Universal functions & aggregation along axes

A universal function (ufunc) is a NumPy function that works element by element on whole arrays in compiled code. np.add, np.sqrt, np.exp, np.maximum and the operators + - * / ** are all ufuncs. Combined with the axis argument, they let you summarise data without a single Python loop.

Element-wise ufuncs

import numpy as np

prices = np.array([120.0, 450.0, 80.0, 999.0])
with_gst = np.round(prices * 1.18, 2)        # 18% GST
log_p = np.log(prices)                        # natural log
capped = np.minimum(prices, 500)              # cap each value at 500
floor_ceiling = np.clip(prices, 100, 800)     # keep within [100, 800]

Category	Examples
Arithmetic	np.add, np.subtract, np.multiply, np.divide, np.power
Maths	np.sqrt, np.exp, np.log, np.log1p, np.abs
Comparison	np.greater, np.equal, np.maximum, np.minimum
Rounding	np.round, np.floor, np.ceil

Understanding axis

For a 2-D array, axis=0 collapses the rows (giving one result per column) and axis=1 collapses the columns (giving one result per row).

# rows = 3 stores, columns = 4 quarters (₹ lakh)
sales = np.array([[12, 15, 11, 20],
                  [ 9, 10, 14, 13],
                  [18, 17, 16, 25]])

sales.sum(axis=0)     # per quarter: [39 42 41 58]
sales.sum(axis=1)     # per store:   [58 46 76]
sales.max(axis=1)     # best quarter value for each store
sales.argmax(axis=1)  # index of best quarter: [3 2 3]
sales.mean()          # overall mean (no axis)

A memory aid: the axis you pass is the axis that disappears from the shape. (3, 4) summed over axis 0 becomes (4,).

keepdims for broadcasting

To divide each store's quarters by that store's total, keep the reduced axis so the shapes line up:

share = sales / sales.sum(axis=1, keepdims=True)   # (3, 4) / (3, 1)
print(share.round(2))

Without keepdims=True, the totals would have shape (3,), which broadcasts against columns and gives a wrong answer or a shape error.

reduce and accumulate

Every binary ufunc has methods for reductions:

np.add.reduce([1, 2, 3, 4])          # 10, same as sum
np.add.accumulate([1, 2, 3, 4])      # [1 3 6 10], same as cumsum
np.maximum.accumulate([3, 1, 4, 2])  # running maximum: [3 3 4 4]

A running maximum is useful for "best sales so far" or drawdown calculations on stock prices.

Handling missing values

np.sum of an array containing np.nan returns nan. Use the nan-aware versions: np.nansum, np.nanmean, np.nanmax, np.nanstd.

Common mistakes

• Mixing up axis 0 and axis 1; check the output shape every time.
• Forgetting keepdims=True when normalising rows.
• Using Python's built-in sum() or max() on large arrays, which is far slower than the NumPy method.
• Getting nan results because one missing value slipped in.