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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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33
Eigen/src/SVD/SVD.h
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@ -79,6 +79,9 @@ template<typename MatrixType> class SVD
void compute(const MatrixType& matrix); void compute(const MatrixType& matrix);
SVD& sort(); SVD& sort();
void computeUnitaryPositive(MatrixUType *unitary, MatrixType *positive) const;
void computePositiveUnitary(MatrixType *positive, MatrixVType *unitary) const;
protected: protected:
/** \internal */ /** \internal */
MatrixUType m_matU; MatrixUType m_matU;
@ -534,6 +537,36 @@ bool SVD<MatrixType>::solve(const MatrixBase<OtherDerived> &b, ResultType* resul
return true; return true;
} }
/** Computes the polar decomposition of the matrix, as a product unitary x positive.
*
* If either pointer is zero, the corresponding computation is skipped.
*
* Only for square matrices.
*/
template<typename MatrixType>
void SVD<MatrixType>::computeUnitaryPositive(typename SVD<MatrixType>::MatrixUType *unitary,
MatrixType *positive) const
{
ei_assert(m_matU.cols() == m_matV.cols() && "Polar decomposition is only for square matrices");
if(unitary) *unitary = m_matU * m_matV.adjoint();
if(positive) *positive = m_matV * m_sigma.asDiagonal() * m_matV.adjoint();
}
/** Computes the polar decomposition of the matrix, as a product positive x unitary.
*
* If either pointer is zero, the corresponding computation is skipped.
*
* Only for square matrices.
*/
template<typename MatrixType>
void SVD<MatrixType>::computePositiveUnitary(MatrixType *positive,
typename SVD<MatrixType>::MatrixVType *unitary) const
{
ei_assert(m_matU.rows() == m_matV.rows() && "Polar decomposition is only for square matrices");
if(unitary) *unitary = m_matU * m_matV.adjoint();
if(positive) *positive = m_matU * m_sigma.asDiagonal() * m_matU.adjoint();
}
/** \svd_module /** \svd_module
* \returns the SVD decomposition of \c *this * \returns the SVD decomposition of \c *this
*/ */

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) if (ei_is_same_type<RealScalar,float>::ret)
largerEps = 1e-3f; largerEps = 1e-3f;
SVD<MatrixType> svd(a); {
MatrixType sigma = MatrixType::Zero(rows,cols); SVD<MatrixType> svd(a);
MatrixType matU = MatrixType::Zero(rows,rows); MatrixType sigma = MatrixType::Zero(rows,cols);
sigma.block(0,0,cols,cols) = svd.singularValues().asDiagonal(); MatrixType matU = MatrixType::Zero(rows,rows);
matU.block(0,0,rows,cols) = svd.matrixU(); 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) if (rows==cols)
{ {
@ -63,6 +65,24 @@ template<typename MatrixType> void svd(const MatrixType& m)
svd.solve(b, &x); svd.solve(b, &x);
VERIFY_IS_APPROX(a * x,b); 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() void test_svd()