CoupledFields.InputSpaceType
InputSpace(X, Y, d, lat)

A type to hold the X and Y fields of the Input space. The fields are whitened if d=[d1, d2] is supplied. Area weighting is applied if lat is supplied.

CoupledFields.KernelParametersType
KernelParameters

An abstract type.

All KernelParameters types contain certain parameters which are later passed to internal functions Kf and ∇Kf.

A KernelParameters type is set using e.g. PolynomialKP(X::Matrix{Float64}) or GaussianKP(X::Matrix{Float64}).

CoupledFields.ModelObjType
ModelObj(W, R, A, T, evals, pars, method)

A type to hold statistical model results, such as the matrices W, R, A, T, where R=XW and T=YA.

CoupledFields.CVfnMethod
CVfn(parm::Matrix, X::Matrix, Y::Matrix, modelfn::Function, kerneltype::DataType; verbose=true, dcv=2)

Cross-validation function

CoupledFields.ccaMethod
cca(v::Array, X::Matrix, Y::Matrix)

Regularized Canonical Correlation Analysis using SVD.

CoupledFields.gKCCAMethod
gKCCA(par::Array, X::Matrix, Y::Matrix, kpars::KernelParameters)

Compute the projection matrices and components for gKCCA.

CoupledFields.gradientFunction
gradient(Z::Array; axs::Tuple=axes(Z), smoothness=1.0)

Compute the gradient of field Z. Use axs to supply a tuple of point ranges for each dimension.

The method is based on the gradient function of a Gaussian kernel: smoothness scales an auto-estimate of Gaussian σ, a large value will make the gradient function linear.

Z can be any dimensions, but the method may be slow if length(Z)>10³.

gradient(X::Matrix, Y::Matrix; smoothness=1.0)

Compute $∇g$ for $Y = g(X)$ where X is the position values (rows = points), and Y is the field values (e.g. a 1-column matrix). The points can have irregular positions. The method may be slow if size(X, 1)>10³.

See Example 3

CoupledFields.gradvecfieldMethod
gradvecfield(par::Array, X::Matrix, Y::Matrix, kpars::KernelParameters)

Compute the gradient vector or gradient matrix at each instance of the X and Y fields, by making use of a kernel feature space.

CoupledFields.whitenMethod
whiten(X::Matrix, d::Float64; lat=nothing)

Whiten X.

d (0-1) Percentage variance of components to retain.

lat Latitudinal area-weighting.