stepfun | 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 from the right,
limits from the left, so that the function is piecewise constant on
intervals that include their left endpoint.
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 left-continuous (i.e., constant
pieces contain their right endpoint).
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 |
y |
numeric vector one longer than |
f |
a number between 0 and 1, indicating how interpolation outside
the given x values should happen. See |
ties |
Handling of tied |
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 |
digits |
number of significant digits to use, see |
... |
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 |
The knots are also available via knots(fn)
.
The objects of class "stepfun"
are not intended to be used for
permanent storage and may change structure between versions of R (and
did at R 3.0.0). They can usually be re-created by
eval(attr(old_obj, "call"), environment(old_obj))
since the data used is stored as part of the object's environment.
Martin Maechler, [email protected] with some basic code from Thomas Lumley.
ecdf
for empirical distribution functions as
special step functions and plot.stepfun
for plotting
step functions.
approxfun
and splinefun
.
y0 <- c(1., 2., 4., 3.) sfun0 <- stepfun(1:3, y0, f = 0) sfun.2 <- stepfun(1:3, y0, f = 0.2) 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
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