# Basic map Routines

MParT.EvaluateFunction
Evaluate(map, points)

Evaluates the function map at points, where each column of points is a different sample.

If map $:\mathbb{R}^m\to\mathbb{R}^n$, then points $\in\mathbb{R}^m\times\mathbb{R}^k$, where $k$ is the number of points.

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MParT.InverseFunction
Inverse(map, y, x)

If map represents function $T(y,x)$, then this function calculates $T(y,\cdot)^{-1}(x)$.

If map is square, you still require y, but it can be a 0 x k matrix.

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MParT.ComposedMapType
ComposedMap(maps::Vector)

Creates a ComposedMap from a vector of ConditionalMapBase objects.

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MParT.MapOptionsFunction
MapOptions(;kwargs...)

Creates options for parameterized map.

All possible keyword arguments are in example, with some important arguments described below. See C++ documentation for an exhaustive description.

Arguments

• basisType::String: Includes "ProbabilistHermite", "PhysicistHermite", "HermiteFunctions"
• basisLB::Float64,basisUB::Float64: The bounds for where we start linearizing the map. These default to infinities, but often making the data near the origin and setting them to a small finite number (e.g. +-3) works well.

Example

julia> MapOptions(basisType="HermiteFunctions", basisLB=-3., basisUB=3.)
basisType = HermiteFunctions
basisLB = -3
basisUB = 3
basisNorm = true
posFuncType = SoftPlus
contDeriv = true
nugget = 0

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MParT.TriangularMapType
TriangularMap(maps::Vector, move_coeffs::Bool = true)

Creates a TriangularMap from a vector of ConditionalMapBase objects.

TODO: The new object takes ownership of the coeffs of the maps in maps if move_coeffs is true.

Examples

julia> dim, order = 5, 3;

julia> msets = [FixedMultiIndexSet(d, order) for d in 1:dim];

julia> opts = MapOptions();

julia> components = [CreateComponent(mset, opts) for mset in msets];

julia> trimap = TriangularMap(components);
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MParT.CreateTriangularFunction
CreateTriangular(inDim::Int, outDim::Int, p::Int, opts::MapOptions)

Creates a total order p map with dimensions inDim and outDim with specifications opts.

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MParT.CreateComponentFunction
CreateComponent(mset::FixedMultiIndexSet, opts::MapOptions)

Create a single-output component with approximation order given by mset and specified by opts

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