Gradient function not matching array dimensions

2023 3 16
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更新时间：2023 3 16
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I have the function
psi=y+atan2(y,x)*0.5/pi;
which is classified as a 51x51 double for its value. How would I take the gradient of x and y for this function?

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Matt J
Matt J 2023-3-16
Ran in:

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Ran in:
Alternatively, why not use the gradient command?
psi =rand(51);
[gradx,grady]=gradient(psi);
whos psi gradx grady
Name Size Bytes Class Attributes gradx 51x51 20808 double grady 51x51 20808 double psi 51x51 20808 double

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Matt J
Matt J 2023-3-16
Ran in:

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Ran in:
The expression for the gradient is very simple. Why not just apply the analytical expression on whatever meshgrid you are working with?
syms x y real
syms psi
psi=y+atan2(y,x)/2/pi;
g=simplify(gradient(psi))
g = 

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Carlos Martinez
Carlos Martinez 2023-3-16
Thanks! Is there a way to separate the components for it? I'm trying to get the u and v values for the stream function
Matt J
Matt J 2023-3-16
Perhaps as follows?
function [Gx,Gy]=mygrad(X,Y)
den=2*pi*(X.^2+Y.^2);
Gx=-Y./den;
Gy=X./den+1;
end

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