ONBasis

An ONBasis (=orthonormal basis) stores information for the orthogonal polynomials of the disctribution, like norms, quadrature rules and cached evaluations at quadrature points. It is the main building brick for the tensorized basis associated to the multi-indices of the stochastic discretization.

ExtendableASGFEM.ONBasis — Type

ONBasis(
    OBT::Type{<:OrthogonalPolynomialType},
    maxorder;
    ...
) -> ONBasis{Float64}
ONBasis(
    OBT::Type{<:OrthogonalPolynomialType},
    maxorder,
    maxquadorder;
    T
) -> ONBasis{Float64}

Constructs an ONBasis for the given OrthogonalPolynomialType (and the associated weight function) and the maximal polynomial order.

ExtendableASGFEM.ONBasis — Type

struct ONBasis{T<:Real, OBT<:OrthogonalPolynomialType, npoly, nquad}

Structure that stores information of an orthogonal basis, i.e., their norms, quadrature rules and values at reference points, and the result of the last evaluate call.

ExtendableASGFEM.OrthogonalPolynomialType — Method

OrthogonalPolynomialType(ONB::ONBasis{T, OBT}) -> Any

returns the OrthogonalPolynomialType

ExtendableASGFEM.distribution — Method

distribution(ONB::ONBasis{T, OBT}) -> Any

returns the distribution associated to the orthogonal polynomials

ExtendableASGFEM.evaluate — Method

evaluate(
    ONB::ONBasis{T, OBT, maxorder},
    x;
    normalize
) -> Vector

Evaluates all basis polynomials at point x

ExtendableASGFEM.integral — Method

integral(ONB::ONBasis, j; normalize) -> Any

Evaluates the integral of a single basis function.

ExtendableASGFEM.norm4poly — Method

norm4poly(ONB::ONBasis, p) -> Any

returns the norm of the p-th polynomial

ExtendableASGFEM.qp — Method

qp(
    ONB::ONBasis
) -> StaticArraysCore.SVector{nquad, T} where {T<:Real, nquad}

returns the quadrature points

ExtendableASGFEM.qw — Method

qw(
    ONB::ONBasis
) -> StaticArraysCore.SVector{nquad, T} where {T<:Real, nquad}

returns the quadrature weights

ExtendableASGFEM.scalar_product — Method

scalar_product(ONB::ONBasis, j, k; normalize) -> Any

Evaluates the scalar product of two basis functions.

ExtendableASGFEM.triple_product — Method

triple_product(ONB::ONBasis, j, k, l; normalize) -> Any

Evaluates the triple product of three basis functions.

ExtendableASGFEM.triple_product_y — Method

triple_product_y(ONB::ONBasis, j, k; normalize) -> Any

Evaluates the triple product of two basis functions and y.

ExtendableASGFEM.vals4poly — Method

vals4poly(ONB::ONBasis, p) -> Any

returns the values of the p-th polynomial at all quadrature points

ExtendableASGFEM.vals4qp — Method

vals4qp(ONB::ONBasis, k) -> Any

returns the values of all polynomials at the k-th quadrature point

ExtendableASGFEM.vals4xref — Method

vals4xref(
    ONB::ONBasis
) -> StaticArraysCore.SMatrix{nquad, npoly, T} where {T<:Real, npoly, nquad}

returns the values of all polynomials at the quadrature points