这是我在Python / Numpy中编写的一些代码,我几乎直接从MATLAB代码中翻译过来。当我在我的机器上运行MATLAB中的代码时,大约需要17秒。当我在我的机器上运行Python / Numpy中的代码时,大约需要233秒。我没有有效地使用Numpy吗?请查看我的Python代码,看看我是否以非有效的方式使用Numpy。
import numpy as np
from numpy import *
import pylab as py
from pylab import *
import math
import time
def heat(D,u0,q,tdim):
xdim = np.size(u0)
Z = np.zeros([xdim,tdim])
Z[:,0]=u0;
for i in range(1,tdim):
for j in range (1,xdim-1):
Z[j,i]=Z[j,i-1]+ D*q*(Z[j-1,i-1]-2*Z[j,i-1]+Z[j+1,i-1])
return Z
start_time = time.clock()
L = 10
D = 0.5
s = 0.03 # magnitude of noise
Tmax = 0.2
xdim = 25
tdim = 75
x = np.linspace(0,L,xdim)
t = np.linspace(0,Tmax,tdim)
dt = t[1]-t[0]
dx = x[1]-x[0]
q = dt/(dx**2)
r1 = 0.75*L
r2 = 0.8*L
################################################
## check the stability criterion dt/(dx^2)<.5 ##
################################################
# Define the actual initial temperature distribution
u0 = np.zeros(xdim)
for i in range(0,xdim):
if(x[i]>=r1 and x[i]<=r2):
u0[i] = 1
xDat = range(1,xdim-1)
tDat = np.array([tdim])
nxDat = len(xDat)
ntDat = 1
tfinal = tdim-1
# synthesize data
Z = heat(D,u0,q,tdim)
u = Z[xDat,tfinal] # matrix
uDat = u + s*randn(nxDat)
# MATLAB PLOTTING
#figure(1);surf(x,t,Z); hold on;
#if ntDat>1, mesh(x(xDat),t(tDat),uDat);
#else set(plot3(x(xDat),t(tDat)*ones(1,nxDat),uDat,'r-o'),'LineWidth',3);
#end; hold off; drawnow
#MCMC run
N = 10000
m = 100
XD = 1.0
X = np.zeros(N)
X[0] = XD
Z = heat(XD,u0,q,tdim)
u = Z[xDat,tfinal]
oLLkd = sum(sum(-(u-uDat)**2))/(2*s**2)
LL = np.zeros(N)
LL[0] = oLLkd
# random walk step size
w = 0.1
for n in range (1,N):
XDp = XD+w*(2*rand(1)-1)
if XDp > 0:
Z = heat(XDp,u0,q,tdim)
u = Z[xDat,tfinal]
nLLkd = sum(sum( -(u-uDat)**2))/(2*s**2)
alpha = exp((nLLkd-oLLkd))
if random() < alpha:
XD = XDp
oLLkd = nLLkd
CZ = Z
X[n] = XD;
LL[n] = oLLkd;
print time.clock() - start_time, "seconds"
答案 0 :(得分:1)
Numpy和Matlab之间在基本阵列/矩阵操作方面的性能差异很可能是因为Numpy是针对较慢的Lapack实现而安装的。为了获得最佳性能,您可以考虑针对LAPACK构建numpy(instructions here)。
在你的代码中,主要的性能影响是你基本上在python for循环中执行convultion。因此,你并没有真正利用Numpy功能。你应该使用专用的卷积函数替换你的double for循环,例如scipy.ndimage.convolve。