pracma (version 1.9.3)

gradient: Discrete Gradient (Matlab Style)

Description

Discrete numerical gradient.

Usage

gradient(F, h1 = 1, h2 = 1)

Arguments

F

vector of function values, or a matrix of values of a function of two variables.

h1

x-coordinates of grid points, or one value for the difference between grid points in x-direction.

h2

y-coordinates of grid points, or one value for the difference between grid points in y-direction.

Value

If F is a vector, one gradient vector will be returned.If F is a matrix, a list with two components will be returned:

X

numerical gradient/slope in x-direction.

Y

numerical gradient/slope in x-direction.

where each matrix is of the same size as F.

Details

Returns the numerical gradient of a vector or matrix as a vector or matrix of discrete slopes in x- (i.e., the differences in horizontal direction) and slopes in y-direction (the differences in vertical direction).

A single spacing value, h, specifies the spacing between points in every direction, where the points are assumed equally spaced.

See Also

fderiv

Examples

x <- seq(0, 1, by=0.2)
y <- c(1, 2, 3)
(M <- meshgrid(x, y))
gradient(M$X^2 + M$Y^2)
gradient(M$X^2 + M$Y^2, x, y)

## Not run: 
# # One-dimensional example
# x <- seq(0, 2*pi, length.out = 100)
# y <- sin(x)
# f <- gradient(y, x)
# max(f - cos(x))      #=> 0.00067086
# plot(x, y, type = "l", col = "blue")
# lines(x, cos(x), col = "gray", lwd = 3)
# lines(x, f, col = "red")
# grid()
# 
# # Two-dimensional example
# v <- seq(-2, 2, by=0.2)
# X <- meshgrid(v, v)$X
# Y <- meshgrid(v, v)$Y
# 
# Z <- X * exp(-X^2 - Y^2)
# image(v, v, t(Z))
# contour(v, v, t(Z), col="black", add = TRUE)
# grid(col="white")
# 
# grX <- gradient(Z, v, v)$X
# grY <- gradient(Z, v, v)$Y
# 
# quiver(X, Y, grX, grY, scale = 0.2, col="blue")
# ## End(Not run)