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"""
MathWorld: "Hundred-Dollar, Hundred-Digit Challenge Problems", Challenge #3.
http://mathworld.wolfram.com/Hundred-DollarHundred-DigitChallengeProblems.html
The Computer Language Benchmarks Game
http://benchmarksgame.alioth.debian.org/u64q/spectralnorm-description.html#spectralnorm
Contributed by Sebastien Loisel
Fixed by Isaac Gouy
Sped up by Josh Goldfoot
Dirtily sped up by Simon Descarpentries
Concurrency by Jason Stitt
"""
from six.moves import xrange, zip as izip
DEFAULT_N = 130
def eval_A(i, j):
return 1.0 / ((i + j) * (i + j + 1) // 2 + i + 1)
def eval_times_u(func, u):
return [func((i, u)) for i in xrange(len(list(u)))]
def eval_AtA_times_u(u):
return eval_times_u(part_At_times_u, eval_times_u(part_A_times_u, u))
def part_A_times_u(i_u):
i, u = i_u
partial_sum = 0
for j, u_j in enumerate(u):
# EDB WAS:
# partial_sum += eval_A(i, j) * u_j
ij = i + j
partial_sum += (1.0 / ((ij) * (ij + 1) // 2 + i + 1)) * u_j
return partial_sum
def part_At_times_u(i_u):
i, u = i_u
partial_sum = 0
for j, u_j in enumerate(u):
# EDB WAS:
# partial_sum += eval_A(j, i) * u_j
ij = i + j
partial_sum += (1.0 / ((ij) * (ij + 1) // 2 + j + 1)) * u_j
return partial_sum
def bench_spectral_norm(loops):
range_it = xrange(loops)
# t0 = pyperf.perf_counter()
for _ in range_it:
u = [1] * DEFAULT_N
for dummy in xrange(10):
v = eval_AtA_times_u(u)
u = eval_AtA_times_u(v)
vBv = vv = 0
for ue, ve in izip(u, v):
vBv += ue * ve
vv += ve * ve
return # pyperf.perf_counter() - t0
if __name__ == "__main__":
bench_spectral_norm(10)
# runner = pyperf.Runner()
# runner.metadata['description'] = (
# 'MathWorld: "Hundred-Dollar, Hundred-Digit Challenge Problems", '
# 'Challenge #3.')
# runner.bench_time_func('spectral_norm', bench_spectral_norm)
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