# NumPy mgrid vs. meshgrid

The meshgrid function is useful for creating coordinate arrays to vectorize function evaluations over a grid. Experienced NumPy users will have noticed some discrepancy between meshgrid and the mgrid, a function that is used just as often, for exactly the same purpose. What is the discrepancy, and why does a discrepancy even exist when "there should be one - and preferably only one - obvious way to do it." [1]

First, recall that meshgrid behaves as follows:

>>> import numpy as np
>>> x1, y1 = np.meshgrid(np.arange(1, 11, 2), np.arange(-12, -3, 3))
>>> x1
array([[1, 3, 5, 7, 9],
[1, 3, 5, 7, 9],
[1, 3, 5, 7, 9]])
>>> y1
array([[-12, -12, -12, -12, -12],
[ -9,  -9,  -9,  -9,  -9],
[ -6,  -6,  -6,  -6,  -6]])


If you have used NumPy for a while or are familiar enough with how Broadcasting works, you will have realized that meshgrid is actually superfluous for NumPy arrays, and that it is actually just an implementation of MATLAB's meshgrid, probably to cater to users coming from a MATLAB background.

Observe the behavior of mgrid, which essentially returns the transpose of meshgrid:

>>> x2, y2 = np.mgrid[1:11:2, -12:-3:3]
>>> x2
array([[1, 1, 1],
[3, 3, 3],
[5, 5, 5],
[7, 7, 7],
[9, 9, 9]])
>>> y2
array([[-12,  -9,  -6],
[-12,  -9,  -6],
[-12,  -9,  -6],
[-12,  -9,  -6],
[-12,  -9,  -6]])
>>> np.all(x1 == x2.T)
True
>>> np.all(y2 == y2.T)
True


Note this this order is actually more natural, since mgrid just fleshes out the open (not fleshed out) grids given by ogrid by broadcasting them to form dense grids, i.e.

>>> a, b = np.ogrid[1:11:2, -12:-3:3]
>>> a
array([[1],
[3],
[5],
[7],
[9]])
>>> b
array([[-12,  -9,  -6]])


and the 5x1 array a is broadcasted with the 1x3 array b to form two 5x3 arrays

>>> x2, y2 = np.broadcast_arrays(a, b)
>>> x2
array([[1, 1, 1],
[3, 3, 3],
[5, 5, 5],
[7, 7, 7],
[9, 9, 9]])
>>> y2
array([[-12,  -9,  -6],
[-12,  -9,  -6],
[-12,  -9,  -6],
[-12,  -9,  -6],
[-12,  -9,  -6]])


which behaves exactly the same way as mgrid. Note that you seldom have to broadcast arrays explicitly, let alone use functions like mgrid or meshgrid, since all arithmetic operations on NumPy arrays already perform broadcasting implicitly. E.g.

>>> x2 + y2
array([[-11,  -8,  -5],
[ -9,  -6,  -3],
[ -7,  -4,  -1],
[ -5,  -2,   1],
[ -3,   0,   3]])
>>> a + b
array([[-11,  -8,  -5],
[ -9,  -6,  -3],
[ -7,  -4,  -1],
[ -5,  -2,   1],
[ -3,   0,   3]])


Finally, if for some reason you must have output like that of meshgrid, just use mgrid with the arguments and unpacking targets reversed.

>>> y3, x3 = np.mgrid[-12:-3:3, 1:11:2]
>>> x3
array([[1, 3, 5, 7, 9],
[1, 3, 5, 7, 9],
[1, 3, 5, 7, 9]])
>>> y3
array([[-12, -12, -12, -12, -12],
[ -9,  -9,  -9,  -9,  -9],
[ -6,  -6,  -6,  -6,  -6]])
>>> np.all(x1 == x3)
True
>>> np.all(y1 == y3)
True


Of course, if you are using np.linspace instead of np.arange, then you're better off sticking with np.meshgrid.

 [1] PEP20 - The Zen of Python (https://www.python.org/dev/peps/pep-0020/)