# approxfun

0th

Percentile

##### Interpolation Functions

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

Keywords
arith, dplot
##### 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 NAs 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[] must be a function to be applied to ties, see above, but if ties[] 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.

spline and splinefun for spline interpolation.
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 ? --> # }