// Ceres Solver - A fast non-linear least squares minimizer

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// http://ceres-solver.org/

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// Author: sameeragarwal@google.com (Sameer Agarwal)

#include "ceres/invert_psd_matrix.h"

#include "ceres/internal/eigen.h"

#include "gtest/gtest.h"

namespace ceres {

namespace internal {

static const bool kFullRank = true;

static const bool kRankDeficient = false;

template <int kSize>

typename EigenTypes<kSize, kSize>::Matrix RandomPSDMatrixWithEigenValues(

    const typename EigenTypes<kSize>::Vector& eigenvalues) {

  typename EigenTypes<kSize, kSize>::Matrix m;

  m.setRandom();

  Eigen::SelfAdjointEigenSolver<typename EigenTypes<kSize, kSize>::Matrix> es(

      m);

  return es.eigenvectors() * eigenvalues.asDiagonal() *

         es.eigenvectors().transpose();

}

TEST(InvertPSDMatrix, Identity3x3) {

  const Matrix m = Matrix::Identity(3, 3);

  const Matrix inverse_m = InvertPSDMatrix<3>(kFullRank, m);

  EXPECT_NEAR((inverse_m - m).norm() / m.norm(),

              0.0,

              std::numeric_limits<double>::epsilon());

}

TEST(InvertPSDMatrix, FullRank5x5) {

  EigenTypes<5>::Vector eigenvalues;

  eigenvalues.setRandom();

  eigenvalues = eigenvalues.array().abs().matrix();

  const Matrix m = RandomPSDMatrixWithEigenValues<5>(eigenvalues);

  const Matrix inverse_m = InvertPSDMatrix<5>(kFullRank, m);

  EXPECT_NEAR((m * inverse_m - Matrix::Identity(5,5)).norm() / 5.0,  0.0,

              std::numeric_limits<double>::epsilon());

}

TEST(InvertPSDMatrix, RankDeficient5x5) {

  EigenTypes<5>::Vector eigenvalues;

  eigenvalues.setRandom();

  eigenvalues = eigenvalues.array().abs().matrix();

  eigenvalues(3) = 0.0;

  const Matrix m = RandomPSDMatrixWithEigenValues<5>(eigenvalues);

  const Matrix inverse_m = InvertPSDMatrix<5>(kRankDeficient, m);

  Matrix pseudo_identity = Matrix::Identity(5, 5);

  pseudo_identity(3, 3) = 0.0;

  EXPECT_NEAR((m * inverse_m * m - m).norm() / m.norm(),

              0.0,

              10 * std::numeric_limits<double>::epsilon());

}

}  // namespace internal

}  // namespace ceres