A julia package for working with coupled fields. This is work in progress.
The main function gradvecfield calculates the gradient vector or gradient matrix for each instance of the coupled fields.
For 𝒀 = g(𝑿), CoupledFields.gradvecfield([a b], X, Y, kernelpars) returns 𝑛 gradient matrices, for 𝑛 random points in 𝑿.
For parameters [𝑎 𝑏]: 𝑎 is a smoothness parameter, and 𝑏 is a ridge parameter.
using CoupledFields
g(x,y,z) = x * exp(-x^2 - y^2 - z^2)
X = -2 .+ 4*rand(100, 3)
Y = g.(X[:,1], X[:,2], X[:,3])
kernelpars = GaussianKP(X)
∇g = gradvecfield([0.5 -7], X, Y[:,1:1], kernelpars)Also CoupledFields doesn’t require a closed-form function, it can be used if you have only the observed fields 𝑿 and 𝒀.
Install using the Julia package manager. From the Julia REPL, type ] to enter the Pkg REPL mode and run:
pkg> add CoupledFields
or from the Julia prompt:
julia> using Pkg; Pkg.add("CoupledFields")