The Computer Language
Benchmarks Game

spectral-norm Python 3 #5 program

source code

# The Computer Language Benchmarks Game
# http://benchmarksgame.alioth.debian.org/

# Contributed by Sebastien Loisel
# Fixed by Isaac Gouy
# Sped up by Josh Goldfoot
# Dirtily sped up by Simon Descarpentries
# Concurrency by Jason Stitt
# 2to3

from multiprocessing import Pool
from math            import sqrt

from sys             import argv

def eval_A (i, j):
    return 1.0 / ((i + j) * (i + j + 1) / 2 + i + 1)

def eval_A_times_u (u):
    args = ((i,u) for i in range(len(u)))
    return pool.map(part_A_times_u, args)

def eval_At_times_u (u):
    args = ((i,u) for i in range(len(u)))
    return pool.map(part_At_times_u, args)

def eval_AtA_times_u (u):
    return eval_At_times_u (eval_A_times_u (u))

def part_A_times_u(xxx_todo_changeme):
    (i,u) = xxx_todo_changeme
    partial_sum = 0
    for j, u_j in enumerate(u):
        partial_sum += eval_A (i, j) * u_j
    return partial_sum

def part_At_times_u(xxx_todo_changeme1):
    (i,u) = xxx_todo_changeme1
    partial_sum = 0
    for j, u_j in enumerate(u):
        partial_sum += eval_A (j, i) * u_j
    return partial_sum

def main():
    n = int(argv[1])
    u = [1] * n

    for dummy in range (10):
        v = eval_AtA_times_u (u)
        u = eval_AtA_times_u (v)

    vBv = vv = 0

    for ue, ve in zip (u, v):
        vBv += ue * ve
        vv  += ve * ve

    print("%0.9f" % (sqrt(vBv/vv)))

if __name__ == '__main__':
    pool = Pool(processes=4)
    main()
    
    

notes, command-line, and program output

NOTES:
64-bit Ubuntu quad core
Python 3.6.0 (default, Feb  5 2017, 10:29:14)
[GCC 5.4.0 20160609] on linux
--enable-optimizations
make profile-opt


Sun, 05 Feb 2017 22:11:41 GMT

MAKE:
mv spectralnorm.python3-5.python3 spectralnorm.python3-5.py
0.01s to complete and log all make actions

COMMAND LINE:
/usr/local/src/Python-3.6.0/bin/python3.6 -OO spectralnorm.python3-5.py 5500

PROGRAM OUTPUT:
1.274224153