Numpy meshgrid

Meshgrid

This always confuses me. Here’s the help on meshgrid:

meshgrid supports two indexing conventions through the indexing
keyword argument.  Giving the string 'ij' returns a meshgrid with
matrix indexing, while 'xy' returns a meshgrid with Cartesian indexing.

In the 2-D case with inputs of length M and N, the outputs are of shape
(N, M) for 'xy' indexing and (M, N) for 'ij' indexing.

In the 3-D case with inputs of length M, N and P,
outputs are of shape (N, M, P) for
'xy' indexing and (M, N, P) for 'ij' indexing.


The difference is illustrated by the following code snippet::

    xv, yv = np.meshgrid(x, y, indexing='ij')
    for i in range(nx):
        for j in range(ny):
            # treat xv[i,j], yv[i,j]

    xv, yv = np.meshgrid(x, y, indexing='xy')
    for i in range(nx):
        for j in range(ny):
            # treat xv[j,i], yv[j,i]

Here is an example, first with Cartesian, default, coordinates. The shape of A is len(b), len(a), because a is laid out in a row and so defines the number of columns!

import numpy as np
a = np.array([0,1,2,3])
b = np.array([0, 5, 10])
A, B = np.meshgrid(a,b, indexing='xy')
A, B, A.shape, A[0], A[:, 0]

(array([[0, 1, 2, 3],
        [0, 1, 2, 3],
        [0, 1, 2, 3]]),
 array([[ 0,  0,  0,  0],
        [ 5,  5,  5,  5],
        [10, 10, 10, 10]]),
 (3, 4),
 array([0, 1, 2, 3]),
 array([0, 0, 0]))

This is generally what you want. The alternative looks like a matrix:

C, D = np.meshgrid(a,b, indexing='ij')
C, D

(array([[0, 0, 0],
        [1, 1, 1],
        [2, 2, 2],
        [3, 3, 3]]),
 array([[ 0,  5, 10],
        [ 0,  5, 10],
        [ 0,  5, 10],
        [ 0,  5, 10]]))

Means along axes

The mean function returns the average of the array “along the given axis”. I don’t find that helpful. Remember: if you average along an axis you remove that axis.

If you average along axis=0 you get one value per axis 1. If you average along a axis 1, you get one value per row. Thus:

print('Average along axis 0, len(a)', A.mean(0))
print('Average along axis 1, len(b)', A.mean(1))

Average along axis 0, len(a) [0. 1. 2. 3.]
Average along axis 1, len(b) [1.5 1.5 1.5]

HTH.