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update Octave Project Developers copyright for the new year In files that have the "Octave Project Developers" copyright notice, update for 2021. In all .txi and .texi files except gpl.txi and gpl.texi in the doc/liboctave and doc/interpreter directories, change the copyright to "Octave Project Developers", the same as used for other source files. Update copyright notices for 2022 (not done since 2019). For gpl.txi and gpl.texi, change the copyright notice to be "Free Software Foundation, Inc." and leave the date at 2007 only because this file only contains the text of the GPL, not anything created by the Octave Project Developers. Add Paul Thomas to contributors.in.
author John W. Eaton <jwe@octave.org>
date Tue, 28 Dec 2021 18:22:40 -0500
parents 7854d5752dd2
children 597f3ee61a48
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1 ########################################################################
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2 ##
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3 ## Copyright (C) 2013-2022 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 ## -*- texinfo -*-
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27 ## @deftypefn {} {@var{x} =} linsolve (@var{A}, @var{b})
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28 ## @deftypefnx {} {@var{x} =} linsolve (@var{A}, @var{b}, @var{opts})
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29 ## @deftypefnx {} {[@var{x}, @var{R}] =} linsolve (@dots{})
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30 ## Solve the linear system @code{A*x = b}.
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31 ##
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32 ## With no options, this function is equivalent to the left division operator
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33 ## @w{(@code{x = A \ b})} or the matrix-left-divide function
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34 ## @w{(@code{x = mldivide (A, b)})}.
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35 ##
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36 ## Octave ordinarily examines the properties of the matrix @var{A} and chooses
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37 ## a solver that best matches the matrix. By passing a structure @var{opts}
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38 ## to @code{linsolve} you can inform Octave directly about the matrix @var{A}.
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39 ## In this case Octave will skip the matrix examination and proceed directly
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40 ## to solving the linear system.
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41 ##
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42 ## @strong{Warning:} If the matrix @var{A} does not have the properties listed
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43 ## in the @var{opts} structure then the result will not be accurate AND no
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44 ## warning will be given. When in doubt, let Octave examine the matrix and
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45 ## choose the appropriate solver as this step takes little time and the result
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46 ## is cached so that it is only done once per linear system.
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47 ##
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48 ## Possible @var{opts} fields (set value to true/false):
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49 ##
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50 ## @table @asis
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51 ## @item LT
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52 ## @var{A} is lower triangular
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53 ##
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54 ## @item UT
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55 ## @var{A} is upper triangular
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56 ##
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57 ## @item UHESS
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58 ## @var{A} is upper Hessenberg (currently makes no difference)
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59 ##
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60 ## @item SYM
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61 ## @var{A} is symmetric or complex Hermitian (currently makes no difference)
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62 ##
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63 ## @item POSDEF
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64 ## @var{A} is positive definite
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65 ##
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66 ## @item RECT
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67 ## @var{A} is general rectangular (currently makes no difference)
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68 ##
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69 ## @item TRANSA
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70 ## Solve @code{A'*x = b} if true rather than @code{A*x = b}
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71 ## @end table
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72 ##
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73 ## The optional second output @var{R} is the inverse condition number of
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74 ## @var{A} (zero if matrix is singular).
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75 ## @seealso{mldivide, matrix_type, rcond}
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76 ## @end deftypefn
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77
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78 function [x, R] = linsolve (A, b, opts)
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79
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80 if (nargin < 2)
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81 print_usage ();
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82 endif
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83
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84 if (! (isnumeric (A) && isnumeric (b)))
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85 error ("linsolve: A and B must be numeric");
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86 endif
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87
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88 trans_A = false;
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89
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90 ## Process any opts
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91 if (nargin > 2)
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92 if (! isstruct (opts))
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93 error ("linsolve: OPTS must be a structure");
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94 endif
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95 if (isfield (opts, "TRANSA") && opts.TRANSA)
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96 trans_A = true;
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97 endif
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98 if (isfield (opts, "POSDEF") && opts.POSDEF)
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99 A = matrix_type (A, "positive definite");
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100 endif
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101 if (isfield (opts, "LT") && opts.LT)
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102 A = matrix_type (A, "lower");
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103 elseif (isfield (opts, "UT") && opts.UT)
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104 A = matrix_type (A, "upper");
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105 endif
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106 endif
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107
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108 ## This way is faster as the transpose is not calculated in Octave,
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109 ## but forwarded as a flag option to BLAS.
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110 if (trans_A)
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111 x = A' \ b;
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112 else
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113 x = A \ b;
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114 endif
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115
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116 if (nargout > 1)
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117 if (issquare (A))
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118 R = rcond (A);
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119 else
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120 R = 0;
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121 endif
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122 endif
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123
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124 endfunction
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125
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126
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127 %!test
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128 %! n = 10;
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129 %! A = rand (n);
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130 %! x = rand (n, 1);
014e942ac29f linsolve.m: Fix regression when calling linsolve with 2 arguments (bug #45212)
Mike Miller <mtmiller@octave.org>
parents: 20030
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131 %! b = A * x;
014e942ac29f linsolve.m: Fix regression when calling linsolve with 2 arguments (bug #45212)
Mike Miller <mtmiller@octave.org>
parents: 20030
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132 %! assert (linsolve (A, b), A \ b);
014e942ac29f linsolve.m: Fix regression when calling linsolve with 2 arguments (bug #45212)
Mike Miller <mtmiller@octave.org>
parents: 20030
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133 %! assert (linsolve (A, b, struct ()), A \ b);
014e942ac29f linsolve.m: Fix regression when calling linsolve with 2 arguments (bug #45212)
Mike Miller <mtmiller@octave.org>
parents: 20030
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134
014e942ac29f linsolve.m: Fix regression when calling linsolve with 2 arguments (bug #45212)
Mike Miller <mtmiller@octave.org>
parents: 20030
diff changeset
135 %!test
014e942ac29f linsolve.m: Fix regression when calling linsolve with 2 arguments (bug #45212)
Mike Miller <mtmiller@octave.org>
parents: 20030
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136 %! n = 10;
20030
91e1da1d1918 linsolve.m: Calculate solution in a BLAS-optimized way (bug #44722).
Rik <rik@octave.org>
parents: 19697
diff changeset
137 %! A = triu (gallery ("condex", n));
17500
b66f068e4468 linsolve.m: Use Octave coding conventions.
Rik <rik@octave.org>
parents: 17499
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138 %! x = rand (n, 1);
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Rik <rik@octave.org>
parents: 17499
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139 %! b = A' * x;
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Rik <rik@octave.org>
parents: 17499
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140 %! opts.UT = true;
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Rik <rik@octave.org>
parents: 17499
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141 %! opts.TRANSA = true;
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Rik <rik@octave.org>
parents: 17499
diff changeset
142 %! assert (linsolve (A, b, opts), A' \ b);
17499
c3a3532e3d98 linsolve.m: Add new function for Matlab compatibility.
Nir Krakauer < nkrakauer@ccny.cuny.edu>
parents:
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143
28896
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin.
Rik <rik@octave.org>
parents: 28789
diff changeset
144 %!error <Invalid call> linsolve ()
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin.
Rik <rik@octave.org>
parents: 28789
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145 %!error <Invalid call> linsolve (1)
17500
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Rik <rik@octave.org>
parents: 17499
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146 %!error linsolve (1,2,3)
b66f068e4468 linsolve.m: Use Octave coding conventions.
Rik <rik@octave.org>
parents: 17499
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147 %!error <A and B must be numeric> linsolve ({1},2)
b66f068e4468 linsolve.m: Use Octave coding conventions.
Rik <rik@octave.org>
parents: 17499
diff changeset
148 %!error <A and B must be numeric> linsolve (1,{2})
b66f068e4468 linsolve.m: Use Octave coding conventions.
Rik <rik@octave.org>
parents: 17499
diff changeset
149 %!error <OPTS must be a structure> linsolve (1,2,3)