Elementwise Math

Scalar Multiply

Every element of a 6-element list scaled by constant k = 3 via a loop. The replay shows v taking each value and result growing one scaled element per iteration.

By hand

With NumPy

a * k multiplies every element of the array by the scalar k. NumPy treats the scalar as if it were broadcast to match the array's shape — each element is multiplied independently in the C loop.

naive.py 
values = [1, 2, 3, 4, 5, 6]
k = 3
result = []
for v in values:
    result.append(v * k)
print('RESULT:', result)
library.py 
import numpy as np

values = [1, 2, 3, 4, 5, 6]
k = 3
a = np.array(values)
result = a * k
print('shape:', result.shape)
print('dtype:', result.dtype)
print('values:', result.tolist())
print('RESULT:', result.tolist())

shape: (6,)
dtype: int64
values: [3, 6, 9, 12, 15, 18]
RESULT: [3, 6, 9, 12, 15, 18]

Implementation notes

  • A scalar operand is broadcast to match the array's shape: a * k is equivalent to a * np.full(a.shape, k). This scalar-to-array broadcast is the simplest case of the general broadcasting rules in ch06.
  • The same pattern works for all arithmetic operators: a + k, a - k, a / k, a ** k. For in-place scaling without allocation, use a *= k.
  • Shape, dtype, and values are shown explicitly here because ndarray.__repr__ output varies with NumPy version and print options.