OrthogonalUniVariateFunctionFamily

class OrthogonalUniVariateFunctionFamily(*args)

Base class for orthogonal univariate polynomial factories.

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()	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.

See also

StandardDistributionPolynomialFactory

__init__(*args)

build(order)

Build the -th order orthogonal univariate polynomial.

Parameters:

kint,

Polynomial order.

Returns:

polynomialOrthogonalUniVariatePolynomial

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_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.

getMeasure()

Accessor to the associated probability measure.

Returns:

measureDistribution

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:

namestr

The name of the object.

setName(name)

Accessor to the object’s name.

Parameters:

namestr

The name of the object.