R: 2-D Barycentric Lagrange Interpolation

barylag2d {pracma} | R Documentation

## 2-D Barycentric Lagrange Interpolation

### Description

Two-dimensional barycentric Lagrange interpolation.

### Usage

    barylag2d(F, xn, yn, xf, yf)

### Arguments

`F` | matrix representing values of a function in two dimensions.
`xn, yn` | x- and y-coordinates of supporting nodes.
`xf, yf` | x- and y-coordinates of an interpolating grid..

### Details

Well-known Lagrange interpolation using barycentric coordinates, here extended to two dimensions. The function is completely vectorized.

x-coordinates run downwards in F, y-coordinates to the right. That conforms to the usage in image or contour plots, see the example below.

### Value

Matrix of size `length(xf)`-by-`length(yf)` giving the interpolated values at al the grid points `(xf, yf)`.

### Note

Copyright (c) 2004 Greg von Winckel of a Matlab function under BSD license; translation to R by Hans W Borchers with permission.

### References

Berrut, J.-P., and L. Nick Trefethen (2004). “Barycentric Lagrange Interpolation”. SIAM Review, Vol. 46(3), pp.501–517.

### See Also

`interp2`, `barylag`

### Examples

    ##  Example from R-help
    xn <- c(4.05, 4.10, 4.15, 4.20, 4.25, 4.30, 4.35)
    yn <- c(60.0, 67.5, 75.0, 82.5, 90.0)
    foo <- matrix(c(
            -137.8379, -158.8240, -165.4389, -166.4026, -166.2593,
            -152.1720, -167.3145, -171.1368, -170.9200, -170.4605,
            -162.2264, -172.5862, -174.1460, -172.9923, -172.2861,
            -168.7746, -175.2218, -174.9667, -173.0803, -172.1853,
            -172.4453, -175.7163, -174.0223, -171.5739, -170.5384,
            -173.7736, -174.4891, -171.6713, -168.8025, -167.6662,
            -173.2124, -171.8940, -168.2149, -165.0431, -163.8390),
                nrow = 7, ncol = 5, byrow = TRUE)
    xf <- c(4.075, 4.1)
    yf <- c(63.75, 67.25)
    barylag2d(foo, xn, yn, xf, yf)
    #  -156.7964 -163.1753
    #  -161.7495 -167.0424

    # Find the minimum of the underlying function
    bar <- function(xy) barylag2d(foo, xn, yn, xy[1], xy[2])
    optim(c(4.25, 67.5), bar)  # "Nelder-Mead"
    # $par
    # 4.230547 68.522747
    # $value
    # -175.7959

    ## Not run:
    # Image and contour plots
    image(xn, yn, foo)
    contour(xn, yn, foo, col="white", add = TRUE)
    xs <- seq(4.05, 4.35, length.out = 51)
    ys <- seq(60.0, 90.0, length.out = 51)
    zz <- barylag2d(foo, xn, yn, xs, ys)
    contour(xs, ys, zz, nlevels = 20, add = TRUE)
    contour(xs, ys, zz, levels=c(-175, -175.5), add = TRUE)
    points(4.23, 68.52)
    ## End(Not run)

[Package pracma version 2.0.4 Index]