calc.tFX: Compute Matrix Product Bewteen Temporal Trends and a Matrix
In SpatioTemporal: Spatio-Temporal Model Estimation

Description Usage Arguments Value Author(s) See Also Examples

Computes the matrix products between the transpose of a sparse matrix F containing temporal trends the and a vector/matrix.

See the examples for details.

1	calc.tFX(F, X, loc.ind, n.loc = max(loc.ind))

`F`	A (number of obs.) - by - (number of temporal trends) matrix containing the temporal trends. Usually `mesa.model$F`, where `mesa.model` is obtained from `createSTmodel`.
`X`	A vector or matrix; needs to be a multiple of `dim(F)[1]`.
`loc.ind`	A vector indicating which location each row in `F` corresponds to, usually `mesa.model$obs$idx`.
`n.loc`	Number of locations.

Returns a matrix of size n.loc*dim(F)[2]-by-coden.x.

Johan Lindstrom and Adam Szpiro

Other block matrix functions: blockMult, calc.FXtF2, calc.FX, calc.mu.B, calc.tFXF, makeCholBlock, makeSigmaB, makeSigmaNu

Other temporal trend functions: calc.FXtF2, calc.FX, calc.tFXF, expandF

##This starts with a couple of simple examples, more elaborate examples
##with real data can be found further down.
require(Matrix)

##create a trend
trend <- cbind(1:5,sin(1:5))
##an index of locations
idx <- c(rep(1:3,3),1:2,2:3)
##a list of time points for each location/observation
T <- c(rep(1:3,each=3),4,4,5,5)
##create a random observations matrix
obs <- rnorm(length(T))

##expand the F matrix to match the locations/times in idx/T.
F <- trend[T,]
F
##compute tF %*% obs
tFobs <- calc.tFX(F, obs, idx)
##or posibly expanded if we have unobserved, trailing locations
tFobs.exp <- calc.tFX(F, obs, idx, 5)

##alternatievly this can be computed as observtions for each location
##multiplied by the trend function at the corresponding time points.
tFobs.alt <- t(expandF(F, idx)) %*% obs

##compare results
print( cbind(tFobs,tFobs.alt) )


##some examples using real data
data(mesa.model)

##Some information about the size(s) of the model.
dim <- loglikeSTdim(mesa.model)

##compute F' %*% obs
tFobs <- calc.tFX(mesa.model$F, mesa.model$obs$obs, mesa.model$obs$idx)

##The resulting matrix contains 75 elements (3 temporal trend at 25
##sites). The first element are the observations at the first site
##multiplied by the constant temporal trend, e.g.
print( tFobs[1] )
print( sum(mesa.model$obs$obs[mesa.model$obs$idx==1]) )


##The 27:th element are the observations at the second site (27-25)
##multiplied by the first temporal trend (second element in F)
print( tFobs[dim$n.obs+2] )
print( sum(mesa.model$obs$obs[mesa.model$obs$idx==2] *
           mesa.model$F[mesa.model$obs$idx==2,2]))