\Header{stepfun}{Step Functions}
\alias{is.stepfun}{stepfun}
\alias{knots}{stepfun}
\methalias{knots.stepfun}{stepfun}
\alias{print.stepfun}{stepfun}
\alias{summary.stepfun}{stepfun}
\keyword{dplot}{stepfun}
\begin{Description}\relax
Given the vectors \eqn{(x_1,\ldots, x_n)}{(x[1],\ldots, x[n])} and
\eqn{(y_0,y_1,\ldots, y_n)}{(y[0],y[1],\ldots, y[n])}  (one value more!),
\code{stepfun(x,y,...)} returns an interpolating ``step'' function,
say \code{fn}. I.e., \eqn{fn(t) = c}{}\eqn{_i}{[i]} (constant) for
\eqn{t \in (x_i, x_{i+1})}{t in ( x[i], x[i+1])} and
\eqn{fn(x_i) = y_i}{fn(x[i]) = y[i]} for \eqn{i=1,\ldots,n}{}.

The value of the constant \eqn{c_i}{c[i]} above depends on the
``continuity'' parameter \code{f}.
For the default, \code{f = 0}, \code{fn} is a ``cadlag'' function, i.e.
continuous at right, limit (``the point'') at left.
In general, \eqn{c_i}{c[i]} is interpolated in between the
neighbouring \eqn{y}{} values,
\eqn{c_i= (1-f) y_i + f\cdot y_{i+1}}{c[i] = (1-f)*y[i] + f*y[i+1]}.
Therefore, for non-0 values of \code{f}, \code{fn} may no longer be a proper
step function, since it can be discontinuous from both sides.\end{Description}
\begin{Usage}
\begin{verbatim}
stepfun(x, y, f = 0, ties = "ordered")

is.stepfun(x)
knots(Fn, ...)

print(x, digits= getOption("digits") - 2, ...)
summary(object, ...)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{x}] numeric vector giving the knots or jump locations of the step
function for \code{stepfun()}.  For the other functions, \code{x} is
as \code{object} below.
\item[\code{y}] numeric vector one longer than \code{x}, giving the heights of
the function values \emph{between} the x values.
\item[\code{f}] a number between 0 and 1, indicating how interpolation outside
the given x values should happen.  See  \code{\Link{approxfun}}.
\item[\code{ties}] Handling of tied \code{x} values. Either a function or
the string \code{"ordered"}.  See  \code{\Link{approxfun}}.
\item[\code{Fn, object}] an \R{} object inheriting from \code{"stepfun"}.
\item[\code{digits}] number of significant digits to use, see \code{\Link{print}}.
\item[\code{...}] potentially further arguments (require by the generic).
\end{ldescription}
\end{Arguments}
\begin{Value}
A function of class \code{"stepfun"}, say \code{fn}.
There are methods available for summarizing (\code{"summary(.)"}),
representing (\code{"print(.)"}) and plotting  (\code{"plot(.)"}, see
\code{\Link{plot.stepfun}}) \code{"stepfun"} objects.

The \code{\Link{environment}} of \code{fn} contains all the
information needed;
\begin{ldescription}
\item[\code{"x","y"}] the original arguments
\item[\code{"n"}] number of knots (x values)
\item[\code{"f"}] continuity parameter
\item[\code{"yleft", "yright"}] the function values \emph{outside} the knots;
\item[\code{"method"}] (always \code{== "constant"}, from
\code{\Link{approxfun}(.)}).
\end{ldescription}

normal-bracket97bracket-normal
The knots are also available by \code{\Link{knots}(fn)}.\end{Value}
\begin{Author}\relax
Martin Maechler, \email{maechler@stat.math.ethz.ch} with some basic
code from Thomas Lumley.\end{Author}
\begin{SeeAlso}\relax
\code{\Link{ecdf}} for empirical distribution functions as
special step functions and \code{\Link{plot.stepfun}} for \emph{plotting}
step functions.

\code{\Link{approxfun}} and \code{\Link{splinefun}}.\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
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))
\end{ExampleCode}
\end{Examples}

