Gradient function not matching array dimensions

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?

Answer 1

[Matt J]

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              

Answer 2

[Matt J]

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 = 

[Carlos Martinez]

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]

Perhaps as follows?

function [Gx,Gy]=mygrad(X,Y)

  den=2*pi*(X.^2+Y.^2);
  
  Gx=-Y./den;
  Gy=X./den+1;


end