Class implementing fixed size matrices of doubles More...

#include <Tensor.h>

Inheritance diagram for PLMD::TensorGeneric< n, m >:

Public Member Functions
template<typename... Args>
	TensorGeneric (double first, Args... arg)
	Constructor accepting n*m double parameters. More...

	TensorGeneric ()
	initialize the tensor to zero More...

	TensorGeneric (const VectorGeneric< n > &v1, const VectorGeneric< m > &v2)
	initialize a tensor as an external product of two Vector More...

double	determinant () const
	returns the determinant More...

template<>
double	determinant () const

VectorGeneric< n >	getCol (unsigned j) const
	get j-th column More...

VectorGeneric< m >	getRow (unsigned i) const
	get i-th row More...

TensorGeneric	inverse () const
	return the matrix inverse More...

template<>
TensorGeneric< 3, 3 >	inverse () const

double &	operator() (unsigned i, unsigned j)
	access element More...

const double &	operator() (unsigned i, unsigned j) const
	access element More...

TensorGeneric &	operator*= (double)
	multiply More...

TensorGeneric	operator+ () const
	return +t More...

TensorGeneric &	operator+= (const TensorGeneric< n, m > &b)
	increment More...

TensorGeneric	operator- () const
	return -t More...

TensorGeneric &	operator-= (const TensorGeneric< n, m > &b)
	decrement More...

TensorGeneric &	operator/= (double)
	divide More...

Row	operator[] (unsigned i)
	access element (with [][] syntax) More...

Const_row	operator[] (unsigned i) const
	access element (with [][] syntax) More...

TensorGeneric &	setCol (unsigned j, const VectorGeneric< n > &c)
	set j-th column More...

TensorGeneric &	setRow (unsigned i, const VectorGeneric< m > &r)
	set i-th row More...

TensorGeneric< m, n >	transpose () const
	return the transpose matrix More...

void	zero ()
	set it to zero More...

Static Public Member Functions
static TensorGeneric< n, n >	identity ()
	return an identity tensor More...

Private Member Functions
void	auxiliaryConstructor ()
	Auxiliary private function for constructor. More...

template<typename... Args>
void	auxiliaryConstructor (double first, Args... arg)
	Auxiliary private function for constructor. More...

Private Attributes
std::array< double, n *m >	d

Friends
TensorGeneric< 3, 3 >	dcrossDv1 (const VectorGeneric< 3 > &, const VectorGeneric< 3 > &)

TensorGeneric< 3, 3 >	dcrossDv2 (const VectorGeneric< 3 > &, const VectorGeneric< 3 > &)

TensorGeneric< 3, 3 >	deriNorm (const VectorGeneric< 3 > &, const TensorGeneric< 3, 3 > &)
	Derivative of a normalized vector. More...

double	determinant (const TensorGeneric< 3, 3 > &)
	returns the determinant of a tensor More...

template<unsigned n_, unsigned m_>
void	diagMatSym (const TensorGeneric< n_, n_ > &, VectorGeneric< m_ > &evals, TensorGeneric< m_, n_ > &evec)
	Diagonalize tensor. More...

template<unsigned n_, unsigned m_>
TensorGeneric< n_, m_ >	extProduct (const VectorGeneric< n > &, const VectorGeneric< m > &)
	returns the transpose of a tensor (same as TensorGeneric(const VectorGeneric&,const VectorGeneric&)) More...

TensorGeneric< 3, 3 >	inverse (const TensorGeneric< 3, 3 > &)
	returns the inverse of a tensor (same as inverse()) More...

template<unsigned n_, unsigned m_, unsigned l_>
TensorGeneric< n_, l_ >	matmul (const TensorGeneric< n_, m_ > &, const TensorGeneric< m_, l_ > &)
	matrix-matrix multiplication More...

template<unsigned n_, unsigned m_>
VectorGeneric< n_ >	matmul (const TensorGeneric< n_, m_ > &, const VectorGeneric< m_ > &)
	matrix-vector multiplication More...

template<unsigned n_, unsigned m_>
VectorGeneric< n_ >	matmul (const VectorGeneric< m_ > &, const TensorGeneric< m_, n_ > &)
	vector-matrix multiplication More...

template<unsigned n_>
double	matmul (const VectorGeneric< n_ > &, const VectorGeneric< n_ > &)
	vector-vector multiplication (maps to dotProduct) More...

template<unsigned n_, unsigned m_, unsigned l_, unsigned i_>
TensorGeneric< n_, i_ >	matmul (const TensorGeneric< n_, m_ > &, const TensorGeneric< m_, l_ > &, const TensorGeneric< l_, i_ > &)
	matrix-matrix-matrix multiplication More...

template<unsigned n_, unsigned m_, unsigned l_>
VectorGeneric< n_ >	matmul (const TensorGeneric< n_, m_ > &, const TensorGeneric< m_, l_ > &, const VectorGeneric< l_ > &)
	matrix-matrix-vector multiplication More...

template<unsigned n_, unsigned m_, unsigned l_>
VectorGeneric< l_ >	matmul (const VectorGeneric< n_ > &, const TensorGeneric< n_, m_ > &, const TensorGeneric< m_, l_ > &)
	vector-matrix-matrix multiplication More...

template<unsigned n_, unsigned m_>
double	matmul (const VectorGeneric< n_ > &, const TensorGeneric< n_, m_ > &, const VectorGeneric< m_ > &)
	vector-matrix-vector multiplication More...

template<unsigned n_, unsigned m_>
TensorGeneric< n_, m_ >	operator* (double, const TensorGeneric< n_, m_ > &)
	scale the tensor by a factor s More...

template<unsigned n_, unsigned m_>
TensorGeneric< n_, m_ >	operator* (const TensorGeneric< n_, m_ > &, double s)
	scale the tensor by a factor s More...

template<unsigned n_, unsigned m_>
TensorGeneric< n_, m_ >	operator+ (const TensorGeneric< n_, m_ > &, const TensorGeneric< n_, m_ > &)
	return t1+t2 More...

template<unsigned n_, unsigned m_>
TensorGeneric< n_, m_ >	operator- (const TensorGeneric< n_, m_ > &, const TensorGeneric< n_, m_ > &)
	return t1+t2 More...

template<unsigned n_, unsigned m_>
TensorGeneric< n_, m_ >	operator/ (const TensorGeneric< n_, m_ > &, double s)
	scale the tensor by a factor 1/s More...

template<unsigned n_, unsigned m_>
std::ostream &	operator<< (std::ostream &os, const TensorGeneric< n_, m_ > &)
	<< operator. More...

template<unsigned n_, unsigned m_>
TensorGeneric< n_, m_ >	transpose (const TensorGeneric< m_, n_ > &)
	returns the transpose of a tensor (same as transpose()) More...

TensorGeneric< 3, 3 >	VcrossTensor (const VectorGeneric< 3 > &, const TensorGeneric< 3, 3 > &)

TensorGeneric< 3, 3 >	VcrossTensor (const TensorGeneric< 3, 3 > &, const VectorGeneric< 3 > &)

Detailed Description

template<unsigned n, unsigned m>
class PLMD::TensorGeneric< n, m >

Class implementing fixed size matrices of doubles

Template Parameters

n	The number rows
m	The number columns

This class implements a matrix of doubles with size fixed at compile time. It is useful for small fixed size objects (e.g. 3x3 tensors) as it does not waste space to store the vector size. Moreover, as the compiler knows the size, it can be completely opimized inline. Most of the loops are explicitly unrolled using PLMD::LoopUnroller class Matrix elements are initialized to zero by default. Notice that this means that constructor is a bit slow. This point might change in future if we find performance issues. It takes advantage of MatrixSquareBracketsAccess to provide both () and [] syntax for access. Several functions are declared as friends even if not necessary so as to properly appear in Doxygen documentation.

Aliases are defined to simplify common declarations (Tensor, Tensor2d, Tensor3d, Tensor4d). Also notice that some operations are only available for 3x3 tensors.

Example of usage

#include "Tensor.h"

using namespace PLMD;

int main(){
  Tensor a;
  TensorGeneric<3,2> b;
  TensorGeneric<3,2> c=matmul(a,b);
  return 0;
}

Constructor & Destructor Documentation

◆ TensorGeneric() [1/3]

template<unsigned n, unsigned m>

template<typename... Args>

PLMD::TensorGeneric< n, m >::TensorGeneric	(	double	first,
		Args...	arg
	)

Constructor accepting n*m double parameters.

Can be used as Tensor<2,2>(1.0,2.0,3.0,4.0) In case a wrong number of parameters is given, a static assertion will fail.

◆ TensorGeneric() [2/3]

template<unsigned n, unsigned m>

PLMD::TensorGeneric< n, m >::TensorGeneric ( )

initialize the tensor to zero

◆ TensorGeneric() [3/3]

template<unsigned n, unsigned m>

PLMD::TensorGeneric< n, m >::TensorGeneric	(	const VectorGeneric< n > &	v1,
		const VectorGeneric< m > &	v2
	)

initialize a tensor as an external product of two Vector

Member Function Documentation

◆ auxiliaryConstructor() [1/2]

template<unsigned n, unsigned m>

void PLMD::TensorGeneric< n, m >::auxiliaryConstructor ( )

private

Auxiliary private function for constructor.

◆ auxiliaryConstructor() [2/2]

template<unsigned n, unsigned m>

template<typename... Args>

void PLMD::TensorGeneric< n, m >::auxiliaryConstructor	(	double	first,
		Args...	arg
	)

private

Auxiliary private function for constructor.

◆ determinant() [1/2]

template<unsigned n, unsigned m>

double PLMD::TensorGeneric< n, m >::determinant ( ) const

returns the determinant

◆ determinant() [2/2]

template<>

double PLMD::TensorGeneric< 3, 3 >::determinant ( ) const

inline

◆ getCol()

template<unsigned n, unsigned m>

VectorGeneric< n > PLMD::TensorGeneric< n, m >::getCol ( unsigned j ) const

get j-th column

◆ getRow()

template<unsigned n, unsigned m>

VectorGeneric< m > PLMD::TensorGeneric< n, m >::getRow ( unsigned i ) const

get i-th row

◆ identity()

template<unsigned n, unsigned m>

TensorGeneric< n, n > PLMD::TensorGeneric< n, m >::identity ( )

inlinestatic

return an identity tensor

◆ inverse() [1/2]

template<unsigned n, unsigned m>

TensorGeneric PLMD::TensorGeneric< n, m >::inverse ( ) const

return the matrix inverse

◆ inverse() [2/2]

template<>

TensorGeneric< 3, 3 > PLMD::TensorGeneric< 3, 3 >::inverse ( ) const

inline

◆ operator()() [1/2]

template<unsigned n, unsigned m>

double & PLMD::TensorGeneric< n, m >::operator()	(	unsigned	i,
		unsigned	j
	)

access element

◆ operator()() [2/2]

template<unsigned n, unsigned m>

const double & PLMD::TensorGeneric< n, m >::operator()	(	unsigned	i,
		unsigned	j
	)		const

access element

◆ operator*=()

template<unsigned n, unsigned m>

TensorGeneric< n, m > & PLMD::TensorGeneric< n, m >::operator*= ( double s )

multiply

◆ operator+()

template<unsigned n, unsigned m>

TensorGeneric< n, m > PLMD::TensorGeneric< n, m >::operator+ ( ) const

return +t

◆ operator+=()

template<unsigned n, unsigned m>

TensorGeneric< n, m > & PLMD::TensorGeneric< n, m >::operator+= ( const TensorGeneric< n, m > & b )

increment

◆ operator-()

template<unsigned n, unsigned m>

TensorGeneric< n, m > PLMD::TensorGeneric< n, m >::operator- ( ) const

return -t

◆ operator-=()

template<unsigned n, unsigned m>

TensorGeneric< n, m > & PLMD::TensorGeneric< n, m >::operator-= ( const TensorGeneric< n, m > & b )

decrement

◆ operator/=()

template<unsigned n, unsigned m>

TensorGeneric< n, m > & PLMD::TensorGeneric< n, m >::operator/= ( double s )

divide

◆ operator[]() [1/2]

MatrixSquareBracketsAccess< TensorGeneric< n, m > , double , unsigned , unsigned >::Row PLMD::MatrixSquareBracketsAccess< TensorGeneric< n, m > , double , unsigned , unsigned >::operator[] ( unsigned i )

inherited

access element (with [][] syntax)

◆ operator[]() [2/2]

MatrixSquareBracketsAccess< TensorGeneric< n, m > , double , unsigned , unsigned >::Const_row PLMD::MatrixSquareBracketsAccess< TensorGeneric< n, m > , double , unsigned , unsigned >::operator[] ( unsigned i ) const

inherited

access element (with [][] syntax)

◆ setCol()

template<unsigned n, unsigned m>

TensorGeneric< n, m > & PLMD::TensorGeneric< n, m >::setCol	(	unsigned	j,
		const VectorGeneric< n > &	c
	)

set j-th column

◆ setRow()

template<unsigned n, unsigned m>

TensorGeneric< n, m > & PLMD::TensorGeneric< n, m >::setRow	(	unsigned	i,
		const VectorGeneric< m > &	r
	)

set i-th row

◆ transpose()

template<unsigned n, unsigned m>

TensorGeneric< m, n > PLMD::TensorGeneric< n, m >::transpose ( ) const

return the transpose matrix

◆ zero()

template<unsigned n, unsigned m>

void PLMD::TensorGeneric< n, m >::zero ( )

set it to zero

Friends And Related Function Documentation

◆ dcrossDv1

template<unsigned n, unsigned m>

TensorGeneric<3,3> dcrossDv1	(	const VectorGeneric< 3 > &	v1,
		const VectorGeneric< 3 > &	v2
	)

friend

◆ dcrossDv2

template<unsigned n, unsigned m>

TensorGeneric<3,3> dcrossDv2	(	const VectorGeneric< 3 > &	v1,
		const VectorGeneric< 3 > &	v2
	)

friend

◆ deriNorm

template<unsigned n, unsigned m>

TensorGeneric<3,3> deriNorm	(	const VectorGeneric< 3 > &	v1,
		const TensorGeneric< 3, 3 > &	v2
	)

friend

Derivative of a normalized vector.

◆ determinant

template<unsigned n, unsigned m>

double determinant ( const TensorGeneric< 3, 3 > & t )

friend

returns the determinant of a tensor

◆ diagMatSym

template<unsigned n, unsigned m>

template<unsigned n_, unsigned m_>

void diagMatSym	(	const TensorGeneric< n_, n_ > &	,
		VectorGeneric< m_ > &	evals,
		TensorGeneric< m_, n_ > &	evec
	)

friend

Diagonalize tensor.

Syntax is the same as Matrix::diagMat. In addition, it is possible to call if with m_ smaller than n_. In this case, only the first (smaller) m_ eigenvalues and eigenvectors are retrieved. If case lapack fails (info!=0) it throws an exception. Notice that tensor is assumed to be symmetric!!!

◆ extProduct

template<unsigned n, unsigned m>

template<unsigned n_, unsigned m_>

TensorGeneric<n_,m_> extProduct	(	const VectorGeneric< n > &	v1,
		const VectorGeneric< m > &	v2
	)

friend

returns the transpose of a tensor (same as TensorGeneric(const VectorGeneric&,const VectorGeneric&))

◆ inverse

template<unsigned n, unsigned m>

TensorGeneric<3,3> inverse ( const TensorGeneric< 3, 3 > & t )

friend

returns the inverse of a tensor (same as inverse())

◆ matmul [1/8]

template<unsigned n, unsigned m>

template<unsigned n_, unsigned m_, unsigned l_>

TensorGeneric<n_,l_> matmul	(	const TensorGeneric< n_, m_ > &	,
		const TensorGeneric< m_, l_ > &
	)

friend

matrix-matrix multiplication

◆ matmul [2/8]

template<unsigned n, unsigned m>

template<unsigned n_, unsigned m_>

VectorGeneric<n_> matmul	(	const TensorGeneric< n_, m_ > &	,
		const VectorGeneric< m_ > &
	)

friend

matrix-vector multiplication

◆ matmul [3/8]

template<unsigned n, unsigned m>

template<unsigned n_, unsigned m_>

VectorGeneric<n_> matmul	(	const VectorGeneric< m_ > &	,
		const TensorGeneric< m_, n_ > &
	)

friend

vector-matrix multiplication

◆ matmul [4/8]

template<unsigned n, unsigned m>

template<unsigned n_>

double matmul	(	const VectorGeneric< n_ > &	a,
		const VectorGeneric< n_ > &	b
	)

friend

vector-vector multiplication (maps to dotProduct)

◆ matmul [5/8]

template<unsigned n, unsigned m>

template<unsigned n_, unsigned m_, unsigned l_, unsigned i_>

TensorGeneric<n_,i_> matmul	(	const TensorGeneric< n_, m_ > &	,
		const TensorGeneric< m_, l_ > &	,
		const TensorGeneric< l_, i_ > &
	)

friend

matrix-matrix-matrix multiplication

◆ matmul [6/8]

template<unsigned n, unsigned m>

template<unsigned n_, unsigned m_, unsigned l_>

VectorGeneric<n_> matmul	(	const TensorGeneric< n_, m_ > &	,
		const TensorGeneric< m_, l_ > &	,
		const VectorGeneric< l_ > &
	)

friend

matrix-matrix-vector multiplication

◆ matmul [7/8]

template<unsigned n, unsigned m>

template<unsigned n_, unsigned m_, unsigned l_>

VectorGeneric<l_> matmul	(	const VectorGeneric< n_ > &	,
		const TensorGeneric< n_, m_ > &	,
		const TensorGeneric< m_, l_ > &
	)

friend

vector-matrix-matrix multiplication

◆ matmul [8/8]

template<unsigned n, unsigned m>

template<unsigned n_, unsigned m_>

double matmul	(	const VectorGeneric< n_ > &	,
		const TensorGeneric< n_, m_ > &	,
		const VectorGeneric< m_ > &
	)

friend

vector-matrix-vector multiplication

◆ operator* [1/2]

template<unsigned n, unsigned m>

template<unsigned n_, unsigned m_>

TensorGeneric<n_,m_> operator*	(	double	,
		const TensorGeneric< n_, m_ > &
	)

friend

scale the tensor by a factor s

◆ operator* [2/2]

template<unsigned n, unsigned m>

template<unsigned n_, unsigned m_>

TensorGeneric<n_,m_> operator*	(	const TensorGeneric< n_, m_ > &	,
		double	s
	)

friend

scale the tensor by a factor s

◆ operator+

template<unsigned n, unsigned m>

template<unsigned n_, unsigned m_>

TensorGeneric<n_,m_> operator+	(	const TensorGeneric< n_, m_ > &	,
		const TensorGeneric< n_, m_ > &
	)

friend

return t1+t2

◆ operator-

template<unsigned n, unsigned m>

template<unsigned n_, unsigned m_>

TensorGeneric<n_,m_> operator-	(	const TensorGeneric< n_, m_ > &	,
		const TensorGeneric< n_, m_ > &
	)

friend

return t1+t2

◆ operator/

template<unsigned n, unsigned m>

template<unsigned n_, unsigned m_>

TensorGeneric<n_,m_> operator/	(	const TensorGeneric< n_, m_ > &	,
		double	s
	)

friend

scale the tensor by a factor 1/s

◆ operator<<

template<unsigned n, unsigned m>

template<unsigned n_, unsigned m_>

std::ostream& operator<<	(	std::ostream &	os,
		const TensorGeneric< n_, m_ > &
	)

friend

<< operator.

Allows printing tensor t with std::cout<<t;

◆ transpose

template<unsigned n, unsigned m>

template<unsigned n_, unsigned m_>

TensorGeneric<n_,m_> transpose ( const TensorGeneric< m_, n_ > & )

friend

returns the transpose of a tensor (same as transpose())

◆ VcrossTensor [1/2]

template<unsigned n, unsigned m>

TensorGeneric<3,3> VcrossTensor	(	const VectorGeneric< 3 > &	v1,
		const TensorGeneric< 3, 3 > &	v2
	)

friend

◆ VcrossTensor [2/2]

template<unsigned n, unsigned m>

TensorGeneric<3,3> VcrossTensor	(	const TensorGeneric< 3, 3 > &	v2,
		const VectorGeneric< 3 > &	v1
	)

friend

Member Data Documentation

◆ d

template<unsigned n, unsigned m>

std::array<double,n*m> PLMD::TensorGeneric< n, m >::d

private

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

tools/Tensor.h

Public Member Functions

Static Public Member Functions

Private Member Functions

Private Attributes

Friends

Detailed Description

template<unsigned n, unsigned m> class PLMD::TensorGeneric< n, m >

Constructor & Destructor Documentation

◆ TensorGeneric() [1/3]

◆ TensorGeneric() [2/3]

◆ TensorGeneric() [3/3]

Member Function Documentation

◆ auxiliaryConstructor() [1/2]

◆ auxiliaryConstructor() [2/2]

◆ determinant() [1/2]

◆ determinant() [2/2]

◆ getCol()

◆ getRow()

◆ identity()

◆ inverse() [1/2]

◆ inverse() [2/2]

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*=()

◆ operator+()

◆ operator+=()

◆ operator-()

◆ operator-=()

◆ operator/=()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ setCol()

◆ setRow()

◆ transpose()

◆ zero()

Friends And Related Function Documentation

◆ dcrossDv1

◆ dcrossDv2

◆ deriNorm

◆ determinant

◆ diagMatSym

◆ extProduct

◆ inverse

◆ matmul [1/8]

◆ matmul [2/8]

◆ matmul [3/8]

◆ matmul [4/8]

◆ matmul [5/8]

◆ matmul [6/8]

◆ matmul [7/8]

◆ matmul [8/8]

◆ operator* [1/2]

◆ operator* [2/2]

◆ operator+

◆ operator-

◆ operator/

◆ operator<<

◆ transpose

◆ VcrossTensor [1/2]

◆ VcrossTensor [2/2]

Member Data Documentation

◆ d

template<unsigned n, unsigned m>
class PLMD::TensorGeneric< n, m >