mfem::DenseMatrix Class Reference

Data type dense matrix. 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)
void	UseExternalData (double *d, int h, int w)
void	ClearExternalData ()
int	Size () const
	For backward compatibility define Size to be synonym of Width() More...
void	SetSize (int s)
	If the matrix is not a square matrix of size s then recreate it. More...
void	SetSize (int h, int w)
	If the matrix is not a matrix of size (h x w) then recreate it. More...
double *	Data () const
	Returns vector of the elements. 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...
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...
double	Det () const
	Calculates the determinant of the matrix (for 2x2 or 3x3 matrices) More...
double	Weight () const
void	Add (const double c, const DenseMatrix &A)
	Adds the matrix A multiplied by the number c to the matrix. More...
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+= (DenseMatrix &m)
DenseMatrix &	operator-= (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...
void	Eigenvalues (Vector &ev)
void	Eigenvalues (Vector &ev, DenseMatrix &evect)
void	Eigensystem (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	GetColumn (int c, Vector &col)
void	GetColumnReference (int c, Vector &col)
void	GetDiag (Vector &d)
	Returns the diagonal of the matrix. More...
void	Getl1Diag (Vector &l)
	Returns the l1 norm of the rows of the matrix v_i = sum_j |a_ij|. 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 (DenseMatrix &A)
	(*this) = A^t More...
void	Symmetrize ()
	(*this) = 1/2 ((*this) + (*this)^t) More...
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. More...
void	CopyCols (DenseMatrix &A, int col1, int col2)
	Copy columns col1 through col2 from A to *this. More...
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. More...
void	CopyMN (DenseMatrix &A, int row_offset, int col_offset)
	Copy matrix A to the location in *this at row_offset, col_offset. More...
void	CopyMNt (DenseMatrix &A, int row_offset, int col_offset)
	Copy matrix A^t to the location in *this at row_offset, col_offset. More...
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	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, 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	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	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...
int	CheckFinite () const
virtual void	Print (std::ostream &out=std::cout, int width_=4) const
	Prints matrix to stream out. More...
virtual void	PrintMatlab (std::ostream &out=std::cout) const
virtual void	PrintT (std::ostream &out=std::cout, int width_=4) const
	Prints the transpose matrix to stream out. More...
void	TestInversion ()
	Invert and print the numerical conditioning of the inversion. More...
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...
virtual void	Finalize (int)
	Finalizes the matrix initialization. More...
virtual	~Matrix ()
	Destroys matrix. More...
Public Member Functions inherited from mfem::Operator
	Operator (int s=0)
	Construct a square Operator with given size s (default 0) More...
	Operator (int h, int w)
int	Height () const
	Get the height (size of output) of the Operator. Synonym with NumRows. More...
int	NumRows () const
int	Width () const
	Get the width (size of input) of the Operator. Synonym with NumCols. More...
int	NumCols () const
virtual Operator &	GetGradient (const Vector &x) const
	Evaluate the gradient operator at the point x. More...
void	PrintMatlab (std::ostream &out, int n=0, int m=0)
	Prints operator with input size n and output size m in matlab format. More...
virtual	~Operator ()

Friends
class	DenseTensor
class	DenseMatrixInverse
void	Mult (const DenseMatrix &b, const DenseMatrix &c, DenseMatrix &a)
	Matrix matrix multiplication. A = B * C. More...

Additional Inherited Members
Protected Attributes inherited from mfem::Operator
int	height
int	width

Detailed Description

Data type dense matrix.

Definition at line 22 of file densemat.hpp.

Constructor & Destructor Documentation

mfem::DenseMatrix::DenseMatrix

(

)

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

Definition at line 32 of file densemat.cpp.

mfem::DenseMatrix::DenseMatrix

(

const DenseMatrix &

m

)

Copy constructor.

Definition at line 37 of file densemat.cpp.

mfem::DenseMatrix::DenseMatrix ( int  s )

explicit

Creates square matrix of size s.

Definition at line 45 of file densemat.cpp.

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

Creates rectangular matrix of size m x n.

Definition at line 54 of file densemat.cpp.

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

Creates rectangular matrix equal to the transpose of mat.

Definition at line 63 of file densemat.cpp.

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

inline

Definition at line 53 of file densemat.hpp.

mfem::DenseMatrix::~DenseMatrix ( )

virtual

Destroys dense matrix.

Definition at line 2422 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 375 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 2246 of file densemat.cpp.

void mfem::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 2272 of file densemat.cpp.

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

y += A.x

Definition at line 184 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 2298 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 2316 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 1739 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 1451 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 254 of file densemat.hpp.

void mfem::DenseMatrix::ClearExternalData ( )

inline

Definition at line 57 of file densemat.hpp.

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

Copy columns col1 through col2 from A to *this.

Definition at line 2179 of file densemat.cpp.

void mfem::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 2188 of file densemat.cpp.

void mfem::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 2199 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 2219 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 2232 of file densemat.cpp.

void mfem::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 2209 of file densemat.cpp.

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

Copy rows row1 through row2 from A to *this.

Definition at line 2170 of file densemat.cpp.

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

inline

Returns vector of the elements.

Definition at line 69 of file densemat.hpp.

double mfem::DenseMatrix::Det

(

)

const

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

Definition at line 321 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 2014 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 2025 of file densemat.cpp.

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

inline

Definition at line 171 of file densemat.hpp.

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

inline

Definition at line 165 of file densemat.hpp.

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

inline

Definition at line 168 of file densemat.hpp.

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

virtual

Returns reference to a_{ij}.

Implements mfem::Matrix.

Definition at line 110 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 115 of file densemat.cpp.

double mfem::DenseMatrix::FNorm

(

)

const

Compute the Frobenius norm of the matrix.

Definition at line 578 of file densemat.cpp.

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

Definition at line 1977 of file densemat.cpp.

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

inline

Definition at line 186 of file densemat.hpp.

void mfem::DenseMatrix::GetDiag

(

Vector &

d

)

Returns the diagonal of the matrix.

Definition at line 1991 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 2307 of file densemat.cpp.

void mfem::DenseMatrix::Getl1Diag

(

Vector &

l

)

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

Definition at line 2001 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.

Definition at line 2096 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 2153 of file densemat.cpp.

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

Compute y^t A x.

Definition at line 202 of file densemat.cpp.

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

inline

Compute y^t A x.

Definition at line 121 of file densemat.hpp.

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

virtual

Returns a pointer to the inverse matrix.

Implements mfem::Matrix.

Definition at line 316 of file densemat.cpp.

void mfem::DenseMatrix::Invert

(

)

Replaces the current matrix with its inverse.

Definition at line 465 of file densemat.cpp.

void mfem::DenseMatrix::InvLeftScaling

(

const Vector &

s

)

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

Definition at line 227 of file densemat.cpp.

void mfem::DenseMatrix::InvRightScaling

(

const Vector &

s

)

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

Definition at line 249 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 282 of file densemat.cpp.

void mfem::DenseMatrix::LeftScaling

(

const Vector &

s

)

LeftScaling this = diag(s) * this.

Definition at line 218 of file densemat.cpp.

void mfem::DenseMatrix::Lump

(

)

Definition at line 2082 of file densemat.cpp.

double mfem::DenseMatrix::MaxMaxNorm

(

)

const

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

Definition at line 562 of file densemat.cpp.

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

Matrix vector multiplication.

Definition at line 120 of file densemat.cpp.

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

virtual

Matrix vector multiplication.

Implements mfem::Operator.

Definition at line 136 of file densemat.cpp.

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

Multiply a vector with the transpose matrix.

Definition at line 161 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 174 of file densemat.cpp.

void mfem::DenseMatrix::Neg

(

)

(*this) = -(*this)

Definition at line 447 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 551 of file densemat.cpp.

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

inline

Returns reference to a_{ij}.

Definition at line 475 of file densemat.hpp.

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

inline

Returns constant reference to a_{ij}.

Definition at line 485 of file densemat.hpp.

double mfem::DenseMatrix::operator*

(

const DenseMatrix &

m

)

const

Matrix inner product: tr(A^t B)

Definition at line 146 of file densemat.cpp.

DenseMatrix & mfem::DenseMatrix::operator*=

(

double

c

)

Definition at line 438 of file densemat.cpp.

DenseMatrix & mfem::DenseMatrix::operator+=

(

DenseMatrix &

m

)

Definition at line 415 of file densemat.cpp.

DenseMatrix & mfem::DenseMatrix::operator-=

(

DenseMatrix &

m

)

Definition at line 427 of file densemat.cpp.

DenseMatrix & mfem::DenseMatrix::operator=

(

double

c

)

Sets the matrix elements equal to constant c.

Definition at line 382 of file densemat.cpp.

DenseMatrix & mfem::DenseMatrix::operator=

(

const double *

d

)

Copy the matrix entries from the given array.

Definition at line 391 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 402 of file densemat.cpp.

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

virtual

Prints matrix to stream out.

Reimplemented from mfem::Matrix.

Definition at line 2353 of file densemat.cpp.

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

virtual

Definition at line 2371 of file densemat.cpp.

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

virtual

Prints the transpose matrix to stream out.

Definition at line 2386 of file densemat.cpp.

int mfem::DenseMatrix::Rank

(

double

tol

)

const

Definition at line 868 of file densemat.cpp.

void mfem::DenseMatrix::RightScaling

(

const Vector &

s

)

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

Definition at line 236 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 2347 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 2341 of file densemat.cpp.

void mfem::DenseMatrix::SetSize

(

int

s

)

If the matrix is not a square matrix of size s then recreate it.

Definition at line 73 of file densemat.cpp.

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

If the matrix is not a matrix of size (h x w) then recreate it.

Definition at line 91 of file densemat.cpp.

void mfem::DenseMatrix::SingularValues

(

Vector &

sv

)

const

Definition at line 829 of file densemat.cpp.

int mfem::DenseMatrix::Size ( ) const

inline

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

Definition at line 60 of file densemat.hpp.

void mfem::DenseMatrix::SymmetricScaling

(

const Vector &

s

)

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

Definition at line 262 of file densemat.cpp.

void mfem::DenseMatrix::Symmetrize

(

)

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

Definition at line 2067 of file densemat.cpp.

void mfem::DenseMatrix::TestInversion

(

)

Invert and print the numerical conditioning of the inversion.

Definition at line 2404 of file densemat.cpp.

double mfem::DenseMatrix::Trace

(

)

const

Trace of a square matrix.

Definition at line 301 of file densemat.cpp.

void mfem::DenseMatrix::Transpose

(

)

(*this) = (*this)^t

Definition at line 2036 of file densemat.cpp.

void mfem::DenseMatrix::Transpose

(

DenseMatrix &

A

)

(*this) = A^t

Definition at line 2058 of file densemat.cpp.

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

inline

Definition at line 54 of file densemat.hpp.

double mfem::DenseMatrix::Weight

(

)

const

Definition at line 348 of file densemat.cpp.

Friends And Related Function Documentation

friend class DenseMatrixInverse

friend

Definition at line 29 of file densemat.hpp.

friend class DenseTensor

friend

Definition at line 24 of file densemat.hpp.

void Mult ( const DenseMatrix &  b, const DenseMatrix &  c, DenseMatrix &  a  )

friend

Matrix matrix multiplication. A = B * C.

Definition at line 2445 of file densemat.cpp.

---

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

• densemat.hpp
• densemat.cpp