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Test singular matrix power with square roots. Exponent laws are too unstable.

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Chen-Pang He 2013-07-15 00:10:17 +08:00
parent cbe92de2b5
commit b8f0364a1c
1 changed files with 47 additions and 49 deletions
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96
unsupported/test/matrix_power.cpp
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@ -1,7 +1,7 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
// 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
@ -9,36 +9,6 @@
#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)
{
@ -126,33 +96,61 @@ void testGeneral(const MatrixType& m, double tol)
}
}
// For complex matrices, any matrix is fine.
template<typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex>
struct processTriangularMatrix
{
static void run(MatrixType&, MatrixType&, const MatrixType&)
{ }
};
// For real matrices, make sure none of the eigenvalues are negative.
template<typename MatrixType>
struct processTriangularMatrix<MatrixType,0>
{
static void run(MatrixType& m, MatrixType& T, const MatrixType& U)
{
typedef typename MatrixType::Index Index;
const Index size = m.cols();
for (Index i=0; i < size; ++i) {
if (i == size - 1 || T.coeff(i+1,i) == 0)
T.coeffRef(i,i) = std::abs(T.coeff(i,i));
else
++i;
}
m = U * T * U.adjoint();
}
};
template<typename MatrixType>
void testSingular(MatrixType m, double tol)
{
typedef typename MatrixType::RealScalar RealScalar;
MatrixType m1, m2, m3, m4, m5;
RealScalar x, y;
const int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex;
typedef typename internal::conditional< IsComplex, MatrixSquareRootTriangular<MatrixType>,
MatrixSquareRootQuasiTriangular<MatrixType> >::type SquareRootType;
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) {
generateSingularMatrix<MatrixType>::run(m1, m.rows());
MatrixPower<MatrixType> mpow(m1);
m.setRandom();
m.col(0).fill(0);
x = internal::random<RealScalar>(0, 1);
y = internal::random<RealScalar>(0, 1);
m2 = mpow(x);
m3 = mpow(y);
schur.compute(m);
T = schur.matrixT();
const MatrixType& U = schur.matrixU();
processTriangularMatrix<MatrixType>::run(m, T, U);
MatrixPower<MatrixType> mpow(m);
m4 = mpow(x+y);
m5.noalias() = m2 * m3;
VERIFY(m4.isApprox(m5, tol));
SquareRootType(T).compute(T);
VERIFY(mpow(0.5).isApprox(U * (TriangularType(T) * U.adjoint()), tol));
m4 = mpow(x*y);
m5 = m2.pow(y);
VERIFY(m4.isApprox(m5, tol));
SquareRootType(T).compute(T);
VERIFY(mpow(0.25).isApprox(U * (TriangularType(T) * U.adjoint()), tol));
m4 = (x * m1).pow(y);
m5 = std::pow(x, y) * m3;
VERIFY(m4.isApprox(m5, tol));
SquareRootType(T).compute(T);
VERIFY(mpow(0.125).isApprox(U * (TriangularType(T) * U.adjoint()), tol));
}
}