Parallelization of a dot product with processes (concurrent.futures)

Uses processes to parallelize a dot product is not a very solution becausep processes do not share memory, they need to exchange data. This parallelisation is efficient if the ratio exchanged data / computation time is low. This example uses concurrent.futures. The cost of creating new processes is also significant.

import numpy
from tqdm import tqdm
from pandas import DataFrame
import matplotlib.pyplot as plt
import concurrent.futures as cf
from td3a_cpp.tools import measure_time


def parallel_numpy_dot(va, vb, max_workers=2):
    if max_workers == 2:
        with cf.ThreadPoolExecutor(max_workers=max_workers) as e:
            m = va.shape[0] // 2
            f1 = e.submit(numpy.dot, va[:m], vb[:m])
            f2 = e.submit(numpy.dot, va[m:], vb[m:])
            return f1.result() + f2.result()
    elif max_workers == 3:
        with cf.ThreadPoolExecutor(max_workers=max_workers) as e:
            m = va.shape[0] // 3
            m2 = va.shape[0] * 2 // 3
            f1 = e.submit(numpy.dot, va[:m], vb[:m])
            f2 = e.submit(numpy.dot, va[m:m2], vb[m:m2])
            f3 = e.submit(numpy.dot, va[m2:], vb[m2:])
            return f1.result() + f2.result() + f3.result()
    else:
        raise NotImplementedError()

We check that it returns the same values.

va = numpy.random.randn(100).astype(numpy.float64)
vb = numpy.random.randn(100).astype(numpy.float64)
print(parallel_numpy_dot(va, vb), numpy.dot(va, vb))

Out:

1.6164566574834773 1.61645665748348

Let’s benchmark.

res = []
for n in tqdm([100000, 1000000, 10000000, 100000000]):
    va = numpy.random.randn(n).astype(numpy.float64)
    vb = numpy.random.randn(n).astype(numpy.float64)

    m1 = measure_time('dot(va, vb, 2)',
                      dict(va=va, vb=vb, dot=parallel_numpy_dot))
    m2 = measure_time('dot(va, vb)',
                      dict(va=va, vb=vb, dot=numpy.dot))
    res.append({'N': n, 'numpy.dot': m2['average'],
                'futures': m1['average']})

df = DataFrame(res).set_index('N')
print(df)
df.plot(logy=True, logx=True)
plt.title("Parallel / numpy dot")

Out:

  0%|          | 0/4 [00:00<?, ?it/s]
 25%|##5       | 1/4 [00:02<00:07,  2.37s/it]
 50%|#####     | 2/4 [00:07<00:08,  4.20s/it]
 75%|#######5  | 3/4 [00:25<00:10, 10.50s/it]
100%|##########| 4/4 [02:43<00:00, 60.60s/it]
100%|##########| 4/4 [02:43<00:00, 40.81s/it]
           numpy.dot   futures
N
100000      0.000067  0.004631
1000000     0.001518  0.008972
10000000    0.011968  0.020017
100000000   0.113832  0.119699

Text(0.5, 1.0, 'Parallel / numpy dot')

The parallelisation is inefficient unless the vectors are big.

plt.show()