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

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) {
  using MType = typename EigenTypes<kSize, kSize>::Matrix;
  const int size = m.rows();

  // If the matrix can be assumed to be full rank, then if it is small
  // (< 5) and fixed size, use Eigen's optimized inverse()
  // implementation.
  //
  // https://eigen.tuxfamily.org/dox/group__TutorialLinearAlgebra.html#title3
  if (assume_full_rank) {
    if (kSize > 0 && kSize < 5) {
      return m.inverse();
    }
    return m.template selfadjointView<Eigen::Upper>().llt().solve(
        MType::Identity(size, size));
  }

  // For a thin SVD the number of columns of the matrix need to be dynamic.
  using SVDMType = typename EigenTypes<kSize, Eigen::Dynamic>::Matrix;
  Eigen::JacobiSVD<SVDMType> svd(m, Eigen::ComputeThinU | Eigen::ComputeThinV);
  return svd.solve(MType::Identity(size, size));
}

}  // namespace internal
}  // namespace ceres

#endif  // CERES_INTERNAL_INVERT_PSD_MATRIX_H_