compute gradient in matlab

To compute the gradient of a function in Matlab, we can use the gradient function which approximates the gradient numerically using finite differences. The syntax for the gradient function is:

main.m
[grad_x, grad_y, grad_z, ...] = gradient(f, stepx, stepy, stepz, ...)
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where f is the function handle or array, and stepx, stepy, stepz, etc. are the step sizes for each dimension. The gradient function returns the gradients along each dimension as separate output variables.

Here's an example of computing the gradient of a function f:

main.m
% define the function
f = @(x, y) x.^2 + 2*y.^2 + exp(x.*y);

% set the step sizes
stepx = 0.1;
stepy = 0.2;

% compute the gradient
[grad_x, grad_y] = gradient(f, stepx, stepy);

% plot the results
[X, Y] = meshgrid(-5:0.1:5);
Z = f(X, Y);
quiver(X, Y, -grad_x, -grad_y);
hold on
contour(X, Y, Z);
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This will generate a plot showing the gradient vectors and contours of the function f: