widals.predict {widals}

WIDALS Interpolation

Description

Interpolate to unmonitored sites using WIDALS

Usage

widals.predict(Z, Hs, Ht, Hst.ls, locs, lags, b.lag, Hs0, Hst0.ls, locs0, 
geodesic = FALSE, wrap.around = NULL, GP, stnd.d = FALSE, ltco = -16)

Arguments

Z

Space-time data. A \tau x n numeric matrix.

Hs

Spacial covariates (of supporting sites). An n x p_s numeric matrix.

Ht

Temporal covariates (of supporting sites). A \tau x p_t numeric matrix.

Hst.ls

Space-time covariates (of supporting sites). A list of length \tau, each element should be a n x p_st numeric matrix.

locs

Locations of supporting sites. An n x 2 numeric matrix, first column is spacial x, second column is spacial y. If the geodesic is TRUE, make sure latitude is in the first column.

lags

Temporal lags for stochastic smoothing. An integer vector or scalar. E.g., if the data's time increment is daily, then lags = c(-1,0,1) would tell the enclosed function crispify smooth today's predictions using yesterdays, today's, and tomorrow's observed residuals.

b.lag

ALS lag. A scalar integer, typically -1 (a-prior), or 0 (a-posteriori).

Hs0

Spacial covariates (of interpolation sites). An n* x p_s matrix, or NULL.

Hst0.ls

Space-time covariates (of interpolation sites). A list of length \tau, each element should be a numeric n x p_st matrix.

locs0

Locations of interpolation sites. An n* x 2 numeric matrix. See locs argument above.

geodesic

Use geodesic distance? Boolean. If true, distance (used internally) is in units kilometers.

wrap.around

**Unused.

GP

Widals hyperparameters. A non-negative vector.

stnd.d

Spacial compression. Boolean.

ltco

Weight threshold. A scalar number. A value of, e.g., -10, will instruct crispify to ignore weights less than 10^(-10) when smoothing.

Value

A \tau x n* matrix. The WIDALS predictions at locs0.

See Also

crispify, H.als.b, widals.snow.

Examples

	
#### similar to example provided in H.als.b.
	
set.seed(99999)


library(SSsimple)

tau <- 70
n.all <- 14

Hs.all <- matrix(rnorm(n.all), nrow=n.all)
Ht <- matrix(rnorm(tau*2), nrow=tau)
Hst.ls.all <- list()
for(i in 1:tau) { Hst.ls.all[[i]] <- matrix(rnorm(n.all*2), nrow=n.all) }

Hst.combined <- list()
for(i in 1:tau) { 
    Hst.combined[[i]] <- cbind( Hs.all, matrix(Ht[i, ], nrow=n.all, ncol=ncol(Ht), 
    byrow=TRUE), Hst.ls.all[[i]] ) 
}

locs.all <- cbind(runif(n.all, -1, 1), runif(n.all, -1, 1))
D.mx.all <- distance(locs.all, locs.all, FALSE)
R.all <- exp(-2*D.mx.all) + diag(0.01, n.all)

######## use SSsimple to simulate
sssim.obj <- SS.sim.tv( 0.999, Hst.combined, 0.01, R.all, tau )


ndx.support <- 1:10
ndx.interp <- 11:14

locs <- locs.all[ndx.support, ]
locs0 <- locs.all[ndx.interp, ]

Z.all <- sssim.obj$Z
Z <- Z.all[ , ndx.support]
Z0 <- Z.all[ , ndx.interp]

Hst.ls <- subsetsites.Hst.ls(Hst.ls.all, ndx.support)
Hst0.ls <- subsetsites.Hst.ls(Hst.ls.all, ndx.interp)

Hs <- Hs.all[ ndx.support, , drop=FALSE]
Hs0 <- Hs.all[ ndx.interp, , drop=FALSE]

test.rng <- 20:tau


################# use ALS
xrho <- 1/10
xreg <- 1/10
xALS <- H.als.b(Z=Z, Hs=Hs, Ht=Ht, Hst.ls=Hst.ls, rho=xrho, reg=xreg, 
b.lag=-1, Hs0=Hs0, Ht0=Ht, Hst0.ls=Hst0.ls) 

errs.sq <- (Z0 - xALS$Z0.hat)^2
sqrt( mean(errs.sq[test.rng, ]) )

################# now use WIDALS

GP <- c(1/10, 1/10, 2, 0, 1)
Zwid <- widals.predict(Z=Z, Hs=Hs, Ht=Ht, Hst.ls=Hst.ls, locs=locs, lags=c(0), 
b.lag=-1, Hs0=Hs0, Hst0.ls=Hst0.ls, locs0=locs0, FALSE, NULL, GP) 

errs.sq <- (Z0 - Zwid)^2
sqrt( mean(errs.sq[test.rng, ]) )