# Loteri Motivation

knitr::opts_chunk\$set( collapse = TRUE, comment = "#>" )

This was made to allow people (like me) to specify lower triangular matrices similar to the domain specific language implemented in nlmixr. Originally I had it included in RxODE, but thought it may have more general applicability, so I separated it into a new package.

For me, specifying the matrices in this way is easier than specifying them using R's default matrix. For instance to fully specify a simple 2x2 matrix, in R you specify:

mat <- matrix(c(1, 0.5, 0.5, 1),nrow=2,ncol=2,dimnames=list(c("a", "b"), c("a", "b")))

With lotri, you simply specify:

library(lotri) mat <- lotri(a+b ~ c(1, 0.5, 1))

I find it more legible and easier to specify, especially if you have a more complex matrix. For instance with the more complex matrix:

mat <- lotri({ a+b ~ c(1, 0.5, 1) c ~ 1 d +e ~ c(1, 0.5, 1) })

To fully specify this in base R you would need to use:

mat <- matrix(c(1, 0.5, 0, 0, 0, 0.5, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0.5, 0, 0, 0, 0.5, 1), nrow=5, ncol=5, dimnames= list(c("a", "b", "c", "d", "e"), c("a", "b", "c", "d", "e")))

Of course with the excellent Matrix package this is a bit easier:

library(Matrix) mat <- matrix(c(1, 0.5, 0.5, 1),nrow=2,ncol=2,dimnames=list(c("a", "b"), c("a", "b"))) mat <- bdiag(list(mat, matrix(1), mat)) ## Convert back to standard matrix mat <- as.matrix(mat) ## dimnames(mat) <- list(c("a", "b", "c", "d", "e"), c("a", "b", "c", "d", "e"))

Regardless, I think lotri is a bit easier to use.