SpatioTemporal (version 1.1.2)

calc.tFX: Compute Matrix Product Bewteen Temporal Trends and a Matrix

Description

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.

Usage

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

Arguments

F

A (number of obs.) - by - (number of temporal trends) matrix containing the temporal trends. Usually mesa.model$F, where mesa.model is obtained f

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.

Value

• Returns a matrix of size n.loc*dim(F)[2]-by-code{n.x}.

See Also

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

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

Examples

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

##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) )
if( max(abs(tFobs-tFobs.alt)) > 1e-13 ){
    stop("calc.tFX 1a: Results not equal")
  }
  if( length(tFobs.exp)!=(dim(F)[2]*5) ){
    stop("calc.tFX 1b: Dimension missmatch")
  }

##some examples using the mesa.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]) )
if( abs(sum(mesa.model$obs$obs[mesa.model$obs$idx==1]) - tFobs[1]) > 1e-10 ){
    stop("calc.tFX - real data 1: Results not equal")
  }

##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]))
if( abs(sum(mesa.model$obs$obs[mesa.model$obs$idx==2] *
              mesa.model$F[mesa.model$obs$idx==2,2]) -
          tFobs[dim$n.obs+2]) > 1e-10 ){
    stop("calc.tFX - real data 2: Results not equal")
  }