widals.predict: WIDALS Interpolation
In widals: Weighting by Inverse Distance with Adaptive Least Squares

Description Usage Arguments Value See Also Examples

Interpolate to unmonitored sites using WIDALS

1 2	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)

`Z`	Space-time data. A τ x n numeric matrix.
`Hs`	Spacial covariates (of supporting sites). An n x p_s numeric matrix.
`Ht`	Temporal covariates (of supporting sites). A τ x p_t numeric matrix.
`Hst.ls`	Space-time covariates (of supporting sites). A list of length τ, 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 τ, 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.

A τ x n* matrix. The WIDALS predictions at locs0.

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

	
#### 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, ]) )