[136] | 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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