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Factorize *SVD::solve to SVDBase

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This commit is contained in:
Gael Guennebaud
2014-09-01 18:31:54 +02:00
parent b3a0365429
commit 1f398dfc82
3 changed files with 71 additions and 72 deletions
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70
Eigen/src/SVD/SVDBase.h
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@@ -190,6 +190,41 @@ public:
inline Index rows() const { return m_rows; }
inline Index cols() const { return m_cols; }
/** \returns a (least squares) solution of \f$ A x = b \f$ using the current SVD decomposition of A.
*
* \param b the right-hand-side of the equation to solve.
*
* \note Solving requires both U and V to be computed. Thin U and V are enough, there is no need for full U or V.
*
* \note SVD solving is implicitly least-squares. Thus, this method serves both purposes of exact solving and least-squares solving.
* In other words, the returned solution is guaranteed to minimize the Euclidean norm \f$ \Vert A x - b \Vert \f$.
*/
#ifdef EIGEN_TEST_EVALUATORS
template<typename Rhs>
inline const Solve<Derived, Rhs>
solve(const MatrixBase<Rhs>& b) const
{
eigen_assert(m_isInitialized && "SVD is not initialized.");
eigen_assert(computeU() && computeV() && "SVD::solve() requires both unitaries U and V to be computed (thin unitaries suffice).");
return Solve<Derived, Rhs>(derived(), b.derived());
}
#else
template<typename Rhs>
inline const internal::solve_retval<SVDBase, Rhs>
solve(const MatrixBase<Rhs>& b) const
{
eigen_assert(m_isInitialized && "SVD is not initialized.");
eigen_assert(computeU() && computeV() && "SVD::solve() requires both unitaries U and V to be computed (thin unitaries suffice).");
return internal::solve_retval<SVDBase, Rhs>(*this, b.derived());
}
#endif
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename RhsType, typename DstType>
EIGEN_DEVICE_FUNC
void _solve_impl(const RhsType &rhs, DstType &dst) const;
#endif
protected:
// return true if already allocated
@@ -220,6 +255,41 @@ protected:
};
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename Derived>
template<typename RhsType, typename DstType>
void SVDBase<Derived>::_solve_impl(const RhsType &rhs, DstType &dst) const
{
eigen_assert(rhs.rows() == rows());
// A = U S V^*
// So A^{-1} = V S^{-1} U^*
Matrix<Scalar, Dynamic, RhsType::ColsAtCompileTime, 0, MatrixType::MaxRowsAtCompileTime, RhsType::MaxColsAtCompileTime> tmp;
Index l_rank = rank();
tmp.noalias() = m_matrixU.leftCols(l_rank).adjoint() * rhs;
tmp = m_singularValues.head(l_rank).asDiagonal().inverse() * tmp;
dst = m_matrixV.leftCols(l_rank) * tmp;
}
#endif
namespace internal {
#ifndef EIGEN_TEST_EVALUATORS
template<typename Derived, typename Rhs>
struct solve_retval<SVDBase<Derived>, Rhs>
: solve_retval_base<SVDBase<Derived>, Rhs>
{
typedef SVDBase<Derived> SVDType;
EIGEN_MAKE_SOLVE_HELPERS(SVDType,Rhs)
template<typename Dest> void evalTo(Dest& dst) const
{
dec().derived()._solve_impl(rhs(), dst);
}
};
#endif
} // end namespace internal
template<typename MatrixType>
bool SVDBase<MatrixType>::allocate(Index rows, Index cols, unsigned int computationOptions)