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add polar decomposition on both sides, in SVD, with test

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This commit is contained in:
Benoit Jacob
2009-01-22 15:00:47 +00:00
parent 32754d806d
commit 876b1fb842
2 changed files with 59 additions and 6 deletions
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32
test/svd.cpp
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@@ -44,13 +44,15 @@ template<typename MatrixType> void svd(const MatrixType& m)
if (ei_is_same_type<RealScalar,float>::ret)
largerEps = 1e-3f;
SVD<MatrixType> svd(a);
MatrixType sigma = MatrixType::Zero(rows,cols);
MatrixType matU = MatrixType::Zero(rows,rows);
sigma.block(0,0,cols,cols) = svd.singularValues().asDiagonal();
matU.block(0,0,rows,cols) = svd.matrixU();
{
SVD<MatrixType> svd(a);
MatrixType sigma = MatrixType::Zero(rows,cols);
MatrixType matU = MatrixType::Zero(rows,rows);
sigma.block(0,0,cols,cols) = svd.singularValues().asDiagonal();
matU.block(0,0,rows,cols) = svd.matrixU();
VERIFY_IS_APPROX(a, matU * sigma * svd.matrixV().transpose());
}
VERIFY_IS_APPROX(a, matU * sigma * svd.matrixV().transpose());
if (rows==cols)
{
@@ -63,6 +65,24 @@ template<typename MatrixType> void svd(const MatrixType& m)
svd.solve(b, &x);
VERIFY_IS_APPROX(a * x,b);
}
if(rows==cols)
{
SVD<MatrixType> svd(a);
MatrixType unitary, positive;
svd.computeUnitaryPositive(&unitary, &positive);
VERIFY_IS_APPROX(unitary * unitary.adjoint(), MatrixType::Identity(unitary.rows(),unitary.rows()));
VERIFY_IS_APPROX(positive, positive.adjoint());
for(int i = 0; i < rows; i++) VERIFY(positive.diagonal()[i] >= 0); // cheap necessary (not sufficient) condition for positivity
VERIFY_IS_APPROX(unitary*positive, a);
svd.computePositiveUnitary(&positive, &unitary);
VERIFY_IS_APPROX(unitary * unitary.adjoint(), MatrixType::Identity(unitary.rows(),unitary.rows()));
VERIFY_IS_APPROX(positive, positive.adjoint());
for(int i = 0; i < rows; i++) VERIFY(positive.diagonal()[i] >= 0); // cheap necessary (not sufficient) condition for positivity
VERIFY_IS_APPROX(positive*unitary, a);
}
}
void test_svd()