GroupedCoefficients

GroupedCoefficientsComplex

A struct to hold complex coefficients belonging to indices in a grouped index set

\[ \mathcal{I}_{\pmb{N}}(U) = \left\{ \pmb{k} \in \Z^d : \mathrm{supp} \pmb{k} \in U, \pmb{k}_{\mathrm{supp} \pmb{k}} \in [- \frac{N_{\mathrm{supp} \pmb{k} }}{2}, \frac{N_{ \mathrm{supp} \pmb{k} }}{2} - 1 ) \right\}.\]

Fields

• setting::Vector{NamedTuple{(:u, :mode, :bandwidths),Tuple{Vector{Int},Module,Vector{Int}}}} - uniquely describes the setting such as the bandlimits $N_{\pmb u}$, 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}}}}
• data::Union{Vector{ComplexF64},Nothing} - the vector of coefficients

Constructor

GroupedCoefficientsComplex( setting, data = nothing )

Additional Constructor

GroupedCoefficients( setting, data = nothing )

GroupedCoefficientsReal

A struct to hold real valued coefficients belonging to indices in a grouped index set

\[ \mathcal{I}_{\pmb{N}}(U) = \left\{ \pmb{k} \in \Z^d : \mathrm{supp} \pmb{k} \in U, \pmb{k}_{\mathrm{supp} \pmb{k}} \in [0, N_{\mathrm{supp} \pmb{k} } - 1 ] \right\}.\]

Fields

• setting::Vector{NamedTuple{(:u, :mode, :bandwidths),Tuple{Vector{Int},Module,Vector{Int}}}} - uniquely describes the setting such as the bandlimits $N_{\pmb u}$, 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}}}}
• data::Union{Vector{Float64},Nothing} - the vector of coefficients

Constructor

GroupedCoefficientsReal( setting, data = nothing )

Additional Constructor

GroupedCoefficients( setting, data = nothing )

*( z::Number, fhat::GroupedCoefficients )::GroupedCoefficients

This function defines the multiplication of a number with a GroupedCoefficients object.

+( z::Number, fhat::GroupedCoefficients )::GroupedCoefficients

This function defines the addition of two GroupedCoefficients objects.

-( z::Number, fhat::GroupedCoefficients )::GroupedCoefficients

This function defines the subtraction of two GroupedCoefficients objects.

fhat::GroupedCoefficients[idx::Int]

This function overloads getindex of GroupedCoefficients such that you can do fhat[1] to obtain the basis coefficient determined by idx.

fhat::GroupedCoefficients[u::Vector{Int}]

This function overloads getindex of GroupedCoefficients such that you can do fhat[[1,3]] to obtain the basis coefficients of the corresponding ANOVA term defined by u.

fhat::GroupedCoefficients[idx::Int] = z::Number

This function overloads setindex of GroupedCoefficients such that you can do fhat[1] = 3 to set the basis coefficient determined by idx.

fhat::GroupedCoefficients[u::Vector{Int}] = fhatu::Union{Vector{ComplexF64},Vector{Float64}}

This function overloads setindex of GroupedCoefficients such that you can do fhat[[1,3]] = [1 2 3] to set the basis coefficients of the corresponding ANOVA term defined by u.

vec( fhat::GroupedCoefficients )::Vector{<:Number}

This function returns the vector of the basis coefficients of fhat. This is useful for working with lsqr or similar.

matrix of variances between two basis functions, needed for wavelet basis, since they are not orthonormal