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#!/usr/bin/env python
# File: auto_diff.py
# Author: Vitalii Vanovschi
# Desc: This program demonstrates parallel computations with pp module
# using class methods as parallel functions (available since pp 1.4).
# Program calculates the partial sums of f(x) = x-x**2/2+x**3/3-x**4/4+...
# and first derivatives f'(x) using automatic differentiation technique.
# In the limit f(x) = ln(x+1) and f'(x) = 1/(x+1).
# Parallel Python Software: http://www.parallelpython.com
import math
import sys
import pp
# Partial implemenmtation of automatic differentiation class
class AD(object):
def __init__(self, x, dx=0.0):
self.x = float(x)
self.dx = float(dx)
def __pow__(self, val):
if isinstance(val, int):
p = self.x**val
return AD(self.x**val, val*self.x**(val-1)*self.dx)
else:
raise TypeError("Second argumnet must be an integer")
def __add__(self, val):
if isinstance(val, AD):
return AD(self.x+val.x, self.dx+val.dx)
else:
return AD(self.x+val, self.dx)
def __radd__(self, val):
return self+val
def __mul__(self, val):
if isinstance(val, AD):
return AD(self.x*val.x, self.x*val.dx+val.x*self.dx)
else:
return AD(self.x*val, val*self.dx)
def __rmul__(self, val):
return self*val
def __div__(self, val):
if isinstance(val, AD):
return self*AD(1/val.x, -val.dx/val.x**2)
else:
return self*(1/float(val))
def __rdiv__(self, val):
return AD(val)/self
def __sub__(self, val):
if isinstance(val, AD):
return AD(self.x-val.x, self.dx-val.dx)
else:
return AD(self.x-val, self.dx)
def __repr__(self):
return str((self.x, self.dx))
class PartialSum(object):
def __init__(self, n):
"""
This class contains methods which will be executed in parallel
"""
self.n = n
def t_log(self, x):
"""
truncated natural logarithm
"""
return self.partial_sum(x-1)
def partial_sum(self, x):
"""
partial sum for truncated natural logarithm
"""
return sum([float(i%2 and 1 or -1)*x**i/i for i in xrange(1, self.n)])
print """Usage: python auto_diff.py [ncpus]
[ncpus] - the number of workers to run in parallel,
if omitted it will be set to the number of processors in the system
"""
# tuple of all parallel python servers to connect with
#ppservers = ("*",) # auto-discover
#ppservers = ("10.0.0.1","10.0.0.2") # list of static IPs
ppservers = ()
if len(sys.argv) > 1:
ncpus = int(sys.argv[1])
# Creates jobserver with ncpus workers
job_server = pp.Server(ncpus, ppservers=ppservers)
else:
# Creates jobserver with automatically detected number of workers
job_server = pp.Server(ppservers=ppservers)
print "Starting pp with", job_server.get_ncpus(), "workers"
proc = PartialSum(20000)
results = []
for i in range(32):
# Creates an object with x = float(i)/32+1 and dx = 1.0
ad_x = AD(float(i)/32+1, 1.0)
# Submits a job of calulating proc.t_log(x).
f = job_server.submit(proc.t_log, (ad_x, ))
results.append((ad_x.x, f))
for x, f in results:
# Retrieves the result of the calculation
val = f()
print "t_log(%lf) = %lf, t_log'(%lf) = %lf" % (x, val.x, x, val.dx)
# Print execution statistics
job_server.print_stats()
# Parallel Python Software: http://www.parallelpython.com
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