diff options
author | Chen-Pang He <jdh8@ms63.hinet.net> | 2013-07-10 02:57:54 +0800 |
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committer | Chen-Pang He <jdh8@ms63.hinet.net> | 2013-07-10 02:57:54 +0800 |
commit | 5c95892b83f9c1b2fb7f5a236cfb965bf8e55c3f (patch) | |
tree | 266773353776e2672c4acfd91b4cc3e068085bf3 /unsupported/test/matrix_power.cpp | |
parent | 639d03d900e844171af0cc3b98dfa98eca79dad5 (diff) |
Test power of singular matrices.
Diffstat (limited to 'unsupported/test/matrix_power.cpp')
-rw-r--r-- | unsupported/test/matrix_power.cpp | 90 |
1 files changed, 80 insertions, 10 deletions
diff --git a/unsupported/test/matrix_power.cpp b/unsupported/test/matrix_power.cpp index 8d53ec94f..a3055c81e 100644 --- a/unsupported/test/matrix_power.cpp +++ b/unsupported/test/matrix_power.cpp @@ -9,6 +9,36 @@ #include "matrix_functions.h" +// for complex matrices, any matrix is fine +template<typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex> +struct generateSingularMatrix +{ + static void run(MatrixType& result, typename MatrixType::Index size) + { + result = MatrixType::Random(size, size); + result.col(0).fill(0); + } +}; + +// for real matrices, make sure none of the eigenvalues are negative +template<typename MatrixType> +struct generateSingularMatrix<MatrixType,0> +{ + static void run(MatrixType& result, typename MatrixType::Index size) + { + MatrixType mat = MatrixType::Random(size, size); + mat.col(0).fill(0); + ComplexSchur<MatrixType> schur(mat); + typename ComplexSchur<MatrixType>::ComplexMatrixType T = schur.matrixT(); + + for (typename MatrixType::Index i = 0; i < size; ++i) { + if (T.coeff(i,i).imag() == 0 && T.coeff(i,i).real() < 0) + T.coeffRef(i,i) = -T.coeff(i,i); + } + result = (schur.matrixU() * (T.template triangularView<Upper>() * schur.matrixU().adjoint())).real(); + } +}; + template<typename T> void test2dRotation(double tol) { @@ -53,7 +83,7 @@ void test2dHyperbolicRotation(double tol) } template<typename MatrixType> -void testExponentLaws(const MatrixType& m, double tol) +void testGeneral(const MatrixType& m, double tol) { typedef typename MatrixType::RealScalar RealScalar; MatrixType m1, m2, m3, m4, m5; @@ -82,6 +112,36 @@ void testExponentLaws(const MatrixType& m, double tol) } } +template<typename MatrixType> +void testSingular(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>(0, 1); + y = internal::random<RealScalar>(0, 1); + 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 = (x * m1).pow(y); + m5 = std::pow(x, y) * m3; + VERIFY(m4.isApprox(m5, tol)); + } +} + typedef Matrix<double,3,3,RowMajor> Matrix3dRowMajor; typedef Matrix<long double,Dynamic,Dynamic> MatrixXe; @@ -94,13 +154,23 @@ void test_matrix_power() CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5)); CALL_SUBTEST_9(test2dHyperbolicRotation<long double>(1e-14)); - CALL_SUBTEST_2(testExponentLaws(Matrix2d(), 1e-13)); - CALL_SUBTEST_7(testExponentLaws(Matrix3dRowMajor(), 1e-13)); - CALL_SUBTEST_3(testExponentLaws(Matrix4cd(), 1e-13)); - CALL_SUBTEST_4(testExponentLaws(MatrixXd(8,8), 2e-12)); - CALL_SUBTEST_1(testExponentLaws(Matrix2f(), 1e-4)); - CALL_SUBTEST_5(testExponentLaws(Matrix3cf(), 1e-4)); - CALL_SUBTEST_8(testExponentLaws(Matrix4f(), 1e-4)); - CALL_SUBTEST_6(testExponentLaws(MatrixXf(2,2), 1e-3)); // see bug 614 - CALL_SUBTEST_9(testExponentLaws(MatrixXe(7,7), 1e-13)); + 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-4)); + CALL_SUBTEST_5(testGeneral(Matrix3cf(), 1e-4)); + CALL_SUBTEST_8(testGeneral(Matrix4f(), 1e-4)); + CALL_SUBTEST_6(testGeneral(MatrixXf(2,2), 1e-3)); // see bug 614 + CALL_SUBTEST_9(testGeneral(MatrixXe(7,7), 1e-13)); + + 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-4)); + CALL_SUBTEST_5(testSingular(Matrix3cf(), 1e-4)); + CALL_SUBTEST_8(testSingular(Matrix4f(), 1e-4)); + CALL_SUBTEST_6(testSingular(MatrixXf(2,2), 1e-3)); + CALL_SUBTEST_9(testSingular(MatrixXe(7,7), 1e-13)); } |