3D Plot with the surf function in MATLAB

I want to do some tasks for a given function below:

f(x) = A * cos(sqrt(x1.^2 + x2.^2)).^2 .* exp(-B * sqrt(x1.^2 + x2.^2))

I need to Write the function sombrero, which should accept

• x: a 2-dimensional vector of coordinates;
• const: a 2-dimensional vector with the value of the constants
  A and B.

and then

• Set A = 2 and B = 0.3
• obtain the value of the function, evaluated in the point
  x = (3, 2)′;
• draw the function in the [-10, 10] square

When I try to run the code below I get this error "Z must be a matrix, not a scalar or vector"

function fx = sombrero(x, const)
    A = const(1);
    B = const(2);

    r = sqrt(x(1)^2 + x(2)^2);
    fx = A * cos(r)^2 * exp(-B * r);
end

% Constants
A = 2;
B = 0.3;

% Coordinates
x = [3; 2];

% Evaluate the function at the given point
fx = sombrero(x, [A, B]);

% Define the range of x and y values
x_range = linspace(-10, 10, 100);
y_range = linspace(-10, 10, 100);

% Create a grid of points
[X, Y] = meshgrid(x_range, y_range);

% Evaluate the function at each point of the grid
Z = sombrero([X(:) Y(:)]', [A, B]);

surf(X,Y,Z)

The error happens when evaluating the last line of code

Your problem is in the sombrero function.

The input x is a 2xN matrix, where the first row is the x coordinate and the second row is the y coordinate. But you extract x(1) and x(2), which give you only the coordinates for the first point (the first column of the array). Instead, use x(1,:) and x(2,:).

Next, since you're now operating on an array instead of a scalar, you must use the element-wise operators. * is a matrix multiplication, .* is an element-wise multiplication. Likewise with ^ vs .^, and / vs ./.

Finally, surf requires 3 matrices as input. X and Y are matrices, but Z is a vector, because you flattened the X and Y matrices to put them into sombrero(). I would suggest keeping them as separate inputs to the function, so you don't need to flatten them to put them into a matrix.

All together, the function should look like this:

function fx = sombrero(X, Y, const)
    A = const(1);
    B = const(2);

    r = sqrt(X.^2 + Y.^2);
    fx = A * cos(r).^2 .* exp(-B * r);
end

(I've left some * in there where you multiply by a scalar.)

Now you'd call the function as follows:

Z = sombrero(X, Y, [A, B]);
surf(X,Y,Z)