Basis¶

class Basis(*args)¶

Basis.

Available constructors:

Basis(functionsColl)

Basis(size)

Parameters:

functionsColllist of Function: Functions constituting the Basis.
sizeint: Size of the Basis.

Examples

>>> import openturns as ot
>>> dimension = 3
>>> input = ['x0', 'x1', 'x2']
>>> functions = []
>>> for i in range(dimension):
...     functions.append(ot.SymbolicFunction(input, [input[i]]))
>>> basis = ot.Basis(functions)

Methods

`add`(elt)	Add a function.
`build`(index)	Build the element of the given index.
`getClassName`()	Accessor to the object's name.
`getId`()	Accessor to the object's id.
`getImplementation`()	Accessor to the underlying implementation.
`getInputDimension`()	Get the input dimension of the Basis.
`getName`()	Accessor to the object's name.
`getOutputDimension`()	Get the output dimension of the Basis.
`getSize`()	Get the size of the Basis.
`getSubBasis`(indices)	Get a sub-basis of the Basis.
`isFinite`()	Tell whether the basis is finite.
`isOrthogonal`()	Tell whether the basis is orthogonal.
`setName`(name)	Accessor to the object's name.

__init__(*args)¶

add(elt)¶

Add a function.

Parameters:

functiona Function: Function to be added.

build(index)¶

Build the element of the given index.

Parameters:

indexint, $index \geq 0$: Index of an element of the Basis.

Returns:

functionFunction: The function at the index index of the Basis.

Examples

>>> import openturns as ot
>>> dimension = 3
>>> input = ['x0', 'x1', 'x2']
>>> functions = []
>>> for i in range(dimension):
...     functions.append(ot.SymbolicFunction(input, [input[i]]))
>>> basis = ot.Basis(functions)
>>> print(basis.build(0).getEvaluation())
[x0,x1,x2]->[x0]

getClassName()¶

Accessor to the object’s name.

Returns:

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

getId()¶

Accessor to the object’s id.

Returns:

idint: Internal unique identifier.

getImplementation()¶

Accessor to the underlying implementation.

Returns:

implImplementation: A copy of the underlying implementation object.

getInputDimension()¶

Get the input dimension of the Basis.

Returns:

inDimint: Input dimension of the functions.

getName()¶

Accessor to the object’s name.

Returns:

namestr: The name of the object.

getOutputDimension()¶

Get the output dimension of the Basis.

Returns:

outDimint: Output dimension of the functions.

getSize()¶

Get the size of the Basis.

Returns:

sizeint: Size of the Basis.

getSubBasis(indices)¶

Get a sub-basis of the Basis.

Parameters:

indiceslist of int: Indices of the terms of the Basis put in the sub-basis.

Returns:

subBasislist of Function: Functions defining a sub-basis.

Examples

>>> import openturns as ot
>>> dimension = 3
>>> input = ['x0', 'x1', 'x2']
>>> functions = []
>>> for i in range(dimension):
...     functions.append(ot.SymbolicFunction(input, [input[i]]))
>>> basis = ot.Basis(functions)
>>> subbasis = basis.getSubBasis([1])
>>> print(subbasis[0].getEvaluation())
[x0,x1,x2]->[x1]