How can I calculate the gradient of my data that is in the polar coordinates in MATLAB 7.8 (R2009a)?

I have a dataset in the polar coordinates and would like to calculate its gradient but cannot find a function for the same.

Answer 1

[MathWorks Support Team]

The ability to directly calculate the gradient of data that is in the polar coordinates in not available in MATLAB 7.8 (R2009a).

The general equation for the polar gradient is:

 gradient(F) = del(F)/del(r) + 1/r * del(F)/del(theta)

As a workaround, given:

F = matrix of F values varying along r and theta

r = vector of radius values

theta = vector of radian values

the following code can be used to calculate the gradient.

      % Take the gradient of F, suppose that the values of r vary along the rows

      % (and are constant along the columns) and that the values of theta vary

      % along the columns and are constant along the rows.

     [ dFr dFt ] = gradient(F,r,theta);

     % Modify the results for dFt, as the second term in the polar gradient

     % is divided by the value of r

      dFt = dFt./(repmat(r(:)',length(theta),1);