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]
isFinite()

Tell whether the basis is finite.

Returns:
isFinitebool

True if the basis is finite.

isOrthogonal()

Tell whether the basis is orthogonal.

Returns:
isOrthogonalbool

True if the basis is orthogonal.

setName(name)

Accessor to the object’s name.

Parameters:
namestr

The name of the object.

Examples using the class

Estimate a GEV on the Port Pirie sea-levels data

Estimate a GEV on the Port Pirie sea-levels data

Estimate a GPD on the daily rainfall data

Estimate a GPD on the daily rainfall data

Estimate a GEV on race times data

Estimate a GEV on race times data

Estimate a GEV on the Fremantle sea-levels data

Estimate a GEV on the Fremantle sea-levels data

Create a functional basis process

Create a functional basis process

Create a process from random vectors and processes

Create a process from random vectors and processes

Trend computation

Trend computation

Create a general linear model metamodel

Create a general linear model metamodel

Mixture of experts

Mixture of experts

Perform stepwise regression

Perform stepwise regression

Kriging: propagate uncertainties

Kriging: propagate uncertainties

Kriging : multiple input dimensions

Kriging : multiple input dimensions

Kriging : draw the likelihood

Kriging : draw the likelihood

Kriging : cantilever beam model

Kriging : cantilever beam model

Kriging: choose an arbitrary trend

Kriging: choose an arbitrary trend

Kriging the cantilever beam model using HMAT

Kriging the cantilever beam model using HMAT

Example of multi output Kriging on the fire satellite model

Example of multi output Kriging on the fire satellite model

Kriging : generate trajectories from a metamodel

Kriging : generate trajectories from a metamodel

Kriging: choose a polynomial trend on the beam model

Kriging: choose a polynomial trend on the beam model

Kriging with an isotropic covariance function

Kriging with an isotropic covariance function

Kriging: metamodel of the Branin-Hoo function

Kriging: metamodel of the Branin-Hoo function

Kriging : quick-start

Kriging : quick-start

Kriging: configure the optimization solver

Kriging: configure the optimization solver

Kriging: choose a polynomial trend

Kriging: choose a polynomial trend

Advanced Kriging

Advanced Kriging

Kriging: metamodel with continuous and categorical variables

Kriging: metamodel with continuous and categorical variables

Estimate Sobol indices on a field to point function

Estimate Sobol indices on a field to point function

Create multivariate functions

Create multivariate functions

Create a multivariate basis of functions from scalar multivariable functions

Create a multivariate basis of functions from scalar multivariable functions

Compute leave-one-out error of a polynomial chaos expansion

Compute leave-one-out error of a polynomial chaos expansion

Compute confidence intervals of a regression model from data

Compute confidence intervals of a regression model from data

EfficientGlobalOptimization examples

EfficientGlobalOptimization examples