// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
// Copyright (C) 2012-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SPARSE_LU_H
#define EIGEN_SPARSE_LU_H
namespace Eigen {
template <typename _MatrixType, typename _OrderingType = COLAMDOrdering<typename _MatrixType::StorageIndex> > class SparseLU;
template <typename MappedSparseMatrixType> struct SparseLUMatrixLReturnType;
template <typename MatrixLType, typename MatrixUType> struct SparseLUMatrixUReturnType;
/** \ingroup SparseLU_Module
* \class SparseLU
*
* \brief Sparse supernodal LU factorization for general matrices
*
* This class implements the supernodal LU factorization for general matrices.
* It uses the main techniques from the sequential SuperLU package
* (http://crd-legacy.lbl.gov/~xiaoye/SuperLU/). It handles transparently real
* and complex arithmetics with single and double precision, depending on the
* scalar type of your input matrix.
* The code has been optimized to provide BLAS-3 operations during supernode-panel updates.
* It benefits directly from the built-in high-performant Eigen BLAS routines.
* Moreover, when the size of a supernode is very small, the BLAS calls are avoided to
* enable a better optimization from the compiler. For best performance,
* you should compile it with NDEBUG flag to avoid the numerous bounds checking on vectors.
*
* An important parameter of this class is the ordering method. It is used to reorder the columns
* (and eventually the rows) of the matrix to reduce the number of new elements that are created during
* numerical factorization. The cheapest method available is COLAMD.
* See \link OrderingMethods_Module the OrderingMethods module \endlink for the list of
* built-in and external ordering methods.
*
* Simple example with key steps
* \code
* VectorXd x(n), b(n);
* SparseMatrix<double, ColMajor> A;
* SparseLU<SparseMatrix<scalar, ColMajor>, COLAMDOrdering<Index> > solver;
* // fill A and b;
* // Compute the ordering permutation vector from the structural pattern of A
* solver.analyzePattern(A);
* // Compute the numerical factorization
* solver.factorize(A);
* //Use the factors to solve the linear system
* x = solver.solve(b);
* \endcode
*
* \warning The input matrix A should be in a \b compressed and \b column-major form.
* Otherwise an expensive copy will be made. You can call the inexpensive makeCompressed() to get a compressed matrix.
*
* \note Unlike the initial SuperLU implementation, there is no step to equilibrate the matrix.
* For badly scaled matrices, this step can be useful to reduce the pivoting during factorization.
* If this is the case for your matrices, you can try the basic scaling method at
* "unsupported/Eigen/src/IterativeSolvers/Scaling.h"
*
* \tparam _MatrixType The type of the sparse matrix. It must be a column-major SparseMatrix<>
* \tparam _OrderingType The ordering method to use, either AMD, COLAMD or METIS. Default is COLMAD
*
* \implsparsesolverconcept
*
* \sa \ref TutorialSparseSolverConcept
* \sa \ref OrderingMethods_Module
*/
template <typename _MatrixType, typename _OrderingType>
class SparseLU : public SparseSolverBase<SparseLU<_MatrixType,_OrderingType> >, public internal::SparseLUImpl<typename _MatrixType::Scalar, typename _MatrixType::StorageIndex>
{
protected:
typedef SparseSolverBase<SparseLU<_MatrixType,_OrderingType> > APIBase;
using APIBase::m_isInitialized;
public:
using APIBase::_solve_impl;
typedef _MatrixType MatrixType;
typedef _OrderingType OrderingType;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef typename MatrixType::StorageIndex StorageIndex;
typedef SparseMatrix<Scalar,ColMajor,StorageIndex> NCMatrix;
typedef internal::MappedSuperNodalMatrix<Scalar, StorageIndex> SCMatrix;
typedef Matrix<Scalar,Dynamic,1> ScalarVector;
typedef Matrix<StorageIndex,Dynamic,1> IndexVector;
typedef PermutationMatrix<Dynamic, Dynamic, StorageIndex> PermutationType;
typedef internal::SparseLUImpl<Scalar, StorageIndex> Base;
enum {
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
};
public:
SparseLU():m_lastError(""),m_Ustore(0,0,0,0,0,0),m_symmetricmode(false),m_diagpivotthresh(1.0),m_detPermR(1)
{
initperfvalues();
}
explicit SparseLU(const MatrixType& matrix)
: m_lastError(""),m_Ustore(0,0,0,0,0,0),m_symmetricmode(false),m_diagpivotthresh(1.0),m_detPermR(1)
{
initperfvalues();
compute(matrix);
}
~SparseLU()
{
// Free all explicit dynamic pointers
}
void analyzePattern (const MatrixType& matrix);
void factorize (const MatrixType& matrix);
void simplicialfactorize(const MatrixType& matrix);
/**
* Compute the symbolic and numeric factorization of the input sparse matrix.
* The input matrix should be in column-major storage.
*/
void compute (const MatrixType& matrix)
{
// Analyze
analyzePattern(matrix);
//Factorize
factorize(matrix);
}
inline Index rows() const { return m_mat.rows(); }
inline Index cols() const { return m_mat.cols(); }
/** Indicate that the pattern of the input matrix is symmetric */
void isSymmetric(bool sym)
{
m_symmetricmode = sym;
}
/** \returns an expression of the matrix L, internally stored as supernodes
* The only operation available with this expression is the triangular solve
* \code
* y = b; matrixL().solveInPlace(y);
* \endcode
*/
SparseLUMatrixLReturnType<SCMatrix> matrixL() const
{
return SparseLUMatrixLReturnType<SCMatrix>(m_Lstore);
}
/** \returns an expression of the matrix U,
* The only operation available with this expression is the triangular solve
* \code
* y = b; matrixU().solveInPlace(y);
* \endcode
*/
SparseLUMatrixUReturnType<SCMatrix,MappedSparseMatrix<Scalar,ColMajor,StorageIndex> > matrixU() const
{
return SparseLUMatrixUReturnType<SCMatrix, MappedSparseMatrix<Scalar,ColMajor,StorageIndex> >(m_Lstore, m_Ustore);
}
/**
* \returns a reference to the row matrix permutation \f$ P_r \f$ such that \f$P_r A P_c^T = L U\f$
* \sa colsPermutation()
*/
inline const PermutationType& rowsPermutation() const
{
return m_perm_r;
}
/**
* \returns a reference to the column matrix permutation\f$ P_c^T \f$ such that \f$P_r A P_c^T = L U\f$
* \sa rowsPermutation()
*/
inline const PermutationType& colsPermutation() const
{
return m_perm_c;
}
/** Set the threshold used for a diagonal entry to be an acceptable pivot. */
void setPivotThreshold(const RealScalar& thresh)
{
m_diagpivotthresh = thresh;
}
#ifdef EIGEN_PARSED_BY_DOXYGEN
/** \returns the solution X of \f$ A X = B \f$ using the current decomposition of A.
*
* \warning the destination matrix X in X = this->solve(B) must be colmun-major.
*
* \sa compute()
*/
template<typename Rhs>
inline const Solve<SparseLU, Rhs> solve(const MatrixBase<Rhs>& B) const;
#endif // EIGEN_PARSED_BY_DOXYGEN
/** \brief Reports whether previous computation was successful.
*
* \returns \c Success if computation was succesful,
* \c NumericalIssue if the LU factorization reports a problem, zero diagonal for instance
* \c InvalidInput if the input matrix is invalid
*
* \sa iparm()
*/
ComputationInfo info() const
{
eigen_assert(m_isInitialized && "Decomposition is not initialized.");
return m_info;
}
/**
* \returns A string describing the type of error
*/
std::string lastErrorMessage() const
{
return m_lastError;
}
template<typename Rhs, typename Dest>
bool _solve_impl(const MatrixBase<Rhs> &B, MatrixBase<Dest> &X_base) const
{
Dest& X(X_base.derived());
eigen_assert(m_factorizationIsOk && "The matrix should be factorized first");
EIGEN_STATIC_ASSERT((Dest::Flags&RowMajorBit)==0,
THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
// Permute the right hand side to form X = Pr*B
// on return, X is overwritten by the computed solution
X.resize(B.rows(),B.cols());
// this ugly const_cast_derived() helps to detect aliasing when applying the permutations
for(Index j = 0; j < B.cols(); ++j)
X.col(j) = rowsPermutation() * B.const_cast_derived().col(j);
//Forward substitution with L
this->matrixL().solveInPlace(X);
this->matrixU().solveInPlace(X);
// Permute back the solution
for (Index j = 0; j < B.cols(); ++j)
X.col(j) = colsPermutation().inverse() * X.col(j);
return true;
}
/**
* \returns the absolute value of the determinant of the matrix of which
* *this is the QR decomposition.
*
* \warning a determinant can be very big or small, so for matrices
* of large enough dimension, there is a risk of overflow/underflow.
* One way to work around that is to use logAbsDeterminant() instead.
*
* \sa logAbsDeterminant(), signDeterminant()
*/
Scalar absDeterminant()
{
using std::abs;
eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
// Initialize with the determinant of the row matrix
Scalar det = Scalar(1.);
// Note that the diagonal blocks of U are stored in supernodes,
// which are available in the L part :)
for (Index j = 0; j < this->cols(); ++j)
{
for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)
{
if(it.index() == j)
{
det *= abs(it.value());
break;
}
}
}
return det;
}
/** \returns the natural log of the absolute value of the determinant of the matrix
* of which **this is the QR decomposition
*
* \note This method is useful to work around the risk of overflow/underflow that's
* inherent to the determinant computation.
*
* \sa absDeterminant(), signDeterminant()
*/
Scalar logAbsDeterminant() const
{
using std::log;
using std::abs;
eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
Scalar det = Scalar(0.);
for (Index j = 0; j < this->cols(); ++j)
{
for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)
{
if(it.row() < j) continue;
if(it.row() == j)
{
det += log(abs(it.value()));
break;
}
}
}
return det;
}
/** \returns A number representing the sign of the determinant
*
* \sa absDeterminant(), logAbsDeterminant()
*/
Scalar signDeterminant()
{
eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
// Initialize with the determinant of the row matrix
Index det = 1;
// Note that the diagonal blocks of U are stored in supernodes,
// which are available in the L part :)
for (Index j = 0; j < this->cols(); ++j)
{
for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)
{
if(it.index() == j)
{
if(it.value()<0)
det = -det;
else if(it.value()==0)
return 0;
break;
}
}
}
return det * m_detPermR * m_detPermC;
}
/** \returns The determinant of the matrix.
*
* \sa absDeterminant(), logAbsDeterminant()
*/
Scalar determinant()
{
eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
// Initialize with the determinant of the row matrix
Scalar det = Scalar(1.);
// Note that the diagonal blocks of U are stored in supernodes,
// which are available in the L part :)
for (Index j = 0; j < this->cols(); ++j)
{
for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)
{
if(it.index() == j)
{
det *= it.value();
break;
}
}
}
return (m_detPermR * m_detPermC) > 0 ? det : -det;
}
protected:
// Functions
void initperfvalues()
{
m_perfv.panel_size = 16;
m_perfv.relax = 1;
m_perfv.maxsuper = 128;
m_perfv.rowblk = 16;
m_perfv.colblk = 8;
m_perfv.fillfactor = 20;
}
// Variables
mutable ComputationInfo m_info;
bool m_factorizationIsOk;
bool m_analysisIsOk;
std::string m_lastError;
NCMatrix m_mat; // The input (permuted ) matrix
SCMatrix m_Lstore; // The lower triangular matrix (supernodal)
MappedSparseMatrix<Scalar,ColMajor,StorageIndex> m_Ustore; // The upper triangular matrix
PermutationType m_perm_c; // Column permutation
PermutationType m_perm_r ; // Row permutation
IndexVector m_etree; // Column elimination tree
typename Base::GlobalLU_t m_glu;
// SparseLU options
bool m_symmetricmode;
// values for performance
internal::perfvalues m_perfv;
RealScalar m_diagpivotthresh; // Specifies the threshold used for a diagonal entry to be an acceptable pivot
Index m_nnzL, m_nnzU; // Nonzeros in L and U factors
Index m_detPermR, m_detPermC; // Determinants of the permutation matrices
private:
// Disable copy constructor
SparseLU (const SparseLU& );
}; // End class SparseLU
// Functions needed by the anaysis phase
/**
* Compute the column permutation to minimize the fill-in
*
* - Apply this permutation to the input matrix -
*
* - Compute the column elimination tree on the permuted matrix
*
* - Postorder the elimination tree and the column permutation
*
*/
template <typename MatrixType, typename OrderingType>
void SparseLU<MatrixType, OrderingType>::analyzePattern(const MatrixType& mat)
{
//TODO It is possible as in SuperLU to compute row and columns scaling vectors to equilibrate the matrix mat.
// Firstly, copy the whole input matrix.
m_mat = mat;
// Compute fill-in ordering
OrderingType ord;
ord(m_mat,m_perm_c);
// Apply the permutation to the column of the input matrix
if (m_perm_c.size())
{
m_mat.uncompress(); //NOTE: The effect of this command is only to create the InnerNonzeros pointers. FIXME : This vector is filled but not subsequently used.
// Then, permute only the column pointers
ei_declare_aligned_stack_constructed_variable(StorageIndex,outerIndexPtr,mat.cols()+1,mat.isCompressed()?const_cast<StorageIndex*>(mat.outerIndexPtr()):0);
// If the input matrix 'mat' is uncompressed, then the outer-indices do not match the ones of m_mat, and a copy is thus needed.
if(!mat.isCompressed())
IndexVector::Map(outerIndexPtr, mat.cols()+1) = IndexVector::Map(m_mat.outerIndexPtr(),mat.cols()+1);
// Apply the permutation and compute the nnz per column.
for (Index i = 0; i < mat.cols(); i++)
{
m_mat.outerIndexPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i];
m_mat.innerNonZeroPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i+1] - outerIndexPtr[i];
}
}
// Compute the column elimination tree of the permuted matrix
IndexVector firstRowElt;
internal::coletree(m_mat, m_etree,firstRowElt);
// In symmetric mode, do not do postorder here
if (!m_symmetricmode) {
IndexVector post, iwork;
// Post order etree
internal::treePostorder(StorageIndex(m_mat.cols()), m_etree, post);
// Renumber etree in postorder
Index m = m_mat.cols();
iwork.resize(m+1);
for (Index i = 0; i < m; ++i) iwork(post(i)) = post(m_etree(i));
m_etree = iwork;
// Postmultiply A*Pc by post, i.e reorder the matrix according to the postorder of the etree
PermutationType post_perm(m);
for (Index i = 0; i < m; i++)
post_perm.indices()(i) = post(i);
// Combine the two permutations : postorder the permutation for future use
if(m_perm_c.size()) {
m_perm_c = post_perm * m_perm_c;
}
} // end postordering
m_analysisIsOk = true;
}
// Functions needed by the numerical factorization phase
/**
* - Numerical factorization
* - Interleaved with the symbolic factorization
* On exit, info is
*
* = 0: successful factorization
*
* > 0: if info = i, and i is
*
* <= A->ncol: U(i,i) is exactly zero. The factorization has
* been completed, but the factor U is exactly singular,
* and division by zero will occur if it is used to solve a
* system of equations.
*
* > A->ncol: number of bytes allocated when memory allocation
* failure occurred, plus A->ncol. If lwork = -1, it is
* the estimated amount of space needed, plus A->ncol.
*/
template <typename MatrixType, typename OrderingType>
void SparseLU<MatrixType, OrderingType>::factorize(const MatrixType& matrix)
{
using internal::emptyIdxLU;
eigen_assert(m_analysisIsOk && "analyzePattern() should be called first");
eigen_assert((matrix.rows() == matrix.cols()) && "Only for squared matrices");
typedef typename IndexVector::Scalar StorageIndex;
m_isInitialized = true;
// Apply the column permutation computed in analyzepattern()
// m_mat = matrix * m_perm_c.inverse();
m_mat = matrix;
if (m_perm_c.size())
{
m_mat.uncompress(); //NOTE: The effect of this command is only to create the InnerNonzeros pointers.
//Then, permute only the column pointers
const StorageIndex * outerIndexPtr;
if (matrix.isCompressed()) outerIndexPtr = matrix.outerIndexPtr();
else
{
StorageIndex* outerIndexPtr_t = new StorageIndex[matrix.cols()+1];
for(Index i = 0; i <= matrix.cols(); i++) outerIndexPtr_t[i] = m_mat.outerIndexPtr()[i];
outerIndexPtr = outerIndexPtr_t;
}
for (Index i = 0; i < matrix.cols(); i++)
{
m_mat.outerIndexPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i];
m_mat.innerNonZeroPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i+1] - outerIndexPtr[i];
}
if(!matrix.isCompressed()) delete[] outerIndexPtr;
}
else
{ //FIXME This should not be needed if the empty permutation is handled transparently
m_perm_c.resize(matrix.cols());
for(StorageIndex i = 0; i < matrix.cols(); ++i) m_perm_c.indices()(i) = i;
}
Index m = m_mat.rows();
Index n = m_mat.cols();
Index nnz = m_mat.nonZeros();
Index maxpanel = m_perfv.panel_size * m;
// Allocate working storage common to the factor routines
Index lwork = 0;
Index info = Base::memInit(m, n, nnz, lwork, m_perfv.fillfactor, m_perfv.panel_size, m_glu);
if (info)
{
m_lastError = "UNABLE TO ALLOCATE WORKING MEMORY\n\n" ;
m_factorizationIsOk = false;
return ;
}
// Set up pointers for integer working arrays
IndexVector segrep(m); segrep.setZero();
IndexVector parent(m); parent.setZero();
IndexVector xplore(m); xplore.setZero();
IndexVector repfnz(maxpanel);
IndexVector panel_lsub(maxpanel);
IndexVector xprune(n); xprune.setZero();
IndexVector marker(m*internal::LUNoMarker); marker.setZero();
repfnz.setConstant(-1);
panel_lsub.setConstant(-1);
// Set up pointers for scalar working arrays
ScalarVector dense;
dense.setZero(maxpanel);
ScalarVector tempv;
tempv.setZero(internal::LUnumTempV(m, m_perfv.panel_size, m_perfv.maxsuper, /*m_perfv.rowblk*/m) );
// Compute the inverse of perm_c
PermutationType iperm_c(m_perm_c.inverse());
// Identify initial relaxed snodes
IndexVector relax_end(n);
if ( m_symmetricmode == true )
Base::heap_relax_snode(n, m_etree, m_perfv.relax, marker, relax_end);
else
Base::relax_snode(n, m_etree, m_perfv.relax, marker, relax_end);
m_perm_r.resize(m);
m_perm_r.indices().setConstant(-1);
marker.setConstant(-1);
m_detPermR = 1; // Record the determinant of the row permutation
m_glu.supno(0) = emptyIdxLU; m_glu.xsup.setConstant(0);
m_glu.xsup(0) = m_glu.xlsub(0) = m_glu.xusub(0) = m_glu.xlusup(0) = Index(0);
// Work on one 'panel' at a time. A panel is one of the following :
// (a) a relaxed supernode at the bottom of the etree, or
// (b) panel_size contiguous columns, <panel_size> defined by the user
Index jcol;
IndexVector panel_histo(n);
Index pivrow; // Pivotal row number in the original row matrix
Index nseg1; // Number of segments in U-column above panel row jcol
Index nseg; // Number of segments in each U-column
Index irep;
Index i, k, jj;
for (jcol = 0; jcol < n; )
{
// Adjust panel size so that a panel won't overlap with the next relaxed snode.
Index panel_size = m_perfv.panel_size; // upper bound on panel width
for (k = jcol + 1; k < (std::min)(jcol+panel_size, n); k++)
{
if (relax_end(k) != emptyIdxLU)
{
panel_size = k - jcol;
break;
}
}
if (k == n)
panel_size = n - jcol;
// Symbolic outer factorization on a panel of columns
Base::panel_dfs(m, panel_size, jcol, m_mat, m_perm_r.indices(), nseg1, dense, panel_lsub, segrep, repfnz, xprune, marker, parent, xplore, m_glu);
// Numeric sup-panel updates in topological order
Base::panel_bmod(m, panel_size, jcol, nseg1, dense, tempv, segrep, repfnz, m_glu);
// Sparse LU within the panel, and below the panel diagonal
for ( jj = jcol; jj< jcol + panel_size; jj++)
{
k = (jj - jcol) * m; // Column index for w-wide arrays
nseg = nseg1; // begin after all the panel segments
//Depth-first-search for the current column
VectorBlock<IndexVector> panel_lsubk(panel_lsub, k, m);
VectorBlock<IndexVector> repfnz_k(repfnz, k, m);
info = Base::column_dfs(m, jj, m_perm_r.indices(), m_perfv.maxsuper, nseg, panel_lsubk, segrep, repfnz_k, xprune, marker, parent, xplore, m_glu);
if ( info )
{
m_lastError = "UNABLE TO EXPAND MEMORY IN COLUMN_DFS() ";
m_info = NumericalIssue;
m_factorizationIsOk = false;
return;
}
// Numeric updates to this column
VectorBlock<ScalarVector> dense_k(dense, k, m);
VectorBlock<IndexVector> segrep_k(segrep, nseg1, m-nseg1);
info = Base::column_bmod(jj, (nseg - nseg1), dense_k, tempv, segrep_k, repfnz_k, jcol, m_glu);
if ( info )
{
m_lastError = "UNABLE TO EXPAND MEMORY IN COLUMN_BMOD() ";
m_info = NumericalIssue;
m_factorizationIsOk = false;
return;
}
// Copy the U-segments to ucol(*)
info = Base::copy_to_ucol(jj, nseg, segrep, repfnz_k ,m_perm_r.indices(), dense_k, m_glu);
if ( info )
{
m_lastError = "UNABLE TO EXPAND MEMORY IN COPY_TO_UCOL() ";
m_info = NumericalIssue;
m_factorizationIsOk = false;
return;
}
// Form the L-segment
info = Base::pivotL(jj, m_diagpivotthresh, m_perm_r.indices(), iperm_c.indices(), pivrow, m_glu);
if ( info )
{
m_lastError = "THE MATRIX IS STRUCTURALLY SINGULAR ... ZERO COLUMN AT ";
std::ostringstream returnInfo;
returnInfo << info;
m_lastError += returnInfo.str();
m_info = NumericalIssue;
m_factorizationIsOk = false;
return;
}
// Update the determinant of the row permutation matrix
// FIXME: the following test is not correct, we should probably take iperm_c into account and pivrow is not directly the row pivot.
if (pivrow != jj) m_detPermR = -m_detPermR;
// Prune columns (0:jj-1) using column jj
Base::pruneL(jj, m_perm_r.indices(), pivrow, nseg, segrep, repfnz_k, xprune, m_glu);
// Reset repfnz for this column
for (i = 0; i < nseg; i++)
{
irep = segrep(i);
repfnz_k(irep) = emptyIdxLU;
}
} // end SparseLU within the panel
jcol += panel_size; // Move to the next panel
} // end for -- end elimination
m_detPermR = m_perm_r.determinant();
m_detPermC = m_perm_c.determinant();
// Count the number of nonzeros in factors
Base::countnz(n, m_nnzL, m_nnzU, m_glu);
// Apply permutation to the L subscripts
Base::fixupL(n, m_perm_r.indices(), m_glu);
// Create supernode matrix L
m_Lstore.setInfos(m, n, m_glu.lusup, m_glu.xlusup, m_glu.lsub, m_glu.xlsub, m_glu.supno, m_glu.xsup);
// Create the column major upper sparse matrix U;
new (&m_Ustore) MappedSparseMatrix<Scalar, ColMajor, StorageIndex> ( m, n, m_nnzU, m_glu.xusub.data(), m_glu.usub.data(), m_glu.ucol.data() );
m_info = Success;
m_factorizationIsOk = true;
}
template<typename MappedSupernodalType>
struct SparseLUMatrixLReturnType : internal::no_assignment_operator
{
typedef typename MappedSupernodalType::Scalar Scalar;
explicit SparseLUMatrixLReturnType(const MappedSupernodalType& mapL) : m_mapL(mapL)
{ }
Index rows() { return m_mapL.rows(); }
Index cols() { return m_mapL.cols(); }
template<typename Dest>
void solveInPlace( MatrixBase<Dest> &X) const
{
m_mapL.solveInPlace(X);
}
const MappedSupernodalType& m_mapL;
};
template<typename MatrixLType, typename MatrixUType>
struct SparseLUMatrixUReturnType : internal::no_assignment_operator
{
typedef typename MatrixLType::Scalar Scalar;
SparseLUMatrixUReturnType(const MatrixLType& mapL, const MatrixUType& mapU)
: m_mapL(mapL),m_mapU(mapU)
{ }
Index rows() { return m_mapL.rows(); }
Index cols() { return m_mapL.cols(); }
template<typename Dest> void solveInPlace(MatrixBase<Dest> &X) const
{
Index nrhs = X.cols();
Index n = X.rows();
// Backward solve with U
for (Index k = m_mapL.nsuper(); k >= 0; k--)
{
Index fsupc = m_mapL.supToCol()[k];
Index lda = m_mapL.colIndexPtr()[fsupc+1] - m_mapL.colIndexPtr()[fsupc]; // leading dimension
Index nsupc = m_mapL.supToCol()[k+1] - fsupc;
Index luptr = m_mapL.colIndexPtr()[fsupc];
if (nsupc == 1)
{
for (Index j = 0; j < nrhs; j++)
{
X(fsupc, j) /= m_mapL.valuePtr()[luptr];
}
}
else
{
Map<const Matrix<Scalar,Dynamic,Dynamic, ColMajor>, 0, OuterStride<> > A( &(m_mapL.valuePtr()[luptr]), nsupc, nsupc, OuterStride<>(lda) );
Map< Matrix<Scalar,Dynamic,Dest::ColsAtCompileTime, ColMajor>, 0, OuterStride<> > U (&(X(fsupc,0)), nsupc, nrhs, OuterStride<>(n) );
U = A.template triangularView<Upper>().solve(U);
}
for (Index j = 0; j < nrhs; ++j)
{
for (Index jcol = fsupc; jcol < fsupc + nsupc; jcol++)
{
typename MatrixUType::InnerIterator it(m_mapU, jcol);
for ( ; it; ++it)
{
Index irow = it.index();
X(irow, j) -= X(jcol, j) * it.value();
}
}
}
} // End For U-solve
}
const MatrixLType& m_mapL;
const MatrixUType& m_mapU;
};
} // End namespace Eigen
#endif