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Add test for matrix power.

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Use Christoph Hertzberg's suggestion to use exponent laws.
This commit is contained in:
Chen-Pang He 2012-08-27 22:48:37 +01:00
parent b55d260ada
commit bfaa7f4ffe
5 changed files with 155 additions and 42 deletions
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1
unsupported/test/CMakeLists.txt
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@ -33,6 +33,7 @@ endif()
ei_add_test(matrix_exponential)
ei_add_test(matrix_function)
ei_add_test(matrix_power)
ei_add_test(matrix_square_root)
ei_add_test(alignedvector3)
ei_add_test(FFT)

12
unsupported/test/matrix_exponential.cpp
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@ -7,8 +7,7 @@
// 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 <unsupported/Eigen/MatrixFunctions>
#include "matrix_functions.h"
double binom(int n, int k)
{
@ -18,12 +17,6 @@ double binom(int n, int k)
return res;
}
template <typename Derived, typename OtherDerived>
double relerr(const MatrixBase<Derived>& A, const MatrixBase<OtherDerived>& B)
{
return std::sqrt((A - B).cwiseAbs2().sum() / (std::min)(A.cwiseAbs2().sum(), B.cwiseAbs2().sum()));
}
template <typename T>
T expfn(T x, int)
{
@ -109,8 +102,7 @@ void randomTest(const MatrixType& m, double tol)
*/
typename MatrixType::Index rows = m.rows();
typename MatrixType::Index cols = m.cols();
MatrixType m1(rows, cols), m2(rows, cols), m3(rows, cols),
identity = MatrixType::Identity(rows, rows);
MatrixType m1(rows, cols), m2(rows, cols), identity = MatrixType::Identity(rows, cols);
typedef typename NumTraits<typename internal::traits<MatrixType>::Scalar>::Real RealScalar;

47
unsupported/test/matrix_functions.h Normal file
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@ -0,0 +1,47 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2011 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 <unsupported/Eigen/MatrixFunctions>
template <typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex>
struct generateTestMatrix;
// for real matrices, make sure none of the eigenvalues are negative
template <typename MatrixType>
struct generateTestMatrix<MatrixType,0>
{
static void run(MatrixType& result, typename MatrixType::Index size)
{
MatrixType mat = MatrixType::Random(size, size);
EigenSolver<MatrixType> es(mat);
typename EigenSolver<MatrixType>::EigenvalueType eivals = es.eigenvalues();
for (typename MatrixType::Index i = 0; i < size; ++i) {
if (eivals(i).imag() == 0 && eivals(i).real() < 0)
eivals(i) = -eivals(i);
}
result = (es.eigenvectors() * eivals.asDiagonal() * es.eigenvectors().inverse()).real();
}
};
// for complex matrices, any matrix is fine
template <typename MatrixType>
struct generateTestMatrix<MatrixType,1>
{
static void run(MatrixType& result, typename MatrixType::Index size)
{
result = MatrixType::Random(size, size);
}
};
template <typename Derived, typename OtherDerived>
double relerr(const MatrixBase<Derived>& A, const MatrixBase<OtherDerived>& B)
{
return std::sqrt((A - B).cwiseAbs2().sum() / (std::min)(A.cwiseAbs2().sum(), B.cwiseAbs2().sum()));
}

104
unsupported/test/matrix_power.cpp Normal file
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@ -0,0 +1,104 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
//
// 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 "matrix_functions.h"
template <typename T>
void test2dRotation(double tol)
{
Matrix<T,2,2> A, B, C;
T angle, c, s;
A << 0, 1, -1, 0;
for (int i = 0; i <= 20; i++) {
angle = pow(10, (i-10) / 5.);
c = std::cos(angle);
s = std::sin(angle);
B << c, s, -s, c;
C = A.pow(std::ldexp(angle, 1) / M_PI);
std::cout << "test2dRotation: i = " << i << " error powerm = " << relerr(C, B) << "\n";
VERIFY(C.isApprox(B, T(tol)));
}
}
template <typename T>
void test2dHyperbolicRotation(double tol)
{
Matrix<std::complex<T>,2,2> A, B, C;
T angle, ch = std::cosh(1);
std::complex<T> ish(0, std::sinh(1));
A << ch, ish, -ish, ch;
for (int i = 0; i <= 20; i++) {
angle = std::ldexp(T(i-10), -1);
ch = std::cosh(angle);
ish = std::complex<T>(0, std::sinh(angle));
B << ch, ish, -ish, ch;
C = A.pow(angle);
std::cout << "test2dHyperbolicRotation: i = " << i << " error powerm = " << relerr(C, B) << "\n";
VERIFY(C.isApprox(B, T(tol)));
}
}
template <typename MatrixType>
void testExponentLaws(const MatrixType& m, double tol)
{
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typename MatrixType::Index rows = m.rows();
typename MatrixType::Index cols = m.cols();
MatrixType m1, m1x, m1y, m2, m3;
RealScalar x = internal::random<RealScalar>(), y = internal::random<RealScalar>();
double err[3];
for(int i = 0; i < g_repeat; i++) {
generateTestMatrix<MatrixType>::run(m1, m.rows());
m1x = m1.pow(x);
m1y = m1.pow(y);
m2 = m1.pow(x + y);
m3 = m1x * m1y;
err[0] = relerr(m2, m3);
VERIFY(m2.isApprox(m3, static_cast<RealScalar>(tol)));
m2 = m1.pow(x * y);
m3 = m1x.pow(y);
err[1] = relerr(m2, m3);
VERIFY(m2.isApprox(m3, static_cast<RealScalar>(tol)));
m2 = (std::abs(x) * m1).pow(y);
m3 = std::pow(std::abs(x), y) * m1y;
err[2] = relerr(m2, m3);
VERIFY(m2.isApprox(m3, static_cast<RealScalar>(tol)));
std::cout << "testExponentLaws: error powerm = " << err[0] << " " << err[1] << " " << err[2] << "\n";
}
}
void test_matrix_power()
{
CALL_SUBTEST_2(test2dRotation<double>(1e-13));
CALL_SUBTEST_1(test2dRotation<float>(2e-5)); // was 1e-5, relaxed for clang 2.8 / linux / x86-64
CALL_SUBTEST_8(test2dRotation<long double>(1e-13));
CALL_SUBTEST_2(test2dHyperbolicRotation<double>(1e-14));
CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5));
CALL_SUBTEST_8(test2dHyperbolicRotation<long double>(1e-14));
CALL_SUBTEST_2(testExponentLaws(Matrix2d(), 1e-13));
CALL_SUBTEST_7(testExponentLaws(Matrix<double,3,3,RowMajor>(), 1e-13));
CALL_SUBTEST_3(testExponentLaws(Matrix4cd(), 1e-13));
CALL_SUBTEST_4(testExponentLaws(MatrixXd(8,8), 1e-13));
CALL_SUBTEST_1(testExponentLaws(Matrix2f(), 1e-4));
CALL_SUBTEST_5(testExponentLaws(Matrix3cf(), 1e-4));
CALL_SUBTEST_1(testExponentLaws(Matrix4f(), 1e-4));
CALL_SUBTEST_6(testExponentLaws(MatrixXf(8,8), 1e-4));
CALL_SUBTEST_9(testExponentLaws(Matrix<long double,Dynamic,Dynamic>(7,7), 1e-13));
}

33
unsupported/test/matrix_square_root.cpp
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@ -7,38 +7,7 @@
// 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 <unsupported/Eigen/MatrixFunctions>
template <typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex>
struct generateTestMatrix;
// for real matrices, make sure none of the eigenvalues are negative
template <typename MatrixType>
struct generateTestMatrix<MatrixType,0>
{
static void run(MatrixType& result, typename MatrixType::Index size)
{
MatrixType mat = MatrixType::Random(size, size);
EigenSolver<MatrixType> es(mat);
typename EigenSolver<MatrixType>::EigenvalueType eivals = es.eigenvalues();
for (typename MatrixType::Index i = 0; i < size; ++i) {
if (eivals(i).imag() == 0 && eivals(i).real() < 0)
eivals(i) = -eivals(i);
}
result = (es.eigenvectors() * eivals.asDiagonal() * es.eigenvectors().inverse()).real();
}
};
// for complex matrices, any matrix is fine
template <typename MatrixType>
struct generateTestMatrix<MatrixType,1>
{
static void run(MatrixType& result, typename MatrixType::Index size)
{
result = MatrixType::Random(size, size);
}
};
#include "matrix_functions.h"
template<typename MatrixType>
void testMatrixSqrt(const MatrixType& m)