MFEM v4.7.0
Finite element discretization library
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mfem::AbstractSparseMatrix Class Referenceabstract

Abstract data type for sparse matrices. More...

#include <matrix.hpp>

Inheritance diagram for mfem::AbstractSparseMatrix:
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Collaboration diagram for mfem::AbstractSparseMatrix:
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Public Member Functions

 AbstractSparseMatrix (int s=0)
 Creates a square matrix of the given size.
 
 AbstractSparseMatrix (int h, int w)
 Creates a matrix of the given height and width.
 
virtual int NumNonZeroElems () const =0
 Returns the number of non-zeros in a matrix.
 
virtual int GetRow (const int row, Array< int > &cols, Vector &srow) const =0
 Gets the columns indexes and values for row row.
 
virtual void EliminateZeroRows (const real_t threshold=1e-12)=0
 If the matrix is square, this method will place 1 on the diagonal (i,i) if row i has "almost" zero l1-norm.
 
virtual void Mult (const Vector &x, Vector &y) const =0
 Matrix-Vector Multiplication y = A*x.
 
virtual void AddMult (const Vector &x, Vector &y, const real_t val=1.) const =0
 Matrix-Vector Multiplication y = y + val*A*x.
 
virtual void MultTranspose (const Vector &x, Vector &y) const =0
 MatrixTranspose-Vector Multiplication y = A'*x.
 
virtual void AddMultTranspose (const Vector &x, Vector &y, const real_t val=1.) const =0
 MatrixTranspose-Vector Multiplication y = y + val*A'*x.
 
virtual ~AbstractSparseMatrix ()
 Destroys AbstractSparseMatrix.
 
- Public Member Functions inherited from mfem::Matrix
 Matrix (int s)
 Creates a square matrix of size s.
 
 Matrix (int h, int w)
 Creates a matrix of the given height and width.
 
bool IsSquare () const
 Returns whether the matrix is a square matrix.
 
virtual real_tElem (int i, int j)=0
 Returns reference to a_{ij}.
 
virtual const real_tElem (int i, int j) const =0
 Returns constant reference to a_{ij}.
 
virtual MatrixInverseInverse () const =0
 Returns a pointer to (an approximation) of the matrix inverse.
 
virtual void Finalize (int)
 Finalizes the matrix initialization.
 
virtual void Print (std::ostream &out=mfem::out, int width_=4) const
 Prints matrix to stream out.
 
virtual ~Matrix ()
 Destroys matrix.
 
- 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 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 OperatorGetGradient (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 OperatorGetProlongation () const
 Prolongation operator from linear algebra (linear system) vectors, to input vectors for the operator. NULL means identity.
 
virtual const OperatorGetRestriction () const
 Restriction operator from input vectors for the operator to linear algebra (linear system) vectors. NULL means identity.
 
virtual const OperatorGetOutputProlongation () const
 Prolongation operator from linear algebra (linear system) vectors, to output vectors for the operator. NULL means identity.
 
virtual const OperatorGetOutputRestrictionTranspose () const
 Transpose of GetOutputRestriction, directly available in this form to facilitate matrix-free RAP-type operators.
 
virtual const OperatorGetOutputRestriction () 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.
 

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

Detailed Description

Abstract data type for sparse matrices.

Definition at line 73 of file matrix.hpp.

Constructor & Destructor Documentation

◆ AbstractSparseMatrix() [1/2]

mfem::AbstractSparseMatrix::AbstractSparseMatrix ( int s = 0)
inlineexplicit

Creates a square matrix of the given size.

Definition at line 77 of file matrix.hpp.

◆ AbstractSparseMatrix() [2/2]

mfem::AbstractSparseMatrix::AbstractSparseMatrix ( int h,
int w )
inlineexplicit

Creates a matrix of the given height and width.

Definition at line 80 of file matrix.hpp.

◆ ~AbstractSparseMatrix()

virtual mfem::AbstractSparseMatrix::~AbstractSparseMatrix ( )
inlinevirtual

Destroys AbstractSparseMatrix.

Definition at line 110 of file matrix.hpp.

Member Function Documentation

◆ AddMult()

virtual void mfem::AbstractSparseMatrix::AddMult ( const Vector & x,
Vector & y,
const real_t val = 1. ) const
pure virtual

Matrix-Vector Multiplication y = y + val*A*x.

Reimplemented from mfem::Operator.

Implemented in mfem::BlockMatrix, and mfem::SparseMatrix.

◆ AddMultTranspose()

virtual void mfem::AbstractSparseMatrix::AddMultTranspose ( const Vector & x,
Vector & y,
const real_t val = 1. ) const
pure virtual

MatrixTranspose-Vector Multiplication y = y + val*A'*x.

Reimplemented from mfem::Operator.

Implemented in mfem::BlockMatrix, and mfem::SparseMatrix.

◆ EliminateZeroRows()

virtual void mfem::AbstractSparseMatrix::EliminateZeroRows ( const real_t threshold = 1e-12)
pure virtual

If the matrix is square, this method will place 1 on the diagonal (i,i) if row i has "almost" zero l1-norm.

If entry (i,i) does not belong to the sparsity pattern of A, then an error will occur.

Implemented in mfem::BlockMatrix, and mfem::SparseMatrix.

◆ GetRow()

virtual int mfem::AbstractSparseMatrix::GetRow ( const int row,
Array< int > & cols,
Vector & srow ) const
pure virtual

Gets the columns indexes and values for row row.

Returns:

  • 0 if cols and srow are copies of the values in the matrix.
  • 1 if cols and srow are views of the values in the matrix.

Implemented in mfem::BlockMatrix, and mfem::SparseMatrix.

◆ Mult()

virtual void mfem::AbstractSparseMatrix::Mult ( const Vector & x,
Vector & y ) const
pure virtual

Matrix-Vector Multiplication y = A*x.

Implements mfem::Operator.

Implemented in mfem::BlockMatrix, and mfem::SparseMatrix.

◆ MultTranspose()

virtual void mfem::AbstractSparseMatrix::MultTranspose ( const Vector & x,
Vector & y ) const
pure virtual

MatrixTranspose-Vector Multiplication y = A'*x.

Reimplemented from mfem::Operator.

Implemented in mfem::BlockMatrix, and mfem::SparseMatrix.

◆ NumNonZeroElems()

virtual int mfem::AbstractSparseMatrix::NumNonZeroElems ( ) const
pure virtual

Returns the number of non-zeros in a matrix.

Implemented in mfem::BlockMatrix, and mfem::SparseMatrix.


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