# lotri: Easily Specify block-diagonal matrices with lower triangular... In lotri: A Simple Way to Specify Symmetric, Block Diagonal Matrices

 lotri R Documentation

## Easily Specify block-diagonal matrices with lower triangular info

### Description

Easily Specify block-diagonal matrices with lower triangular info

### Usage

```lotri(x, ..., envir = parent.frame(), default = "id")
```

### Arguments

 `x` list, matrix or expression, see details `...` Other arguments treated as a list that will be concatenated then reapplied to this function. `envir` the `environment` in which `expr` is to be evaluated. May also be `NULL`, a list, a data frame, a pairlist or an integer as specified to `sys.call`. `default` Is the default factor when no conditioning is implemented.

### Details

This can take an R matrix, a list including matrices or expressions, or expressions

Expressions can take the form

name ~ estimate

Or the lower triangular matrix when "adding" the names

name1 + name2 ~ c(est1, est2, est3)

The matrices are concatenated into a block diagonal matrix, like `bdiag`, but allows expressions to specify matrices easier.

### Value

named symmetric matrix useful in 'rxode2()' simulations (and perhaps elsewhere)

Matthew L Fidler

### Examples

```
## A few ways to specify the same matrix
lotri({et2 + et3 + et4 ~ c(40,
0.1, 20,
0.1, 0.1, 30)})

## You  do not need to enclose in {}
lotri(et2 + et3 + et4 ~ c(40,
0.1, 20,
0.1, 0.1, 30),
et5 ~ 6)
## But if you do enclose in {}, you can use
## multi-line matrix specifications:

lotri({et2 + et3 + et4 ~ c(40,
0.1, 20,
0.1, 0.1, 30)
et5 ~ 6
})

## You can also add lists or actual R matrices as in this example:
lotri(list(et2 + et3 + et4 ~ c(40,
0.1, 20,
0.1, 0.1, 30),
matrix(1,dimnames=list("et5","et5"))))

## Overall this is a flexible way to specify symmetric block
## diagonal matrices.

## For rxode2, you may also condition based on different levels of
## nesting with lotri;  Here is an example:

mat <- lotri(lotri(iov.Ka ~ 0.5,
iov.Cl ~ 0.6),
lotri(occ.Ka ~ 0.5,
occ.Cl ~ 0.6) | occ(lower=4,nu=3))

mat

## you may access features of the matrix simply by `\$` that is

mat\$lower # Shows the lower bound for each condition

mat\$lower\$occ # shows the lower bound for the occasion variable

## Note that `lower` fills in defaults for parameters.  This is true
## for `upper` true;  In fact when accessing this the defaults
## are put into the list

mat\$upper

## However all other values return NULL if they are not present like

mat\$lotri

## And values that are specified once are only returned on one list:

mat\$nu

mat\$nu\$occ
mat\$nu\$id

## You can also change the default condition with `as.lotri`

mat <- as.lotri(mat, default="id")

mat

```

lotri documentation built on June 18, 2022, 5:06 p.m.