fastbeta (version 0.5.1)

fastbeta.matrix: Calculate Coefficient Matrix for Iteration Step

Description

Calculates the coefficient matrix corresponding to one step of the iteration carried out by fastbeta:

y <- c(1, E, I, R, S)
for (pos in seq_len(nrow(series) - 1L)) {
    L <- fastbeta.matrix(pos, series, ...)
    y <- L %*% y
}

Usage

fastbeta.matrix(pos,
                series, sigma = 1, gamma = 1, delta = 0,
                m = 1L, n = 1L)

Value

A lower triangular matrix of size 1+m+n+1+1.

Arguments

pos

an integer indexing a row (but not the last row) of series.

series

a “multiple time series” object, inheriting from class mts, with three columns storing (“parallel”, equally spaced) time series of incidence, births, and the per capita natural mortality rate, in that order.

sigma, gamma, delta

non-negative numbers. m*sigma, n*gamma, and delta are the rates of removal from each latent, infectious, and recovered compartment.

m

a non-negative integer indicating a number of latent stages.

n

a positive integer indicating a number of infectious stages.

Examples

# \dontshow{
## for R_DEFAULT_PACKAGES=NULL
library(stats, pos = "package:base", verbose = FALSE)
library(utils, pos = "package:base", verbose = FALSE)
# }
if (requireNamespace("adaptivetau")) withAutoprint({

data(seir.ts02, package = "fastbeta")
a <- attributes(seir.ts02); p <- length(a[["init"]])
str(seir.ts02)
plot(seir.ts02)

## We suppose that we have perfect knowledge of incidence,
## births, and the data-generating parameters
series <- cbind.ts(seir.ts02[, c("Z", "B")], mu = a[["mu"]](0))

args <- c(list(series = series),
          a[c("sigma", "gamma", "delta", "init", "m", "n")])
str(args)

X <- unclass(do.call(fastbeta, args))[, seq_len(p)]
colnames(X)
Y <- Y. <- cbind(1, X[, c(2L:p, 1L)], deparse.level = 2L)
colnames(Y)

args <- c(list(pos = 1L, series = series),
          a[c("sigma", "gamma", "delta", "m", "n")])
str(args)

L <- do.call(fastbeta.matrix, args)
str(L)
symnum(L != 0)

for (pos in seq_len(nrow(series) - 1L)) {
    args[["pos"]] <- pos
    L. <- do.call(fastbeta.matrix, args)
    Y.[pos + 1L, ] <- L. %*% Y.[pos, ]
}
stopifnot(all.equal(Y, Y.))

})