A Tensor represents a Cartesian tensor. More...

#include <Tensor.h>

Public Member Functions
Constructors
	Tensor ()
	Default constructor. More...

	Tensor (const Tensor &t)
	Copy constructor. More...

	Tensor (double scalar)
	Constructor, initialize all elements to a scalar value. More...

	Tensor (const double a[][Dimension])
	Construct Tensor from double [][Dimension] 2D C array. More...

Assignment
Tensor &	operator= (const Tensor &t)
	Copy assignment. More...

Tensor &	operator= (const double a[][Dimension])
	Assignment from C double [Dimension][Dimension] 2D array. More...

Arithmetic Assignment
void	operator+= (const Tensor &dt)
	Add tensor dt to this tensor. More...

void	operator-= (const Tensor &dt)
	Subtract tensor dt from this tensor. More...

void	operator*= (double s)
	Multiply this tensor by scalar s. More...

void	operator/= (double s)
	Divide this tensor by scalar s. More...

Array Subscript
const double &	operator() (int i, int j) const
	Return one element by value. More...

double &	operator() (int i, int j)
	Return one element by non-const reference. More...

Tensor valued functions (result assigned to invoking object)
Tensor &	zero ()
	Set all elements of this tensor to zero. More...

Tensor &	identity ()
	Set this to the identity (unity) tensor. More...

Tensor &	setRow (int i, const Vector &r)
	Set row i of this Tensor to elements of Vector r. More...

Tensor &	setColumn (int i, const Vector &r)
	Set column i of this Tensor to elements of Vector r. More...

Tensor &	add (const Tensor &t1, const Tensor &t2)
	Add tensors t1 and t2. More...

Tensor &	subtract (const Tensor &t1, const Tensor &t2)
	Subtract tensor t2 from t1. More...

Tensor &	multiply (const Tensor &t, double s)
	Multiply a tensor t by a scalar s. More...

Tensor &	divide (const Tensor &t, double s)
	Divide a Tensor t by a scalar s. More...

Tensor &	transpose (const Tensor &t)
	Compute transpose of a tensor. More...

Tensor &	transpose ()
	Transpose this tensor. More...

Tensor &	symmetrize (const Tensor &t)
	Compute symmetric part of a tensor t. More...

Tensor &	symmetrize ()
	Symmetrize this tensor. More...

Tensor &	dyad (const Vector &v1, const Vector &v2)
	Create dyad of two vectors. More...

Miscellaneous
double	trace () const
	Return the trace of this tensor. More...

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)
	Serialize this to/from an archive. More...

Static Members
static const Tensor	Zero = Tensor(0.0)
	Constant Tensor with all zero elements. More...

static const Tensor	Identity = Tensor().identity()
	Constant idenity Tensor (diagonal diagonal elements all 1). More...

static void	initStatic ()
	Call to guarantee initialization of Zero and Identity tensors. More...

static void	commitMpiType ()
	Commit MPI datatype MpiTraits<Tensor>::type. More...

bool	operator== (const Tensor &t1, const Tensor &t2)
	Equality for Tensors. More...

bool	operator== (const Tensor &t1, const double t2[][Dimension])
	Equality of Tensor and 2D C array. More...

std::istream &	operator>> (std::istream &in, Tensor &tensor)
	istream extractor for a Tensor. More...

std::ostream &	operator<< (std::ostream &out, const Tensor &tensor)
	ostream inserter for a Tensor. More...

Detailed Description

A Tensor represents a Cartesian tensor.

Definition at line 32 of file Tensor.h.

Constructor & Destructor Documentation

◆ Tensor() [1/4]

Util::Tensor::Tensor ( )

inline

Default constructor.

Definition at line 399 of file Tensor.h.

◆ Tensor() [2/4]

Util::Tensor::Tensor ( const Tensor & t )

inline

Copy constructor.

Definition at line 406 of file Tensor.h.

References Util::DimensionSq.

◆ Tensor() [3/4]

Util::Tensor::Tensor ( double scalar )

inlineexplicit

Constructor, initialize all elements to a scalar value.

Parameters

scalar initial value for all elements.

Definition at line 417 of file Tensor.h.

References Util::DimensionSq.

◆ Tensor() [4/4]

Util::Tensor::Tensor ( const double a[][Dimension] )

inlineexplicit

Construct Tensor from double [][Dimension] 2D C array.

Parameters

a	2D array a[Dimension][Dimension]

Definition at line 428 of file Tensor.h.

References Util::Dimension.

Member Function Documentation

◆ operator=() [1/2]

Tensor & Util::Tensor::operator= ( const Tensor & t )

inline

Copy assignment.

Parameters

t	Tensor to assign.

Definition at line 468 of file Tensor.h.

References Util::DimensionSq.

◆ operator=() [2/2]

Tensor & Util::Tensor::operator= ( const double a[][Dimension] )

inline

Assignment from C double [Dimension][Dimension] 2D array.

Parameters

a	2D array a[Dimension][Dimension]

Definition at line 480 of file Tensor.h.

References Util::Dimension.

◆ operator+=()

void Util::Tensor::operator+= ( const Tensor & dt )

inline

Add tensor dt to this tensor.

Upon return, *this = *this + dt.

Parameters

dt	tensor increment (input)

Definition at line 495 of file Tensor.h.

References Util::DimensionSq.

◆ operator-=()

void Util::Tensor::operator-= ( const Tensor & dt )

inline

Subtract tensor dt from this tensor.

Upon return, *this = *this - dt.

Parameters

dt	tensor increment (input)

Definition at line 506 of file Tensor.h.

References Util::DimensionSq.

◆ operator*=()

void Util::Tensor::operator*= ( double s )

inline

Multiply this tensor by scalar s.

Upon return, *this = (*this)*s.

Parameters

s	scalar multiplier

Definition at line 517 of file Tensor.h.

References Util::DimensionSq.

◆ operator/=()

void Util::Tensor::operator/= ( double s )

inline

Divide this tensor by scalar s.

Upon return, *this = (*this)/s.

Parameters

s	scalar divisor (input)

Definition at line 528 of file Tensor.h.

References Util::DimensionSq.

◆ operator()() [1/2]

const double & Util::Tensor::operator()	(	int	i,
		int	j
	)		const

inline

Return one element by value.

Parameters

i	row element index
j	column element index

Returns: element (i, j) of the tensor

Definition at line 539 of file Tensor.h.

References Util::Dimension.

◆ operator()() [2/2]

double & Util::Tensor::operator()	(	int	i,
		int	j
	)

inline

Return one element by non-const reference.

Parameters

i	row element index
j	column element index

Returns: element i of the tensor

Definition at line 552 of file Tensor.h.

References Util::Dimension.

◆ zero()

Tensor & Util::Tensor::zero ( )

inline

Set all elements of this tensor to zero.

Returns: reference to this tensor

Definition at line 441 of file Tensor.h.

References Util::DimensionSq.

Referenced by Util::setToZero().

◆ identity()

Tensor & Util::Tensor::identity ( )

inline

Set this to the identity (unity) tensor.

Returns: reference to this tensor

Definition at line 453 of file Tensor.h.

References Util::Dimension, and Util::DimensionSq.

◆ setRow()

Tensor & Util::Tensor::setRow	(	int	i,
		const Vector &	r
	)

inline

Set row i of this Tensor to elements of Vector r.

Returns: reference to this tensor

Definition at line 737 of file Tensor.h.

References Util::Dimension.

◆ setColumn()

Tensor & Util::Tensor::setColumn	(	int	i,
		const Vector &	r
	)

inline

Set column i of this Tensor to elements of Vector r.

Returns: reference to this tensor

Definition at line 749 of file Tensor.h.

References Util::Dimension.

◆ add()

Tensor & Util::Tensor::add	(	const Tensor &	t1,
		const Tensor &	t2
	)

inline

Add tensors t1 and t2.

Upon return, *this = t1 + t2.

Parameters

t1	tensor
t2	tensor

Returns: reference to this tensor

Definition at line 567 of file Tensor.h.

References Util::DimensionSq.

◆ subtract()

Tensor & Util::Tensor::subtract	(	const Tensor &	t1,
		const Tensor &	t2
	)

inline

Subtract tensor t2 from t1.

Upon return, *this == t1 - t2.

Parameters

t1	tensor (input)
t2	tensor (input)

Returns: reference to this tensor

Definition at line 581 of file Tensor.h.

References Util::DimensionSq.

◆ multiply()

Tensor & Util::Tensor::multiply	(	const Tensor &	t,
		double	s
	)

inline

Multiply a tensor t by a scalar s.

Upon return, *this == v*s.

Parameters

t	tensor factor
s	scalar factor

Returns: reference to this tensor

Definition at line 595 of file Tensor.h.

References Util::DimensionSq.

◆ divide()

Tensor & Util::Tensor::divide	(	const Tensor &	t,
		double	s
	)

inline

Divide a Tensor t by a scalar s.

Upon return, *this = v/s;

Parameters

t	tensor input
s	scalar denominator

Returns: reference to this tensor

Definition at line 609 of file Tensor.h.

References Util::DimensionSq.

◆ transpose() [1/2]

Tensor & Util::Tensor::transpose ( const Tensor & t )

inline

Compute transpose of a tensor.

Upon return, *this is the transpose of t

Parameters

t	input tensor

Returns: reference to this tensor

Definition at line 636 of file Tensor.h.

References Util::Dimension.

◆ transpose() [2/2]

Tensor & Util::Tensor::transpose ( )

inline

Transpose this tensor.

Upon return, *this is transposed.

Returns: reference to this tensor

Definition at line 657 of file Tensor.h.

References Util::Dimension.

◆ symmetrize() [1/2]

Tensor & Util::Tensor::symmetrize ( const Tensor & t )

inline

Compute symmetric part of a tensor t.

Upon return, *this = [t + t.transpose()]/2

Parameters

t	tensor input

Returns: reference to this tensor

Definition at line 678 of file Tensor.h.

References Util::Dimension.

◆ symmetrize() [2/2]

Tensor & Util::Tensor::symmetrize ( )

inline

Symmetrize this tensor.

Upon return, this is symmetrized, equal to half the sum of the original tensor and its transpose.

Returns: reference to this tensor

Definition at line 701 of file Tensor.h.

References Util::Dimension.

◆ dyad()

Tensor & Util::Tensor::dyad	(	const Vector &	v1,
		const Vector &	v2
	)

inline

Create dyad of two vectors.

Upon return, *this equals the dyad v1 ^ v2. Equivalently: (*this)(i , j) == v1[i]*v2[j]

Parameters

v1	vector input
v2	vector input

Returns: reference to this tensor

Definition at line 763 of file Tensor.h.

References Util::Dimension.

◆ trace()

double Util::Tensor::trace ( ) const

inline

Return the trace of this tensor.

Definition at line 621 of file Tensor.h.

References Util::Dimension, and trace().

Referenced by trace().

◆ serialize()

template<class Archive >

void Util::Tensor::serialize	(	Archive &	ar,
		const unsigned int	version
	)

inline

Serialize this to/from an archive.

Parameters

ar	archive
version	archive version id

Definition at line 720 of file Tensor.h.

References Util::DimensionSq.

◆ initStatic()

void Util::Tensor::initStatic ( )

static

Call to guarantee initialization of Zero and Identity tensors.

Call this function once to guarantee that this file is linked.

Definition at line 27 of file Tensor.cpp.

References UTIL_THROW.

Referenced by Util::initStatic().

◆ commitMpiType()

void Util::Tensor::commitMpiType ( )

static

Commit MPI datatype MpiTraits<Tensor>::type.

Definition at line 125 of file Tensor.cpp.

References Util::MpiStructBuilder::addMember(), Util::MpiStructBuilder::commit(), Util::Dimension, and Util::MpiStructBuilder::setBase().

Friends And Related Function Documentation

◆ operator== [1/2]

bool operator==	(	const Tensor &	t1,
		const Tensor &	t2
	)

friend

Equality for Tensors.

Definition at line 43 of file Tensor.cpp.

◆ operator== [2/2]

bool operator==	(	const Tensor &	t1,
		const double	t2[][Dimension]
	)

friend

Equality of Tensor and 2D C array.

Definition at line 56 of file Tensor.cpp.

◆ operator>>

std::istream & operator>>	(	std::istream &	in,
		Tensor &	tensor
	)

friend

istream extractor for a Tensor.

Input elements of a tensor from stream, without line breaks.

Parameters

in	input stream
tensor	Tensor to be read from stream

Returns: modified input stream

Definition at line 93 of file Tensor.cpp.

◆ operator<<

std::ostream & operator<<	(	std::ostream &	out,
		const Tensor &	tensor
	)

friend

ostream inserter for a Tensor.

Output elements of a tensor to stream, without line breaks.

Parameters

out	output stream
tensor	Tensor to be written to stream

Returns: modified output stream

Definition at line 104 of file Tensor.cpp.

Member Data Documentation

◆ Zero

const Tensor Util::Tensor::Zero = Tensor(0.0)

static

Constant Tensor with all zero elements.

Definition at line 297 of file Tensor.h.

◆ Identity

const Tensor Util::Tensor::Identity = Tensor().identity()

static

Constant idenity Tensor (diagonal diagonal elements all 1).

Definition at line 302 of file Tensor.h.

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

Public Member Functions

Static Members

Detailed Description

Constructor & Destructor Documentation

◆ Tensor() [1/4]

◆ Tensor() [2/4]

◆ Tensor() [3/4]

◆ Tensor() [4/4]

Member Function Documentation

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator+=()

◆ operator-=()

◆ operator*=()

◆ operator/=()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ zero()

◆ identity()

◆ setRow()

◆ setColumn()

◆ add()

◆ subtract()

◆ multiply()

◆ divide()

◆ transpose() [1/2]

◆ transpose() [2/2]

◆ symmetrize() [1/2]

◆ symmetrize() [2/2]

◆ dyad()

◆ trace()

◆ serialize()

◆ initStatic()

◆ commitMpiType()

Friends And Related Function Documentation

◆ operator== [1/2]

◆ operator== [2/2]

◆ operator>>

◆ operator<<

Member Data Documentation

◆ Zero

◆ Identity