# approxfun

##### Interpolation Functions

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’.

##### 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.

##### 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.

##### References

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

##### See Also

##### Examples

`library(stats)`

```
# 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 ? -->
# }
```

*Documentation reproduced from package stats, version 3.6.2, License: Part of R 3.6.2*