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 0.027860324999892327

python implementation

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

python implementation 5.810410273999878

cython implementation

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

cython implementation 0.10331855200001883

cython implementation parallelized

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

cython implementation parallelized 0.04946396800005459

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 0.012492371999996976

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 208.555007 faster than pure python.
numpy is 3.708447 faster than cython.
numpy is 1.775427 faster than parallelized cython.
numpy is 0.448393 faster than avx parallelized cython.