lotri: Easily Specify block-diagonal matrices with lower triangular...

In lotri: A Simple Way to Specify Symmetric, Block Diagonal Matrices

Easily Specify block-diagonal matrices with lower triangular info

Description

Easily Specify block-diagonal matrices with lower triangular info

Usage

lotri(x, ..., cov = FALSE, rcm = FALSE, 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.
cov	either a boolean or a function accepting a matrix input. When a boolean, 'cov' describes if this matrix definition is actually a rxode2/nlmixr2-style covariance matrix. If so, 'lotri()' will enforce certain regularity conditions: - When diagonal elements are zero, the off-diagonal elements are zero. This means the covariance element is fixed to zero and not truly part of the covariance matrix in general. - For the rest of the matrix, 'lotri' will check that it is non-positive definite (which is required for covariance matrix in general) It is sometimes difficult to adjust covariance matrices to be non-positive definite. For this reason 'cov' may also be a function accepting a matrix input and returning a non-positive definite matrix from this matrix input. When this is a function, it is equivalent to 'cov=TRUE' with the additional ability to correct the matrix to be non-positive definite if needed.
rcm	logical; if 'TRUE', the matrix will be reordered to change the matrix to a banded matrix, which is easier to express in 'lotri' than a full matrix. The RCM stands for the reverse Cuthill McKee (RCM) algorithm which is used for this matrix permutation. (see 'rcm()')
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)

Author(s)

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 Aug. 8, 2025, 6:12 p.m.