这是我正在使用的更大代码的MWE。基本上，它针对位于特定阈值以下的所有值对KDE（kernel density estimate）执行蒙特卡洛积分（在此问题上提出了积分方法BTW：Integrate 2D kernel density estimate）。
import numpy as np
from scipy import stats
import time
# Generate some random two-dimensional data:
def measure(n):
"Measurement model, return two coupled measurements."
m1 = np.random.normal(size=n)
m2 = np.random.normal(scale=0.5, size=n)
return m1+m2, m1-m2
# Get data.
m1, m2 = measure(20000)
# Define limits.
xmin = m1.min()
xmax = m1.max()
ymin = m2.min()
ymax = m2.max()
# Perform a kernel density estimate on the data.
x, y = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]
values = np.vstack([m1, m2])
kernel = stats.gaussian_kde(values)
# Define point below which to integrate the kernel.
x1, y1 = 0.5, 0.5
# Get kernel value for this point.
tik = time.time()
iso = kernel((x1,y1))
print 'iso: ', time.time()-tik
# Sample from KDE distribution (Monte Carlo process).
tik = time.time()
sample = kernel.resample(size=1000)
print 'resample: ', time.time()-tik
# Filter the sample leaving only values for which
# the kernel evaluates to less than what it does for
# the (x1, y1) point defined above.
tik = time.time()
insample = kernel(sample) < iso
print 'filter/sample: ', time.time()-tik
# Integrate for all values below iso.
tik = time.time()
integral = insample.sum() / float(insample.shape[0])
print 'integral: ', time.time()-tik
输出看起来像这样：
iso: 0.00259208679199
resample: 0.000817060470581
filter/sample: 2.10829401016
integral: 4.2200088501e-05
这显然意味着过滤器/示例调用几乎消耗了代码用于运行的所有时间。我必须迭代地运行这段代码几千次，这样才能耗费时间。
有没有办法加快过滤/采样过程？
这是一个稍微更实际的MWE我的实际代码，其中写有Ophion的多线程解决方案：
import numpy as np
from scipy import stats
from multiprocessing import Pool
def kde_integration(m_list):
m1, m2 = [], []
for item in m_list:
# Color data.
m1.append(item[0])
# Magnitude data.
m2.append(item[1])
# Define limits.
xmin, xmax = min(m1), max(m1)
ymin, ymax = min(m2), max(m2)
# Perform a kernel density estimate on the data:
x, y = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]
values = np.vstack([m1, m2])
kernel = stats.gaussian_kde(values)
out_list = []
for point in m_list:
# Compute the point below which to integrate.
iso = kernel((point[0], point[1]))
# Sample KDE distribution
sample = kernel.resample(size=1000)
#Create definition.
def calc_kernel(samp):
return kernel(samp)
#Choose number of cores and split input array.
cores = 4
torun = np.array_split(sample, cores, axis=1)
#Calculate
pool = Pool(processes=cores)
results = pool.map(calc_kernel, torun)
#Reintegrate and calculate results
insample_mp = np.concatenate(results) < iso
# Integrate for all values below iso.
integral = insample_mp.sum() / float(insample_mp.shape[0])
out_list.append(integral)
return out_list
# Generate some random two-dimensional data:
def measure(n):
"Measurement model, return two coupled measurements."
m1 = np.random.normal(size=n)
m2 = np.random.normal(scale=0.5, size=n)
return m1+m2, m1-m2
# Create list to pass.
m_list = []
for i in range(60):
m1, m2 = measure(5)
m_list.append(m1.tolist())
m_list.append(m2.tolist())
# Call KDE integration function.
print 'Integral result: ', kde_integration(m_list)
Ophion 提供的解决方案在我提供的原始代码上运行良好，但在此版本中失败并出现以下错误：
Integral result: Exception in thread Thread-3:
Traceback (most recent call last):
File "/usr/lib/python2.7/threading.py", line 551, in __bootstrap_inner
self.run()
File "/usr/lib/python2.7/threading.py", line 504, in run
self.__target(*self.__args, **self.__kwargs)
File "/usr/lib/python2.7/multiprocessing/pool.py", line 319, in _handle_tasks
put(task)
PicklingError: Can't pickle <type 'function'>: attribute lookup __builtin__.function failed
我尝试移动calc_kernel函数，因为此问题Multiprocessing: How to use Pool.map on a function defined in a class?中的一个答案指出“您为map（）提供的函数必须通过导入您的模块“;但我仍然无法使用此代码。
非常感谢任何帮助。
实施 Ophion的建议，删除calc_kernel功能并简单地使用：
results = pool.map(kernel, torun)
可以摆脱PicklingError，但现在我看到如果我创建了大约62-63个项目的初始m_list，我会收到此错误：
Traceback (most recent call last):
File "~/gauss_kde_temp.py", line 67, in <module>
print 'Integral result: ', kde_integration(m_list)
File "~/gauss_kde_temp.py", line 38, in kde_integration
pool = Pool(processes=cores)
File "/usr/lib/python2.7/multiprocessing/__init__.py", line 232, in Pool
return Pool(processes, initializer, initargs, maxtasksperchild)
File "/usr/lib/python2.7/multiprocessing/pool.py", line 161, in __init__
self._result_handler.start()
File "/usr/lib/python2.7/threading.py", line 494, in start
_start_new_thread(self.__bootstrap, ())
thread.error: can't start new thread
由于我在实际执行此代码中的实际列表最多可包含2000个项目，因此此问题会导致代码无法使用。第38行是这一行：
pool = Pool(processes=cores)
此问题"Can't start a new thread error" in Python建议使用：
threading.active_count()
检查我收到错误时的线程数。我检查过，当它到达374个线程时总是崩溃。我该如何围绕这个问题进行编码？
以下是处理上一期问题的新问题：Thread error: can't start new thread
答案 0 :(得分：4)
加快提升速度的最简单方法可能是并行化kernel(sample)：
使用此代码片段：
tik = time.time()
insample = kernel(sample) < iso
print 'filter/sample: ', time.time()-tik
#filter/sample: 1.94065904617
将其更改为使用multiprocessing：
from multiprocessing import Pool
tik = time.time()
#Create definition.
def calc_kernel(samp):
return kernel(samp)
#Choose number of cores and split input array.
cores = 4
torun = np.array_split(sample, cores, axis=1)
#Calculate
pool = Pool(processes=cores)
results = pool.map(calc_kernel, torun)
#Reintegrate and calculate results
insample_mp = np.concatenate(results) < iso
print 'multiprocessing filter/sample: ', time.time()-tik
#multiprocessing filter/sample: 0.496874094009
仔细检查他们会回答相同的答案：
print np.all(insample==insample_mp)
#True
4核增加3.9倍。不知道你在运行什么，但在大约6个处理器后，你的输入数组大小不足以获得相当大的收益。例如，使用20个处理器，其速度仅提高了约5.8倍。
答案 1 :(得分：2)
本文评论部分（下面的链接）中的声明是
“SciPy的gaussian_kde不使用FFT，而有一个statsmodels实现”
......这可能是导致观察到性能不佳的原因。它继续使用FFT报告数量级的改进。请参阅@ jseabold的回复。
免责声明：我没有使用statsmodels或scipy的经验。