Weighted phase Laplacian formula

We have the following equation (weighted phase Laplacian):

\$c_{i,j} = U(i,j)\Delta^{^x}_{i,j} - U(i-l, j)\Delta^{x}_{i-1,j} + V(i,j)\Delta^{y}_{i,j} - V(i,j-1)\Delta^{y}_{i,j-1}\$

Where

\$U(i,j) = min(w^2_{i+1}, w^2_{i+1})V(i,j) = min(w^2_{j+1}, w^2_{j+1})\$

with \$U, V, \Delta \$ (N,N) matrices

I coded the following code:

def compute_Weights(w):
    U = np.zeros_like(w)
    V = np.zeros_like(w)
    U = np.minimum(w[1:, :]**2, w[:-1, :]**2)
    V = np.minimum(w[:, 1:]**2, w[:, :-1]**2)

    """add the last ones rows and cols
    """
    U = np.vstack((U, U[-1]))
    V = np.vstack((V.T, V.T[-1])).transpose()

    return U, V

def Gradient(p1, p2):
    r = p1 - p2
    if r > np.pi:
        return r - 2 * np.pi
    if r  0 else k + 1
            k3 = k + cols if j  0 else k + cols

            w1 = U[k]
            w2 = U[k-1] if i > 0 else U[k]
            w3 = V[k]
            w4 = V[k-cols] if j > 0 else V[k]

            rho[k] = w1 * Gradient(phi[k], phi[k1]) \
                + w2 * Gradient(phi[k], phi[k2]) \
                + w3 * Gradient(phi[k], phi[k3]) \
                + w4 * Gradient(phi[k], phi[k4])

    return rho

I want to know if there is a "pythonic way" to write this. I'm a C/C++ programmer so this was my perspective. Maybe something to avoid to work with flattened arrays, and to work with 2D arrays.

I.e:

phase = np.load('phase.npy') #phase 512x512 float array
U,V = ComputeWeigths(W) #W 512x512 float array with values in (0,1)
uphase = ComputePhaseLaplacian(phase, U, V) #uphase 512x512 float array

A few points. In your code, some of these render others irrelevant, but they may be relevant in other code you write:

• Try to follow PEP8

• It should be possible to vectorize ComputePhaseLaplacian.

• It is better to loop over rows and columns directly rather than looping over indexes. You can use enumerate to keep track of the rows and columns.

• You shouldn't flatten, you can index in two dimensions.

• Instead of vstack, you should use pad in this case.

• You create U and V, then immediately overwrite them. This is redundant.

• You should use ravel instead of flatten since it doesn't make a copy.

StackExchange Code Review Q#93995, answer score: 5