প্যারালাল ও ভেক্টরাইজড নিউমেরিক্যাল কম্পিউটিং

import random

random.seed(7)

def make_matrix(n):
    return [[round(random.uniform(-3, 3), 2) for _ in range(n)] for _ in range(n)]

def make_vector(n):
    return [round(random.uniform(-3, 3), 2) for _ in range(n)]

def manual_matvec(M, v):
    n = len(M)
    result = [0.0]*n
    py_level_scalar_ops = 0  # ইন্টারপ্রেটার প্রকৃতপক্ষে যতবার multiply-add চালায়
    for i in range(n):
        s = 0.0
        for j in range(n):
            s += M[i][j]*v[j]
            py_level_scalar_ops += 1
        result[i] = s
    return result, py_level_scalar_ops

def manual_matmul(A, B):
    n = len(A)
    result = [[0.0]*n for _ in range(n)]
    py_level_scalar_ops = 0
    for i in range(n):
        for j in range(n):
            s = 0.0
            for k in range(n):
                s += A[i][k]*B[k][j]
                py_level_scalar_ops += 1
            result[i][j] = s
    return result, py_level_scalar_ops

print(f"{'n':>4} | {'matvec: Python-level scalar ops':>32} | {'vectorized call count':>22}")
for n in [4, 8, 16, 32, 64]:
    M = make_matrix(n)
    v = make_vector(n)
    _, ops = manual_matvec(M, v)
    print(f"{n:4d} | {ops:32d} | {1:22d}")

print()
print(f"{'n':>4} | {'matmul: Python-level scalar ops':>32} | {'vectorized call count':>22}")
for n in [4, 8, 16, 32]:
    A = make_matrix(n)
    B = make_matrix(n)
    _, ops = manual_matmul(A, B)
    print(f"{n:4d} | {ops:32d} | {1:22d}")

print()
n1, n2 = 16, 32
M1, v1 = make_matrix(n1), make_vector(n1)
M2, v2 = make_matrix(n2), make_vector(n2)
_, ops1 = manual_matvec(M1, v1)
_, ops2 = manual_matvec(M2, v2)
print(f"matvec অপারেশন n={n1}: {ops1}, n={n2}: {ops2}, অনুপাত: {ops2/ops1:.2f} (O(n^2)-এর জন্য প্রত্যাশিত ~{(n2/n1)**2:.2f})")

A1, B1 = make_matrix(n1), make_matrix(n1)
A2, B2 = make_matrix(n2), make_matrix(n2)
_, mops1 = manual_matmul(A1, B1)
_, mops2 = manual_matmul(A2, B2)
print(f"matmul অপারেশন n={n1}: {mops1}, n={n2}: {mops2}, অনুপাত: {mops2/mops1:.2f} (O(n^3)-এর জন্য প্রত্যাশিত ~{(n2/n1)**3:.2f})")