svd_fill.h File Reference

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Functions
template<typename T >
Array< T, 4, 1 >	four_denorms ()
template<>
Array4f	four_denorms ()
template<typename MatrixType >
void	svd_fill_random (MatrixType &m, int Option=0)

Function Documentation

four_denorms() [1/2]

template<>

Array4d four_denorms

(

)

                       {
  return Array4f(5.60844e-39f, -5.60844e-39f, 4.94e-44f, -4.94e-44f);
}

four_denorms() [2/2]

template<typename T >

Array< T, 4, 1 > four_denorms

(

)

                              {
  return four_denorms<double>().cast<T>();
}

svd_fill_random()

template<typename MatrixType >

void svd_fill_random	(	MatrixType &	m,
		int	Option = 0
	)

                                                    {
  using std::pow;
  typedef typename MatrixType::Scalar Scalar;
  typedef typename MatrixType::RealScalar RealScalar;
  Index diagSize = (std::min)(m.rows(), m.cols());
  RealScalar s = std::numeric_limits<RealScalar>::max_exponent10 / 4;
  s = internal::random<RealScalar>(1, s);
  Matrix<RealScalar, Dynamic, 1> d = Matrix<RealScalar, Dynamic, 1>::Random(diagSize);
  for (Index k = 0; k < diagSize; ++k) d(k) = d(k) * pow(RealScalar(10), internal::random<RealScalar>(-s, s));
 
  bool dup = internal::random<int>(0, 10) < 3;
  bool unit_uv =
      internal::random<int>(0, 10) < (dup ? 7 : 3);  // if we duplicate some diagonal entries, then increase the chance
                                                     // to preserve them using unitary U and V factors
 
  // duplicate some singular values
  if (dup) {
    Index n = internal::random<Index>(0, d.size() - 1);
    for (Index i = 0; i < n; ++i)
      d(internal::random<Index>(0, d.size() - 1)) = d(internal::random<Index>(0, d.size() - 1));
  }
 
  Matrix<Scalar, Dynamic, Dynamic> U(m.rows(), diagSize);
  Matrix<Scalar, Dynamic, Dynamic> VT(diagSize, m.cols());
  if (unit_uv) {
    // in very rare cases let's try with a pure diagonal matrix
    if (internal::random<int>(0, 10) < 1) {
      U.setIdentity();
      VT.setIdentity();
    } else {
      createRandomPIMatrixOfRank(diagSize, U.rows(), U.cols(), U);
      createRandomPIMatrixOfRank(diagSize, VT.rows(), VT.cols(), VT);
    }
  } else {
    U.setRandom();
    VT.setRandom();
  }
 
  Matrix<Scalar, Dynamic, 1> samples(9);
  samples << Scalar(0), four_denorms<RealScalar>(), -RealScalar(1) / NumTraits<RealScalar>::highest(),
      RealScalar(1) / NumTraits<RealScalar>::highest(), (std::numeric_limits<RealScalar>::min)(),
      pow((std::numeric_limits<RealScalar>::min)(), RealScalar(0.8));
 
  if (Option == Symmetric) {
    m = U * d.asDiagonal() * U.transpose();
 
    // randomly nullify some rows/columns
    {
      Index count = internal::random<Index>(-diagSize, diagSize);
      for (Index k = 0; k < count; ++k) {
        Index i = internal::random<Index>(0, diagSize - 1);
        m.row(i).setZero();
        m.col(i).setZero();
      }
      if (count < 0)
        // (partly) cancel some coeffs
        if (!(dup && unit_uv)) {
          Index n = internal::random<Index>(0, m.size() - 1);
          for (Index k = 0; k < n; ++k) {
            Index i = internal::random<Index>(0, m.rows() - 1);
            Index j = internal::random<Index>(0, m.cols() - 1);
            m(j, i) = m(i, j) = samples(internal::random<Index>(0, samples.size() - 1));
            if (NumTraits<Scalar>::IsComplex)
              *(&numext::real_ref(m(j, i)) + 1) = *(&numext::real_ref(m(i, j)) + 1) =
                  samples.real()(internal::random<Index>(0, samples.size() - 1));
          }
        }
    }
  } else {
    m = U * d.asDiagonal() * VT;
    // (partly) cancel some coeffs
    if (!(dup && unit_uv)) {
      Index n = internal::random<Index>(0, m.size() - 1);
      for (Index k = 0; k < n; ++k) {
        Index i = internal::random<Index>(0, m.rows() - 1);
        Index j = internal::random<Index>(0, m.cols() - 1);
        m(i, j) = samples(internal::random<Index>(0, samples.size() - 1));
        if (NumTraits<Scalar>::IsComplex)
          *(&numext::real_ref(m(i, j)) + 1) = samples.real()(internal::random<Index>(0, samples.size() - 1));
      }
    }
  }
}

References Eigen::createRandomPIMatrixOfRank(), i, Eigen::GenericNumTraits< T >::IsComplex, j, k, m, min, n, Eigen::bfloat16_impl::pow(), Eigen::ArrayBase< Derived >::pow(), Eigen::numext::real_ref(), s, samples, Eigen::Symmetric, and RachelsAdvectionDiffusion::U.

Referenced by EIGEN_DECLARE_TEST(), jacobisvd_full_options(), jacobisvd_thin_options(), jacobisvd_verify_assert(), jacobisvd_verify_inputs(), selfadjointeigensolver(), svd_check_max_size_matrix(), svd_option_checks_full_only(), svd_thin_option_checks(), svd_verify_assert(), svd_verify_assert_full_only(), and svd_verify_constructor_options_assert().