如何用python numpy向量化解決這個練習？

Question

如何解決這個練習4.5第2頁與Python Numpy矢量化？

鏈接下載：

https://dl.dropbox.com/u/92795325/Python%20Scripting%20for%20Computational%20Scien%20-%20H.P.%20%20Langtangen.pdf

我試圖與Python的循環，但我需要矢量版本。

from numpy import * 
import time 

def fun1(x): 
     return 2*x+1 

def integ(a,b,n): 
     t0 = time.time() 
     h = (b-a)/n 
     a1 = (h/2)*fun1(a) 
     b1 = (h/2)*fun1(b) 
     c1 = 0 
     for i in range(1,n,1): 
       c1 = fun1((a+i*h))+c1 
     t1 = time.time() 
     return a1+b1+h*c1, t1-t0 

Answer 1

要「矢量化」使用numpy，這一切都意味着，而不是做一個明確的循環一樣，

for i in range(1, n): 
    c = c + f(i) 

然後，而不是你應該做i成numpy的數組，隨便拿其總和：

i = np.arange(1,n) 
c = i.sum() 

numpy自動爲您做矢量化。這個速度更快的原因是因爲numpy循環比普通的python循環更好的優化方式，出於各種原因。一般來說，迴路/陣列越長，優勢越好。這裏是你的梯形積分來實現：

import numpy as np 

def f1(x): 
    return 2*x + 1 

# Here's your original function modified just a little bit: 
def integ(f,a,b,n): 
    h = (b-a)/n 
    a1 = (h/2)*f(a) 
    b1 = (h/2)*f(b) 
    c1 = 0 
    for i in range(1,n,1): 
     c1 = f((a+i*h))+c1 
    return a1 + b1 + h*c1 

# Here's the 'vectorized' function: 
def vinteg(f, a, b, n): 
    h = (b-a)/n 
    ab = 0.5 * h * (f(a)+f(b)) #only divide h/2 once 

    # use numpy to make `i` a 1d array: 
    i = np.arange(1, n) 
    # then, passing a numpy array to `f()` means that `f` returns an array 
    c = f(a + h*i) # now c is a numpy array 

    return ab + c.sum() # ab + np.sum(c) is equivalent 

在這裏，我將導入我叫tmp.py爲ipython會議的時機更容易比使用time.time：快

import trap 
f = trap.f1 
a = 0 
b = 100 
n = 1000 

timeit trap.integ(f, a, b, n) 
#1000 loops, best of 3: 378 us per loop 

timeit trap.vinteg(f, a, b, n) 
#10000 loops, best of 3: 51.6 us per loop 

哇，七次。

看它是否有助於多的小n

n = 10 

timeit trap.integ(f, a, b, n) 
#100000 loops, best of 3: 6 us per loop 

timeit trap.vinteg(f, a, b, n) 
#10000 loops, best of 3: 43.4 us per loop 

不，小環形慢得多！那麼非常大的n？

n = 10000 

timeit trap.integ(f, a, b, n) 
#100 loops, best of 3: 3.69 ms per loop 

timeit trap.vinteg(f, a, b, n) 
#10000 loops, best of 3: 111 us per loop 

快三十倍！