## Step Functions

## Usage

    fn <- stepfun(x, y, f=0)
    is.stepfun(fn)
    knots(fn)
    plot(fn, ...)
    print(fn, ...)
    summary(fn)

## Arguments

`x` | numeric vector giving the ``knots'' or jump locations of the step function.
`y` | numeric vector one longer than `x`, giving the heights of the function values between the x values.
`f` | a number between 0 and 1, indicating how interpolation outside the given x values should happen. See `approxfun`.
`fn` | an R object inheriting from `"stepfun"`.

## Description

Given the vectors (x[1],..., x[n]) and (y[0],y[1],..., y[n]) (one value more!), `stepfun(x,y,...)` returns an interpolating ``step'' function, say `fn`. I.e., fn(t) = c[i] (constant) for t in ( x[i], x[i+1]) and fn(x[i]) = y[i] for i=1,...,n.

The value of the constant c[i] above depends on the ``continuity'' parameter `f`. For the default, `f = 0`, `fn` is a ``cadlag'' function, i.e. continuous at right, limit (``the point'') at left. In general, c[i] is interpolated in between the neighbouring y values, c[i] = (1-f)*y[i] + f*y[i+1]. Therefore, for non-0 values of `f`, `fn` may no longer be a proper step function, since it can be discontinuous from both sides.

## Value

A function of class `"stepfun"`, say `fn`. There are methods available for summarizing (`"summary(.)"`), representing (`"print(.)"`) and plotting (`"plot(.)"`, see `plot.stepfun`) `"stepfun"` objects.

The `environment` of `fn` contains all the information needed; `"x","y"`: the original arguments; `"n"`: number of knots (x values); `"f"`: continuity parameter; `"yleft", "yright"` the function values outside the knots; `"method"` (always `== "constant"`; not used, from `approxfun(.)`). The knots are also available by `knots(fn)`.

## Author(s)

Martin Maechler, maechler@stat.math.ethz.ch with some basic code from Thomas Lumley.

## See Also

`ecdf` for empiricial distribution functions as special step functions and `plot.stepfun` for plotting step functions.

`approxfun` and `splinefun`.

## Examples

    y0 <- c(1,2,4,3)
    sfun0  <- stepfun(1:3, y0, f = 0)
    sfun.2 <- stepfun(1:3, y0, f = .2)
    sfun1  <- stepfun(1:3, y0, f = 1)
    sfun0
    summary(sfun0)
    summary(sfun.2)

    x0 <- seq(0.5,3.5, by = 0.25)
    rbind(x=x0, f.f0 = sfun0(x0), f.f02= sfun.2(x0), f.f1 = sfun1(x0))

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