#include <superlu.hpp>

Inheritance diagram for mfem::SuperLUSolver:

Collaboration diagram for mfem::SuperLUSolver:

Public Member Functions
	SuperLUSolver (MPI_Comm comm, int npdep=1)
	Constructor with MPI_Comm parameter.

	SuperLUSolver (SuperLURowLocMatrix &A, int npdep=1)
	Constructor with SuperLU matrix object.

	~SuperLUSolver ()
	Default destructor.

void	SetOperator (const Operator &op)
	Set the operator/matrix.

void	Mult (const Vector &x, Vector &y) const
	Factor and solve the linear system \( y = Op^{-1} x \).

void	ArrayMult (const Array< const Vector * > &X, Array< Vector * > &Y) const
	Factor and solve the linear systems \( y_i = Op^{-1} x_i \) for all i in the X and Y arrays.

void	MultTranspose (const Vector &x, Vector &y) const
	Factor and solve the transposed linear system \( y = Op^{-T} x \).

void	ArrayMultTranspose (const Array< const Vector * > &X, Array< Vector * > &Y) const
	Factor and solve the transposed linear systems \( y_i = Op^{-T} x_i \) for all i in the X and Y arrays.

void	SetPrintStatistics (bool print_stat)
	Specify whether to print the solver statistics (default true)

void	SetEquilibriate (bool equil)
	Specify whether to equibrate the system scaling to make the rows and columns have unit norms. (default true)

void	SetColumnPermutation (superlu::ColPerm col_perm)
	Specify how to permute the columns of the matrix.

void	SetRowPermutation (superlu::RowPerm row_perm)
	Specify how to permute the rows of the matrix.

void	SetIterativeRefine (superlu::IterRefine iter_ref)
	Specify how to handle iterative refinement.

void	SetReplaceTinyPivot (bool rtp)
	Specify whether to replace tiny diagonals encountered during pivot with \( \sqrt{\epsilon} \lVert A \rVert \) (default false)

void	SetNumLookAheads (int num_lookaheads)
	Specify the number of levels in the look-ahead factorization (default 10)

void	SetLookAheadElimTree (bool etree)
	Specifies whether to use the elimination tree computed from the serial symbolic factorization to perform static scheduling (default false)

void	SetSymmetricPattern (bool sym)
	Specify whether the matrix has a symmetric pattern to avoid extra work (default false)

void	SetParSymbFact (bool par)
	Specify whether to perform parallel symbolic factorization.

void	SetFact (superlu::Fact fact)
	Specify what information has been provided ahead of time about the factorization of A.

Public Member Functions inherited from mfem::Solver
	Solver (int s=0, bool iter_mode=false)
	Initialize a square Solver with size s.

	Solver (int h, int w, bool iter_mode=false)
	Initialize a Solver with height h and width w.

Public Member Functions inherited from mfem::Operator
void	InitTVectors (const Operator Po, const Operator Ri, const Operator *Pi, Vector &x, Vector &b, Vector &X, Vector &B) const
	Initializes memory for true vectors of linear system.

	Operator (int s=0)
	Construct a square Operator with given size s (default 0).

	Operator (int h, int w)
	Construct an Operator with the given height (output size) and width (input size).

int	Height () const
	Get the height (size of output) of the Operator. Synonym with NumRows().

int	NumRows () const
	Get the number of rows (size of output) of the Operator. Synonym with Height().

int	Width () const
	Get the width (size of input) of the Operator. Synonym with NumCols().

int	NumCols () const
	Get the number of columns (size of input) of the Operator. Synonym with Width().

virtual MemoryClass	GetMemoryClass () const
	Return the MemoryClass preferred by the Operator.

virtual void	AddMult (const Vector &x, Vector &y, const real_t a=1.0) const
	Operator application: `y+=A(x)` (default) or `y+=a*A(x)`.

virtual void	AddMultTranspose (const Vector &x, Vector &y, const real_t a=1.0) const
	Operator transpose application: `y+=A^t(x)` (default) or `y+=a*A^t(x)`.

virtual void	ArrayAddMult (const Array< const Vector * > &X, Array< Vector * > &Y, const real_t a=1.0) const
	Operator application on a matrix: `Y+=A(X)` (default) or `Y+=a*A(X)`.

virtual void	ArrayAddMultTranspose (const Array< const Vector * > &X, Array< Vector * > &Y, const real_t a=1.0) const
	Operator transpose application on a matrix: `Y+=A^t(X)` (default) or `Y+=a*A^t(X)`.

virtual Operator &	GetGradient (const Vector &x) const
	Evaluate the gradient operator at the point x. The default behavior in class Operator is to generate an error.

virtual void	AssembleDiagonal (Vector &diag) const
	Computes the diagonal entries into diag. Typically, this operation only makes sense for linear Operators. In some cases, only an approximation of the diagonal is computed.

virtual const Operator *	GetProlongation () const
	Prolongation operator from linear algebra (linear system) vectors, to input vectors for the operator. `NULL` means identity.

virtual const Operator *	GetRestriction () const
	Restriction operator from input vectors for the operator to linear algebra (linear system) vectors. `NULL` means identity.

virtual const Operator *	GetOutputProlongation () const
	Prolongation operator from linear algebra (linear system) vectors, to output vectors for the operator. `NULL` means identity.

virtual const Operator *	GetOutputRestrictionTranspose () const
	Transpose of GetOutputRestriction, directly available in this form to facilitate matrix-free RAP-type operators.

virtual const Operator *	GetOutputRestriction () const
	Restriction operator from output vectors for the operator to linear algebra (linear system) vectors. `NULL` means identity.

void	FormLinearSystem (const Array< int > &ess_tdof_list, Vector &x, Vector &b, Operator *&A, Vector &X, Vector &B, int copy_interior=0)
	Form a constrained linear system using a matrix-free approach.

void	FormRectangularLinearSystem (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, Vector &x, Vector &b, Operator *&A, Vector &X, Vector &B)
	Form a column-constrained linear system using a matrix-free approach.

virtual void	RecoverFEMSolution (const Vector &X, const Vector &b, Vector &x)
	Reconstruct a solution vector x (e.g. a GridFunction) from the solution X of a constrained linear system obtained from Operator::FormLinearSystem() or Operator::FormRectangularLinearSystem().

void	FormSystemOperator (const Array< int > &ess_tdof_list, Operator *&A)
	Return in A a parallel (on truedofs) version of this square operator.

void	FormRectangularSystemOperator (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, Operator *&A)
	Return in A a parallel (on truedofs) version of this rectangular operator (including constraints).

void	FormDiscreteOperator (Operator *&A)
	Return in A a parallel (on truedofs) version of this rectangular operator.

void	PrintMatlab (std::ostream &out, int n, int m=0) const
	Prints operator with input size n and output size m in Matlab format.

virtual void	PrintMatlab (std::ostream &out) const
	Prints operator in Matlab format.

virtual	~Operator ()
	Virtual destructor.

Type	GetType () const
	Return the type ID of the Operator class.

Public Attributes
const int	nprow_

const int	npcol_

const int	npdep_

Public Attributes inherited from mfem::Solver
bool	iterative_mode
	If true, use the second argument of Mult() as an initial guess.

Protected Attributes
const SuperLURowLocMatrix *	APtr_

Vector	sol_

int	nrhs_

void *	optionsPtr_

void *	ScalePermstructPtr_

void *	LUstructPtr_

void *	SOLVEstructPtr_

void *	gridPtr_

Protected Attributes inherited from mfem::Operator
int	height
	Dimension of the output / number of rows in the matrix.

int	width
	Dimension of the input / number of columns in the matrix.

Additional Inherited Members
Public Types inherited from mfem::Operator
enum	DiagonalPolicy { DIAG_ZERO , DIAG_ONE , DIAG_KEEP }
	Defines operator diagonal policy upon elimination of rows and/or columns. More...

enum	Type { ANY_TYPE , MFEM_SPARSEMAT , Hypre_ParCSR , PETSC_MATAIJ , PETSC_MATIS , PETSC_MATSHELL , PETSC_MATNEST , PETSC_MATHYPRE , PETSC_MATGENERIC , Complex_Operator , MFEM_ComplexSparseMat , Complex_Hypre_ParCSR , Complex_DenseMat , MFEM_Block_Matrix , MFEM_Block_Operator }
	Enumeration defining IDs for some classes derived from Operator. More...

Protected Member Functions inherited from mfem::Operator
void	FormConstrainedSystemOperator (const Array< int > &ess_tdof_list, ConstrainedOperator *&Aout)
	see FormSystemOperator()

void	FormRectangularConstrainedSystemOperator (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, RectangularConstrainedOperator *&Aout)
	see FormRectangularSystemOperator()

Operator *	SetupRAP (const Operator Pi, const Operator Po)
	Returns RAP Operator of this, using input/output Prolongation matrices Pi corresponds to "P", Po corresponds to "Rt".

Detailed Description

The MFEM wrapper around the SuperLU Direct Solver class.

The mfem::SuperLUSolver class uses the SuperLU_DIST library to perform LU factorization of a parallel sparse matrix. The solver is capable of handling double precision types. It is currently maintained by Xiaoye Sherry Li at NERSC, see http://crd-legacy.lbl.gov/~xiaoye/SuperLU/.

Definition at line 161 of file superlu.hpp.

Constructor & Destructor Documentation

◆ SuperLUSolver() [1/2]

mfem::SuperLUSolver::SuperLUSolver	(	MPI_Comm	comm,
		int	npdep = 1 )

Constructor with MPI_Comm parameter.

npdep is the replication factor for the matrix data and must be a power of 2 and divide evenly into the number of processors.

Definition at line 262 of file superlu.cpp.

◆ SuperLUSolver() [2/2]

mfem::SuperLUSolver::SuperLUSolver	(	SuperLURowLocMatrix &	A,
		int	npdep = 1 )

Constructor with SuperLU matrix object.

npdep is the replication factor for the matrix data and must be a power of 2 and divide evenly into the number of processors.

Definition at line 272 of file superlu.cpp.

◆ ~SuperLUSolver()

mfem::SuperLUSolver::~SuperLUSolver ( )

Default destructor.

Definition at line 278 of file superlu.cpp.

Member Function Documentation

◆ ArrayMult()

void mfem::SuperLUSolver::ArrayMult	(	const Array< const Vector * > &	X,
		Array< Vector * > &	Y ) const

virtual

Factor and solve the linear systems \( y_i = Op^{-1} x_i \) for all i in the X and Y arrays.

Note: Factorization modifies the operator matrix.

Reimplemented from mfem::Operator.

Definition at line 596 of file superlu.cpp.

◆ ArrayMultTranspose()

void mfem::SuperLUSolver::ArrayMultTranspose	(	const Array< const Vector * > &	X,
		Array< Vector * > &	Y ) const

virtual

Factor and solve the transposed linear systems \( y_i = Op^{-T} x_i \) for all i in the X and Y arrays.

Note: Factorization modifies the operator matrix.

Reimplemented from mfem::Operator.

Definition at line 712 of file superlu.cpp.

◆ Mult()

void mfem::SuperLUSolver::Mult	(	const Vector &	x,
		Vector &	y ) const

virtual

Factor and solve the linear system \( y = Op^{-1} x \).

Note: Factorization modifies the operator matrix.

Implements mfem::Operator.

Definition at line 587 of file superlu.cpp.

◆ MultTranspose()

void mfem::SuperLUSolver::MultTranspose	(	const Vector &	x,
		Vector &	y ) const

virtual

Factor and solve the transposed linear system \( y = Op^{-T} x \).

Note: Factorization modifies the operator matrix.

Reimplemented from mfem::Operator.

Definition at line 701 of file superlu.cpp.

◆ SetColumnPermutation()

void mfem::SuperLUSolver::SetColumnPermutation ( superlu::ColPerm col_perm )

Specify how to permute the columns of the matrix.

Supported options are: superlu::NATURAL, superlu::MMD_ATA, superlu::MMD_AT_PLUS_A, superlu::COLAMD, superlu::METIS_AT_PLUS_A (default), superlu::PARMETIS, superlu::ZOLTAN, superlu::MY_PERMC

Definition at line 399 of file superlu.cpp.

◆ SetEquilibriate()

void mfem::SuperLUSolver::SetEquilibriate ( bool equil )

Specify whether to equibrate the system scaling to make the rows and columns have unit norms. (default true)

Definition at line 392 of file superlu.cpp.

◆ SetFact()

void mfem::SuperLUSolver::SetFact ( superlu::Fact fact )

Specify what information has been provided ahead of time about the factorization of A.

Supported options are: superlu::DOFACT, superlu::SamePattern, superlu::SamePattern_SameRowPerm, superlu::FACTORED

Definition at line 468 of file superlu.cpp.

◆ SetIterativeRefine()

void mfem::SuperLUSolver::SetIterativeRefine ( superlu::IterRefine iter_ref )

Specify how to handle iterative refinement.

Supported options are: superlu::NOREFINE, superlu::SLU_SINGLE, superlu::SLU_DOUBLE (default), superlu::SLU_EXTRA

Definition at line 427 of file superlu.cpp.

◆ SetLookAheadElimTree()

void mfem::SuperLUSolver::SetLookAheadElimTree ( bool etree )

Specifies whether to use the elimination tree computed from the serial symbolic factorization to perform static scheduling (default false)

Definition at line 447 of file superlu.cpp.

◆ SetNumLookAheads()

void mfem::SuperLUSolver::SetNumLookAheads ( int num_lookaheads )

Specify the number of levels in the look-ahead factorization (default 10)

Definition at line 441 of file superlu.cpp.

◆ SetOperator()

void mfem::SuperLUSolver::SetOperator ( const Operator & op )

virtual

Set the operator/matrix.

Note: A must be a SuperLURowLocMatrix.

Implements mfem::Solver.

Definition at line 475 of file superlu.cpp.

◆ SetParSymbFact()

void mfem::SuperLUSolver::SetParSymbFact ( bool par )

Specify whether to perform parallel symbolic factorization.

Note: If true SuperLU will use superlu::PARMETIS for the Column Permutation regardless of the setting

Definition at line 461 of file superlu.cpp.

◆ SetPrintStatistics()

void mfem::SuperLUSolver::SetPrintStatistics ( bool print_stat )

Specify whether to print the solver statistics (default true)

Definition at line 385 of file superlu.cpp.

◆ SetReplaceTinyPivot()

void mfem::SuperLUSolver::SetReplaceTinyPivot ( bool rtp )

Specify whether to replace tiny diagonals encountered during pivot with \( \sqrt{\epsilon} \lVert A \rVert \) (default false)

Definition at line 434 of file superlu.cpp.

◆ SetRowPermutation()

void mfem::SuperLUSolver::SetRowPermutation ( superlu::RowPerm row_perm )

Specify how to permute the rows of the matrix.

Supported options are: superlu::NOROWPERM, superlu::LargeDiag (default), superlu::MY_PERMR for SuperLU version 5. For later versions the supported options are: superlu::NOROWPERM, superlu::LargeDiag_MC64 (default), superlu::LargeDiag_HWPM, superlu::MY_PERMR

Definition at line 415 of file superlu.cpp.

◆ SetSymmetricPattern()

void mfem::SuperLUSolver::SetSymmetricPattern ( bool sym )

Specify whether the matrix has a symmetric pattern to avoid extra work (default false)

Definition at line 454 of file superlu.cpp.

Member Data Documentation

◆ APtr_

const SuperLURowLocMatrix* mfem::SuperLUSolver::APtr_

protected

Definition at line 277 of file superlu.hpp.

◆ gridPtr_

void* mfem::SuperLUSolver::gridPtr_

protected

Definition at line 291 of file superlu.hpp.

◆ LUstructPtr_

void* mfem::SuperLUSolver::LUstructPtr_

protected

Definition at line 289 of file superlu.hpp.

◆ npcol_

const int mfem::SuperLUSolver::npcol_

Definition at line 267 of file superlu.hpp.

◆ npdep_

const int mfem::SuperLUSolver::npdep_

Definition at line 267 of file superlu.hpp.

◆ nprow_

const int mfem::SuperLUSolver::nprow_

Definition at line 267 of file superlu.hpp.

◆ nrhs_

int mfem::SuperLUSolver::nrhs_

mutableprotected

Definition at line 279 of file superlu.hpp.

◆ optionsPtr_

void* mfem::SuperLUSolver::optionsPtr_

protected

The actual types of the following pointers are hidden to avoid exposing the SuperLU header files to the entire library. Their types are given in the trailing comments. The reason that this is necessary is that SuperLU defines these structs differently for use with its real and complex solvers. If we want to add support for SuperLU's complex solvers one day we will need to hide these types to avoid name conflicts.

Definition at line 287 of file superlu.hpp.

◆ ScalePermstructPtr_

void* mfem::SuperLUSolver::ScalePermstructPtr_

protected

Definition at line 288 of file superlu.hpp.

◆ sol_

Vector mfem::SuperLUSolver::sol_

mutableprotected

Definition at line 278 of file superlu.hpp.

◆ SOLVEstructPtr_

void* mfem::SuperLUSolver::SOLVEstructPtr_

protected

Definition at line 290 of file superlu.hpp.

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

linalg/superlu.hpp
linalg/superlu.cpp

Public Member Functions

Public Attributes

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ SuperLUSolver() [1/2]

◆ SuperLUSolver() [2/2]

◆ ~SuperLUSolver()

Member Function Documentation

◆ ArrayMult()

◆ ArrayMultTranspose()

◆ Mult()

◆ MultTranspose()

◆ SetColumnPermutation()

◆ SetEquilibriate()

◆ SetFact()

◆ SetIterativeRefine()

◆ SetLookAheadElimTree()

◆ SetNumLookAheads()

◆ SetOperator()

◆ SetParSymbFact()

◆ SetPrintStatistics()

◆ SetReplaceTinyPivot()

◆ SetRowPermutation()

◆ SetSymmetricPattern()

Member Data Documentation

◆ APtr_

◆ gridPtr_

◆ LUstructPtr_

◆ npcol_

◆ npdep_

◆ nprow_

◆ nrhs_

◆ optionsPtr_

◆ ScalePermstructPtr_

◆ sol_

◆ SOLVEstructPtr_