stats (version 3.6.1)

# approxfun: Interpolation Functions

## Description

Return a list of points which linearly interpolate given data points, or a function performing the linear (or constant) interpolation.

## Usage

```approx   (x, y = NULL, xout, method = "linear", n = 50,
yleft, yright, rule = 1, f = 0, ties = mean)approxfun(x, y = NULL,       method = "linear",
yleft, yright, rule = 1, f = 0, ties = mean)```

## Arguments

x, y

numeric vectors giving the coordinates of the points to be interpolated. Alternatively a single plotting structure can be specified: see `xy.coords`.

xout

an optional set of numeric values specifying where interpolation is to take place.

method

specifies the interpolation method to be used. Choices are `"linear"` or `"constant"`.

n

If `xout` is not specified, interpolation takes place at `n` equally spaced points spanning the interval [`min(x)`, `max(x)`].

yleft

the value to be returned when input `x` values are less than `min(x)`. The default is defined by the value of `rule` given below.

yright

the value to be returned when input `x` values are greater than `max(x)`. The default is defined by the value of `rule` given below.

rule

an integer (of length 1 or 2) describing how interpolation is to take place outside the interval [`min(x)`, `max(x)`]. If `rule` is `1` then `NA`s are returned for such points and if it is `2`, the value at the closest data extreme is used. Use, e.g., `rule = 2:1`, if the left and right side extrapolation should differ.

f

for `method = "constant"` a number between 0 and 1 inclusive, indicating a compromise between left- and right-continuous step functions. If `y0` and `y1` are the values to the left and right of the point then the value is `y0` if `f == 0`, `y1` if `f == 1`, and ` y0*(1-f)+y1*f` for intermediate values. In this way the result is right-continuous for `f == 0` and left-continuous for ```f == 1```, even for non-finite `y` values.

ties

handling of tied `x` values. The string `"ordered"` or a function (or the name of a function) taking a single vector argument and returning a single number or a `list` of both, e.g., `list("ordered", mean)`, see ‘Details’.

## Value

`approx` returns a list with components `x` and `y`, containing `n` coordinates which interpolate the given data points according to the `method` (and `rule`) desired.

The function `approxfun` returns a function performing (linear or constant) interpolation of the given data points. For a given set of `x` values, this function will return the corresponding interpolated values. It uses data stored in its environment when it was created, the details of which are subject to change.

## Warning

The value returned by `approxfun` contains references to the code in the current version of R: it is not intended to be saved and loaded into a different R session. This is safer for R >= 3.0.0.

## Details

The inputs can contain missing values which are deleted, so at least two complete `(x, y)` pairs are required (for ```method = "linear"```, one otherwise). If there are duplicated (tied) `x` values and `ties` contains a function it is applied to the `y` values for each distinct `x` value to produce `(x,y)` pairs with unique `x`. Useful functions in this context include `mean`, `min`, and `max`.

If `ties = "ordered"` the `x` values are assumed to be already ordered (and unique) and ties are not checked but kept if present. This is the fastest option for large `length(x)`.

If `ties` is a `list` of length two, `ties[[2]]` must be a function to be applied to ties, see above, but if `ties[[1]]` is identical to `"ordered"`, the `x` values are assumed to be sorted and are only checked for ties. Consequently, `ties = list("ordered", mean)` will be slightly more efficient than the default `ties = mean` in such a case.

The first `y` value will be used for interpolation to the left and the last one for interpolation to the right.

## References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

`spline` and `splinefun` for spline interpolation.

## Examples

Run this code
``````# NOT RUN {
require(graphics)

x <- 1:10
y <- rnorm(10)
par(mfrow = c(2,1))
plot(x, y, main = "approx(.) and approxfun(.)")
points(approx(x, y), col = 2, pch = "*")
points(approx(x, y, method = "constant"), col = 4, pch = "*")

f <- approxfun(x, y)
curve(f(x), 0, 11, col = "green2")
points(x, y)
is.function(fc <- approxfun(x, y, method = "const")) # TRUE
curve(fc(x), 0, 10, col = "darkblue", add = TRUE)
## different extrapolation on left and right side :
plot(approxfun(x, y, rule = 2:1), 0, 11,
col = "tomato", add = TRUE, lty = 3, lwd = 2)

## Show treatment of 'ties' :

x <- c(2,2:4,4,4,5,5,7,7,7)
y <- c(1:6, 5:4, 3:1)
(amy <- approx(x, y, xout = x)\$y) # warning, can be avoided by specifying 'ties=':
op <- options(warn=2) # warnings would be error
stopifnot(identical(amy, approx(x, y, xout = x, ties=mean)\$y))
options(op) # revert
(ay  <- approx(x, y, xout = x, ties = "ordered")\$y)
stopifnot(amy == c(1.5,1.5, 3, 5,5,5, 4.5,4.5, 2,2,2),
ay  == c(2, 2,    3, 6,6,6, 4, 4,    1,1,1))
approx(x, y, xout = x, ties = min)\$y
approx(x, y, xout = x, ties = max)\$y

# }
# NOT RUN {
<!-- %%-- MM has nice utility plotting -- do in demo ? -->
# }
``````

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