You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
115 lines
4.1 KiB
115 lines
4.1 KiB
// This file is part of Eigen, a lightweight C++ template library
|
|
// for linear algebra.
|
|
//
|
|
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
|
|
// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
|
|
//
|
|
// This Source Code Form is subject to the terms of the Mozilla
|
|
// Public License v. 2.0. If a copy of the MPL was not distributed
|
|
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
|
|
|
#include "main.h"
|
|
#include <limits>
|
|
#include <Eigen/Eigenvalues>
|
|
#include <Eigen/LU>
|
|
|
|
/* Check that two column vectors are approximately equal upto permutations,
|
|
by checking that the k-th power sums are equal for k = 1, ..., vec1.rows() */
|
|
template<typename VectorType>
|
|
void verify_is_approx_upto_permutation(const VectorType& vec1, const VectorType& vec2)
|
|
{
|
|
typedef typename NumTraits<typename VectorType::Scalar>::Real RealScalar;
|
|
|
|
VERIFY(vec1.cols() == 1);
|
|
VERIFY(vec2.cols() == 1);
|
|
VERIFY(vec1.rows() == vec2.rows());
|
|
for (int k = 1; k <= vec1.rows(); ++k)
|
|
{
|
|
VERIFY_IS_APPROX(vec1.array().pow(RealScalar(k)).sum(), vec2.array().pow(RealScalar(k)).sum());
|
|
}
|
|
}
|
|
|
|
|
|
template<typename MatrixType> void eigensolver(const MatrixType& m)
|
|
{
|
|
typedef typename MatrixType::Index Index;
|
|
/* this test covers the following files:
|
|
ComplexEigenSolver.h, and indirectly ComplexSchur.h
|
|
*/
|
|
Index rows = m.rows();
|
|
Index cols = m.cols();
|
|
|
|
typedef typename MatrixType::Scalar Scalar;
|
|
typedef typename NumTraits<Scalar>::Real RealScalar;
|
|
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
|
|
typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealVectorType;
|
|
typedef typename std::complex<typename NumTraits<typename MatrixType::Scalar>::Real> Complex;
|
|
|
|
MatrixType a = MatrixType::Random(rows,cols);
|
|
MatrixType symmA = a.adjoint() * a;
|
|
|
|
ComplexEigenSolver<MatrixType> ei0(symmA);
|
|
VERIFY_IS_EQUAL(ei0.info(), Success);
|
|
VERIFY_IS_APPROX(symmA * ei0.eigenvectors(), ei0.eigenvectors() * ei0.eigenvalues().asDiagonal());
|
|
|
|
ComplexEigenSolver<MatrixType> ei1(a);
|
|
VERIFY_IS_EQUAL(ei1.info(), Success);
|
|
VERIFY_IS_APPROX(a * ei1.eigenvectors(), ei1.eigenvectors() * ei1.eigenvalues().asDiagonal());
|
|
// Note: If MatrixType is real then a.eigenvalues() uses EigenSolver and thus
|
|
// another algorithm so results may differ slightly
|
|
verify_is_approx_upto_permutation(a.eigenvalues(), ei1.eigenvalues());
|
|
|
|
ComplexEigenSolver<MatrixType> eiNoEivecs(a, false);
|
|
VERIFY_IS_EQUAL(eiNoEivecs.info(), Success);
|
|
VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues());
|
|
|
|
// Regression test for issue #66
|
|
MatrixType z = MatrixType::Zero(rows,cols);
|
|
ComplexEigenSolver<MatrixType> eiz(z);
|
|
VERIFY((eiz.eigenvalues().cwiseEqual(0)).all());
|
|
|
|
MatrixType id = MatrixType::Identity(rows, cols);
|
|
VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1));
|
|
|
|
if (rows > 1)
|
|
{
|
|
// Test matrix with NaN
|
|
a(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
|
|
ComplexEigenSolver<MatrixType> eiNaN(a);
|
|
VERIFY_IS_EQUAL(eiNaN.info(), NoConvergence);
|
|
}
|
|
}
|
|
|
|
template<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m)
|
|
{
|
|
ComplexEigenSolver<MatrixType> eig;
|
|
VERIFY_RAISES_ASSERT(eig.eigenvectors());
|
|
VERIFY_RAISES_ASSERT(eig.eigenvalues());
|
|
|
|
MatrixType a = MatrixType::Random(m.rows(),m.cols());
|
|
eig.compute(a, false);
|
|
VERIFY_RAISES_ASSERT(eig.eigenvectors());
|
|
}
|
|
|
|
void test_eigensolver_complex()
|
|
{
|
|
int s;
|
|
for(int i = 0; i < g_repeat; i++) {
|
|
CALL_SUBTEST_1( eigensolver(Matrix4cf()) );
|
|
s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
|
|
CALL_SUBTEST_2( eigensolver(MatrixXcd(s,s)) );
|
|
CALL_SUBTEST_3( eigensolver(Matrix<std::complex<float>, 1, 1>()) );
|
|
CALL_SUBTEST_4( eigensolver(Matrix3f()) );
|
|
}
|
|
|
|
CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4cf()) );
|
|
s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
|
|
CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXcd(s,s)) );
|
|
CALL_SUBTEST_3( eigensolver_verify_assert(Matrix<std::complex<float>, 1, 1>()) );
|
|
CALL_SUBTEST_4( eigensolver_verify_assert(Matrix3f()) );
|
|
|
|
// Test problem size constructors
|
|
CALL_SUBTEST_5(ComplexEigenSolver<MatrixXf>(s));
|
|
|
|
EIGEN_UNUSED_VARIABLE(s)
|
|
}
|