Compute divergence of vector field using python

Question

Is there a function that could be used for calculation of the divergence of the vectorial field? (in matlab) I would expect it exists in numpy/scipy but I can not find it us

Answer 1

The answer of @user2818943 is good, but it can be optimized a little:

def divergence(F):
    """ compute the divergence of n-D scalar field `F` """
    return reduce(np.add,np.gradient(F))

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Timeit:

F = np.random.rand(100,100)
timeit reduce(np.add,np.gradient(F))
# 1000 loops, best of 3: 318 us per loop

timeit np.sum(np.gradient(F),axis=0)
# 100 loops, best of 3: 2.27 ms per loop

About 7 times faster: sum implicitely construct a 3d array from the list of gradient fields which are returned by np.gradient. This is avoided using reduce

---

Now, in your question what do you mean by div[A * grad(F)]?

1. about A * grad(F): A is a 2d array, and grad(f) is a list of 2d arrays. So I considered it means to multiply each gradient field by A.
2. about applying divergence to the (scaled by A) gradient field is unclear. By definition, div(F) = d(F)/dx + d(F)/dy + .... I guess this is just an error of formulation.

For 1, multiplying summed elements Bi by a same factor A can be factorized:

Sum(A*Bi) = A*Sum(Bi)

Thus, you can get this weighted gradient simply with: A*divergence(F)

If ̀A is instead a list of factor, one for each dimension, then the solution would be:

def weighted_divergence(W,F):
    """
    Return the divergence of n-D array `F` with gradient weighted by `W`

    ̀`W` is a list of factors for each dimension of F: the gradient of `F` over
    the `i`th dimension is multiplied by `W[i]`. Each `W[i]` can be a scalar
    or an array with same (or broadcastable) shape as `F`.
    """
    wGrad = return map(np.multiply, W, np.gradient(F))
    return reduce(np.add,wGrad)

result = weighted_divergence(A,F)