GroupedTransform

GroupedTransform

A struct to describe a GroupedTransformation

Fields

• system::String - choice of "exp" or "cos" or "chui1" or "chui2" or "chui3" or "chui4"
• setting::Vector{NamedTuple{(:u, :mode, :bandwidths),Tuple{Vector{Int},Module,Vector{Int}}}} - vector of the dimensions, mode, and bandwidths for each term/group, see also get_setting(system::String,d::Int,ds::Int,N::Vector{Int})::Vector{NamedTuple{(:u, :mode, :bandwidths),Tuple{Vector{Int},Module,Vector{Int}}}} and get_setting(system::String,U::Vector{Vector{Int}},N::Vector{Int})::Vector{NamedTuple{(:u, :mode, :bandwidths),Tuple{Vector{Int},Module,Vector{Int}}}}
• X::Array{Float64} - array of nodes
• transforms::Vector{Tuple{Int64,Int64}} - holds the low-dimensional sub transformations

Constructor

GroupedTransform( system, setting, X )

Additional Constructor

GroupedTransform( system, d, ds, N::Vector{Int}, X )
GroupedTransform( system, U, N, X )

*( F::GroupedTransform, fhat::GroupedCoefficients )::Vector{<:Number}

Overloads the * notation in order to achieve f = F*fhat.

*( F::GroupedTransform, f::Vector{<:Number} )::GroupedCoefficients

Overloads the * notation in order to achieve the adjoint transform f = F*f.

adjoint( F::GroupedTransform )::GroupedTransform

Overloads the F' notation and gives back the same GroupdTransform. GroupedTransform decides by the input if it is the normal trafo or the adjoint so this is only for convinience.

F::GroupedTransform[u::Vector{Int}]::LinearMap{<:Number} or SparseArray

This function overloads getindex of GroupedTransform such that you can do F[[1,3]] to obtain the transform of the corresponding ANOVA term defined by u.

get_matrix( F::GroupedTransform )::Matrix{<:Number}

This function returns the actual matrix of the transformation. This is not available for the wavelet basis