stepfun
Step Functions - Creation and Class
Given the vectors \((x_1, \ldots, x_n)\) and
\((y_0,y_1,\ldots, y_n)\) (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
\(i=1,\ldots,n\).
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,
\(c_i= (1-f) y_i + f\cdot y_{i+1}\).
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, …)
# S3 method for stepfun
print(x, digits = getOption("digits") - 2, …)
# S3 method for stepfun
summary(object, …)
Arguments
- x
numeric vector giving the knots or jump locations of the step function for
stepfun()
. For the other functions,x
is asobject
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"
. 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 "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;
the original arguments
number of knots (x values)
continuity parameter
the function values outside the knots
(always == "constant"
, from
approxfun(.)
).
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)
# NOT RUN {
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
# }