Minmax normalization cast away the complex part?

Question

I am currently trying to normalize an numpy.ndarray containing complex numbers, but for some reason is my implementation casting away the complex part.. Why?...

def numpy_minmax(X):
    xmin =  X.min()
    print X.min()
    print X.max()
    return (2*(X - xmin) / (X.max() - xmin)-1)*0.9

Answer 1

The minimum or maximum of complex numbers is an undefined concept. This is why NumPy ignores the imaginary part when taking max or min of an array.

Generally, normalization consists of centering and scaling.

A natural notion of center of an array of complex numbers is the center of the smallest disk containing them. But this (the Chebyshev center) is somewhat difficult to compute. A simpler way to center is to take the smallest axes-aligned rectangle containing the numbers. This involves looking at max/min of real and imaginary parts separately:

a = (np.real(X).min() + np.real(X).max())/2.0
b = (np.imag(X).min() + np.imag(X).max())/2.0
Y = X - complex(a, b)

Next, the scaling. Looks like you want the absolute values of the numbers to be at most 0.9. This can be arranged by using the maximum of absolute values of elements of Y.

return 0.9*Y/np.abs(Y).max()

This is not the only way one could proceed; but to me the above appears to be the most straightforward adaptation of your code to the complex case.