Data type dense matrix. More...

#include <densemat.hpp>

Inheritance diagram for DenseMatrix:

Collaboration diagram for DenseMatrix:

Public Member Functions
	DenseMatrix ()
	DenseMatrix (const DenseMatrix &)
	Copy constructor.
	DenseMatrix (int s)
	Creates square matrix of size s.
	DenseMatrix (int m, int n)
	Creates rectangular matrix of size n and height m.
	DenseMatrix (const DenseMatrix &mat, char ch)
	Creates rectangular matrix equal to the transpose of mat.
	DenseMatrix (double *d, int h, int w)
void	UseExternalData (double *d, int h, int w)
void	ClearExternalData ()
void	SetSize (int s)
	If the matrix is not a square matrix of size s then recreate it.
void	SetSize (int h, int w)
	If the matrix is not a matrix of size (h x w) then recreate it.
int	Height () const
	Returns the height of the matrix.
int	Width () const
	Returns the width of the matrix.
double *	Data () const
	Returns vector of the elements.
double &	operator() (int i, int j)
	Returns reference to a_{ij}. Index i, j = 0 .. size-1.
const double &	operator() (int i, int j) const
	Returns constant reference to a_{ij}. Index i, j = 0 .. size-1.
double	operator* (const DenseMatrix &m) const
	Matrix inner product: tr(A^t B)
double	Trace () const
	Trace of a square matrix.
virtual double &	Elem (int i, int j)
	Returns reference to a_{ij}. Index i, j = 0 .. size-1.
virtual const double &	Elem (int i, int j) const
	Returns constant reference to a_{ij}. Index i, j = 0 .. size-1.
void	Mult (const double x, double y) const
	Matrix vector multiplication.
virtual void	Mult (const Vector &x, Vector &y) const
	Matrix vector multiplication.
virtual void	MultTranspose (const Vector &x, Vector &y) const
	Multiply a vector with the transpose matrix.
void	AddMult (const Vector &x, Vector &y) const
	y += A.x
double	InnerProduct (const double x, const double y) const
	Compute y^t A x.
double	InnerProduct (const Vector &x, const Vector &y) const
	Compute y^t A x.
virtual MatrixInverse *	Inverse () const
	Returns a pointer to the inverse matrix.
void	Invert ()
	Replaces the current matrix with its inverse.
double	Det () const
	Calculates the determinant of the matrix (for 2x2 or 3x3 matrices)
double	Weight () const
void	Add (const double c, DenseMatrix &A)
	Adds the matrix A multiplied by the number c to the matrix.
DenseMatrix &	operator= (double c)
	Sets the matrix elements equal to constant c.
DenseMatrix &	operator= (const DenseMatrix &m)
	Sets the matrix size and elements equal to those of m.
DenseMatrix &	operator+= (DenseMatrix &m)
DenseMatrix &	operator-= (DenseMatrix &m)
DenseMatrix &	operator*= (double c)
void	Neg ()
	(this) = -(this)
void	Norm2 (double *v) const
	Take the 2-norm of the columns of A and store in v.
double	FNorm () const
void	Eigenvalues (Vector &ev)
void	Eigenvalues (Vector &ev, DenseMatrix &evect)
void	Eigensystem (Vector &ev, DenseMatrix &evect)
void	SingularValues (Vector &sv) const
double	CalcSingularvalue (const int i) const
	Return the i-th singular value (decreasing order) of a 2x2 or 3x3 matrix.
void	CalcEigenvalues (double lambda, double vec) const
void	GetColumn (int c, Vector &col)
void	GetColumnReference (int c, Vector &col)
void	Diag (double c, int n)
	Creates n x n diagonal matrix with diagonal elements c.
void	Diag (double *diag, int n)
	Creates n x n diagonal matrix with diagonal given by diag.
void	Transpose ()
	(this) = (this)^t
void	Transpose (DenseMatrix &A)
	(*this) = A^t
void	Symmetrize ()
	(this) = 1/2 ((this) + (*this)^t)
void	Lump ()
void	GradToCurl (DenseMatrix &curl)
void	GradToDiv (Vector &div)
void	CopyRows (DenseMatrix &A, int row1, int row2)
	Copy rows row1 through row2 from A to *this.
void	CopyCols (DenseMatrix &A, int col1, int col2)
	Copy columns col1 through col2 from A to *this.
void	CopyMN (DenseMatrix &A, int m, int n, int Aro, int Aco)
	Copy the m x n submatrix of A at (Aro)ffset, (Aco)loffset to *this.
void	CopyMN (DenseMatrix &A, int row_offset, int col_offset)
	Copy matrix A to the location in *this at row_offset, col_offset.
void	CopyMNt (DenseMatrix &A, int row_offset, int col_offset)
	Copy matrix A^t to the location in *this at row_offset, col_offset.
void	CopyMNDiag (double c, int n, int row_offset, int col_offset)
	Copy c on the diagonal of size n to *this at row_offset, col_offset.
void	CopyMNDiag (double *diag, int n, int row_offset, int col_offset)
	Copy diag on the diagonal of size n to *this at row_offset, col_offset.
void	AddMatrix (DenseMatrix &A, int ro, int co)
	Perform (ro+i,co+j)+=A(i,j) for 0<=i<A.Height, 0<=j<A.Width.
void	AddMatrix (double a, DenseMatrix &A, int ro, int co)
	Perform (ro+i,co+j)+=a*A(i,j) for 0<=i<A.Height, 0<=j<A.Width.
void	AddToVector (int offset, Vector &v) const
	Add the matrix 'data' to the Vector 'v' at the given 'offset'.
void	GetFromVector (int offset, const Vector &v)
	Get the matrix 'data' from the Vector 'v' at the given 'offset'.
void	AdjustDofDirection (Array< int > &dofs)
virtual void	Print (ostream &out=cout, int width=4) const
	Prints matrix to stream out.
virtual void	PrintT (ostream &out=cout, int width=4) const
	Prints the transpose matrix to stream out.
void	TestInversion ()
	Invert and print the numerical conditioning of the inversion.
virtual	~DenseMatrix ()
	Destroys dense matrix.
Private Member Functions
void	Eigensystem (Vector &ev, DenseMatrix *evect=NULL)
Private Attributes
int	height
double *	data
Friends
class	DenseTensor
class	DenseMatrixInverse
void	Mult (const DenseMatrix &b, const DenseMatrix &c, DenseMatrix &a)
	Matrix matrix multiplication. A = B * C.

Detailed Description

Data type dense matrix.

Definition at line 16 of file densemat.hpp.

Constructor & Destructor Documentation

DenseMatrix::DenseMatrix ( )

Default constructor for DenseMatrix. Sets data = NULL size = height = 0

Definition at line 26 of file densemat.cpp.

References data, and height.

DenseMatrix::DenseMatrix ( const DenseMatrix & m )

Copy constructor.

Definition at line 32 of file densemat.cpp.

References data, height, and Operator::size.

DenseMatrix::DenseMatrix ( int s ) [explicit]

Creates square matrix of size s.

Definition at line 41 of file densemat.cpp.

References data, and height.

DenseMatrix::DenseMatrix	(	int	m,
		int	n
	)

Creates rectangular matrix of size n and height m.

Definition at line 52 of file densemat.cpp.

References data, and height.

DenseMatrix::DenseMatrix	(	const DenseMatrix &	mat,
		char	ch
	)

Creates rectangular matrix equal to the transpose of mat.

Definition at line 63 of file densemat.cpp.

References data, height, and Operator::size.

DenseMatrix::DenseMatrix	(	double *	d,
		int	h,
		int	w
	)		`[inline]`

Definition at line 48 of file densemat.hpp.

References data, and height.

DenseMatrix::~DenseMatrix ( ) [virtual]

Destroys dense matrix.

Definition at line 1787 of file densemat.cpp.

References data.

Member Function Documentation

void DenseMatrix::Add	(	const double	c,
		DenseMatrix &	A
	)

Adds the matrix A multiplied by the number c to the matrix.

Definition at line 273 of file densemat.cpp.

References Height(), and Operator::Size().

Referenced by aGMRES(), and GMRES().

void DenseMatrix::AddMatrix	(	DenseMatrix &	A,
		int	ro,
		int	co
	)

Perform (ro+i,co+j)+=A(i,j) for 0<=i<A.Height, 0<=j<A.Width.

Definition at line 1637 of file densemat.cpp.

References data, Height(), mfem_error(), and Width().

Referenced by VectorMassIntegrator::AssembleElementMatrix().

void DenseMatrix::AddMatrix	(	double	a,
		DenseMatrix &	A,
		int	ro,
		int	co
	)

Perform (ro+i,co+j)+=a*A(i,j) for 0<=i<A.Height, 0<=j<A.Width.

Definition at line 1663 of file densemat.cpp.

References data, Height(), mfem_error(), and Width().

void DenseMatrix::AddMult	(	const Vector &	x,
		Vector &	y
	)		const

y += A.x

Definition at line 176 of file densemat.cpp.

References height, mfem_error(), Vector::Size(), and Operator::size.

Referenced by VectorFEDomainLFIntegrator::AssembleRHSElementVect().

void DenseMatrix::AddToVector	(	int	offset,
		Vector &	v
	)		const

Add the matrix 'data' to the Vector 'v' at the given 'offset'.

Definition at line 1689 of file densemat.cpp.

References data, Vector::GetData(), height, and Operator::size.

void DenseMatrix::AdjustDofDirection ( Array< int > & dofs )

If (dofs[i] < 0 and dofs[j] >= 0) or (dofs[i] >= 0 and dofs[j] < 0) then (*this)(i,j) = -(*this)(i,j).

Definition at line 1707 of file densemat.cpp.

References Height(), mfem_error(), Array< T >::Size(), and Width().

void DenseMatrix::CalcEigenvalues	(	double *	lambda,
		double *	vec
	)		const

Return the eigenvalues (in increasing order) and eigenvectors of a 2x2 or 3x3 symmetric matrix.

Definition at line 1120 of file densemat.cpp.

References data, Height(), mfem_error(), and Width().

double DenseMatrix::CalcSingularvalue ( const int i ) const

Return the i-th singular value (decreasing order) of a 2x2 or 3x3 matrix.

Definition at line 738 of file densemat.cpp.

References data, Height(), mfem_error(), and Width().

Referenced by Mesh::GetElementSize(), and Mesh::PrintCharacteristics().

void DenseMatrix::ClearExternalData ( ) [inline]

Definition at line 52 of file densemat.hpp.

References data, height, and Operator::size.

Referenced by BilinearForm::ComputeElementMatrices(), and DenseTensor::~DenseTensor().

void DenseMatrix::CopyCols	(	DenseMatrix &	A,
		int	col1,
		int	col2
	)

Copy columns col1 through col2 from A to *this.

Definition at line 1570 of file densemat.cpp.

References Height(), and SetSize().

void DenseMatrix::CopyMN	(	DenseMatrix &	A,
		int	m,
		int	n,
		int	Aro,
		int	Aco
	)

Copy the m x n submatrix of A at (Aro)ffset, (Aco)loffset to *this.

Definition at line 1579 of file densemat.cpp.

References SetSize().

void DenseMatrix::CopyMN	(	DenseMatrix &	A,
		int	row_offset,
		int	col_offset
	)

Copy matrix A to the location in *this at row_offset, col_offset.

Definition at line 1590 of file densemat.cpp.

References data, Height(), and Operator::Size().

void DenseMatrix::CopyMNDiag	(	double	c,
		int	n,
		int	row_offset,
		int	col_offset
	)

Copy c on the diagonal of size n to *this at row_offset, col_offset.

Definition at line 1610 of file densemat.cpp.

void DenseMatrix::CopyMNDiag	(	double *	diag,
		int	n,
		int	row_offset,
		int	col_offset
	)

Copy diag on the diagonal of size n to *this at row_offset, col_offset.

Definition at line 1623 of file densemat.cpp.

void DenseMatrix::CopyMNt	(	DenseMatrix &	A,
		int	row_offset,
		int	col_offset
	)

Copy matrix A^t to the location in *this at row_offset, col_offset.

Definition at line 1600 of file densemat.cpp.

References data, Height(), and Operator::Size().

void DenseMatrix::CopyRows	(	DenseMatrix &	A,
		int	row1,
		int	row2
	)

Copy rows row1 through row2 from A to *this.

Definition at line 1561 of file densemat.cpp.

References SetSize(), and Operator::Size().

double* DenseMatrix::Data ( ) const [inline]

Returns vector of the elements.

Definition at line 67 of file densemat.hpp.

References data.

Referenced by NURBS1DFiniteElement::CalcDShape(), L2_SegmentElement::CalcDShape(), CalcInverse(), DenseMatrixEigensystem::DenseMatrixEigensystem(), DetOfLinComb(), dsyev_Eigensystem(), dsyevr_Eigensystem(), DenseMatrixEigensystem::Eigenvector(), DenseMatrixSVD::Eval(), DenseMatrixEigensystem::Eval(), MultABt(), and MultAtB().

double DenseMatrix::Det ( ) const

Calculates the determinant of the matrix (for 2x2 or 3x3 matrices)

Definition at line 223 of file densemat.cpp.

References data, Height(), mfem_error(), and Width().

Referenced by CalcInverse(), CalcInverseTranspose(), Mesh::CheckElementOrientation(), Mesh::GetElementSize(), Mesh::PrintCharacteristics(), and Weight().

void DenseMatrix::Diag	(	double	c,
		int	n
	)

Creates n x n diagonal matrix with diagonal elements c.

Definition at line 1426 of file densemat.cpp.

References data, and SetSize().

void DenseMatrix::Diag	(	double *	diag,
		int	n
	)

Creates n x n diagonal matrix with diagonal given by diag.

Definition at line 1437 of file densemat.cpp.

References data, and SetSize().

void DenseMatrix::Eigensystem	(	Vector &	ev,
		DenseMatrix &	evect
	)		`[inline]`

Definition at line 146 of file densemat.hpp.

References Eigensystem().

Referenced by Eigensystem().

void DenseMatrix::Eigensystem	(	Vector &	ev,
		DenseMatrix *	evect = `NULL`
	)		`[private]`

Definition at line 684 of file densemat.cpp.

References dsyev_Eigensystem(), and mfem_error().

Referenced by Eigenvalues().

void DenseMatrix::Eigenvalues ( Vector & ev ) [inline]

Definition at line 140 of file densemat.hpp.

References Eigensystem().

void DenseMatrix::Eigenvalues	(	Vector &	ev,
		DenseMatrix &	evect
	)		`[inline]`

Definition at line 143 of file densemat.hpp.

References Eigensystem().

double & DenseMatrix::Elem	(	int	i,
		int	j
	)		`[virtual]`

Returns reference to a_{ij}. Index i, j = 0 .. size-1.

Implements Matrix.

Definition at line 114 of file densemat.cpp.

const double & DenseMatrix::Elem	(	int	i,
		int	j
	)		const `[virtual]`

Returns constant reference to a_{ij}. Index i, j = 0 .. size-1.

Implements Matrix.

Definition at line 119 of file densemat.cpp.

double DenseMatrix::FNorm ( ) const

Definition at line 448 of file densemat.cpp.

References data, Height(), and Operator::Size().

Referenced by CalcInverse(), and TestInversion().

void DenseMatrix::GetColumn	(	int	c,
		Vector &	col
	)

Definition at line 1412 of file densemat.cpp.

References data, Vector::GetData(), Height(), and Vector::SetSize().

void DenseMatrix::GetColumnReference	(	int	c,
		Vector &	col
	)		`[inline]`

Definition at line 160 of file densemat.hpp.

References data, height, and Vector::SetDataAndSize().

Referenced by VectorCoefficient::Eval(), GridFunction::GetGradients(), and GridFunction::GetVectorValues().

void DenseMatrix::GetFromVector	(	int	offset,
		const Vector &	v
	)

Get the matrix 'data' from the Vector 'v' at the given 'offset'.

Definition at line 1698 of file densemat.cpp.

References data, Vector::GetData(), height, and Operator::size.

void DenseMatrix::GradToCurl ( DenseMatrix & curl )

Given a DShape matrix (from a scalar FE), stored in *this, returns the CurlShape matrix. If *this is a N by 3 matrix, then curl is a 3*N by 3 matrix. The size of curl must be set outside.

Definition at line 1508 of file densemat.cpp.

References Height(), mfem_error(), and Width().

void DenseMatrix::GradToDiv ( Vector & div )

Given a DShape matrix (from a scalar FE), stored in *this, returns the DivShape vector. If *this is a N by dim matrix, then div is a dim*N vector. The size of div must be set outside.

Definition at line 1544 of file densemat.cpp.

References data, Vector::GetData(), height, Height(), mfem_error(), Operator::size, Vector::Size(), and Width().

Referenced by ElasticityIntegrator::AssembleElementMatrix(), and VectorDivergenceIntegrator::AssembleElementMatrix2().

int DenseMatrix::Height ( ) const [inline]

Returns the height of the matrix.

Definition at line 61 of file densemat.hpp.

References height.

Referenced by Add(), Add(), AddMatrix(), AddMult_a_AAt(), AddMult_a_VVt(), AddMultABt(), AddMultADAt(), AddMultVWt(), AdjustDofDirection(), CalcAdjugate(), CalcAdjugateTranspose(), Linear3DFiniteElement::CalcDShape(), CalcEigenvalues(), CalcInverse(), CalcInverseTranspose(), CalcSingularvalue(), VectorFiniteElement::CalcVShape_ND(), CopyCols(), CopyMN(), CopyMNt(), DenseMatrixSVD::DenseMatrixSVD(), Det(), dsyev_Eigensystem(), dsyevr_Eigensystem(), DenseMatrixEigensystem::Eigenvector(), DenseMatrixSVD::Eval(), FNorm(), GetColumn(), DenseTensor::GetData(), GradToCurl(), GradToDiv(), Invert(), IsoparametricTransformation::Jacobian(), Lump(), Mult_a_AAt(), MultAAt(), MultABt(), MultADAt(), MultAtB(), MultVWt(), Neg(), Norm2(), operator*(), operator*=(), operator=(), Mesh::PrintVTK(), GridFunction::SaveVTK(), SetSize(), SingularValues(), DenseTensor::SizeI(), Symmetrize(), Trace(), IntegrationPointTransformation::Transform(), IsoparametricTransformation::Transform(), Transpose(), and Weight().