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// 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 MatrixType, int IsComplex = NumTraits<typename MatrixType::Scalar>::IsComplex>
struct generateTriangularMatrix;
// for real matrices, make sure none of the eigenvalues are negative
template <typename MatrixType>
struct generateTriangularMatrix<MatrixType,0>
{
static void run(MatrixType& result, typename MatrixType::Index size)
{
result.resize(size, size);
result.template triangularView<Upper>() = MatrixType::Random(size, size);
for (typename MatrixType::Index i = 0; i < size; ++i)
result.coeffRef(i,i) = std::abs(result.coeff(i,i));
}
};
// for complex matrices, any matrix is fine
template <typename MatrixType>
struct generateTriangularMatrix<MatrixType,1>
{
static void run(MatrixType& result, typename MatrixType::Index size)
{
result.resize(size, size);
result.template triangularView<Upper>() = MatrixType::Random(size, size);
}
};
template<typename T>
void test2dRotation(double tol)
{
Matrix<T,2,2> A, B, C;
T angle, c, s;
A << 0, 1, -1, 0;
MatrixPower<Matrix<T,2,2> > Apow(A);
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 = Apow(std::ldexp(angle,1) / M_PI);
std::cout << "test2dRotation: i = " << i << " error powerm = " << relerr(C,B) << '\n';
VERIFY(C.isApprox(B, static_cast<T>(tol)));
}
}
template<typename T>
void test2dHyperbolicRotation(double tol)
{
Matrix<std::complex<T>,2,2> A, B, C;
T angle, ch = std::cosh((T)1);
std::complex<T> ish(0, std::sinh((T)1));
A << ch, ish, -ish, ch;
MatrixPower<Matrix<std::complex<T>,2,2> > Apow(A);
for (int i=0; i<=20; ++i) {
angle = std::ldexp(static_cast<T>(i-10), -1);
ch = std::cosh(angle);
ish = std::complex<T>(0, std::sinh(angle));
B << ch, ish, -ish, ch;
C = Apow(angle);
std::cout << "test2dHyperbolicRotation: i = " << i << " error powerm = " << relerr(C,B) << '\n';
VERIFY(C.isApprox(B, static_cast<T>(tol)));
}
}
template<typename MatrixType>
void testExponentLaws(const MatrixType& m, double tol)
{
typedef typename MatrixType::RealScalar RealScalar;
MatrixType m1, m2, m3, m4, m5;
RealScalar x, y;
for (int i=0; i < g_repeat; ++i) {
generateTestMatrix<MatrixType>::run(m1, m.rows());
MatrixPower<MatrixType> mpow(m1);
x = internal::random<RealScalar>();
y = internal::random<RealScalar>();
m2 = mpow(x);
m3 = mpow(y);
m4 = mpow(x+y);
m5.noalias() = m2 * m3;
VERIFY(m4.isApprox(m5, static_cast<RealScalar>(tol)));
m4 = mpow(x*y);
m5 = m2.pow(y);
VERIFY(m4.isApprox(m5, static_cast<RealScalar>(tol)));
m4 = (std::abs(x) * m1).pow(y);
m5 = std::pow(std::abs(x), y) * m3;
VERIFY(m4.isApprox(m5, static_cast<RealScalar>(tol)));
}
}
template<typename MatrixType, typename VectorType>
void testProduct(const MatrixType& m, const VectorType& v, double tol)
{
typedef typename MatrixType::RealScalar RealScalar;
MatrixType m1;
VectorType v1, v2, v3;
RealScalar p;
for (int i=0; i < g_repeat; ++i) {
generateTestMatrix<MatrixType>::run(m1, m.rows());
MatrixPower<MatrixType> mpow(m1);
v1 = VectorType::Random(v.rows(), v.cols());
p = internal::random<RealScalar>();
v2.noalias() = mpow(p) * v1;
v3.noalias() = mpow(p).eval() * v1;
std::cout << "testProduct: error powerm = " << relerr(v2, v3) << '\n';
VERIFY(v2.isApprox(v3, static_cast<RealScalar>(tol)));
}
}
template<typename MatrixType, typename VectorType>
void testTriangularProduct(const MatrixType& m, const VectorType& v, double tol)
{
typedef typename MatrixType::RealScalar RealScalar;
MatrixType m1;
VectorType v1, v2, v3;
RealScalar p;
for (int i=0; i < g_repeat; ++i) {
generateTriangularMatrix<MatrixType>::run(m1, m.rows());
MatrixPowerTriangular<MatrixType> mpow(m1);
v1 = VectorType::Random(v.rows(), v.cols());
p = internal::random<RealScalar>();
v2.noalias() = mpow(p) * v1;
v3.noalias() = mpow(p).eval() * v1;
std::cout << "testTriangularProduct: error powerm = " << relerr(v2, v3) << '\n';
VERIFY(v2.isApprox(v3, static_cast<RealScalar>(tol)));
}
}
template<typename MatrixType, typename VectorType>
void testMatrixVector(const MatrixType& m, const VectorType& v, double tol)
{
testExponentLaws(m,tol);
testProduct(m,v,tol);
testTriangularProduct(m,v,tol);
}
void test_matrix_power()
{
typedef Matrix<double,3,3,RowMajor> Matrix3dRowMajor;
typedef Matrix<long double,Dynamic,Dynamic> MatrixXe;
typedef Matrix<long double,Dynamic,1> VectorXe;
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_9(test2dRotation<long double>(1e-13));
CALL_SUBTEST_2(test2dHyperbolicRotation<double>(1e-14));
CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5));
CALL_SUBTEST_9(test2dHyperbolicRotation<long double>(1e-14));
CALL_SUBTEST_2(testMatrixVector(Matrix2d(), Vector2d(), 1e-13));
CALL_SUBTEST_7(testMatrixVector(Matrix3dRowMajor(), MatrixXd(3,5), 1e-13));
CALL_SUBTEST_3(testMatrixVector(Matrix4cd(), Vector4cd(), 1e-13));
CALL_SUBTEST_4(testMatrixVector(MatrixXd(8,8), VectorXd(8), 2e-12));
CALL_SUBTEST_1(testMatrixVector(Matrix2f(), Vector2f(), 1e-4));
CALL_SUBTEST_5(testMatrixVector(Matrix3cf(), Vector3cf(), 1e-4));
CALL_SUBTEST_8(testMatrixVector(Matrix4f(), Vector4f(), 1e-4));
CALL_SUBTEST_6(testMatrixVector(MatrixXf(8,8), VectorXf(8), 1e-3));
CALL_SUBTEST_9(testMatrixVector(MatrixXe(7,7), VectorXe(7), 1e-13));
}
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