annotate scripts/linear-algebra/linsolve.m @ 20614:10ec79b47808

use new string_value method to handle value extraction errors * __voronoi__.cc, chol.cc, colamd.cc, fftw.cc: Use new string_value method.
author John W. Eaton <jwe@octave.org>
date Thu, 08 Oct 2015 18:15:56 -0400
parents 014e942ac29f
children
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1 ## Copyright (C) 2013-2015 Nir Krakauer
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify
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6 ## it under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or
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8 ## (at your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful,
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11 ## but WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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13 ## GNU General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; If not, see <http://www.gnu.org/licenses/>.
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17
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18 ## -*- texinfo -*-
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19 ## @deftypefn {Function File} {@var{x} =} linsolve (@var{A}, @var{b})
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20 ## @deftypefnx {Function File} {@var{x} =} linsolve (@var{A}, @var{b}, @var{opts})
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21 ## @deftypefnx {Function File} {[@var{x}, @var{R}] =} linsolve (@dots{})
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22 ## Solve the linear system @code{A*x = b}.
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23 ##
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24 ## With no options, this function is equivalent to the left division operator
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25 ## @w{(@code{x = A \ b})} or the matrix-left-divide function
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26 ## @w{(@code{x = mldivide (A, b)})}.
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27 ##
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28 ## Octave ordinarily examines the properties of the matrix @var{A} and chooses
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29 ## a solver that best matches the matrix. By passing a structure @var{opts}
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30 ## to @code{linsolve} you can inform Octave directly about the matrix @var{A}.
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31 ## In this case Octave will skip the matrix examination and proceed directly
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32 ## to solving the linear system.
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33 ##
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34 ## @strong{Warning:} If the matrix @var{A} does not have the properties
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35 ## listed in the @var{opts} structure then the result will not be accurate
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36 ## AND no warning will be given. When in doubt, let Octave examine the matrix
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37 ## and choose the appropriate solver as this step takes little time and the
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38 ## result is cached so that it is only done once per linear system.
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39 ##
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40 ## Possible @var{opts} fields (set value to true/false):
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41 ##
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42 ## @table @asis
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43 ## @item LT
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44 ## @var{A} is lower triangular
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45 ##
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46 ## @item UT
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47 ## @var{A} is upper triangular
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48 ##
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49 ## @item UHESS
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50 ## @var{A} is upper Hessenberg (currently makes no difference)
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51 ##
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52 ## @item SYM
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53 ## @var{A} is symmetric or complex Hermitian (currently makes no difference)
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54 ##
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55 ## @item POSDEF
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56 ## @var{A} is positive definite
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57 ##
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58 ## @item RECT
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59 ## @var{A} is general rectangular (currently makes no difference)
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60 ##
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61 ## @item TRANSA
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62 ## Solve @code{A'*x = b} by @code{transpose (A) \ b}
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63 ## @end table
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64 ##
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65 ## The optional second output @var{R} is the inverse condition number of
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66 ## @var{A} (zero if matrix is singular).
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67 ## @seealso{mldivide, matrix_type, rcond}
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68 ## @end deftypefn
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69
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70 ## Author: Nir Krakauer <nkrakauer@ccny.cuny.edu>
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71
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72 function [x, R] = linsolve (A, b, opts)
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73
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74 if (nargin < 2 || nargin > 3)
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75 print_usage ();
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76 endif
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77
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78 if (! (isnumeric (A) && isnumeric (b)))
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79 error ("linsolve: A and B must be numeric");
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80 endif
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81
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82 trans_A = false;
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83
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84 ## Process any opts
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85 if (nargin > 2)
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86 if (! isstruct (opts))
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87 error ("linsolve: OPTS must be a structure");
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88 endif
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89 if (isfield (opts, "TRANSA") && opts.TRANSA)
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90 trans_A = true;
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91 endif
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92 if (isfield (opts, "POSDEF") && opts.POSDEF)
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93 A = matrix_type (A, "positive definite");
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94 endif
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95 if (isfield (opts, "LT") && opts.LT)
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96 A = matrix_type (A, "lower");
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97 elseif (isfield (opts, "UT") && opts.UT)
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98 A = matrix_type (A, "upper");
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99 endif
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100 endif
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101
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102 ## This way is faster as the transpose is not calculated in Octave,
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103 ## but forwarded as a flag option to BLAS.
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104 if (trans_A)
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105 x = A' \ b;
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106 else
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107 x = A \ b;
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108 endif
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109
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110 if (nargout > 1)
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111 if (issquare (A))
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112 R = rcond (A);
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113 else
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114 R = 0;
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115 endif
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116 endif
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117
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118 endfunction
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119
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120
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121 %!test
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122 %! n = 10;
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123 %! A = rand (n);
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124 %! x = rand (n, 1);
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125 %! b = A * x;
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126 %! assert (linsolve (A, b), A \ b);
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127 %! assert (linsolve (A, b, struct ()), A \ b);
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128
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129 %!test
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130 %! n = 10;
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131 %! A = triu (gallery ("condex", n));
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Rik <rik@octave.org>
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132 %! x = rand (n, 1);
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133 %! b = A' * x;
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134 %! opts.UT = true;
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135 %! opts.TRANSA = true;
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136 %! assert (linsolve (A, b, opts), A' \ b);
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Nir Krakauer < nkrakauer@ccny.cuny.edu>
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137
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138 %!error linsolve ()
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139 %!error linsolve (1)
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140 %!error linsolve (1,2,3)
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141 %!error <A and B must be numeric> linsolve ({1},2)
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142 %!error <A and B must be numeric> linsolve (1,{2})
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Rik <rik@octave.org>
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143 %!error <OPTS must be a structure> linsolve (1,2,3)