When to use .^ notation?

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Jay
Jay 2018-12-4
评论： Jay 2018-12-5
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:
vectorfield1.PNG
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:
vectorfield2.PNG
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!

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采纳的回答

madhan ravi
madhan ravi 2018-12-4
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 .^
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Jay
Jay 2018-12-4
Thank you so much!

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更多回答（1 个）

Image Analyst
Image Analyst 2018-12-4
编辑：Image Analyst 2018-12-4
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);
0000 Screenshot.png
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.
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Jay
Jay 2018-12-5
That makes so much more sense. Thank you so much for your help and explanation!

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