unsupported/Eigen/src/LevenbergMarquardt/LMcovar.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This code initially comes from MINPACK whose original authors are:
// Copyright Jorge More - Argonne National Laboratory
// Copyright Burt Garbow - Argonne National Laboratory
// Copyright Ken Hillstrom - Argonne National Laboratory
//
// This Source Code Form is subject to the terms of the Minpack license
// (a BSD-like license) described in the campaigned CopyrightMINPACK.txt file.

#ifndef EIGEN_LMCOVAR_H
#define EIGEN_LMCOVAR_H

// IWYU pragma: private
#include "./InternalHeaderCheck.h"

namespace Eigen {

namespace internal {

template <typename Scalar>
void covar(Matrix<Scalar, Dynamic, Dynamic>& r, const VectorXi& ipvt,
           Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())) {
  using std::abs;
  /* Local variables */
  Index i, j, k, l, ii, jj;
  bool sing;
  Scalar temp;

  /* Function Body */
  const Index n = r.cols();
  const Scalar tolr = tol * abs(r(0, 0));
  Matrix<Scalar, Dynamic, 1> wa(n);
  eigen_assert(ipvt.size() == n);

  /* form the inverse of r in the full upper triangle of r. */
  l = -1;
  for (k = 0; k < n; ++k)
    if (abs(r(k, k)) > tolr) {
      r(k, k) = 1. / r(k, k);
      for (j = 0; j <= k - 1; ++j) {
        temp = r(k, k) * r(j, k);
        r(j, k) = 0.;
        r.col(k).head(j + 1) -= r.col(j).head(j + 1) * temp;
      }
      l = k;
    }

  /* form the full upper triangle of the inverse of (r transpose)*r */
  /* in the full upper triangle of r. */
  for (k = 0; k <= l; ++k) {
    for (j = 0; j <= k - 1; ++j) r.col(j).head(j + 1) += r.col(k).head(j + 1) * r(j, k);
    r.col(k).head(k + 1) *= r(k, k);
  }

  /* form the full lower triangle of the covariance matrix */
  /* in the strict lower triangle of r and in wa. */
  for (j = 0; j < n; ++j) {
    jj = ipvt[j];
    sing = j > l;
    for (i = 0; i <= j; ++i) {
      if (sing) r(i, j) = 0.;
      ii = ipvt[i];
      if (ii > jj) r(ii, jj) = r(i, j);
      if (ii < jj) r(jj, ii) = r(i, j);
    }
    wa[jj] = r(j, j);
  }

  /* symmetrize the covariance matrix in r. */
  r.topLeftCorner(n, n).template triangularView<StrictlyUpper>() = r.topLeftCorner(n, n).transpose();
  r.diagonal() = wa;
}

}  // end namespace internal

}  // end namespace Eigen

#endif  // EIGEN_LMCOVAR_H