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 | // This code initially comes from MINPACK whose original authors are:
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5 | // Copyright Jorge More - Argonne National Laboratory
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6 | // Copyright Burt Garbow - Argonne National Laboratory
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7 | // Copyright Ken Hillstrom - Argonne National Laboratory
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8 | //
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9 | // This Source Code Form is subject to the terms of the Minpack license
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10 | // (a BSD-like license) described in the campaigned CopyrightMINPACK.txt file.
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11 |
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12 | #ifndef EIGEN_LMPAR_H
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13 | #define EIGEN_LMPAR_H
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14 |
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15 | namespace Eigen {
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16 |
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17 | namespace internal {
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18 |
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19 | template <typename QRSolver, typename VectorType>
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20 | void lmpar2(
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21 | const QRSolver &qr,
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22 | const VectorType &diag,
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23 | const VectorType &qtb,
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24 | typename VectorType::Scalar m_delta,
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25 | typename VectorType::Scalar &par,
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26 | VectorType &x)
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27 |
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28 | {
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29 | using std::sqrt;
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30 | using std::abs;
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31 | typedef typename QRSolver::MatrixType MatrixType;
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32 | typedef typename QRSolver::Scalar Scalar;
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33 | typedef typename QRSolver::Index Index;
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34 |
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35 | /* Local variables */
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36 | Index j;
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37 | Scalar fp;
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38 | Scalar parc, parl;
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39 | Index iter;
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40 | Scalar temp, paru;
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41 | Scalar gnorm;
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42 | Scalar dxnorm;
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43 |
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44 | // Make a copy of the triangular factor.
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45 | // This copy is modified during call the qrsolv
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46 | MatrixType s;
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47 | s = qr.matrixR();
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48 |
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49 | /* Function Body */
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50 | const Scalar dwarf = (std::numeric_limits<Scalar>::min)();
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51 | const Index n = qr.matrixR().cols();
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52 | eigen_assert(n==diag.size());
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53 | eigen_assert(n==qtb.size());
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54 |
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55 | VectorType wa1, wa2;
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56 |
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57 | /* compute and store in x the gauss-newton direction. if the */
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58 | /* jacobian is rank-deficient, obtain a least squares solution. */
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59 |
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60 | // const Index rank = qr.nonzeroPivots(); // exactly double(0.)
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61 | const Index rank = qr.rank(); // use a threshold
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62 | wa1 = qtb;
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63 | wa1.tail(n-rank).setZero();
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64 | //FIXME There is no solve in place for sparse triangularView
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65 | wa1.head(rank) = s.topLeftCorner(rank,rank).template triangularView<Upper>().solve(qtb.head(rank));
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66 |
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67 | x = qr.colsPermutation()*wa1;
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68 |
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69 | /* initialize the iteration counter. */
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70 | /* evaluate the function at the origin, and test */
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71 | /* for acceptance of the gauss-newton direction. */
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72 | iter = 0;
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73 | wa2 = diag.cwiseProduct(x);
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74 | dxnorm = wa2.blueNorm();
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75 | fp = dxnorm - m_delta;
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76 | if (fp <= Scalar(0.1) * m_delta) {
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77 | par = 0;
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78 | return;
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79 | }
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80 |
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81 | /* if the jacobian is not rank deficient, the newton */
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82 | /* step provides a lower bound, parl, for the zero of */
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83 | /* the function. otherwise set this bound to zero. */
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84 | parl = 0.;
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85 | if (rank==n) {
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86 | wa1 = qr.colsPermutation().inverse() * diag.cwiseProduct(wa2)/dxnorm;
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87 | s.topLeftCorner(n,n).transpose().template triangularView<Lower>().solveInPlace(wa1);
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88 | temp = wa1.blueNorm();
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89 | parl = fp / m_delta / temp / temp;
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90 | }
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91 |
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92 | /* calculate an upper bound, paru, for the zero of the function. */
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93 | for (j = 0; j < n; ++j)
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94 | wa1[j] = s.col(j).head(j+1).dot(qtb.head(j+1)) / diag[qr.colsPermutation().indices()(j)];
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95 |
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96 | gnorm = wa1.stableNorm();
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97 | paru = gnorm / m_delta;
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98 | if (paru == 0.)
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99 | paru = dwarf / (std::min)(m_delta,Scalar(0.1));
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100 |
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101 | /* if the input par lies outside of the interval (parl,paru), */
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102 | /* set par to the closer endpoint. */
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103 | par = (std::max)(par,parl);
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104 | par = (std::min)(par,paru);
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105 | if (par == 0.)
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106 | par = gnorm / dxnorm;
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107 |
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108 | /* beginning of an iteration. */
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109 | while (true) {
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110 | ++iter;
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111 |
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112 | /* evaluate the function at the current value of par. */
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113 | if (par == 0.)
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114 | par = (std::max)(dwarf,Scalar(.001) * paru); /* Computing MAX */
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115 | wa1 = sqrt(par)* diag;
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116 |
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117 | VectorType sdiag(n);
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118 | lmqrsolv(s, qr.colsPermutation(), wa1, qtb, x, sdiag);
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119 |
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120 | wa2 = diag.cwiseProduct(x);
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121 | dxnorm = wa2.blueNorm();
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122 | temp = fp;
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123 | fp = dxnorm - m_delta;
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124 |
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125 | /* if the function is small enough, accept the current value */
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126 | /* of par. also test for the exceptional cases where parl */
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127 | /* is zero or the number of iterations has reached 10. */
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128 | if (abs(fp) <= Scalar(0.1) * m_delta || (parl == 0. && fp <= temp && temp < 0.) || iter == 10)
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129 | break;
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130 |
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131 | /* compute the newton correction. */
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132 | wa1 = qr.colsPermutation().inverse() * diag.cwiseProduct(wa2/dxnorm);
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133 | // we could almost use this here, but the diagonal is outside qr, in sdiag[]
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134 | for (j = 0; j < n; ++j) {
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135 | wa1[j] /= sdiag[j];
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136 | temp = wa1[j];
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137 | for (Index i = j+1; i < n; ++i)
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138 | wa1[i] -= s.coeff(i,j) * temp;
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139 | }
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140 | temp = wa1.blueNorm();
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141 | parc = fp / m_delta / temp / temp;
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142 |
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143 | /* depending on the sign of the function, update parl or paru. */
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144 | if (fp > 0.)
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145 | parl = (std::max)(parl,par);
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146 | if (fp < 0.)
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147 | paru = (std::min)(paru,par);
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148 |
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149 | /* compute an improved estimate for par. */
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150 | par = (std::max)(parl,par+parc);
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151 | }
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152 | if (iter == 0)
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153 | par = 0.;
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154 | return;
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155 | }
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156 | } // end namespace internal
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157 |
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158 | } // end namespace Eigen
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159 |
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160 | #endif // EIGEN_LMPAR_H
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