# matern15_scaledim: Matern covariance function, smoothess = 1.5, different range... In GpGp: Fast Gaussian Process Computation Using Vecchia's Approximation

## Description

From a matrix of locations and covariance parameters of the form (variance, range_1, ..., range_d, nugget), return the square matrix of all pairwise covariances.

## Usage

 ```1 2 3``` ```matern15_scaledim(covparms, locs) d_matern15_scaledim(covparms, locs) ```

## Arguments

 `covparms` A vector with covariance parameters in the form (variance, range_1, ..., range_d, nugget) `locs` A matrix with `n` rows and `d` columns. Each row of locs is a point in R^d.

## 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_matern15_scaledim`: Derivatives with respect to parameters

## Parameterization

The covariance parameter vector is (variance, range_1, ..., range_d, nugget). The covariance function is parameterized as

M(x,y) = σ^2 (1 + || D^{-1}(x - y) || ) exp( - || D^{-1}(x - y) || )

where D is a diagonal matrix with (range_1, ..., range_d) on the diagonals. The nugget value σ^2 τ^2 is added to the diagonal of the covariance matrix. NOTE: the nugget is σ^2 τ^2 , not τ^2 .

GpGp documentation built on June 10, 2021, 1:07 a.m.