R: Interpolation Functions

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 `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’.
`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[[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

[Package stats version 4.0.5 Index]