Class for representing a dense system matrix. More...

#include <DenseMatrix.h>

Inheritance diagram for DenseMatrix:

Collaboration diagram for DenseMatrix:

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Public Member Functions
	DenseMatrix (size_t m=0, size_t n=0, bool s=false)
	Default constructor.

	DenseMatrix (const DenseMatrix &A)
	Copy constructor.

	DenseMatrix (const RealArray &data, size_t nrows=0)
	Special constructor taking data from a one-dimensional array.

	DenseMatrix (const Matrix &A, bool s=false)
	Special constructor, type conversion from Matrix.

virtual	~DenseMatrix ()
	The destructor frees the dynamically allocated arrays.

virtual LinAlg::MatrixType	getType () const
	Returns the matrix type.

virtual SystemMatrix *	copy () const
	Creates a copy of the system matrix and returns a pointer to it.

bool	redim (size_t r, size_t c)
	Resizes the matrix to dimension \(r \times c\).

void	setSymmetric (bool s=true)
	Marks the matrix as symmetric.

virtual size_t	dim (int idim) const
	Returns the dimension of the system matrix.

Matrix &	getMat ()
	Access to the matrix itself.

Real &	operator() (size_t r, size_t c)
	Index-1 based element access.

const Real &	operator() (size_t r, size_t c) const
	Index-1 based element reference.

virtual void	dump (std::ostream &os, LinAlg::StorageFormat format, const char *label)
	Dumps the system matrix on a specified format.

virtual void	initAssembly (const SAM &sam, char)
	Initializes the element assembly process.

virtual void	init ()
	Initializes the matrix to zero assuming it is properly dimensioned.

virtual bool	assemble (const Matrix &eM, const SAM &sam, int e)
	Adds an element matrix into the associated system matrix.

virtual bool	assemble (const Matrix &eM, const SAM &sam, SystemVector &B, int e)
	Adds an element matrix into the associated system matrix.

virtual bool	assemble (const Matrix &eM, const SAM &sam, SystemVector &B, const std::vector< int > &meq)
	Adds an element matrix into the associated system matrix.

virtual bool	assemble (const Matrix &eM, const IntVec &meq)
	Adds an element matrix into the associated system matrix.

virtual bool	augment (const SystemMatrix &B, size_t r0, size_t c0)
	Augments a similar matrix symmetrically to the current matrix.

virtual void	mult (Real alpha)
	Multiplication with a scalar.

virtual bool	add (const SystemMatrix &B, Real alpha)
	Adds a matrix with similar dimension to the current matrix.

virtual bool	add (Real sigma, int ieq)
	Adds the constant σ to the diagonal of this matrix.

virtual bool	multiply (const SystemVector &B, SystemVector &C) const
	Performs the matrix-vector multiplication C = this B.

virtual bool	solve (SystemVector &B, Real *rc=nullptr)
	Solves the linear system of equations for a given right-hand-side.

bool	solve (Matrix &B)
	Solves the linear system of equations for a given right-hand-side.

bool	solveEig (RealArray &eigVal, Matrix &eigVec, int nev)
	Solves a standard symmetric-definite eigenproblem.

bool	solveEigNon (RealArray &r_val, RealArray &c_val)
	Solves a non-symmetric eigenproblem.

bool	solveEig (DenseMatrix &B, RealArray &eigVal, Matrix &eigVec, int nev, Real shift=Real(0))
	Solves a generalized symmetric-definite eigenproblem.

virtual Real	Linfnorm () const
	Returns the L-infinity norm of the matrix.

virtual bool	load (const char *fileName, bool binary)
	Loads the system matrix from specified file.

virtual bool	solve (SystemVector &b, Real *rc=nullptr)=0
	Solves the linear system of equations for a given right-hand-side.

virtual bool	solve (const SystemVector &b, SystemVector &x)
	Solves the linear system of equations for a given right-hand-side.

virtual bool	solve (SystemVector &b, Matrix &x)
	Solves a linear system of equations for multiple right-hand-sides.

Public Member Functions inherited from SystemMatrix
virtual	~SystemMatrix ()
	Empty destructor.

virtual bool	lockPattern (bool)
	Locks or unlocks the sparsity pattern.

virtual bool	empty () const
	Checks if the matrix is empty.

bool	isZero () const
	Checks if the matrix have no non-zero contributions.

virtual void	preAssemble (const std::vector< IntVec > &, size_t=0)
	Initializes the element sparsity pattern based on node connections.

virtual void	compressPattern ()
	Compresses the sparsity pattern.

void	initNonZeroEqs ()
	Initializes the nonZeroEqs flags.

bool	flagNonZeroEq (int ieq=0)
	Flags equation ieq as pivot element with non-zero contributions.

bool	flagNonZeroEqs (const SAM &sam, const IntVec &meq)
	Flags the equations meq as pivots with non-zero contributions.

bool	flagNonZeroEqs (const SystemMatrix &B)
	Flags the non-zero equations from B as non-zero pivots in this.

virtual bool	endAssembly ()
	Finalizes the system matrix assembly.

virtual bool	truncate (Real=Real(1.0e-16))
	Truncates all small matrix elements to zero.

virtual void	dump (const char *fileName, std::streamsize precision=0, LinAlg::StorageFormat format=LinAlg::FLAT)
	Dumps the system matrix to specified file.

StdVector	operator* (const SystemVector &b) const
	Calculates a matrix-vector product.

StdVector	operator/ (const SystemVector &b)
	Solves a linear equation system.

Protected Member Functions
bool	augment (const Matrix &B, size_t r0, size_t c0)
	Augments a dense matrix symmetrically to the current matrix.

bool	augment (const SparseMatrix &B, size_t r0, size_t c0)
	Augments a sparse matrix symmetrically to the current matrix.

bool	solve (Real B, size_t nrhs, Real rcond=nullptr)
	Solves the linear system of equations for a given right-hand-side.

virtual std::ostream &	write (std::ostream &os) const
	Writes the system matrix to the given output stream.

Protected Member Functions inherited from SystemMatrix
	SystemMatrix ()
	Default constructor.

	SystemMatrix (const SystemMatrix &a)
	Copy constructor.

Private Attributes
Matrix	myMat
	The actual dense matrix.

int *	ipiv
	Pivot indices used in solve.

bool	symm
	Flags whether the matrix is symmetric or not.

Additional Inherited Members
Static Public Member Functions inherited from SystemMatrix
static SystemMatrix *	create (const ProcessAdm *adm, LinAlg::MatrixType mType, int num_thread_SLU=1)
	Static method creating a matrix of the given type.

static SystemMatrix *	create (const ProcessAdm *adm, LinAlg::MatrixType mType, const LinSolParams &spar)
	Static method creating a matrix of the given type.

Detailed Description

Class for representing a dense system matrix.

Member Function Documentation

◆ add() [1/2]

bool DenseMatrix::add	(	const SystemMatrix &	B,
		Real	alpha
	)

virtual

Adds a matrix with similar dimension to the current matrix.

Parameters

[in]	B	The matrix to be added
[in]	alpha	Scale factor for matrix B

Reimplemented from SystemMatrix.

References utl::matrix< T >::add(), utl::matrix< T >::cols(), SystemMatrix::flagNonZeroEqs(), SystemMatrix::isZero(), myMat, and utl::matrix< T >::rows().

◆ add() [2/2]

bool DenseMatrix::add	(	Real	sigma,
		int	ieq
	)

virtual

Adds the constant σ to the diagonal of this matrix.

Reimplemented from SystemMatrix.

References SystemMatrix::flagNonZeroEq(), myMat, utl::matrixBase< T >::ptr(), and utl::matrix< T >::rows().

◆ assemble() [1/4]

bool DenseMatrix::assemble	(	const Matrix &	eM,
		const IntVec &	meq
	)

virtual

Adds an element matrix into the associated system matrix.

Parameters

[in]	eM	The element matrix
[in]	meq	Matrix of element equation numbers (0 based)

Returns: true on successful assembly, otherwise false

Implements SystemMatrix.

References SystemMatrix::flagNonZeroEq(), and myMat.

◆ assemble() [2/4]

bool DenseMatrix::assemble	(	const Matrix &	eM,
		const SAM &	sam,
		int	e
	)

virtual

Adds an element matrix into the associated system matrix.

Parameters

[in]	eM	The element matrix
[in]	sam	Auxiliary data for FE assembly management
[in]	e	Identifier for the element that eM belongs to

Returns: true on successful assembly, otherwise false

Implements SystemMatrix.

References assemDense(), utl::matrix< T >::cols(), SystemMatrix::flagNonZeroEqs(), SAM::getElmEqns(), SAM::madof, SAM::meqn, SAM::mmceq, SAM::mmnpc, SAM::mpar, SAM::mpmceq, SAM::mpmnpc, myMat, SAM::neq, utl::matrixBase< T >::ptr(), Real, utl::matrix< T >::rows(), and SAM::ttcc.

◆ assemble() [3/4]

bool DenseMatrix::assemble	(	const Matrix &	eM,
		const SAM &	sam,
		SystemVector &	B,
		const std::vector< int > &	meq
	)

virtual

Adds an element matrix into the associated system matrix.

Parameters

[in]	eM	The element matrix
[in]	sam	Auxiliary data for FE assembly management
	B	The system right-hand-side vector
[in]	meq	Matrix of element equation numbers

Returns: true on successful assembly, otherwise false

When multi-point constraints are present, contributions from these are also added into the system right-hand-side vector, B.

Implements SystemMatrix.

References assemDense(), utl::matrix< T >::cols(), SystemMatrix::flagNonZeroEqs(), SAM::meqn, SAM::mmceq, SAM::mpmceq, myMat, SAM::neq, utl::matrix< T >::rows(), and SAM::ttcc.

◆ assemble() [4/4]

bool DenseMatrix::assemble	(	const Matrix &	eM,
		const SAM &	sam,
		SystemVector &	B,
		int	e
	)

virtual

Adds an element matrix into the associated system matrix.

Parameters

[in]	eM	The element matrix
[in]	sam	Auxiliary data describing the FE model topology, nodal DOF status and constraint equations
	B	The system right-hand-side vector
[in]	e	Identifier for the element that eM belongs to

Returns: true on successful assembly, otherwise false

When multi-point constraints are present, contributions from these are also added into the system right-hand-side vector, B.

Implements SystemMatrix.

References assemDense(), utl::matrix< T >::cols(), SystemMatrix::flagNonZeroEqs(), SAM::getElmEqns(), SystemVector::getPtr(), SAM::madof, SAM::meqn, SAM::mmceq, SAM::mmnpc, SAM::mpar, SAM::mpmceq, SAM::mpmnpc, myMat, SAM::neq, utl::matrixBase< T >::ptr(), utl::matrix< T >::rows(), and SAM::ttcc.

◆ augment() [1/3]

bool DenseMatrix::augment	(	const Matrix &	B,
		size_t	r0,
		size_t	c0
	)

protected

Augments a dense matrix symmetrically to the current matrix.

Parameters

[in]	B	The matrix to be augmented
[in]	r0	Row offset for the augmented matrix
[in]	c0	Column offset for the augmented matrix

References utl::matrix< T >::cols(), myMat, redim(), and utl::matrix< T >::rows().

◆ augment() [2/3]

bool DenseMatrix::augment	(	const SparseMatrix &	B,
		size_t	r0,
		size_t	c0
	)

protected

Augments a sparse matrix symmetrically to the current matrix.

Parameters

[in]	B	The matrix to be augmented
[in]	r0	Row offset for the augmented matrix
[in]	c0	Column offset for the augmented matrix

References SparseMatrix::cols(), SparseMatrix::getValues(), myMat, redim(), and SparseMatrix::rows().

◆ augment() [3/3]

bool DenseMatrix::augment	(	const SystemMatrix &	B,
		size_t	r0,
		size_t	c0
	)

virtual

Augments a similar matrix symmetrically to the current matrix.

Parameters

[in]	B	The matrix to be augmented
[in]	r0	Row offset for the augmented matrix
[in]	c0	Column offset for the augmented matrix

Reimplemented from SystemMatrix.

References augment(), and myMat.

Referenced by augment().

◆ copy()

virtual SystemMatrix * DenseMatrix::copy ( ) const

inlinevirtual

Creates a copy of the system matrix and returns a pointer to it.

Implements SystemMatrix.

◆ dim()

virtual size_t DenseMatrix::dim ( int idim ) const

inlinevirtual

Returns the dimension of the system matrix.

Parameters

[in] idim Which direction to return the dimension in

Implements SystemMatrix.

References utl::matrixBase< T >::dim(), myMat, and utl::matrixBase< T >::size().

◆ dump()

void DenseMatrix::dump	(	std::ostream &	os,
		LinAlg::StorageFormat	format,
		const char *	label
	)

virtual

Dumps the system matrix on a specified format.

Reimplemented from SystemMatrix.

References LinAlg::BINARY, utl::matrix< T >::cols(), LinAlg::FLAT, ipiv, LinAlg::MATLAB, LinAlg::MATRIX_MARKET, myMat, utl::matrixBase< T >::ptr(), Real, utl::matrix< T >::rows(), utl::matrixBase< T >::size(), symm, and utl::writeMatlab().

◆ getType()

virtual LinAlg::MatrixType DenseMatrix::getType ( ) const

inlinevirtual

Returns the matrix type.

Implements SystemMatrix.

References LinAlg::DENSE.

◆ init()

void DenseMatrix::init ( )

virtual

Initializes the matrix to zero assuming it is properly dimensioned.

Implements SystemMatrix.

References utl::matrix< T >::fill(), ipiv, myMat, and Real.

◆ initAssembly()

void DenseMatrix::initAssembly	(	const SAM &	sam,
		char
	)

virtual

Initializes the element assembly process.

Parameters

[in] sam Auxiliary data describing the FE model topology, etc.

Implements SystemMatrix.

References myMat, SAM::neq, and utl::matrix< T >::resize().

◆ Linfnorm()

virtual Real DenseMatrix::Linfnorm ( ) const

inlinevirtual

Returns the L-infinity norm of the matrix.

Implements SystemMatrix.

References myMat, and utl::matrix< T >::normInf().

◆ load()

bool DenseMatrix::load	(	const char *	fileName,
		bool	binary
	)

virtual

Loads the system matrix from specified file.

Reimplemented from SystemMatrix.

References utl::matrix< T >::cols(), SystemMatrix::flagNonZeroEq(), ipiv, myMat, utl::matrixBase< T >::ptr(), Real, utl::matrix< T >::rows(), and symm.

◆ mult()

virtual void DenseMatrix::mult ( Real alpha )

inlinevirtual

Multiplication with a scalar.

Implements SystemMatrix.

References utl::matrix< T >::multiply(), and myMat.

◆ multiply()

bool DenseMatrix::multiply	(	const SystemVector &	B,
		SystemVector &	C
	)		const

virtual

Performs the matrix-vector multiplication C = *this * B.

Reimplemented from SystemMatrix.

References utl::matrix< T >::multiply(), and myMat.

◆ redim()

bool DenseMatrix::redim	(	size_t	r,
		size_t	c
	)

Resizes the matrix to dimension \(r \times c\).

Will preserve existing matrix content within the new dimension.

References utl::matrix< T >::cols(), utl::matrix< T >::fillColumn(), utl::matrix< T >::getColumn(), myMat, utl::matrix< T >::resize(), utl::matrix< T >::rows(), and symm.

Referenced by augment(), and augment().

◆ setSymmetric()

void DenseMatrix::setSymmetric ( bool s = true )

inline

Marks the matrix as symmetric.

If marked as symmetric, Cholesky factorization will be employed.

References utl::matrix< T >::cols(), myMat, utl::matrix< T >::rows(), and symm.

◆ solve() [1/6]

virtual bool SystemMatrix::solve	(	const SystemVector &	b,
		SystemVector &	x
	)

inlinevirtual

Solves the linear system of equations for a given right-hand-side.

Parameters

[in]	b	Right-hand-side vector
[out]	x	Solution vector

Reimplemented from SystemMatrix.

◆ solve() [2/6]

bool DenseMatrix::solve ( Matrix & B )

Solves the linear system of equations for a given right-hand-side.

Parameters

B	Right-hand-side matrix on input, solution matrix on output

References utl::matrix< T >::cols(), utl::matrixBase< T >::ptr(), and solve().

◆ solve() [3/6]

bool DenseMatrix::solve	(	Real *	B,
		size_t	nrhs,
		Real *	rcond = `nullptr`
	)

protected

Solves the linear system of equations for a given right-hand-side.

Parameters

	B	Right-hand-side vectors on input, solution vectors on output
[in]	nrhs	Number of right-hand-side vectors
[out]	rcond	Reciprocal condition number of the LHS-matrix (optional)

This is the function which actually solves the equation system, using the LAPack library subroutines. The two public solve methods just forward to this method.

References utl::matrix< T >::cols(), dgecon_(), dgesv_(), dgetrs_(), dlange_(), dposv_(), dpotrs_(), ipiv, myMat, utl::matrixBase< T >::ptr(), Real, utl::matrix< T >::rows(), and symm.

◆ solve() [4/6]

bool SystemMatrix::solve	(	SystemVector &	b,
		Matrix &	x
	)

virtual

Solves a linear system of equations for multiple right-hand-sides.

Parameters

	b	Right-hand-side vectors on input, solution vectors on output
[out]	x	Matrix of solution vectors (row-oriented)

Reimplemented from SystemMatrix.

◆ solve() [5/6]

bool DenseMatrix::solve	(	SystemVector &	B,
		Real *	rc = `nullptr`
	)

virtual

Solves the linear system of equations for a given right-hand-side.

Parameters

	B	Right-hand-side vector on input, solution vector on output
[out]	rc	Reciprocal condition number of the LHS-matrix (optional)

Implements SystemMatrix.

References SystemVector::dim(), SystemVector::getPtr(), myMat, utl::matrix< T >::rows(), and solve().

Referenced by SplineInterpolator::interpolate(), SplineInterpolator::leastsquare_approximation(), SplineInterpolator::quasiinterpolate(), ASMs2D::scRecovery(), ASMu2D::scRecovery(), ASMu3D::scRecovery(), solve(), and solve().

◆ solve() [6/6]

virtual bool SystemMatrix::solve	(	SystemVector &	b,
		Real *	rc = `nullptr`
	)

virtual

Solves the linear system of equations for a given right-hand-side.

Parameters

	b	Right-hand-side vector on input, solution vector on output
[out]	rc	Reciprocal condition number of the LHS-matrix (optional)

Implements SystemMatrix.

◆ solveEig() [1/2]

bool DenseMatrix::solveEig	(	DenseMatrix &	B,
		RealArray &	eigVal,
		Matrix &	eigVec,
		int	nev,
		Real	shift = `Real(0)`
	)

Solves a generalized symmetric-definite eigenproblem.

Parameters

	B	Symmetric and positive definite mass matrix.
[out]	eigVal	Computed eigenvalues
[out]	eigVec	Computed eigenvectors stored column by column
[in]	nev	The number of eigenvalues and eigenvectors to compute
[in]	shift	Eigenvalue shift (unused)

The eigenproblem is assumed to be on the form A x = λ B x where A ( = *this ) and B both are assumed to be symmetric and B also to be positive definite. The eigenproblem is solved by the LAPack library subroutine DSYGVX.

See also: LAPack library documentation https://www.netlib.org/lapack/.

References utl::matrix< T >::cols(), dsygvx_(), myMat, utl::matrixBase< T >::ptr(), Real, utl::matrix< T >::resize(), and utl::matrix< T >::rows().

◆ solveEig() [2/2]

bool DenseMatrix::solveEig	(	RealArray &	eigVal,
		Matrix &	eigVec,
		int	nev
	)

Solves a standard symmetric-definite eigenproblem.

Parameters

[out]	eigVal	Computed eigenvalues
[out]	eigVec	Computed eigenvectors stored column by column
[in]	nev	The number of eigenvalues and eigenvectors to compute

The eigenproblem is assumed to be on the form A x = λ x where A ( = *this ) is assumed to be symmetric and positive definite. The eigenproblem is solved by the LAPack library subroutine DSYEVX.

See also: LAPack library documentation https://www.netlib.org/lapack/.

References utl::matrix< T >::cols(), dsyevx_(), myMat, utl::matrixBase< T >::ptr(), Real, utl::matrix< T >::resize(), and utl::matrix< T >::rows().

Referenced by eig::solve().

◆ solveEigNon()

bool DenseMatrix::solveEigNon	(	RealArray &	r_val,
		RealArray &	c_val
	)

Solves a non-symmetric eigenproblem.

See also: LAPack library documentation.

Parameters

[out]	r_val	Real part of the computed eigenvalues
[out]	c_val	Complex part of the computed eigenvalues

The eigenproblem is assumed to be on the form A x = λ x where A ( = *this ) is a square non-symmetric matrix. The eigenproblem is solved by the LAPack library subroutine DGEEV.

See also: LAPack library documentation https://www.netlib.org/lapack/.

References dgeev_(), myMat, utl::matrixBase< T >::ptr(), Real, and utl::matrix< T >::rows().

Referenced by Legendre::GL().

◆ write()

virtual std::ostream & DenseMatrix::write ( std::ostream & os ) const

inlineprotectedvirtual

Writes the system matrix to the given output stream.

Reimplemented from SystemMatrix.

References myMat.

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

/home/runner/work/IFEM-2/IFEM-2/src/LinAlg/DenseMatrix.h
/home/runner/work/IFEM-2/IFEM-2/src/LinAlg/DenseMatrix.C

Public Member Functions

Protected Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ add() [1/2]

◆ add() [2/2]

◆ assemble() [1/4]

◆ assemble() [2/4]

◆ assemble() [3/4]

◆ assemble() [4/4]

◆ augment() [1/3]

◆ augment() [2/3]

◆ augment() [3/3]

◆ copy()

◆ dim()

◆ dump()

◆ getType()

◆ init()

◆ initAssembly()

◆ Linfnorm()

◆ load()

◆ mult()

◆ multiply()

◆ redim()

◆ setSymmetric()

◆ solve() [1/6]

◆ solve() [2/6]

◆ solve() [3/6]

◆ solve() [4/6]

◆ solve() [5/6]

◆ solve() [6/6]

◆ solveEig() [1/2]

◆ solveEig() [2/2]

◆ solveEigNon()

◆ write()