SymmetricTensor

class SymmetricTensor(*args)

Symmetric tensor.

Available constructors:

SymmetricTensor(n_rows, n_sheets)

SymmetricTensor(n_rows, n_sheets, values)

SymmetricTensor(sequence)

Parameters:

n_rows : int, n_r > 0

Number of rows and columns.

n_sheets : int, n_s > 0

Number of sheets.

values : sequence of float with size n_r \times n_r \times n_s, optional

Values. OpenTURNS uses column-major ordering (like Fortran) for reshaping the flat list of values. If not mentioned, a zero tensor is created.

sequence : sequence of float

Values.

Examples

>>> import openturns as ot
>>> print(ot.SymmetricTensor(2, 2, [0, 1]))
sheet #0
[[ 0 1 ]
 [ 1 0 ]]
sheet #1
[[ 0 0 ]
 [ 0 0 ]]
>>> T = ot.SymmetricTensor(2, 3, range(2*2*3))
>>> print(T)
sheet #0
[[  0  1 ]
 [  1  3 ]]
sheet #1
[[  4  5 ]
 [  5  7 ]]
sheet #2
[[  8  9 ]
 [  9 11 ]]

Get or set terms:

>>> print(T[0, 0, 0])
0.0
>>> T[0, 0, 0] = 1.0
>>> print(T[0, 0, 0])
1.0

Create an openturns tensor from a sequence:

>>> T = ot.SymmetricTensor([[[1.0, 2.0, 3.0], [7.0, 8.0, 9.0]], [[7.0, 8.0, 9.0], [10.0, 11.0, 12.0]]])
>>> print(T)
sheet #0
[[  1  7 ]
 [  7 10 ]]
sheet #1
[[  2  8 ]
 [  8 11 ]]
sheet #2
[[  3  9 ]
 [  9 12 ]]

Methods

checkSymmetry() Check if the internal representation is really symmetric.
clean(threshold) Set elements smaller than a threshold to zero.
getClassName() Accessor to the object’s name.
getId() Accessor to the object’s id.
getImplementation(*args) Accessor to the underlying implementation.
getName() Accessor to the object’s name.
getNbColumns() Accessor to the number of columns.
getNbRows() Accessor to the number of rows.
getNbSheets() Accessor to the number of sheets.
getSheet(k) Get a sheet of the tensor.
isEmpty() Tell if the tensor is empty.
setName(name) Accessor to the object’s name.
setSheet(k, m) Set a matrix as a sheet of the complex tensor.
__init__(*args)
checkSymmetry()

Check if the internal representation is really symmetric.

clean(threshold)

Set elements smaller than a threshold to zero.

Parameters:

threshold : float

Threshold for zeroing elements.

Returns:

cleaned_tensor : Tensor

Input tensor with elements smaller than the threshold set to zero.

getClassName()

Accessor to the object’s name.

Returns:

class_name : str

The object class name (object.__class__.__name__).

getId()

Accessor to the object’s id.

Returns:

id : int

Internal unique identifier.

getImplementation(*args)

Accessor to the underlying implementation.

Returns:

impl : Implementation

The implementation class.

getName()

Accessor to the object’s name.

Returns:

name : str

The name of the object.

getNbColumns()

Accessor to the number of columns.

Returns:n_columns : int
getNbRows()

Accessor to the number of rows.

Returns:n_rows : int
getNbSheets()

Accessor to the number of sheets.

Returns:n_sheets : int

Examples

>>> import openturns as ot
>>> T = ot.Tensor(2, 2, 3, range(2*2*3))
>>> print(T.getNbSheets())
3
getSheet(k)

Get a sheet of the tensor.

Parameters:

sheet : int

Index of sheet element.

Returns:

M : Matrix

The sheet element.

Examples

>>> import openturns as ot
>>> T = ot.Tensor(2, 2, 3, range(2*2*3))
>>> print(T.getSheet(1))
[[ 4 6 ]
 [ 5 7 ]]
isEmpty()

Tell if the tensor is empty.

Returns:

is_empty : bool

True if the tensor contains no element.

Examples

>>> import openturns as ot
>>> T = ot.Tensor()
>>> T.isEmpty()
True
setName(name)

Accessor to the object’s name.

Parameters:

name : str

The name of the object.

setSheet(k, m)

Set a matrix as a sheet of the complex tensor.

Parameters:

sheet : int

Index of sheet element.

M : Matrix

The matrix.

Examples

>>> import openturns as ot
>>> T = ot.Tensor(2, 2, 3, range(2*2*3))
>>> print(T)
sheet #0
[[  0  2 ]
 [  1  3 ]]
sheet #1
[[  4  6 ]
 [  5  7 ]]
sheet #2
[[  8 10 ]
 [  9 11 ]]
>>> M = ot.Matrix([[1, 2],[3, 4]])
>>> T.setSheet(0, M)
>>> print(T)
sheet #0
[[  1  2 ]
 [  3  4 ]]
sheet #1
[[  4  6 ]
 [  5  7 ]]
sheet #2
[[  8 10 ]
 [  9 11 ]]