Compares matrix multiplication implementations with timeit

numpy has a very fast implementation of matrix multiplication. There are many ways to be slower. The following uses timeit to compare implementations.

Compared implementations:

• multiply_matrix multiply_matrix

• c_multiply_matrix c_multiply_matrix

• c_multiply_matrix_parallel c_multiply_matrix_parallel

• c_multiply_matrix_parallel_transposed c_multiply_matrix_parallel_transposed

Preparation

import timeit
import numpy

from teachcompute.validation.cython.td_mul_cython import (
    multiply_matrix,
    c_multiply_matrix,
    c_multiply_matrix_parallel,
    c_multiply_matrix_parallel_transposed as cmulparamtr,
)


va = numpy.random.randn(150, 100).astype(numpy.float64)
vb = numpy.random.randn(100, 100).astype(numpy.float64)
ctx = {
    "va": va,
    "vb": vb,
    "c_multiply_matrix": c_multiply_matrix,
    "multiply_matrix": multiply_matrix,
    "c_multiply_matrix_parallel": c_multiply_matrix_parallel,
    "c_multiply_matrix_parallel_transposed": cmulparamtr,
}

Measures

numpy

res0 = timeit.timeit("va @ vb", number=100, globals=ctx)
print("numpy time", res0)

numpy time 0.01842639899950882

python implementation

res1 = timeit.timeit("multiply_matrix(va, vb)", number=10, globals=ctx)
print("python implementation", res1)

python implementation 7.716383171000416

cython implementation

res2 = timeit.timeit("c_multiply_matrix(va, vb)", number=100, globals=ctx)
print("cython implementation", res2)

cython implementation 0.12932565300070564

cython implementation parallelized

res3 = timeit.timeit("c_multiply_matrix_parallel(va, vb)", number=100, globals=ctx)
print("cython implementation parallelized", res3)

cython implementation parallelized 0.0375761989998864

cython implementation parallelized, AVX + transposed

res4 = timeit.timeit(
    "c_multiply_matrix_parallel_transposed(va, vb)", number=100, globals=ctx
)
print("cython implementation parallelized avx", res4)

cython implementation parallelized avx 0.013369381998927565

Speed up…

print(f"numpy is {res1 / res0:f} faster than pure python.")
print(f"numpy is {res2 / res0:f} faster than cython.")
print(f"numpy is {res3 / res0:f} faster than parallelized cython.")
print(f"numpy is {res4 / res0:f} faster than avx parallelized cython.")

numpy is 418.767833 faster than pure python.
numpy is 7.018498 faster than cython.
numpy is 2.039259 faster than parallelized cython.
numpy is 0.725556 faster than avx parallelized cython.