OrthogonalUniVariatePolynomialFamily¶

class
OrthogonalUniVariatePolynomialFamily
(*args)¶ Base class for orthogonal univariate polynomial factories.
Methods
build
(degree)Build the th order orthogonal univariate polynomial.
Accessor to the object’s name.
getId
()Accessor to the object’s id.
Accessor to the underlying implementation.
Accessor to the associated probability measure.
getName
()Accessor to the object’s name.
Build the th order quadrature scheme.
Accessor to the recurrence coefficients of the th order.
getRoots
(n)Accessor to the recurrence coefficients of the th order.
setName
(name)Accessor to the object’s name.

__init__
(*args)¶ Initialize self. See help(type(self)) for accurate signature.

build
(degree)¶ Build the th order orthogonal univariate polynomial.
 Parameters
 kint,
Polynomial order.
 Returns
 polynomial
OrthogonalUniVariatePolynomial
Requested orthogonal univariate polynomial.
 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
The implementation class.

getMeasure
()¶ Accessor to the associated probability measure.
 Returns
 measure
Distribution
The associated probability measure (according to which the polynomials are orthogonal).
 measure
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.

getNodesAndWeights
(n)¶ Build the th order quadrature scheme.
Associated with the orthogonal univariate polynomials family.
 Parameters
 kint,
Polynomial order.
 Returns
Examples
>>> import openturns as ot >>> polynomial_factory = ot.HermiteFactory() >>> nodes, weights = polynomial_factory.getNodesAndWeights(3) >>> print(nodes) [1.73205,...,1.73205] >>> print(weights) [0.166667,0.666667,0.166667]

getRecurrenceCoefficients
(n)¶ Accessor to the recurrence coefficients of the th order.
Of the orthogonal univariate polynomial.
 Parameters
 kint,
Polynomial order.
 Returns
 recurrence_coefficients
Point
The recurrence coefficients of the th order orthogonal univariate polynomial.
 recurrence_coefficients
Notes
Any sequence of orthogonal polynomials has a recurrence formula relating any three consecutive polynomials as follows:
Examples
>>> import openturns as ot >>> polynomial_factory = ot.HermiteFactory() >>> print(polynomial_factory.getRecurrenceCoefficients(3)) [0.5,0,0.866025]

getRoots
(n)¶ Accessor to the recurrence coefficients of the th order.
Of the orthogonal univariate polynomial.
 Parameters
 kint,
Polynomial order.
 Returns
 roots
Point
The roots of the th order orthogonal univariate polynomial.
 roots
Examples
>>> import openturns as ot >>> polynomial_factory = ot.HermiteFactory() >>> print(polynomial_factory.getRoots(3)) [1.73205,...,1.73205]

setName
(name)¶ Accessor to the object’s name.
 Parameters
 namestr
The name of the object.
