Package Scientific :: Package Geometry :: Class Tensor

Class Tensor

Tensor in 3D space

Tensors support the usual arithmetic operations ('t1', 't2': tensors, 'v': vector, 's': scalar):

't1+t2' (addition)
't1-t2' (subtraction)
't1*t2' (tensorial (outer) product)
't1*v' (contraction with a vector, same as t1.dot(v.asTensor()))
's*t1', 't1*s' (multiplication with a scalar)
't1/s' (division by a scalar)

The coordinates can be extracted by indexing; a tensor of rank N can be indexed like an array of dimension N.

Tensors are immutable, i.e. their elements cannot be changed.

Tensor elements can be any objects on which the standard arithmetic operations are defined. However, eigenvalue calculation is supported only for float elements.

Instance Methods

__add__(self, other)

__cmp__(self, other)

__div__(self, other)

__getitem__(self, index)

__init__(self, elements, nocheck=None)

__len__(self)

__mul__(self, other)

__neg__(self)

__radd__(self, other)

__rdiv__(self, other)

__repr__(self)

__rmul__(self, other)

__rsub__(self, other)

__str__(self)

__sub__(self, other)

Scientific.Geometry.Vector

asVector(self)
Returns: an equivalent vector object

Tensor

asymmetricalPart(self)
Returns: the asymmetrical part of the tensor

diagonal(self, axis1=0, axis2=1)

(Numeric.array, Tensor)

diagonalization(self)
Returns: the eigenvalues of the tensor and a tensor representing the rotation matrix to the diagonal form

Tensor

dot(self, other)
Returns: the contraction with other

Numeric.array

eigenvalues(self)
Returns: the eigenvalues of the tensor

Tensor

inverse(self)
Returns: the inverse of the tensor

Tensor

symmetricalPart(self)
Returns: the symmetrical part of the tensor

type of tensor elements

trace(self, axis1=0, axis2=1)
Returns: the trace of the tensor

Tensor

transpose(self)
Returns: the transposed (index reversed) tensor

Class Variables
	is_tensor = `1`

Method Details

init(self, elements, nocheck=None)
(Constructor)

Parameters:

elements (Numeric.array or list) - 2D array or nested list specifying the nine tensor components [[xx, xy, xz], [yx, yy, yz], [zx, zy, zz]]

asVector(self)

Returns: Scientific.Geometry.Vector

an equivalent vector object

Raises:

ValueError - if rank > 1

asymmetricalPart(self)

Returns: Tensor

the asymmetrical part of the tensor

Raises:

ValueError - if rank !=2

diagonalization(self)

Returns: (Numeric.array, Tensor)

the eigenvalues of the tensor and a tensor representing the rotation matrix to the diagonal form

Raises:

ValueError - if rank !=2

dot(self, other)

Returns: Tensor: the contraction with other

eigenvalues(self)

Returns: Numeric.array

the eigenvalues of the tensor

Raises:

ValueError - if rank !=2

inverse(self)

Returns: Tensor

the inverse of the tensor

Raises:

ValueError - if rank !=2

symmetricalPart(self)

Returns: Tensor

the symmetrical part of the tensor

Raises:

ValueError - if rank !=2

trace(self, axis1=0, axis2=1)

Returns: type of tensor elements

the trace of the tensor

Raises:

ValueError - if rank !=2

transpose(self)

Returns: Tensor: the transposed (index reversed) tensor

Class Tensor

__init__(self, elements, nocheck=None) (Constructor)

asVector(self)

asymmetricalPart(self)

diagonalization(self)

dot(self, other)

eigenvalues(self)

inverse(self)

symmetricalPart(self)

trace(self, axis1=0, axis2=1)

transpose(self)

init(self, elements, nocheck=None)
(Constructor)