TransportMaps.jl

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Bases ​

Index ​

Types ​

TransportMaps.HermiteBasis Type
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HermiteBasis

Probabilist Hermite polynomial basis.

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TransportMaps.LinearizedHermiteBasis Type
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LinearizedHermiteBasis

Probabilist Hermite polynomial basis with linearization outside specified bounds.

Fields

  • linearizationbounds::Vector{Float64}: lower and upper bounds for linearization.

  • normalization::Vector{Float64}: normalization factors for each degree.

Constructors

  • LinearizedHermiteBasis(; lower=-Inf, upper=Inf, normalization=Float64[]): Explicit constructor with specified bounds and normalization.

  • LinearizedHermiteBasis(max_degree::Int): Construct with default normalization for given maximum degree.

  • LinearizedHermiteBasis(samples::Vector{<:Real}, max_degree::Int, k::Int): Construct bounds from 1st and 99th percentile of samples.

  • LinearizedHermiteBasis(density::Distributions.UnivariateDistribution, max_degree::Int, k::Int): Construct bounds from 1st and 99th percentile of reference density.

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TransportMaps.CubicSplineHermiteBasis Type
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CubicSplineHermiteBasis

Probabilist Hermite polynomial basis with cubic spline edge control.

Fields

  • radius::Float64: radius of the spline for edge control.

Constructors

  • CubicSplineHermiteBasis(radius::Float64=3.0): Explicit constructor with radius=3.0

  • CubicSplineHermiteBasis(samples::Vector{<:Real}): Construct radius from from 1st and 99th percentile of samples.

  • CubicSplineHermiteBasis(density::Distributions.UnivariateDistribution): Construct radius from 1st and 99th percentile of reference density.

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TransportMaps.GaussianWeightedHermiteBasis Type
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GaussianWeightedHermiteBasis

Probabilist Hermite polynomial basis with Gaussian weight for edge control.

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TransportMaps.LegendreBasis Type
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LegendreBasis

Legendre polynomial basis, orthogonal with respect to uniform measure on [-1, 1].

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TransportMaps.ShiftedLegendreBasis Type
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ShiftedLegendreBasis

Shifted Legendre polynomial basis, orthogonal with respect to uniform measure on [0, 1]. The shifted Legendre polynomials are obtained by transforming the standard Legendre polynomials:   .

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TransportMaps.MultivariateBasis Type
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MultivariateBasis{T<:AbstractPolynomialBasis}

A multivariate polynomial basis function constructed as a tensor product of univariate polynomial bases.

Fields

  • multiindexset::Vector{Int}: Multi-index representing the polynomial degrees for each dimension

  • univariatebases::Vector{T}: Vector of univariate basis functions, one for each dimension

Constructors

  • MultivariateBasis(multiindexset::Vector{Int}, ::Type{T}) where T<:AbstractPolynomialBasis: Create a multivariate basis with the specified multi-index and basis type.

  • MultivariateBasis(multiindexset::Vector{Int}, basistype::AbstractPolynomialBasis): Constructor that accepts a basis instance instead of a type.

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Functions ​

TransportMaps.basisfunction Function
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basisfunction(basis::HermiteBasis, αᵢ::Int, zᵢ::Real)

Evaluate HermiteBasis with degree αᵢ at zᵢ.

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basisfunction(basis::LegendreBasis, αᵢ::Int, zᵢ::Real)

Evaluate LegendreBasis with degree αᵢ at zᵢ.

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basisfunction(basis::ShiftedLegendreBasis, αᵢ::Int, zᵢ::Real)

Evaluate ShiftedLegendreBasis with degree αᵢ at zᵢ ∈ [0,1].

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basisfunction(basis::LinearizedHermiteBasis, αᵢ::Int, zᵢ::Real)

Evaluate LinearizedHermiteBasis with degree αᵢ at zᵢ.

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basisfunction(basis::CubicSplineHermiteBasis, αᵢ::Int, zᵢ::Real)

Evaluate CubicSplineHermiteBasis with degree αᵢ at zᵢ.

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basisfunction(basis::GaussianWeightedHermiteBasis, αᵢ::Int, zᵢ::Real)

Evaluate GaussianWeightedHermiteBasis with degree αᵢ at zᵢ.

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TransportMaps.basisfunction_derivative Function
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basisfunction_derivative(basis::HermiteBasis, αᵢ::Int, zᵢ::Real)

Evaluate derivative of HermiteBasis with degree αᵢ at zᵢ.

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basisfunction_derivative(basis::LegendreBasis, αᵢ::Int, zᵢ::Real)

Evaluate derivative of LegendreBasis with degree αᵢ at zᵢ.

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basisfunction_derivative(basis::ShiftedLegendreBasis, αᵢ::Int, zᵢ::Real)

Evaluate derivative of ShiftedLegendreBasis with degree αᵢ at zᵢ ∈ [0,1].

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basisfunction_derivative(basis::LinearizedHermiteBasis, αᵢ::Int, zᵢ::Real)

Evaluate derivative of LinearizedHermiteBasis with degree αᵢ at zᵢ.

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basisfunction_derivative(basis::CubicSplineHermiteBasis, αᵢ::Int, zᵢ::Real)

Evaluate derivative of CubicSplineHermiteBasis with degree αᵢ at zᵢ.

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basisfunction_derivative(basis::GaussianWeightedHermiteBasis, αᵢ::Int, zᵢ::Real)

Evaluate derivative of GaussianWeightedHermiteBasis with degree αᵢ at zᵢ.

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