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Add internal method _solve_impl_transposed() to LU decomposition classes that solves A^T x = b or A^* x = b.

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This commit is contained in:
Rasmus Munk Larsen
2015-11-30 13:39:24 -08:00
parent 274b2272b7
commit 1663d15da7
3 changed files with 148 additions and 23 deletions
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45
Eigen/src/LU/PartialPivLU.h
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@@ -11,7 +11,7 @@
#ifndef EIGEN_PARTIALLU_H
#define EIGEN_PARTIALLU_H
namespace Eigen {
namespace Eigen {
namespace internal {
template<typename _MatrixType> struct traits<PartialPivLU<_MatrixType> >
@@ -185,7 +185,7 @@ template<typename _MatrixType> class PartialPivLU
inline Index rows() const { return m_lu.rows(); }
inline Index cols() const { return m_lu.cols(); }
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename RhsType, typename DstType>
EIGEN_DEVICE_FUNC
@@ -206,17 +206,44 @@ template<typename _MatrixType> class PartialPivLU
m_lu.template triangularView<UnitLower>().solveInPlace(dst);
// Step 3
m_lu.template triangularView<Upper>().solveInPlace(dst);
m_lu.template triangularView<Upper>().solveInPlace(dst);
}
template<bool Conjugate, typename RhsType, typename DstType>
EIGEN_DEVICE_FUNC
void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const {
/* The decomposition PA = LU can be rewritten as A = P^{-1} L U.
* So we proceed as follows:
* Step 1: compute c = Pb.
* Step 2: replace c by the solution x to Lx = c.
* Step 3: replace c by the solution x to Ux = c.
*/
eigen_assert(rhs.rows() == m_lu.cols());
if (Conjugate) {
// Step 1
dst = m_lu.template triangularView<Upper>().adjoint().solve(rhs);
// Step 2
m_lu.template triangularView<UnitLower>().adjoint().solveInPlace(dst);
} else {
// Step 1
dst = m_lu.template triangularView<Upper>().transpose().solve(rhs);
// Step 2
m_lu.template triangularView<UnitLower>().transpose().solveInPlace(dst);
}
// Step 3
dst = permutationP().transpose() * dst;
}
#endif
protected:
static void check_template_parameters()
{
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
}
MatrixType m_lu;
PermutationType m_p;
TranspositionType m_rowsTranspositions;
@@ -295,7 +322,7 @@ struct partial_lu_impl
{
Index rrows = rows-k-1;
Index rcols = cols-k-1;
Index row_of_biggest_in_col;
Score biggest_in_corner
= lu.col(k).tail(rows-k).unaryExpr(Scoring()).maxCoeff(&row_of_biggest_in_col);
@@ -436,10 +463,10 @@ template<typename InputType>
PartialPivLU<MatrixType>& PartialPivLU<MatrixType>::compute(const EigenBase<InputType>& matrix)
{
check_template_parameters();
// the row permutation is stored as int indices, so just to be sure:
eigen_assert(matrix.rows()<NumTraits<int>::highest());
m_lu = matrix.derived();
eigen_assert(matrix.rows() == matrix.cols() && "PartialPivLU is only for square (and moreover invertible) matrices");
@@ -492,7 +519,7 @@ struct Assignment<DstXprType, Inverse<PartialPivLU<MatrixType> >, internal::assi
typedef PartialPivLU<MatrixType> LuType;
typedef Inverse<LuType> SrcXprType;
static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar> &)
{
{
dst = src.nestedExpression().solve(MatrixType::Identity(src.rows(), src.cols()));
}
};