spBayes (version 0.2-4)

covInvLogDet: Utility function for constructing predictive process covariance matrices

Description

Utility function for constructing predictive process covariance matrices

Usage

covInvLogDet(coords, knots, cov.model, sigma.sq,
                  tau.sq, theta, modified.pp=TRUE, SWM=TRUE, ...)

Arguments

coords

a $n \times 2$ matrix of the observation coordinates in $R^2$ (e.g., easting and northing).

knots

a $m \times 2$ matrix of knot coordinates.

sigma.sq

partial sill value.

tau.sq

nugget value.

theta

if cov.model is matern then theta is a vector of the spatial decay and smoothness parameters; otherwise, theta is the spatial decay.

modified.pp

a logical value indicating if the modified predictive process should be used.

cov.model

a quoted key word that specifies the covariance function used to model the spatial dependence structure among the observations. Supported covariance model key words are: "exponential", "matern", "spherical"

SWM

a logical value indicating if the Sherman-Woodbury-Morrison equation should be used for computing the inverse (this is ignored if modified.pp is FALSE).

...

currently no additional arguments.

Value

• Returns the covariance matrix, log-determinant, and inverse.

Examples

set.seed(1)

n <- 100
coords <- cbind(runif(n),runif(n))

m <- 50
knots <- cbind(runif(m), runif(m))

theta <- c(6, 2)
sigma.sq <- 1
tau.sq <- 1
tol <- 1.0e-5

##
##non bias-adjusted predictive process
##
c1 <- covInvLogDet(coords=coords, knots=knots, cov.model="exponential",
                   sigma.sq=sigma.sq, tau.sq=tau.sq, theta=theta,
                   modified.pp=FALSE, SWM=FALSE)

if(max(abs(chol2inv(chol(c1$C)) - c1$C.inv)) > tol) stop("test-1 failed")
if(max(abs(2*sum(log(diag(chol(c1$C)))) - c1$log.det)) > tol)
stop("test-1 failed")


c2 <- covInvLogDet(coords=coords, knots=knots, cov.model="matern",
                   sigma.sq=sigma.sq, tau.sq=tau.sq, theta=theta,
                   modified.pp=FALSE, SWM=FALSE)

if(max(abs(chol2inv(chol(c2$C)) - c2$C.inv)) > tol) stop("test-2 failed")
if(max(abs(2*sum(log(diag(chol(c2$C)))) - c2$log.det)) > tol)
stop("test-2 failed")

##
##bias-adjusted predictive process
##
c3 <- covInvLogDet(coords=coords, knots=knots, cov.model="exponential",
                   sigma.sq=sigma.sq, tau.sq=tau.sq, theta=theta,
                   modified.pp=TRUE, SWM=FALSE)

if(max(abs(chol2inv(chol(c3$C)) - c3$C.inv)) > tol) stop("test-3 failed")
if(max(abs(2*sum(log(diag(chol(c3$C)))) - c3$log.det)) > tol)
stop("test-3 failed")


c4 <- covInvLogDet(coords=coords, knots=knots, cov.model="matern",
                   sigma.sq=sigma.sq, tau.sq=tau.sq, theta=theta,
                   modified.pp=TRUE, SWM=FALSE)

if(max(abs(chol2inv(chol(c4$C)) - c4$C.inv)) > tol) stop("test-4 failed")
if(max(abs(2*sum(log(diag(chol(c4$C)))) - c4$log.det)) > tol)
stop("test-4 failed")

##
##non bias-adjusted predictive process using SWM
##
c5 <- covInvLogDet(coords=coords, knots=knots, cov.model="exponential",
                   sigma.sq=sigma.sq, tau.sq=tau.sq, theta=theta,
                   modified.pp=FALSE, SWM=TRUE)

if(max(abs(chol2inv(chol(c5$C)) - c5$C.inv)) > tol) stop("test-5 failed")
if(max(abs(2*sum(log(diag(chol(c5$C)))) - c5$log.det)) > tol)
stop("test-5 failed")

c6 <- covInvLogDet(coords=coords, knots=knots, cov.model="matern",
                   sigma.sq=sigma.sq, tau.sq=tau.sq, theta=theta,
                   modified.pp=FALSE, SWM=TRUE)

if(max(abs(chol2inv(chol(c6$C)) - c6$C.inv)) > tol) stop("test-6 failed")
if(max(abs(2*sum(log(diag(chol(c6$C)))) - c6$log.det)) > tol)
stop("test-6 failed")

##
##Check SWM
##
##c.str <- sigma.sq*exp(-theta[1]*iDist(knots))
##ct <- sigma.sq*exp(-theta[1]*iDist(coords,knots))
##C.inv.swm <- diag(1/tau.sq,n)-diag(1/tau.sq,n)/%*/%ct/%*/%
##  chol2inv(chol(c.str+t(ct)/%*/%diag(1/tau.sq,n)/%*/%ct))/%*/%
##  t(ct)/%*/%diag(1/tau.sq,n)
##if(max(abs(C.inv.swm - c5$C.inv)) > tol) stop("test-5a failed")

##
##bias-adjusted predictive process using SWM
##
c7 <- covInvLogDet(coords=coords, knots=knots, cov.model="exponential",
                   sigma.sq=sigma.sq, tau.sq=tau.sq, theta=theta,
                   modified.pp=TRUE, SWM=TRUE)

if(max(abs(chol2inv(chol(c7$C)) - c7$C.inv)) > tol) stop("test-7 failed")
if(max(abs(2*sum(log(diag(chol(c7$C)))) - c7$log.det)) > tol)
stop("test-7 failed")

c8 <- covInvLogDet(coords=coords, knots=knots, cov.model="matern",
                   sigma.sq=sigma.sq, tau.sq=tau.sq, theta=theta,
                   modified.pp=TRUE, SWM=TRUE)

if(max(abs(chol2inv(chol(c8$C)) - c8$C.inv)) > tol) stop("test-8 failed")
if(max(abs(2*sum(log(diag(chol(c8$C)))) - c8$log.det)) > tol)
stop("test-8 failed")