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uni-m.cds-adv-prog/ex0.1/spectral-norm/spectral-norm.py

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2019-10-30 09:02:41 +01:00
# The Computer Language Benchmarks Game
# https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
#
# Contributed by Sebastien Loisel
# Fixed by Isaac Gouy
# Sped up by Josh Goldfoot
# Dirtily sped up by Simon Descarpentries
# Used list comprehension by Vadim Zelenin
# 2to3
from math import sqrt
from sys import argv
def eval_A(i, j):
ij = i+j
return 1.0 / (ij * (ij + 1) / 2 + i + 1)
def eval_A_times_u(u):
local_eval_A = eval_A
return [ sum([ local_eval_A(i, j) * u_j
for j, u_j in enumerate(u)
]
)
for i in range(len(u))
]
def eval_At_times_u(u):
local_eval_A = eval_A
return [ sum([ local_eval_A(j, i) * u_j
for j, u_j in enumerate(u)
]
)
for i in range(len(u))
]
def eval_AtA_times_u(u):
return eval_At_times_u(eval_A_times_u(u))
def main():
n = int(argv[1])
u = [1] * n
local_eval_AtA_times_u = eval_AtA_times_u
for dummy in range(10):
v = local_eval_AtA_times_u(u)
u = local_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)))
main()