Step Functions - Creation and Class
Given the vectors $(x, \dots, x[n])$ and
$(y, y, \dots, y[n])$ (one value
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
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
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, ...)"print"(x, digits = getOption("digits") - 2, ...)"summary"(object, ...)
- numeric vector giving the knots or jump locations of the step
stepfun(). For the other functions,
- numeric vector one longer than
x, giving the heights of the function values between the x values.
- a number between 0 and 1, indicating how interpolation outside
the given x values should happen. See
- Handling of tied
xvalues. Either a function or the string
- 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
- number of significant digits to use, see
- potentially further arguments (required by the generic).
A function of class
- the original arguments
- number of knots (x values)
- continuity parameter
- "yleft", "yright"
- the function values outside the knots
== "constant", from
approxfun(.)). The knots are also available via
fn.There are methods available for summarizing (
"summary(.)"), representing (
"print(.)") and plotting (
fncontains all the information needed;
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.
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