OrthogonalUniVariateFunctionFamily¶

class OrthogonalUniVariateFunctionFamily(*args)¶

Base class for orthogonal univariate polynomial factories.

See also

Attributes:	`thisown` The membership flag

Methods

`build`(order)	Build the $k$ -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 $k$ -th order orthogonal univariate polynomial.

Parameters:	k : int, $0 \leq k$ 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 $w(x) \di{x}$ if and only if their dot product:

$\langle P, Q \rangle = \int_{\alpha}^{\beta} P(x) Q(x) w(x)\di{x} = 0$

where $\alpha \in \Rset \cup \{-\infty\}$ and $\beta \in \Rset \cup \{+\infty\}$ .

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.

OpenTURNS