# exponential_isotropic: Isotropic exponential covariance function In GpGp: Fast Gaussian Process Computation Using Vecchia's Approximation

## Description

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

## Usage

 ```1 2 3 4 5 6 7``` ```exponential_isotropic(covparms, locs) d_exponential_isotropic(covparms, locs) d_matern15_isotropic(covparms, locs) d_matern25_isotropic(covparms, locs) ```

## Arguments

 `covparms` A vector with covariance parameters in the form (variance, range, 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_exponential_isotropic`: Derivatives of isotropic exponential covariance

• `d_matern15_isotropic`: Derivatives of isotropic matern covariance with smoothness 1.5

• `d_matern25_isotropic`: Derivatives of isotropic matern covariance function with smoothness 2.5

## Parameterization

The covariance parameter vector is (variance, range, nugget) = (σ^2,α,τ^2), and the covariance function is parameterized as

M(x,y) = σ^2 exp( - || x - y ||/ α )

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.