# lotri v0.1.1

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## A Simple Way to Specify Symmetric, Block Diagonal Matrices

Provides a simple mechanism to specify a symmetric block diagonal matrices (often used for covariance matrices). This is based on the domain specific language implemented in 'nlmixr' but expanded to create matrices in R generally instead of specifying parts of matrices to estimate.

# lotri

Easily Specify block-diagonal matrices with (lo)wer (tri)angular matrices. Its as if you have won the (badly spelled) lotri (or lottery).

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 matricies 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.

## Functions in lotri

 Name Description lotri Easily Specify block-diagonal matrices with lower triangular info No Results!