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

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[[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

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)[[1]] <- 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