# makeSigmaNu: Create Block Covariance Matrix (Unequal Block Sizes) In SpatioTemporal: Spatio-Temporal Model Estimation

## Description

Function that creates a block covariance matrix with unequally sized blocks. Used to construct the Sigma_nu matrix.

## Usage

 ```1 2 3 4``` ```makeSigmaNu(pars, dist, type = "exp", nugget = 0, random.effect = 0, symmetry = dim(dist)[1] == dim(dist)[2], blocks1 = dim(dist)[1], blocks2 = dim(dist)[2], ind1 = 1:dim(dist)[1], ind2 = 1:dim(dist)[2], ind2.to.1 = 1:dim(dist)[2], sparse = FALSE, diff = 0) ```

## Arguments

 `pars` Vector of parameters, as suggested by `parsCovFuns`. `dist` Distance matrix. `type` Name of the covariance function to use, see `namesCovFuns`. `nugget` A value of the nugget or a vector of length `dim(dist)[1]` giving (possibly) location specific nuggets. `random.effect` A constant variance to add to the covariance matrix, can be interpereted as either and partial sill with infinite range or as a random effect with variance given by `random.effect` for the mean value. `symmetry` `TRUE`/`FALSE` flag if the `dist` matrix is symmetric. If also `ind1==ind2` and `blocks1==blocks2` the resulting covariance matrix will be symmetric. `blocks1, blocks2` Vectors with the size(s) of each of the diagonal blocks, usually `mesa.model\$nt`. If `symmetry=TRUE` then `blocks2` defaults to `blocks1` if missing. `ind1, ind2` Vectors indicating the location of each element in the covariance matrix, used to index the `dist`-matrix to determine the distance between locations, usually `mesa.model\$obs\$idx`. If `symmetry=TRUE` and then `ind2` defaults to `ind1` if missing. `ind2.to.1` Vectors, that for each index along the second dimension, `ind2`, gives a first dimension index, `ind1`, used only if `symmetry=FALSE` to determine which covariances should have an added nugget (collocated sites). `sparse` If `TRUE`, return a block diagonal sparse matrix, see `bdiag.spam`. `diff` Vector with two components indicating with respect to which parameter(s) that first and/or second derivatives should be computed. E.g. `diff=c(0,0)` indicates no derivatives, `diff=c(1,0)` indicates first derivative wrt the first parameter, `diff=c(1,2)` indicates second cross derivative wrt the first and second parameters, etc.

## Value

Block covariance matrix of size `length(ind1)`-by-`length(ind2)`.

## Author(s)

Johan Lindstrom

Other block matrix functions: `blockMult`, `calc.FXtF2`, `calc.FX`, `calc.mu.B`, `calc.tFXF`, `calc.tFX`, `makeCholBlock`, `makeSigmaB`
Other covariance functions: `crossDist`, `evalCovFuns`, `makeSigmaB`, `namesCovFuns`, `parsCovFuns`, `updateCovf`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30``` ```##First create some random locations x <- rnorm(5) y <- rnorm(5) ##compute distance matrix D <- crossDist( cbind(x,y) ) #a vector of locations I <- c(1,2,3,1,4,4,3,2,1,1) T <- c(1,1,1,2,2,3,3,3,3,4) ##create a block diagonal matrix consisting of four parts with ##exponential covariance. sigma.nu <- makeSigmaNu(c(.4,2), D, "exp", nugget=0.1, blocks1 = c(3,2,4,1), ind1 = I) ##and cross covariance sigma.nu.c <- makeSigmaNu(c(.4,2), D, "exp", nugget=0.1, blocks1 = c(3,2,4,1), ind1 = I, blocks2 = c(0,0,3,1), ind2 = I[7:10]) ##compare the cross-covariance with the relevant part of sigma.nu range(sigma.nu.c-sigma.nu[,7:10]) ##an alternative showing the use of loc.ind2.to.1 sigma.nu.c <- makeSigmaNu(c(.4,2), D[,4:3], "exp", nugget=0.1, blocks1 = c(3,2,4,1), ind1 = I, blocks2 = c(0,0,2,0), ind2 = 1:2, ind2.to.1=4:3) ##compare the cross-covariance with the relevant part of sigma.nu range(sigma.nu.c-sigma.nu[,6:7]) ```