exponential_anisotropic3D {GpGp}

Geometrically anisotropic exponential covariance function (three dimensions)

Description

From a matrix of locations and covariance parameters of the form (variance, L11, L21, L22, L31, L32, L33, nugget), return the square matrix of all pairwise covariances.

Usage

exponential_anisotropic3D(covparms, locs)

d_exponential_anisotropic3D(covparms, locs)

Arguments

covparms

A vector with covariance parameters in the form (variance, L11, L21, L22, L31, L32, L33, nugget)

locs

A matrix with n rows and 3 columns. Each row of locs is a point in R^3.

Value

A matrix with n rows and n columns, with the i,j entry containing the covariance between observations at locs[i,] and locs[j,].

Functions

• d_exponential_anisotropic3D(): Derivatives of anisotropic exponential covariance

Parameterization

The covariance parameter vector is (variance, L11, L21, L22, L31, L32, L33, nugget) where L11, L21, L22, L31, L32, L33 are the six non-zero entries of a lower-triangular matrix L. The covariances are

M(x,y) = \sigma^2 exp(-|| L x - L y || )

This means that L11 is interpreted as an inverse range parameter in the first dimension. The nugget value \sigma^2 \tau^2 is added to the diagonal of the covariance matrix. NOTE: the nugget is \sigma^2 \tau^2 , not \tau^2 .