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).

1 2 3 4 5 6 7 8 9 10 11 12 | ```
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 |

`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 |

`"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

1 | ```
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`

.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
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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