Public Types | Public Member Functions | Protected Member Functions | Protected Attributes | Private Member Functions | List of all members
Eigen::SparseLU< _MatrixType, _OrderingType > Class Template Reference

Sparse supernodal LU factorization for general matrices. More...

#include <SparseLU.h>

Inheritance diagram for Eigen::SparseLU< _MatrixType, _OrderingType >:
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Public Types

typedef internal::SparseLUImpl< Scalar, Index > Base
 
typedef MatrixType::Index Index
 
typedef Matrix< Index, Dynamic, 1 > IndexVector
 
typedef _MatrixType MatrixType
 
typedef SparseMatrix< Scalar, ColMajor, Index > NCMatrix
 
typedef _OrderingType OrderingType
 
typedef PermutationMatrix< Dynamic, Dynamic, Index > PermutationType
 
typedef MatrixType::RealScalar RealScalar
 
typedef MatrixType::Scalar Scalar
 
typedef Matrix< Scalar, Dynamic, 1 > ScalarVector
 
typedef internal::MappedSuperNodalMatrix< Scalar, Index > SCMatrix
 
- Public Types inherited from Eigen::internal::SparseLUImpl< _MatrixType::Scalar, _MatrixType::Index >
typedef Ref< Matrix< _MatrixType::Index, Dynamic, 1 > > BlockIndexVector
 
typedef Ref< Matrix< _MatrixType::Scalar, Dynamic, 1 > > BlockScalarVector
 
typedef LU_GlobalLU_t< IndexVector, ScalarVector > GlobalLU_t
 
typedef Matrix< _MatrixType::Index, Dynamic, 1 > IndexVector
 
typedef SparseMatrix< _MatrixType::Scalar, ColMajor, _MatrixType::Index > MatrixType
 
typedef ScalarVector::RealScalar RealScalar
 
typedef Matrix< _MatrixType::Scalar, Dynamic, 1 > ScalarVector
 

Public Member Functions

template<typename Rhs , typename Dest >
bool _solve (const MatrixBase< Rhs > &B, MatrixBase< Dest > &_X) const
 
Scalar absDeterminant ()
 
void analyzePattern (const MatrixType &matrix)
 
Index cols () const
 
const PermutationType & colsPermutation () const
 
void compute (const MatrixType &matrix)
 
void factorize (const MatrixType &matrix)
 
ComputationInfo info () const
 Reports whether previous computation was successful. More...
 
void isSymmetric (bool sym)
 
std::string lastErrorMessage () const
 
Scalar logAbsDeterminant () const
 
SparseLUMatrixLReturnType< SCMatrix > matrixL () const
 
SparseLUMatrixUReturnType< SCMatrix, MappedSparseMatrix< Scalar, ColMajor, Index > > matrixU () const
 
Index rows () const
 
const PermutationType & rowsPermutation () const
 
void setPivotThreshold (const RealScalar &thresh)
 
Scalar signDeterminant ()
 
void simplicialfactorize (const MatrixType &matrix)
 
template<typename Rhs >
const internal::solve_retval< SparseLU, Rhs > solve (const MatrixBase< Rhs > &B) const
 
template<typename Rhs >
const internal::sparse_solve_retval< SparseLU, Rhs > solve (const SparseMatrixBase< Rhs > &B) const
 
 SparseLU ()
 
 SparseLU (const MatrixType &matrix)
 
 ~SparseLU ()
 

Protected Member Functions

void initperfvalues ()
 
- Protected Member Functions inherited from Eigen::internal::SparseLUImpl< _MatrixType::Scalar, _MatrixType::Index >
_MatrixType::Index column_bmod (const _MatrixType::Indexjcol, const _MatrixType::Indexnseg, BlockScalarVector dense, ScalarVector &tempv, BlockIndexVector segrep, BlockIndexVector repfnz, _MatrixType::Indexfpanelc, GlobalLU_t &glu)
 Performs numeric block updates (sup-col) in topological order. More...
 
_MatrixType::Index column_dfs (const _MatrixType::Indexm, const _MatrixType::Indexjcol, IndexVector &perm_r, _MatrixType::Indexmaxsuper, _MatrixType::Index &nseg, BlockIndexVector lsub_col, IndexVector &segrep, BlockIndexVector repfnz, IndexVector &xprune, IndexVector &marker, IndexVector &parent, IndexVector &xplore, GlobalLU_t &glu)
 Performs a symbolic factorization on column jcol and decide the supernode boundary. More...
 
_MatrixType::Index copy_to_ucol (const _MatrixType::Indexjcol, const _MatrixType::Indexnseg, IndexVector &segrep, BlockIndexVector repfnz, IndexVector &perm_r, BlockScalarVector dense, GlobalLU_t &glu)
 Performs numeric block updates (sup-col) in topological order. More...
 
void countnz (const _MatrixType::Indexn, _MatrixType::Index &nnzL, _MatrixType::Index &nnzU, GlobalLU_t &glu)
 Count Nonzero elements in the factors. More...
 
void dfs_kernel (const _MatrixType::Indexjj, IndexVector &perm_r, _MatrixType::Index &nseg, IndexVector &panel_lsub, IndexVector &segrep, Ref< IndexVector > repfnz_col, IndexVector &xprune, Ref< IndexVector > marker, IndexVector &parent, IndexVector &xplore, GlobalLU_t &glu, _MatrixType::Index &nextl_col, _MatrixType::Indexkrow, Traits &traits)
 
_MatrixType::Index expand (VectorType &vec, _MatrixType::Index &length, _MatrixType::IndexnbElts, _MatrixType::Indexkeep_prev, _MatrixType::Index &num_expansions)
 
void fixupL (const _MatrixType::Indexn, const IndexVector &perm_r, GlobalLU_t &glu)
 Fix up the data storage lsub for L-subscripts. More...
 
void heap_relax_snode (const _MatrixType::Indexn, IndexVector &et, const _MatrixType::Indexrelax_columns, IndexVector &descendants, IndexVector &relax_end)
 Identify the initial relaxed supernodes. More...
 
_MatrixType::Index memInit (_MatrixType::Indexm, _MatrixType::Indexn, _MatrixType::Indexannz, _MatrixType::Indexlwork, _MatrixType::Indexfillratio, _MatrixType::Indexpanel_size, GlobalLU_t &glu)
 Allocate various working space for the numerical factorization phase. More...
 
_MatrixType::Index memXpand (VectorType &vec, _MatrixType::Index &maxlen, _MatrixType::IndexnbElts, MemType memtype, _MatrixType::Index &num_expansions)
 Expand the existing storage. More...
 
void panel_bmod (const _MatrixType::Indexm, const _MatrixType::Indexw, const _MatrixType::Indexjcol, const _MatrixType::Indexnseg, ScalarVector &dense, ScalarVector &tempv, IndexVector &segrep, IndexVector &repfnz, GlobalLU_t &glu)
 Performs numeric block updates (sup-panel) in topological order. More...
 
void panel_dfs (const _MatrixType::Indexm, const _MatrixType::Indexw, const _MatrixType::Indexjcol, MatrixType &A, IndexVector &perm_r, _MatrixType::Index &nseg, ScalarVector &dense, IndexVector &panel_lsub, IndexVector &segrep, IndexVector &repfnz, IndexVector &xprune, IndexVector &marker, IndexVector &parent, IndexVector &xplore, GlobalLU_t &glu)
 Performs a symbolic factorization on a panel of columns [jcol, jcol+w) More...
 
_MatrixType::Index pivotL (const _MatrixType::Indexjcol, const RealScalar &diagpivotthresh, IndexVector &perm_r, IndexVector &iperm_c, _MatrixType::Index &pivrow, GlobalLU_t &glu)
 Performs the numerical pivotin on the current column of L, and the CDIV operation. More...
 
void pruneL (const _MatrixType::Indexjcol, const IndexVector &perm_r, const _MatrixType::Indexpivrow, const _MatrixType::Indexnseg, const IndexVector &segrep, BlockIndexVector repfnz, IndexVector &xprune, GlobalLU_t &glu)
 Prunes the L-structure. More...
 
void relax_snode (const _MatrixType::Indexn, IndexVector &et, const _MatrixType::Indexrelax_columns, IndexVector &descendants, IndexVector &relax_end)
 Identify the initial relaxed supernodes. More...
 
_MatrixType::Index snode_bmod (const _MatrixType::Indexjcol, const _MatrixType::Indexfsupc, ScalarVector &dense, GlobalLU_t &glu)
 
_MatrixType::Index snode_dfs (const _MatrixType::Indexjcol, const _MatrixType::Indexkcol, const MatrixType &mat, IndexVector &xprune, IndexVector &marker, GlobalLU_t &glu)
 

Protected Attributes

bool m_analysisIsOk
 
Index m_detPermR
 
RealScalar m_diagpivotthresh
 
IndexVector m_etree
 
bool m_factorizationIsOk
 
Base::GlobalLU_t m_glu
 
ComputationInfo m_info
 
bool m_isInitialized
 
std::string m_lastError
 
SCMatrix m_Lstore
 
NCMatrix m_mat
 
Index m_nnzL
 
Index m_nnzU
 
internal::perfvalues< Index > m_perfv
 
PermutationType m_perm_c
 
PermutationType m_perm_r
 
bool m_symmetricmode
 
MappedSparseMatrix< Scalar, ColMajor, Index > m_Ustore
 

Private Member Functions

 SparseLU (const SparseLU &)
 

Detailed Description

template<typename _MatrixType, typename _OrderingType>
class Eigen::SparseLU< _MatrixType, _OrderingType >

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 the OrderingMethods module for the list of built-in and external ordering methods.

Simple example with key steps

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);
Warning
The input matrix A should be in a compressed and 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"
Template Parameters
_MatrixTypeThe type of the sparse matrix. It must be a column-major SparseMatrix<>
_OrderingTypeThe ordering method to use, either AMD, COLAMD or METIS. Default is COLMAD
See also
TutorialSparseDirectSolvers
OrderingMethods_Module

Definition at line 17 of file SparseLU.h.

Member Typedef Documentation

template<typename _MatrixType , typename _OrderingType >
typedef internal::SparseLUImpl<Scalar, Index> Eigen::SparseLU< _MatrixType, _OrderingType >::Base

Definition at line 86 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
typedef MatrixType::Index Eigen::SparseLU< _MatrixType, _OrderingType >::Index

Definition at line 80 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
typedef Matrix<Index,Dynamic,1> Eigen::SparseLU< _MatrixType, _OrderingType >::IndexVector

Definition at line 84 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
typedef _MatrixType Eigen::SparseLU< _MatrixType, _OrderingType >::MatrixType

Definition at line 76 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
typedef SparseMatrix<Scalar,ColMajor,Index> Eigen::SparseLU< _MatrixType, _OrderingType >::NCMatrix

Definition at line 81 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
typedef _OrderingType Eigen::SparseLU< _MatrixType, _OrderingType >::OrderingType

Definition at line 77 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
typedef PermutationMatrix<Dynamic, Dynamic, Index> Eigen::SparseLU< _MatrixType, _OrderingType >::PermutationType

Definition at line 85 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
typedef MatrixType::RealScalar Eigen::SparseLU< _MatrixType, _OrderingType >::RealScalar

Definition at line 79 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
typedef MatrixType::Scalar Eigen::SparseLU< _MatrixType, _OrderingType >::Scalar

Definition at line 78 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
typedef Matrix<Scalar,Dynamic,1> Eigen::SparseLU< _MatrixType, _OrderingType >::ScalarVector

Definition at line 83 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
typedef internal::MappedSuperNodalMatrix<Scalar, Index> Eigen::SparseLU< _MatrixType, _OrderingType >::SCMatrix

Definition at line 82 of file SparseLU.h.

Constructor & Destructor Documentation

template<typename _MatrixType , typename _OrderingType >
Eigen::SparseLU< _MatrixType, _OrderingType >::SparseLU ( )
inline

Definition at line 89 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
Eigen::SparseLU< _MatrixType, _OrderingType >::SparseLU ( const MatrixType &  matrix)
inline

Definition at line 93 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
Eigen::SparseLU< _MatrixType, _OrderingType >::~SparseLU ( )
inline

Definition at line 99 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
Eigen::SparseLU< _MatrixType, _OrderingType >::SparseLU ( const SparseLU< _MatrixType, _OrderingType > &  )
private

Member Function Documentation

template<typename _MatrixType , typename _OrderingType >
template<typename Rhs , typename Dest >
bool Eigen::SparseLU< _MatrixType, _OrderingType >::_solve ( const MatrixBase< Rhs > &  B,
MatrixBase< Dest > &  _X 
) const
inline

Definition at line 222 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
Scalar Eigen::SparseLU< _MatrixType, _OrderingType >::absDeterminant ( )
inline
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.
See also
logAbsDeterminant(), signDeterminant()

Definition at line 256 of file SparseLU.h.

template<typename MatrixType , typename OrderingType >
void Eigen::SparseLU< MatrixType, OrderingType >::analyzePattern ( const MatrixType &  mat)

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

Definition at line 369 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
Index Eigen::SparseLU< _MatrixType, _OrderingType >::cols ( void  ) const
inline

Definition at line 121 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
const PermutationType& Eigen::SparseLU< _MatrixType, _OrderingType >::colsPermutation ( ) const
inline
Returns
a reference to the column matrix permutation $ P_c^T $ such that $P_r A P_c^T = L U$
See also
rowsPermutation()

Definition at line 161 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
void Eigen::SparseLU< _MatrixType, _OrderingType >::compute ( const MatrixType &  matrix)
inline

Compute the symbolic and numeric factorization of the input sparse matrix. The input matrix should be in column-major storage.

Definition at line 112 of file SparseLU.h.

template<typename MatrixType , typename OrderingType >
void Eigen::SparseLU< MatrixType, OrderingType >::factorize ( const MatrixType &  matrix)
  • 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.

Definition at line 452 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
ComputationInfo Eigen::SparseLU< _MatrixType, _OrderingType >::info ( ) const
inline

Reports whether previous computation was successful.

Returns
Success if computation was succesful, NumericalIssue if the LU factorization reports a problem, zero diagonal for instance InvalidInput if the input matrix is invalid
See also
iparm()

Definition at line 207 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
void Eigen::SparseLU< _MatrixType, _OrderingType >::initperfvalues ( )
inlineprotected

Definition at line 317 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
void Eigen::SparseLU< _MatrixType, _OrderingType >::isSymmetric ( bool  sym)
inline

Indicate that the pattern of the input matrix is symmetric

Definition at line 123 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
std::string Eigen::SparseLU< _MatrixType, _OrderingType >::lastErrorMessage ( ) const
inline
Returns
A string describing the type of error

Definition at line 216 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
Scalar Eigen::SparseLU< _MatrixType, _OrderingType >::logAbsDeterminant ( ) const
inline
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.
See also
absDeterminant(), signDeterminant()

Definition at line 286 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
SparseLUMatrixLReturnType<SCMatrix> Eigen::SparseLU< _MatrixType, _OrderingType >::matrixL ( ) const
inline
Returns
an expression of the matrix L, internally stored as supernodes The only operation available with this expression is the triangular solve
y = b; matrixL().solveInPlace(y);

Definition at line 134 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
SparseLUMatrixUReturnType<SCMatrix,MappedSparseMatrix<Scalar,ColMajor,Index> > Eigen::SparseLU< _MatrixType, _OrderingType >::matrixU ( ) const
inline
Returns
an expression of the matrix U, The only operation available with this expression is the triangular solve
y = b; matrixU().solveInPlace(y);

Definition at line 144 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
Index Eigen::SparseLU< _MatrixType, _OrderingType >::rows ( void  ) const
inline

Definition at line 120 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
const PermutationType& Eigen::SparseLU< _MatrixType, _OrderingType >::rowsPermutation ( ) const
inline
Returns
a reference to the row matrix permutation $ P_r $ such that $P_r A P_c^T = L U$
See also
colsPermutation()

Definition at line 153 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
void Eigen::SparseLU< _MatrixType, _OrderingType >::setPivotThreshold ( const RealScalar &  thresh)
inline

Set the threshold used for a diagonal entry to be an acceptable pivot.

Definition at line 166 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
Scalar Eigen::SparseLU< _MatrixType, _OrderingType >::signDeterminant ( )
inline
Returns
A number representing the sign of the determinant
See also
absDeterminant(), logAbsDeterminant()

Definition at line 309 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
void Eigen::SparseLU< _MatrixType, _OrderingType >::simplicialfactorize ( const MatrixType &  matrix)
template<typename _MatrixType , typename _OrderingType >
template<typename Rhs >
const internal::solve_retval<SparseLU, Rhs> Eigen::SparseLU< _MatrixType, _OrderingType >::solve ( const MatrixBase< Rhs > &  B) const
inline
Returns
the solution X of $ A X = B $ using the current decomposition of A.
Warning
the destination matrix X in X = this->solve(B) must be colmun-major.
See also
compute()

Definition at line 178 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
template<typename Rhs >
const internal::sparse_solve_retval<SparseLU, Rhs> Eigen::SparseLU< _MatrixType, _OrderingType >::solve ( const SparseMatrixBase< Rhs > &  B) const
inline
Returns
the solution X of $ A X = B $ using the current decomposition of A.
See also
compute()

Definition at line 191 of file SparseLU.h.

Member Data Documentation

template<typename _MatrixType , typename _OrderingType >
bool Eigen::SparseLU< _MatrixType, _OrderingType >::m_analysisIsOk
protected

Definition at line 331 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
Index Eigen::SparseLU< _MatrixType, _OrderingType >::m_detPermR
protected

Definition at line 348 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
RealScalar Eigen::SparseLU< _MatrixType, _OrderingType >::m_diagpivotthresh
protected

Definition at line 346 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
IndexVector Eigen::SparseLU< _MatrixType, _OrderingType >::m_etree
protected

Definition at line 338 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
bool Eigen::SparseLU< _MatrixType, _OrderingType >::m_factorizationIsOk
protected

Definition at line 330 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
Base::GlobalLU_t Eigen::SparseLU< _MatrixType, _OrderingType >::m_glu
protected

Definition at line 340 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
ComputationInfo Eigen::SparseLU< _MatrixType, _OrderingType >::m_info
mutableprotected

Definition at line 328 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
bool Eigen::SparseLU< _MatrixType, _OrderingType >::m_isInitialized
protected

Definition at line 329 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
std::string Eigen::SparseLU< _MatrixType, _OrderingType >::m_lastError
protected

Definition at line 332 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
SCMatrix Eigen::SparseLU< _MatrixType, _OrderingType >::m_Lstore
protected

Definition at line 334 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
NCMatrix Eigen::SparseLU< _MatrixType, _OrderingType >::m_mat
protected

Definition at line 333 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
Index Eigen::SparseLU< _MatrixType, _OrderingType >::m_nnzL
protected

Definition at line 347 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
Index Eigen::SparseLU< _MatrixType, _OrderingType >::m_nnzU
protected

Definition at line 347 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
internal::perfvalues<Index> Eigen::SparseLU< _MatrixType, _OrderingType >::m_perfv
protected

Definition at line 345 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
PermutationType Eigen::SparseLU< _MatrixType, _OrderingType >::m_perm_c
protected

Definition at line 336 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
PermutationType Eigen::SparseLU< _MatrixType, _OrderingType >::m_perm_r
protected

Definition at line 337 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
bool Eigen::SparseLU< _MatrixType, _OrderingType >::m_symmetricmode
protected

Definition at line 343 of file SparseLU.h.

template<typename _MatrixType , typename _OrderingType >
MappedSparseMatrix<Scalar,ColMajor,Index> Eigen::SparseLU< _MatrixType, _OrderingType >::m_Ustore
protected

Definition at line 335 of file SparseLU.h.

The documentation for this class was generated from the following file:

tuw_aruco
Author(s): Lukas Pfeifhofer
autogenerated on Mon Jun 10 2019 15:41:11