Discrete Gradient (Matlab Style)

Discrete numerical gradient.

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.

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.

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.

Note

TODO: If h2 is missing, it will not automatically be adapted.

See also

fderiv

Examples

x <- seq(0, 1, by=0.2)
y <- c(1, 2, 3)
(M <- meshgrid(x, y))
#> $X
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,]    0  0.2  0.4  0.6  0.8    1
#> [2,]    0  0.2  0.4  0.6  0.8    1
#> [3,]    0  0.2  0.4  0.6  0.8    1
#> 
#> $Y
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,]    1    1    1    1    1    1
#> [2,]    2    2    2    2    2    2
#> [3,]    3    3    3    3    3    3
#> 
gradient(M$X^2 + M$Y^2)
#> $X
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0.04 0.08 0.16 0.24 0.32 0.36
#> [2,] 0.04 0.08 0.16 0.24 0.32 0.36
#> [3,] 0.04 0.08 0.16 0.24 0.32 0.36
#> 
#> $Y
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,]    3    3    3    3    3    3
#> [2,]    4    4    4    4    4    4
#> [3,]    5    5    5    5    5    5
#> 
gradient(M$X^2 + M$Y^2, x, y)
#> $X
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,]  0.2  0.4  0.8  1.2  1.6  1.8
#> [2,]  0.2  0.4  0.8  1.2  1.6  1.8
#> [3,]  0.2  0.4  0.8  1.2  1.6  1.8
#> 
#> $Y
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,]    3    3    3    3    3    3
#> [2,]    4    4    4    4    4    4
#> [3,]    5    5    5    5    5    5
#> 

if (FALSE) { # \dontrun{
# 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")
} # }