Easily Specify block-diagonal matrices with lower triangular info

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.

Value

named symmetric matrix useful in RxODE simulations (and perhaps elsewhere)

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

Author

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)})
#>      et2  et3  et4
#> et2 40.0  0.1  0.1
#> et3  0.1 20.0  0.1
#> et4  0.1  0.1 30.0

## You  do not need to enclose in {}
lotri(et2 + et3 + et4 ~ c(40,
                          0.1, 20,
                          0.1, 0.1, 30),
          et5 ~ 6)
#>      et2  et3  et4 et5
#> et2 40.0  0.1  0.1   0
#> et3  0.1 20.0  0.1   0
#> et4  0.1  0.1 30.0   0
#> et5  0.0  0.0  0.0   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
          })
#>      et2  et3  et4 et5
#> et2 40.0  0.1  0.1   0
#> et3  0.1 20.0  0.1   0
#> et4  0.1  0.1 30.0   0
#> et5  0.0  0.0  0.0   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"))))
#>      et2  et3  et4 et5
#> et2 40.0  0.1  0.1   0
#> et3  0.1 20.0  0.1   0
#> et4  0.1  0.1 30.0   0
#> et5  0.0  0.0  0.0   1

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

## For RxODE, 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
#> [[1]]
#>        iov.Ka iov.Cl
#> iov.Ka    0.5    0.0
#> iov.Cl    0.0    0.6
#> 
#> $occ
#>        occ.Ka occ.Cl
#> occ.Ka    0.5    0.0
#> occ.Cl    0.0    0.6
#> 
#> Properties: lower, nu 

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

mat$lower # Shows the lower bound for each condition
#> [[1]]
#> iov.Ka iov.Cl 
#>   -Inf   -Inf 
#> 
#> $occ
#> occ.Ka occ.Cl 
#>      4      4 
#> 

mat$lower$occ # shows the lower bound for the occasion variable
#> occ.Ka occ.Cl 
#>      4      4 

## 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
#> [[1]]
#> numeric(0)
#> 
#> $occ
#> occ.Ka occ.Cl 
#>    Inf    Inf 
#> 

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

mat$lotri
#> NULL

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

mat$nu
#> $occ
#> [1] 3
#> 

mat$nu$occ
#> [1] 3
mat$nu$id
#> NULL

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

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

mat
#> $id
#>        iov.Ka iov.Cl
#> iov.Ka    0.5    0.0
#> iov.Cl    0.0    0.6
#> 
#> $occ
#>        occ.Ka occ.Cl
#> occ.Ka    0.5    0.0
#> occ.Cl    0.0    0.6
#> 
#> Properties: lower, nu