OrthogonalUniVariateFunctionFamily

class OrthogonalUniVariateFunctionFamily(*args)

Base class for orthogonal univariate polynomial factories.

Methods

build(self, order)

Build the k-th order orthogonal univariate polynomial.

getClassName(self)

Accessor to the object’s name.

getId(self)

Accessor to the object’s id.

getImplementation(self, \*args)

Accessor to the underlying implementation.

getMeasure(self)

Accessor to the associated probability measure.

getName(self)

Accessor to the object’s name.

setName(self, name)

Accessor to the object’s name.

__init__(self, *args)

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

build(self, order)

Build the k-th order orthogonal univariate polynomial.

Parameters
kint, 0 \leq k

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(self)

Accessor to the object’s name.

Returns
class_namestr

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

getId(self)

Accessor to the object’s id.

Returns
idint

Internal unique identifier.

getImplementation(self, *args)

Accessor to the underlying implementation.

Returns
implImplementation

The implementation class.

getMeasure(self)

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 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(self)

Accessor to the object’s name.

Returns
namestr

The name of the object.

setName(self, name)

Accessor to the object’s name.

Parameters
namestr

The name of the object.