Matrix-matrix multiplication: Cannon's algorithm

cannon.py

#!/usr/bin/env python3

import numpy as np

# Assume that P = N * N.
N = 4

A = np.arange(0, 2 * N * N, 2).reshape(N, N)
B = np.arange(1, 2 * N * N, 2).reshape(N, N)
C_gt = A.dot(B)

# Procedure 1: Shift A[i, :] to left by i
print('Original A:')
print(A)
print()

for i in range(N):
    A[i, :] = np.roll(A[i, :], -i)

print('A after setup:')
print(A)
print()

# Procedure 2: Shift B[:, j] to upper by j
print('Original B:')
print(B)
print()

for j in range(N):
    B[:, j] = np.roll(B[:, j], -j)

print('B after setup:')
print(B)
print()

# Procedure 3: Zero-clear C
C = np.zeros((N, N), dtype = int)

# Procedure 4: Repeat N times (k = 0, 1, ..., N-1)
for k in range(N):
    for i in range(N):
        for j in range(N):
            C[i, j] += A[i, j] * B[i, j]

    # Procedure 4.1: Shift A to left by 1
    A = np.roll(A, -1, axis = 1)

    # Procedure 4.2: Shift B to upper by 1
    B = np.roll(B, -1, axis = 0)

print('C (ground truth):')
print(C_gt)
print()

print('C with Cannon\'s algorithm:')
print(C)
print()

print('Matched' if np.allclose(C, C_gt) else 'Not matched')

result.txt

Original A:
[[ 0  2  4  6]
 [ 8 10 12 14]
 [16 18 20 22]
 [24 26 28 30]]

A after setup:
[[ 0  2  4  6]
 [10 12 14  8]
 [20 22 16 18]
 [30 24 26 28]]

Original B:
[[ 1  3  5  7]
 [ 9 11 13 15]
 [17 19 21 23]
 [25 27 29 31]]

B after setup:
[[ 1 11 21 31]
 [ 9 19 29  7]
 [17 27  5 15]
 [25  3 13 23]]

C (ground truth):
[[ 236  260  284  308]
 [ 652  740  828  916]
 [1068 1220 1372 1524]
 [1484 1700 1916 2132]]

C with Cannon's algorithm:
[[ 236  260  284  308]
 [ 652  740  828  916]
 [1068 1220 1372 1524]
 [1484 1700 1916 2132]]

Matched