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1 @node Matrix Factorizations, Ranges, Matrix and Vector Operations, Top |
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2333
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2 @chapter Matrix Factorizations |
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3 @cindex matrix factorizations |
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4 @cindex factorizations |
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5 |
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6 @deftypefn {} {}AEPBALANCE (void) |
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7 @deftypefnx {} {}AEPBALANCE (const Matrix &@var{a}, const char *@var{balance_job}) |
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8 @deftypefnx {} {}AEPBALANCE (const AEPBALANCE &@var{a}) |
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9 @end deftypefn |
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10 |
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11 @deftypefn {} AEPBALANCE& {operator =} (const AEPBALANCE &@var{a}) |
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12 @end deftypefn |
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13 |
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14 @deftypefn {} Matrix balanced_matrix (void) const |
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15 @deftypefnx {} Matrix balancing_matrix (void) const |
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16 @end deftypefn |
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17 |
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18 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const AEPBALANCE &@var{a}) |
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19 @end deftypefn |
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20 |
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21 @deftypefn {} ComplexAEPBALANCE (void) |
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22 @deftypefnx {} ComplexAEPBALANCE (const ComplexMatrix &@var{a}, const char *@var{balance_job}) |
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23 @deftypefnx {} ComplexAEPBALANCE (const ComplexAEPBALANCE &@var{a}) |
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24 @end deftypefn |
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25 |
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26 @deftypefn {} ComplexAEPBALANCE& {operator =} (const ComplexAEPBALANCE &@var{a}) |
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27 @end deftypefn |
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28 |
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29 @deftypefn {} ComplexMatrix balanced_matrix (void) const |
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30 @deftypefnx {} ComplexMatrix balancing_matrix (void) const |
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31 @end deftypefn |
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32 |
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33 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexAEPBALANCE &@var{a}) |
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34 @end deftypefn |
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35 |
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36 @deftypefn {} {}DET (void) |
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37 @deftypefnx {} {}DET (const DET &@var{a}) |
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38 @end deftypefn |
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39 |
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40 @deftypefn {} DET& {operator =} (const DET &@var{a}) |
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41 @end deftypefn |
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42 |
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43 @deftypefn {} int value_will_overflow (void) const |
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44 @deftypefnx {} int value_will_underflow (void) const |
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45 @end deftypefn |
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46 |
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47 @deftypefn {} double coefficient (void) const |
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48 @deftypefnx {} int exponent (void) const |
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49 @deftypefnx {} double value (void) const |
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50 @end deftypefn |
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51 |
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52 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const DET &@var{a}) |
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53 @end deftypefn |
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54 |
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55 @deftypefn {} {}ComplexDET (void) |
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56 @deftypefnx {} {}ComplexDET (const ComplexDET &@var{a}) |
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57 @end deftypefn |
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58 |
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59 @deftypefn {} ComplexDET& {operator =} (const ComplexDET &@var{a}) |
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60 @end deftypefn |
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61 |
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62 @deftypefn {} int value_will_overflow (void) const |
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63 @deftypefnx {} int value_will_underflow (void) const |
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64 @end deftypefn |
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65 |
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66 @deftypefn {} Complex coefficient (void) const |
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67 @deftypefnx {} int exponent (void) const |
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68 @deftypefnx {} Complex value (void) const |
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69 @end deftypefn |
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70 |
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71 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexDET &@var{a}) |
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72 @end deftypefn |
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73 |
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74 @deftypefn {} {}GEPBALANCE (void) |
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75 @deftypefnx {} {}GEPBALANCE (const Matrix &@var{a}, const Matrix &, const char *@var{balance_job}) |
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76 @deftypefnx {} {}GEPBALANCE (const GEPBALANCE &@var{a}) |
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77 @end deftypefn |
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78 |
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79 @deftypefn {} GEPBALANCE& {operator =} (const GEPBALANCE &@var{a}) |
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80 @end deftypefn |
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81 |
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82 @deftypefn {} Matrix balanced_a_matrix (void) const |
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83 @deftypefnx {} Matrix balanced_b_matrix (void) const |
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84 @deftypefnx {} Matrix left_balancing_matrix (void) const |
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85 @deftypefnx {} Matrix right_balancing_matrix (void) const |
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86 @end deftypefn |
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87 |
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88 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const GEPBALANCE &@var{a}) |
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89 @end deftypefn |
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90 |
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91 @deftypefn {} {}CHOL (void) |
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92 @deftypefnx {} {}CHOL (const Matrix &@var{a}) |
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93 @deftypefnx {} {}CHOL (const Matrix &@var{a}, int &@var{info}) |
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94 @deftypefnx {} {}CHOL (const CHOL &@var{a}) |
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95 @end deftypefn |
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96 |
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97 @deftypefn {} CHOL& {operator =} (const CHOL &@var{a}) |
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98 @end deftypefn |
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99 |
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100 @deftypefn {} Matrix chol_matrix (void) const |
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101 @end deftypefn |
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102 |
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103 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const CHOL &@var{a}) |
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104 @end deftypefn |
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105 |
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106 @deftypefn {} {}ComplexCHOL (void) |
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107 @deftypefnx {} {}ComplexCHOL (const ComplexMatrix &@var{a}) |
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108 @deftypefnx {} {}ComplexCHOL (const ComplexMatrix &@var{a}, int &@var{info}) |
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109 @deftypefnx {} {}ComplexCHOL (const ComplexCHOL &@var{a}) |
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110 @end deftypefn |
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111 |
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112 @deftypefn {} ComplexCHOL& {operator =} (const ComplexCHOL &@var{a}) |
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113 @end deftypefn |
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114 |
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115 @deftypefn {} ComplexMatrix chol_matrix (void) const |
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116 @end deftypefn |
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117 |
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118 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexCHOL &@var{a}) |
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119 @end deftypefn |
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120 |
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121 @deftypefn {} {}HESS (void) |
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122 @deftypefnx {} {}HESS (const Matrix &@var{a}) |
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123 @deftypefnx {} {}HESS (const Matrix&a, int &@var{info}) |
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124 @deftypefnx {} {}HESS (const HESS &@var{a}) |
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125 @end deftypefn |
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126 |
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127 @deftypefn {} HESS& {operator =} (const HESS &@var{a}) |
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128 @end deftypefn |
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129 |
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130 @deftypefn {} Matrix hess_matrix (void) const |
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131 @deftypefnx {} Matrix unitary_hess_matrix (void) const |
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132 @end deftypefn |
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133 |
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134 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const HESS &@var{a}) |
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135 @end deftypefn |
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136 |
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137 @deftypefn {} {}ComplexHESS (void) |
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138 @deftypefnx {} {}ComplexHESS (const ComplexMatrix &@var{a}) |
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139 @deftypefnx {} {}ComplexHESS (const ComplexMatrix &@var{a}, int &@var{info}) |
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140 @deftypefnx {} {}ComplexHESS (const ComplexHESS &@var{a}) |
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141 @end deftypefn |
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142 |
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143 @deftypefn {} ComplexHESS& {operator =} (const ComplexHESS &@var{a}) |
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144 @end deftypefn |
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145 |
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146 @deftypefn {} ComplexMatrix hess_matrix (void) const |
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147 @deftypefnx {} ComplexMatrix unitary_hess_matrix (void) const |
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148 @end deftypefn |
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149 |
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150 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexHESS &@var{a}) |
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151 @end deftypefn |
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152 |
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153 @deftypefn {} {}SCHUR (void) |
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154 @deftypefnx {} {}SCHUR (const Matrix &@var{a}, const char *@var{ord}) |
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155 @deftypefnx {} {}SCHUR (const Matrix &@var{a}, const char *@var{ord}, int &@var{info}) |
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156 @deftypefnx {} {}SCHUR (const SCHUR &@var{a}, const char *@var{ord}) |
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157 @end deftypefn |
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158 |
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159 @deftypefn {} SCHUR& {operator =} (const SCHUR &@var{a}) |
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160 @end deftypefn |
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161 |
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162 @deftypefn {} Matrix schur_matrix (void) const |
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163 @deftypefnx {} Matrix unitary_matrix (void) const |
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164 @end deftypefn |
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165 |
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166 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const SCHUR &@var{a}) |
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167 @end deftypefn |
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168 |
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169 @deftypefn {} {}ComplexSCHUR (void) |
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170 @deftypefnx {} {}ComplexSCHUR (const ComplexMatrix &@var{a}, const char *@var{ord}) |
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171 @deftypefnx {} {}ComplexSCHUR (const ComplexMatrix &@var{a}, const char *@var{ord}, int &@var{info}) |
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172 @deftypefnx {} {}ComplexSCHUR (const ComplexSCHUR &@var{a}, const char *@var{ord}) |
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173 @end deftypefn |
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174 |
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175 @deftypefn {} ComplexSCHUR& {operator =} (const ComplexSCHUR &@var{a}) |
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176 @end deftypefn |
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177 |
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178 @deftypefn {} ComplexMatrix schur_matrix (void) const |
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179 @deftypefnx {} ComplexMatrix unitary_matrix (void) const |
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180 @end deftypefn |
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181 |
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182 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexSCHUR &@var{a}) |
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183 @end deftypefn |
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184 |
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185 @deftypefn {} {}SVD (void) |
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186 @deftypefnx {} {}SVD (const Matrix &@var{a}) |
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187 @deftypefnx {} {}SVD (const Matrix &@var{a}, int &@var{info}) |
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188 @deftypefnx {} {}SVD (const SVD &@var{a}) |
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189 @end deftypefn |
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190 |
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191 @deftypefn {} SVD& {operator =} (const SVD &@var{a}) |
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192 @end deftypefn |
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193 |
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194 @deftypefn {} DiagMatrix singular_values (void) const |
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195 @deftypefnx {} Matrix left_singular_matrix (void) const |
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196 @deftypefnx {} Matrix right_singular_matrix (void) const |
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197 @end deftypefn |
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198 |
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199 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const SVD &@var{a}) |
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200 @end deftypefn |
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201 |
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202 @deftypefn {} {}ComplexSVD (void) |
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203 @deftypefnx {} {}ComplexSVD (const ComplexMatrix &@var{a}) |
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204 @deftypefnx {} {}ComplexSVD (const ComplexMatrix &@var{a}, int &@var{info}) |
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205 @deftypefnx {} {}ComplexSVD (const ComplexSVD &@var{a}) |
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206 @end deftypefn |
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207 |
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208 @deftypefn {} ComplexSVD& {operator =} (const ComplexSVD &@var{a}) |
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209 @end deftypefn |
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210 |
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211 @deftypefn {} DiagMatrix singular_values (void) const |
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212 @deftypefnx {} ComplexMatrix left_singular_matrix (void) const |
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213 @deftypefnx {} ComplexMatrix right_singular_matrix (void) const |
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214 @end deftypefn |
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215 |
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216 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexSVD &@var{a}) |
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217 @end deftypefn |
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218 |
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219 @deftypefn {} {}EIG (void) |
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220 @deftypefnx {} {}EIG (const Matrix &@var{a}) |
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221 @deftypefnx {} {}EIG (const Matrix &@var{a}, int &@var{info}) |
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222 @deftypefnx {} {}EIG (const ComplexMatrix &@var{a}) |
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223 @deftypefnx {} {}EIG (const ComplexMatrix &@var{a}, int &@var{info}) |
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224 @deftypefnx {} {}EIG (const EIG &@var{a}) |
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225 @end deftypefn |
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226 |
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227 @deftypefn {} EIG& {operator =} (const EIG &@var{a}) |
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228 @end deftypefn |
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229 |
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230 @deftypefn {} ComplexColumnVector eigenvalues (void) const |
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231 @end deftypefn |
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232 |
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233 @deftypefn {} ComplexMatrix eigenvectors (void) const |
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234 @end deftypefn |
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235 |
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236 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const EIG &@var{a}) |
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237 @end deftypefn |
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238 |
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239 @deftypefn {} {}LU (void) |
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240 @deftypefnx {} {}LU (const Matrix &@var{a}) |
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241 @deftypefnx {} {}LU (const LU &@var{a}) |
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242 @end deftypefn |
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243 |
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244 @deftypefn {} LU& {operator =} (const LU &@var{a}) |
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245 @end deftypefn |
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246 |
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247 @deftypefn {} Matrix L (void) const |
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248 @deftypefnx {} Matrix U (void) const |
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249 @deftypefnx {} Matrix P (void) const |
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250 @end deftypefn |
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251 |
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252 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const LU &@var{a}) |
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253 @end deftypefn |
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254 |
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255 @deftypefn {} {}ComplexLU (void) |
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256 @deftypefnx {} {}ComplexLU (const ComplexMatrix &@var{a}) |
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257 @deftypefnx {} {}ComplexLU (const ComplexLU &@var{a}) |
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258 @end deftypefn |
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259 |
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260 @deftypefn {} ComplexLU& {operator =} (const ComplexLU &@var{a}) |
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261 @end deftypefn |
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262 |
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263 @deftypefn {} ComplexMatrix L (void) const |
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264 @deftypefnx {} ComplexMatrix U (void) const |
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265 @deftypefnx {} Matrix P (void) const |
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266 @end deftypefn |
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267 |
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268 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexLU &@var{a}) |
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269 @end deftypefn |
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270 |
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271 @deftypefn {} {}QR (void) |
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272 @deftypefnx {} {}QR (const Matrix &@var{A}) |
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273 @deftypefnx {} {}QR (const QR &@var{a}) |
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274 @end deftypefn |
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275 |
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276 @deftypefn {} QR& {operator =} (const QR &@var{a}) |
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277 @end deftypefn |
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278 |
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279 @deftypefn {} Matrix Q (void) const |
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280 @deftypefnx {} Matrix R (void) const |
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281 @end deftypefn |
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282 |
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283 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const QR &@var{a}) |
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284 @end deftypefn |
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285 |
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286 @deftypefn {} {}ComplexQR (void) |
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287 @deftypefnx {} {}ComplexQR (const ComplexMatrix &@var{A}) |
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288 @deftypefnx {} {}ComplexQR (const ComplexQR &@var{a}) |
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289 @end deftypefn |
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290 |
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291 @deftypefn {} ComplexQR& {operator =} (const ComplexQR &@var{a}) |
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292 @end deftypefn |
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293 |
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294 @deftypefn {} ComplexMatrix Q (void) const |
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295 @deftypefnx {} ComplexMatrix R (void) const |
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296 @end deftypefn |
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297 |
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298 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexQR &@var{a}) |
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299 @end deftypefn |
