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)

    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 `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. Either a function with a single vector argument returning a single number result or the string `"ordered"`.

### 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` 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.

### 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)

    ## 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 3.1.2 Index]