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133 lines
4.2 KiB
133 lines
4.2 KiB
// 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) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
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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 "matrix_functions.h"
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template <typename MatrixType, int IsComplex = NumTraits<typename MatrixType::Scalar>::IsComplex>
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struct generateTriangularMatrix;
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// for real matrices, make sure none of the eigenvalues are negative
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template <typename MatrixType>
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struct generateTriangularMatrix<MatrixType,0>
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{
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static void run(MatrixType& result, typename MatrixType::Index size)
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{
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result.resize(size, size);
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result.template triangularView<Upper>() = MatrixType::Random(size, size);
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for (typename MatrixType::Index i = 0; i < size; ++i)
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result.coeffRef(i,i) = std::abs(result.coeff(i,i));
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}
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};
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// for complex matrices, any matrix is fine
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template <typename MatrixType>
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struct generateTriangularMatrix<MatrixType,1>
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{
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static void run(MatrixType& result, typename MatrixType::Index size)
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{
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result.resize(size, size);
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result.template triangularView<Upper>() = MatrixType::Random(size, size);
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}
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};
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template<typename T>
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void test2dRotation(double tol)
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{
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Matrix<T,2,2> A, B, C;
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T angle, c, s;
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A << 0, 1, -1, 0;
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MatrixPower<Matrix<T,2,2> > Apow(A);
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for (int i=0; i<=20; ++i) {
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angle = pow(10, (i-10) / 5.);
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c = std::cos(angle);
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s = std::sin(angle);
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B << c, s, -s, c;
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C = Apow(std::ldexp(angle,1) / M_PI);
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std::cout << "test2dRotation: i = " << i << " error powerm = " << relerr(C,B) << '\n';
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VERIFY(C.isApprox(B, static_cast<T>(tol)));
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}
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}
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template<typename T>
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void test2dHyperbolicRotation(double tol)
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{
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Matrix<std::complex<T>,2,2> A, B, C;
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T angle, ch = std::cosh((T)1);
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std::complex<T> ish(0, std::sinh((T)1));
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A << ch, ish, -ish, ch;
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MatrixPower<Matrix<std::complex<T>,2,2> > Apow(A);
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for (int i=0; i<=20; ++i) {
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angle = std::ldexp(static_cast<T>(i-10), -1);
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ch = std::cosh(angle);
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ish = std::complex<T>(0, std::sinh(angle));
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B << ch, ish, -ish, ch;
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C = Apow(angle);
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std::cout << "test2dHyperbolicRotation: i = " << i << " error powerm = " << relerr(C,B) << '\n';
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VERIFY(C.isApprox(B, static_cast<T>(tol)));
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}
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}
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template<typename MatrixType>
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void testExponentLaws(const MatrixType& m, double tol)
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{
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typedef typename MatrixType::RealScalar RealScalar;
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MatrixType m1, m2, m3, m4, m5;
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RealScalar x, y;
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for (int i=0; i < g_repeat; ++i) {
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generateTestMatrix<MatrixType>::run(m1, m.rows());
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MatrixPower<MatrixType> mpow(m1);
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x = internal::random<RealScalar>();
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y = internal::random<RealScalar>();
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m2 = mpow(x);
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m3 = mpow(y);
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m4 = mpow(x+y);
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m5.noalias() = m2 * m3;
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VERIFY(m4.isApprox(m5, static_cast<RealScalar>(tol)));
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m4 = mpow(x*y);
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m5 = m2.pow(y);
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VERIFY(m4.isApprox(m5, static_cast<RealScalar>(tol)));
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m4 = (std::abs(x) * m1).pow(y);
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m5 = std::pow(std::abs(x), y) * m3;
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VERIFY(m4.isApprox(m5, static_cast<RealScalar>(tol)));
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}
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}
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typedef Matrix<double,3,3,RowMajor> Matrix3dRowMajor;
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typedef Matrix<long double,Dynamic,Dynamic> MatrixXe;
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void test_matrix_power()
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{
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CALL_SUBTEST_2(test2dRotation<double>(1e-13));
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CALL_SUBTEST_1(test2dRotation<float>(2e-5)); // was 1e-5, relaxed for clang 2.8 / linux / x86-64
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CALL_SUBTEST_9(test2dRotation<long double>(1e-13));
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CALL_SUBTEST_2(test2dHyperbolicRotation<double>(1e-14));
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CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5));
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CALL_SUBTEST_9(test2dHyperbolicRotation<long double>(1e-14));
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CALL_SUBTEST_2(testExponentLaws(Matrix2d(), 1e-13));
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CALL_SUBTEST_7(testExponentLaws(Matrix3dRowMajor(), 1e-13));
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CALL_SUBTEST_3(testExponentLaws(Matrix4cd(), 1e-13));
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CALL_SUBTEST_4(testExponentLaws(MatrixXd(8,8), 2e-12));
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CALL_SUBTEST_1(testExponentLaws(Matrix2f(), 1e-4));
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CALL_SUBTEST_5(testExponentLaws(Matrix3cf(), 1e-4));
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CALL_SUBTEST_8(testExponentLaws(Matrix4f(), 1e-4));
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CALL_SUBTEST_6(testExponentLaws(MatrixXf(2,2), 1e-3)); // see bug 614
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CALL_SUBTEST_9(testExponentLaws(MatrixXe(7,7), 1e-13));
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}
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