mfem::BatchedDirectSolver Class Reference

Solve block-diagonal systems using batched LU or inverses. More...

#include <solver.hpp>

Inheritance diagram for mfem::BatchedDirectSolver:

Collaboration diagram for mfem::BatchedDirectSolver:

Public Types
enum	Mode { LU , INVERSE }
	Solver mode: whether to use LU factorization or inverses. More...
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...

Public Member Functions
	BatchedDirectSolver (const DenseTensor &A_, Mode mode_, BatchedLinAlg::Backend backend_=BatchedLinAlg::GetActiveBackend())
	Constructor.
void	Mult (const Vector &x, Vector &y) const
	Sets $y=A^{-1}x$.
void	SetOperator (const Operator &op)
	Not supported (aborts).
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	MultTranspose (const Vector &x, Vector &y) const
	Action of the transpose operator: y=A^t(x). The default behavior in class Operator is to generate an error.
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	ArrayMult (const Array< const Vector * > &X, Array< Vector * > &Y) const
	Operator application on a matrix: Y=A(X).
virtual void	ArrayMultTranspose (const Array< const Vector * > &X, Array< Vector * > &Y) const
	Action of the transpose operator on a matrix: Y=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.

Protected Attributes
DenseTensor	A
	The LU factors/inverses of the input matrices.
Array< int >	P
	Pivots (needed only for LU factors).
Mode	mode
	Solver mode.
BatchedLinAlg::Backend	backend
	Requested batched linear algebra backend.
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 Attributes inherited from mfem::Solver
bool	iterative_mode
	If true, use the second argument of Mult() as an initial guess.
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

Solve block-diagonal systems using batched LU or inverses.

LU factorization is more numerically stable, but exposes less fine-grained parallelism. Inverse matrices have worse conditioning (and increased setup time), but solving the system is more efficient in parallel (e.g. on GPUs).

Definition at line 26 of file solver.hpp.

Member Enumeration Documentation

Mode

enum mfem::BatchedDirectSolver::Mode

Solver mode: whether to use LU factorization or inverses.

Enumerator
LU	LU factorization.
INVERSE	Inverse matrices.

Definition at line 30 of file solver.hpp.

Constructor & Destructor Documentation

BatchedDirectSolver()

mfem::BatchedDirectSolver::BatchedDirectSolver	(	const DenseTensor &	A_,
		Mode	mode_,
		BatchedLinAlg::Backend	backend_ = BatchedLinAlg::GetActiveBackend() )

Constructor.

The DenseTensor A_ has dimensions $(m,m,n)$, and represents a block diagonal matrix $A$ with $n$ blocks of size $m\times m$.

A deep copy is made of the input A_, and so it does not need to be retained by the caller.

Definition at line 17 of file solver.cpp.

Member Function Documentation

Mult()

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

virtual

Sets $y=A^{-1}x$.

Implements mfem::Operator.

Definition at line 32 of file solver.cpp.

SetOperator()

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

virtual

Not supported (aborts).

Implements mfem::Solver.

Definition at line 45 of file solver.cpp.

Member Data Documentation

A

DenseTensor mfem::BatchedDirectSolver::A

protected

The LU factors/inverses of the input matrices.

Definition at line 36 of file solver.hpp.

backend

BatchedLinAlg::Backend mfem::BatchedDirectSolver::backend

protected

Requested batched linear algebra backend.

Definition at line 39 of file solver.hpp.

mode

Mode mfem::BatchedDirectSolver::mode

protected

Solver mode.

Definition at line 38 of file solver.hpp.

P

Array<int> mfem::BatchedDirectSolver::P

protected

Pivots (needed only for LU factors).

Definition at line 37 of file solver.hpp.

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

• linalg/batched/solver.hpp
• linalg/batched/solver.cpp