Data type dense matrix using column-major storage. More...

#include <densemat.hpp>

Inheritance diagram for mfem::DenseMatrix:

Collaboration diagram for mfem::DenseMatrix:

Public Member Functions
	DenseMatrix ()

	DenseMatrix (const DenseMatrix &)
	Copy constructor. More...

	DenseMatrix (int s)
	Creates square matrix of size s. More...

	DenseMatrix (int m, int n)
	Creates rectangular matrix of size m x n. More...

	DenseMatrix (const DenseMatrix &mat, char ch)
	Creates rectangular matrix equal to the transpose of mat. More...

	DenseMatrix (double *d, int h, int w)
	Construct a DenseMatrix using an existing data array. More...

template<int M, int N>
	DenseMatrix (const double(&values)[M][N])

void	UseExternalData (double *d, int h, int w)
	Change the data array and the size of the DenseMatrix. More...

void	Reset (double *d, int h, int w)
	Change the data array and the size of the DenseMatrix. More...

void	ClearExternalData ()

void	Clear ()
	Delete the matrix data array (if owned) and reset the matrix state. More...

int	Size () const
	For backward compatibility define Size to be synonym of Width() More...

void	SetSize (int s)
	Change the size of the DenseMatrix to s x s. More...

void	SetSize (int h, int w)
	Change the size of the DenseMatrix to h x w. More...

double *	Data () const
	Returns the matrix data array. More...

double *	GetData () const
	Returns the matrix data array. More...

Memory< double > &	GetMemory ()

const Memory< double > &	GetMemory () const

bool	OwnsData () const
	Return the DenseMatrix data (host pointer) ownership flag. More...

double &	operator() (int i, int j)
	Returns reference to a_{ij}. More...

const double &	operator() (int i, int j) const
	Returns constant reference to a_{ij}. More...

double	operator* (const DenseMatrix &m) const
	Matrix inner product: tr(A^t B) More...

double	Trace () const
	Trace of a square matrix. More...

virtual double &	Elem (int i, int j)
	Returns reference to a_{ij}. More...

virtual const double &	Elem (int i, int j) const
	Returns constant reference to a_{ij}. More...

void	Mult (const double x, double y) const
	Matrix vector multiplication. More...

virtual void	Mult (const Vector &x, Vector &y) const
	Matrix vector multiplication. More...

void	MultTranspose (const double x, double y) const
	Multiply a vector with the transpose matrix. More...

virtual void	MultTranspose (const Vector &x, Vector &y) const
	Multiply a vector with the transpose matrix. More...

void	AddMult (const Vector &x, Vector &y) const
	y += A.x More...

void	AddMultTranspose (const Vector &x, Vector &y) const
	y += A^t x More...

void	AddMult_a (double a, const Vector &x, Vector &y) const
	y += a * A.x More...

void	AddMultTranspose_a (double a, const Vector &x, Vector &y) const
	y += a * A^t x More...

double	InnerProduct (const double x, const double y) const
	Compute y^t A x. More...

void	LeftScaling (const Vector &s)
	LeftScaling this = diag(s) * this. More...

void	InvLeftScaling (const Vector &s)
	InvLeftScaling this = diag(1./s) * this. More...

void	RightScaling (const Vector &s)
	RightScaling: this = this * diag(s);. More...

void	InvRightScaling (const Vector &s)
	InvRightScaling: this = this * diag(1./s);. More...

void	SymmetricScaling (const Vector &s)
	SymmetricScaling this = diag(sqrt(s)) * this * diag(sqrt(s)) More...

void	InvSymmetricScaling (const Vector &s)
	InvSymmetricScaling this = diag(sqrt(1./s)) * this * diag(sqrt(1./s)) More...

double	InnerProduct (const Vector &x, const Vector &y) const
	Compute y^t A x. More...

virtual MatrixInverse *	Inverse () const
	Returns a pointer to the inverse matrix. More...

void	Invert ()
	Replaces the current matrix with its inverse. More...

void	SquareRootInverse ()
	Replaces the current matrix with its square root inverse. More...

double	Det () const

double	Weight () const

void	Set (double alpha, const double *A)
	Set the matrix to alpha * A, assuming that A has the same dimensions as the matrix and uses column-major layout. More...

void	Set (double alpha, const DenseMatrix &A)
	Set the matrix to alpha * A. More...

void	Add (const double c, const DenseMatrix &A)
	Adds the matrix A multiplied by the number c to the matrix. More...

void	Add (const double c, const double *A)

DenseMatrix &	operator= (double c)
	Sets the matrix elements equal to constant c. More...

DenseMatrix &	operator= (const double *d)
	Copy the matrix entries from the given array. More...

DenseMatrix &	operator= (const DenseMatrix &m)
	Sets the matrix size and elements equal to those of m. More...

DenseMatrix &	operator+= (const double *m)

DenseMatrix &	operator+= (const DenseMatrix &m)

DenseMatrix &	operator-= (const DenseMatrix &m)

DenseMatrix &	operator*= (double c)

void	Neg ()
	(this) = -(this) More...

void	Norm2 (double *v) const
	Take the 2-norm of the columns of A and store in v. More...

double	MaxMaxNorm () const
	Compute the norm \|\|A\|\| = max_{ij} \|A_{ij}\|. More...

double	FNorm () const
	Compute the Frobenius norm of the matrix. More...

double	FNorm2 () const
	Compute the square of the Frobenius norm of the matrix. More...

void	Eigenvalues (Vector &ev)
	Compute eigenvalues of A x = ev x where A = *this. More...

void	Eigenvalues (Vector &ev, DenseMatrix &evect)
	Compute eigenvalues and eigenvectors of A x = ev x where A = *this. More...

void	Eigensystem (Vector &ev, DenseMatrix &evect)
	Compute eigenvalues and eigenvectors of A x = ev x where A = *this. More...

void	Eigenvalues (DenseMatrix &b, Vector &ev)

void	Eigenvalues (DenseMatrix &b, Vector &ev, DenseMatrix &evect)
	Compute generalized eigenvalues of A x = ev B x, where A = *this. More...

void	Eigensystem (DenseMatrix &b, Vector &ev, DenseMatrix &evect)

void	SingularValues (Vector &sv) const

int	Rank (double tol) const

double	CalcSingularvalue (const int i) const
	Return the i-th singular value (decreasing order) of NxN matrix, N=1,2,3. More...

void	CalcEigenvalues (double lambda, double vec) const

void	GetRow (int r, Vector &row) const

void	GetColumn (int c, Vector &col) const

double *	GetColumn (int col)

const double *	GetColumn (int col) const

void	GetColumnReference (int c, Vector &col)

void	SetRow (int r, const double *row)

void	SetRow (int r, const Vector &row)

void	SetCol (int c, const double *col)

void	SetCol (int c, const Vector &col)

void	SetRow (int row, double value)
	Set all entries of a row to the specified value. More...

void	SetCol (int col, double value)
	Set all entries of a column to the specified value. More...

void	GetDiag (Vector &d) const
	Returns the diagonal of the matrix. More...

void	Getl1Diag (Vector &l) const
	Returns the l1 norm of the rows of the matrix v_i = sum_j \|a_ij\|. More...

void	GetRowSums (Vector &l) const
	Compute the row sums of the DenseMatrix. More...

void	Diag (double c, int n)
	Creates n x n diagonal matrix with diagonal elements c. More...

void	Diag (double *diag, int n)
	Creates n x n diagonal matrix with diagonal given by diag. More...

void	Transpose ()
	(this) = (this)^t More...

void	Transpose (const DenseMatrix &A)
	(*this) = A^t More...

void	Symmetrize ()
	(this) = 1/2 ((this) + (*this)^t) More...

void	Lump ()

void	GradToCurl (DenseMatrix &curl)

void	GradToVectorCurl2D (DenseMatrix &curl)

void	GradToDiv (Vector &div)

void	CopyRows (const DenseMatrix &A, int row1, int row2)
	Copy rows row1 through row2 from A to *this. More...

void	CopyCols (const DenseMatrix &A, int col1, int col2)
	Copy columns col1 through col2 from A to *this. More...

void	CopyMN (const DenseMatrix &A, int m, int n, int Aro, int Aco)
	Copy the m x n submatrix of A at row/col offsets Aro/Aco to *this. More...

void	CopyMN (const DenseMatrix &A, int row_offset, int col_offset)
	Copy matrix A to the location in *this at row_offset, col_offset. More...

void	CopyMNt (const DenseMatrix &A, int row_offset, int col_offset)
	Copy matrix A^t to the location in *this at row_offset, col_offset. More...

void	CopyMN (const DenseMatrix &A, int m, int n, int Aro, int Aco, int row_offset, int 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. More...

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. More...

void	CopyExceptMN (const DenseMatrix &A, int m, int n)
	Copy All rows and columns except m and n from A. More...

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. More...

void	AddMatrix (double a, const DenseMatrix &A, int ro, int co)
	Perform (ro+i,co+j)+=a*A(i,j) for 0<=i<A.Height, 0<=j<A.Width. More...

void	GetSubMatrix (const Array< int > &idx, DenseMatrix &A) const

void	GetSubMatrix (const Array< int > &idx_i, const Array< int > &idx_j, DenseMatrix &A) const

void	GetSubMatrix (int ibeg, int iend, DenseMatrix &A)

void	GetSubMatrix (int ibeg, int iend, int jbeg, int jend, DenseMatrix &A)

void	SetSubMatrix (const Array< int > &idx, const DenseMatrix &A)
	Set (*this)(idx[i],idx[j]) = A(i,j) More...

void	SetSubMatrix (const Array< int > &idx_i, const Array< int > &idx_j, const DenseMatrix &A)
	Set (*this)(idx_i[i],idx_j[j]) = A(i,j) More...

void	SetSubMatrix (int ibeg, const DenseMatrix &A)

void	SetSubMatrix (int ibeg, int jbeg, const DenseMatrix &A)

void	AddSubMatrix (const Array< int > &idx, const DenseMatrix &A)
	(*this)(idx[i],idx[j]) += A(i,j) More...

void	AddSubMatrix (const Array< int > &idx_i, const Array< int > &idx_j, const DenseMatrix &A)
	(*this)(idx_i[i],idx_j[j]) += A(i,j) More...

void	AddSubMatrix (int ibeg, const DenseMatrix &A)

void	AddSubMatrix (int ibeg, int jbeg, const DenseMatrix &A)

void	AddToVector (int offset, Vector &v) const
	Add the matrix 'data' to the Vector 'v' at the given 'offset'. More...

void	GetFromVector (int offset, const Vector &v)
	Get the matrix 'data' from the Vector 'v' at the given 'offset'. More...

void	AdjustDofDirection (Array< int > &dofs)

void	Threshold (double eps)
	Replace small entries, abs(a_ij) <= eps, with zero. More...

int	CheckFinite () const

virtual void	Print (std::ostream &out=mfem::out, int width_=4) const
	Prints matrix to stream out. More...

virtual void	PrintMatlab (std::ostream &out=mfem::out) const
	Prints operator in Matlab format. More...

virtual void	PrintT (std::ostream &out=mfem::out, int width_=4) const
	Prints the transpose matrix to stream out. More...

void	TestInversion ()
	Invert and print the numerical conditioning of the inversion. More...

std::size_t	MemoryUsage () const

const double *	Read (bool on_dev=true) const
	Shortcut for mfem::Read( GetMemory(), TotalSize(), on_dev). More...

const double *	HostRead () const
	Shortcut for mfem::Read(GetMemory(), TotalSize(), false). More...

double *	Write (bool on_dev=true)
	Shortcut for mfem::Write(GetMemory(), TotalSize(), on_dev). More...

double *	HostWrite ()
	Shortcut for mfem::Write(GetMemory(), TotalSize(), false). More...

double *	ReadWrite (bool on_dev=true)
	Shortcut for mfem::ReadWrite(GetMemory(), TotalSize(), on_dev). More...

double *	HostReadWrite ()
	Shortcut for mfem::ReadWrite(GetMemory(), TotalSize(), false). More...

void	Swap (DenseMatrix &other)

virtual	~DenseMatrix ()
	Destroys dense matrix. More...

Public Member Functions inherited from mfem::Matrix
	Matrix (int s)
	Creates a square matrix of size s. More...

	Matrix (int h, int w)
	Creates a matrix of the given height and width. More...

bool	IsSquare () const
	Returns whether the matrix is a square matrix. More...

virtual void	Finalize (int)
	Finalizes the matrix initialization. More...

virtual	~Matrix ()
	Destroys matrix. More...

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. More...

	Operator (int s=0)
	Construct a square Operator with given size s (default 0). More...

	Operator (int h, int w)
	Construct an Operator with the given height (output size) and width (input size). More...

int	Height () const
	Get the height (size of output) of the Operator. Synonym with NumRows(). More...

int	NumRows () const
	Get the number of rows (size of output) of the Operator. Synonym with Height(). More...

int	Width () const
	Get the width (size of input) of the Operator. Synonym with NumCols(). More...

int	NumCols () const
	Get the number of columns (size of input) of the Operator. Synonym with Width(). More...

virtual MemoryClass	GetMemoryClass () const
	Return the MemoryClass preferred by the Operator. More...

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. More...

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. More...

virtual const Operator *	GetProlongation () const
	Prolongation operator from linear algebra (linear system) vectors, to input vectors for the operator. `NULL` means identity. More...

virtual const Operator *	GetRestriction () const
	Restriction operator from input vectors for the operator to linear algebra (linear system) vectors. `NULL` means identity. More...

virtual const Operator *	GetOutputProlongation () const
	Prolongation operator from linear algebra (linear system) vectors, to output vectors for the operator. `NULL` means identity. More...

virtual const Operator *	GetOutputRestrictionTranspose () const
	Transpose of GetOutputRestriction, directly available in this form to facilitate matrix-free RAP-type operators. More...

virtual const Operator *	GetOutputRestriction () const
	Restriction operator from output vectors for the operator to linear algebra (linear system) vectors. `NULL` means identity. More...

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. More...

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. More...

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(). More...

void	FormSystemOperator (const Array< int > &ess_tdof_list, Operator *&A)
	Return in A a parallel (on truedofs) version of this square operator. More...

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). More...

void	FormDiscreteOperator (Operator *&A)
	Return in A a parallel (on truedofs) version of this rectangular operator. More...

void	PrintMatlab (std::ostream &out, int n, int m=0) const
	Prints operator with input size n and output size m in Matlab format. More...

virtual	~Operator ()
	Virtual destructor. More...

Type	GetType () const
	Return the type ID of the Operator class. More...

Friends
class	DenseTensor

class	DenseMatrixInverse

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() More...

void	FormRectangularConstrainedSystemOperator (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, RectangularConstrainedOperator *&Aout)
	see FormRectangularSystemOperator() More...

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". More...

Protected Attributes inherited from mfem::Operator
int	height
	Dimension of the output / number of rows in the matrix. More...

int	width
	Dimension of the input / number of columns in the matrix. More...

Detailed Description

Data type dense matrix using column-major storage.

Definition at line 23 of file densemat.hpp.

Constructor & Destructor Documentation

mfem::DenseMatrix::DenseMatrix ( )

Default constructor for DenseMatrix. Sets data = NULL and height = width = 0.

Definition at line 90 of file densemat.cpp.

mfem::DenseMatrix::DenseMatrix ( const DenseMatrix & m )

Copy constructor.

Definition at line 92 of file densemat.cpp.

mfem::DenseMatrix::DenseMatrix ( int s )

explicit

Creates square matrix of size s.

Definition at line 103 of file densemat.cpp.

mfem::DenseMatrix::DenseMatrix	(	int	m,
		int	n
	)

Creates rectangular matrix of size m x n.

Definition at line 113 of file densemat.cpp.

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

Creates rectangular matrix equal to the transpose of mat.

Definition at line 125 of file densemat.cpp.

mfem::DenseMatrix::DenseMatrix	(	double *	d,
		int	h,
		int	w
	)

inline

Construct a DenseMatrix using an existing data array.

The DenseMatrix does not assume ownership of the data array, i.e. it will not delete the array.

Definition at line 58 of file densemat.hpp.

template<int M, int N>

mfem::DenseMatrix::DenseMatrix ( const double(&) values[M][N] )

inlineexplicit

Create a dense matrix using a braced initializer list The inner lists correspond to rows of the matrix

Definition at line 64 of file densemat.hpp.

mfem::DenseMatrix::~DenseMatrix ( )

virtual

Destroys dense matrix.

Definition at line 2275 of file densemat.cpp.

Member Function Documentation

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

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

Definition at line 542 of file densemat.cpp.

void mfem::DenseMatrix::Add	(	const double	c,
		const double *	A
	)

Adds the matrix A multiplied by the number c to the matrix, assuming A has the same dimensions and uses column-major layout.

Definition at line 553 of file densemat.cpp.

void mfem::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 1684 of file densemat.cpp.

void mfem::DenseMatrix::AddMatrix	(	double	a,
		const 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 1714 of file densemat.cpp.

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

y += A.x

Definition at line 224 of file densemat.cpp.

void mfem::DenseMatrix::AddMult_a	(	double	a,
		const Vector &	x,
		Vector &	y
	)		const

y += a * A.x

Definition at line 260 of file densemat.cpp.

void mfem::DenseMatrix::AddMultTranspose	(	const Vector &	x,
		Vector &	y
	)		const

y += A^t x

Definition at line 242 of file densemat.cpp.

void mfem::DenseMatrix::AddMultTranspose_a	(	double	a,
		const Vector &	x,
		Vector &	y
	)		const

y += a * A^t x

Definition at line 278 of file densemat.cpp.

void mfem::DenseMatrix::AddSubMatrix	(	const Array< int > &	idx,
		const DenseMatrix &	A
	)

(*this)(idx[i],idx[j]) += A(i,j)

Definition at line 1961 of file densemat.cpp.

void mfem::DenseMatrix::AddSubMatrix	(	const Array< int > &	idx_i,
		const Array< int > &	idx_j,
		const DenseMatrix &	A
	)

(*this)(idx_i[i],idx_j[j]) += A(i,j)

Definition at line 1989 of file densemat.cpp.

void mfem::DenseMatrix::AddSubMatrix	(	int	ibeg,
		const DenseMatrix &	A
	)

Add the submatrix A to this with row and column offset ibeg

Definition at line 2020 of file densemat.cpp.

void mfem::DenseMatrix::AddSubMatrix	(	int	ibeg,
		int	jbeg,
		const DenseMatrix &	A
	)

Add the submatrix A to this with row and column offsets ibeg and jbeg respectively

Definition at line 2046 of file densemat.cpp.

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

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

Definition at line 2074 of file densemat.cpp.

void mfem::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 2096 of file densemat.cpp.

void mfem::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 1254 of file densemat.cpp.

double mfem::DenseMatrix::CalcSingularvalue ( const int i ) const

Return the i-th singular value (decreasing order) of NxN matrix, N=1,2,3.

Definition at line 1229 of file densemat.cpp.

int mfem::DenseMatrix::CheckFinite ( ) const

inline

Count the number of entries in the matrix for which isfinite is false, i.e. the entry is a NaN or +/-Inf.

Definition at line 429 of file densemat.hpp.

void mfem::DenseMatrix::Clear ( )

inline

Delete the matrix data array (if owned) and reset the matrix state.

Definition at line 98 of file densemat.hpp.

void mfem::DenseMatrix::ClearExternalData ( )

inline

Clear the data array and the dimensions of the DenseMatrix. This method should not be used with DenseMatrix that owns its current data array.

Definition at line 95 of file densemat.hpp.

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

Copy columns col1 through col2 from A to *this.

Definition at line 1540 of file densemat.cpp.

void mfem::DenseMatrix::CopyExceptMN	(	const DenseMatrix &	A,
		int	m,
		int	n
	)

Copy All rows and columns except m and n from A.

Definition at line 1658 of file densemat.cpp.

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

Copy the m x n submatrix of A at row/col offsets Aro/Aco to *this.

Definition at line 1553 of file densemat.cpp.

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

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

Definition at line 1566 of file densemat.cpp.

void mfem::DenseMatrix::CopyMN	(	const DenseMatrix &	A,
		int	m,
		int	n,
		int	Aro,
		int	Aco,
		int	row_offset,
		int	col_offset
	)

Copy the m x n submatrix of A at row/col offsets Aro/Aco to *this at row_offset, col_offset

Definition at line 1592 of file densemat.cpp.

void mfem::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 1623 of file densemat.cpp.

void mfem::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 1640 of file densemat.cpp.

void mfem::DenseMatrix::CopyMNt	(	const 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 1579 of file densemat.cpp.

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

Copy rows row1 through row2 from A to *this.

Definition at line 1527 of file densemat.cpp.

double* mfem::DenseMatrix::Data ( ) const

inline

Returns the matrix data array.

Definition at line 111 of file densemat.hpp.

double mfem::DenseMatrix::Det ( ) const

Calculates the determinant of the matrix (optimized for 2x2, 3x3, and 4x4 matrices)

Definition at line 449 of file densemat.cpp.

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

Creates n x n diagonal matrix with diagonal elements c.

Definition at line 1351 of file densemat.cpp.

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

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

Definition at line 1366 of file densemat.cpp.

void mfem::DenseMatrix::Eigensystem	(	Vector &	ev,
		DenseMatrix &	evect
	)

inline

Compute eigenvalues and eigenvectors of A x = ev x where A = *this.

Definition at line 257 of file densemat.hpp.

void mfem::DenseMatrix::Eigensystem	(	DenseMatrix &	b,
		Vector &	ev,
		DenseMatrix &	evect
	)

inline

Compute generalized eigenvalues and eigenvectors of A x = ev B x, where A = *this

Definition at line 271 of file densemat.hpp.

void mfem::DenseMatrix::Eigenvalues ( Vector & ev )

inline

Compute eigenvalues of A x = ev x where A = *this.

Definition at line 249 of file densemat.hpp.

void mfem::DenseMatrix::Eigenvalues	(	Vector &	ev,
		DenseMatrix &	evect
	)

inline

Compute eigenvalues and eigenvectors of A x = ev x where A = *this.

Definition at line 253 of file densemat.hpp.

void mfem::DenseMatrix::Eigenvalues	(	DenseMatrix &	b,
		Vector &	ev
	)

inline

Compute generalized eigenvalues and eigenvectors of A x = ev B x, where A = *this

Definition at line 262 of file densemat.hpp.

void mfem::DenseMatrix::Eigenvalues	(	DenseMatrix &	b,
		Vector &	ev,
		DenseMatrix &	evect
	)

inline

Compute generalized eigenvalues of A x = ev B x, where A = *this.

Definition at line 266 of file densemat.hpp.

double & mfem::DenseMatrix::Elem	(	int	i,
		int	j
	)

virtual

Returns reference to a_{ij}.

Implements mfem::Matrix.

Definition at line 163 of file densemat.cpp.

const double & mfem::DenseMatrix::Elem	(	int	i,
		int	j
	)		const

virtual

Returns constant reference to a_{ij}.

Implements mfem::Matrix.

Definition at line 168 of file densemat.cpp.

double mfem::DenseMatrix::FNorm ( ) const

inline

Compute the Frobenius norm of the matrix.

Definition at line 243 of file densemat.hpp.

double mfem::DenseMatrix::FNorm2 ( ) const

inline

Compute the square of the Frobenius norm of the matrix.

Definition at line 246 of file densemat.hpp.

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

Definition at line 1292 of file densemat.cpp.

double* mfem::DenseMatrix::GetColumn ( int col )

inline

Definition at line 286 of file densemat.hpp.

const double* mfem::DenseMatrix::GetColumn ( int col ) const

inline

Definition at line 287 of file densemat.hpp.

void mfem::DenseMatrix::GetColumnReference	(	int	c,
		Vector &	col
	)

inline

Definition at line 289 of file densemat.hpp.

double* mfem::DenseMatrix::GetData ( ) const

inline

Returns the matrix data array.

Definition at line 115 of file densemat.hpp.

void mfem::DenseMatrix::GetDiag ( Vector & d ) const

Returns the diagonal of the matrix.

Definition at line 1306 of file densemat.cpp.

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

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

Definition at line 2085 of file densemat.cpp.

void mfem::DenseMatrix::Getl1Diag ( Vector & l ) const

Returns the l1 norm of the rows of the matrix v_i = sum_j |a_ij|.

Definition at line 1320 of file densemat.cpp.

Memory<double>& mfem::DenseMatrix::GetMemory ( )

inline

Definition at line 117 of file densemat.hpp.

const Memory<double>& mfem::DenseMatrix::GetMemory ( ) const

inline

Definition at line 118 of file densemat.hpp.

void mfem::DenseMatrix::GetRow	(	int	r,
		Vector &	row
	)		const

Definition at line 1276 of file densemat.cpp.

void mfem::DenseMatrix::GetRowSums ( Vector & l ) const

Compute the row sums of the DenseMatrix.

Definition at line 1337 of file densemat.cpp.

void mfem::DenseMatrix::GetSubMatrix	(	const Array< int > &	idx,
		DenseMatrix &	A
	)		const

Get the square submatrix which corresponds to the given indices idx. Note: the A matrix will be resized to accommodate the data

Definition at line 1744 of file densemat.cpp.

void mfem::DenseMatrix::GetSubMatrix	(	const Array< int > &	idx_i,
		const Array< int > &	idx_j,
		DenseMatrix &	A
	)		const

Get the rectangular submatrix which corresponds to the given indices idx_i and idx_j. Note: the A matrix will be resized to accommodate the data

Definition at line 1765 of file densemat.cpp.

void mfem::DenseMatrix::GetSubMatrix	(	int	ibeg,
		int	iend,
		DenseMatrix &	A
	)

Get the square submatrix which corresponds to the range [ ibeg, iend ). Note: the A matrix will be resized to accommodate the data

Definition at line 1791 of file densemat.cpp.

void mfem::DenseMatrix::GetSubMatrix	(	int	ibeg,
		int	iend,
		int	jbeg,
		int	jend,
		DenseMatrix &	A
	)

Get the square submatrix which corresponds to the range i ∈ [ ibeg, iend ) and j ∈ [ jbeg, jend ) Note: the A matrix will be resized to accommodate the data

Definition at line 1815 of file densemat.cpp.

void mfem::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 D matrix, then curl is a D*N by D(D-1)/2 matrix. The size of curl must be set outside. The dimension D can be either 2 or 3. In 2D this computes the scalar-valued curl of a 2D vector field

Definition at line 1439 of file densemat.cpp.

void mfem::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 1512 of file densemat.cpp.

void mfem::DenseMatrix::GradToVectorCurl2D ( DenseMatrix & curl )

Given a DShape matrix (from a scalar FE), stored in *this, returns the CurlShape matrix. This computes the vector-valued curl of a scalar field. this is N by 2 matrix and curl is N by 2 matrix as well.

Definition at line 1498 of file densemat.cpp.

const double* mfem::DenseMatrix::HostRead ( ) const

inline

Shortcut for mfem::Read(GetMemory(), TotalSize(), false).

Definition at line 447 of file densemat.hpp.

double* mfem::DenseMatrix::HostReadWrite ( )

inline

Shortcut for mfem::ReadWrite(GetMemory(), TotalSize(), false).

Definition at line 463 of file densemat.hpp.

double* mfem::DenseMatrix::HostWrite ( )

inline

Shortcut for mfem::Write(GetMemory(), TotalSize(), false).

Definition at line 455 of file densemat.hpp.

double mfem::DenseMatrix::InnerProduct	(	const double *	x,
		const double *	y
	)		const

Compute y^t A x.

Definition at line 297 of file densemat.cpp.

double mfem::DenseMatrix::InnerProduct	(	const Vector &	x,
		const Vector &	y
	)		const

inline

Compute y^t A x.

Definition at line 182 of file densemat.hpp.

MatrixInverse * mfem::DenseMatrix::Inverse ( ) const

virtual

Returns a pointer to the inverse matrix.

Implements mfem::Matrix.

Definition at line 444 of file densemat.cpp.

void mfem::DenseMatrix::Invert ( )

Replaces the current matrix with its inverse.

Definition at line 640 of file densemat.cpp.

void mfem::DenseMatrix::InvLeftScaling ( const Vector & s )

InvLeftScaling this = diag(1./s) * this.

Definition at line 328 of file densemat.cpp.

void mfem::DenseMatrix::InvRightScaling ( const Vector & s )

InvRightScaling: this = this * diag(1./s);.

Definition at line 356 of file densemat.cpp.

void mfem::DenseMatrix::InvSymmetricScaling ( const Vector & s )

InvSymmetricScaling this = diag(sqrt(1./s)) * this * diag(sqrt(1./s))

Definition at line 398 of file densemat.cpp.

void mfem::DenseMatrix::LeftScaling ( const Vector & s )

LeftScaling this = diag(s) * this.

Definition at line 315 of file densemat.cpp.

void mfem::DenseMatrix::Lump ( )

Definition at line 1425 of file densemat.cpp.

double mfem::DenseMatrix::MaxMaxNorm ( ) const

Compute the norm ||A|| = max_{ij} |A_{ij}|.

Definition at line 808 of file densemat.cpp.

std::size_t mfem::DenseMatrix::MemoryUsage ( ) const

inline

Definition at line 440 of file densemat.hpp.

void mfem::DenseMatrix::Mult	(	const double *	x,
		double *	y
	)		const

Matrix vector multiplication.

Definition at line 173 of file densemat.cpp.

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

virtual

Matrix vector multiplication.

Implements mfem::Operator.

Definition at line 178 of file densemat.cpp.

void mfem::DenseMatrix::MultTranspose	(	const double *	x,
		double *	y
	)		const

Multiply a vector with the transpose matrix.

Definition at line 201 of file densemat.cpp.

void mfem::DenseMatrix::MultTranspose	(	const Vector &	x,
		Vector &	y
	)		const

virtual

Multiply a vector with the transpose matrix.

Reimplemented from mfem::Operator.

Definition at line 216 of file densemat.cpp.

void mfem::DenseMatrix::Neg ( )

(*this) = -(*this)

Definition at line 631 of file densemat.cpp.

void mfem::DenseMatrix::Norm2 ( double * v ) const

Take the 2-norm of the columns of A and store in v.

Definition at line 795 of file densemat.cpp.

double & mfem::DenseMatrix::operator()	(	int	i,
		int	j
	)

inline

Returns reference to a_{ij}.

Definition at line 1145 of file densemat.hpp.

const double & mfem::DenseMatrix::operator()	(	int	i,
		int	j
	)		const

inline

Returns constant reference to a_{ij}.

Definition at line 1151 of file densemat.hpp.

double mfem::DenseMatrix::operator* ( const DenseMatrix & m ) const

Matrix inner product: tr(A^t B)

Definition at line 186 of file densemat.cpp.

DenseMatrix & mfem::DenseMatrix::operator*= ( double c )

Definition at line 621 of file densemat.cpp.

DenseMatrix & mfem::DenseMatrix::operator+= ( const double * m )

Definition at line 595 of file densemat.cpp.

DenseMatrix & mfem::DenseMatrix::operator+= ( const DenseMatrix & m )

Definition at line 601 of file densemat.cpp.

DenseMatrix & mfem::DenseMatrix::operator-= ( const DenseMatrix & m )

Definition at line 608 of file densemat.cpp.

DenseMatrix & mfem::DenseMatrix::operator= ( double c )

Sets the matrix elements equal to constant c.

Definition at line 562 of file densemat.cpp.

DenseMatrix & mfem::DenseMatrix::operator= ( const double * d )

Copy the matrix entries from the given array.

Definition at line 572 of file densemat.cpp.

DenseMatrix & mfem::DenseMatrix::operator= ( const DenseMatrix & m )

Sets the matrix size and elements equal to those of m.

Definition at line 582 of file densemat.cpp.

bool mfem::DenseMatrix::OwnsData ( ) const

inline

Return the DenseMatrix data (host pointer) ownership flag.

Definition at line 121 of file densemat.hpp.

void mfem::DenseMatrix::Print	(	std::ostream &	out = `mfem::out`,
		int	width_ = `4`
	)		const

virtual

Prints matrix to stream out.

Reimplemented from mfem::Matrix.

Definition at line 2183 of file densemat.cpp.

void mfem::DenseMatrix::PrintMatlab ( std::ostream & out = mfem::out ) const

virtual

Prints operator in Matlab format.

Reimplemented from mfem::Operator.

Definition at line 2209 of file densemat.cpp.

void mfem::DenseMatrix::PrintT	(	std::ostream &	out = `mfem::out`,
		int	width_ = `4`
	)		const

virtual

Prints the transpose matrix to stream out.

Definition at line 2228 of file densemat.cpp.

int mfem::DenseMatrix::Rank ( double tol ) const

Definition at line 1214 of file densemat.cpp.

const double* mfem::DenseMatrix::Read ( bool on_dev = true ) const

inline

Shortcut for mfem::Read( GetMemory(), TotalSize(), on_dev).

Definition at line 443 of file densemat.hpp.

double* mfem::DenseMatrix::ReadWrite ( bool on_dev = true )

inline

Shortcut for mfem::ReadWrite(GetMemory(), TotalSize(), on_dev).

Definition at line 459 of file densemat.hpp.

void mfem::DenseMatrix::Reset	(	double *	d,
		int	h,
		int	w
	)

inline

Change the data array and the size of the DenseMatrix.

The DenseMatrix does not assume ownership of the data array, i.e. it will not delete the new array d. This method will delete the current data array, if owned.

Definition at line 90 of file densemat.hpp.

void mfem::DenseMatrix::RightScaling ( const Vector & s )

RightScaling: this = this * diag(s);.

Definition at line 341 of file densemat.cpp.

void mfem::DenseMatrix::Set	(	double	alpha,
		const double *	A
	)

Set the matrix to alpha * A, assuming that A has the same dimensions as the matrix and uses column-major layout.

Definition at line 533 of file densemat.cpp.

void mfem::DenseMatrix::Set	(	double	alpha,
		const DenseMatrix &	A
	)

inline

Set the matrix to alpha * A.

Definition at line 204 of file densemat.hpp.

void mfem::DenseMatrix::SetCol	(	int	c,
		const double *	col
	)

Definition at line 2154 of file densemat.cpp.

void mfem::DenseMatrix::SetCol	(	int	c,
		const Vector &	col
	)

Definition at line 2163 of file densemat.cpp.

void mfem::DenseMatrix::SetCol	(	int	col,
		double	value
	)

Set all entries of a column to the specified value.

Definition at line 2131 of file densemat.cpp.

void mfem::DenseMatrix::SetRow	(	int	r,
		const double *	row
	)

Definition at line 2139 of file densemat.cpp.

void mfem::DenseMatrix::SetRow	(	int	r,
		const Vector &	row
	)

Definition at line 2148 of file densemat.cpp.

void mfem::DenseMatrix::SetRow	(	int	row,
		double	value
	)

Set all entries of a row to the specified value.

Definition at line 2123 of file densemat.cpp.

void mfem::DenseMatrix::SetSize ( int s )

inline

Change the size of the DenseMatrix to s x s.

Definition at line 105 of file densemat.hpp.

void mfem::DenseMatrix::SetSize	(	int	h,
		int	w
	)

Change the size of the DenseMatrix to h x w.

Definition at line 144 of file densemat.cpp.

void mfem::DenseMatrix::SetSubMatrix	(	const Array< int > &	idx,
		const DenseMatrix &	A
	)

Set (*this)(idx[i],idx[j]) = A(i,j)

Definition at line 1848 of file densemat.cpp.

void mfem::DenseMatrix::SetSubMatrix	(	const Array< int > &	idx_i,
		const Array< int > &	idx_j,
		const DenseMatrix &	A
	)

Set (*this)(idx_i[i],idx_j[j]) = A(i,j)

Definition at line 1877 of file densemat.cpp.

void mfem::DenseMatrix::SetSubMatrix	(	int	ibeg,
		const DenseMatrix &	A
	)

Set a submatrix of (this) to the given matrix A with row and column offset ibeg

Definition at line 1907 of file densemat.cpp.

void mfem::DenseMatrix::SetSubMatrix	(	int	ibeg,
		int	jbeg,
		const DenseMatrix &	A
	)

Set a submatrix of (this) to the given matrix A with row and column offset ibeg and jbeg respectively

Definition at line 1933 of file densemat.cpp.

void mfem::DenseMatrix::SingularValues ( Vector & sv ) const

Definition at line 1174 of file densemat.cpp.

int mfem::DenseMatrix::Size ( ) const

inline

For backward compatibility define Size to be synonym of Width()

Definition at line 102 of file densemat.hpp.

void mfem::DenseMatrix::SquareRootInverse ( )

Replaces the current matrix with its square root inverse.

Definition at line 750 of file densemat.cpp.

void mfem::DenseMatrix::Swap ( DenseMatrix & other )

Definition at line 2268 of file densemat.cpp.

void mfem::DenseMatrix::SymmetricScaling ( const Vector & s )

SymmetricScaling this = diag(sqrt(s)) * this * diag(sqrt(s))

Definition at line 370 of file densemat.cpp.

void mfem::DenseMatrix::Symmetrize ( )

(*this) = 1/2 ((*this) + (*this)^t)

Definition at line 1414 of file densemat.cpp.

void mfem::DenseMatrix::TestInversion ( )

Invert and print the numerical conditioning of the inversion.

Definition at line 2254 of file densemat.cpp.

void mfem::DenseMatrix::Threshold ( double eps )

Replace small entries, abs(a_ij) <= eps, with zero.

Definition at line 2169 of file densemat.cpp.

double mfem::DenseMatrix::Trace ( ) const

Trace of a square matrix.

Definition at line 425 of file densemat.cpp.

void mfem::DenseMatrix::Transpose ( )

(*this) = (*this)^t

Definition at line 1381 of file densemat.cpp.

void mfem::DenseMatrix::Transpose ( const DenseMatrix & A )

(*this) = A^t

Definition at line 1403 of file densemat.cpp.

void mfem::DenseMatrix::UseExternalData	(	double *	d,
		int	h,
		int	w
	)

inline

Change the data array and the size of the DenseMatrix.

The DenseMatrix does not assume ownership of the data array, i.e. it will not delete the data array d. This method should not be used with DenseMatrix that owns its current data array.

Definition at line 80 of file densemat.hpp.

double mfem::DenseMatrix::Weight ( ) const

Definition at line 506 of file densemat.cpp.

double* mfem::DenseMatrix::Write ( bool on_dev = true )

inline

Shortcut for mfem::Write(GetMemory(), TotalSize(), on_dev).

Definition at line 451 of file densemat.hpp.

Friends And Related Function Documentation

friend class DenseMatrixInverse

friend

Definition at line 26 of file densemat.hpp.

friend class DenseTensor

friend

Definition at line 25 of file densemat.hpp.

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

linalg/densemat.hpp
linalg/densemat.cpp

Public Member Functions

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation