Shuffling non-zero elements of each row in an array – Python / NumPy

You could use the non-inplace numpy.random.permutation with explicit non-zero indexing:

>>> X = np.array([[2,3,1,0], [0,0,2,1]])
>>> for i in range(len(X)):
...     idx = np.nonzero(X[i])
...     X[i][idx] = np.random.permutation(X[i][idx])
... 
>>> X
array([[3, 2, 1, 0],
       [0, 0, 2, 1]])