## Apply a Function Over a ``Ragged'' Array

## Usage

    tapply(x, INDEX, FUN = NULL, simplify = TRUE, ...)

## Arguments

`x` | an atomic object, typically a vector.
`INDEX` | list of factors, each of same length as `x`.
`FUN` | the function to be applied. In the case of functions like `+`, `%*%`, etc., the function name must be quoted. If `FUN` is `NULL`, tapply returns a vector which can be used to subscript the multi-way array `tapply` normally produces.
`simplify` | If `FALSE`, `tapply` always returns an array of mode `"list"`. If `TRUE` (the default), then if `FUN` always returns a scalar, `tapply` returns an array with the mode of the scalar, and if the array would be one dimensional the dimension is removed, to make it a vector.
`...` | optional arguments to `FUN`.

## Value

When `FUN` is present, `tapply` calls `FUN` for each cell that has any data in it. If `FUN` returns a single atomic value for each cell (e.g., functions `mean` or `var`), then `tapply` returns a multi-way array containing the values. The array has the same number of dimensions as `INDEX` has components; the number of levels in a dimension is the number of levels (`nlevels(.)`) in the corresponding component of `INDEX`. This is a vector if `INDEX` has only one component.

If `FUN` does not return a single atomic value, `tapply` returns an array of mode `"list"` whose components are the values of the individual calls to `FUN`, i.e., the result is a list with a `dim` attribute.

## See Also

`apply`, `lapply` with its version `sapply`.

## Examples

    groups <- as.factor(rbinom(32, n = 5, p = .4))
    tapply(groups, groups, length) #- is almost the same as
    table(groups)

    n <- 17; fac <- factor(rep(1:3, len = n), levels = 1:5)
    table(fac)
    tapply(1:n, fac, sum)
    tapply(1:n, fac, sum, simplify = FALSE) #- does not yet print okay
    tapply(1:n, fac, range)			#- .. nor does this
    tapply(1:n, fac, quantile)		#- ... or this

    ind <- list(c(1, 2, 2), c("A", "A", "B"))
    table(ind)
    tapply(1:3, ind) #-> the split vector
    tapply(1:3, ind, sum)

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