gradient

Arguments

f

matrix of doubles, representing sampled data

h, hx, hy, ..., hn

real scalar or vector, corresponding to step size(s) along each dimension. Default is 1.

gx, gy, ..., gn

matrix of doubles, corresponding to the gradient of f with respect to each dimension. Each matrix has the same size as f.

Description

The gradient function computes the partial derivatives of a matrix f using central differences for interior points and first-order differences at the boudaries.

gx = gradient(f) returns the gradient along rows, i.e x-direction. The step between each point of f is equal to 1.

[gx, gy] = gradient(f) returns two matrices: gx gradient along rows, i.e x-direction and gy, gradient along columns y-direction. The step between each point of f is equal to 1.

[gx, gy, ..., gn] = gradient(f) returns n matrices if f is a n-dimensional matrix.

If h is provided, it scales the differences accordingly. It can be:

• a scalar: uniform step size in all direction.
• a vector: individual step sizes per dimension.

Examples

2D gradient

f = [1 2 4; 
    3 6 9; 
    0 5 8];
[gx, gy] = gradient(f)

Gradient with step size

f = [1 2 4; 
    3 6 9; 
    0 5 8];
[gx, gy] = gradient(f, 0.5) // assumes 0.5 spacing in both directions

[x, y] = meshgrid(-2:0.5:2, -2:0.5:2);
f = x.^2 + y.^2;

[gx, gy] = gradient(f, 0.5);

// at point x0 = 1 and y0 = 1;
t = x == 1 & y == -1
// exact value of the gradient at the point (1,-1) is [2 -2]
[gx(t), gy(t)]

See also

• diff — Difference and discrete derivative
• diffxy — derivative of y with respect to x
• numderivative — approximate derivatives of a function (Jacobian or Hessian)

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