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.

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 \(|\nabla h|\) as g, \(\partial h/\partial x\) as gx, and \(\partial h/\partial y\) as gy, each of which is a matrix of the same dimension as h.

See also

Other things 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))