A Tensor represents a Cartesian tensor. More...

#include <Tensor.h>

Public Member Functions
Constructors
	Tensor ()
	Default constructor.
	Tensor (const Tensor &t)
	Copy constructor.
	Tensor (double scalar)
	Constructor, initialize all elements to a scalar value.
	Tensor (const double a[][Dimension])
	Construct Tensor from double [][Dimension] 2D C array.
Assignment
Tensor &	operator= (const Tensor &t)
	Copy assignment.
Tensor &	operator= (const double a[][Dimension])
	Assignment from C double [Dimension][Dimension] 2D array.
Arithmetic Assignment
void	operator+= (const Tensor &dt)
	Add tensor dt to this tensor.
void	operator-= (const Tensor &dt)
	Subtract tensor dt from this tensor.
void	operator*= (double s)
	Multiply this tensor by scalar s.
void	operator/= (double s)
	Divide this tensor by scalar s.
Array Subscript
const double &	operator() (int i, int j) const
	Return one element by value.
double &	operator() (int i, int j)
	Return one element by non-const reference.
Tensor valued functions (result assigned to invoking object)
Tensor &	zero ()
	Set all elements of this tensor to zero.
Tensor &	identity ()
	Set this to the identity (unity) tensor.
Tensor &	setRow (int i, const Vector &r)
	Set row i of this Tensor to elements of Vector r.
Tensor &	setColumn (int i, const Vector &r)
	Set column i of this Tensor to elements of Vector r.
Tensor &	add (const Tensor &t1, const Tensor &t2)
	Add tensors t1 and t2.
Tensor &	subtract (const Tensor &t1, const Tensor &t2)
	Subtract tensor t2 from t1.
Tensor &	multiply (const Tensor &t, double s)
	Multiply a tensor t by a scalar s.
Tensor &	divide (const Tensor &t, double s)
	Divide a Tensor t by a scalar s.
Tensor &	transpose (const Tensor &t)
	Compute transpose of a tensor.
Tensor &	transpose ()
	Transpose this tensor.
Tensor &	symmetrize (const Tensor &t)
	Compute symmetric part of a tensor t.
Tensor &	symmetrize ()
	Symmetrize this tensor.
Tensor &	dyad (const Vector &v1, const Vector &v2)
	Create dyad of two vectors.
Miscellaneous
double	trace () const
	Return the trace of this tensor.
template<class Archive>
void	serialize (Archive &ar, const unsigned int version)
	Serialize this to/from an archive.

Static Members
static const Tensor	Zero = Tensor(0.0)
	Constant Tensor with all zero elements.
static const Tensor	Identity = Tensor().identity()
	Constant idenity Tensor (diagonal diagonal elements all 1).
static void	initStatic ()
	Call to guarantee initialization of Zero and Identity tensors.
bool	operator== (const Tensor &t1, const Tensor &t2)
	Equality for Tensors.
bool	operator== (const Tensor &t1, const double t2[][Dimension])
	Equality of Tensor and 2D C array.
std::istream &	operator>> (std::istream &in, Tensor &tensor)
	istream extractor for a Tensor.
std::ostream &	operator<< (std::ostream &out, const Tensor &tensor)
	ostream inserter for a Tensor.

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.

Referenced by add(), divide(), dyad(), identity(), multiply(), operator+=(), operator-=(), operator<<, operator=(), operator=(), operator==, operator==, operator>>, setColumn(), setRow(), subtract(), symmetrize(), symmetrize(), Tensor(), transpose(), transpose(), and zero().

◆ Tensor() [2/4]

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

inline

Copy constructor.

Definition at line 406 of file Tensor.h.

References Util::DimensionSq, and Tensor().

◆ 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, and Tensor().

◆ 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, and Tensor().

◆ 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, and Tensor().

◆ 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, and Tensor().

◆ 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, and Tensor().

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, Util::DimensionSq, and Tensor().

◆ 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, and Tensor().

◆ 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, and Tensor().

◆ 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, and Tensor().

◆ 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, and Tensor().

◆ 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, and Tensor().

◆ 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, and Tensor().

◆ 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, and Tensor().

◆ 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, and Tensor().

◆ 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, and Tensor().

◆ 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, and Tensor().

◆ 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, and Tensor().

◆ 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_CHECK.

Referenced by Util::initStatic().

◆ operator== [1/2]

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

friend

Equality for Tensors.

Definition at line 41 of file Tensor.cpp.

References Util::DimensionSq, and Tensor().

◆ operator== [2/2]

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

friend

Equality of Tensor and 2D C array.

Definition at line 54 of file Tensor.cpp.

References Util::Dimension, and Tensor().

◆ 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 91 of file Tensor.cpp.

References Util::DimensionSq, and Tensor().

◆ 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 102 of file Tensor.cpp.

References Util::DimensionSq, and Tensor().

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()

Friends And Related Symbol Documentation

◆ operator== [1/2]

◆ operator== [2/2]

◆ operator>>

◆ operator<<

Member Data Documentation

◆ Zero

◆ Identity