R: Univariate Akima interpolation

aspline {akima} | R Documentation

## Univariate Akima interpolation

### Description

The function returns a list of points which smoothly interpolate given data points, similar to a curve drawn by hand.

### Usage

      aspline(x, y=NULL, xout, n = 50, ties = mean, method="original", degree=3)

### Arguments

`x, y` | 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 values specifying where interpolation is to take place.
`n` | If `xout` is not specified, interpolation takes place at `n` equally spaced points spanning the interval [`min(x)`, `max(x)`].
`ties` | Handling of tied `x` values. Either a function with a single vector argument returning a single number result or the string `"ordered"`.
`method` | either `"original"` method after Akima (1970) or `"improved"` method after Akima (1991)
`degree` | if improved algorithm is selected: degree of the polynomials for the interpolating function

### Details

The original algorithm is based on a piecewise function composed of a set of polynomials, each of degree three, at most, and applicable to successive interval of the given points. In this method, the slope of the curve is determined at each given point locally, and each polynomial representing a portion of the curve between a pair of given points is determined by the coordinates of and the slopes at the points.

### Value

A list with components `x` and `y`, containing `n` coordinates which interpolate the given data points.

### References

Akima, H. (1970) A new method of interpolation and smooth curve fitting based on local procedures, J. ACM 17(4), 589-602

Akima, H. (1991) A Method of Univariate Interpolation that Has the Accuracy of a Third-degree Polynomial. ACM Transactions on Mathematical Software, 17(3), 341-366.

### See Also

`approx`, `spline`

### Examples

    ## regular spaced data
    x <- 1:10
    y <- c(rnorm(5), c(1,1,1,1,3))

    xnew <- seq(-1, 11, 0.1)
    plot(x, y, ylim=c(-3, 3), xlim=range(xnew))
    lines(spline(x, y, xmin=min(xnew), xmax=max(xnew), n=200), col="blue")

    lines(aspline(x, y, xnew), col="red")
    lines(aspline(x, y, xnew, method="improved"), col="black", lty="dotted")
    lines(aspline(x, y, xnew, method="improved", degree=10), col="green", lty="dashed")

    ## irregular spaced data
    x <- sort(runif(10, max=10))
    y <- c(rnorm(5), c(1,1,1,1,3))

    xnew <- seq(-1, 11, 0.1)
    plot(x, y, ylim=c(-3, 3), xlim=range(xnew))
    lines(spline(x, y, xmin=min(xnew), xmax=max(xnew), n=200), col="blue")

    lines(aspline(x, y, xnew), col="red")
    lines(aspline(x, y, xnew, method="improved"), col="black", lty="dotted")
    lines(aspline(x, y, xnew, method="improved", degree=10), col="green", lty="dashed")

    ## an example of Akima, 1991
    x <- c(-3, -2, -1, 0,  1,  2, 2.5, 3)
    y <- c( 0,  0,  0, 0, -1, -1, 0,   2)

    plot(x, y, ylim=c(-3, 3))
    lines(spline(x, y, n=200), col="blue")

    lines(aspline(x, y, n=200), col="red")
    lines(aspline(x, y, n=200, method="improved"), col="black", lty="dotted")
    lines(aspline(x, y, n=200, method="improved", degree=10), col="green", lty="dashed")

[Package akima version 0.6-2 Index]