stepfun {stats} | R Documentation |
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 at the abscissa values, if (by default)
right = FALSE
, fn(x[i]) = y[i] and for
right = TRUE
, fn(x[i]) = y[i-1], for
i=1,...,n.
The value of the constant c[i] above depends on the
“continuity” parameter f
.
For the default, right = FALSE, 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, unless
right = TRUE, f = 1
which is right-continuous.
stepfun(x, y, f = as.numeric(right), ties = "ordered", right = FALSE) is.stepfun(x) knots(Fn, ...) as.stepfun(x, ...) ## S3 method for class 'stepfun': print(x, digits = getOption("digits") - 2, ...) ## S3 method for class 'stepfun': summary(object, ...)
x |
numeric vector giving the knots or jump locations of the step
function for stepfun() . For the other functions, x is
as object below. |
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 . |
ties |
Handling of tied x values. Either a function or
the string "ordered" . See approxfun . |
right |
logical, indicating if the intervals should be closed on the right (and open on the left) or vice versa. |
Fn, object |
an R object inheriting from "stepfun" . |
digits |
number of significant digits to use, see print . |
... |
potentially further arguments (required by the generic). |
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" , from
approxfun(.) ). |
The knots are also available via knots(fn)
.
Martin Maechler, maechler@stat.math.ethz.ch with some basic code from Thomas Lumley.
ecdf
for empirical distribution functions as
special step functions and plot.stepfun
for plotting
step functions.
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) sfun1c <- stepfun(1:3, y0, right=TRUE)# hence f=1 sfun0 summary(sfun0) summary(sfun.2) ## look at the internal structure: unclass(sfun0) ls(envir = environment(sfun0)) 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), f.f1c = sfun1c(x0)) ## Identities : stopifnot(identical(y0[-1], sfun0 (1:3)),# right = FALSE identical(y0[-4], sfun1c(1:3)))# right = TRUE