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Eigen: Updated to 3.2.5 version
git-svn-id: svn://ultimatepp.org/upp/trunk@8966 f0d560ea-af0d-0410-9eb7-867de7ffcac7
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160 changed files with 12055 additions and 478 deletions
193
uppsrc/plugin/Eigen/unsupported/test/matrix_function.cpp
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uppsrc/plugin/Eigen/unsupported/test/matrix_function.cpp
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#include "main.h"
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#include <unsupported/Eigen/MatrixFunctions>
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// Variant of VERIFY_IS_APPROX which uses absolute error instead of
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// relative error.
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#define VERIFY_IS_APPROX_ABS(a, b) VERIFY(test_isApprox_abs(a, b))
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template<typename Type1, typename Type2>
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inline bool test_isApprox_abs(const Type1& a, const Type2& b)
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{
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return ((a-b).array().abs() < test_precision<typename Type1::RealScalar>()).all();
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}
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// Returns a matrix with eigenvalues clustered around 0, 1 and 2.
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template<typename MatrixType>
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MatrixType randomMatrixWithRealEivals(const typename MatrixType::Index size)
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{
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typedef typename MatrixType::Index Index;
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typedef typename MatrixType::Scalar Scalar;
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typedef typename MatrixType::RealScalar RealScalar;
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MatrixType diag = MatrixType::Zero(size, size);
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for (Index i = 0; i < size; ++i) {
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diag(i, i) = Scalar(RealScalar(internal::random<int>(0,2)))
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+ internal::random<Scalar>() * Scalar(RealScalar(0.01));
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}
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MatrixType A = MatrixType::Random(size, size);
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HouseholderQR<MatrixType> QRofA(A);
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return QRofA.householderQ().inverse() * diag * QRofA.householderQ();
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}
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template <typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex>
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struct randomMatrixWithImagEivals
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{
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// Returns a matrix with eigenvalues clustered around 0 and +/- i.
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static MatrixType run(const typename MatrixType::Index size);
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};
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// Partial specialization for real matrices
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template<typename MatrixType>
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struct randomMatrixWithImagEivals<MatrixType, 0>
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{
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static MatrixType run(const typename MatrixType::Index size)
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{
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typedef typename MatrixType::Index Index;
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typedef typename MatrixType::Scalar Scalar;
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MatrixType diag = MatrixType::Zero(size, size);
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Index i = 0;
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while (i < size) {
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Index randomInt = internal::random<Index>(-1, 1);
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if (randomInt == 0 || i == size-1) {
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diag(i, i) = internal::random<Scalar>() * Scalar(0.01);
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++i;
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} else {
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Scalar alpha = Scalar(randomInt) + internal::random<Scalar>() * Scalar(0.01);
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diag(i, i+1) = alpha;
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diag(i+1, i) = -alpha;
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i += 2;
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}
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}
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MatrixType A = MatrixType::Random(size, size);
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HouseholderQR<MatrixType> QRofA(A);
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return QRofA.householderQ().inverse() * diag * QRofA.householderQ();
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}
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};
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// Partial specialization for complex matrices
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template<typename MatrixType>
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struct randomMatrixWithImagEivals<MatrixType, 1>
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{
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static MatrixType run(const typename MatrixType::Index size)
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{
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typedef typename MatrixType::Index Index;
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typedef typename MatrixType::Scalar Scalar;
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typedef typename MatrixType::RealScalar RealScalar;
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const Scalar imagUnit(0, 1);
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MatrixType diag = MatrixType::Zero(size, size);
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for (Index i = 0; i < size; ++i) {
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diag(i, i) = Scalar(RealScalar(internal::random<Index>(-1, 1))) * imagUnit
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+ internal::random<Scalar>() * Scalar(RealScalar(0.01));
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}
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MatrixType A = MatrixType::Random(size, size);
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HouseholderQR<MatrixType> QRofA(A);
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return QRofA.householderQ().inverse() * diag * QRofA.householderQ();
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}
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};
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template<typename MatrixType>
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void testMatrixExponential(const MatrixType& A)
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{
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typedef typename internal::traits<MatrixType>::Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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typedef std::complex<RealScalar> ComplexScalar;
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VERIFY_IS_APPROX(A.exp(), A.matrixFunction(StdStemFunctions<ComplexScalar>::exp));
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}
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template<typename MatrixType>
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void testMatrixLogarithm(const MatrixType& A)
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{
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typedef typename internal::traits<MatrixType>::Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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MatrixType scaledA;
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RealScalar maxImagPartOfSpectrum = A.eigenvalues().imag().cwiseAbs().maxCoeff();
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if (maxImagPartOfSpectrum >= 0.9 * M_PI)
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scaledA = A * 0.9 * M_PI / maxImagPartOfSpectrum;
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else
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scaledA = A;
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// identity X.exp().log() = X only holds if Im(lambda) < pi for all eigenvalues of X
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MatrixType expA = scaledA.exp();
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MatrixType logExpA = expA.log();
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VERIFY_IS_APPROX(logExpA, scaledA);
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}
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template<typename MatrixType>
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void testHyperbolicFunctions(const MatrixType& A)
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{
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// Need to use absolute error because of possible cancellation when
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// adding/subtracting expA and expmA.
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VERIFY_IS_APPROX_ABS(A.sinh(), (A.exp() - (-A).exp()) / 2);
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VERIFY_IS_APPROX_ABS(A.cosh(), (A.exp() + (-A).exp()) / 2);
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}
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template<typename MatrixType>
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void testGonioFunctions(const MatrixType& A)
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{
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typedef typename MatrixType::Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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typedef std::complex<RealScalar> ComplexScalar;
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typedef Matrix<ComplexScalar, MatrixType::RowsAtCompileTime,
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MatrixType::ColsAtCompileTime, MatrixType::Options> ComplexMatrix;
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ComplexScalar imagUnit(0,1);
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ComplexScalar two(2,0);
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ComplexMatrix Ac = A.template cast<ComplexScalar>();
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ComplexMatrix exp_iA = (imagUnit * Ac).exp();
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ComplexMatrix exp_miA = (-imagUnit * Ac).exp();
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ComplexMatrix sinAc = A.sin().template cast<ComplexScalar>();
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VERIFY_IS_APPROX_ABS(sinAc, (exp_iA - exp_miA) / (two*imagUnit));
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ComplexMatrix cosAc = A.cos().template cast<ComplexScalar>();
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VERIFY_IS_APPROX_ABS(cosAc, (exp_iA + exp_miA) / 2);
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}
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template<typename MatrixType>
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void testMatrix(const MatrixType& A)
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{
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testMatrixExponential(A);
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testMatrixLogarithm(A);
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testHyperbolicFunctions(A);
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testGonioFunctions(A);
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}
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template<typename MatrixType>
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void testMatrixType(const MatrixType& m)
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{
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// Matrices with clustered eigenvalue lead to different code paths
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// in MatrixFunction.h and are thus useful for testing.
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typedef typename MatrixType::Index Index;
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const Index size = m.rows();
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for (int i = 0; i < g_repeat; i++) {
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testMatrix(MatrixType::Random(size, size).eval());
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testMatrix(randomMatrixWithRealEivals<MatrixType>(size));
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testMatrix(randomMatrixWithImagEivals<MatrixType>::run(size));
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}
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}
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void test_matrix_function()
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{
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CALL_SUBTEST_1(testMatrixType(Matrix<float,1,1>()));
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CALL_SUBTEST_2(testMatrixType(Matrix3cf()));
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CALL_SUBTEST_3(testMatrixType(MatrixXf(8,8)));
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CALL_SUBTEST_4(testMatrixType(Matrix2d()));
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CALL_SUBTEST_5(testMatrixType(Matrix<double,5,5,RowMajor>()));
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CALL_SUBTEST_6(testMatrixType(Matrix4cd()));
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CALL_SUBTEST_7(testMatrixType(MatrixXd(13,13)));
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}
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