approxfun {stats}R Documentation

Interpolation Functions


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


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)


x, y 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 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 describing how interpolation is to take place outside the interval [min(x), max(x)]. If rule is 1 then NAs are returned for such points and if it is 2, the value at the closest data extreme is used.
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*(1-f)+y1*f so that f=0 is right-continuous and f=1 is left-continuous.
ties Handling of tied x values. Either a function with a single vector argument returning a single number result or the string "ordered".


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 is a function it is applied to the y values for each distinct x value. Useful functions in this context include mean, min, and max. If ties="ordered" the x values are assumed to be already ordered. The first y value will be used for interpolation to the left and the last one for interpolation to the right.


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. This is often more useful than approx.


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

See Also

spline and splinefun for spline interpolation.


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, 10, col = "green")
points(x, y)
is.function(fc <- approxfun(x, y, method = "const")) # TRUE
curve(fc(x), 0, 10, col = "darkblue", add = TRUE)

## Show treatment of 'ties' :

x <- c(2,2:4,4,4,5,5,7,7,7)
y <- c(1:6, 5:4, 3:1)
approx(x,y, xout=x)$y # warning
(ay <- approx(x,y, xout=x, ties = "ordered")$y)
stopifnot(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

[Package stats version 2.5.0 Index]