NUMPY:Aggregations, axes, reshape, and stacking

Axis 0 goes down, axis 1 goes across

sum, mean, min, max, and std can reduce a whole array or a single axis. For a 2-D array, axis=0 collapses rows, so you get one number per column. axis=1 collapses columns, so you get one number per row.

import numpy as np

scores = np.array([
    [70, 80, 90],
    [60, 75, 85],
])

print(scores.mean())
print(scores.mean(axis=0))
print(scores.mean(axis=1))

Output:

76.66666666666667
[65.  77.5 87.5]
[80.         73.33333333]

The overall mean is one number. The column means are the average of the two students on each assignment. The row means are each student's average.

keepdims=True keeps the reduced axis as length 1, which makes broadcasting the mean back onto the original array straightforward:

import numpy as np

scores = np.array([
    [70, 80, 90],
    [60, 75, 85],
])
centered = scores - scores.mean(axis=1, keepdims=True)
print(centered)

Output:

[[-10.           0.          10.        ]
 [-13.33333333   1.66666667  11.66666667]]

Reshape does not copy the story, it rewraps it

reshape rereads the same elements in order. The new shape must hold the same number of elements.

import numpy as np

flat = np.arange(6)
print(flat.reshape(2, 3))
print(flat.reshape(3, -1))

Output:

[[0 1 2]
 [3 4 5]]
[[0 1]
 [2 3]
 [4 5]]

-1 means "figure this axis out". reshape(3, -1) on 6 elements is 3 rows and 2 columns.

Stacking joins arrays

import numpy as np

a = np.array([[1, 2]])
b = np.array([[3, 4]])
print(np.vstack([a, b]))
print(np.hstack([a, b]))

Output:

[[1 2]
 [3 4]]
[[1 2 3 4]]

vstack adds rows. hstack adds columns. The axes you are not stacking along have to match.

What to notice

• If a mean has the wrong length, the axis is backwards. Swap 0 and 1 before you change the data.
• reshape fails when the element count changes. Fix the count, not the error message.
• Centering a row needs keepdims=True or an explicit reshape to (n, 1). Without it, broadcasting aligns the mean with columns and you subtract the wrong numbers.

Where to practice

Open the NumPy notebooks and run the array-math practice, then the Iris exercise. The lab already has NumPy, and the Iris file is on disk as iris.csv.

After NumPy, the Pandas course puts these arrays into labeled tables.