1D with 2D: Per-Column

Suppose every match was played on a different pitch, and the analyst gives each match a pitch difficulty multiplier — one number per match. You want to apply that multiplier to every player's score in that match. The squad table is 2D, the multipliers are 1D. This is the most common useful broadcast: 1D with 2D.

Definition

When a 1D array of length n is combined with a 2D array of shape (rows, n), NumPy treats the 1D array as shape (1, n) and repeats it down every row. Each value of the 1D array is applied to one column of the 2D array.

• Length n must equal the number of columns (the last dimension) — because shapes are aligned from the right.
• (1, n) — the missing leading dimension becomes 1, which then stretches to rows.
• One value per column — in our squad table, columns are matches, so this gives a per-match adjustment.

Picture it

squad_scores        (5, 6)   <- 5 players, 6 matches
pitch_multiplier       (6,)  <- one value per match

Conceptually pitch_multiplier becomes:
[[m1, m2, m3, m4, m5, m6],   <- reused for Virat
 [m1, m2, m3, m4, m5, m6],   <- reused for Rohit
 [m1, m2, m3, m4, m5, m6],   <- reused for Hardik
 [m1, m2, m3, m4, m5, m6],   <- reused for Shubman
 [m1, m2, m3, m4, m5, m6]]   <- reused for Shreyas

Nothing is actually copied — NumPy re-reads the same 6 numbers for each row.

Syntax

result = array_2d  <op>  array_1d     # array_1d.shape == (array_2d.shape[1],)

Example — per-match pitch multiplier

import numpy as np

squad_scores = np.array([
    [72, 45, 88, 31, 64,  0],   # Virat
    [56,  0, 74, 88, 32, 45],   # Rohit
    [45, 32,  0, 67, 18, 54],   # Hardik
    [33, 61, 45,  0, 77, 83],   # Shubman
    [88, 14, 57, 72,  0, 38],   # Shreyas
])
pitch_multiplier = np.array([1.0, 1.2, 0.9, 1.1, 1.0, 1.3])

print("squad_scores shape:    ", squad_scores.shape)
print("pitch_multiplier shape:", pitch_multiplier.shape)
adjusted = squad_scores * pitch_multiplier
print(adjusted.round(1))
print(adjusted.shape)

squad_scores shape:     (5, 6)
pitch_multiplier shape: (6,)
[[ 72.   54.   79.2  34.1  64.    0. ]
 [ 56.    0.   66.6  96.8  32.   58.5]
 [ 45.   38.4   0.   73.7  18.   70.2]
 [ 33.   73.2  40.5   0.   77.  107.9]
 [ 88.   16.8  51.3  79.2   0.   49.4]]
(5, 6)

How it works: right-aligned, 6 vs 6 match; the missing dimension (1) stretches to 5. So column 2 (match 2, multiplier 1.2) is multiplied by 1.2 for every player: Virat 45 → 54.0, Shubman 61 → 73.2.

Example — marks as a percentage of each subject's maximum

From class: 4 students × 3 subjects (science, maths, English), each subject has a different maximum.

marks = np.array([[10, 11, 15],
                  [11, 14, 12],
                  [ 9, 17, 13],
                  [12, 18, 14]])
max_marks = np.array([15, 20, 15])
print((marks / max_marks * 100).round(1))

[[ 66.7  55.  100. ]
 [ 73.3  70.   80. ]
 [ 60.   85.   86.7]
 [ 80.   90.   93.3]]

How it works: (4, 3) with (3,) → each column is divided by its own maximum. Science /15, maths /20, English /15 — for all 4 students at once.

Example — compare each score with the match average

A very common pattern is aggregate, then broadcast back. mean(axis=0) gives one value per column, shape (6,) — exactly the shape that broadcasts across rows.

match_avg = squad_scores.mean(axis=0)
print(match_avg.round(1))
print((squad_scores - match_avg).round(1))

[58.8 30.4 52.8 51.6 38.2 44. ]
[[ 13.2  14.6  35.2 -20.6  25.8 -44. ]
 [ -2.8 -30.4  21.2  36.4  -6.2   1. ]
 [-13.8   1.6 -52.8  15.4 -20.2  10. ]
 [-25.8  30.6  -7.8 -51.6  38.8  39. ]
 [ 29.2 -16.4   4.2  20.4 -38.2  -6. ]]

How it works: positive numbers = scored above that match's average, negative = below. Virat's 88 in match 3 is +35.2 above the average of 52.8.

Comparison — which 1D shape goes where?

Common mistakes

• ❌ Using a 1D array whose length equals the number of rows. ✅ Plain 1D always matches the last dimension (columns). For rows, see the next topic.
• ❌ Forgetting that mean(axis=0) gives per-column values and mean(axis=1) per-row values. ✅ Per-column results broadcast back directly; per-row results need reshape(-1, 1) or keepdims=True.
• ❌ On a square table, assuming a 1D array was applied per row because there was no error. ✅ It was applied per column — check with a tiny example.

Interview tip

Q: You have X of shape (1000, 4) (1000 rows, 4 features). How do you standardise every feature column in one line? A: (X - X.mean(axis=0)) / X.std(axis=0) — both statistics have shape (4,), which broadcasts across all 1000 rows.