<>根据我的经验,在3D中找到邻居列表有两种最快的方法:一种是使用最简单的双环来编写C++或Cython的循环代码(在我的例子中,两者都是)。它在N^2下运行,但对于小型系统来说非常快。另一种方法是使用线性时间算法。Scipy ckdtree是一个不错的选择,但也有局限性。分子动力学软件中的邻居列表查找器功能最强大,但很难包装,而且初始化时间可能很慢。在</p>
<p>下面我比较四种方法:</p>
<ul>
<li>天真的cython代码</li>
<li>围绕<a href="https://simtk.org/home/openmm" rel="noreferrer">OpenMM</a>的包装器(很难安装,请参见下文)</li>
<li><code>Scipy.spatial.ckdtree</code></li>
<li><code>scipy.spatial.distance.pdist</code></li>
</ul>
<p>测试设置:<code>n</code>点分散在体积密度为0.2的矩形框中。系统大小从10到1000000(一百万)个粒子。接触半径取自<code>0.5, 1, 2, 4, 7, 10</code>。注意,因为密度是0.2,在接触半径为0.5时,我们平均每个粒子有0.1个接触点,1=0.8,2=6.4,10-大约800!对小系统重复多次接触发现,对大于30k粒子的系统重复一次。如果每次呼叫的时间超过5秒,则中止运行。在</p>
<p>设置:dual xeon 2687Wv3,128GB内存,Ubuntu 14.04,python 2.7.11,scipy 0.16.0,numpy 1.10.1。所有的代码都没有使用并行优化(除了OpenMM,尽管并行部分运行得非常快,以至于在CPU图上甚至都不明显,但大部分时间都是通过管道将数据从OpenMM传递出去)。在</p>
<p><strong>结果:</strong>请注意,下面的曲线图是对数标度,分布在6个数量级上。即使是很小的视觉差异,实际上也可能是10倍。
对于少于1000个粒子的系统,<code>Cython</code>代码总是更快。但是,1000个粒子之后,结果取决于接触半径。<code>pdist</code>实现总是比cython慢,并且占用更多的内存,因为它显式地创建了一个距离矩阵,这是由于sqrt而导致的。在</p>
<ul>
<li>在较小的接触半径下(每个粒子1个接触),<code>ckdtree</code>是所有系统尺寸的好选择。在</li>
<li>在中等接触半径(每个粒子5-50个接触)下,朴素的cython实现是最好的,最多10000个粒子,然后OpenMM开始以几个数量级的优势获胜,但是<code>ckdtree</code>的性能仅差3-10倍</li>
<li>在高接触半径(每个粒子接触200个以上)时,简单的方法可以处理多达100k或1M的粒子,然后OpenMM可能会获胜。在</li>
</ul>
<p>安装OpenMM非常棘手;您可以在<a href="http://bitbucket.org/mirnylab/openmm-polymer" rel="noreferrer">http://bitbucket.org/mirnylab/openmm-polymer</a>文件中阅读更多内容”联系人地图.py“或者在自述中。然而,下面的结果表明,对于N>;100k粒子,每个粒子只有5-50个接触点才是有利的。在</p>
<p><a href="https://i.stack.imgur.com/JMYyd.png" rel="noreferrer"><img src="https://i.stack.imgur.com/JMYyd.png" alt="enter image description here"/></a></p>
<p>Cython代码如下:</p>
<pre><code>import numpy as np
cimport numpy as np
cimport cython
cdef extern from "<vector>" namespace "std":
cdef cppclass vector[T]:
cppclass iterator:
T operator*()
iterator operator++()
bint operator==(iterator)
bint operator!=(iterator)
vector()
void push_back(T&)
T& operator[](int)
T& at(int)
iterator begin()
iterator end()
np.import_array() # initialize C API to call PyArray_SimpleNewFromData
cdef public api tonumpyarray(int* data, long long size) with gil:
if not (data and size >= 0): raise ValueError
cdef np.npy_intp dims = size
#NOTE: it doesn't take ownership of `data`. You must free `data` yourself
return np.PyArray_SimpleNewFromData(1, &dims, np.NPY_INT, <void*>data)
@cython.boundscheck(False)
@cython.wraparound(False)
def contactsCython(inArray, cutoff):
inArray = np.asarray(inArray, dtype = np.float64, order = "C")
cdef int N = len(inArray)
cdef np.ndarray[np.double_t, ndim = 2] data = inArray
cdef int j,i
cdef double curdist
cdef double cutoff2 = cutoff * cutoff # IMPORTANT to avoid slow sqrt calculation
cdef vector[int] contacts1
cdef vector[int] contacts2
for i in range(N):
for j in range(i+1, N):
curdist = (data[i,0] - data[j,0]) **2 +(data[i,1] - data[j,1]) **2 + (data[i,2] - data[j,2]) **2
if curdist < cutoff2:
contacts1.push_back(i)
contacts2.push_back(j)
cdef int M = len(contacts1)
cdef np.ndarray[np.int32_t, ndim = 2] contacts = np.zeros((M,2), dtype = np.int32)
for i in range(M):
contacts[i,0] = contacts1[i]
contacts[i,1] = contacts2[i]
return contacts
</code></pre>
<p>Cython代码的编译(或生成文件):</p>
^{pr2}$
<p>测试代码:</p>
<pre><code>from __future__ import print_function, division
import signal
import time
from contextlib import contextmanager
import matplotlib
import matplotlib.pyplot as plt
import numpy as np
from scipy.spatial import ckdtree
from scipy.spatial.distance import pdist
from contactmaps import giveContactsOpenMM # remove this unless you have OpenMM and openmm-polymer libraries installed
from fastContacts import contactsCython
class TimeoutException(Exception): pass
@contextmanager
def time_limit(seconds):
def signal_handler(signum, frame):
raise TimeoutException("Timed out!")
signal.signal(signal.SIGALRM, signal_handler)
signal.alarm(seconds)
try:
yield
finally:
signal.alarm(0)
matplotlib.rcParams.update({'font.size': 8})
def close_pairs_ckdtree(X, max_d):
tree = ckdtree.cKDTree(X)
pairs = tree.query_pairs(max_d)
return np.array(list(pairs))
def condensed_to_pair_indices(n, k):
x = n - (4. * n ** 2 - 4 * n - 8 * k + 1) ** .5 / 2 - .5
i = x.astype(int)
j = k + i * (i + 3 - 2 * n) / 2 + 1
return np.array([i, j]).T
def close_pairs_pdist(X, max_d):
d = pdist(X)
k = (d < max_d).nonzero()[0]
return condensed_to_pair_indices(X.shape[0], k)
a = np.random.random((100, 3)) * 3 # test set
methods = {"cython": contactsCython, "ckdtree": close_pairs_ckdtree, "OpenMM": giveContactsOpenMM,
"pdist": close_pairs_pdist}
# checking that each method gives the same value
allUniqueInds = []
for ind, method in methods.items():
contacts = method(a, 1)
uniqueInds = contacts[:, 0] + 100 * contacts[:, 1] # unique index of each contacts
allUniqueInds.append(np.sort(uniqueInds)) # adding sorted unique conatcts
for j in allUniqueInds:
assert np.allclose(j, allUniqueInds[0])
# now actually doing testing
repeats = [30,30,30, 30, 30, 20, 20, 10, 5, 3, 2 , 1, 1, 1]
sizes = [10,30,100, 200, 300, 500, 1000, 2000, 3000, 10000, 30000, 100000, 300000, 1000000]
systems = [[np.random.random((n, 3)) * ((n / 0.2) ** 0.333333) for k in range(repeat)] for n, repeat in
zip(sizes, repeats)]
for j, radius in enumerate([0.5, 1, 2, 4, 7, 10]):
plt.subplot(2, 3, j + 1)
plt.title("Radius = {0}; {1:.2f} cont per particle".format(radius, 0.2 * (4 / 3 * np.pi * radius ** 3)))
times = {i: [] for i in methods}
for name, method in methods.items():
for n, system, repeat in zip(sizes, systems, repeats):
if name == "pdist" and n > 30000:
break # memory issues
st = time.time()
try:
with time_limit(5 * repeat):
for ind in range(repeat):
k = len(method(system[ind], radius))
except:
print("Run aborted")
break
end = time.time()
mytime = (end - st) / repeat
times[name].append((n, mytime))
print("{0} radius={1} n={2} time={3} repeat={4} contPerParticle={5}".format(name, radius, n, mytime,repeat, 2 * k / n))
for name in sorted(times.keys()):
plt.plot(*zip(*times[name]), label=name)
plt.xscale("log")
plt.yscale("log")
plt.xlabel("System size")
plt.ylabel("Time (seconds)")
plt.legend(loc=0)
plt.show()
</code></pre>