1 | // Copyright (C) 2013 Conrad Sanderson |
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2 | // Copyright (C) 2013 NICTA (www.nicta.com.au) |
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3 | // |
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4 | // This Source Code Form is subject to the terms of the Mozilla Public |
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5 | // License, v. 2.0. If a copy of the MPL was not distributed with this |
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6 | // file, You can obtain one at http://mozilla.org/MPL/2.0/. |
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7 | |
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8 | |
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9 | //! \addtogroup fn_eig_pair |
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10 | //! @{ |
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11 | |
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12 | |
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13 | //! eigenvalues for pair of N-by-N general real matrices (A,B) |
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14 | template<typename T, typename T1> |
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15 | inline |
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16 | Col< std::complex<T> > |
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17 | eig_pair |
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18 | ( |
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19 | const Base<T, T1>& A, |
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20 | const Base<T, T1>& B, |
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21 | const typename arma_blas_type_only<T>::result* junk1 = 0, |
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22 | const typename arma_not_cx<T>::result* junk2 = 0 |
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23 | ) |
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24 | { |
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25 | arma_extra_debug_sigprint(); |
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26 | arma_ignore(junk1); |
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27 | arma_ignore(junk2); |
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28 | |
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29 | Mat<T> l_eigvec; |
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30 | Mat<T> r_eigvec; |
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31 | |
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32 | Col< std::complex<T> > eigval; |
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33 | |
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34 | const bool status = auxlib::eig_pair(eigval, l_eigvec, r_eigvec, A, B, 'n'); |
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35 | |
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36 | if(status == false) |
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37 | { |
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38 | eigval.reset(); |
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39 | arma_bad("eig_pair(): failed to converge"); |
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40 | } |
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41 | |
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42 | return eigval; |
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43 | } |
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44 | |
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45 | |
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46 | |
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47 | //! eigenvalues for pair of N-by-N general complex matrices (A,B) |
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48 | template<typename T, typename T1> |
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49 | inline |
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50 | Col< std::complex<T> > |
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51 | eig_pair |
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52 | ( |
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53 | const Base< std::complex<T>, T1>& A, |
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54 | const Base< std::complex<T>, T1>& B, |
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55 | const typename arma_blas_type_only< std::complex<T> >::result* junk1 = 0, |
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56 | const typename arma_cx_only< std::complex<T> >::result* junk2 = 0 |
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57 | ) |
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58 | { |
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59 | arma_extra_debug_sigprint(); |
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60 | arma_ignore(junk1); |
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61 | arma_ignore(junk2); |
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62 | |
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63 | Mat< std::complex<T> > l_eigvec; |
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64 | Mat< std::complex<T> > r_eigvec; |
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65 | |
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66 | Col< std::complex<T> > eigval; |
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67 | |
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68 | const bool status = auxlib::eig_pair(eigval, l_eigvec, r_eigvec, A, B, 'n'); |
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69 | |
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70 | if(status == false) |
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71 | { |
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72 | eigval.reset(); |
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73 | arma_bad("eig_pair(): failed to converge"); |
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74 | } |
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75 | |
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76 | return eigval; |
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77 | } |
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78 | |
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79 | |
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80 | |
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81 | //! eigenvalues for pair of N-by-N general real matrices (A,B) |
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82 | template<typename eT, typename T1, typename T2> |
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83 | inline |
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84 | bool |
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85 | eig_pair |
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86 | ( |
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87 | Col< std::complex<eT> >& eigval, |
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88 | const Base< eT, T1 >& A, |
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89 | const Base< eT, T2 >& B, |
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90 | const typename arma_blas_type_only<typename T1::elem_type>::result* junk = 0 |
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91 | ) |
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92 | { |
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93 | arma_extra_debug_sigprint(); |
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94 | arma_ignore(junk); |
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95 | |
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96 | Mat<eT> l_eigvec; |
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97 | Mat<eT> r_eigvec; |
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98 | |
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99 | const bool status = auxlib::eig_pair(eigval, l_eigvec, r_eigvec, A, B, 'n'); |
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100 | |
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101 | if(status == false) |
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102 | { |
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103 | eigval.reset(); |
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104 | arma_bad("eig_pair(): failed to converge", false); |
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105 | } |
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106 | |
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107 | return status; |
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108 | } |
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109 | |
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110 | |
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111 | |
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112 | //! eigenvalues for pair of N-by-N general complex matrices (A,B) |
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113 | template<typename T, typename T1, typename T2> |
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114 | inline |
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115 | bool |
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116 | eig_pair |
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117 | ( |
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118 | Col< std::complex<T> >& eigval, |
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119 | const Base< std::complex<T>, T1 >& A, |
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120 | const Base< std::complex<T>, T2 >& B, |
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121 | const typename arma_blas_type_only<typename T1::elem_type>::result* junk = 0 |
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122 | ) |
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123 | { |
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124 | arma_extra_debug_sigprint(); |
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125 | arma_ignore(junk); |
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126 | |
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127 | Mat< std::complex<T> > l_eigvec; |
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128 | Mat< std::complex<T> > r_eigvec; |
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129 | |
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130 | const bool status = auxlib::eig_pair(eigval, l_eigvec, r_eigvec, A, B, 'n'); |
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131 | |
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132 | if(status == false) |
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133 | { |
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134 | eigval.reset(); |
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135 | arma_bad("eig_pair(): failed to converge", false); |
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136 | } |
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137 | |
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138 | return status; |
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139 | } |
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140 | |
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141 | |
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142 | |
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143 | //! eigenvalues and eigenvectors for pair of N-by-N general real matrices (A,B) |
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144 | template<typename eT, typename T1, typename T2> |
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145 | inline |
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146 | bool |
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147 | eig_pair |
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148 | ( |
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149 | Col< std::complex<eT> >& eigval, |
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150 | Mat< std::complex<eT> >& eigvec, |
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151 | const Base< eT, T1 >& A, |
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152 | const Base< eT, T2 >& B, |
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153 | const typename arma_blas_type_only<typename T1::elem_type>::result* junk = 0 |
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154 | ) |
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155 | { |
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156 | arma_extra_debug_sigprint(); |
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157 | arma_ignore(junk); |
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158 | |
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159 | arma_debug_check( ( ((void*)(&eigval)) == ((void*)(&eigvec)) ), "eig_pair(): eigval is an alias of eigvec" ); |
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160 | |
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161 | Mat<eT> dummy_eigvec; |
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162 | Mat<eT> tmp_eigvec; |
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163 | |
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164 | const bool status = auxlib::eig_pair(eigval, dummy_eigvec, tmp_eigvec, A, B, 'r'); |
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165 | |
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166 | if(status == false) |
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167 | { |
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168 | eigval.reset(); |
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169 | eigvec.reset(); |
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170 | arma_bad("eig_pair(): failed to converge", false); |
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171 | } |
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172 | else |
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173 | { |
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174 | const uword n = eigval.n_elem; |
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175 | |
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176 | if(n > 0) |
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177 | { |
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178 | eigvec.set_size(n,n); |
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179 | |
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180 | // from LAPACK docs: |
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181 | // If the j-th and (j+1)-th eigenvalues form a complex conjugate pair, then |
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182 | // v(j) = VR(:,j)+i*VR(:,j+1) and v(j+1) = VR(:,j)-i*VR(:,j+1). |
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183 | |
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184 | for(uword j=0; j<n; ++j) |
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185 | { |
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186 | if( (j < n-1) && (eigval[j] == std::conj(eigval[j+1])) ) |
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187 | { |
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188 | // eigvec.col(j) = Mat< std::complex<eT> >( tmp_eigvec.col(j), tmp_eigvec.col(j+1) ); |
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189 | // eigvec.col(j+1) = Mat< std::complex<eT> >( tmp_eigvec.col(j), -tmp_eigvec.col(j+1) ); |
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190 | |
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191 | for(uword i=0; i<n; ++i) |
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192 | { |
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193 | eigvec.at(i,j) = std::complex<eT>( tmp_eigvec.at(i,j), tmp_eigvec.at(i,j+1) ); |
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194 | eigvec.at(i,j+1) = std::complex<eT>( tmp_eigvec.at(i,j), -tmp_eigvec.at(i,j+1) ); |
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195 | } |
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196 | |
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197 | ++j; |
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198 | } |
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199 | else |
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200 | { |
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201 | // eigvec.col(i) = tmp_eigvec.col(i); |
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202 | |
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203 | for(uword i=0; i<n; ++i) |
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204 | { |
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205 | eigvec.at(i,j) = std::complex<eT>(tmp_eigvec.at(i,j), eT(0)); |
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206 | } |
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207 | } |
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208 | } |
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209 | } |
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210 | } |
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211 | |
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212 | return status; |
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213 | } |
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214 | |
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215 | |
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216 | |
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217 | //! eigenvalues and eigenvectors for pair of N-by-N general complex matrices (A,B) |
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218 | template<typename T, typename T1, typename T2> |
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219 | inline |
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220 | bool |
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221 | eig_pair |
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222 | ( |
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223 | Col< std::complex<T> >& eigval, |
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224 | Mat< std::complex<T> >& eigvec, |
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225 | const Base< std::complex<T>, T1 >& A, |
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226 | const Base< std::complex<T>, T2 >& B, |
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227 | const typename arma_blas_type_only<typename T1::elem_type>::result* junk = 0 |
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228 | ) |
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229 | { |
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230 | arma_extra_debug_sigprint(); |
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231 | arma_ignore(junk); |
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232 | |
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233 | arma_debug_check( ( ((void*)(&eigval)) == ((void*)(&eigvec)) ), "eig_pair(): eigval is an alias of eigvec" ); |
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234 | |
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235 | Mat< std::complex<T> > dummy_eigvec; |
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236 | |
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237 | const bool status = auxlib::eig_pair(eigval, dummy_eigvec, eigvec, A, B, 'r'); |
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238 | |
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239 | if(status == false) |
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240 | { |
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241 | eigval.reset(); |
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242 | eigvec.reset(); |
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243 | arma_bad("eig_pair(): failed to converge", false); |
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244 | } |
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245 | |
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246 | return status; |
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247 | } |
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248 | |
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249 | |
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250 | //! @} |
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