Vector and matrix classes. More...

Classes
class	BMatrix< T_ >
	To handle band matrices. More...

class	DMatrix< T_ >
	To handle dense matrices. More...

class	DSMatrix< T_ >
	To handle symmetric dense matrices. More...

class	LocalMatrix< T_, NR_, NC_ >
	Handles small size matrices like element matrices, with a priori known size. More...

class	LocalVect< T_, N_ >
	Handles small size vectors like element vectors. More...

class	SkMatrix< T_ >
	To handle square matrices in skyline storage format. More...

class	SkSMatrix< T_ >
	To handle symmetric matrices in skyline storage format. More...

class	SpMatrix< T_ >
	To handle matrices in sparse storage format. More...

class	TrMatrix< T_ >
	To handle tridiagonal matrices. More...

class	Vect< T_ >
	To handle general purpose vectors. More...

Functions
template<class T_ , size_t N_, class E_ >
void	element_assembly (const E_ &e, const LocalMatrix< T_, N_, N_ > &ae, Vect< T_ > &b)
	Assemble diagonal local vector into global vector. More...

template<class T_ , size_t N_, class E_ >
void	element_assembly (const E_ &e, const LocalMatrix< T_, N_, N_ > &ae, Matrix< T_ > *A)
	Assemble local matrix into global matrix. More...

template<class T_ , size_t N_, class E_ >
void	element_assembly (const E_ &e, const LocalMatrix< T_, N_, N_ > &ae, SkMatrix< T_ > &A)
	Assemble local matrix into global skyline matrix. More...

template<class T_ , size_t N_, class E_ >
void	element_assembly (const E_ &e, const LocalMatrix< T_, N_, N_ > &ae, SkSMatrix< T_ > &A)
	Assemble local matrix into global symmetric skyline matrix. More...

template<class T_ , size_t N_, class E_ >
void	element_assembly (const E_ &e, const LocalMatrix< T_, N_, N_ > &ae, SpMatrix< T_ > &A)
	Assemble local matrix into global sparse matrix. More...

template<class T_ , size_t N_>
void	side_assembly (const Element &e, const LocalMatrix< T_, N_, N_ > &ae, SkSMatrix< T_ > &A)
	Side assembly of local matrix into global matrix (as instance of class SkSMatrix). More...

template<class T_ , size_t N_>
void	side_assembly (const Element &e, const LocalMatrix< T_, N_, N_ > &ae, SkMatrix< T_ > &A)
	Side assembly of local matrix into global matrix (as instance of class SkMatrix). More...

template<class T_ , size_t N_>
void	side_assembly (const Element &e, const LocalVect< T_, N_ > &be, Vect< T_ > &b)
	Side assembly of local vector into global vector. More...

template<class T_ >
Vect< T_ >	operator* (const BMatrix< T_ > &A, const Vect< T_ > &b)
	Operator * (Multiply vector by matrix and return resulting vector. More...

template<class T_ >
BMatrix< T_ >	operator* (T_ a, const BMatrix< T_ > &A)
	Operator * (Premultiplication of matrix by constant) More...

template<class T_ >
ostream &	operator<< (ostream &s, const BMatrix< T_ > &a)
	Output matrix in output stream.

template<class T_ >
Vect< T_ >	operator* (const DMatrix< T_ > &A, const Vect< T_ > &b)
	Operator * (Multiply vector by matrix and return resulting vector. More...

template<class T_ >
ostream &	operator<< (ostream &s, const DMatrix< T_ > &a)
	Output matrix in output stream.

template<class T_ >
Vect< T_ >	operator* (const DSMatrix< T_ > &A, const Vect< T_ > &b)
	Operator * (Multiply vector by matrix and return resulting vector. More...

template<class T_ >
ostream &	operator<< (ostream &s, const DSMatrix< T_ > &a)
	Output matrix in output stream.

template<class T_ , size_t NR_, size_t NC_>
LocalMatrix< T_, NR_, NC_ >	operator* (T_ a, const LocalMatrix< T_, NR_, NC_ > &x)
	Operator * (Multiply matrix `x` by scalar `a`) More...

template<class T_ , size_t NR_, size_t NC_>
LocalVect< T_, NR_ >	operator* (const LocalMatrix< T_, NR_, NC_ > &A, const LocalVect< T_, NC_ > &x)
	Operator `*` (Multiply matrix `A` by vector `x`) More...

template<class T_ , size_t NR_, size_t NC_>
LocalMatrix< T_, NR_, NC_ >	operator/ (T_ a, const LocalMatrix< T_, NR_, NC_ > &x)
	Operator `/` (Divide matrix `x` by scalar `a`) More...

template<class T_ , size_t NR_, size_t NC_>
LocalMatrix< T_, NR_, NC_ >	operator+ (const LocalMatrix< T_, NR_, NC_ > &x, const LocalMatrix< T_, NR_, NC_ > &y)
	Operator `+` (Add matrix x to y) More...

template<class T_ , size_t NR_, size_t NC_>
LocalMatrix< T_, NR_, NC_ >	operator- (const LocalMatrix< T_, NR_, NC_ > &x, const LocalMatrix< T_, NR_, NC_ > &y)
	Operator `-` (Subtract matrix y from x) More...

template<class T_ , size_t NR_, size_t NC_>
ostream &	operator<< (ostream &s, const LocalMatrix< T_, NR_, NC_ > &A)
	Output vector in output stream.

template<class T_ , size_t N_>
LocalVect< T_, N_ >	operator+ (const LocalVect< T_, N_ > &x, const LocalVect< T_, N_ > &y)
	Operator + (Add two vectors) More...

template<class T_ , size_t N_>
LocalVect< T_, N_ >	operator- (const LocalVect< T_, N_ > &x, const LocalVect< T_, N_ > &y)
	Operator - (Subtract two vectors) More...

template<class T_ , size_t N_>
LocalVect< T_, N_ >	operator* (T_ a, const LocalVect< T_, N_ > &x)
	Operator * (Premultiplication of vector by constant) More...

template<class T_ , size_t N_>
LocalVect< T_, N_ >	operator/ (T_ a, const LocalVect< T_, N_ > &x)
	Operator / (Division of vector by constant) More...

template<class T_ , size_t N_>
real_t	Dot (const LocalVect< T_, N_ > &a, const LocalVect< T_, N_ > &b)
	Calculate dot product of 2 vectors (instances of class LocalVect) More...

template<class T_ , size_t N_>
void	Scale (T_ a, const LocalVect< T_, N_ > &x, LocalVect< T_, N_ > &y)
	Multiply vector `x` by constant `a` and store result in `y`.

template<class T_ , size_t N_>
void	Scale (T_ a, LocalVect< T_, N_ > &x)
	Multiply vector `x` by constant `a` and store result in `x`.

template<class T_ , size_t N_>
void	Axpy (T_ a, const LocalVect< T_, N_ > &x, LocalVect< T_, N_ > &y)
	Add `a*x` to vector `y`.

template<class T_ , size_t N_>
void	Copy (const LocalVect< T_, N_ > &x, LocalVect< T_, N_ > &y)
	Copy vector x into vector y.

template<class T_ , size_t N_>
ostream &	operator<< (ostream &s, const LocalVect< T_, N_ > &v)
	Output vector in output stream.

template<class T_ >
Vect< T_ >	operator* (const SkMatrix< T_ > &A, const Vect< T_ > &b)
	Operator * (Multiply vector by matrix and return resulting vector. More...

template<class T_ >
ostream &	operator<< (ostream &s, const SkMatrix< T_ > &a)
	Output matrix in output stream. More...

template<class T_ >
Vect< T_ >	operator* (const SkSMatrix< T_ > &A, const Vect< T_ > &b)
	Operator * (Multiply vector by matrix and return resulting vector. More...

template<class T_ >
ostream &	operator<< (ostream &s, const SkSMatrix< T_ > &a)
	Output matrix in output stream. More...

template<class T_ >
Vect< T_ >	operator* (const SpMatrix< T_ > &A, const Vect< T_ > &b)
	Operator * (Multiply vector by matrix and return resulting vector. More...

template<class T_ >
ostream &	operator<< (ostream &s, const SpMatrix< T_ > &A)
	Output matrix in output stream. More...

template<class T_ >
Vect< T_ >	operator* (const TrMatrix< T_ > &A, const Vect< T_ > &b)
	Operator * (Multiply vector by matrix and return resulting vector. More...

template<class T_ >
TrMatrix< T_ >	operator* (T_ a, const TrMatrix< T_ > &A)
	Operator * (Premultiplication of matrix by constant) More...

template<class T_ >
ostream &	operator<< (ostream &s, const TrMatrix< T_ > &A)
	Output matrix in output stream. More...

template<class T_ >
Vect< T_ >	operator+ (const Vect< T_ > &x, const Vect< T_ > &y)
	Operator + (Addition of two instances of class Vect) More...

template<class T_ >
Vect< T_ >	operator- (const Vect< T_ > &x, const Vect< T_ > &y)
	Operator - (Difference between two vectors of class Vect) More...

template<class T_ >
Vect< T_ >	operator* (const T_ &a, const Vect< T_ > &x)
	Operator * (Premultiplication of vector by constant) More...

template<class T_ >
Vect< T_ >	operator* (const Vect< T_ > &x, const T_ &a)
	Operator * (Postmultiplication of vector by constant) More...

template<class T_ >
Vect< T_ >	operator/ (const Vect< T_ > &x, const T_ &a)
	Operator / (Divide vector entries by constant) More...

template<class T_ >
T_	Dot (const Vect< T_ > &x, const Vect< T_ > &y)
	Calculate dot product of two vectors. More...

void	Modulus (const Vect< complex_t > &x, Vect< real_t > &y)
	Calculate modulus of complex vector. More...

void	Real (const Vect< complex_t > &x, Vect< real_t > &y)
	Calculate real part of complex vector. More...

void	Imag (const Vect< complex_t > &x, Vect< real_t > &y)
	Calculate imaginary part of complex vector. More...

template<class T_ >
istream &	operator>> (istream &s, Vect< T_ > &v)

template<class T_ >
ostream &	operator<< (ostream &s, const Vect< T_ > &v)
	Output vector in output stream. More...

real_t	operator* (const vector< real_t > &x, const vector< real_t > &y)
	Operator * (Dot product of 2 vector instances) More...

Detailed Description

Vector and matrix classes.

Function Documentation

◆ Dot() [1/2]

double Dot	(	const LocalVect< T_, N_ > &	a,
		const LocalVect< T_, N_ > &	b
	)

Calculate dot product of 2 vectors (instances of class LocalVect)

Returns: Dot product

◆ Dot() [2/2]

T_ Dot	(	const Vect< T_ > &	x,
		const Vect< T_ > &	y
	)

Calculate dot product of two vectors.

Returns: Dot (inner or scalar) product Calculate dot (scalar) product of two vectors

◆ element_assembly() [1/5]

void element_assembly	(	const E_ &	e,
		const LocalMatrix< T_, N_, N_ > &	ae,
		Matrix< T_ > *	A
	)

Assemble local matrix into global matrix.

This function is to be called with an abstract pointer to matrix (class Matrix)

Parameters

[in]	e	Reference to local entity (Element or Side)
[in]	ae	Local matrix
[in,out]	A	Pointer to global matrix

Author: Rachid Touzani

Copyright: GNU Lesser Public License

◆ element_assembly() [2/5]

void element_assembly	(	const E_ &	e,
		const LocalMatrix< T_, N_, N_ > &	ae,
		SkMatrix< T_ > &	A
	)

Assemble local matrix into global skyline matrix.

Parameters

[in]	e	Reference to local entity (Element or Side)
[in]	ae	Local matrix
[in,out]	A	Global matrix

Author: Rachid Touzani

Copyright: GNU Lesser Public License

◆ element_assembly() [3/5]

void element_assembly	(	const E_ &	e,
		const LocalMatrix< T_, N_, N_ > &	ae,
		SkSMatrix< T_ > &	A
	)

Assemble local matrix into global symmetric skyline matrix.

Parameters

[in]	e	Reference to local entity (Element or Side)
[in]	ae	Local matrix
[in,out]	A	Global matrix

Author: Rachid Touzani

Copyright: GNU Lesser Public License

◆ element_assembly() [4/5]

void element_assembly	(	const E_ &	e,
		const LocalMatrix< T_, N_, N_ > &	ae,
		SpMatrix< T_ > &	A
	)

Assemble local matrix into global sparse matrix.

Parameters

[in]	e	Reference to local entity (Element or Side)
[in]	ae	Local matrix
[in,out]	A	Global matrix

Author: Rachid Touzani

Copyright: GNU Lesser Public License

◆ element_assembly() [5/5]

void element_assembly	(	const E_ &	e,
		const LocalMatrix< T_, N_, N_ > &	ae,
		Vect< T_ > &	b
	)

Assemble diagonal local vector into global vector.

Parameters

[in]	e	Reference to local entity (Element or Side)
[in]	ae	Local matrix
[in,out]	b	Global vector

Author: Rachid Touzani

Copyright: GNU Lesser Public License

◆ Imag()

void Imag	(	const Vect< complex_t > &	x,
		Vect< real_t > &	y
	)

Calculate imaginary part of complex vector.

Parameters

[in]	x	Vector with complex value entries
[out]	y	Vector containing imaginary parts of entries of `x`

◆ Modulus()

void Modulus	(	const Vect< complex_t > &	x,
		Vect< real_t > &	y
	)

Calculate modulus of complex vector.

Parameters

[in]	x	Vector with complex value entries
[out]	y	Vector containing moduli of entries of `x`

◆ operator*() [1/15]

Vect< T_ > operator*	(	const BMatrix< T_ > &	A,
		const Vect< T_ > &	b
	)

Operator * (Multiply vector by matrix and return resulting vector.

Parameters

[in]	A	BMatrix instance to multiply by vector
[in]	b	Vect instance

Returns: Vect instance containing A*b

◆ operator*() [2/15]

Vect< T_ > operator*	(	const DMatrix< T_ > &	A,
		const Vect< T_ > &	b
	)

Operator * (Multiply vector by matrix and return resulting vector.

Parameters

[in]	A	DMatrix instance to multiply by vector
[in]	b	Vect instance

Returns: Vect instance containing A*b

◆ operator*() [3/15]

Vect< T_ > operator*	(	const DSMatrix< T_ > &	A,
		const Vect< T_ > &	b
	)

Operator * (Multiply vector by matrix and return resulting vector.

Parameters

[in]	A	DSMatrix instance to multiply by vector
[in]	b	Vect instance

Returns: Vect instance containing A*b

◆ operator*() [4/15]

LocalVect< T_, NR_, NC_ > operator*	(	const LocalMatrix< T_, NR_, NC_ > &	x,
		const LocalVect< T_, NC_ > &	x
	)

Operator * (Multiply matrix A by vector x)

This function performs a matrix-vector product and returns resulting vector as a reference to LocalVect instance

Returns: A*x

◆ operator*() [5/15]

Vect< T_ > operator*	(	const SkMatrix< T_ > &	A,
		const Vect< T_ > &	b
	)

Operator * (Multiply vector by matrix and return resulting vector.

Parameters

[in]	A	SkMatrix instance to multiply by vector
[in]	b	Vect instance

Returns: Vect instance containing A*b

Author: Rachid Touzani

Copyright: GNU Lesser Public License

◆ operator*() [6/15]

Vect< T_ > operator*	(	const SkSMatrix< T_ > &	A,
		const Vect< T_ > &	b
	)

Operator * (Multiply vector by matrix and return resulting vector.

Parameters

[in]	A	SkSMatrix instance to multiply by vector
[in]	b	Vect instance

Returns: Vect instance containing A*b

Author: Rachid Touzani

Copyright: GNU Lesser Public License

◆ operator*() [7/15]

Vect< T_ > operator*	(	const SpMatrix< T_ > &	A,
		const Vect< T_ > &	b
	)

Operator * (Multiply vector by matrix and return resulting vector.

Parameters

[in]	A	SpMatrix instance to multiply by vector
[in]	b	Vect instance

Returns: Vect instance containing A*b

Author: Rachid Touzani

Copyright: GNU Lesser Public License

◆ operator*() [8/15]

Vect< T_ > operator*	(	const T_ &	a,
		const Vect< T_ > &	x
	)

Operator * (Premultiplication of vector by constant)

Returns: a*x

◆ operator*() [9/15]

Vect< T_ > operator*	(	const TrMatrix< T_ > &	A,
		const Vect< T_ > &	b
	)

Operator * (Multiply vector by matrix and return resulting vector.

Parameters

[in]	A	TrMatrix instance to multiply by vector
[in]	b	Vect instance

Returns: Vect instance containing A*b

Author: Rachid Touzani

Copyright: GNU Lesser Public License

◆ operator*() [10/15]

Vect< T_ > operator*	(	const Vect< T_ > &	x,
		const T_ &	a
	)

Operator * (Postmultiplication of vector by constant)

Returns: x*a

◆ operator*() [11/15]

real_t operator*	(	const vector< real_t > &	x,
		const vector< real_t > &	y
	)

Operator * (Dot product of 2 vector instances)

Returns: x.y

◆ operator*() [12/15]

BMatrix< T_ > operator*	(	T_	a,
		const BMatrix< T_ > &	A
	)

Operator * (Premultiplication of matrix by constant)

Returns: a*A

◆ operator*() [13/15]

LocalMatrix< T_, NR_, NC_ > operator*	(	T_	a,
		const LocalMatrix< T_, NR_, NC_ > &	x
	)

Operator * (Multiply matrix x by scalar a)

Returns: a*x

◆ operator*() [14/15]

LocalVect< T_, N_ > operator*	(	T_	a,
		const LocalVect< T_, N_ > &	x
	)

Operator * (Premultiplication of vector by constant)

Returns: a*x

◆ operator*() [15/15]

TrMatrix< T_ > operator*	(	T_	a,
		const TrMatrix< T_ > &	A
	)

Operator * (Premultiplication of matrix by constant)

Returns: a*A

Author: Rachid Touzani

Copyright: GNU Lesser Public License

◆ operator+() [1/3]

LocalMatrix< T_, NR_, NC_ > operator+	(	const LocalMatrix< T_, NR_, NC_ > &	x,
		const LocalMatrix< T_, NR_, NC_ > &	y
	)

Operator + (Add matrix x to y)

Returns: x+y

◆ operator+() [2/3]

LocalVect< T_, N_ > operator+	(	const LocalVect< T_, N_ > &	x,
		const LocalVect< T_, N_ > &	y
	)

Operator + (Add two vectors)

Returns: x+y

◆ operator+() [3/3]

Vect< T_ > operator+	(	const Vect< T_ > &	x,
		const Vect< T_ > &	y
	)

Operator + (Addition of two instances of class Vect)

Returns: x + y

◆ operator-() [1/3]

LocalMatrix< T_, NR_, NC_ > operator-	(	const LocalMatrix< T_, NR_, NC_ > &	x,
		const LocalMatrix< T_, NR_, NC_ > &	y
	)

Operator - (Subtract matrix y from x)

Returns: x-y

◆ operator-() [2/3]

LocalVect< T_, N_ > operator-	(	const LocalVect< T_, N_ > &	x,
		const LocalVect< T_, N_ > &	y
	)

Operator - (Subtract two vectors)

Returns: x-y

◆ operator-() [3/3]

Vect< T_ > operator-	(	const Vect< T_ > &	x,
		const Vect< T_ > &	y
	)

Operator - (Difference between two vectors of class Vect)

Returns: x - y

◆ operator/() [1/3]

Vect< T_ > operator/	(	const Vect< T_ > &	x,
		const T_ &	a
	)

Operator / (Divide vector entries by constant)

Returns: x/a

◆ operator/() [2/3]

LocalMatrix< T_, NR_, NC_ > operator/	(	T_	a,
		const LocalMatrix< T_, NR_, NC_ > &	x
	)

Operator / (Divide matrix x by scalar a)

Returns: x/a

◆ operator/() [3/3]

LocalVect< T_, N_ > operator/	(	T_	a,
		const LocalVect< T_, N_ > &	x
	)

Operator / (Division of vector by constant)

Returns: x/a

◆ operator<<() [1/5]

ostream & operator<<	(	ostream &	s,
		const SkMatrix< T_ > &	a
	)

Output matrix in output stream.

Author: Rachid Touzani

Copyright: GNU Lesser Public License

Author: Rachid Touzani

Copyright: GNU Lesser Public License

◆ operator<<() [2/5]

ostream & operator<<	(	ostream &	s,
		const SkSMatrix< T_ > &	a
	)

Output matrix in output stream.

Author: Rachid Touzani

Copyright: GNU Lesser Public License

◆ operator<<() [3/5]

ostream & operator<<	(	ostream &	s,
		const SpMatrix< T_ > &	A
	)

Output matrix in output stream.

Author: Rachid Touzani

Copyright: GNU Lesser Public License

◆ operator<<() [4/5]

ostream & operator<<	(	ostream &	s,
		const TrMatrix< T_ > &	a
	)

Output matrix in output stream.

Author: Rachid Touzani

Copyright: GNU Lesser Public License

◆ operator<<() [5/5]

ostream & operator<<	(	ostream &	s,
		const Vect< T_ > &	v
	)

Output vector in output stream.

Level of vector output depends on the global variable Verbosity

If Verbosity=0, this function outputs vector size only.
If Verbosity>0, this function outputs vector size, vector name, value of time, and number of components
If Verbosity>1, this function outputs in addition the first 10 entries in vector
If Verbosity>2, this function outputs in addition the first 50 entries in vector
If Verbosity>3, this function outputs in addition the first 100 entries in vector
If Verbosity>4, this function outputs all vector entries

Author: Rachid Touzani

Copyright: GNU Lesser Public License

◆ operator>>()

istream & operator>>	(	istream &	s,
		Vect< T_ > &	a
	)

Read vector from input stream

◆ Real()

void Real	(	const Vect< complex_t > &	x,
		Vect< real_t > &	y
	)

Calculate real part of complex vector.

Parameters

[in]	x	Vector with complex value entries
[out]	y	Vector containing real parts of entries of `x`

◆ side_assembly() [1/3]

void side_assembly	(	const Element &	e,
		const LocalMatrix< T_, N_, N_ > &	ae,
		SkMatrix< T_ > &	A
	)

Side assembly of local matrix into global matrix (as instance of class SkMatrix).

Parameters

[in]	e	Reference to local Element
[in]	ae	Local matrix
[in,out]	A	Global matrix

Author: Rachid Touzani

Copyright: GNU Lesser Public License

◆ side_assembly() [2/3]

void side_assembly	(	const Element &	e,
		const LocalMatrix< T_, N_, N_ > &	ae,
		SkSMatrix< T_ > &	A
	)

Side assembly of local matrix into global matrix (as instance of class SkSMatrix).

Parameters

[in]	e	Reference to local Element
[in]	ae	Local matrix
[in,out]	A	Global matrix

Author: Rachid Touzani

Copyright: GNU Lesser Public License

◆ side_assembly() [3/3]

void side_assembly	(	const Element &	e,
		const LocalVect< T_, N_ > &	be,
		Vect< T_ > &	b
	)

Side assembly of local vector into global vector.

Parameters

[in]	e	Reference to local Element
[in]	be	Local vector
[in,out]	b	Global vector

Author: Rachid Touzani

Copyright: GNU Lesser Public License

Classes

Functions

Detailed Description

Function Documentation

◆ Dot() [1/2]

◆ Dot() [2/2]

◆ element_assembly() [1/5]

◆ element_assembly() [2/5]

◆ element_assembly() [3/5]

◆ element_assembly() [4/5]

◆ element_assembly() [5/5]

◆ Imag()

◆ Modulus()

◆ operator*() [1/15]

◆ operator*() [2/15]

◆ operator*() [3/15]

◆ operator*() [4/15]

◆ operator*() [5/15]

◆ operator*() [6/15]

◆ operator*() [7/15]

◆ operator*() [8/15]

◆ operator*() [9/15]

◆ operator*() [10/15]

◆ operator*() [11/15]

◆ operator*() [12/15]

◆ operator*() [13/15]

◆ operator*() [14/15]

◆ operator*() [15/15]

◆ operator+() [1/3]

◆ operator+() [2/3]

◆ operator+() [3/3]

◆ operator-() [1/3]

◆ operator-() [2/3]

◆ operator-() [3/3]

◆ operator/() [1/3]

◆ operator/() [2/3]

◆ operator/() [3/3]

◆ operator<<() [1/5]

◆ operator<<() [2/5]

◆ operator<<() [3/5]

◆ operator<<() [4/5]

◆ operator<<() [5/5]

◆ operator>>()

◆ Real()

◆ side_assembly() [1/3]

◆ side_assembly() [2/3]

◆ side_assembly() [3/3]