Broadcasting

Add Vector to Rows

A 2-row × 3-column grid and a 3-element vector added together by hand. A nested loop walks each row, then each column, adding the matching vector element to the cell. The replay shows new_row building column by column before being appended to result.

By hand

With NumPy

a + v broadcasts v (shape (3,)) across both rows of a (shape (2, 3)), adding the same vector to every row in one call.

naive.py 
grid = [[1, 2, 3], [4, 5, 6]]
vec = [10, 20, 30]
result = []
for row in grid:
    new_row = []
    for j in range(len(vec)):
        new_row.append(row[j] + vec[j])
    result.append(new_row)
print('RESULT:', result)
library.py 
import numpy as np

grid = [[1, 2, 3], [4, 5, 6]]
vec = [10, 20, 30]
a = np.array(grid)
v = np.array(vec)
result = a + v
print('shape:', a.shape)
print('dtype:', result.dtype)
print('values:', result.tolist())
print('RESULT:', result.tolist())

shape: (2, 3)
dtype: int64
values: [[11, 22, 33], [14, 25, 36]]
RESULT: [[11, 22, 33], [14, 25, 36]]

Implementation notes

  • Broadcasting rule: NumPy aligns shapes from the right. v is (3,), a is (2, 3) — the trailing dimension matches, so v is virtually replicated along the rows axis without copying memory.
  • The result dtype is int64 because both inputs are integer arrays. If either were float64, the result would promote to float64.
  • Shape, dtype, and values are shown explicitly here because ndarray.__repr__ output varies with NumPy version and print options.