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Test power of singular matrices.

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This commit is contained in:
Chen-Pang He 2013-07-10 02:57:54 +08:00
parent 639d03d900
commit 5c95892b83
1 changed files with 80 additions and 10 deletions
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90
unsupported/test/matrix_power.cpp
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@ -9,6 +9,36 @@
#include "matrix_functions.h" #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> template<typename T>
void test2dRotation(double tol) void test2dRotation(double tol)
{ {
@ -53,7 +83,7 @@ void test2dHyperbolicRotation(double tol)
} }
template<typename MatrixType> template<typename MatrixType>
void testExponentLaws(const MatrixType& m, double tol) void testGeneral(const MatrixType& m, double tol)
{ {
typedef typename MatrixType::RealScalar RealScalar; typedef typename MatrixType::RealScalar RealScalar;
MatrixType m1, m2, m3, m4, m5; 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<double,3,3,RowMajor> Matrix3dRowMajor;
typedef Matrix<long double,Dynamic,Dynamic> MatrixXe; typedef Matrix<long double,Dynamic,Dynamic> MatrixXe;
@ -94,13 +154,23 @@ void test_matrix_power()
CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5)); CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5));
CALL_SUBTEST_9(test2dHyperbolicRotation<long double>(1e-14)); CALL_SUBTEST_9(test2dHyperbolicRotation<long double>(1e-14));
CALL_SUBTEST_2(testExponentLaws(Matrix2d(), 1e-13)); CALL_SUBTEST_2(testGeneral(Matrix2d(), 1e-13));
CALL_SUBTEST_7(testExponentLaws(Matrix3dRowMajor(), 1e-13)); CALL_SUBTEST_7(testGeneral(Matrix3dRowMajor(), 1e-13));
CALL_SUBTEST_3(testExponentLaws(Matrix4cd(), 1e-13)); CALL_SUBTEST_3(testGeneral(Matrix4cd(), 1e-13));
CALL_SUBTEST_4(testExponentLaws(MatrixXd(8,8), 2e-12)); CALL_SUBTEST_4(testGeneral(MatrixXd(8,8), 2e-12));
CALL_SUBTEST_1(testExponentLaws(Matrix2f(), 1e-4)); CALL_SUBTEST_1(testGeneral(Matrix2f(), 1e-4));
CALL_SUBTEST_5(testExponentLaws(Matrix3cf(), 1e-4)); CALL_SUBTEST_5(testGeneral(Matrix3cf(), 1e-4));
CALL_SUBTEST_8(testExponentLaws(Matrix4f(), 1e-4)); CALL_SUBTEST_8(testGeneral(Matrix4f(), 1e-4));
CALL_SUBTEST_6(testExponentLaws(MatrixXf(2,2), 1e-3)); // see bug 614 CALL_SUBTEST_6(testGeneral(MatrixXf(2,2), 1e-3)); // see bug 614
CALL_SUBTEST_9(testExponentLaws(MatrixXe(7,7), 1e-13)); 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));
} }