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For consistency, Simplicial* now factorizes P A P^-1 (instead of P^-1 A P).

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Document how is applied the permutation in Simplicial* .
This commit is contained in:
Gael Guennebaud 2012-06-07 16:24:46 +02:00
parent 63c6ab3e42
commit 1e5e66b642
1 changed files with 20 additions and 10 deletions
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30
Eigen/src/SparseCholesky/SimplicialCholesky.h
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@ -77,6 +77,9 @@ enum SimplicialCholeskyMode {
* selfadjoint and positive definite. The factorization allows for solving A.X = B where
* X and B can be either dense or sparse.
*
* In order to reduce the fill-in, a symmetric permutation P is applied prior to the factorization
* such that the factorized matrix is P A P^-1.
*
* \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
* or Upper. Default is Lower.
@ -208,7 +211,7 @@ class SimplicialCholeskyBase : internal::noncopyable
return;
if(m_P.size()>0)
dest = m_Pinv * b;
dest = m_P * b;
else
dest = b;
@ -222,7 +225,7 @@ class SimplicialCholeskyBase : internal::noncopyable
derived().matrixU().solveInPlace(dest);
if(m_P.size()>0)
dest = m_P * dest;
dest = m_Pinv * dest;
}
/** \internal */
@ -268,7 +271,7 @@ class SimplicialCholeskyBase : internal::noncopyable
eigen_assert(a.rows()==a.cols());
int size = a.cols();
CholMatrixType ap(size,size);
ap.template selfadjointView<Upper>() = a.template selfadjointView<UpLo>().twistedBy(m_Pinv);
ap.template selfadjointView<Upper>() = a.template selfadjointView<UpLo>().twistedBy(m_P);
factorize_preordered<DoLDLT>(ap);
}
@ -359,6 +362,9 @@ template<typename _MatrixType, int _UpLo> struct traits<SimplicialCholesky<_Matr
* selfadjoint and positive definite. The factorization allows for solving A.X = B where
* X and B can be either dense or sparse.
*
* In order to reduce the fill-in, a symmetric permutation P is applied prior to the factorization
* such that the factorized matrix is P A P^-1.
*
* \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
* or Upper. Default is Lower.
@ -444,6 +450,9 @@ public:
* selfadjoint and positive definite. The factorization allows for solving A.X = B where
* X and B can be either dense or sparse.
*
* In order to reduce the fill-in, a symmetric permutation P is applied prior to the factorization
* such that the factorized matrix is P A P^-1.
*
* \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
* or Upper. Default is Lower.
@ -628,7 +637,7 @@ public:
return;
if(Base::m_P.size()>0)
dest = Base::m_Pinv * b;
dest = Base::m_P * b;
else
dest = b;
@ -652,7 +661,7 @@ public:
}
if(Base::m_P.size()>0)
dest = Base::m_P * dest;
dest = Base::m_Pinv * dest;
}
Scalar determinant() const
@ -678,22 +687,23 @@ void SimplicialCholeskyBase<Derived>::ordering(const MatrixType& a, CholMatrixTy
eigen_assert(a.rows()==a.cols());
const Index size = a.rows();
// TODO allows to configure the permutation
// Note that amd compute the inverse permutation
{
CholMatrixType C;
C = a.template selfadjointView<UpLo>();
// remove diagonal entries:
// seems not to be needed
// C.prune(keep_diag());
internal::minimum_degree_ordering(C, m_P);
internal::minimum_degree_ordering(C, m_Pinv);
}
if(m_P.size()>0)
m_Pinv = m_P.inverse();
if(m_Pinv.size()>0)
m_P = m_Pinv.inverse();
else
m_Pinv.resize(0);
m_P.resize(0);
ap.resize(size,size);
ap.template selfadjointView<Upper>() = a.template selfadjointView<UpLo>().twistedBy(m_Pinv);
ap.template selfadjointView<Upper>() = a.template selfadjointView<UpLo>().twistedBy(m_P);
}
template<typename Derived>