Note
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Compares dot implementations (numpy, c++, sse, openmp)¶
numpy has a very fast implementation of the dot product. It is difficult to be better and very easy to be slower. This example looks into a couple of slower implementations with cython. The tested functions are the following:
import numpy
import matplotlib.pyplot as plt
from pandas import DataFrame, concat
from teachcompute.validation.cython.dot_cython import ddot_array_16_sse, ddot_array
from teachcompute.validation.cython.dot_cython_omp import (
ddot_cython_array_omp,
ddot_array_openmp,
get_omp_max_threads,
ddot_array_openmp_16,
)
from teachcompute.ext_test_case import measure_time_dim, unit_test_going
def get_vectors(fct, n, h=250, dtype=numpy.float64):
ctxs = [
dict(
va=numpy.random.randn(n).astype(dtype),
vb=numpy.random.randn(n).astype(dtype),
dot=fct,
x_name=n,
)
for n in range(10, n, h)
]
return ctxs
Number of threads¶
print(get_omp_max_threads())
10
Several cython dot¶
def numpy_dot(va, vb):
return numpy.dot(va, vb)
def ddot_omp(va, vb):
return ddot_cython_array_omp(va, vb)
def ddot_omp_static(va, vb):
return ddot_cython_array_omp(va, vb, schedule=1)
def ddot_omp_dyn(va, vb):
return ddot_cython_array_omp(va, vb, schedule=2)
def ddot_omp_cpp(va, vb):
return ddot_array_openmp(va, vb)
def ddot_omp_cpp_16(va, vb):
return ddot_array_openmp_16(va, vb)
dfs = []
for fct in [
numpy_dot,
ddot_array,
ddot_array_16_sse,
ddot_omp,
ddot_omp_static,
ddot_omp_dyn,
ddot_omp_cpp,
ddot_omp_cpp_16,
]:
ctxs = get_vectors(fct, 400 if unit_test_going() else 40000)
print(fct.__name__)
df = DataFrame(list(measure_time_dim("dot(va, vb)", ctxs, verbose=1)))
df["fct"] = fct.__name__
dfs.append(df)
print(df.tail(n=3))
numpy_dot
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average deviation min_exec max_exec repeat number ttime context_size warmup_time x_name fct
157 0.000031 0.000072 0.000006 0.000248 10 50 0.000308 184 0.000020 39260 numpy_dot
158 0.000624 0.001273 0.000006 0.004053 10 50 0.006240 184 0.000029 39510 numpy_dot
159 0.000602 0.001374 0.000005 0.004639 10 50 0.006015 184 0.000023 39760 numpy_dot
ddot_array
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average deviation min_exec max_exec repeat number ttime context_size warmup_time x_name fct
157 0.000034 5.379273e-07 0.000033 0.000035 10 50 0.000340 184 0.000043 39260 ddot_array
158 0.000034 5.291191e-07 0.000034 0.000035 10 50 0.000342 184 0.000054 39510 ddot_array
159 0.000035 1.512740e-06 0.000033 0.000039 10 50 0.000352 184 0.000050 39760 ddot_array
ddot_array_16_sse
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average deviation min_exec max_exec repeat number ttime context_size warmup_time x_name fct
157 0.000014 0.000002 0.000011 0.000018 10 50 0.000143 184 0.000035 39260 ddot_array_16_sse
158 0.000017 0.000003 0.000013 0.000023 10 50 0.000171 184 0.000065 39510 ddot_array_16_sse
159 0.000014 0.000002 0.000012 0.000017 10 50 0.000139 184 0.000042 39760 ddot_array_16_sse
ddot_omp
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average deviation min_exec max_exec repeat number ttime context_size warmup_time x_name fct
157 0.000014 1.649187e-06 0.000013 0.000017 10 50 0.000139 184 0.000024 39260 ddot_omp
158 0.000014 1.319730e-06 0.000012 0.000017 10 50 0.000143 184 0.000051 39510 ddot_omp
159 0.000014 7.013416e-07 0.000013 0.000015 10 50 0.000140 184 0.000025 39760 ddot_omp
ddot_omp_static
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average deviation min_exec max_exec repeat number ttime context_size warmup_time x_name fct
157 0.000015 0.000002 0.000013 0.000020 10 50 0.000153 184 0.000033 39260 ddot_omp_static
158 0.000015 0.000001 0.000013 0.000017 10 50 0.000148 184 0.000033 39510 ddot_omp_static
159 0.000016 0.000002 0.000014 0.000020 10 50 0.000165 184 0.000039 39760 ddot_omp_static
ddot_omp_dyn
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average deviation min_exec max_exec repeat number ttime context_size warmup_time x_name fct
157 0.000064 0.000005 0.000058 0.000075 10 50 0.000638 184 0.000084 39260 ddot_omp_dyn
158 0.000076 0.000010 0.000060 0.000093 10 50 0.000759 184 0.000119 39510 ddot_omp_dyn
159 0.000088 0.000003 0.000082 0.000092 10 50 0.000877 184 0.000097 39760 ddot_omp_dyn
ddot_omp_cpp
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average deviation min_exec max_exec repeat number ttime context_size warmup_time x_name fct
157 0.000012 9.622883e-07 0.000011 0.000014 10 50 0.000120 184 0.000020 39260 ddot_omp_cpp
158 0.000016 2.446743e-06 0.000011 0.000020 10 50 0.000159 184 0.000019 39510 ddot_omp_cpp
159 0.000013 1.154813e-06 0.000012 0.000016 10 50 0.000133 184 0.000025 39760 ddot_omp_cpp
ddot_omp_cpp_16
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average deviation min_exec max_exec repeat number ttime context_size warmup_time x_name fct
157 0.000010 0.000001 0.000009 0.000013 10 50 0.000097 184 0.000026 39260 ddot_omp_cpp_16
158 0.000011 0.000001 0.000009 0.000012 10 50 0.000105 184 0.000047 39510 ddot_omp_cpp_16
159 0.000011 0.000001 0.000009 0.000013 10 50 0.000106 184 0.000024 39760 ddot_omp_cpp_16
Let’s display the results¶
cc = concat(dfs)
cc["N"] = cc["x_name"]
fig, ax = plt.subplots(2, 2, figsize=(10, 10))
cc[cc.N <= 1000].pivot(index="N", columns="fct", values="average").plot(
logy=True, ax=ax[0, 0]
)
cc.pivot(index="N", columns="fct", values="average").plot(logy=True, ax=ax[0, 1])
cc.pivot(index="N", columns="fct", values="average").plot(
logy=True, logx=True, ax=ax[1, 1]
)
cc[
(
(cc.fct.str.contains("omp") | (cc.fct == "ddot_array"))
& ~cc.fct.str.contains("dyn")
)
].pivot(index="N", columns="fct", values="average").plot(logy=True, ax=ax[1, 0])
ax[0, 0].set_title("Comparison of cython ddot implementations")
ax[0, 1].set_title("Comparison of cython ddot implementations\nwithout dot_product")
Text(0.5, 1.0, 'Comparison of cython ddot implementations\nwithout dot_product')
Total running time of the script: (0 minutes 31.023 seconds)