OrthogonalUniVariateFunctionFamily

class OrthogonalUniVariateFunctionFamily(*args)

Base class for orthogonal univariate polynomial factories.

See also

StandardDistributionPolynomialFactory

Methods

build(order)	Build the -th order orthogonal univariate polynomial.
getClassName()	Accessor to the object’s name.
getId()	Accessor to the object’s id.
getImplementation(*args)	Accessor to the underlying implementation.
getMeasure()	Accessor to the associated probability measure.
getName()	Accessor to the object’s name.
setName(name)	Accessor to the object’s name.

__init__(*args)

Initialize self. See help(type(self)) for accurate signature.

build(order)

Build the -th order orthogonal univariate polynomial.

Parameters:

k : int,

Polynomial order.

Returns:

polynomial : OrthogonalUniVariatePolynomial

Requested orthogonal univariate polynomial.

Examples

>>> import openturns as ot
>>> polynomial_factory = ot.HermiteFactory()
>>> print(polynomial_factory.build(2))
-0.707107 + 0.707107 * X^2

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.

getMeasure()

Accessor to the associated probability measure.

Returns:

measure : Distribution

The associated probability measure (according to which the polynomials are orthogonal).

Notes

Two polynomials P and Q are orthogonal with respect to the probability measure if and only if their dot product:

where and .

Examples

>>> import openturns as ot
>>> polynomial_factory = ot.HermiteFactory()
>>> print(polynomial_factory.getMeasure())
Normal(mu = 0, sigma = 1)

getName()

Accessor to the object’s name.

Returns:

name : str

The name of the object.

setName(name)

Accessor to the object’s name.

Parameters:

name : str

The name of the object.