使用numba的收益来自纯粹的numpy代码？

Question

我想了解当使用Numba来加速numpyfor循环中的纯代码时,收益来自哪里.是否有任何分析工具可以让您查看jitted功能？

演示代码(如下所示)只是使用非常基本的矩阵乘法来为计算机提供工作.观察到的收益来自:

1. 更快loop,
2. 重新编译在编译过程中numpy截获的函数jit,或者
3. jitnumpy外包通过包装函数执行到低级库的开销较少LINPACK

%matplotlib inline
import numpy as np
from numba import jit
import pandas as pd

#Dimensions of Matrices
i = 100 
j = 100

def pure_python(N,i,j):
    for n in range(N):
        a = np.random.rand(i,j)
        b = np.random.rand(i,j)
        c = np.dot(a,b)

@jit(nopython=True)
def jit_python(N,i,j):
    for n in range(N):
        a = np.random.rand(i,j)
        b = np.random.rand(i,j)
        c = np.dot(a,b)

time_python = []
time_jit = []
N = [1,10,100,500,1000,2000]
for n in N:
    time = %timeit -oq pure_python(n,i,j)
    time_python.append(time.average)
    time = %timeit -oq jit_python(n,i,j)
    time_jit.append(time.average)

df = pd.DataFrame({'pure_python' : time_python, 'jit_python' : time_jit}, index=N)
df.index.name = 'Iterations'
df[["pure_python", "jit_python"]].plot()

生成以下图表.

Answer 1

TL:DR随机和循环加速,但矩阵乘法除了小矩阵大小外没有.在小矩阵/循环大小,似乎有可能与python开销有关的显着加速.在大N时,矩阵乘法开始占主导地位且jit不太有用

函数定义,为简单起见使用方形矩阵.

from IPython.display import display
import numpy as np
from numba import jit
import pandas as pd

#Dimensions of Matrices
N = 1000

def py_rand(i, j):
    a = np.random.rand(i, j)

jit_rand = jit(nopython=True)(py_rand)

def py_matmul(a, b):
    c = np.dot(a, b)

jit_matmul = jit(nopython=True)(py_matmul)

def py_loop(N, val):
    count = 0
    for i in range(N):
        count += val     


jit_loop = jit(nopython=True)(py_loop)      

def pure_python(N,i,j):
    for n in range(N):
        a = np.random.rand(i,j)
        b = np.random.rand(i,j)
        c = np.dot(a,a)

jit_func = jit(nopython=True)(pure_python)

定时:

df = pd.DataFrame(columns=['Func', 'jit', 'N', 'Time'])
def meantime(f, *args, **kwargs):
    t = %timeit -oq -n5 f(*args, **kwargs)
    return t.average


for N in [10, 100, 1000, 2000]:
    a = np.random.randn(N, N)
    b = np.random.randn(N, N)

    df = df.append({'Func': 'jit_rand', 'N': N, 'Time': meantime(jit_rand, N, N)}, ignore_index=True)
    df = df.append({'Func': 'py_rand', 'N': N, 'Time': meantime(py_rand, N, N)}, ignore_index=True)

    df = df.append({'Func': 'jit_matmul', 'N': N, 'Time': meantime(jit_matmul, a, b)}, ignore_index=True)
    df = df.append({'Func': 'py_matmul', 'N': N, 'Time': meantime(py_matmul, a, b)}, ignore_index=True)

    df = df.append({'Func': 'jit_loop', 'N': N, 'Time': meantime(jit_loop, N, 2.0)}, ignore_index=True)
    df = df.append({'Func': 'py_loop', 'N': N, 'Time': meantime(py_loop, N, 2.0)}, ignore_index=True)

    df = df.append({'Func': 'jit_func', 'N': N, 'Time': meantime(jit_func, 5, N, N)}, ignore_index=True)
    df = df.append({'Func': 'py_func', 'N': N, 'Time': meantime(pure_python, 5, N, N)}, ignore_index=True)

df['jit'] = df['Func'].str.contains('jit')
df['Func'] = df['Func'].apply(lambda s: s.split('_')[1])
df.set_index('Func')
display(df)

结果:

    Func    jit     N   Time
0   rand    True    10  1.030686e-06
1   rand    False   10  1.115149e-05
2   matmul  True    10  2.250371e-06
3   matmul  False   10  2.199343e-06
4   loop    True    10  2.706000e-07
5   loop    False   10  7.274286e-07
6   func    True    10  1.217046e-05
7   func    False   10  2.495837e-05
8   rand    True    100 5.199217e-05
9   rand    False   100 8.149794e-05
10  matmul  True    100 7.848071e-05
11  matmul  False   100 2.130794e-05
12  loop    True    100 2.728571e-07
13  loop    False   100 3.003743e-06
14  func    True    100 6.739634e-04
15  func    False   100 1.146594e-03
16  rand    True    1000    5.644258e-03
17  rand    False   1000    8.012790e-03
18  matmul  True    1000    1.476098e-02
19  matmul  False   1000    1.613211e-02
20  loop    True    1000    2.846572e-07
21  loop    False   1000    3.539849e-05
22  func    True    1000    1.256926e-01
23  func    False   1000    1.581177e-01
24  rand    True    2000    2.061612e-02
25  rand    False   2000    3.204709e-02
26  matmul  True    2000    9.866484e-02
27  matmul  False   2000    1.007234e-01
28  loop    True    2000    3.011143e-07
29  loop    False   2000    7.477454e-05
30  func    True    2000    1.033560e+00
31  func    False   2000    1.199969e+00

看起来numba正在优化循环,所以我不打算在比较中包括它

情节:

def jit_speedup(d):
    py_time = d[d['jit'] == False]['Time'].mean()
    jit_time = d[d['jit'] == True]['Time'].mean()
    return py_time / jit_time 

import seaborn as sns
result = df.groupby(['Func', 'N']).apply(jit_speedup).reset_index().rename(columns={0: 'Jit Speedup'})
result = result[result['Func'] != 'loop']
sns.factorplot(data=result, x='N', y='Jit Speedup', hue='Func')

因此,对于5次重复的循环,jit可以非常稳定地加速,直到矩阵乘法变得足够昂贵,相比之下,其他开销变得微不足道.