142 lines
4.3 KiB
C++
142 lines
4.3 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
|
|
// for linear algebra.
|
|
//
|
|
// Copyright (C) 2009 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 "matrix_functions.h"
|
|
|
|
double binom(int n, int k)
|
|
{
|
|
double res = 1;
|
|
for (int i=0; i<k; i++)
|
|
res = res * (n-k+i+1) / (i+1);
|
|
return res;
|
|
}
|
|
|
|
template <typename T>
|
|
T expfn(T x, int)
|
|
{
|
|
return std::exp(x);
|
|
}
|
|
|
|
template <typename T>
|
|
void test2dRotation(double tol)
|
|
{
|
|
Matrix<T,2,2> A, B, C;
|
|
T angle;
|
|
|
|
A << 0, 1, -1, 0;
|
|
for (int i=0; i<=20; i++)
|
|
{
|
|
angle = static_cast<T>(pow(10, i / 5. - 2));
|
|
B << std::cos(angle), std::sin(angle), -std::sin(angle), std::cos(angle);
|
|
|
|
C = (angle*A).matrixFunction(expfn);
|
|
std::cout << "test2dRotation: i = " << i << " error funm = " << relerr(C, B);
|
|
VERIFY(C.isApprox(B, static_cast<T>(tol)));
|
|
|
|
C = (angle*A).exp();
|
|
std::cout << " error expm = " << 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;
|
|
std::complex<T> imagUnit(0,1);
|
|
T angle, ch, sh;
|
|
|
|
for (int i=0; i<=20; i++)
|
|
{
|
|
angle = static_cast<T>((i-10) / 2.0);
|
|
ch = std::cosh(angle);
|
|
sh = std::sinh(angle);
|
|
A << 0, angle*imagUnit, -angle*imagUnit, 0;
|
|
B << ch, sh*imagUnit, -sh*imagUnit, ch;
|
|
|
|
C = A.matrixFunction(expfn);
|
|
std::cout << "test2dHyperbolicRotation: i = " << i << " error funm = " << relerr(C, B);
|
|
VERIFY(C.isApprox(B, static_cast<T>(tol)));
|
|
|
|
C = A.exp();
|
|
std::cout << " error expm = " << relerr(C, B) << "\n";
|
|
VERIFY(C.isApprox(B, static_cast<T>(tol)));
|
|
}
|
|
}
|
|
|
|
template <typename T>
|
|
void testPascal(double tol)
|
|
{
|
|
for (int size=1; size<20; size++)
|
|
{
|
|
Matrix<T,Dynamic,Dynamic> A(size,size), B(size,size), C(size,size);
|
|
A.setZero();
|
|
for (int i=0; i<size-1; i++)
|
|
A(i+1,i) = static_cast<T>(i+1);
|
|
B.setZero();
|
|
for (int i=0; i<size; i++)
|
|
for (int j=0; j<=i; j++)
|
|
B(i,j) = static_cast<T>(binom(i,j));
|
|
|
|
C = A.matrixFunction(expfn);
|
|
std::cout << "testPascal: size = " << size << " error funm = " << relerr(C, B);
|
|
VERIFY(C.isApprox(B, static_cast<T>(tol)));
|
|
|
|
C = A.exp();
|
|
std::cout << " error expm = " << relerr(C, B) << "\n";
|
|
VERIFY(C.isApprox(B, static_cast<T>(tol)));
|
|
}
|
|
}
|
|
|
|
template<typename MatrixType>
|
|
void randomTest(const MatrixType& m, double tol)
|
|
{
|
|
/* this test covers the following files:
|
|
Inverse.h
|
|
*/
|
|
typename MatrixType::Index rows = m.rows();
|
|
typename MatrixType::Index cols = m.cols();
|
|
MatrixType m1(rows, cols), m2(rows, cols), identity = MatrixType::Identity(rows, cols);
|
|
|
|
typedef typename NumTraits<typename internal::traits<MatrixType>::Scalar>::Real RealScalar;
|
|
|
|
for(int i = 0; i < g_repeat; i++) {
|
|
m1 = MatrixType::Random(rows, cols);
|
|
|
|
m2 = m1.matrixFunction(expfn) * (-m1).matrixFunction(expfn);
|
|
std::cout << "randomTest: error funm = " << relerr(identity, m2);
|
|
VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol)));
|
|
|
|
m2 = m1.exp() * (-m1).exp();
|
|
std::cout << " error expm = " << relerr(identity, m2) << "\n";
|
|
VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol)));
|
|
}
|
|
}
|
|
|
|
EIGEN_DECLARE_TEST(matrix_exponential)
|
|
{
|
|
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_6(testPascal<float>(1e-6));
|
|
CALL_SUBTEST_5(testPascal<double>(1e-15));
|
|
CALL_SUBTEST_2(randomTest(Matrix2d(), 1e-13));
|
|
CALL_SUBTEST_7(randomTest(Matrix<double,3,3,RowMajor>(), 1e-13));
|
|
CALL_SUBTEST_3(randomTest(Matrix4cd(), 1e-13));
|
|
CALL_SUBTEST_4(randomTest(MatrixXd(8,8), 1e-13));
|
|
CALL_SUBTEST_1(randomTest(Matrix2f(), 1e-4));
|
|
CALL_SUBTEST_5(randomTest(Matrix3cf(), 1e-4));
|
|
CALL_SUBTEST_1(randomTest(Matrix4f(), 1e-4));
|
|
CALL_SUBTEST_6(randomTest(MatrixXf(8,8), 1e-4));
|
|
CALL_SUBTEST_9(randomTest(Matrix<long double,Dynamic,Dynamic>(7,7), 1e-13));
|
|
}
|