When to use .^ notation?

For an assignment, I am supposed to use MatLab to plot the vector field. I've tried

[x,y]=meshgrid(-5:1:5,-5:1:5);
quiver(x,y,0.2*(x.^2+y.^2),0.2*(x-y),0);

which gives me the following picture:

I have also tried this:

[x,y]=meshgrid(-5:1:5,-5:1:5);
quiver(x,y,0.2*(x^2+y^2),0.2*(x-y),0);

which gives me this picture:

These are so different, and I'm not sure which one is correct because I don't understand why .^ is giving a different result than just ^ alone.

Any advice is greatly appreciated. Thank you!

Answer 1

[madhan ravi]

when you have a vector the right usage is .^ which is element wise operation each element is raised to the power ^ is only for scalars so use .^

[Jay]

So since x and y are not vectors, does that mean the second image is the correct image since it was generated with just the ^ notation?

[madhan ravi]

I am not the one who says this is correct and that is wrong you should learn about Array vs Matrix operations. Basically what happens is if a matrix is square ^ performs matrix multiplication and .^ performs element wise operation so now you are the one to decide which one is apt for your need.

[Jay]

Thank you so much!

[madhan ravi]

Anytime :)

Answer 2

[Image Analyst]

Well you're sort of close - at least you tried - but I don't think either of your attempts is correct. Madhan is correct in that using dot means that it's element-by-element raising to a power. But you need to look at what quiver wants, and that is vectors whereas your x and y are matrices. If you take a second look at it, I think you'll realize you need to use (:) to turn them into vectors when you compute u and v, and you'll get something like this:

[x, y] = meshgrid(-5:1:5, -5:1:5);
u = 0.2 * (x(:) .^ 2 + y(:) .^ 2);
v = 0.2 * (x(:) - y(:));
% Plot quiver:
subplot(2, 1, 1);
quiver(x(:), y(:), u, v, 'LineWidth', 1);
grid on;
axis square;
xlabel('x', 'FontSize', 20);
ylabel('y', 'FontSize', 20);
title('Quiver Plot', 'FontSize', 20);
% Plot surface of the magnitude
subplot(2, 1, 2);
z = reshape(sqrt(u .^ 2 + v .^ 2), [11,11]);
surf(-5:1:5, -5:1:5, z);
xlabel('x', 'FontSize', 20);
ylabel('y', 'FontSize', 20);
title('Magnitude Plot', 'FontSize', 20);

Notice that when x = y (along the diagonal), the vectors are flat, meaning no vertical component, as you'd expect from the equation which involves x-y.

[Jay]

That makes so much more sense. Thank you so much for your help and explanation!