Tensor Class Reference

Class for a matrix 3x3 system object. More...

#include <Tensor.h>

Collaboration diagram for Tensor:

Public Member Functions
	Tensor ()
	Tensor (const Tensor &tensor)
	Tensor (const double &xx, const double &xy, const double &xz, const double &yx, const double &yy, const double &yz, const double &zx, const double &zy, const double &zz)
	Tensor (const Coord &x, const Coord &y, const Coord &z)
	~Tensor ()
const double &	getElement (const int &element) const
	Return the value of the specific element of the Tensor object.
const double &	getXX () const
	Return the value of the xx-element of the Tensor object.
const double &	getXY () const
	Return the value of the xy-element of the Tensor object.
const double &	getXZ () const
	Return the value of the xz-element of the Tensor object.
const double &	getYX () const
	Return the value of the yx-element of the Tensor object.
const double &	getYY () const
	Return the value of the yy-element of the Tensor object.
const double &	getYZ () const
	Return the value of the yz-element of the Tensor object.
const double &	getZX () const
	Return the value of the zx-element of the Tensor object.
const double &	getZY () const
	Return the value of the zy-element of the Tensor object.
const double &	getZZ () const
	Return the value of the zz-element of the Tensor object.
void	setXX (const double &xx)
	Set the value in the xx-element of the Tensor object.
void	setXY (const double &xy)
	Set the value in the xy-element of the Tensor object.
void	setXZ (const double &xz)
	Set the value in the xz-element of the Tensor object.
void	setYX (const double &xx)
	Set the value in the yx-element of the Tensor object.
void	setYY (const double &xy)
	Set the value in the yy-element of the Tensor object.
void	setYZ (const double &xz)
	Set the value in the yz-element of the Tensor object.
void	setZX (const double &xx)
	Set the value in the zx-element of the Tensor object.
void	setZY (const double &xy)
	Set the value in the zy-element of the Tensor object.
void	setZZ (const double &xz)
	Set the value in the zz-element of the Tensor object.
void	setTensor (const Tensor &tensor)
	Set the Tensor object.
void	setTensor (const double &value)
	Set all the elements of the Tensor object to a scalar value.
void	identity ()
	Set the Tensor object to identity.
void	correctZeros ()
	Set to perfect zero each of the epsilon terms.
Coord	scalar (const Coord &a) const
	Return the scalar product between the Tensor and the Coord.
void	localProjection (const Coord &normal, const Coord &tangent, const Coord &binormal)
	Projection in the local coordinate system which is defined by the transmitted normal, tangent and binormal.
void	reverseProjection (const Coord &normal, const Coord &tangent, const Coord &binormal)
	Reverse projection in the absolute Cartesian coordinate system.
void	setTensorByLines (const Coord &x, const Coord &y, const Coord &z)
void	setTensorByColumns (const Coord &x, const Coord &y, const Coord &z)
void	tensorToCoords (Coord &x, Coord &y, Coord &z) const
	Transform the Tensor into Coords (vectors).
void	tensorToArray (double *array) const
	Transform the Tensor into 1D array (pointer).
void	arrayToTensor (const double *array)
	Transform the 1D array (pointer) into Tensor.
void	transpose (Tensor &transposedTensor) const
	Compute the transpose of the tensor.
void	matrixProduct (const Tensor &tensor2, Tensor &resultingTensor) const
	Compute the matrix product of the two tensors.
double	trace () const
	Return the trace of the tensor.
double	determinant () const
	Return the determinant of the tensor.
void	inverse (Tensor &inverseTensor) const
	Compute the inverse of the tensor.
double	infinityNorm () const
	Compute the infinity norm of the tensor.
double	frobeniusNorm () const
	Compute the Frobenius (L2) norm of the tensor.
void	exponentialPade (Tensor &tensorExpPade)
	Compute the exponential of the tensor using a Padé 6*6 algorithm.
bool	isIdentity () const
	Return true if equal to identity.
void	eigen (Tensor &eigenvalues, Tensor &eigenvectors) const
	Compute the eigenvalues and eigenvectors of the tensor with Jacobi's algorithm.
Tensor &	operator= (const double &scalar)
Tensor &	operator= (const Tensor &a)
Tensor &	operator*= (const double &scalar)
Tensor &	operator/= (const double &scalar)
Tensor	operator* (const double &scalar) const
Tensor	operator/ (const double &scalar) const
Tensor &	operator+= (const Tensor &a)
Tensor &	operator-= (const Tensor &a)

Static Public Attributes
static const Tensor	defaultTensor = Tensor()
	Default Tensor object (const version).
static Tensor	defaultTensorNonConst = Tensor()
	Default Tensor object (non-const version).

Protected Attributes
std::array< double, 9 >	m_array

Detailed Description

Class for a matrix 3x3 system object.

Constructor & Destructor Documentation

Tensor() [1/4]

Tensor::Tensor

(

)

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Tensor() [2/4]

Tensor::Tensor

(

const Tensor &

tensor

)

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Tensor() [3/4]

Tensor::Tensor	(	const double &	xx,
		const double &	xy,
		const double &	xz,
		const double &	yx,
		const double &	yy,
		const double &	yz,
		const double &	zx,
		const double &	zy,
		const double &	zz )

Tensor() [4/4]

Tensor::Tensor	(	const Coord &	x,
		const Coord &	y,
		const Coord &	z )

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~Tensor()

Tensor::~Tensor

(

)

Member Function Documentation

arrayToTensor()

void Tensor::arrayToTensor

(

const double *

array

)

Transform the 1D array (pointer) into Tensor.

Parameters

array

1D array (pointer)

correctZeros()

void Tensor::correctZeros

(

)

Set to perfect zero each of the epsilon terms.

determinant()

double Tensor::determinant

(

)

const

Return the determinant of the tensor.

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eigen()

void Tensor::eigen	(	Tensor &	eigenvalues,
		Tensor &	eigenvectors ) const

Compute the eigenvalues and eigenvectors of the tensor with Jacobi's algorithm.

Parameters

eigenvalues	tensor whose diagonal elements are eigenvalues (Tensor)
eigenvectors	tensor whose columns are eigenvectors (Tensor)

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exponentialPade()

void Tensor::exponentialPade

(

Tensor &

tensorExpPade

)

Compute the exponential of the tensor using a Padé 6*6 algorithm.

Parameters

tensorExpPade

resulting tensor (exponential Padé)

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frobeniusNorm()

double Tensor::frobeniusNorm

(

)

const

Compute the Frobenius (L2) norm of the tensor.

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getElement()

const double & Tensor::getElement ( const int & element ) const

inline

Return the value of the specific element of the Tensor object.

getXX()

const double & Tensor::getXX ( ) const

inline

Return the value of the xx-element of the Tensor object.

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getXY()

const double & Tensor::getXY ( ) const

inline

Return the value of the xy-element of the Tensor object.

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getXZ()

const double & Tensor::getXZ ( ) const

inline

Return the value of the xz-element of the Tensor object.

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getYX()

const double & Tensor::getYX ( ) const

inline

Return the value of the yx-element of the Tensor object.

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getYY()

const double & Tensor::getYY ( ) const

inline

Return the value of the yy-element of the Tensor object.

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getYZ()

const double & Tensor::getYZ ( ) const

inline

Return the value of the yz-element of the Tensor object.

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getZX()

const double & Tensor::getZX ( ) const

inline

Return the value of the zx-element of the Tensor object.

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getZY()

const double & Tensor::getZY ( ) const

inline

Return the value of the zy-element of the Tensor object.

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getZZ()

const double & Tensor::getZZ ( ) const

inline

Return the value of the zz-element of the Tensor object.

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identity()

void Tensor::identity

(

)

Set the Tensor object to identity.

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infinityNorm()

double Tensor::infinityNorm

(

)

const

Compute the infinity norm of the tensor.

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inverse()

void Tensor::inverse

(

Tensor &

inverseTensor

)

const

Compute the inverse of the tensor.

Parameters

inverseTensor

inverse tensor (Tensor)

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isIdentity()

bool Tensor::isIdentity

(

)

const

Return true if equal to identity.

localProjection()

void Tensor::localProjection	(	const Coord &	normal,
		const Coord &	tangent,
		const Coord &	binormal )

Projection in the local coordinate system which is defined by the transmitted normal, tangent and binormal.

Parameters

normal	normal vector (Coord)
tangent	tangent vector (Coord)
binormal	binormal vector (Coord)

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matrixProduct()

void Tensor::matrixProduct	(	const Tensor &	tensor2,
		Tensor &	resultingTensor ) const

Compute the matrix product of the two tensors.

Parameters

tensor2	second tensor (Tensor)
resultingTensor	resulting tensor of the product (Tensor)

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operator*()

Tensor Tensor::operator*

(

const double &

scalar

)

const

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operator*=()

Tensor & Tensor::operator*=

(

const double &

scalar

)

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operator+=()

Tensor & Tensor::operator+=

(

const Tensor &

a

)

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operator-=()

Tensor & Tensor::operator-=

(

const Tensor &

a

)

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operator/()

Tensor Tensor::operator/

(

const double &

scalar

)

const

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operator/=()

Tensor & Tensor::operator/=

(

const double &

scalar

)

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operator=() [1/2]

Tensor & Tensor::operator=

(

const double &

scalar

)

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operator=() [2/2]

Tensor & Tensor::operator=

(

const Tensor &

a

)

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reverseProjection()

void Tensor::reverseProjection	(	const Coord &	normal,
		const Coord &	tangent,
		const Coord &	binormal )

Reverse projection in the absolute Cartesian coordinate system.

Parameters

normal	normal vector (Coord)
tangent	tangent vector (Coord)
binormal	binormal vector (Coord)

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scalar()

Coord Tensor::scalar

(

const Coord &

a

)

const

Return the scalar product between the Tensor and the Coord.

Parameters

a	vector (Coord)

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setTensor() [1/2]

void Tensor::setTensor

(

const double &

value

)

Set all the elements of the Tensor object to a scalar value.

Parameters

value

scalar value to set all elements

setTensor() [2/2]

void Tensor::setTensor

(

const Tensor &

tensor

)

Set the Tensor object.

Parameters

tensor

tensor

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setTensorByColumns()

void Tensor::setTensorByColumns	(	const Coord &	x,
		const Coord &	y,
		const Coord &	z )

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setTensorByLines()

void Tensor::setTensorByLines	(	const Coord &	x,
		const Coord &	y,
		const Coord &	z )

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setXX()

void Tensor::setXX

(

const double &

xx

)

Set the value in the xx-element of the Tensor object.

Parameters

xx	value of the xx-element coordinate

setXY()

void Tensor::setXY

(

const double &

xy

)

Set the value in the xy-element of the Tensor object.

Parameters

xy	value of the xy-element coordinate

setXZ()

void Tensor::setXZ

(

const double &

xz

)

Set the value in the xz-element of the Tensor object.

Parameters

xz	value of the xz-element coordinate

setYX()

void Tensor::setYX

(

const double &

xx

)

Set the value in the yx-element of the Tensor object.

Parameters

xx	value of the yx-element coordinate

setYY()

void Tensor::setYY

(

const double &

xy

)

Set the value in the yy-element of the Tensor object.

Parameters

xy	value of the yy-element coordinate

setYZ()

void Tensor::setYZ

(

const double &

xz

)

Set the value in the yz-element of the Tensor object.

Parameters

xz	value of the yz-element coordinate

setZX()

void Tensor::setZX

(

const double &

xx

)

Set the value in the zx-element of the Tensor object.

Parameters

xx	value of the zx-element coordinate

setZY()

void Tensor::setZY

(

const double &

xy

)

Set the value in the zy-element of the Tensor object.

Parameters

xy	value of the zy-element coordinate

setZZ()

void Tensor::setZZ

(

const double &

xz

)

Set the value in the zz-element of the Tensor object.

Parameters

xz	value of the zz-element coordinate

tensorToArray()

void Tensor::tensorToArray

(

double *

array

)

const

Transform the Tensor into 1D array (pointer).

Parameters

array

1D array (pointer)

tensorToCoords()

void Tensor::tensorToCoords	(	Coord &	x,
		Coord &	y,
		Coord &	z ) const

Transform the Tensor into Coords (vectors).

Parameters

x	x vector (Coord)
y	y vector (Coord)
z	z vector (Coord)

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trace()

double Tensor::trace

(

)

const

Return the trace of the tensor.

transpose()

void Tensor::transpose

(

Tensor &

transposedTensor

)

const

Compute the transpose of the tensor.

Parameters

transposedTensor

transposed tensor (Tensor)

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Member Data Documentation

defaultTensor

const Tensor Tensor::defaultTensor = Tensor()

static

Default Tensor object (const version).

Used when returning a const Tensor&

defaultTensorNonConst

Tensor Tensor::defaultTensorNonConst = Tensor()

static

Default Tensor object (non-const version).

Used when returning a const Tensor&

m_array

std::array<double, 9> Tensor::m_array

protected

---

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

• /home/runner/work/ECOGEN/ECOGEN/doc_sources/src/Maths/Tensor.h
• /home/runner/work/ECOGEN/ECOGEN/doc_sources/src/Maths/Tensor.cpp