Step Functions - Creation and Class

Description

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).

Usage

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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, ...)

Arguments

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).

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;

"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).

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

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    eval(attr(old_obj, "call"), environment(old_obj))

since the data used is stored as part of the object's environment.

Author(s)

Martin Maechler, maechler@stat.math.ethz.ch with some basic code from Thomas Lumley.

See Also

ecdf for empirical distribution functions as special step functions and plot.stepfun for plotting step functions.

approxfun and splinefun.

Examples

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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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