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diff changeset
250 %!test
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251 %! fail ("A = inv (diag ([1, 0, 1]))", "warning", "matrix singular");
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252 %! assert (A, diag ([Inf, Inf, Inf]));
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diff changeset
253
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254 %!error <inverse of the null matrix not defined> inv (diag ([0, 0]))
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255 %!error <inverse of the null matrix not defined> inv (diag (complex ([0, 0])))
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marco.caliari@univr.it
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diff changeset
256
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257 %!testif HAVE_UMFPACK <*56232>
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258 %! fail ("A = inv (sparse ([1, 0, 0; 0, 0, 0; 0, 0, 1]))", "warning", "matrix singular");
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259 %! assert (A, sparse ([Inf, 0, 0; 0, 0, 0; 0, 0, Inf]));
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diff changeset
260
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diff changeset
261 %!error inv ()
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diff changeset
262 %!error inv ([1, 2; 3, 4], 2)
21110
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diff changeset
263 %!error <must be a square matrix> inv ([1, 2; 3, 4; 5, 6])
27093
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diff changeset
264 %!error <inverse of the null matrix not defined> inv (sparse (2, 2, 0))
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diff changeset
265 */
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David Bateman <dbateman@free.fr>
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diff changeset
266
23453
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diff changeset
267 DEFALIAS (inverse, inv);