qr_fullpivoting.cpp File Reference

#include "main.h"
#include <Eigen/QR>
#include "solverbase.h"

Functions
template<typename MatrixType >
void	qr ()
template<typename MatrixType >
void	qr_invertible ()
template<typename MatrixType >
void	qr_verify_assert ()
	EIGEN_DECLARE_TEST (qr_fullpivoting)

Function Documentation

EIGEN_DECLARE_TEST()

EIGEN_DECLARE_TEST

(

qr_fullpivoting

)

                                    {
  for (int i = 0; i < 1; i++) {
    CALL_SUBTEST_5(qr<Matrix3f>());
    CALL_SUBTEST_6(qr<Matrix3d>());
    CALL_SUBTEST_8(qr<Matrix2f>());
    CALL_SUBTEST_1(qr<MatrixXf>());
    CALL_SUBTEST_2(qr<MatrixXd>());
    CALL_SUBTEST_3(qr<MatrixXcd>());
  }
 
  for (int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST_1(qr_invertible<MatrixXf>());
    CALL_SUBTEST_2(qr_invertible<MatrixXd>());
    CALL_SUBTEST_4(qr_invertible<MatrixXcf>());
    CALL_SUBTEST_3(qr_invertible<MatrixXcd>());
  }
 
  CALL_SUBTEST_5(qr_verify_assert<Matrix3f>());
  CALL_SUBTEST_6(qr_verify_assert<Matrix3d>());
  CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
  CALL_SUBTEST_2(qr_verify_assert<MatrixXd>());
  CALL_SUBTEST_4(qr_verify_assert<MatrixXcf>());
  CALL_SUBTEST_3(qr_verify_assert<MatrixXcd>());
 
  // Test problem size constructors
  CALL_SUBTEST_7(FullPivHouseholderQR<MatrixXf>(10, 20));
  CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float, 10, 20> >(10, 20)));
  CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float, 10, 20> >(Matrix<float, 10, 20>::Random())));
  CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float, 20, 10> >(20, 10)));
  CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float, 20, 10> >(Matrix<float, 20, 10>::Random())));
}

References CALL_SUBTEST_1, CALL_SUBTEST_2, CALL_SUBTEST_3, CALL_SUBTEST_4, CALL_SUBTEST_5, CALL_SUBTEST_6, CALL_SUBTEST_7, CALL_SUBTEST_8, Eigen::g_repeat, and i.

qr()

template<typename MatrixType >

void qr

(

)

          {
  static const int Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime;
  Index max_size = EIGEN_TEST_MAX_SIZE;
  Index min_size = numext::maxi(1, EIGEN_TEST_MAX_SIZE / 10);
  Index rows = Rows == Dynamic ? internal::random<Index>(min_size, max_size) : Rows,
        cols = Cols == Dynamic ? internal::random<Index>(min_size, max_size) : Cols,
        cols2 = Cols == Dynamic ? internal::random<Index>(min_size, max_size) : Cols,
        rank = internal::random<Index>(1, (std::min)(rows, cols) - 1);
 
  typedef typename MatrixType::Scalar Scalar;
  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
  MatrixType m1;
  createRandomPIMatrixOfRank(rank, rows, cols, m1);
  FullPivHouseholderQR<MatrixType> qr(m1);
  VERIFY_IS_EQUAL(rank, qr.rank());
  VERIFY_IS_EQUAL(cols - qr.rank(), qr.dimensionOfKernel());
  VERIFY(!qr.isInjective());
  VERIFY(!qr.isInvertible());
  VERIFY(!qr.isSurjective());
 
  MatrixType r = qr.matrixQR();
 
  MatrixQType q = qr.matrixQ();
  VERIFY_IS_UNITARY(q);
 
  // FIXME need better way to construct trapezoid
  for (int i = 0; i < rows; i++)
    for (int j = 0; j < cols; j++)
      if (i > j) r(i, j) = Scalar(0);
 
  MatrixType c = qr.matrixQ() * r * qr.colsPermutation().inverse();
 
  VERIFY_IS_APPROX(m1, c);
 
  // stress the ReturnByValue mechanism
  MatrixType tmp;
  VERIFY_IS_APPROX(tmp.noalias() = qr.matrixQ() * r, (qr.matrixQ() * r).eval());
 
  check_solverbase<MatrixType, MatrixType>(m1, qr, rows, cols, cols2);
 
  {
    MatrixType m2, m3;
    Index size = rows;
    do {
      m1 = MatrixType::Random(size, size);
      qr.compute(m1);
    } while (!qr.isInvertible());
    MatrixType m1_inv = qr.inverse();
    m3 = m1 * MatrixType::Random(size, cols2);
    m2 = qr.solve(m3);
    VERIFY_IS_APPROX(m2, m1_inv * m3);
  }
}

References calibrate::c, cols, Eigen::createRandomPIMatrixOfRank(), Eigen::Dynamic, EIGEN_TEST_MAX_SIZE, i, j, m1, m2(), Eigen::numext::maxi(), min, Eigen::numext::q, UniformPSDSelfTest::r, rows, size, tmp, VERIFY, VERIFY_IS_APPROX, VERIFY_IS_EQUAL, and VERIFY_IS_UNITARY.

Referenced by qr_invertible(), and qr_verify_assert().

qr_invertible()

template<typename MatrixType >

void qr_invertible

(

)

                     {
  using std::abs;
  using std::log;
  typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
  typedef typename MatrixType::Scalar Scalar;
 
  Index max_size = numext::mini(50, EIGEN_TEST_MAX_SIZE);
  Index min_size = numext::maxi(1, EIGEN_TEST_MAX_SIZE / 10);
  Index size = internal::random<Index>(min_size, max_size);
 
  MatrixType m1(size, size), m2(size, size), m3(size, size);
  m1 = MatrixType::Random(size, size);
 
  if (internal::is_same<RealScalar, float>::value) {
    // let's build a matrix more stable to inverse
    MatrixType a = MatrixType::Random(size, size * 2);
    m1 += a * a.adjoint();
  }
 
  FullPivHouseholderQR<MatrixType> qr(m1);
  VERIFY(qr.isInjective());
  VERIFY(qr.isInvertible());
  VERIFY(qr.isSurjective());
 
  check_solverbase<MatrixType, MatrixType>(m1, qr, size, size, size);
 
  // now construct a matrix with prescribed determinant
  m1.setZero();
  for (int i = 0; i < size; i++) m1(i, i) = internal::random<Scalar>();
  Scalar det = m1.diagonal().prod();
  RealScalar absdet = abs(det);
  m3 = qr.matrixQ();  // get a unitary
  m1 = m3 * m1 * m3.adjoint();
  qr.compute(m1);
  VERIFY_IS_APPROX(det, qr.determinant());
  VERIFY_IS_APPROX(absdet, qr.absDeterminant());
  VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
  VERIFY_IS_APPROX(numext::sign(det), qr.signDeterminant());
}

References a, abs(), EIGEN_TEST_MAX_SIZE, i, Eigen::bfloat16_impl::log(), m1, m2(), Eigen::numext::maxi(), Eigen::numext::mini(), qr(), SYCL::sign(), size, Eigen::value, VERIFY, and VERIFY_IS_APPROX.

qr_verify_assert()

template<typename MatrixType >

void qr_verify_assert

(

)

                        {
  MatrixType tmp;
 
  FullPivHouseholderQR<MatrixType> qr;
  VERIFY_RAISES_ASSERT(qr.matrixQR())
  VERIFY_RAISES_ASSERT(qr.solve(tmp))
  VERIFY_RAISES_ASSERT(qr.transpose().solve(tmp))
  VERIFY_RAISES_ASSERT(qr.adjoint().solve(tmp))
  VERIFY_RAISES_ASSERT(qr.matrixQ())
  VERIFY_RAISES_ASSERT(qr.dimensionOfKernel())
  VERIFY_RAISES_ASSERT(qr.isInjective())
  VERIFY_RAISES_ASSERT(qr.isSurjective())
  VERIFY_RAISES_ASSERT(qr.isInvertible())
  VERIFY_RAISES_ASSERT(qr.inverse())
  VERIFY_RAISES_ASSERT(qr.determinant())
  VERIFY_RAISES_ASSERT(qr.absDeterminant())
  VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
  VERIFY_RAISES_ASSERT(qr.signDeterminant())
}

References qr(), tmp, and VERIFY_RAISES_ASSERT.