gradient

Syntax

dx = gradient(yc,xc)

dx = gradient(m)

[dx,dy,...] = gradient(m)

[...] = gradient(m,d)

[...] = gradient(m,x,y,...)

[...] = gradient(f,p)

[...] = gradient(f,p,d)

[...] = gradient(f,p,x,y,...)

Inputs

yc: Sampled y coordinate data from which to compute the gradient, paired with xc.; A vector can be either a row or a column. For a 2D matrix, gradients are computed by row.; The gradients at the first and last points are computed with forward and backward differences, respectively. The other points use central differences.; Type: double; Dimension: vector | matrix
xc: Sampled x coordinate data from which to compute the gradient, paired with yc.; A vector is used for each computed gradient vector in yc. A 2D matrix must have the same dimensions as yc.; Type: double; Dimension: vector | matrix
m: A matrix of sampled data from which to compute the gradient.; Data with two or more dimensions is stored by column. One dimensional data can be stored either as a row or a column.; The gradients at the first and last points are computed with forward and backward differences, respectively. The other points use central differences.; The first and second dimensions are assigned to 'y' and 'x', respectively. This convention is so that the 'x' axis is horizontal.; Type: double; Dimension: matrix
f: The function for which to compute the gradient.; The function must operate on vector arguments for each coordinate. See the example below.; Type: char | string | handle
p: The points at which to compute the gradient when using f.; Data with two or more dimensions is stored by column. One dimensional data can be stored either as a row or a column.; Type: double; Dimension: matrix
d: One half of the central difference interval, used in all dimensions.; The default is 1.; Type: double; Dimension: scalar
x,y,...: Each value is one half of the central difference interval used in its corresponding dimension.; The default for each value is 1.; Type: double; Dimension: scalar

Outputs

dx,dy,...: The gradient vector components for each dimension.; Type: double

Example

Function input with a common interval size for all dimensions:

function obj = Func(x,y)
    obj = 2*(x-3).^2 - 5*(x-3).*(y-2) + 4*(y-2).^2 + 6;
end

points = [2,5;3,6;4,7];
[dx,dy] = gradient(@Func, points, 0.001)

dx = [Matrix] 3 x 1
-19.00000
-20.00000
-21.00000
dy = [Matrix] 3 x 1
29.00000
32.00000
35.00000

Matrix data input wtih separate interval sizes for each dimension:

m = [1 125 729 2197; 8 216 1000 2744; 27 343 1331 3375; 64 512 1728 4096];
[dx,dy] = gradient(m, 0.1, 0.2)

dx = [Matrix] 4 x 4
1240  3640  10360  14680
2080  4960  12640  17440
3160  6520  15160  20440
4480  8320  17920  23680
dy = [Matrix] 4 x 4
 35  455  1355  2735
 65  545  1505  2945
140  740  1820  3380
185  845  1985  3605

Matrix inputs with (x,y) coordinate data:

yc = [1, 4, 9, 16; 25, 36, 49, 64];
xc = [1, 2, 3, 4];
dx = gradient(yc, xc)

dx = [Matrix] 2 x 4
 3   4   6   7
11  12  14  15