Class that represents a rank 2 tensor. More...

#include <RealTensor2.H>

Public Member Functions
	RealTensor2 ()
	Construct a RealTensor2 of all zeros.

	RealTensor2 (const Real &xx, const Real &xy, const Real &xz, const Real &yx, const Real &yy, const Real &yz, const Real &zx, const Real &zy, const Real &zz)
	Construct a RealTensor2 from nine scalars.

	RealTensor2 (const RealVec &a, const RealVec &b)
	Construct a RealTensor2 as the outer product of two RealVecs.

Real &	operator() (int i, int j)
	Return an element of the tensor.

const Real &	operator() (int i, int j) const
	Return a const ref to an element of the tensor.

Real &	operator[] (int i)
	Return an element of the tensor.

const Real &	operator[] (int i) const
	Return a const ref to an element of the tensor.

RealTensor2	operator- () const
	Return the negative of a RealTensor2.

RealTensor2 &	operator+= (const Real a)
	Add a scalar to the RealTensor2 elementwise.

RealTensor2 &	operator-= (const Real a)
	Subtract a scalar from the RealTensor2 elementwise.

RealTensor2 &	operator*= (const Real a)
	Multiply a scalar by the RealTensor2 elementwise.

RealTensor2 &	operator/= (const Real a)
	Divide the RealTensor2 by a scalar elementwise.

RealTensor2 &	operator+= (const RealTensor2 &a)
	Add another RealTensor2 to the RealTensor2 elementwise.

RealTensor2 &	operator-= (const RealTensor2 &a)
	Subtract another RealTensor2 from the RealTensor2 elementwise.

RealTensor2 &	operator*= (const RealTensor2 &a)
	Multiply another RealTensor2 by the RealTensor2 elementwise.

RealTensor2 &	operator/= (const RealTensor2 &a)
	Divide this RealTensor2 by another RealTensor2 elementwise.

RealTensor2 &	operator= (const Real a)
	Assign a scalar value to every element of a RealTensor2.

RealTensor2	operator+ (const Real a) const
	Add a scalar and a RealTensor2 elementwise.

RealTensor2	operator- (const Real a) const
	Subtract a scalar from a RealTensor2 elementwise.

RealTensor2	operator* (const Real a) const
	Multiply a scalar by a RealTensor2 elementwise.

RealTensor2	operator/ (const Real a) const
	Divide a RealTensor2 by a scalar elementwise.

RealVec	operator* (const RealVec &v) const
	Matrix-vector multiplication.

RealTensor2	operator+ (const RealTensor2 &a) const
	Add two RealTensor2s elementwise.

RealTensor2	operator- (const RealTensor2 &a) const
	Subtract two RealTensor2s elementwise.

RealTensor2	operator* (const RealTensor2 &a) const
	Multiply two RealTensor2s elementwise.

RealTensor2	operator/ (const RealTensor2 &a) const
	Divide two RealTensor2s elementwise.

RealVec	contract1 (const RealVec &v) const
	Compute the tensor contraction v_i T_ij.

RealVec	contract2 (const RealVec &v) const
	Compute the tensor contraction v_j T_ij.

Real	contract (const RealVec &a, const RealVec &b) const
	Compute the tensor contraction a_i b_j T_ij.

Real	contract (const RealTensor2 &a) const
	Compute the contraction of this tensor with another tensor.

Real	divTangent (const RealVec &v) const
	Compute the divergence of the tangent vector.

Real	trace () const
	Return the trace of this tensor.

RealTensor2	T () const
	Return the transpose of this tensor.

void	transpose ()
	Transpose this tensor in place.

Real	mag ()
	Total magnitude.

Real	det () const
	Compute the determinant.

RealVec	eVal () const
	Compute the eigenvalues of a symmetric tensor.

RealTensor2	eVec () const
	Compute the eigenvectors of a symmetric tensor.

void	eigenDecompose (RealVec &eVal, RealTensor2 &eVec) const
	Compute the eigendecomposition of a symmetric tensor.

RealTensor2	inv () const
	Compute the inverse of a symmetric tensor.

RealTensor2	sqrt () const
	Compute the square root of a symmetric tensor.

RealTensor2	invSqrt () const
	Compute the inverse of the square root of a symmetric tensor.

Public Attributes
Real	t [9]

Detailed Description

Class that represents a rank 2 tensor.

This class represents a rank 2 tensor in 3 dimensional space, and provides algebraic operations on this tensor. The tensor is indexed so that element ij is stored at memory position 3*i + j.

Constructor & Destructor Documentation

◆ RealTensor2() [1/3]

criptic::RealTensor2::RealTensor2 ( )

inline

Construct a RealTensor2 of all zeros.

◆ RealTensor2() [2/3]

criptic::RealTensor2::RealTensor2	(	const Real &	xx,
		const Real &	xy,
		const Real &	xz,
		const Real &	yx,
		const Real &	yy,
		const Real &	yz,
		const Real &	zx,
		const Real &	zy,
		const Real &	zz
	)

inline

Construct a RealTensor2 from nine scalars.

Parameters

xx	xx element of tensor
xy	xy element of tensor
xz	xz element of tensor
yx	yx element of tensor
yy	yy element of tensor
yz	yz element of tensor
zx	zx element of tensor
zy	zy element of tensor
zz	zz element of tensor

◆ RealTensor2() [3/3]

criptic::RealTensor2::RealTensor2	(	const RealVec &	a,
		const RealVec &	b
	)

inline

Construct a RealTensor2 as the outer product of two RealVecs.

Parameters

a	The first vector
b	The second vector

The constructed RealTensor2 will be indexed as T_ij = a_i * b_j

Member Function Documentation

◆ contract() [1/2]

Real criptic::RealTensor2::contract ( const RealTensor2 & a ) const

inline

Compute the contraction of this tensor with another tensor.

Parameters

a	The tensor with which to contract this tensor

Returns: The contraction T_ij a_ij

◆ contract() [2/2]

Real criptic::RealTensor2::contract	(	const RealVec &	a,
		const RealVec &	b
	)		const

inline

Compute the tensor contraction a_i b_j T_ij.

Parameters

a	First vector with which to contract
b	Second vector with which to contract

Returns: The contraction

◆ contract1()

RealVec criptic::RealTensor2::contract1 ( const RealVec & v ) const

inline

Compute the tensor contraction v_i T_ij.

Parameters

v	The vector with which to contract this tensor

Returns: A RealVec containing the tensor contraction v_i T_ij

◆ contract2()

RealVec criptic::RealTensor2::contract2 ( const RealVec & v ) const

inline

Compute the tensor contraction v_j T_ij.

Parameters

v	The vector with which to contract this tensor

Returns: A RealVec containing the tensor contraction v_j T_ij

◆ det()

Real criptic::RealTensor2::det ( ) const

inline

Compute the determinant.

Returns: The determinant of this tensor

◆ divTangent()

Real criptic::RealTensor2::divTangent ( const RealVec & v ) const

inline

Compute the divergence of the tangent vector.

Parameters

v	The vector field

Returns: Divergence of tangent vector

Assuming that this tensor represents the gradient of a vector field at some point, and that v is the corresponding value of the vector field itself, this routine computes the divergence of the tangent vector to the vector field.

◆ eigenDecompose()

void criptic::RealTensor2::eigenDecompose	(	RealVec &	eVal,
		RealTensor2 &	eVec
	)		const

inline

Compute the eigendecomposition of a symmetric tensor.

Parameters

eVal	The eigenvalues
eVec	The eigenvectors

The eigenvectors are returned in another tensor, which can be interpreted as the rotation matrix required to diagonalize the tensor. This method assumes that the tensor is symmetric; if it is not, the results are undefined.

◆ eVal()

RealVec criptic::RealTensor2::eVal ( ) const

inline

Compute the eigenvalues of a symmetric tensor.

Returns: The eigenvalues of the tensor

This method assumes that the tensor is symmetric; if it is not, the results are undefined.

◆ eVec()

RealTensor2 criptic::RealTensor2::eVec ( ) const

inline

Compute the eigenvectors of a symmetric tensor.

Returns: The eigenvectors of the tensor

This method assumes that the tensor is symmetric; if it is not, the results are undefined.

◆ inv()

RealTensor2 criptic::RealTensor2::inv ( ) const

inline

Compute the inverse of a symmetric tensor.

Returns: The inverse of the tensor

This method assumes that the tensor is symmetric; if it is not, the results are undefined.

◆ invSqrt()

RealTensor2 criptic::RealTensor2::invSqrt ( ) const

inline

Compute the inverse of the square root of a symmetric tensor.

Returns: The inverse square root of the tensor

This method assumes that the tensor is symmetric; if it is not, the results are undefined.

◆ mag()

Real criptic::RealTensor2::mag ( )

inline

Total magnitude.

Returns: Square root of the sum of the squares of all elements

◆ operator()() [1/2]

criptic::RealTensor2::operator()	(	int	i,
		int	j
	)

inline

Return an element of the tensor.

Parameters

i	First tensor index
j	Second tensor index

Returns: Tensor element (i,j)

◆ operator()() [2/2]

criptic::RealTensor2::operator()	(	int	i,
		int	j
	)		const

inline

Return a const ref to an element of the tensor.

Parameters

i	First tensor index
j	Second tensor index

Returns: Tensor element (i,j)

◆ operator*() [1/3]

criptic::RealTensor2::operator* ( const Real a ) const

inline

Multiply a scalar by a RealTensor2 elementwise.

Parameters

a	The scalar

Returns: A RealTensor2 containing the elementwise product

◆ operator*() [2/3]

criptic::RealTensor2::operator* ( const RealTensor2 & a ) const

inline

Multiply two RealTensor2s elementwise.

Parameters

a	The RealTensor2 to multiply

Returns: A RealTensor2 containing the elementwise product

◆ operator*() [3/3]

criptic::RealTensor2::operator* ( const RealVec & v ) const

inline

Matrix-vector multiplication.

Parameters

v	The vector by which to multiply

Returns: The product T_ij v_j

◆ operator*=() [1/2]

criptic::RealTensor2::operator*= ( const Real a )

inline

Multiply a scalar by the RealTensor2 elementwise.

Parameters

a	The scalar

Returns: A reference to the modified RealTensor2

◆ operator*=() [2/2]

criptic::RealTensor2::operator*= ( const RealTensor2 & a )

inline

Multiply another RealTensor2 by the RealTensor2 elementwise.

Parameters

a	The RealTensor2 to multiply

Returns: A reference to the modified RealTensor2

◆ operator+() [1/2]

criptic::RealTensor2::operator+ ( const Real a ) const

inline

Add a scalar and a RealTensor2 elementwise.

Parameters

a	The scalar

Returns: A RealTensor2 containing the elementwise sum

◆ operator+() [2/2]

criptic::RealTensor2::operator+ ( const RealTensor2 & a ) const

inline

Add two RealTensor2s elementwise.

Parameters

a	The RealTensor2 to add

Returns: A RealTensor2 containing the elementwise sum

◆ operator+=() [1/2]

criptic::RealTensor2::operator+= ( const Real a )

inline

Add a scalar to the RealTensor2 elementwise.

Parameters

a	The scalar

Returns: A reference to the modified RealTensor2

◆ operator+=() [2/2]

criptic::RealTensor2::operator+= ( const RealTensor2 & a )

inline

Add another RealTensor2 to the RealTensor2 elementwise.

Parameters

a	The RealTensor2 to add

Returns: A reference to the modified RealTensor2

◆ operator-() [1/3]

criptic::RealTensor2::operator- ( ) const

inline

Return the negative of a RealTensor2.

Returns: A copy of the RealTensor2 with every element multiplied by -1

◆ operator-() [2/3]

criptic::RealTensor2::operator- ( const Real a ) const

inline

Subtract a scalar from a RealTensor2 elementwise.

Parameters

a	The scalar

Returns: A RealTensor2 containing the elementwise difference

◆ operator-() [3/3]

criptic::RealTensor2::operator- ( const RealTensor2 & a ) const

inline

Subtract two RealTensor2s elementwise.

Parameters

a	The RealTensor2 to subtract

Returns: A RealTensor2 containing the elementwise difference

◆ operator-=() [1/2]

criptic::RealTensor2::operator-= ( const Real a )

inline

Subtract a scalar from the RealTensor2 elementwise.

Parameters

a	The scalar

Returns: A reference to the modified RealTensor2

◆ operator-=() [2/2]

criptic::RealTensor2::operator-= ( const RealTensor2 & a )

inline

Subtract another RealTensor2 from the RealTensor2 elementwise.

Parameters

a	The RealTensor2 to subtract

Returns: A reference to the modified RealTensor2

◆ operator/() [1/2]

criptic::RealTensor2::operator/ ( const Real a ) const

inline

Divide a RealTensor2 by a scalar elementwise.

Parameters

a	The scalar

Returns: A RealTensor2 containing the elementwise dividend

◆ operator/() [2/2]

criptic::RealTensor2::operator/ ( const RealTensor2 & a ) const

inline

Divide two RealTensor2s elementwise.

Parameters

a	The RealTensor2 to divide by

Returns: A RealTensor2 containing the elementwise dividend

◆ operator/=() [1/2]

criptic::RealTensor2::operator/= ( const Real a )

inline

Divide the RealTensor2 by a scalar elementwise.

Parameters

a	The scalar

Returns: A reference to the modified RealTensor2

◆ operator/=() [2/2]

criptic::RealTensor2::operator/= ( const RealTensor2 & a )

inline

Divide this RealTensor2 by another RealTensor2 elementwise.

Parameters

a	The RealTensor2 to divide by

Returns: A reference to the modified RealTensor2

◆ operator=()

criptic::RealTensor2::operator= ( const Real a )

inline

Assign a scalar value to every element of a RealTensor2.

Parameters

a	The scalar

Returns: The RealTensor2 with every element set equal to a

◆ operator[]() [1/2]

criptic::RealTensor2::operator[] ( int i )

inline

Return an element of the tensor.

Parameters

i	1D index of the tensor

Returns: Tensor element (i/3, i mod 3)

◆ operator[]() [2/2]

criptic::RealTensor2::operator[] ( int i ) const

inline

Return a const ref to an element of the tensor.

Parameters

i	1D index of the tensor

Returns: Tensor element (i/3, i mod 3)

◆ sqrt()

RealTensor2 criptic::RealTensor2::sqrt ( ) const

inline

Compute the square root of a symmetric tensor.

Returns: The square root of the tensor

This method assumes that the tensor is symmetric; if it is not, the results are undefined.

◆ T()

RealTensor2 criptic::RealTensor2::T ( ) const

inline

Return the transpose of this tensor.

Returns: The transpose of this tensor

◆ trace()

Real criptic::RealTensor2::trace ( ) const

inline

Return the trace of this tensor.

◆ transpose()

void criptic::RealTensor2::transpose ( )

inline

Transpose this tensor in place.

Member Data Documentation

◆ t

Real criptic::RealTensor2::t[9]

Data in RealTensor2

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

Src/Utils/RealTensor2.H

Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ RealTensor2() [1/3]

◆ RealTensor2() [2/3]

◆ RealTensor2() [3/3]

Member Function Documentation

◆ contract() [1/2]

◆ contract() [2/2]

◆ contract1()

◆ contract2()

◆ det()

◆ divTangent()

◆ eigenDecompose()

◆ eVal()

◆ eVec()

◆ inv()

◆ invSqrt()

◆ mag()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+() [1/2]

◆ operator+() [2/2]

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-() [1/3]

◆ operator-() [2/3]

◆ operator-() [3/3]

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/() [1/2]

◆ operator/() [2/2]

◆ operator/=() [1/2]

◆ operator/=() [2/2]

◆ operator=()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ sqrt()

◆ T()

◆ trace()

◆ transpose()

Member Data Documentation

◆ t