MFEM v4.7.0 Finite element discretization library
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mfem::DenseMatrixInverse Class Reference

#include <densemat.hpp>

Inheritance diagram for mfem::DenseMatrixInverse:
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Collaboration diagram for mfem::DenseMatrixInverse:
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## Public Member Functions

DenseMatrixInverse (bool spd_=false)
Default constructor.

DenseMatrixInverse (const DenseMatrix &mat, bool spd_=false)

DenseMatrixInverse (const DenseMatrix *mat, bool spd_=false)
Same as above but does not factorize the matrix.

int Size () const
Get the size of the inverse matrix.

void Factor ()
Factor the current DenseMatrix, *a.

void Factor (const DenseMatrix &mat)
Factor a new DenseMatrix of the same size.

virtual void SetOperator (const Operator &op)
Set/update the solver for the given operator.

void Mult (const real_t *x, real_t *y) const
Matrix vector multiplication with the inverse of dense matrix.

virtual void Mult (const Vector &x, Vector &y) const
Matrix vector multiplication with the inverse of dense matrix.

void Mult (const DenseMatrix &B, DenseMatrix &X) const
Multiply the inverse matrix by another matrix: X = A^{-1} B.

void Mult (DenseMatrix &X) const
Multiply the inverse matrix by another matrix: X <- A^{-1} X.

void GetInverseMatrix (DenseMatrix &Ainv) const
Compute and return the inverse matrix in Ainv.

real_t Det () const
Compute the determinant of the original DenseMatrix using the LU factors.

void TestInversion ()
Print the numerical conditioning of the inversion: ||A^{-1} A - I||.

virtual ~DenseMatrixInverse ()
Destroys dense inverse matrix.

Public Member Functions inherited from mfem::MatrixInverse
MatrixInverse ()

MatrixInverse (const Matrix &mat)
Creates approximation of the inverse of square matrix.

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 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...

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()

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

Data type for inverse of square dense matrix. Stores matrix factors, i.e., Cholesky factors if the matrix is SPD, LU otherwise.

Definition at line 829 of file densemat.hpp.

## ◆ DenseMatrixInverse() [1/3]

 mfem::DenseMatrixInverse::DenseMatrixInverse ( bool spd_ = false )
inline

Default constructor.

Definition at line 840 of file densemat.hpp.

## ◆ DenseMatrixInverse() [2/3]

 mfem::DenseMatrixInverse::DenseMatrixInverse ( const DenseMatrix & mat, bool spd_ = false )

Creates square dense matrix. Computes factorization of mat and stores its factors.

Definition at line 4168 of file densemat.cpp.

## ◆ DenseMatrixInverse() [3/3]

 mfem::DenseMatrixInverse::DenseMatrixInverse ( const DenseMatrix * mat, bool spd_ = false )

Same as above but does not factorize the matrix.

Definition at line 4177 of file densemat.cpp.

## ◆ ~DenseMatrixInverse()

 mfem::DenseMatrixInverse::~DenseMatrixInverse ( )
virtual

Destroys dense inverse matrix.

Definition at line 4263 of file densemat.cpp.

## ◆ Det()

 real_t mfem::DenseMatrixInverse::Det ( ) const
inline

Compute the determinant of the original DenseMatrix using the LU factors.

Definition at line 878 of file densemat.hpp.

## ◆ Factor() [1/2]

 void mfem::DenseMatrixInverse::Factor ( )

Factor the current DenseMatrix, *a.

Definition at line 4185 of file densemat.cpp.

## ◆ Factor() [2/2]

 void mfem::DenseMatrixInverse::Factor ( const DenseMatrix & mat )

Factor a new DenseMatrix of the same size.

Definition at line 4203 of file densemat.cpp.

## ◆ GetInverseMatrix()

 void mfem::DenseMatrixInverse::GetInverseMatrix ( DenseMatrix & Ainv ) const

Compute and return the inverse matrix in Ainv.

Definition at line 4197 of file densemat.cpp.

## ◆ Mult() [1/4]

 void mfem::DenseMatrixInverse::Mult ( const DenseMatrix & B, DenseMatrix & X ) const

Multiply the inverse matrix by another matrix: X = A^{-1} B.

Definition at line 4246 of file densemat.cpp.

## ◆ Mult() [2/4]

 void mfem::DenseMatrixInverse::Mult ( const real_t * x, real_t * y ) const

Matrix vector multiplication with the inverse of dense matrix.

Definition at line 4231 of file densemat.cpp.

## ◆ Mult() [3/4]

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

Matrix vector multiplication with the inverse of dense matrix.

Implements mfem::Operator.

Definition at line 4240 of file densemat.cpp.

## ◆ Mult() [4/4]

 void mfem::DenseMatrixInverse::Mult ( DenseMatrix & X ) const
inline

Multiply the inverse matrix by another matrix: X <- A^{-1} X.

Definition at line 870 of file densemat.hpp.

## ◆ SetOperator()

 void mfem::DenseMatrixInverse::SetOperator ( const Operator & op )
virtual

Set/update the solver for the given operator.

Implements mfem::Solver.

Definition at line 4224 of file densemat.cpp.

## ◆ Size()

 int mfem::DenseMatrixInverse::Size ( ) const
inline

Get the size of the inverse matrix.

Definition at line 850 of file densemat.hpp.

## ◆ TestInversion()

 void mfem::DenseMatrixInverse::TestInversion ( )

Print the numerical conditioning of the inversion: ||A^{-1} A - I||.

Definition at line 4252 of file densemat.cpp.

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