stepfun
Step Functions - Creation and Class
Given the vectors $(x[1], \dots, x[n])$ and
$(y[0], y[1], \dots, y[n])$ (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
$i=1, \dots, n$.
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).
- Keywords
- dplot
Usage
stepfun(x, y, f = as.numeric(right), ties = "ordered", right = FALSE)
is.stepfun(x)
knots(Fn, ...)
as.stepfun(x, ...)
"print"(x, digits = getOption("digits") - 2, ...)
"summary"(object, ...)Arguments
- x
- numeric vector giving the knots or jump locations of the step
function for
stepfun(). For the other functions,xis asobjectbelow. - 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
xvalues. Either a function or the string"ordered". Seeapproxfun. - 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).
Value
-
A function of class
- "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", fromapproxfun(.)). The knots are also available via
"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;
knots(fn).
Note
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.
See Also
ecdf for empirical distribution functions as
special step functions and plot.stepfun for plotting
step functions.
Examples
library(stats)
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