linear transformation

lenear_transformation_by_block_matrix.py

import numpy  as np

test_a = np.array([
    [1, 2, 3, 4, 5, 6],
    [7, 8, 9, 10, 11, 12],
    [13, 14, 15, 16, 17, 18],
    [19, 20, 21, 22, 23, 24],
    [25, 26, 27, 28, 29, 30],
    [31, 32, 33, 34, 35, 36],
])

test_b = np.array([37, 38, 39, 40, 41, 42])
expect = np.dot(test_a.T, test_b)

test_a_0 = test_a[0:3, 0:3]
test_a_1 = test_a[0:3, 3:6]
test_a_2 = test_a[3:6, 0:3]
test_a_3 = test_a[3:6, 3:6]

test_b_0 = test_b[0:3]
test_b_1 = test_b[3:6]

actual = np.vstack(
    (
        np.dot(test_a_0.T, test_b_0) + np.dot(test_a_2.T, test_b_1),
        np.dot(test_a_1.T, test_b_0) + np.dot(test_a_3.T, test_b_1)
    )
).reshape(-1)

print(actual)
print(expect)
print(np.array_equal(expect, actual)) # => True