Elementwise Math

Elementwise Product

Two 6-element lists multiplied position by position in an index loop. The trace shows i stepping through each index and result accumulating one pairwise product per iteration.

By hand

Walk each index i from 0 to len(a) - 1. Multiply a[i] by b[i] and append the product to result.

naive.py
Replay: real traced execution (multi-file project)
a = [1, 2, 3, 4, 5, 6]
b = [2, 3, 4, 5, 6, 7]
result = []
for i in range(len(a)):
    result.append(a[i] * b[i])
print('RESULT:', result)

  1. a ← [1, 2, 3, 4, 5, 6]

    1a = [1, 2, 3, 4, 5, 6]2b = [2, 3, 4, 5, 6, 7]
    values this step[1, 2, 3, 4, 5, 6]a

  2. b ← [2, 3, 4, 5, 6, 7]

    1a = [1, 2, 3, 4, 5, 6]2b = [2, 3, 4, 5, 6, 7]3result = []
    values this step[2, 3, 4, 5, 6, 7]b

  3. result ← []

    2b = [2, 3, 4, 5, 6, 7]3result = []4for i in range(len(a)):
    values this step[]result

  4. i ← 0

    3result = []4for i in range(len(a)):5    result.append(a[i] * b[i])
    values this step0i

  5. result ← [2]

    4for i in range(len(a)):5    result.append(a[i] * b[i])6print('RESULT:', result)
    values this step[] → [2]result

  6. i ← 1

    3result = []4for i in range(len(a)):5    result.append(a[i] * b[i])
    values this step0 → 1i

  7. result ← [2, 6]

    4for i in range(len(a)):5    result.append(a[i] * b[i])6print('RESULT:', result)
    values this step[2] → [2, 6]result

  8. i ← 2

    3result = []4for i in range(len(a)):5    result.append(a[i] * b[i])
    values this step1 → 2i

  9. result ← [2, 6, 12]

    4for i in range(len(a)):5    result.append(a[i] * b[i])6print('RESULT:', result)
    values this step[2, 6] → [2, 6, 12]result

  10. i ← 3

    3result = []4for i in range(len(a)):5    result.append(a[i] * b[i])
    values this step2 → 3i

  11. result ← [2, 6, 12, 20]

    4for i in range(len(a)):5    result.append(a[i] * b[i])6print('RESULT:', result)
    values this step[2, 6, 12] → [2, 6, 12, 20]result

  12. i ← 4

    3result = []4for i in range(len(a)):5    result.append(a[i] * b[i])
    values this step3 → 4i

  13. result ← [2, 6, 12, 20, 30]

    4for i in range(len(a)):5    result.append(a[i] * b[i])6print('RESULT:', result)
    values this step[2, 6, 12, 20] → [2, 6, 12, 20, 30]result

  14. i ← 5

    3result = []4for i in range(len(a)):5    result.append(a[i] * b[i])
    values this step4 → 5i

  15. result ← [2, 6, 12, 20, 30, 42]

    4for i in range(len(a)):5    result.append(a[i] * b[i])6print('RESULT:', result)
    values this step[2, 6, 12, 20, 30] → [2, 6, 12, 20, 30, 42]result

  16. for i in range(len(a)):

    3result = []4for i in range(len(a)):5    result.append(a[i] * b[i])

  17. stdout ← RESULT: [2, 6, 12, 20, 30, 42]

    5    result.append(a[i] * b[i])6print('RESULT:', result)
    values this stepRESULT: [2, 6, 12, 20, 30, 42]stdout

With NumPy

arr_a * arr_b multiplies the two arrays elementwise without an explicit loop, producing the Hadamard (elementwise) product.

library.py 
import numpy as np

a = [1, 2, 3, 4, 5, 6]
b = [2, 3, 4, 5, 6, 7]
arr_a = np.array(a)
arr_b = np.array(b)
result = arr_a * arr_b
print('shape:', result.shape)
print('dtype:', result.dtype)
print('values:', result.tolist())
print('RESULT:', result.tolist())

shape: (6,)
dtype: int64
values: [2, 6, 12, 20, 30, 42]
RESULT: [2, 6, 12, 20, 30, 42]

Implementation notes

  • This is the Hadamard product: position i of the output is a[i] * b[i]. It is NOT the dot product (sum of pairwise products). For dot product use np.dot(a, b) or a @ b — that scalar output lesson is in the roadmap linear-algebra chapter.
  • Both arrays must have compatible shapes. The resulting array has the same shape as the inputs; no reduction occurs.
  • Shape, dtype, and values are shown explicitly here because ndarray.__repr__ output varies with NumPy version and print options.