SpatioTemporal (version 0.9.2)

calc.iS.X: Matrix Multiplication with Block Matrices

Description

Computes either the product between a block diagonal, square matrix iS and a block matrix X; the quadratic form of a block diagonal, square matrix, t(X)*iS*X; or a block matrix multiplied by a vector, X*alpha.

Usage

calc.iS.X(X, iS, dim)
calc.X.iS.X(X, iS.X, dim)
calc.mu.B(dim, X, alpha)

Arguments

X

A list of matrices with which to form the block matrix. Usually mesa.data.model$X, where mesa.data.model is obtained from create.da

iS

A block diagonal, square matrix, with dim$m blocks each of size dim$n - by - dim$n.

iS.X

Matrix containing the product of iS and X. Output from calc.iS.X.

dim

Information regarding parameter dimension, output from loglike.dim.

alpha

A list of dim$m vectors, with the i:th vector being of length dim$p[i].

Value

• Returns iS*X, X'*iS*X, or X*alpha.

encoding

latin1

See Also

Block matrices can be created by make.sigma.B, make.sigma.B.full and make.sigma.nu. Other block matrix functions makeCholBlock, block.mult, calc.tF.times.mat, dot.prod, sumLogDiag. This function is called by loglike.

Examples

## Create a block diagonal matrix, ...
iS <- rbind(c(2,1,0,0),c(1,3,0,0),
            c(0,0,3,2),c(0,0,2,4))
## ... a block matrix ...
X <- list(matrix(c(1,2)),matrix(c(2,2,3,4),2,2))
## ... with alternative form, ...
Xt <- rbind(cbind(X[[1]],matrix(0,2,2)),
            cbind(matrix(0,2,1),X[[2]]))
## ... and a vector alpha.
alpha <- list(c(1),c(-2,1))
## Create matching dimension structure.
dim <- list(p=c(1,2), m=2, n=2)

## Compute iS * X
iS.X <- calc.iS.X(X,iS,dim)
## or
iS %*% Xt
if( max(abs(iS.X - (iS %*% Xt))) > 1e-13 ){
  stop("calc.iS.X: Results not equal")
}
## Compute X'* iS * X
calc.X.iS.X(X, iS.X, dim)
## or
t(Xt) %*% iS %*% Xt
if( max(abs(calc.X.iS.X(X, iS.X, dim) -
            (t(Xt) %*% iS %*% Xt))) > 1e-13 ){
  stop("calc.X.iS.X: Results not equal")
}
## Compute X* alpha
calc.mu.B(dim, X, alpha)
## or
cbind(X[[1]] %*% alpha[[1]], X[[2]] %*% alpha[[2]])
if( max(abs(cbind(X[[1]] %*% alpha[[1]], X[[2]] %*% alpha[[2]]) -
            calc.mu.B(dim, X, alpha))) > 1e-13 ){
  stop("calc.mu.B: Results not equal")
}