To handle dense matrices. More...

Inheritance diagram for DMatrix< T_ >:

Public Member Functions
	DMatrix ()
	Default constructor. More...

	DMatrix (size_t nr)
	Constructor for a matrix with `nr` rows and `nr` columns. More...

	DMatrix (size_t nr, size_t nc)
	Constructor for a matrix with `nr` rows and `nc` columns. More...

	DMatrix (Vect< T_ > &v)
	Constructor that uses a Vect instance. The class uses the memory space occupied by this vector. More...

	DMatrix (const DMatrix< T_ > &m)
	Copy Constructor. More...

	DMatrix (Mesh &mesh, size_t dof=0, int is_diagonal=false)
	Constructor using mesh to initialize structure of matrix. More...

	~DMatrix ()
	Destructor.

void	setDiag ()
	Store diagonal entries in a separate internal vector.

void	setDiag (const T_ &a)
	Set matrix as diagonal and assign its diagonal entries as a constant. More...

void	setDiag (const vector< T_ > &d)
	Set matrix as diagonal and assign its diagonal entries. More...

void	setSize (size_t size)
	Set size (number of rows) of matrix. More...

void	setSize (size_t nr, size_t nc)
	Set size (number of rows and columns) of matrix. More...

void	getColumn (size_t j, Vect< T_ > &v) const
	Get `j`-th column vector. More...

Vect< T_ >	getColumn (size_t j) const
	Get `j`-th column vector. More...

void	getRow (size_t i, Vect< T_ > &v) const
	Get `i`-th row vector. More...

Vect< T_ >	getRow (size_t i) const
	Get `i`-th row vector. More...

void	set (size_t i, size_t j, const T_ &val)
	Assign a constant value to an entry of the matrix. More...

void	reset ()
	Set matrix to 0 and reset factorization parameter. More...

void	setRow (size_t i, const Vect< T_ > &v)
	Copy a given vector to a prescribed row in the matrix. More...

void	setColumn (size_t j, const Vect< T_ > &v)
	Copy a given vector to a prescribed column in the matrix. More...

void	MultAdd (T_ a, const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply matrix by vector `a*x` and add result to `y`. More...

void	MultAdd (const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply matrix by vector `x` and add result to `y`. More...

void	Mult (const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply matrix by vector `x` and save result in `y`. More...

void	TMult (const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply transpose of matrix by vector `x` and add result in `y`. More...

void	add (size_t i, size_t j, const T_ &val)
	Add constant `val` to entry `(i,j)` of the matrix. More...

void	Axpy (T_ a, const DMatrix< T_ > &m)
	Add to matrix the product of a matrix by a scalar. More...

void	Axpy (T_ a, const Matrix< T_ > *m)
	Add to matrix the product of a matrix by a scalar. More...

int	setQR ()
	Construct a QR factorization of the matrix. More...

int	setTransQR ()
	Construct a QR factorization of the transpose of the matrix. More...

int	solveQR (const Vect< T_ > &b, Vect< T_ > &x)
	Solve a linear system by QR decomposition. More...

int	solveTransQR (const Vect< T_ > &b, Vect< T_ > &x)
	Solve a transpose linear system by QR decomposition. More...

T_	at (size_t i, size_t j)
	Return a value of a matrix entry. More...

T_	operator() (size_t i, size_t j) const
	Operator () (Constant version). Return `a(i,j)` More...

T_ &	operator() (size_t i, size_t j)
	Operator () (Non constant version). Return `a(i,j)` More...

int	setLU ()
	Factorize the matrix (LU factorization) More...

int	setTransLU ()
	Factorize the transpose of the matrix (LU factorization) More...

int	solve (Vect< T_ > &b, bool fact=true)
	Solve linear system. More...

int	solveTrans (Vect< T_ > &b, bool fact=true)
	Solve the transpose linear system. More...

int	solve (const Vect< T_ > &b, Vect< T_ > &x, bool fact=true)
	Solve linear system. More...

int	solveTrans (const Vect< T_ > &b, Vect< T_ > &x, bool fact=true)
	Solve the transpose linear system. More...

DMatrix &	operator= (DMatrix< T_ > &m)
	Operator `=` More...

DMatrix &	operator+= (const DMatrix< T_ > &m)
	Operator +=. More...

DMatrix &	operator-= (const DMatrix< T_ > &m)
	Operator -=. More...

DMatrix &	operator= (const T_ &x)
	Operator `=` More...

DMatrix &	operator*= (const T_ &x)
	Operator `*=` More...

DMatrix &	operator+= (const T_ &x)
	Operator `+=` More...

DMatrix &	operator-= (const T_ &x)
	Operator `-=` More...

const T_ *	getArray ()
	Return matrix as C-Array. More...

T_	get (size_t i, size_t j) const
	Return entry `(i,j)` of matrix.

void	add (size_t i, const T_ &val)
	Add `val` to entry `i`.

Public Member Functions inherited from Matrix< T_ >
	Matrix ()
	Default constructor. More...

	Matrix (const Matrix< T_ > &m)
	Copy Constructor.

virtual	~Matrix ()
	Destructor.

size_t	getNbRows () const
	Return number of rows.

size_t	getNbColumns () const
	Return number of columns.

string	getName () const
	Return name of matrix.

MatrixSize	getMatrixSize () const
	Return storage type.

void	setPenal (real_t p)
	Set Penalty Parameter (For boundary condition prescription).

void	setDiagonal ()
	Set the matrix as diagonal.

T_	getDiag (size_t k) const
	Return `k`-th diagonal entry of matrix. More...

size_t	size () const
	Return matrix dimension (Number of rows and columns).

void	setDiagonal (Mesh &mesh)
	Initialize matrix storage in the case where only diagonal terms are stored. More...

virtual void	clear ()
	brief Set all matrix entries to zero

void	Assembly (const Element &el, T_ *a)
	Assembly of element matrix into global matrix. More...

void	Assembly (const Side &sd, T_ *a)
	Assembly of side matrix into global matrix. More...

void	Prescribe (Vect< T_ > &b, const Vect< T_ > &u, int flag=0)
	Impose by a penalty method an essential boundary condition, using the Mesh instance provided by the constructor. More...

void	Prescribe (int dof, int code, Vect< T_ > &b, const Vect< T_ > &u, int flag=0)
	Impose by a penalty method an essential boundary condition to a given degree of freedom for a given code. More...

void	Prescribe (Vect< T_ > &b, int flag=0)
	Impose by a penalty method a homegeneous (=0) essential boundary condition. More...

void	Prescribe (size_t dof, Vect< T_ > &b, const Vect< T_ > &u, int flag=0)
	Impose by a penalty method an essential boundary condition when only one DOF is treated. More...

void	PrescribeSide ()
	Impose by a penalty method an essential boundary condition when DOFs are supported by sides. More...

virtual int	Factor ()=0
	Factorize matrix. Available only if the storage class enables it.

int	FactorAndSolve (Vect< T_ > &b)
	Factorize matrix and solve the linear system. More...

int	FactorAndSolve (const Vect< T_ > &b, Vect< T_ > &x)
	Factorize matrix and solve the linear system. More...

size_t	getLength () const
	Return number of stored terms in matrix.

int	isDiagonal () const
	Say if matrix is diagonal or not.

int	isFactorized () const
	Say if matrix is factorized or not. More...

virtual size_t	getColInd (size_t i) const
	Return Column index for column `i` (See the description for class SpMatrix).

virtual size_t	getRowPtr (size_t i) const
	Return Row pointer for row `i` (See the description for class SpMatrix).

T_	operator() (size_t i) const
	Operator () with one argument (Constant version). More...

T_ &	operator() (size_t i)
	Operator () with one argument (Non Constant version). More...

T_ &	operator[] (size_t k)
	Operator [] (Non constant version). More...

T_	operator[] (size_t k) const
	Operator [] (Constant version). More...

Matrix &	operator= (Matrix< T_ > &m)
	Operator =. More...

Matrix &	operator+= (const Matrix< T_ > &m)
	Operator +=. More...

Matrix &	operator-= (const Matrix< T_ > &m)
	Operator -=. More...

Matrix &	operator= (const T_ &x)
	Operator =. More...

Matrix &	operator*= (const T_ &x)
	Operator *=. More...

Matrix &	operator+= (const T_ &x)
	Operator +=. More...

Matrix &	operator-= (const T_ &x)
	Operator -=. More...

Detailed Description

template<class T_>
class OFELI::DMatrix< T_ >

To handle dense matrices.

This class enables storing and manipulating general dense matrices. Matrices can be square or rectangle ones.

Template Parameters

T_	Data type (double, float, complex<double>, ...)

Author: Rachid Touzani

Copyright: GNU Lesser Public License

Constructor & Destructor Documentation

◆ DMatrix() [1/6]

DMatrix ( )

Default constructor.

Initializes a zero-dimension matrix.

◆ DMatrix() [2/6]

DMatrix ( size_t nr )

Constructor for a matrix with nr rows and nr columns.

Matrix entries are set to 0.

◆ DMatrix() [3/6]

DMatrix	(	size_t	nr,
		size_t	nc
	)

Constructor for a matrix with nr rows and nc columns.

Matrix entries are set to 0.

◆ DMatrix() [4/6]

DMatrix ( Vect< T_ > & v )

Constructor that uses a Vect instance. The class uses the memory space occupied by this vector.

Parameters

[in] v Vector to copy

◆ DMatrix() [5/6]

DMatrix ( const DMatrix< T_ > & m )

Copy Constructor.

Parameters

[in] m Matrix to copy

◆ DMatrix() [6/6]

DMatrix	(	Mesh &	mesh,
		size_t	dof = `0`,
		int	is_diagonal = `false`
	)

Constructor using mesh to initialize structure of matrix.

Parameters

[in]	mesh	Mesh instance for which matrix graph is determined.
[in]	dof	Option parameter, with default value `0`. `dof=1` means that only one degree of freedom for each node (or element or side) is taken to determine matrix structure. The value `dof=0` means that matrix structure is determined using all DOFs.
[in]	is_diagonal	Boolean argument to say is the matrix is actually a diagonal matrix or not.

Member Function Documentation

◆ add()

void add	(	size_t	i,
		size_t	j,
		const T_ &	val
	)

virtual

Add constant val to entry (i,j) of the matrix.

Parameters

[in]	i	row index
[in]	j	column index
[in]	val	Constant to add

Implements Matrix< T_ >.

◆ at()

T_ at	(	size_t	i,
		size_t	j
	)

virtual

Return a value of a matrix entry.

Parameters

[in]	i	Row index (starts at 1)
[in]	j	Column index (starts at 1)

Implements Matrix< T_ >.

◆ Axpy() [1/2]

void Axpy	(	T_	a,
		const DMatrix< T_ > &	m
	)

Add to matrix the product of a matrix by a scalar.

Parameters

[in]	a	Scalar to premultiply
[in]	m	Matrix by which `a` is multiplied. The result is added to current instance

◆ Axpy() [2/2]

void Axpy	(	T_	a,
		const Matrix< T_ > *	m
	)

virtual

Add to matrix the product of a matrix by a scalar.

Parameters

[in]	a	Scalar to premultiply
[in]	m	Matrix by which `a` is multiplied. The result is added to current instance

Implements Matrix< T_ >.

◆ getArray()

const T_* getArray ( )

Return matrix as C-Array.

Matrix is stored row by row.

◆ getColumn() [1/2]

void getColumn	(	size_t	j,
		Vect< T_ > &	v
	)		const

Get j-th column vector.

Parameters

[in]	j	Index of column to extract
[out]	v	Reference to Vect instance where the column is stored

Remarks: Vector v does not need to be sized before. It is resized in the function

◆ getColumn() [2/2]

Vect<T_> getColumn ( size_t j ) const

Get j-th column vector.

Parameters

[in] j Index of column to extract

Returns: Vect instance where the column is stored

Remarks: Vector v does not need to be sized before. It is resized in the function

◆ getRow() [1/2]

void getRow	(	size_t	i,
		Vect< T_ > &	v
	)		const

Get i-th row vector.

Parameters

[in]	i	Index of row to extract
[out]	v	Reference to Vect instance where the row is stored

Remarks: Vector v does not need to be sized before. It is resized in the function

◆ getRow() [2/2]

Vect<T_> getRow ( size_t i ) const

Get i-th row vector.

Parameters

[in] i Index of row to extract

Returns: Vect instance where the row is stored

Remarks: Vector v does not need to be sized before. It is resized in the function

◆ Mult()

void Mult	(	const Vect< T_ > &	x,
		Vect< T_ > &	y
	)		const

virtual

Multiply matrix by vector x and save result in y.

Parameters

[in]	x	Vector to add to `y`
[out]	y	Result.

Implements Matrix< T_ >.

◆ MultAdd() [1/2]

void MultAdd	(	T_	a,
		const Vect< T_ > &	x,
		Vect< T_ > &	y
	)		const

virtual

Multiply matrix by vector a*x and add result to y.

Parameters

[in]	a	constant to multiply by
[in]	x	Vector to multiply by `a`
[in,out]	y	on input, vector to add to. On output, result.

Implements Matrix< T_ >.

◆ MultAdd() [2/2]

void MultAdd	(	const Vect< T_ > &	x,
		Vect< T_ > &	y
	)		const

virtual

Multiply matrix by vector x and add result to y.

Parameters

[in]	x	Vector to add to `y`
[in,out]	y	on input, vector to add to. On output, result.

Implements Matrix< T_ >.

◆ operator()() [1/2]

T_ operator()	(	size_t	i,
		size_t	j
	)		const

virtual

Operator () (Constant version). Return a(i,j)

Parameters

[in]	i	row index
[in]	j	column index

Implements Matrix< T_ >.

◆ operator()() [2/2]

T_& operator()	(	size_t	i,
		size_t	j
	)

virtual

Operator () (Non constant version). Return a(i,j)

Parameters

[in]	i	row index
[in]	j	column index

Implements Matrix< T_ >.

◆ operator*=()

DMatrix& operator*= ( const T_ & x )

Operator *=

Premultiply matrix entries by constant value x.

◆ operator+=() [1/2]

DMatrix& operator+= ( const DMatrix< T_ > & m )

Operator +=.

Add matrix m to current matrix instance.

◆ operator+=() [2/2]

DMatrix& operator+= ( const T_ & x )

Operator +=

Add constant value x to matrix entries

◆ operator-=() [1/2]

DMatrix& operator-= ( const DMatrix< T_ > & m )

Operator -=.

Subtract matrix m from current matrix instance.

◆ operator-=() [2/2]

DMatrix& operator-= ( const T_ & x )

Operator -=

Subtract constant value x from matrix entries.

◆ operator=() [1/2]

DMatrix& operator= ( DMatrix< T_ > & m )

Operator =

Copy matrix m to current matrix instance.

◆ operator=() [2/2]

DMatrix& operator= ( const T_ & x )

Operator =

Assign matrix to identity times x

◆ reset()

void reset ( )

virtual

Set matrix to 0 and reset factorization parameter.

Warning: This function must be used if after a factorization, the matrix has modified

Reimplemented from Matrix< T_ >.

◆ set()

void set	(	size_t	i,
		size_t	j,
		const T_ &	val
	)

virtual

Assign a constant value to an entry of the matrix.

Parameters

[in]	i	row index of matrix
[in]	j	column index of matrix
[in]	val	Value to assign to `a(i,j)`.

Implements Matrix< T_ >.

◆ setColumn()

void setColumn	(	size_t	j,
		const Vect< T_ > &	v
	)

Copy a given vector to a prescribed column in the matrix.

Parameters

[in]	j	column index to be assigned
[in]	v	Vect instance to copy

◆ setDiag() [1/2]

void setDiag ( const T_ & a )

Set matrix as diagonal and assign its diagonal entries as a constant.

Parameters

[in] a Value to assign to all diagonal entries

◆ setDiag() [2/2]

void setDiag ( const vector< T_ > & d )

Set matrix as diagonal and assign its diagonal entries.

Parameters

[in] d Vector entries to assign to matrix diagonal entries

◆ setLU()

int setLU ( )

Factorize the matrix (LU factorization)

LU factorization of the matrix is realized. Note that since this is an in place factorization, the contents of the matrix are modified.

Returns

0 if factorization was normally performed,
n if the n-th pivot is null.

Remarks: A flag in this class indicates after factorization that this one has been realized, so that, if the member function solve is called after this no further factorization is done.

◆ setQR()

int setQR ( )

Construct a QR factorization of the matrix.

This function constructs the QR decomposition using the Householder method. The upper triangular matrix R is returned in the upper triangle of the current matrix, except for the diagonal elements of R which are stored in an internal vector. The orthogonal matrix Q is represented as a product of n-1 Householder matrices Q1 . . . Qn-1, where Qj = 1 - uj.uj /cj . The i-th component of uj is zero for i = 1, ..., j-1 while the nonzero components are returned in a[i][j] for i = j, ..., n.

Returns: 0 if the decomposition was successful, k is the k-th row is singular

Remarks: The matrix can be square or rectangle

◆ setRow()

void setRow	(	size_t	i,
		const Vect< T_ > &	v
	)

Copy a given vector to a prescribed row in the matrix.

Parameters

[in]	i	row index to be assigned
[in]	v	Vect instance to copy

◆ setSize() [1/2]

void setSize ( size_t size )

Set size (number of rows) of matrix.

Parameters

[in] size Number of rows and columns.

◆ setSize() [2/2]

void setSize	(	size_t	nr,
		size_t	nc
	)

Set size (number of rows and columns) of matrix.

Parameters

[in]	nr	Number of rows.
[in]	nc	Number of columns.

◆ setTransLU()

int setTransLU ( )

Factorize the transpose of the matrix (LU factorization)

LU factorization of the transpose of the matrix is realized. Note that since this is an in place factorization, the contents of the matrix are modified.

Returns

0 if factorization was normally performed,
n if the n-th pivot is null.

Remarks: A flag in this class indicates after factorization that this one has been realized, so that, if the member function solve is called after this no further factorization is done.

◆ setTransQR()

int setTransQR ( )

Construct a QR factorization of the transpose of the matrix.

This function constructs the QR decomposition using the Householder method. The upper triangular matrix R is returned in the upper triangle of the current matrix, except for the diagonal elements of R which are stored in an internal vector. The orthogonal matrix Q is represented as a product of n-1 Householder matrices Q1 . . . Qn-1, where Qj = 1 - uj.uj /cj . The i-th component of uj is zero for i = 1, ..., j-1 while the nonzero components are returned in a[i][j] for i = j, ..., n.

Returns: 0 if the decomposition was successful, k is the k-th row is singular

Remarks: The matrix can be square or rectangle

◆ solve() [1/2]

int solve	(	Vect< T_ > &	b,
		bool	fact = `true`
	)

virtual

Solve linear system.

The linear system having the current instance as a matrix is solved by using the LU decomposition. Solution is thus realized after a factorization step and a forward/backward substitution step. The factorization step is realized only if this was not already done.
Note that this function modifies the matrix contents is a factorization is performed. Naturally, if the the matrix has been modified after using this function, the user has to refactorize it using the function setLU. This is because the class has no non-expensive way to detect if the matrix has been modified. The function setLU realizes the factorization step only.

Parameters

[in,out]	b	Vect instance that contains right-hand side on input and solution on output.
[in]	fact	Set true if matrix is to be factorized (Default value), false if not

Returns

0 if solution was normally performed,
n if the n-th pivot is null.

Implements Matrix< T_ >.

◆ solve() [2/2]

int solve	(	const Vect< T_ > &	b,
		Vect< T_ > &	x,
		bool	fact = `true`
	)

virtual

Solve linear system.

The linear system having the current instance as a matrix is solved by using the LU decomposition. Solution is thus realized after a factorization step and a forward/backward substitution step. The factorization step is realized only if this was not already done.
Note that this function modifies the matrix contents is a factorization is performed. Naturally, if the the matrix has been modified after using this function, the user has to refactorize it using the function setLU. This is because the class has no non-expensive way to detect if the matrix has been modified. The function setLU realizes the factorization step only.

Parameters

[in]	b	Vect instance that contains right-hand side.
[out]	x	Vect instance that contains solution
[in]	fact	Set true if matrix is to be factorized (Default value), false if not

Returns

0 if solution was normally performed,
n if the n-th pivot is null.

Implements Matrix< T_ >.

◆ solveQR()

int solveQR	(	const Vect< T_ > &	b,
		Vect< T_ > &	x
	)

Solve a linear system by QR decomposition.

This function constructs the QR decomposition, if this was not already done by using the member function QR and solves the linear system

Parameters

[in]	b	Right-hand side vector
[out]	x	Solution vector. Must have been sized before using this function.

Returns: The same value as returned by the function QR

◆ solveTrans() [1/2]

int solveTrans	(	Vect< T_ > &	b,
		bool	fact = `true`
	)

Solve the transpose linear system.

The linear system having the current instance as a transpose matrix is solved by using the LU decomposition. Solution is thus realized after a factorization step and a forward/backward substitution step. The factorization step is realized only if this was not already done.
Note that this function modifies the matrix contents is a factorization is performed. Naturally, if the the matrix has been modified after using this function, the user has to refactorize it using the function setLU. This is because the class has no non-expensive way to detect if the matrix has been modified. The function setLU realizes the factorization step only.

Parameters

[in,out]	b	Vect instance that contains right-hand side on input and solution on output.
[in]	fact	Set true if matrix is to be factorized (Default value), false if not

Returns

0 if solution was normally performed,
n if the n-th pivot is null.

◆ solveTrans() [2/2]

int solveTrans	(	const Vect< T_ > &	b,
		Vect< T_ > &	x,
		bool	fact = `true`
	)

Solve the transpose linear system.

The linear system having the current instance as a transpose matrix is solved by using the LU decomposition. Solution is thus realized after a factorization step and a forward/backward substitution step. The factorization step is realized only if this was not already done.
Note that this function modifies the matrix contents is a factorization is performed. Naturally, if the the matrix has been modified after using this function, the user has to refactorize it using the function setLU. This is because the class has no non-expensive way to detect if the matrix has been modified. The function setLU realizes the factorization step only.

Parameters

[in]	b	Vect instance that contains right-hand side.
[out]	x	Vect instance that contains solution
[in]	fact	Set true if matrix is to be factorized (Default value), false if not

Returns

0 if solution was normally performed,
n if the n-th pivot is null.

◆ solveTransQR()

int solveTransQR	(	const Vect< T_ > &	b,
		Vect< T_ > &	x
	)

Solve a transpose linear system by QR decomposition.

This function constructs the QR decomposition, if this was not already done by using the member function QR and solves the linear system

Parameters

[in]	b	Right-hand side vector
[out]	x	Solution vector. Must have been sized before using this function.

Returns: The same value as returned by the function QR

◆ TMult()

void TMult	(	const Vect< T_ > &	x,
		Vect< T_ > &	y
	)		const

virtual

Multiply transpose of matrix by vector x and add result in y.

Parameters

[in]	x	Vector to add to `y`
[in,out]	y	on input, vector to add to. On output, result.

Implements Matrix< T_ >.

Public Member Functions

Detailed Description

template<class T_> class OFELI::DMatrix< T_ >

Constructor & Destructor Documentation

◆ DMatrix() [1/6]

◆ DMatrix() [2/6]

◆ DMatrix() [3/6]

◆ DMatrix() [4/6]

◆ DMatrix() [5/6]

◆ DMatrix() [6/6]

Member Function Documentation

◆ add()

◆ at()

◆ Axpy() [1/2]

◆ Axpy() [2/2]

◆ getArray()

◆ getColumn() [1/2]

◆ getColumn() [2/2]

◆ getRow() [1/2]

◆ getRow() [2/2]

◆ Mult()

◆ MultAdd() [1/2]

◆ MultAdd() [2/2]

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*=()

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ reset()

◆ set()

◆ setColumn()

◆ setDiag() [1/2]

◆ setDiag() [2/2]

◆ setLU()

◆ setQR()

◆ setRow()

◆ setSize() [1/2]

◆ setSize() [2/2]

◆ setTransLU()

◆ setTransQR()

◆ solve() [1/2]

◆ solve() [2/2]

◆ solveQR()

◆ solveTrans() [1/2]

◆ solveTrans() [2/2]

◆ solveTransQR()

◆ TMult()

template<class T_>
class OFELI::DMatrix< T_ >