Base class for sparseLU. More...

#include <SparseLUImpl.h>

Public Types
typedef Matrix< Scalar, Dynamic, 1 >	ScalarVector

typedef Matrix< StorageIndex, Dynamic, 1 >	IndexVector

typedef Matrix< Scalar, Dynamic, Dynamic, ColMajor >	ScalarMatrix

typedef Map< ScalarMatrix, 0, OuterStride<> >	MappedMatrixBlock

typedef ScalarVector::RealScalar	RealScalar

typedef Ref< Matrix< Scalar, Dynamic, 1 > >	BlockScalarVector

typedef Ref< Matrix< StorageIndex, Dynamic, 1 > >	BlockIndexVector

typedef LU_GlobalLU_t< IndexVector, ScalarVector >	GlobalLU_t

typedef SparseMatrix< Scalar, ColMajor, StorageIndex >	MatrixType

Protected Member Functions
template<typename VectorType >
Index	expand (VectorType &vec, Index &length, Index nbElts, Index keep_prev, Index &num_expansions)
	Expand the existing storage to accomodate more fill-ins.

Index	memInit (Index m, Index n, Index annz, Index lwork, Index fillratio, Index panel_size, GlobalLU_t &glu)
	Allocate various working space for the numerical factorization phase.

template<typename VectorType >
Index	memXpand (VectorType &vec, Index &maxlen, Index nbElts, MemType memtype, Index &num_expansions)
	Expand the existing storage.

void	heap_relax_snode (const Index n, IndexVector &et, const Index relax_columns, IndexVector &descendants, IndexVector &relax_end)
	Identify the initial relaxed supernodes.

void	relax_snode (const Index n, IndexVector &et, const Index relax_columns, IndexVector &descendants, IndexVector &relax_end)
	Identify the initial relaxed supernodes.

Index	snode_dfs (const Index jcol, const Index kcol, const MatrixType &mat, IndexVector &xprune, IndexVector &marker, GlobalLU_t &glu)

Index	snode_bmod (const Index jcol, const Index fsupc, ScalarVector &dense, GlobalLU_t &glu)

Index	pivotL (const Index jcol, const RealScalar &diagpivotthresh, IndexVector &perm_r, IndexVector &iperm_c, Index &pivrow, GlobalLU_t &glu)
	Performs the numerical pivotin on the current column of L, and the CDIV operation.

template<typename Traits >
void	dfs_kernel (const StorageIndex jj, IndexVector &perm_r, Index &nseg, IndexVector &panel_lsub, IndexVector &segrep, Ref< IndexVector > repfnz_col, IndexVector &xprune, Ref< IndexVector > marker, IndexVector &parent, IndexVector &xplore, GlobalLU_t &glu, Index &nextl_col, Index krow, Traits &traits)

void	panel_dfs (const Index m, const Index w, const Index jcol, MatrixType &A, IndexVector &perm_r, 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)

void	panel_bmod (const Index m, const Index w, const Index jcol, const Index nseg, ScalarVector &dense, ScalarVector &tempv, IndexVector &segrep, IndexVector &repfnz, GlobalLU_t &glu)
	Performs numeric block updates (sup-panel) in topological order.

Index	column_dfs (const Index m, const Index jcol, IndexVector &perm_r, Index maxsuper, 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.

Index	column_bmod (const Index jcol, const Index nseg, BlockScalarVector dense, ScalarVector &tempv, BlockIndexVector segrep, BlockIndexVector repfnz, Index fpanelc, GlobalLU_t &glu)
	Performs numeric block updates (sup-col) in topological order.

Index	copy_to_ucol (const Index jcol, const Index nseg, IndexVector &segrep, BlockIndexVector repfnz, IndexVector &perm_r, BlockScalarVector dense, GlobalLU_t &glu)
	Performs numeric block updates (sup-col) in topological order.

void	pruneL (const Index jcol, const IndexVector &perm_r, const Index pivrow, const Index nseg, const IndexVector &segrep, BlockIndexVector repfnz, IndexVector &xprune, GlobalLU_t &glu)
	Prunes the L-structure.

void	countnz (const Index n, Index &nnzL, Index &nnzU, GlobalLU_t &glu)
	Count Nonzero elements in the factors.

void	fixupL (const Index n, const IndexVector &perm_r, GlobalLU_t &glu)
	Fix up the data storage lsub for L-subscripts.

Friends
template<typename , typename >
struct	column_dfs_traits

Detailed Description

template<typename Scalar, typename StorageIndex>
class Eigen::internal::SparseLUImpl< Scalar, StorageIndex >

Base class for sparseLU.

Member Function Documentation

◆ column_bmod()

template<typename Scalar , typename StorageIndex >

Index SparseLUImpl< Scalar, StorageIndex >::column_bmod	(	const Index	jcol,
		const Index	nseg,
		BlockScalarVector	dense,
		ScalarVector &	tempv,
		BlockIndexVector	segrep,
		BlockIndexVector	repfnz,
		Index	fpanelc,
		GlobalLU_t &	glu
	)

protected

Performs numeric block updates (sup-col) in topological order.

Parameters

jcol	current column to update
nseg	Number of segments in the U part
dense	Store the full representation of the column
tempv	working array
segrep	segment representative ...
repfnz	??? First nonzero column in each row ??? ...
fpanelc	First column in the current panel
glu	Global LU data.

Returns: 0 - successful return > 0 - number of bytes allocated when run out of space

◆ column_dfs()

template<typename Scalar , typename StorageIndex >

Index SparseLUImpl< Scalar, StorageIndex >::column_dfs	(	const Index	m,
		const Index	jcol,
		IndexVector &	perm_r,
		Index	maxsuper,
		Index &	nseg,
		BlockIndexVector	lsub_col,
		IndexVector &	segrep,
		BlockIndexVector	repfnz,
		IndexVector &	xprune,
		IndexVector &	marker,
		IndexVector &	parent,
		IndexVector &	xplore,
		GlobalLU_t &	glu
	)

protected

Performs a symbolic factorization on column jcol and decide the supernode boundary.

A supernode representative is the last column of a supernode. The nonzeros in U[*,j] are segments that end at supernodes representatives. The routine returns a list of the supernodal representatives in topological order of the dfs that generates them. The location of the first nonzero in each supernodal segment (supernodal entry location) is also returned.

Parameters

	m	number of rows in the matrix
	jcol	Current column
	perm_r	Row permutation
	maxsuper	Maximum number of column allowed in a supernode
[in,out]	nseg	Number of segments in current U[*,j] - new segments appended
	lsub_col	defines the rhs vector to start the dfs
[in,out]	segrep	Segment representatives - new segments appended
	repfnz	First nonzero location in each row
	xprune
	marker	marker[i] == jj, if i was visited during dfs of current column jj;
	parent
	xplore	working array
	glu	global LU data

Returns: 0 success > 0 number of bytes allocated when run out of space

◆ copy_to_ucol()

template<typename Scalar , typename StorageIndex >

Index SparseLUImpl< Scalar, StorageIndex >::copy_to_ucol	(	const Index	jcol,
		const Index	nseg,
		IndexVector &	segrep,
		BlockIndexVector	repfnz,
		IndexVector &	perm_r,
		BlockScalarVector	dense,
		GlobalLU_t &	glu
	)

protected

Performs numeric block updates (sup-col) in topological order.

Parameters

jcol	current column to update
nseg	Number of segments in the U part
segrep	segment representative ...
repfnz	First nonzero column in each row ...
perm_r	Row permutation
dense	Store the full representation of the column
glu	Global LU data.

Returns: 0 - successful return > 0 - number of bytes allocated when run out of space

◆ expand()

template<typename Scalar , typename StorageIndex >

template<typename VectorType >

Index SparseLUImpl< Scalar, StorageIndex >::expand	(	VectorType &	vec,
		Index &	length,
		Index	nbElts,
		Index	keep_prev,
		Index &	num_expansions
	)

protected

Expand the existing storage to accomodate more fill-ins.

Parameters

	vec	Valid pointer to the vector to allocate or expand
[in,out]	length	At input, contain the current length of the vector that is to be increased. At output, length of the newly allocated vector
[in]	nbElts	Current number of elements in the factors
	keep_prev	1: use length and do not expand the vector; 0: compute new_len and expand
[in,out]	num_expansions	Number of times the memory has been expanded

◆ fixupL()

template<typename Scalar , typename StorageIndex >

void SparseLUImpl< Scalar, StorageIndex >::fixupL	(	const Index	n,
		const IndexVector &	perm_r,
		GlobalLU_t &	glu
	)

protected

Fix up the data storage lsub for L-subscripts.

It removes the subscripts sets for structural pruning, and applies permutation to the remaining subscripts

◆ heap_relax_snode()

template<typename Scalar , typename StorageIndex >

void SparseLUImpl< Scalar, StorageIndex >::heap_relax_snode	(	const Index	n,
		IndexVector &	et,
		const Index	relax_columns,
		IndexVector &	descendants,
		IndexVector &	relax_end
	)

protected

Identify the initial relaxed supernodes.

This routine applied to a symmetric elimination tree. It assumes that the matrix has been reordered according to the postorder of the etree

Parameters

n	The number of columns
et	elimination tree
relax_columns	Maximum number of columns allowed in a relaxed snode
descendants	Number of descendants of each node in the etree
relax_end	last column in a supernode

◆ memInit()

template<typename Scalar , typename StorageIndex >

Index SparseLUImpl< Scalar, StorageIndex >::memInit	(	Index	m,
		Index	n,
		Index	annz,
		Index	lwork,
		Index	fillratio,
		Index	panel_size,
		GlobalLU_t &	glu
	)

protected

Allocate various working space for the numerical factorization phase.

Parameters

m	number of rows of the input matrix
n	number of columns
annz	number of initial nonzeros in the matrix
lwork	if lwork=-1, this routine returns an estimated size of the required memory
glu	persistent data to facilitate multiple factors : will be deleted later ??
fillratio	estimated ratio of fill in the factors
panel_size	Size of a panel

Returns: an estimated size of the required memory if lwork = -1; otherwise, return the size of actually allocated memory when allocation failed, and 0 on success

Note: Unlike SuperLU, this routine does not support successive factorization with the same pattern and the same row permutation

◆ memXpand()

template<typename Scalar , typename StorageIndex >

template<typename VectorType >

Index SparseLUImpl< Scalar, StorageIndex >::memXpand	(	VectorType &	vec,
		Index &	maxlen,
		Index	nbElts,
		MemType	memtype,
		Index &	num_expansions
	)

protected

Expand the existing storage.

Parameters

	vec	vector to expand
[in,out]	maxlen	On input, previous size of vec (Number of elements to copy ). on output, new size
	nbElts	current number of elements in the vector.
	memtype	Type of the element to expand
	num_expansions	Number of expansions

Returns: 0 on success, > 0 size of the memory allocated so far

◆ panel_bmod()

template<typename Scalar , typename StorageIndex >

void SparseLUImpl< Scalar, StorageIndex >::panel_bmod	(	const Index	m,
		const Index	w,
		const Index	jcol,
		const Index	nseg,
		ScalarVector &	dense,
		ScalarVector &	tempv,
		IndexVector &	segrep,
		IndexVector &	repfnz,
		GlobalLU_t &	glu
	)

protected

Performs numeric block updates (sup-panel) in topological order.

Before entering this routine, the original nonzeros in the panel were already copied i nto the spa[m,w]

Parameters

m	number of rows in the matrix
w	Panel size
jcol	Starting column of the panel
nseg	Number of segments in the U part
dense	Store the full representation of the panel
tempv	working array
segrep	segment representative... first row in the segment
repfnz	First nonzero rows
glu	Global LU data.

◆ panel_dfs()

template<typename Scalar , typename StorageIndex >

void SparseLUImpl< Scalar, StorageIndex >::panel_dfs	(	const Index	m,
		const Index	w,
		const Index	jcol,
		MatrixType &	A,
		IndexVector &	perm_r,
		Index &	nseg,
		ScalarVector &	dense,
		IndexVector &	panel_lsub,
		IndexVector &	segrep,
		IndexVector &	repfnz,
		IndexVector &	xprune,
		IndexVector &	marker,
		IndexVector &	parent,
		IndexVector &	xplore,
		GlobalLU_t &	glu
	)

protected

Performs a symbolic factorization on a panel of columns [jcol, jcol+w)

A supernode representative is the last column of a supernode. The nonzeros in U[*,j] are segments that end at supernodes representatives

The routine returns a list of the supernodal representatives in topological order of the dfs that generates them. This list is a superset of the topological order of each individual column within the panel. The location of the first nonzero in each supernodal segment (supernodal entry location) is also returned. Each column has a separate list for this purpose.

Two markers arrays are used for dfs : marker[i] == jj, if i was visited during dfs of current column jj; marker1[i] >= jcol, if i was visited by earlier columns in this panel;

Parameters

[in]	m	number of rows in the matrix
[in]	w	Panel size
[in]	jcol	Starting column of the panel
[in]	A	Input matrix in column-major storage
[in]	perm_r	Row permutation
[out]	nseg	Number of U segments
[out]	dense	Accumulate the column vectors of the panel
[out]	panel_lsub	Subscripts of the row in the panel
[out]	segrep	Segment representative i.e first nonzero row of each segment
[out]	repfnz	First nonzero location in each row
[out]	xprune	The pruned elimination tree
[out]	marker	work vector
	parent	The elimination tree
	xplore	work vector
	glu	The global data structure

◆ pivotL()

template<typename Scalar , typename StorageIndex >

Index SparseLUImpl< Scalar, StorageIndex >::pivotL	(	const Index	jcol,
		const RealScalar &	diagpivotthresh,
		IndexVector &	perm_r,
		IndexVector &	iperm_c,
		Index &	pivrow,
		GlobalLU_t &	glu
	)

protected

Performs the numerical pivotin on the current column of L, and the CDIV operation.

Pivot policy : (1) Compute thresh = u * max_(i>=j) abs(A_ij); (2) IF user specifies pivot row k and abs(A_kj) >= thresh THEN pivot row = k; ELSE IF abs(A_jj) >= thresh THEN pivot row = j; ELSE pivot row = m;

Note: If you absolutely want to use a given pivot order, then set u=0.0.

Parameters

	jcol	The current column of L
	diagpivotthresh	diagonal pivoting threshold
[in,out]	perm_r	Row permutation (threshold pivoting)
[in]	iperm_c	column permutation - used to finf diagonal of PcAPc'
[out]	pivrow	The pivot row
	glu	Global LU data

Returns: 0 if success, i > 0 if U(i,i) is exactly zero

◆ pruneL()

template<typename Scalar , typename StorageIndex >

void SparseLUImpl< Scalar, StorageIndex >::pruneL	(	const Index	jcol,
		const IndexVector &	perm_r,
		const Index	pivrow,
		const Index	nseg,
		const IndexVector &	segrep,
		BlockIndexVector	repfnz,
		IndexVector &	xprune,
		GlobalLU_t &	glu
	)

protected

Prunes the L-structure.

It prunes the L-structure of supernodes whose L-structure contains the current pivot row "pivrow"

Parameters

	jcol	The current column of L
[in]	perm_r	Row permutation
[out]	pivrow	The pivot row
	nseg	Number of segments
	segrep
	repfnz
[out]	xprune
	glu	Global LU data

◆ relax_snode()

template<typename Scalar , typename StorageIndex >

void SparseLUImpl< Scalar, StorageIndex >::relax_snode	(	const Index	n,
		IndexVector &	et,
		const Index	relax_columns,
		IndexVector &	descendants,
		IndexVector &	relax_end
	)

protected

Identify the initial relaxed supernodes.

This routine is applied to a column elimination tree. It assumes that the matrix has been reordered according to the postorder of the etree

Parameters

n	the number of columns
et	elimination tree
relax_columns	Maximum number of columns allowed in a relaxed snode
descendants	Number of descendants of each node in the etree
relax_end	last column in a supernode

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

External/Eigen/src/SparseLU/SparseLUImpl.h
External/Eigen/src/SparseLU/SparseLU_column_bmod.h
External/Eigen/src/SparseLU/SparseLU_column_dfs.h
External/Eigen/src/SparseLU/SparseLU_copy_to_ucol.h
External/Eigen/src/SparseLU/SparseLU_heap_relax_snode.h
External/Eigen/src/SparseLU/SparseLU_Memory.h
External/Eigen/src/SparseLU/SparseLU_panel_bmod.h
External/Eigen/src/SparseLU/SparseLU_panel_dfs.h
External/Eigen/src/SparseLU/SparseLU_pivotL.h
External/Eigen/src/SparseLU/SparseLU_pruneL.h
External/Eigen/src/SparseLU/SparseLU_relax_snode.h
External/Eigen/src/SparseLU/SparseLU_Utils.h

Public Types

Protected Member Functions

Friends

Detailed Description

Member Function Documentation

◆ column_bmod()

◆ column_dfs()

◆ copy_to_ucol()

◆ expand()

◆ fixupL()

◆ heap_relax_snode()

◆ memInit()

◆ memXpand()

◆ panel_bmod()

◆ panel_dfs()

◆ pivotL()

◆ pruneL()

◆ relax_snode()