Tensor Class Reference

Simple class for representing a non-symmetric second-order tensor. More...

#include <Tensor.h>

Inheritance diagram for Tensor:

Collaboration diagram for Tensor:

Public Member Functions
	Tensor (const t_ind nsd, bool identity=false)
	Constructor creating a zero or identity tesnor.
	Tensor (const Vec3 &vn, bool vnIsX=false)
	Constructor creating a transformation from a face normal vector. More...
	Tensor (const Vec3 &t1, const Vec3 &t2, bool t1isZ=false, bool t2isXZ=false)
	Constructor creating a transformation from two tangent vectors. More...
	Tensor (const Vec3 &v1, const Vec3 &v2, const Vec3 &v3)
	Constructor creating a transformation from three unit vectors. More...
	Tensor (Real a1, Real a2, Real a3)
	Constructor creating a transformation from three rotation angles. More...
	Tensor (const Tensor &T, bool transpose=false)
	Copy constructor, optionally creating the transpose of T.
	Tensor (const std::vector< Real > &a, bool transpose=false)
	Constructor copying its content from a one-dimensional array.
virtual	~Tensor ()
	Empty destructor.
void	zero ()
	Sets *this to the 0-tensor.
void	diag (Real value=Real(1))
	Sets *this to a diagonal tensor with value on the diagonal.
void	diag (const Vec3 &diagonal)
	Sets *this to a diagonal tensor with given vector as diagonal.
	operator const std::vector< Real > & () const
	Type casting to a one-dimensional vector, for referencing.
	operator std::vector< Real > & ()
	Type casting to a one-dimensional vector, for assignment.
const Real *	ptr () const
	Reference through a pointer.
const Real &	operator() (t_ind i, t_ind j) const
	Index-1 based component reference.
Real &	operator() (t_ind i, t_ind j)
	Index-1 based component access.
Vec3	operator[] (t_ind i) const
	Index-0 based column reference.
Tensor &	operator= (const Tensor &T)
	Assignment operator.
Tensor &	operator= (const std::vector< Real > &val)
	Overloaded assignment operator.
Tensor &	operator= (Real val)
	Overloaded assignment operator.
Tensor &	operator+= (const Tensor &T)
	Incrementation operator.
Tensor &	operator+= (Real val)
	Incrementation operator.
Tensor &	operator-= (const Tensor &T)
	Decrementation operator.
Tensor &	operator-= (Real val)
	Decrementation operator.
Tensor &	operator*= (Real val)
	Scaling operator.
Tensor &	operator*= (const Tensor &B)
	Post-multiplication with another Tensor.
Tensor &	postMult (const Tensor &B)
	Post-multiplication with another Tensor.
Tensor &	preMult (const Tensor &A)
	Pre-multiplication with another Tensor.
Tensor &	rotate (Real alpha, t_ind axis)
	Rotates the tensor about given coordinate axis.
Tensor &	outerProd (const Vec3 &a, const Vec3 &b)
	Dyadic (outer) product between two vectors.
Real	innerProd (const Tensor &T) const
	Returns the inner-product of *this and the given tensor.
t_ind	dim () const
	Returns the dimension of this tensor.
size_t	size () const
	Returns the size of this tensor.
virtual bool	symmetric () const
	Query whether this tensor is symmetric or not.
bool	equal (const Tensor &T, Real tol=Real(1.0e-6)) const
	Query whether this tensor equals another within given tolerance.
bool	isZero (Real tol=Real(1.0e-6)) const
	Query whether this tensor is zero within given tolerance.
virtual Tensor &	transpose ()
	Transposes the tensor.
virtual Tensor &	symmetrize ()
	Makes the tensor symmetric.
Tensor &	shift (short int idx=1)
	Performs a cyclic permutation of the tensor columns.
virtual Real	trace () const
	Returns the trace of the tensor.
virtual Real	det () const
	Returns the determinant of the tensor.
virtual Real	inverse (Real tol=Real(0))
	Inverts the tensor. More...
Vec3	rotVec () const
	Returns the rotation angles corresponding to the tensor.
virtual std::ostream &	print (std::ostream &os, int prec=0) const
	Prints out the tensor to an output stream.

Protected Types
using	t_ind = unsigned short int
	Tensor index type (for convenience)

Protected Member Functions
virtual t_ind	index (t_ind i, t_ind j) const
	Returns a 0-based array index for the given tensor indices. More...

Protected Attributes
const t_ind	n
	Number of spatial dimensions for the tensor.
std::vector< Real >	v
	The actual tensor component values.

Private Member Functions
void	define3Dtransform (const Vec3 &v1, const Vec3 &v2, const Vec3 &v3)
	Creates a 3D transformation from three unit vectors.

Friends
Vec3	operator* (const Tensor &T, const Vec3 &v)
	Multiplication between a tensor and a point vector.
Vec3	operator* (const Vec3 &v, const Tensor &T)
	Multiplication between a point vector and transpose of a tensor.
Tensor	operator* (const Tensor &A, const Tensor &B)
	Multiplication between two tensors.
Tensor	operator* (Real a, const Tensor &T)
	Multiplication between a scalar and a tensor.
std::ostream &	operator<< (std::ostream &os, const Tensor &T)
	Output stream operator.

Detailed Description

Simple class for representing a non-symmetric second-order tensor.

Constructor & Destructor Documentation

Tensor() [1/4]

Tensor::Tensor ( const Vec3 &  vn, bool  vnIsX = false  )

explicit

Constructor creating a transformation from a face normal vector.

The provided vector vn is taken as the local Z-axis. The local X- and Y-axes are then defined by projecting either the global X- or Y-axis onto the normal plane, depending on whether vn points mostly in the global Y- or X-direction, respectively.

If vnIsX is true, vn is taken as the local X-axis instead and the other two axes are shifted accordingly.

References Vec3::cross(), define3Dtransform(), Vec3::normalize(), Vec3::x, Vec3::y, and Vec3::z.

Tensor() [2/4]

Tensor::Tensor	(	const Vec3 &	t1,
		const Vec3 &	t2,
		bool	t1isZ = false,
		bool	t2isXZ = false
	)

Constructor creating a transformation from two tangent vectors.

The first tangent vector t1 is taken as the local X-axis (or Z-axis, if t1isZ is true). The local Z-axis (X-axis) is then defined as the cross product between t1 and t2. If t2isXZ is true, the local Y-axis is instead defined as the cross product between t2 and t1.

References Vec3::cross(), define3Dtransform(), and Vec3::normalize().

Tensor() [3/4]

Tensor::Tensor	(	const Vec3 &	v1,
		const Vec3 &	v2,
		const Vec3 &	v3
	)

Constructor creating a transformation from three unit vectors.

This constructor assumes the three vectors provided form an orthonormal basis.

References define3Dtransform().

Tensor() [4/4]

Tensor::Tensor	(	Real	a1,
		Real	a2,
		Real	a3
	)

Constructor creating a transformation from three rotation angles.

This constructor computes an incremental rotation tensor from the given rotation angles via a quaternion representation of the rotation. The angles provided are those related to a Rodrigues parameterization.

References epsZ, Vec3::length(), Real, v, Vec3::x, Vec3::y, and Vec3::z.

Member Function Documentation

index()

virtual t_ind Tensor::index ( t_ind  i, t_ind  j  ) const

inlineprotectedvirtual

Returns a 0-based array index for the given tensor indices.

Assuming column-wise storage for non-symmetric tensors.

Reimplemented in SymmTensor.

References n.

Referenced by operator()(), and rotVec().

inverse()

Real Tensor::inverse ( Real  tol = Real(0) )

virtual

Inverts the tensor.

Parameters

[in]

tol

Division by zero tolerance

Returns

Determinant of the tensor

Reimplemented in SymmTensor.

References det(), n, Real, and v.

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

• src/Utility/Tensor.h
• src/Utility/Tensor.C