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1 @c Copyright (C) 1996-2011 John W. Eaton |
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2 @c |
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3 @c This file is part of Octave. |
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4 @c |
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5 @c Octave is free software; you can redistribute it and/or modify it |
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6 @c under the terms of the GNU General Public License as published by the |
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7 @c Free Software Foundation; either version 3 of the License, or (at |
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8 @c your option) any later version. |
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9 @c |
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10 @c Octave is distributed in the hope that it will be useful, but WITHOUT |
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11 @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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12 @c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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13 @c for more details. |
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14 @c |
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15 @c You should have received a copy of the GNU General Public License |
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16 @c along with Octave; see the file COPYING. If not, see |
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17 @c <http://www.gnu.org/licenses/>. |
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18 |
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19 @node Matrix Factorizations, Ranges, Matrix and Vector Operations, Top |
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20 @chapter Matrix Factorizations |
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21 @cindex matrix factorizations |
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22 @cindex factorizations |
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23 |
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24 @deftypefn {} {} AEPBALANCE (void) |
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25 @deftypefnx {} {} AEPBALANCE (const Matrix &@var{a}, const char *@var{balance_job}) |
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26 @deftypefnx {} {} AEPBALANCE (const AEPBALANCE &@var{a}) |
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27 @end deftypefn |
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28 |
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29 @deftypefn {} AEPBALANCE& {operator =} (const AEPBALANCE &@var{a}) |
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30 @end deftypefn |
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31 |
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32 @deftypefn {} Matrix balanced_matrix (void) const |
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33 @deftypefnx {} Matrix balancing_matrix (void) const |
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34 @end deftypefn |
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35 |
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36 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const AEPBALANCE &@var{a}) |
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37 @end deftypefn |
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38 |
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39 @deftypefn {} {} ComplexAEPBALANCE (void) |
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40 @deftypefnx {} {} ComplexAEPBALANCE (const ComplexMatrix &@var{a}, const char *@var{balance_job}) |
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41 @deftypefnx {} {} ComplexAEPBALANCE (const ComplexAEPBALANCE &@var{a}) |
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42 @end deftypefn |
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43 |
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44 @deftypefn {} ComplexAEPBALANCE& {operator =} (const ComplexAEPBALANCE &@var{a}) |
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45 @end deftypefn |
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46 |
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47 @deftypefn {} ComplexMatrix balanced_matrix (void) const |
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48 @deftypefnx {} ComplexMatrix balancing_matrix (void) const |
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49 @end deftypefn |
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50 |
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51 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexAEPBALANCE &@var{a}) |
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52 @end deftypefn |
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53 |
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54 @deftypefn {} {} DET (void) |
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55 @deftypefnx {} {} DET (const DET &@var{a}) |
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56 @end deftypefn |
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57 |
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58 @deftypefn {} DET& {operator =} (const DET &@var{a}) |
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59 @end deftypefn |
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60 |
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61 @deftypefn {} int value_will_overflow (void) const |
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62 @deftypefnx {} int value_will_underflow (void) const |
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63 @end deftypefn |
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64 |
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65 @deftypefn {} double coefficient (void) const |
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66 @deftypefnx {} int exponent (void) const |
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67 @deftypefnx {} double value (void) const |
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68 @end deftypefn |
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69 |
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70 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const DET &@var{a}) |
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71 @end deftypefn |
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72 |
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73 @deftypefn {} {} ComplexDET (void) |
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74 @deftypefnx {} {} ComplexDET (const ComplexDET &@var{a}) |
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75 @end deftypefn |
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76 |
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77 @deftypefn {} ComplexDET& {operator =} (const ComplexDET &@var{a}) |
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78 @end deftypefn |
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79 |
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80 @deftypefn {} int value_will_overflow (void) const |
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81 @deftypefnx {} int value_will_underflow (void) const |
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82 @end deftypefn |
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83 |
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84 @deftypefn {} Complex coefficient (void) const |
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85 @deftypefnx {} int exponent (void) const |
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86 @deftypefnx {} Complex value (void) const |
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87 @end deftypefn |
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88 |
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89 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexDET &@var{a}) |
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90 @end deftypefn |
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91 |
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92 @deftypefn {} {} GEPBALANCE (void) |
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93 @deftypefnx {} {} GEPBALANCE (const Matrix &@var{a}, const Matrix &, const char *@var{balance_job}) |
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94 @deftypefnx {} {} GEPBALANCE (const GEPBALANCE &@var{a}) |
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95 @end deftypefn |
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96 |
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97 @deftypefn {} GEPBALANCE& {operator =} (const GEPBALANCE &@var{a}) |
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98 @end deftypefn |
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99 |
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100 @deftypefn {} Matrix balanced_a_matrix (void) const |
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101 @deftypefnx {} Matrix balanced_b_matrix (void) const |
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102 @deftypefnx {} Matrix left_balancing_matrix (void) const |
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103 @deftypefnx {} Matrix right_balancing_matrix (void) const |
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104 @end deftypefn |
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105 |
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106 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const GEPBALANCE &@var{a}) |
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107 @end deftypefn |
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108 |
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109 @deftypefn {} {} CHOL (void) |
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110 @deftypefnx {} {} CHOL (const Matrix &@var{a}) |
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111 @deftypefnx {} {} CHOL (const Matrix &@var{a}, int &@var{info}) |
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112 @deftypefnx {} {} CHOL (const CHOL &@var{a}) |
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113 @end deftypefn |
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114 |
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115 @deftypefn {} CHOL& {operator =} (const CHOL &@var{a}) |
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116 @end deftypefn |
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117 |
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118 @deftypefn {} Matrix chol_matrix (void) const |
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119 @end deftypefn |
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120 |
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121 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const CHOL &@var{a}) |
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122 @end deftypefn |
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123 |
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124 @deftypefn {} {} ComplexCHOL (void) |
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125 @deftypefnx {} {} ComplexCHOL (const ComplexMatrix &@var{a}) |
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126 @deftypefnx {} {} ComplexCHOL (const ComplexMatrix &@var{a}, int &@var{info}) |
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127 @deftypefnx {} {} ComplexCHOL (const ComplexCHOL &@var{a}) |
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128 @end deftypefn |
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129 |
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130 @deftypefn {} ComplexCHOL& {operator =} (const ComplexCHOL &@var{a}) |
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131 @end deftypefn |
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132 |
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133 @deftypefn {} ComplexMatrix chol_matrix (void) const |
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134 @end deftypefn |
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135 |
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136 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexCHOL &@var{a}) |
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137 @end deftypefn |
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138 |
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139 @deftypefn {} {} HESS (void) |
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140 @deftypefnx {} {} HESS (const Matrix &@var{a}) |
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141 @deftypefnx {} {} HESS (const Matrix&a, int &@var{info}) |
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142 @deftypefnx {} {} HESS (const HESS &@var{a}) |
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143 @end deftypefn |
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144 |
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145 @deftypefn {} HESS& {operator =} (const HESS &@var{a}) |
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146 @end deftypefn |
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147 |
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148 @deftypefn {} Matrix hess_matrix (void) const |
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149 @deftypefnx {} Matrix unitary_hess_matrix (void) const |
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150 @end deftypefn |
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151 |
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152 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const HESS &@var{a}) |
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153 @end deftypefn |
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154 |
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155 @deftypefn {} {} ComplexHESS (void) |
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156 @deftypefnx {} {} ComplexHESS (const ComplexMatrix &@var{a}) |
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157 @deftypefnx {} {} ComplexHESS (const ComplexMatrix &@var{a}, int &@var{info}) |
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158 @deftypefnx {} {} ComplexHESS (const ComplexHESS &@var{a}) |
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159 @end deftypefn |
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160 |
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161 @deftypefn {} ComplexHESS& {operator =} (const ComplexHESS &@var{a}) |
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162 @end deftypefn |
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163 |
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164 @deftypefn {} ComplexMatrix hess_matrix (void) const |
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165 @deftypefnx {} ComplexMatrix unitary_hess_matrix (void) const |
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166 @end deftypefn |
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167 |
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168 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexHESS &@var{a}) |
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169 @end deftypefn |
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170 |
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171 @deftypefn {} {} SCHUR (void) |
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172 @deftypefnx {} {} SCHUR (const Matrix &@var{a}, const char *@var{ord}) |
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173 @deftypefnx {} {} SCHUR (const Matrix &@var{a}, const char *@var{ord}, int &@var{info}) |
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174 @deftypefnx {} {} SCHUR (const SCHUR &@var{a}, const char *@var{ord}) |
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175 @end deftypefn |
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176 |
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177 @deftypefn {} SCHUR& {operator =} (const SCHUR &@var{a}) |
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178 @end deftypefn |
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179 |
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180 @deftypefn {} Matrix schur_matrix (void) const |
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181 @deftypefnx {} Matrix unitary_matrix (void) const |
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182 @end deftypefn |
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183 |
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184 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const SCHUR &@var{a}) |
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185 @end deftypefn |
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186 |
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187 @deftypefn {} {} ComplexSCHUR (void) |
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188 @deftypefnx {} {} ComplexSCHUR (const ComplexMatrix &@var{a}, const char *@var{ord}) |
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189 @deftypefnx {} {} ComplexSCHUR (const ComplexMatrix &@var{a}, const char *@var{ord}, int &@var{info}) |
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190 @deftypefnx {} {} ComplexSCHUR (const ComplexSCHUR &@var{a}, const char *@var{ord}) |
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191 @end deftypefn |
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192 |
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193 @deftypefn {} ComplexSCHUR& {operator =} (const ComplexSCHUR &@var{a}) |
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194 @end deftypefn |
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195 |
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196 @deftypefn {} ComplexMatrix schur_matrix (void) const |
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197 @deftypefnx {} ComplexMatrix unitary_matrix (void) const |
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198 @end deftypefn |
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199 |
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200 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexSCHUR &@var{a}) |
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201 @end deftypefn |
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202 |
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203 @deftypefn {} {} SVD (void) |
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204 @deftypefnx {} {} SVD (const Matrix &@var{a}) |
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205 @deftypefnx {} {} SVD (const Matrix &@var{a}, int &@var{info}) |
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206 @deftypefnx {} {} SVD (const SVD &@var{a}) |
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207 @end deftypefn |
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208 |
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209 @deftypefn {} SVD& {operator =} (const SVD &@var{a}) |
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210 @end deftypefn |
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211 |
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212 @deftypefn {} DiagMatrix singular_values (void) const |
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213 @deftypefnx {} Matrix left_singular_matrix (void) const |
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214 @deftypefnx {} Matrix right_singular_matrix (void) const |
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215 @end deftypefn |
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216 |
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217 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const SVD &@var{a}) |
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218 @end deftypefn |
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219 |
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220 @deftypefn {} {} ComplexSVD (void) |
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221 @deftypefnx {} {} ComplexSVD (const ComplexMatrix &@var{a}) |
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222 @deftypefnx {} {} ComplexSVD (const ComplexMatrix &@var{a}, int &@var{info}) |
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223 @deftypefnx {} {} ComplexSVD (const ComplexSVD &@var{a}) |
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224 @end deftypefn |
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225 |
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226 @deftypefn {} ComplexSVD& {operator =} (const ComplexSVD &@var{a}) |
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227 @end deftypefn |
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228 |
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229 @deftypefn {} DiagMatrix singular_values (void) const |
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230 @deftypefnx {} ComplexMatrix left_singular_matrix (void) const |
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231 @deftypefnx {} ComplexMatrix right_singular_matrix (void) const |
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232 @end deftypefn |
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233 |
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234 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexSVD &@var{a}) |
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235 @end deftypefn |
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236 |
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237 @deftypefn {} {} EIG (void) |
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238 @deftypefnx {} {} EIG (const Matrix &@var{a}) |
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239 @deftypefnx {} {} EIG (const Matrix &@var{a}, int &@var{info}) |
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240 @deftypefnx {} {} EIG (const ComplexMatrix &@var{a}) |
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241 @deftypefnx {} {} EIG (const ComplexMatrix &@var{a}, int &@var{info}) |
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242 @deftypefnx {} {} EIG (const EIG &@var{a}) |
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243 @end deftypefn |
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244 |
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245 @deftypefn {} EIG& {operator =} (const EIG &@var{a}) |
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246 @end deftypefn |
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247 |
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248 @deftypefn {} ComplexColumnVector eigenvalues (void) const |
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249 @end deftypefn |
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250 |
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251 @deftypefn {} ComplexMatrix eigenvectors (void) const |
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252 @end deftypefn |
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253 |
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254 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const EIG &@var{a}) |
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255 @end deftypefn |
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256 |
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257 @deftypefn {} {} LU (void) |
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258 @deftypefnx {} {} LU (const Matrix &@var{a}) |
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259 @deftypefnx {} {} LU (const LU &@var{a}) |
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260 @end deftypefn |
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261 |
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262 @deftypefn {} LU& {operator =} (const LU &@var{a}) |
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263 @end deftypefn |
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264 |
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265 @deftypefn {} Matrix L (void) const |
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266 @deftypefnx {} Matrix U (void) const |
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267 @deftypefnx {} Matrix P (void) const |
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268 @end deftypefn |
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269 |
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270 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const LU &@var{a}) |
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271 @end deftypefn |
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272 |
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273 @deftypefn {} {} ComplexLU (void) |
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274 @deftypefnx {} {} ComplexLU (const ComplexMatrix &@var{a}) |
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275 @deftypefnx {} {} ComplexLU (const ComplexLU &@var{a}) |
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276 @end deftypefn |
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277 |
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278 @deftypefn {} ComplexLU& {operator =} (const ComplexLU &@var{a}) |
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279 @end deftypefn |
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280 |
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281 @deftypefn {} ComplexMatrix L (void) const |
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282 @deftypefnx {} ComplexMatrix U (void) const |
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283 @deftypefnx {} Matrix P (void) const |
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284 @end deftypefn |
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285 |
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286 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexLU &@var{a}) |
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287 @end deftypefn |
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288 |
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289 @deftypefn {} {} QR (void) |
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290 @deftypefnx {} {} QR (const Matrix &@var{A}) |
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291 @deftypefnx {} {} QR (const QR &@var{a}) |
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292 @end deftypefn |
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293 |
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294 @deftypefn {} QR& {operator =} (const QR &@var{a}) |
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295 @end deftypefn |
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296 |
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297 @deftypefn {} Matrix Q (void) const |
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298 @deftypefnx {} Matrix R (void) const |
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299 @end deftypefn |
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300 |
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301 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const QR &@var{a}) |
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302 @end deftypefn |
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303 |
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304 @deftypefn {} {} ComplexQR (void) |
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305 @deftypefnx {} {} ComplexQR (const ComplexMatrix &@var{A}) |
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306 @deftypefnx {} {} ComplexQR (const ComplexQR &@var{a}) |
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307 @end deftypefn |
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308 |
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309 @deftypefn {} ComplexQR& {operator =} (const ComplexQR &@var{a}) |
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310 @end deftypefn |
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311 |
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312 @deftypefn {} ComplexMatrix Q (void) const |
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313 @deftypefnx {} ComplexMatrix R (void) const |
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314 @end deftypefn |
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315 |
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316 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexQR &@var{a}) |
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317 @end deftypefn |
