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add computeRotationScaling and computeScalingRotation in SVD

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add convenience functions in Transform
reimplement Transform::rotation() to use that
add unit-test
This commit is contained in:
Benoit Jacob
2009-01-22 16:39:08 +00:00
parent 876b1fb842
commit 291ee89684
3 changed files with 138 additions and 43 deletions
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77
Eigen/src/SVD/SVD.h
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@@ -79,8 +79,14 @@ template<typename MatrixType> class SVD
void compute(const MatrixType& matrix);
SVD& sort();
void computeUnitaryPositive(MatrixUType *unitary, MatrixType *positive) const;
void computePositiveUnitary(MatrixType *positive, MatrixVType *unitary) const;
template<typename UnitaryType, typename PositiveType>
void computeUnitaryPositive(UnitaryType *unitary, PositiveType *positive) const;
template<typename PositiveType, typename UnitaryType>
void computePositiveUnitary(PositiveType *positive, UnitaryType *unitary) const;
template<typename RotationType, typename ScalingType>
void computeRotationScaling(RotationType *unitary, ScalingType *positive) const;
template<typename ScalingType, typename RotationType>
void computeScalingRotation(ScalingType *positive, RotationType *unitary) const;
protected:
/** \internal */
@@ -542,10 +548,13 @@ bool SVD<MatrixType>::solve(const MatrixBase<OtherDerived> &b, ResultType* resul
* If either pointer is zero, the corresponding computation is skipped.
*
* Only for square matrices.
*
* \sa computePositiveUnitary(), computeRotationScaling()
*/
template<typename MatrixType>
void SVD<MatrixType>::computeUnitaryPositive(typename SVD<MatrixType>::MatrixUType *unitary,
MatrixType *positive) const
template<typename UnitaryType, typename PositiveType>
void SVD<MatrixType>::computeUnitaryPositive(UnitaryType *unitary,
PositiveType *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();
@@ -557,16 +566,72 @@ void SVD<MatrixType>::computeUnitaryPositive(typename SVD<MatrixType>::MatrixUTy
* If either pointer is zero, the corresponding computation is skipped.
*
* Only for square matrices.
*
* \sa computeUnitaryPositive(), computeRotationScaling()
*/
template<typename MatrixType>
void SVD<MatrixType>::computePositiveUnitary(MatrixType *positive,
typename SVD<MatrixType>::MatrixVType *unitary) const
template<typename UnitaryType, typename PositiveType>
void SVD<MatrixType>::computePositiveUnitary(UnitaryType *positive,
PositiveType *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();
}
/** decomposes the matrix as a product rotation x scaling, the scaling being
* not necessarily positive.
*
* If either pointer is zero, the corresponding computation is skipped.
*
* This method requires the Geometry module.
*
* \sa computeScalingRotation(), computeUnitaryPositive()
*/
template<typename MatrixType>
template<typename RotationType, typename ScalingType>
void SVD<MatrixType>::computeRotationScaling(RotationType *rotation, ScalingType *scaling) const
{
ei_assert(m_matU.rows() == m_matV.rows() && "Polar decomposition is only for square matrices");
Scalar x = (m_matU * m_matV.adjoint()).determinant(); // so x has absolute value 1
Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> sv(m_sigma);
sv.coeffRef(0) *= x;
if(scaling) scaling->lazyAssign(m_matV * sv.asDiagonal() * m_matV.adjoint());
if(rotation)
{
MatrixType m(m_matU);
m.col(0) /= x;
rotation->lazyAssign(m * m_matV.adjoint());
}
}
/** decomposes the matrix as a product scaling x rotation, the scaling being
* not necessarily positive.
*
* If either pointer is zero, the corresponding computation is skipped.
*
* This method requires the Geometry module.
*
* \sa computeRotationScaling(), computeUnitaryPositive()
*/
template<typename MatrixType>
template<typename ScalingType, typename RotationType>
void SVD<MatrixType>::computeScalingRotation(ScalingType *scaling, RotationType *rotation) const
{
ei_assert(m_matU.rows() == m_matV.rows() && "Polar decomposition is only for square matrices");
Scalar x = (m_matU * m_matV.adjoint()).determinant(); // so x has absolute value 1
Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> sv(m_sigma);
sv.coeffRef(0) *= x;
if(scaling) scaling->lazyAssign(m_matU * sv.asDiagonal() * m_matU.adjoint());
if(rotation)
{
MatrixType m(m_matU);
m.col(0) /= x;
rotation->lazyAssign(m * m_matV.adjoint());
}
}
/** \svd_module
* \returns the SVD decomposition of \c *this
*/