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Implement square root for real matrices via Schur.

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This commit is contained in:
Jitse Niesen
2011-05-08 22:18:37 +01:00
parent 6b4e215710
commit 6e1573f66a
2 changed files with 231 additions and 16 deletions
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43
unsupported/test/matrix_square_root.cpp
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@@ -25,16 +25,45 @@
#include "main.h"
#include <unsupported/Eigen/MatrixFunctions>
template <typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex>
struct generateTestMatrix;
// for real matrices, make sure none of the eigenvalues are negative
template <typename MatrixType>
struct generateTestMatrix<MatrixType,0>
{
static void run(MatrixType& result, typename MatrixType::Index size)
{
MatrixType mat = MatrixType::Random(size, size);
EigenSolver<MatrixType> es(mat);
typename EigenSolver<MatrixType>::EigenvalueType eivals = es.eigenvalues();
for (typename MatrixType::Index i = 0; i < size; ++i) {
if (eivals(i).imag() == 0 && eivals(i).real() < 0)
eivals(i) = -eivals(i);
}
result = (es.eigenvectors() * eivals.asDiagonal() * es.eigenvectors().inverse()).real();
}
};
// for complex matrices, any matrix is fine
template <typename MatrixType>
struct generateTestMatrix<MatrixType,1>
{
static void run(MatrixType& result, typename MatrixType::Index size)
{
result = MatrixType::Random(size, size);
}
};
template<typename MatrixType>
void testMatrixSqrt(const MatrixType& m)
{
typedef typename MatrixType::Index Index;
const Index size = m.rows();
MatrixType A = MatrixType::Random(size, size);
MatrixType A;
generateTestMatrix<MatrixType>::run(A, m.rows());
MatrixSquareRoot<MatrixType> msr(A);
MatrixType S;
msr.compute(S);
VERIFY_IS_APPROX(S*S, A);
MatrixType sqrtA;
msr.compute(sqrtA);
VERIFY_IS_APPROX(sqrtA * sqrtA, A);
}
void test_matrix_square_root()
@@ -42,5 +71,7 @@ void test_matrix_square_root()
for (int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1(testMatrixSqrt(Matrix3cf()));
CALL_SUBTEST_2(testMatrixSqrt(MatrixXcd(12,12)));
CALL_SUBTEST_3(testMatrixSqrt(Matrix4f()));
CALL_SUBTEST_4(testMatrixSqrt(Matrix<double,Dynamic,Dynamic,RowMajor>(9, 9)));
}
}