比较Speed Python3和Julia

我开始编写一个程序进行非线性光束计算.我之所以选择 Python是因为它的Matlab就像代码一样,而且我正在进行速度测试(确保python是正确的语言来进行快速数值计算)并尝试熟悉python3.
我尝试了一种算法,计算从t = 1到n的1 / t ^ 2之和(来自书Julia High Perfromance),以比较python3与julia的速度.
现在我有一些问题：

1)在我的计算中,朱莉娅没有预期的那么快？ Julia ist JIT编译.它应该非常快.为什么python更快？

2)为什么python中的循环如此缓慢？

3)为什么python sum方法比numpy.sum方法慢

4)为什么python geting的sum函数与numpy.sum函数的解决方案略有不同？

我希望你能帮助我.

代码：

# Benchmark Python vs Julia
# (from Julia High Performance page 7 from Avik Sengupta)

import scipy as sp
import time

# Sum of 1/t^2 from t = 1 to n by using loops:
# --------------------------------------------
def pisum(w,n):
    u_sum = 0
    for vi in range(w):
        u_sum = 0
        for vj in range(1,n+1,1):
            u_sum += 1.0/(vj*vj)
    return u_sum

# Sum of 1/t^2 from t = 1 to n by using scipy functions:
# ------------------------------------------------------
def pisum1(w,n):
    for vi in range(w):
        vj = sp.arange(1,1)
        vj = sp.multiply(vj,vj)
        u_sum_sp = (sp.divide(sp.ones(n),vj)).sum()
    return u_sum_sp

# Sum of 1/t^2 from t = 1 to n by using scipy functions & calculating 
# the sum via pure python:
# -------------------------------------------------------------------
def pisum2(w,vj)
        u_sum_py = sum(sp.divide(sp.ones(n),vj))
    return u_sum_py

# Benchmarking the methods :
# ==========================   

w = 500 
n = 10000

# 1) Loops:
# ---------    
ta = time.clock()
u_sum_loops = pisum(w,n)
eltime_loops = time.clock() - ta

# 2) scipy:
# ---------
ta = time.clock()
u_sum_sp = pisum1(w,n)
eltime_sp= time.clock() - ta


# 3) scipy & sum via python:
# --------------------------
ta = time.clock()
u_sum_py = pisum2(w,n)
eltime_py= time.clock() - ta

# Julia with loops:
# -----------------
eltime_ju_loops = 0.150857295
u_sum_ju = 1.6448340718480652

row_format = '{:<35} {:<5} {:<5} {:<} {:<}'
print("Overview calculation time:")
print("-"*50)
print(row_format.format("elapsed time using loops:","%.5f" % eltime_loops,"sec. (","%.2f"% (eltime_loops/eltime_ju_loops),"*time Julia)"))
print(row_format.format("elapsed time using scipy:","%.5f" % eltime_sp,"%.2f"% (eltime_sp/eltime_ju_loops),"*time Julia)"))
print(row_format.format("elapsed time using python:","%.5f" % eltime_py,"%.2f"% (eltime_py/eltime_ju_loops),"*time Julia)"))
print(row_format.format("elapsed time using Julia and loops:","%.5f" % eltime_ju_loops,"sec.","","n"))

line1 = "sum loops:",u_sum_loops
line2 = "sum scipy:",u_sum_sp
line3 = "sum scipy and sum via python:",u_sum_py
line4 = "sum_julia:",u_sum_ju
row_format = '{:<29} {:<18}'
print("Overview Sum:")
print("-"*50)
print(row_format.format(*line1))
print(row_format.format(*line2))
print(row_format.format(*line3))
print(row_format.format(*line4))

# Julia Code:
# ===========

# function pisum(w,n)
#     u_sum = 0;
#     for vi = 1:w
#         u_sum = 0;
#         for vj = 1:n
#             u_sum += 1.0/(vj*vj);
#         end
#     end
#     u_sum
# end
# 
# tic()
# u_sum = pisum(500,10000)
# eltime = toc()

function pisum(w,n)
    u_sum = 0.0;
    for vi = 1:w
        u_sum = 0.0;
        for vj = 1:n
            u_sum += 1.0/(vj*vj);
        end
    end
    u_sum
end
@time u_sum = pisum(500,10000)