R: Calculate Matrix Gradient

grad {oce} | R Documentation

## Calculate Matrix Gradient

### Description

In the interior of the matrix, centred second-order differences are used to infer the components of the grad. Along the edges, first-order differences are used.

### Usage

    grad(
      h,
      x = seq(0, 1, length.out = nrow(h)),
      y = seq(0, 1, length.out = ncol(h))
    )

### Arguments

`h` | a matrix of values
`x` | vector of coordinates along matrix columns (defaults to integers)
`y` | vector of coordinates along matrix rows (defaults to integers)

### Value

A list containing abs(grad(h)) as `g`, dh/dx as `gx`, and dh/dy as `gy`, each of which is a matrix of the same dimension as `h`.

### Author(s)

Dan Kelley, based on advice of Clark Richards, and mimicking a matlab function.

### See Also

Other functions relating to vector calculus: `curl()`

### Examples

    ## 1. Built-in volcano dataset
    g <- grad(volcano)
    par(mfrow=c(2, 2), mar=c(3, 3, 1, 1), mgp=c(2, 0.7, 0))
    imagep(volcano, zlab="h")
    imagep(g$g, zlab="|grad(h)|")
    zlim <- c(-1, 1) * max(g$g)
    imagep(g$gx, zlab="dh/dx", zlim=zlim)
    imagep(g$gy, zlab="dh/dy", zlim=zlim)

    ## 2. Geostrophic flow around an eddy
    library(oce)
    dx <- 5e3
    dy <- 10e3
    x <- seq(-200e3, 200e3, dx)
    y <- seq(-200e3, 200e3, dy)
    R <- 100e3
    h <- outer(x, y, function(x, y) 500*exp(-(x^2+y^2)/R^2))
    grad <- grad(h, x, y)
    par(mfrow=c(2, 2), mar=c(3, 3, 1, 1), mgp=c(2, 0.7, 0))
    contour(x,y,h,asp=1, main=expression(h))
    f <- 1e-4
    gprime <- 9.8 * 1 / 1024
    u <- -(gprime / f) * grad$gy
    v <-  (gprime / f) * grad$gx
    contour(x, y, u, asp=1, main=expression(u))
    contour(x, y, v, asp=1, main=expression(v))
    contour(x, y, sqrt(u^2+v^2), asp=1, main=expression(speed))

[Package oce version 1.2-0 Index]