Mercurial > octave
annotate libinterp/corefcn/matrix_type.cc @ 30564:796f54d4ddbf stable
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> |
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date | Tue, 28 Dec 2021 18:22:40 -0500 |
parents | 32c3a5805893 |
children | 83f9f8bda883 |
rev | line source |
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 2005-2022 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 //////////////////////////////////////////////////////////////////////// |
5323 | 25 |
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26 #if defined (HAVE_CONFIG_H) |
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27 # include "config.h" |
5323 | 28 #endif |
29 | |
5403 | 30 #include <algorithm> |
31 | |
5323 | 32 #include "ov.h" |
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33 #include "defun.h" |
5323 | 34 #include "error.h" |
5785 | 35 #include "ov-re-mat.h" |
36 #include "ov-cx-mat.h" | |
5323 | 37 #include "ov-re-sparse.h" |
38 #include "ov-cx-sparse.h" | |
5785 | 39 #include "MatrixType.h" |
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40 #include "oct-locbuf.h" |
5323 | 41 |
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42 OCTAVE_NAMESPACE_BEGIN |
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43 |
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44 DEFUN (matrix_type, args, , |
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45 doc: /* -*- texinfo -*- |
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46 @deftypefn {} {@var{type} =} matrix_type (@var{A}) |
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47 @deftypefnx {} {@var{type} =} matrix_type (@var{A}, "nocompute") |
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48 @deftypefnx {} {@var{A} =} matrix_type (@var{A}, @var{type}) |
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49 @deftypefnx {} {@var{A} =} matrix_type (@var{A}, "upper", @var{perm}) |
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50 @deftypefnx {} {@var{A} =} matrix_type (@var{A}, "lower", @var{perm}) |
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51 @deftypefnx {} {@var{A} =} matrix_type (@var{A}, "banded", @var{nl}, @var{nu}) |
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52 Identify the matrix type or mark a matrix as a particular type. |
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53 |
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54 This allows more rapid solutions of linear equations involving @var{A} to be |
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55 performed. |
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56 |
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57 Called with a single argument, @code{matrix_type} returns the type of the |
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58 matrix and caches it for future use. |
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59 |
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60 Called with more than one argument, @code{matrix_type} allows the type of |
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61 the matrix to be defined. |
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62 |
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63 If the option @qcode{"nocompute"} is given, the function will not attempt |
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64 to guess the type if it is still unknown. This is useful for debugging |
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65 purposes. |
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66 |
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67 The possible matrix types depend on whether the matrix is full or sparse, |
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68 and can be one of the following |
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69 |
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70 @table @asis |
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71 @item @qcode{"unknown"} |
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72 Remove any previously cached matrix type, and mark type as unknown. |
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73 |
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74 @item @qcode{"full"} |
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75 Mark the matrix as full. |
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76 |
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77 @item @qcode{"positive definite"} |
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78 Probable full positive definite matrix. |
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79 |
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80 @item @qcode{"diagonal"} |
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81 Diagonal matrix. (Sparse matrices only) |
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82 |
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83 @item @qcode{"permuted diagonal"} |
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84 Permuted Diagonal matrix. The permutation does not need to be specifically |
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85 indicated, as the structure of the matrix explicitly gives this. (Sparse |
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86 matrices only) |
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87 |
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88 @item @qcode{"upper"} |
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89 Upper triangular. If the optional third argument @var{perm} is given, the |
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90 matrix is assumed to be a permuted upper triangular with the permutations |
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91 defined by the vector @var{perm}. |
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92 |
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93 @item @qcode{"lower"} |
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94 Lower triangular. If the optional third argument @var{perm} is given, the |
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95 matrix is assumed to be a permuted lower triangular with the permutations |
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96 defined by the vector @var{perm}. |
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97 |
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98 @item @qcode{"banded"} |
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99 @itemx @qcode{"banded positive definite"} |
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100 Banded matrix with the band size of @var{nl} below the diagonal and @var{nu} |
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101 above it. If @var{nl} and @var{nu} are 1, then the matrix is tridiagonal |
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102 and treated with specialized code. In addition the matrix can be marked as |
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103 probably a positive definite. (Sparse matrices only) |
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104 |
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105 @item @qcode{"singular"} |
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106 The matrix is assumed to be singular and will be treated with a minimum norm |
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107 solution. |
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108 |
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109 @end table |
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110 |
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111 Note that the matrix type will be discovered automatically on the first |
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112 attempt to solve a linear equation involving @var{A}. Therefore |
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113 @code{matrix_type} is only useful to give Octave hints of the matrix type. |
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114 Incorrectly defining the matrix type will result in incorrect results from |
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115 solutions of linear equations; it is entirely @strong{the responsibility of |
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116 the user} to correctly identify the matrix type. |
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117 |
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118 Also, the test for positive definiteness is a low-cost test for a Hermitian |
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119 matrix with a real positive diagonal. This does not guarantee that the |
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120 matrix is positive definite, but only that it is a probable candidate. When |
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121 such a matrix is factorized, a Cholesky@tie{}factorization is first |
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122 attempted, and if that fails the matrix is then treated with an |
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123 LU@tie{}factorization. Once the matrix has been factorized, |
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124 @code{matrix_type} will return the correct classification of the matrix. |
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125 @end deftypefn */) |
5323 | 126 { |
127 int nargin = args.length (); | |
128 | |
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129 if (nargin == 0 || nargin > 4) |
5823 | 130 print_usage (); |
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131 |
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132 bool autocomp = true; |
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133 if (nargin == 2 && args(1).is_string () |
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134 && args(1).string_value () == "nocompute") |
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135 { |
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136 nargin = 1; |
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137 autocomp = false; |
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138 } |
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139 |
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140 octave_value retval; |
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141 |
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142 if (args(0).is_scalar_type ()) |
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143 { |
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144 if (nargin == 1) |
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145 retval = octave_value ("Diagonal"); |
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146 else |
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147 retval = args(0); |
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148 } |
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149 else if (args(0).issparse ()) |
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150 { |
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151 if (nargin == 1) |
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152 { |
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153 MatrixType mattyp; |
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154 |
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155 if (args(0).iscomplex ()) |
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156 { |
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157 mattyp = args(0).matrix_type (); |
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158 |
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159 if (mattyp.is_unknown () && autocomp) |
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160 { |
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161 SparseComplexMatrix m |
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162 = args(0).sparse_complex_matrix_value (); |
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163 |
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164 mattyp = MatrixType (m); |
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165 args(0).matrix_type (mattyp); |
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166 } |
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167 } |
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168 else |
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169 { |
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170 mattyp = args(0).matrix_type (); |
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171 |
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172 if (mattyp.is_unknown () && autocomp) |
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173 { |
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174 SparseMatrix m = args(0).sparse_matrix_value (); |
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175 |
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176 mattyp = MatrixType (m); |
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177 args(0).matrix_type (mattyp); |
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178 } |
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179 } |
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180 |
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181 int typ = mattyp.type (); |
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182 |
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183 if (typ == MatrixType::Diagonal) |
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184 retval = octave_value ("Diagonal"); |
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185 else if (typ == MatrixType::Permuted_Diagonal) |
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186 retval = octave_value ("Permuted Diagonal"); |
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187 else if (typ == MatrixType::Upper) |
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188 retval = octave_value ("Upper"); |
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189 else if (typ == MatrixType::Permuted_Upper) |
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190 retval = octave_value ("Permuted Upper"); |
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191 else if (typ == MatrixType::Lower) |
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192 retval = octave_value ("Lower"); |
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193 else if (typ == MatrixType::Permuted_Lower) |
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194 retval = octave_value ("Permuted Lower"); |
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195 else if (typ == MatrixType::Banded) |
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196 retval = octave_value ("Banded"); |
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197 else if (typ == MatrixType::Banded_Hermitian) |
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198 retval = octave_value ("Banded Positive Definite"); |
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199 else if (typ == MatrixType::Tridiagonal) |
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200 retval = octave_value ("Tridiagonal"); |
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201 else if (typ == MatrixType::Tridiagonal_Hermitian) |
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202 retval = octave_value ("Tridiagonal Positive Definite"); |
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203 else if (typ == MatrixType::Hermitian) |
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204 retval = octave_value ("Positive Definite"); |
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205 else if (typ == MatrixType::Rectangular) |
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206 { |
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207 if (args(0).rows () == args(0).columns ()) |
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208 retval = octave_value ("Singular"); |
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209 else |
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210 retval = octave_value ("Rectangular"); |
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211 } |
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212 else if (typ == MatrixType::Full) |
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213 retval = octave_value ("Full"); |
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214 else |
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215 retval = octave_value ("Unknown"); |
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216 } |
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217 else |
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218 { |
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219 // Ok, we're changing the matrix type |
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220 std::string str_typ = args(1).xstring_value ("matrix_type: TYPE must be a string"); |
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221 |
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222 // FIXME: why do I have to explicitly call the constructor? |
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223 MatrixType mattyp = MatrixType (); |
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224 |
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225 octave_idx_type nl = 0; |
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226 octave_idx_type nu = 0; |
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227 |
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228 // Use STL function to convert to lower case |
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229 std::transform (str_typ.begin (), str_typ.end (), |
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230 str_typ.begin (), tolower); |
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231 |
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232 if (str_typ == "diagonal") |
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233 mattyp.mark_as_diagonal (); |
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234 if (str_typ == "permuted diagonal") |
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235 mattyp.mark_as_permuted_diagonal (); |
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236 else if (str_typ == "upper") |
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237 mattyp.mark_as_upper_triangular (); |
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238 else if (str_typ == "lower") |
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239 mattyp.mark_as_lower_triangular (); |
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240 else if (str_typ == "banded" |
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241 || str_typ == "banded positive definite") |
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242 { |
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243 if (nargin != 4) |
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244 error ("matrix_type: banded matrix type requires 4 arguments"); |
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245 |
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246 nl = args(2).xnint_value ("matrix_type: band size NL, NU must be integers"); |
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247 nu = args(3).xnint_value ("matrix_type: band size NL, NU must be integers"); |
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248 |
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249 if (nl == 1 && nu == 1) |
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250 mattyp.mark_as_tridiagonal (); |
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251 else |
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252 mattyp.mark_as_banded (nu, nl); |
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253 |
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254 if (str_typ == "banded positive definite") |
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255 mattyp.mark_as_symmetric (); |
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256 } |
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257 else if (str_typ == "positive definite") |
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258 { |
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259 mattyp.mark_as_full (); |
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260 mattyp.mark_as_symmetric (); |
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261 } |
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262 else if (str_typ == "singular") |
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263 mattyp.mark_as_rectangular (); |
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264 else if (str_typ == "full") |
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265 mattyp.mark_as_full (); |
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266 else if (str_typ == "unknown") |
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267 mattyp.invalidate_type (); |
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268 else |
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269 error ("matrix_type: Unknown matrix type %s", str_typ.c_str ()); |
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270 |
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271 if (nargin == 3 |
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272 && (str_typ == "upper" || str_typ == "lower")) |
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273 { |
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274 const ColumnVector perm = args(2).xvector_value ("matrix_type: Invalid permutation vector PERM"); |
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275 |
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276 octave_idx_type len = perm.numel (); |
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277 dim_vector dv = args(0).dims (); |
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278 |
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279 if (len != dv(0)) |
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280 error ("matrix_type: Invalid permutation vector PERM"); |
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281 |
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282 OCTAVE_LOCAL_BUFFER (octave_idx_type, p, len); |
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283 |
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284 for (octave_idx_type i = 0; i < len; i++) |
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285 p[i] = static_cast<octave_idx_type> (perm (i)) - 1; |
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286 |
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287 mattyp.mark_as_permuted (len, p); |
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288 } |
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289 else if (nargin != 2 |
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290 && str_typ != "banded positive definite" |
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291 && str_typ != "banded") |
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292 error ("matrix_type: Invalid number of arguments"); |
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293 |
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294 // Set the matrix type |
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295 if (args(0).iscomplex ()) |
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296 retval = octave_value (args(0).sparse_complex_matrix_value (), |
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297 mattyp); |
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298 else |
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299 retval = octave_value (args(0).sparse_matrix_value (), |
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300 mattyp); |
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301 } |
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302 } |
5323 | 303 else |
304 { | |
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305 if (nargin == 1) |
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306 { |
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307 MatrixType mattyp; |
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308 |
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309 if (args(0).iscomplex ()) |
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310 { |
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311 mattyp = args(0).matrix_type (); |
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313 if (mattyp.is_unknown () && autocomp) |
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314 { |
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315 if (args(0).is_single_type ()) |
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316 { |
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317 FloatComplexMatrix m; |
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318 m = args(0).float_complex_matrix_value (); |
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319 |
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320 mattyp = MatrixType (m); |
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321 args(0).matrix_type (mattyp); |
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322 } |
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323 else |
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324 { |
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325 ComplexMatrix m = args(0).complex_matrix_value (); |
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326 |
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327 mattyp = MatrixType (m); |
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328 args(0).matrix_type (mattyp); |
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329 } |
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330 } |
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331 } |
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332 else |
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333 { |
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334 mattyp = args(0).matrix_type (); |
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335 |
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336 if (mattyp.is_unknown () && autocomp) |
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337 { |
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338 if (args(0).is_single_type ()) |
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339 { |
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340 FloatMatrix m = args(0).float_matrix_value (); |
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341 |
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342 mattyp = MatrixType (m); |
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343 args(0).matrix_type (mattyp); |
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344 } |
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345 else |
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346 { |
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347 Matrix m = args(0).matrix_value (); |
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349 mattyp = MatrixType (m); |
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350 args(0).matrix_type (mattyp); |
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351 } |
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352 } |
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353 } |
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354 |
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355 int typ = mattyp.type (); |
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356 |
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357 if (typ == MatrixType::Upper) |
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358 retval = octave_value ("Upper"); |
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359 else if (typ == MatrixType::Permuted_Upper) |
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360 retval = octave_value ("Permuted Upper"); |
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361 else if (typ == MatrixType::Lower) |
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362 retval = octave_value ("Lower"); |
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363 else if (typ == MatrixType::Permuted_Lower) |
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364 retval = octave_value ("Permuted Lower"); |
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365 else if (typ == MatrixType::Hermitian) |
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366 retval = octave_value ("Positive Definite"); |
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367 else if (typ == MatrixType::Rectangular) |
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368 { |
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369 if (args(0).rows () == args(0).columns ()) |
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370 retval = octave_value ("Singular"); |
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371 else |
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372 retval = octave_value ("Rectangular"); |
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373 } |
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374 else if (typ == MatrixType::Full) |
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375 retval = octave_value ("Full"); |
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376 else |
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377 retval = octave_value ("Unknown"); |
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378 } |
5323 | 379 else |
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380 { |
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381 // Ok, we're changing the matrix type |
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382 std::string str_typ = args(1).xstring_value ("matrix_type: TYPE must be a string"); |
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384 // FIXME: why do I have to explicitly call the constructor? |
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385 MatrixType mattyp = MatrixType (MatrixType::Unknown, true); |
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386 |
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387 // Use STL function to convert to lower case |
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388 std::transform (str_typ.begin (), str_typ.end (), |
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389 str_typ.begin (), tolower); |
5785 | 390 |
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391 if (str_typ == "upper") |
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392 mattyp.mark_as_upper_triangular (); |
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393 else if (str_typ == "lower") |
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394 mattyp.mark_as_lower_triangular (); |
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395 else if (str_typ == "positive definite") |
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396 { |
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397 mattyp.mark_as_full (); |
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398 mattyp.mark_as_symmetric (); |
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399 } |
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400 else if (str_typ == "singular") |
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401 mattyp.mark_as_rectangular (); |
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402 else if (str_typ == "full") |
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403 mattyp.mark_as_full (); |
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404 else if (str_typ == "unknown") |
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405 mattyp.invalidate_type (); |
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406 else |
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407 error ("matrix_type: Unknown matrix type %s", str_typ.c_str ()); |
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408 |
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409 if (nargin == 3 && (str_typ == "upper" || str_typ == "lower")) |
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410 { |
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411 const ColumnVector perm = args(2).xvector_value ("matrix_type: Invalid permutation vector PERM"); |
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412 |
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413 octave_idx_type len = perm.numel (); |
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414 dim_vector dv = args(0).dims (); |
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415 |
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416 if (len != dv(0)) |
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417 error ("matrix_type: Invalid permutation vector PERM"); |
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418 |
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419 OCTAVE_LOCAL_BUFFER (octave_idx_type, p, len); |
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420 |
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421 for (octave_idx_type i = 0; i < len; i++) |
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422 p[i] = static_cast<octave_idx_type> (perm (i)) - 1; |
5785 | 423 |
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424 mattyp.mark_as_permuted (len, p); |
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425 } |
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426 else if (nargin != 2) |
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427 error ("matrix_type: Invalid number of arguments"); |
5785 | 428 |
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429 // Set the matrix type |
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430 if (args(0).is_single_type ()) |
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431 { |
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432 if (args(0).iscomplex ()) |
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433 retval = octave_value (args(0).float_complex_matrix_value (), |
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434 mattyp); |
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435 else |
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436 retval = octave_value (args(0).float_matrix_value (), |
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437 mattyp); |
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438 } |
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439 else |
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440 { |
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441 if (args(0).iscomplex ()) |
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442 retval = octave_value (args(0).complex_matrix_value (), |
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443 mattyp); |
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444 else |
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445 retval = octave_value (args(0).matrix_value (), mattyp); |
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446 } |
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447 } |
5323 | 448 } |
449 | |
450 return retval; | |
451 } | |
452 | |
453 /* | |
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454 ## FIXME: |
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455 ## Disable tests for lower under-determined and upper over-determined |
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456 ## matrices as this detection is disabled in MatrixType due to issues |
5681 | 457 ## of non minimum norm solution being found. |
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458 |
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459 %!assert (matrix_type (speye (10,10)), "Diagonal") |
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460 %!assert (matrix_type (speye (10,10)([2:10,1],:)), "Permuted Diagonal") |
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461 %!assert (matrix_type ([[speye(10,10);sparse(1,10)],[1;sparse(9,1);1]]), "Upper") |
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462 %!assert (matrix_type ([[speye(10,10);sparse(1,10)],[1;sparse(9,1);1]](:,[2,1,3:11])), "Permuted Upper") |
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463 %!assert (matrix_type ([speye(10,10),sparse(10,1);1,sparse(1,9),1]), "Lower") |
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464 %!assert (matrix_type ([speye(10,10),sparse(10,1);1,sparse(1,9),1]([2,1,3:11],:)), "Permuted Lower") |
5610 | 465 |
466 %!test | |
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467 %! bnd = spparms ("bandden"); |
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468 %! spparms ("bandden", 0.5); |
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469 %! a = spdiags (rand (10,3)-0.5,[-1,0,1],10,10); |
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470 %! assert (matrix_type (a), "Tridiagonal"); |
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471 %! assert (matrix_type (a'+a+2*speye (10)), "Tridiagonal Positive Definite"); |
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472 %! spparms ("bandden", bnd); |
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473 %!test |
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474 %! bnd=spparms ("bandden"); |
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475 %! spparms ("bandden", 0.5); |
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476 %! a = spdiags (randn (10,4),[-2:1],10,10); |
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477 %! assert (matrix_type (a), "Banded"); |
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478 %! assert (matrix_type (a'*a), "Banded Positive Definite"); |
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479 %! spparms ("bandden", bnd); |
5610 | 480 %!test |
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481 %! a = [speye(10,10),[sparse(9,1);1];-1,sparse(1,9),1]; |
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482 %! assert (matrix_type (a), "Full"); |
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483 %! assert (matrix_type (a'*a), "Positive Definite"); |
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484 |
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485 %!assert (matrix_type (speye (10,11)), "Diagonal") |
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486 %!assert (matrix_type (speye (10,11)([2:10,1],:)), "Permuted Diagonal") |
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487 %!assert (matrix_type (speye (11,10)), "Diagonal") |
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488 %!assert (matrix_type (speye (11,10)([2:11,1],:)), "Permuted Diagonal") |
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489 %#!assert (matrix_type ([[speye(10,10);sparse(1,10)],[[1,1];sparse(9,2);[1,1]]]), "Upper") |
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490 %#!assert (matrix_type ([[speye(10,10);sparse(1,10)],[[1,1];sparse(9,2);[1,1]]](:,[2,1,3:12])), "Permuted Upper") |
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491 %!assert (matrix_type ([speye(11,9),[1;sparse(8,1);1;0]]), "Upper") |
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492 %!assert (matrix_type ([speye(11,9),[1;sparse(8,1);1;0]](:,[2,1,3:10])), "Permuted Upper") |
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493 %#!assert (matrix_type ([speye(10,10),sparse(10,1);[1;1],sparse(2,9),[1;1]]), "Lower") |
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494 %#!assert (matrix_type ([speye(10,10),sparse(10,1);[1;1],sparse(2,9),[1;1]]([2,1,3:12],:)), "Permuted Lower") |
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495 %!assert (matrix_type ([speye(9,11);[1,sparse(1,8),1,0]]), "Lower") |
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496 %!assert (matrix_type ([speye(9,11);[1,sparse(1,8),1,0]]([2,1,3:10],:)), "Permuted Lower") |
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497 %!assert (matrix_type (spdiags (randn (10,4),[-2:1],10,9)), "Rectangular") |
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498 |
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499 %!assert (matrix_type (1i*speye (10,10)), "Diagonal") |
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500 %!assert (matrix_type (1i*speye (10,10)([2:10,1],:)), "Permuted Diagonal") |
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501 %!assert (matrix_type ([[speye(10,10);sparse(1,10)],[1i;sparse(9,1);1]]), "Upper") |
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502 %!assert (matrix_type ([[speye(10,10);sparse(1,10)],[1i;sparse(9,1);1]](:,[2,1,3:11])), "Permuted Upper") |
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503 %!assert (matrix_type ([speye(10,10),sparse(10,1);1i,sparse(1,9),1]), "Lower") |
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504 %!assert (matrix_type ([speye(10,10),sparse(10,1);1i,sparse(1,9),1]([2,1,3:11],:)), "Permuted Lower") |
5610 | 505 |
506 %!test | |
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507 %! bnd = spparms ("bandden"); |
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508 %! spparms ("bandden", 0.5); |
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509 %! assert (matrix_type (spdiags (1i*randn (10,3),[-1,0,1],10,10)), "Tridiagonal"); |
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510 %! a = 1i*(rand (9,1)-0.5); |
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511 %! a = [[a;0],ones(10,1),[0;-a]]; |
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512 %! assert (matrix_type (spdiags (a,[-1,0,1],10,10)), "Tridiagonal Positive Definite"); |
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513 %! spparms ("bandden", bnd); |
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514 %!test |
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515 %! bnd = spparms ("bandden"); |
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516 %! spparms ("bandden", 0.5); |
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517 %! assert (matrix_type (spdiags (1i*randn (10,4),[-2:1],10,10)), "Banded"); |
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518 %! a = 1i*(rand (9,2)-0.5); |
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519 %! a = [[a;[0,0]],ones(10,1),[[0;-a(:,2)],[0;0;-a(1:8,1)]]]; |
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520 %! assert (matrix_type (spdiags (a,[-2:2],10,10)), "Banded Positive Definite"); |
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521 %! spparms ("bandden", bnd); |
5785 | 522 %!test |
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523 %! a = [speye(10,10),[sparse(9,1);1i];-1,sparse(1,9),1]; |
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524 %! assert (matrix_type (a), "Full"); |
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525 %! assert (matrix_type (a'*a), "Positive Definite"); |
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526 |
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527 %!assert (matrix_type (1i*speye (10,11)), "Diagonal") |
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528 %!assert (matrix_type (1i*speye (10,11)([2:10,1],:)), "Permuted Diagonal") |
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529 %!assert (matrix_type (1i*speye (11,10)), "Diagonal") |
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530 %!assert (matrix_type (1i*speye (11,10)([2:11,1],:)), "Permuted Diagonal") |
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531 %#!assert (matrix_type ([[speye(10,10);sparse(1,10)],[[1i,1i];sparse(9,2);[1i,1i]]]), "Upper") |
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532 %#!assert (matrix_type ([[speye(10,10);sparse(1,10)],[[1i,1i];sparse(9,2);[1i,1i]]](:,[2,1,3:12])), "Permuted Upper") |
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533 %!assert (matrix_type ([speye(11,9),[1i;sparse(8,1);1i;0]]), "Upper") |
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534 %!assert (matrix_type ([speye(11,9),[1i;sparse(8,1);1i;0]](:,[2,1,3:10])), "Permuted Upper") |
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535 %#!assert (matrix_type ([speye(10,10),sparse(10,1);[1i;1i],sparse(2,9),[1i;1i]]), "Lower") |
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536 %#!assert (matrix_type ([speye(10,10),sparse(10,1);[1i;1i],sparse(2,9),[1i;1i]]([2,1,3:12],:)), "Permuted Lower") |
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537 %!assert (matrix_type ([speye(9,11);[1i,sparse(1,8),1i,0]]), "Lower") |
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538 %!assert (matrix_type ([speye(9,11);[1i,sparse(1,8),1i,0]]([2,1,3:10],:)), "Permuted Lower") |
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539 %!assert (matrix_type (1i*spdiags(randn(10,4),[-2:1],10,9)), "Rectangular") |
5785 | 540 |
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541 %!test |
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542 %! a = matrix_type (spdiags (randn (10,3),[-1,0,1],10,10), "Singular"); |
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543 %! assert (matrix_type (a), "Singular"); |
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544 |
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545 %!assert (matrix_type (triu (ones (10,10))), "Upper") |
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546 %!assert (matrix_type (triu (ones (10,10),-1)), "Full") |
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547 %!assert (matrix_type (tril (ones (10,10))), "Lower") |
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548 %!assert (matrix_type (tril (ones (10,10),1)), "Full") |
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549 %!assert (matrix_type (10*eye (10,10) + ones (10,10)), "Positive Definite") |
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550 %!assert (matrix_type (ones (11,10)), "Rectangular") |
5785 | 551 %!test |
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552 %! a = matrix_type (ones (10,10), "Singular"); |
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553 %! assert (matrix_type (a), "Singular"); |
5785 | 554 |
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555 %!assert (matrix_type (triu (1i*ones (10,10))), "Upper") |
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556 %!assert (matrix_type (triu (1i*ones (10,10),-1)), "Full") |
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557 %!assert (matrix_type (tril (1i*ones (10,10))), "Lower") |
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558 %!assert (matrix_type (tril (1i*ones (10,10),1)), "Full") |
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559 %!assert (matrix_type (10*eye (10,10) + 1i*triu (ones (10,10),1) -1i*tril (ones (10,10),-1)), "Positive Definite") |
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560 %!assert (matrix_type (ones (11,10)), "Rectangular") |
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561 %!test |
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562 %! a = matrix_type (ones (10,10), "Singular"); |
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563 %! assert (matrix_type (a), "Singular"); |
5610 | 564 */ |
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565 |
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566 OCTAVE_NAMESPACE_END |