approxfun {stats} R Documentation

## 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, na.rm = TRUE)

approxfun(x, y = NULL,       method = "linear",
yleft, yright, rule = 1, f = 0, ties = mean, na.rm = TRUE)


### 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’. na.rm logical specifying how missing values (NA's) should be handled. Setting na.rm=FALSE will propagate NA's in y to the interpolated values, also depending on the rule set. Note that in this case, NA's in x are invalid, see also the examples.

### Details

The inputs can contain missing values which are deleted (if na.rm is true, i.e., by default), 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.

### Examples

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)

### Treatment of 'NA's -- are kept if  na.rm=FALSE :

xn <- 1:4
yn <- c(1,NA,3:4)
xout <- (1:9)/2
## Default behavior (na.rm = TRUE): NA's omitted; extrapolation gives NA
data.frame(approx(xn,yn, xout))
data.frame(approx(xn,yn, xout, rule = 2))# -> *constant* extrapolation
## New (2019-2020)  na.rm = FALSE: NA's are "kept"
data.frame(approx(xn,yn, xout, na.rm=FALSE, rule = 2))
data.frame(approx(xn,yn, xout, na.rm=FALSE, rule = 2, method="constant"))

## NA's in x[] are not allowed:
stopifnot(inherits( try( approx(yn,yn, na.rm=FALSE) ), "try-error"))

## Give a nice overview of all possibilities  rule * method * na.rm :
##             -----------------------------  ====   ======   =====
## extrapolations "N":= NA;   "C":= Constant :
rules <- list(N=1, C=2, NC=1:2, CN=2:1)
methods <- c("constant","linear")
ry <- sapply(rules, function(R) {
sapply(methods, function(M)
sapply(setNames(,c(TRUE,FALSE)), function(na.)
approx(xn, yn, xout=xout, method=M, rule=R, na.rm=na.)$y), simplify="array") }, simplify="array") names(dimnames(ry)) <- c("x = ", "na.rm", "method", "rule") dimnames(ry)[] <- format(xout) ftable(aperm(ry, 4:1)) # --> (4 * 2 * 2) x length(xout) = 16 x 9 matrix ## Show treatment of 'ties' : x <- c(2,2:4,4,4,5,5,7,7,7) y <- c(1:6, 5:4, 3:1) (amy <- approx(x, y, xout = x)$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)$y)) (ay <- approx(x, y, xout = x, ties = "ordered")$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
options(op) # revert 'warn'ing level


[Package stats version 4.2.1 Index]