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

I don't think the answer by @Daniel is correct, especially when the input is in order [Fx, Fy, Fz, ...].

A simple test case

See the MATLAB code:

a = [1 2 3;1 2 3; 1 2 3];
b = [[7 8 9] ;[1 5 8] ;[2 4 7]];
divergence(a,b)

which gives the result:

ans =

   -5.0000   -2.0000         0
   -1.5000   -1.0000         0
    2.0000         0         0

and Daniel's solution:

def divergence(f):
    """
    Daniel's solution
    Computes the divergence of the vector field f, corresponding to dFx/dx + dFy/dy + ...
    :param f: List of ndarrays, where every item of the list is one dimension of the vector field
    :return: Single ndarray of the same shape as each of the items in f, which corresponds to a scalar field
    """
    num_dims = len(f)
    return np.ufunc.reduce(np.add, [np.gradient(f[i], axis=i) for i in range(num_dims)])


if __name__ == '__main__':
    a = np.array([[1, 2, 3]] * 3)
    b = np.array([[7, 8, 9], [1, 5, 8], [2, 4, 7]])
    div = divergence([a, b])
    print(div)
    pass

which gives:

[[1.  1.  1. ]
 [4.  3.5 3. ]
 [2.  2.5 3. ]]

Explanation

The mistake of Daniel's solution is, in Numpy, the x axis is the last axis instead of the first axis. When using np.gradient(x, axis=0), Numpy actually gives the gradient of y direction (when x is a 2d array).

My solution

There is my solution based on Daniel's answer.

def divergence(f):
    """
    Computes the divergence of the vector field f, corresponding to dFx/dx + dFy/dy + ...
    :param f: List of ndarrays, where every item of the list is one dimension of the vector field
    :return: Single ndarray of the same shape as each of the items in f, which corresponds to a scalar field
    """
    num_dims = len(f)
    return np.ufunc.reduce(np.add, [np.gradient(f[num_dims - i - 1], axis=i) for i in range(num_dims)])

which gives the same result as MATLAB divergence in my test case.