1 | // This file is part of Eigen, a lightweight C++ template library
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2 | // for linear algebra.
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3 | //
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4 | // Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
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5 | // Copyright (C) 2012 Desire Nuentsa <desire.nuentsa_wakam@inria.fr>
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6 | //
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7 | // This code initially comes from MINPACK whose original authors are:
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8 | // Copyright Jorge More - Argonne National Laboratory
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9 | // Copyright Burt Garbow - Argonne National Laboratory
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10 | // Copyright Ken Hillstrom - Argonne National Laboratory
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11 | //
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12 | // This Source Code Form is subject to the terms of the Minpack license
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13 | // (a BSD-like license) described in the campaigned CopyrightMINPACK.txt file.
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14 |
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15 | #ifndef EIGEN_LMQRSOLV_H
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16 | #define EIGEN_LMQRSOLV_H
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17 |
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18 | namespace Eigen {
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19 |
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20 | namespace internal {
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21 |
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22 | template <typename Scalar,int Rows, int Cols, typename Index>
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23 | void lmqrsolv(
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24 | Matrix<Scalar,Rows,Cols> &s,
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25 | const PermutationMatrix<Dynamic,Dynamic,Index> &iPerm,
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26 | const Matrix<Scalar,Dynamic,1> &diag,
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27 | const Matrix<Scalar,Dynamic,1> &qtb,
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28 | Matrix<Scalar,Dynamic,1> &x,
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29 | Matrix<Scalar,Dynamic,1> &sdiag)
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30 | {
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31 |
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32 | /* Local variables */
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33 | Index i, j, k, l;
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34 | Scalar temp;
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35 | Index n = s.cols();
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36 | Matrix<Scalar,Dynamic,1> wa(n);
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37 | JacobiRotation<Scalar> givens;
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38 |
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39 | /* Function Body */
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40 | // the following will only change the lower triangular part of s, including
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41 | // the diagonal, though the diagonal is restored afterward
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42 |
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43 | /* copy r and (q transpose)*b to preserve input and initialize s. */
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44 | /* in particular, save the diagonal elements of r in x. */
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45 | x = s.diagonal();
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46 | wa = qtb;
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47 |
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48 |
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49 | s.topLeftCorner(n,n).template triangularView<StrictlyLower>() = s.topLeftCorner(n,n).transpose();
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50 | /* eliminate the diagonal matrix d using a givens rotation. */
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51 | for (j = 0; j < n; ++j) {
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52 |
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53 | /* prepare the row of d to be eliminated, locating the */
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54 | /* diagonal element using p from the qr factorization. */
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55 | l = iPerm.indices()(j);
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56 | if (diag[l] == 0.)
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57 | break;
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58 | sdiag.tail(n-j).setZero();
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59 | sdiag[j] = diag[l];
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60 |
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61 | /* the transformations to eliminate the row of d */
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62 | /* modify only a single element of (q transpose)*b */
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63 | /* beyond the first n, which is initially zero. */
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64 | Scalar qtbpj = 0.;
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65 | for (k = j; k < n; ++k) {
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66 | /* determine a givens rotation which eliminates the */
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67 | /* appropriate element in the current row of d. */
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68 | givens.makeGivens(-s(k,k), sdiag[k]);
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69 |
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70 | /* compute the modified diagonal element of r and */
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71 | /* the modified element of ((q transpose)*b,0). */
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72 | s(k,k) = givens.c() * s(k,k) + givens.s() * sdiag[k];
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73 | temp = givens.c() * wa[k] + givens.s() * qtbpj;
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74 | qtbpj = -givens.s() * wa[k] + givens.c() * qtbpj;
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75 | wa[k] = temp;
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76 |
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77 | /* accumulate the tranformation in the row of s. */
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78 | for (i = k+1; i<n; ++i) {
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79 | temp = givens.c() * s(i,k) + givens.s() * sdiag[i];
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80 | sdiag[i] = -givens.s() * s(i,k) + givens.c() * sdiag[i];
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81 | s(i,k) = temp;
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82 | }
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83 | }
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84 | }
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85 |
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86 | /* solve the triangular system for z. if the system is */
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87 | /* singular, then obtain a least squares solution. */
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88 | Index nsing;
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89 | for(nsing=0; nsing<n && sdiag[nsing]!=0; nsing++) {}
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90 |
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91 | wa.tail(n-nsing).setZero();
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92 | s.topLeftCorner(nsing, nsing).transpose().template triangularView<Upper>().solveInPlace(wa.head(nsing));
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93 |
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94 | // restore
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95 | sdiag = s.diagonal();
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96 | s.diagonal() = x;
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97 |
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98 | /* permute the components of z back to components of x. */
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99 | x = iPerm * wa;
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100 | }
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101 |
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102 | template <typename Scalar, int _Options, typename Index>
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103 | void lmqrsolv(
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104 | SparseMatrix<Scalar,_Options,Index> &s,
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105 | const PermutationMatrix<Dynamic,Dynamic> &iPerm,
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106 | const Matrix<Scalar,Dynamic,1> &diag,
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107 | const Matrix<Scalar,Dynamic,1> &qtb,
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108 | Matrix<Scalar,Dynamic,1> &x,
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109 | Matrix<Scalar,Dynamic,1> &sdiag)
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110 | {
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111 | /* Local variables */
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112 | typedef SparseMatrix<Scalar,RowMajor,Index> FactorType;
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113 | Index i, j, k, l;
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114 | Scalar temp;
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115 | Index n = s.cols();
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116 | Matrix<Scalar,Dynamic,1> wa(n);
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117 | JacobiRotation<Scalar> givens;
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118 |
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119 | /* Function Body */
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120 | // the following will only change the lower triangular part of s, including
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121 | // the diagonal, though the diagonal is restored afterward
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122 |
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123 | /* copy r and (q transpose)*b to preserve input and initialize R. */
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124 | wa = qtb;
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125 | FactorType R(s);
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126 | // Eliminate the diagonal matrix d using a givens rotation
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127 | for (j = 0; j < n; ++j)
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128 | {
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129 | // Prepare the row of d to be eliminated, locating the
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130 | // diagonal element using p from the qr factorization
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131 | l = iPerm.indices()(j);
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132 | if (diag(l) == Scalar(0))
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133 | break;
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134 | sdiag.tail(n-j).setZero();
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135 | sdiag[j] = diag[l];
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136 | // the transformations to eliminate the row of d
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137 | // modify only a single element of (q transpose)*b
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138 | // beyond the first n, which is initially zero.
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139 |
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140 | Scalar qtbpj = 0;
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141 | // Browse the nonzero elements of row j of the upper triangular s
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142 | for (k = j; k < n; ++k)
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143 | {
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144 | typename FactorType::InnerIterator itk(R,k);
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145 | for (; itk; ++itk){
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146 | if (itk.index() < k) continue;
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147 | else break;
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148 | }
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149 | //At this point, we have the diagonal element R(k,k)
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150 | // Determine a givens rotation which eliminates
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151 | // the appropriate element in the current row of d
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152 | givens.makeGivens(-itk.value(), sdiag(k));
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153 |
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154 | // Compute the modified diagonal element of r and
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155 | // the modified element of ((q transpose)*b,0).
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156 | itk.valueRef() = givens.c() * itk.value() + givens.s() * sdiag(k);
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157 | temp = givens.c() * wa(k) + givens.s() * qtbpj;
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158 | qtbpj = -givens.s() * wa(k) + givens.c() * qtbpj;
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159 | wa(k) = temp;
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160 |
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161 | // Accumulate the transformation in the remaining k row/column of R
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162 | for (++itk; itk; ++itk)
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163 | {
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164 | i = itk.index();
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165 | temp = givens.c() * itk.value() + givens.s() * sdiag(i);
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166 | sdiag(i) = -givens.s() * itk.value() + givens.c() * sdiag(i);
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167 | itk.valueRef() = temp;
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168 | }
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169 | }
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170 | }
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171 |
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172 | // Solve the triangular system for z. If the system is
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173 | // singular, then obtain a least squares solution
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174 | Index nsing;
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175 | for(nsing = 0; nsing<n && sdiag(nsing) !=0; nsing++) {}
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176 |
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177 | wa.tail(n-nsing).setZero();
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178 | // x = wa;
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179 | wa.head(nsing) = R.topLeftCorner(nsing,nsing).template triangularView<Upper>().solve/*InPlace*/(wa.head(nsing));
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180 |
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181 | sdiag = R.diagonal();
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182 | // Permute the components of z back to components of x
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183 | x = iPerm * wa;
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184 | }
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185 | } // end namespace internal
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186 |
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187 | } // end namespace Eigen
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188 |
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189 | #endif // EIGEN_LMQRSOLV_H
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