splinefun {stats} | R Documentation

## Interpolating Splines

### Description

Perform cubic spline interpolation of given data points, returning either a list of points obtained by the interpolation or a function performing the interpolation.

### Usage

    splinefun(x, y = NULL, method = "fmm")

    spline(x, y = NULL, n = 3*length(x), method = "fmm",
           xmin = min(x), xmax = max(x))

### Arguments

`x,y` | vectors giving the coordinates of the points to be interpolated. Alternatively a single plotting structure can be specified: see `xy.coords.`
`method` | specifies the type of spline to be used. Possible values are `"fmm"`, `"natural"` and `"periodic"`.
`n` | interpolation takes place at `n` equally spaced points spanning the interval [`xmin`, `xmax`].
`xmin` | left-hand endpoint of the interpolation interval.
`xmax` | right-hand endpoint of the interpolation interval.

### Details

If `method = "fmm"`, the spline used is that of Forsythe, Malcolm and Moler (an exact cubic is fitted through the four points at each end of the data, and this is used to determine the end conditions). Natural splines are used when `method = "natural"`, and periodic splines when `method = "periodic"`.

These interpolation splines can also be used for extrapolation, that is prediction at points outside the range of `x`. Extrapolation makes little sense for `method = "fmm"`; for natural splines it is linear using the slope of the interpolating curve at the nearest data point.

### Value

`spline` returns a list containing components `x` and `y` which give the ordinates where interpolation took place and the interpolated values.
`splinefun` returns a function which will perform cubic spline interpolation of the given data points. This is often more useful than `spline`.

### References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

Forsythe, G. E., Malcolm, M. A. and Moler, C. B. (1977) Computer Methods for Mathematical Computations.

### See Also

`approx` and `approxfun` for constant and linear interpolation.

Package splines, especially `interpSpline` and `periodicSpline` for interpolation splines. That package also generates spline bases that can be used for regression splines.

`smooth.spline` in package modreg for smoothing splines.

### Examples

    op <- par(mfrow = c(2,1), mgp = c(2,.8,0), mar = .1+c(3,3,3,1))
    n <- 9
    x <- 1:n
    y <- rnorm(n)
    plot(x, y, main = paste("spline[fun](.) through", n, "points"))
    lines(spline(x, y))
    lines(spline(x, y, n = 201), col = 2)

    y <- (x-6)^2
    plot(x, y, main = "spline(.) -- 3 methods")
    lines(spline(x, y, n = 201), col = 2)
    lines(spline(x, y, n = 201, method = "natural"), col = 3)
    lines(spline(x, y, n = 201, method = "periodic"), col = 4)
    legend(6,25, c("fmm","natural","periodic"), col=2:4, lty=1)

    f <- splinefun(x, y)
    ls(envir = environment(f))
    splinecoef <- eval(expression(z), envir = environment(f))
    curve(f(x), 1, 10, col = "green", lwd = 1.5)
    points(splinecoef, col = "purple", cex = 2)
    par(op)

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