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))

---

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)

Answer 2

http://www.scipy.org/Topical_Software#head-85e01502b533f2477ab8c643b38ee92706a377bb

Even if it doesn't have the divergence hand-packaged for you, divergence is pretty simple and the derivative tools they give you in scipy (the ones linked above) give you about 90% of the code prepackaged in a nice, efficient way.

Answer 3

import numpy as np

def divergence(field):
    "return the divergence of a n-D field"
    return np.sum(np.gradient(field),axis=0)

Answer 4

As far as I can tell, the answer is that there is no native divergence function in numpy. Therefore, the best method for calculating divergence is to sum the components of the gradient vector i.e. calculate the divergence.