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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012, 2013 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(const T& 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 = std::pow(T(10), T(i-10) / T(5.));
c = std::cos(angle);
s = std::sin(angle);
B << c, s, -s, c;
C = Apow(std::ldexp(angle,1) / T(EIGEN_PI));
std::cout << "test2dRotation: i = " << i << " error powerm = " << relerr(C,B) << '\n';
VERIFY(C.isApprox(B, tol));
}
}
template<typename T>
void test2dHyperbolicRotation(const T& 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, tol));
}
}
template<typename T>
void test3dRotation(const T& tol)
{
Matrix<T,3,1> v;
T angle;
for (int i=0; i<=20; ++i) {
v = Matrix<T,3,1>::Random();
v.normalize();
angle = std::pow(T(10), T(i-10) / T(5.));
VERIFY(AngleAxis<T>(angle, v).matrix().isApprox(AngleAxis<T>(1,v).matrix().pow(angle), tol));
}
}
template<typename MatrixType>
void testGeneral(const MatrixType& m, const typename MatrixType::RealScalar& 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, tol));
m4 = mpow(x*y);
m5 = m2.pow(y);
VERIFY(m4.isApprox(m5, tol));
m4 = (std::abs(x) * m1).pow(y);
m5 = std::pow(std::abs(x), y) * m3;
VERIFY(m4.isApprox(m5, tol));
}
}
template<typename MatrixType>
void testSingular(const MatrixType& m_const, const typename MatrixType::RealScalar& tol)
{
// we need to pass by reference in order to prevent errors with
// MSVC for aligned data types ...
MatrixType& m = const_cast<MatrixType&>(m_const);
const int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex;
typedef typename internal::conditional<IsComplex, TriangularView<MatrixType,Upper>, const MatrixType&>::type TriangularType;
typename internal::conditional< IsComplex, ComplexSchur<MatrixType>, RealSchur<MatrixType> >::type schur;
MatrixType T;
for (int i=0; i < g_repeat; ++i) {
m.setRandom();
m.col(0).fill(0);
schur.compute(m);
T = schur.matrixT();
const MatrixType& U = schur.matrixU();
processTriangularMatrix<MatrixType>::run(m, T, U);
MatrixPower<MatrixType> mpow(m);
T = T.sqrt();
VERIFY(mpow(0.5L).isApprox(U * (TriangularType(T) * U.adjoint()), tol));
T = T.sqrt();
VERIFY(mpow(0.25L).isApprox(U * (TriangularType(T) * U.adjoint()), tol));
T = T.sqrt();
VERIFY(mpow(0.125L).isApprox(U * (TriangularType(T) * U.adjoint()), tol));
}
}
template<typename MatrixType>
void testLogThenExp(const MatrixType& m_const, const typename MatrixType::RealScalar& tol)
{
// we need to pass by reference in order to prevent errors with
// MSVC for aligned data types ...
MatrixType& m = const_cast<MatrixType&>(m_const);
typedef typename MatrixType::Scalar Scalar;
Scalar x;
for (int i=0; i < g_repeat; ++i) {
generateTestMatrix<MatrixType>::run(m, m.rows());
x = internal::random<Scalar>();
VERIFY(m.pow(x).isApprox((x * m.log()).exp(), tol));
}
}
typedef Matrix<double,3,3,RowMajor> Matrix3dRowMajor;
typedef Matrix<long double,3,3> Matrix3e;
typedef Matrix<long double,Dynamic,Dynamic> MatrixXe;
EIGEN_DECLARE_TEST(matrix_power)
{
CALL_SUBTEST_2(test2dRotation<double>(1e-13));
CALL_SUBTEST_1(test2dRotation<float>(2e-5f)); // was 1e-5, relaxed for clang 2.8 / linux / x86-64
CALL_SUBTEST_9(test2dRotation<long double>(1e-13L));
CALL_SUBTEST_2(test2dHyperbolicRotation<double>(1e-14));
CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5f));
CALL_SUBTEST_9(test2dHyperbolicRotation<long double>(1e-14L));
CALL_SUBTEST_10(test3dRotation<double>(1e-13));
CALL_SUBTEST_11(test3dRotation<float>(1e-5f));
CALL_SUBTEST_12(test3dRotation<long double>(1e-13L));
CALL_SUBTEST_2(testGeneral(Matrix2d(), 1e-13));
CALL_SUBTEST_7(testGeneral(Matrix3dRowMajor(), 1e-13));
CALL_SUBTEST_3(testGeneral(Matrix4cd(), 1e-13));
CALL_SUBTEST_4(testGeneral(MatrixXd(8,8), 2e-12));
CALL_SUBTEST_1(testGeneral(Matrix2f(), 1e-4f));
CALL_SUBTEST_5(testGeneral(Matrix3cf(), 1e-4f));
CALL_SUBTEST_8(testGeneral(Matrix4f(), 1e-4f));
CALL_SUBTEST_6(testGeneral(MatrixXf(2,2), 1e-3f)); // see bug 614
CALL_SUBTEST_9(testGeneral(MatrixXe(7,7), 1e-13L));
CALL_SUBTEST_10(testGeneral(Matrix3d(), 1e-13));
CALL_SUBTEST_11(testGeneral(Matrix3f(), 1e-4f));
CALL_SUBTEST_12(testGeneral(Matrix3e(), 1e-13L));
CALL_SUBTEST_2(testSingular(Matrix2d(), 1e-13));
CALL_SUBTEST_7(testSingular(Matrix3dRowMajor(), 1e-13));
CALL_SUBTEST_3(testSingular(Matrix4cd(), 1e-13));
CALL_SUBTEST_4(testSingular(MatrixXd(8,8), 2e-12));
CALL_SUBTEST_1(testSingular(Matrix2f(), 1e-4f));
CALL_SUBTEST_5(testSingular(Matrix3cf(), 1e-4f));
CALL_SUBTEST_8(testSingular(Matrix4f(), 1e-4f));
CALL_SUBTEST_6(testSingular(MatrixXf(2,2), 1e-3f));
CALL_SUBTEST_9(testSingular(MatrixXe(7,7), 1e-13L));
CALL_SUBTEST_10(testSingular(Matrix3d(), 1e-13));
CALL_SUBTEST_11(testSingular(Matrix3f(), 1e-4f));
CALL_SUBTEST_12(testSingular(Matrix3e(), 1e-13L));
CALL_SUBTEST_2(testLogThenExp(Matrix2d(), 1e-13));
CALL_SUBTEST_7(testLogThenExp(Matrix3dRowMajor(), 1e-13));
CALL_SUBTEST_3(testLogThenExp(Matrix4cd(), 1e-13));
CALL_SUBTEST_4(testLogThenExp(MatrixXd(8,8), 2e-12));
CALL_SUBTEST_1(testLogThenExp(Matrix2f(), 1e-4f));
CALL_SUBTEST_5(testLogThenExp(Matrix3cf(), 1e-4f));
CALL_SUBTEST_8(testLogThenExp(Matrix4f(), 1e-4f));
CALL_SUBTEST_6(testLogThenExp(MatrixXf(2,2), 1e-3f));
CALL_SUBTEST_9(testLogThenExp(MatrixXe(7,7), 1e-13L));
CALL_SUBTEST_10(testLogThenExp(Matrix3d(), 1e-13));
CALL_SUBTEST_11(testLogThenExp(Matrix3f(), 1e-4f));
CALL_SUBTEST_12(testLogThenExp(Matrix3e(), 1e-13L));
}
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