Surf function won't graph 2D Gaussian

Question

I'm trying to graph a simple 2D Gaussian in MATLAB using the surf function, but I'm getting an error saying that the last value in surf must be a matrix and not a vector. I don't understand how to graph the function then as every other example I've found while searching has had the third value as a vector. I feel as if I'm completely off base here with the surf function. Any ideas?

amp = 10;
x0 = 0;
y0 = 0;
sigmaX = 10
sigmaY = 10
X = 1:1:100;
Y = 1:1:100;
Z = amp*exp(-(X-x0).^2/(2*sigmaX^2)+(Y-y0).^2/(2*sigmaY^2));
disp(size(Z))
surf(X, Y, Z);

Edit

When I plot this using @Suever's answer, I get something that doesn't look like a Gaussian at all.

Here's the plot

amp = 1;
x0 = 0;
y0 = 0;
sigmaX = 1;
sigmaY = 1;
%X = 1:1:100;
%Y = 1:1:100;
[X,Y] = meshgrid(-3:.1:3);
%Z = X .* exp(-X.^2 - Y.^2);
Z = amp*exp(-(X-x0).^2/(2*sigmaX^2)+(Y-y0).^2/(2*sigmaY^2));
surf(X, Y, Z);

Answer 1

You have used X and Y to define a 2D domain over which you would like to compute your gaussian. If you want Z to be a function of X and Y, you need to define Z for all permutations of X and Y. If you don't provide a matrix of Z values, MATLAB has no idea how to create a surface over the X Y ranges you've provided.

You can create all permutations of X and Y using meshgrid and then compute Z over this entire domain. Then you will be able to display the result with surf.

amp = 10; x0 = 50; y0 = 50; sigmaX = 10; sigmaY = 10;

[X, Y] = meshgrid(1:100, 1:100);

% Z as you had it written (see correct version below)
Z = amp*exp(-(X-x0).^2./(2*sigmaX^2)+(Y-y0).^2./(2*sigmaY^2));

surf(X, Y, Z);

Update

Your equation for the 2D Gaussian is wrong. The - sign should be outside of the addition of the two components. The way that you had it written, you negated the X-component and then added to the Y component.

Z = amp*exp(-((X-x0).^2./(2*sigmaX^2)+(Y-y0).^2./(2*sigmaY^2)));