ceres-solver/internal/ceres/invert_psd_matrix.h

// Ceres Solver - A fast non-linear least squares minimizer
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// Author: sameeragarwal@google.com (Sameer Agarwal)

#ifndef CERES_INTERNAL_INVERT_PSD_MATRIX_H_
#define CERES_INTERNAL_INVERT_PSD_MATRIX_H_

#include "ceres/internal/eigen.h"
#include "glog/logging.h"
#include "Eigen/Dense"

namespace ceres {
namespace internal {

// Helper routine to compute the inverse or pseudo-inverse of a
// symmetric positive semi-definite matrix.
//
// assume_full_rank controls whether a Cholesky factorization or an
// Singular Value Decomposition is used to compute the inverse and the
// pseudo-inverse respectively.
//
// The template parameter kSize can either be Eigen::Dynamic or a
// positive integer equal to the number of rows of m.
template <int kSize>
typename EigenTypes<kSize, kSize>::Matrix InvertPSDMatrix(
    const bool assume_full_rank,
    const typename EigenTypes<kSize, kSize>::Matrix& m) {
  const int size = m.rows();

  // If the matrix can be assumed to be full rank, then just use the
  // Cholesky factorization to invert it.
  if (assume_full_rank) {
    return m.template selfadjointView<Eigen::Upper>().llt().solve(
        Matrix::Identity(size, size));
  }

  Eigen::JacobiSVD<typename EigenTypes<kSize, kSize>::Matrix> svd(
      m, Eigen::ComputeThinU | Eigen::ComputeThinV);
  const double tolerance =
      std::numeric_limits<double>::epsilon() * size * svd.singularValues()(0);

  return svd.matrixV() *
         (svd.singularValues().array() > tolerance)
             .select(svd.singularValues().array().inverse(), 0)
             .matrix()
             .asDiagonal() *
         svd.matrixU().adjoint();
}

}  // namespace internal
}  // namespace ceres

#endif // CERES_INTERNAL_INVERT_PSD_MATRIX_H_