[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_LMCOVAR_H
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| 13 | #define EIGEN_LMCOVAR_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 Scalar>
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| 20 | void covar(
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| 21 | Matrix< Scalar, Dynamic, Dynamic > &r,
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| 22 | const VectorXi& ipvt,
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| 23 | Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon()) )
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| 24 | {
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| 25 | using std::abs;
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| 26 | typedef DenseIndex Index;
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| 27 | /* Local variables */
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| 28 | Index i, j, k, l, ii, jj;
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| 29 | bool sing;
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| 30 | Scalar temp;
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| 31 |
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| 32 | /* Function Body */
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| 33 | const Index n = r.cols();
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| 34 | const Scalar tolr = tol * abs(r(0,0));
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| 35 | Matrix< Scalar, Dynamic, 1 > wa(n);
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| 36 | eigen_assert(ipvt.size()==n);
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| 37 |
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| 38 | /* form the inverse of r in the full upper triangle of r. */
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| 39 | l = -1;
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| 40 | for (k = 0; k < n; ++k)
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| 41 | if (abs(r(k,k)) > tolr) {
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| 42 | r(k,k) = 1. / r(k,k);
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| 43 | for (j = 0; j <= k-1; ++j) {
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| 44 | temp = r(k,k) * r(j,k);
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| 45 | r(j,k) = 0.;
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| 46 | r.col(k).head(j+1) -= r.col(j).head(j+1) * temp;
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| 47 | }
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| 48 | l = k;
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| 49 | }
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| 50 |
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| 51 | /* form the full upper triangle of the inverse of (r transpose)*r */
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| 52 | /* in the full upper triangle of r. */
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| 53 | for (k = 0; k <= l; ++k) {
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| 54 | for (j = 0; j <= k-1; ++j)
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| 55 | r.col(j).head(j+1) += r.col(k).head(j+1) * r(j,k);
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| 56 | r.col(k).head(k+1) *= r(k,k);
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| 57 | }
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| 58 |
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| 59 | /* form the full lower triangle of the covariance matrix */
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| 60 | /* in the strict lower triangle of r and in wa. */
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| 61 | for (j = 0; j < n; ++j) {
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| 62 | jj = ipvt[j];
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| 63 | sing = j > l;
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| 64 | for (i = 0; i <= j; ++i) {
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| 65 | if (sing)
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| 66 | r(i,j) = 0.;
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| 67 | ii = ipvt[i];
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| 68 | if (ii > jj)
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| 69 | r(ii,jj) = r(i,j);
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| 70 | if (ii < jj)
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| 71 | r(jj,ii) = r(i,j);
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| 72 | }
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| 73 | wa[jj] = r(j,j);
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| 74 | }
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| 75 |
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| 76 | /* symmetrize the covariance matrix in r. */
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| 77 | r.topLeftCorner(n,n).template triangularView<StrictlyUpper>() = r.topLeftCorner(n,n).transpose();
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| 78 | r.diagonal() = wa;
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| 79 | }
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| 80 |
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| 81 | } // end namespace internal
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| 82 |
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| 83 | } // end namespace Eigen
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| 84 |
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| 85 | #endif // EIGEN_LMCOVAR_H
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