If you have to fit a complex function to a very big data set it would be nice to be able to use all the cores your cpu has. Because the data set is very big it should be efficient to simply split the data set over a number of cores and calculate the total error sum (sum squared error) in parts in parallel. This sounds simple but it took me some effort to do this in python/Cython on both linux and windows. After googling for a while, I decided that using the multiProcessing module should work best for my specific situation (which contains a lot of python code which makes it difficult to turn the GIL temporarily off). On linux I had things running relatively fast, but on windows I could not get it to function. The difference is caused by the lack of real processes on windows (or at least they work differently). On a fork() in linux everything is copied but this does not happen on windows and you have to take care that all data is correctly passed to the child process (read "Explicitly pass resources to child processes" in the multiprocessing
documentation).
To try things out I started with a simple example:
#!/usr/bin/env python
from multiprocessing import Process,Queue
import sys,numpy,pylab
class TFitFunc:
def __init__(self,X0,x,y,pid=1):
self.a=X0[0]
self.b=X0[1]
self.c=X0[2]
self.x=x[:]
self.y=y[:]
self.pid=pid
def __call__(self,X):
self.a=X[0]
self.b=X[1]
self.c=X[2]
errsum=0
for i in range(100):
ymod=self.a*self.x**2+self.b*self.x+self.c
errsum+=numpy.sum((ymod[:]-self.y[:])**2)
return(errsum)
class TFitFuncComplex:
def __init__(self,X0,x,y,pid=1):
self.a=X0[0]
self.b=X0[1]
self.c=X0[2]
self.x=x[:]
self.y=y[:]
self.pid=pid
def __call__(self,X):
self.a=X[0]
self.b=X[1]
self.c=X[2]
errsum=0
for i in range(100):
ymod=self.a*self.x**2+self.b*self.x+self.c+\
numpy.sin(numpy.sqrt(self.x))*numpy.cos(self.x+0.5)\
/self.a*numpy.sqrt(self.b)
errsum+=numpy.sum((ymod[:]-self.y[:])**2)
return(errsum)
def f(fitfunc,X,Q=None):
errsum=fitfunc(X)
print "%d: errsum:%e"%(fitfunc.pid,errsum)
if(Q!=None):
Q.put(errsum)
return(errsum)
def main():
a=1.0
b=2.0
c=3.0
x1=numpy.r_[0:10:-10000000j]
x2=numpy.r_[0:10:-10000000j]
y1=a*x1**2+b*x1+c
y1+=y1*0.35*(numpy.random.random(len(x1))-0.5)
y2=a*x2**2+b*x2+c
y2+=y2*0.35*(numpy.random.random(len(x2))-0.5)
X0=[0.5,2.5,1.5]
f1=TFitFunc(X0,x1,y1,1)
f2=TFitFunc(X0,x2,y2,2)
ps=[]
for i in range(2):
if(i==0):
p=Process(target=f,args=(f1,X0))
else:
p=Process(target=f,args=(f2,X0))
p.start()
ps.append(p)
for p in ps:
p.join()
def main_complex():
a=1.0
b=2.0
c=3.0
x1=numpy.r_[0:10:-1000000j]
x2=numpy.r_[0:10:-1000000j]
y1=a*x1**2+b*x1+c
y1+=y1*0.35*(numpy.random.random(len(x1))-0.5)
y2=a*x2**2+b*x2+c
y2+=y2*0.35*(numpy.random.random(len(x2))-0.5)
X0=[0.5,2.5,1.5]
f1=TFitFuncComplex(X0,x1,y1,1)
f2=TFitFuncComplex(X0,x2,y2,2)
ps=[]
Qs=[]
errSum=0.0
for i in range(2):
Qs.append(Queue())
if(i==0):
p=Process(target=f,args=(f1,X0,Qs[i]))
else:
p=Process(target=f,args=(f2,X0,Qs[i]))
p.start()
ps.append(p)
for i in range(2):
errSum+=Qs[i].get()
ps[i].join()
print "Total errsum: %e"%(errSum)
def main_single_complex():
a=1.0
b=2.0
c=3.0
x1=numpy.r_[0:10:-1000000j]
x2=numpy.r_[0:10:-1000000j]
y1=a*x1**2+b*x1+c
y1+=y1*0.35*(numpy.random.random(len(x1))-0.5)
y2=a*x2**2+b*x2+c
y2+=y2*0.35*(numpy.random.random(len(x2))-0.5)
X0=[0.5,2.5,1.5]
f1=TFitFuncComplex(X0,x1,y1,1)
f2=TFitFuncComplex(X0,x2,y2,2)
errSum=f(f1,X0)
errSum+=f(f2,X0)
print "Total errsum: %e"%(errSum)
def main_single():
a=1.0
b=2.0
c=3.0
x1=numpy.r_[0:10:-10000000j]
x2=numpy.r_[0:10:-10000000j]
y1=a*x1**2+b*x1+c
y1+=y1*0.35*(numpy.random.random(len(x1))-0.5)
y2=a*x2**2+b*x2+c
y2+=y2*0.35*(numpy.random.random(len(x2))-0.5)
X0=[0.5,2.5,1.5]
f1=TFitFunc(X0,x1,y1,1)
f2=TFitFunc(X0,x2,y2,2)
f(f1,X0)
f(f2,X0)
if __name__=='__main__':
main_single()
#~ main()
#~ main_complex()
#~ main_single_complex()
This works fine on linux and windows. However, this is pure python. Normally, I use a lot of Cython code in extension types (aka cython classes). And this I could not get to work without some
more research. Now first my solution. The first part shows the .pyx file with two classes, one normal python class with some cython code in it and one real extension type. The second part shows the script using these classes.
TFitFunctions.pyx
#!/usr/bin/env python
import numpy as np
cimport numpy as np
class TFitFunc:
"""
Simple demonstration class to be used as fit function.
By definition of the __call__ member function an object of this
class is callable (functor). All additional data required
to calculate the error sum should be passed to the constructor.
The function here is simply
y=a*x**2+b*x+c
"""
def __init__(self,X0,x,y,pid=1):
"""
Constructor.
Arguments:
X0: list of initial values for the three model parameters [a, b, c]
x: array of x values
y: array of y values (typically experimentally determined data points)
pid: optional "process id"
"""
self.a=X0[0]
self.b=X0[1]
self.c=X0[2]
self.x=x[:]
self.y=y[:]
self._pid=pid
def pid(self):
return(self._pid)
def __call__(self,X):
"""
Make objects of this class callable. The argument is a list/array
of model parameter values [a,b,c]
The function returns the sum squared error
"""
cdef double errsum
cdef int i
self.a=X[0] #could also have used X directly in the calculation below
self.b=X[1]
self.c=X[2]
errsum=0
for i in range(100): #do this a hundred times to waste some CPU time
ymod=self.a*self.x**2+self.b*self.x+self.c #calculate model values
errsum+=np.sum((ymod[:]-self.y[:])**2) # calculate summed square error
errsum/=100.0
return(errsum)
cdef class TFitFuncComplex:
"""
Simple demonstration class to be used as fit function.
Very similar to TFitFunc but with a more complex (and time consuming)
function. Another big difference is that now the class is defined
as an extension type.
By definition of the __call__ member function an object of this
class is callable (functor). All additional data required
to calculate the error sum should be passed to the constructor.
The function here is simply
y=a*x**2+b*x+c+sin(sqrt(x))*cos(x+0.5)/(a*b*b)
"""
cdef double a,b,c #in an extension type class member variables must be defined here
cdef int _pid
cdef np.ndarray x,y
def __init__(self,X0,np.ndarray[double, ndim=1]x,np.ndarray[double, ndim=1]y,int pid=1):
"""
Constructor.
Arguments:
X0: list/array of initial values for the three model parameters [a, b, c]
x: array of x values
y: array of y values (typically experimentally determined data points)
pid: optional "process id"
"""
self.a=X0[0]
self.b=X0[1]
self.c=X0[2]
self.x=x[:]
self.y=y[:]
self._pid=pid
def pid(self):
return(self._pid)
def __call__(self,X):
"""
Make objects of this class callable. The argument is a list/array
of model parameter values [a,b,c]
The function returns the sum squared error
"""
cdef double errsum
cdef int i
self.a=X[0] #could also have used X directly in the calculation below
self.b=X[1]
self.c=X[2]
errsum=0
for i in xrange(100):#do this a hundred times to waste some CPU time
ymod=self.a*self.x**2+self.b*self.x+self.c+\
np.sin(np.sqrt(self.x))*np.cos(self.x+0.5)\
/self.a*np.sqrt(self.b) #calculate model values
errsum+=np.sum((ymod[:]-self.y[:])**2) # calculate summed square error
errsum/=100.0
return(errsum)
def __reduce__(self):
"""
Without this function the code will not run with multiProcessing
on Windows.
It has something to do with making an extension type
pickable. For a normal python class this is not required
(see TFitFunc)
"""
return TFitFuncComplex, ([self.a,self.b,self.c],self.x,self.y,self._pid)
calling script:
#!/usr/bin/env python
from multiprocessing import Process,Queue
import sys,numpy
from TFitFunctions import TFitFunc,TFitFuncComplex
"""
Demonstration of use Process with a callable Python/Cython classes
Can be easily extended into a real multiProcessing fitting
setup for use with (e.g.) fmin
The basic idea is that you have a huge amount of data points
that must be evaluated for the calculation of the summed squared error.
These data points are independent by nature and thus ideal for
parallel processing.
"""
def f(fitfunc,X,Q=None):
"""
Function to be passed to Process as target. The function
will call fitfunc with X as argument and put the result in the
Queue Q is one is passed as argument.
"""
errsum=fitfunc(X)
print "%d: errsum:%e"%(fitfunc.pid(),errsum)
if(Q!=None):
Q.put(errsum)
return(errsum)
def main():
"""
Demonstration of use of TFitFunc
"""
a=1.0 #model parameters
b=2.0
c=3.0
x1=numpy.r_[0:10:-10000000j] #data points for first process (x)
x2=numpy.r_[0:10:-10000000j] #measurement points for second process (x)
y1=a*x1**2+b*x1+c #"measured" data for process 1
y1+=y1*0.35*(numpy.random.random(len(x1))-0.5) #add some noise
y2=a*x2**2+b*x2+c #"measured" data for process 2
y2+=y2*0.35*(numpy.random.random(len(x2))-0.5) #add some noise
X0=[0.5,2.5,1.5] #initial guess for model parameters
f1=TFitFunc(X0,x1,y1,1) #Create fit function for process 1
f2=TFitFunc(X0,x2,y2,2) #Create fit function for process 2
ps=[] #to contain process
Qs=[]
errSum=0.0
for i in range(2):
Qs.append(Queue())
if(i==0):
p=Process(target=f,args=(f1,X0,Qs[i])) #create process 1
else:
p=Process(target=f,args=(f2,X0,Qs[i])) #create process 2
p.start() #start process
ps.append(p) #add process "handle"
for i in range(2):
errSum+=Qs[i].get() #collect error sums from processes
ps[i].join() #wait for process to finish
print "Total errsum: %e"%(errSum)
def main_complex():
"""
Same as main but now with TFitFuncComplex
"""
a=1.0
b=2.0
c=3.0
x1=numpy.r_[0:10:-1000000j]
x2=numpy.r_[0:10:-1000000j]
y1=a*x1**2+b*x1+c
y1+=y1*0.35*(numpy.random.random(len(x1))-0.5)
y2=a*x2**2+b*x2+c
y2+=y2*0.35*(numpy.random.random(len(x2))-0.5)
X0=[0.5,2.5,1.5]
f1=TFitFuncComplex(X0,x1,y1,1)
f2=TFitFuncComplex(X0,x2,y2,2)
ps=[]
Qs=[]
errSum=0.0
for i in range(2):
Qs.append(Queue())
if(i==0):
p=Process(target=f,args=(f1,X0,Qs[i]))
else:
p=Process(target=f,args=(f2,X0,Qs[i]))
p.start()
ps.append(p)
for i in range(2):
errSum+=Qs[i].get()
ps[i].join()
print "Total errsum: %e"%(errSum)
def calcErrorSum(X,fitfuncs):
"""
Calculate error sum for given model parameters (X)
by using the functions in fitfuncs in (parallel) processes
"""
ps=[]
Qs=[]
errSum=0.0
for i in range(len(fitfuncs)):
Qs.append(Queue())
p=Process(target=f,args=(fitfuncs[i],X,Qs[i]))
p.start()
ps.append(p)
for i in range(2):
errSum+=Qs[i].get()
ps[i].join()
print "Total errsum: %e"%(errSum)
return(errSum)
def main_complex2():
"""
Same as main_complex but now with data creation part seperated
from function evaluation part. PLease note that
the function calcErrorSum can be used as a (multiProcessing)
argument to (e.g.) fmin
"""
a=1.0
b=2.0
c=3.0
x1=numpy.r_[0:10:-1000000j]
x2=numpy.r_[0:10:-1000000j]
y1=a*x1**2+b*x1+c
y1+=y1*0.35*(numpy.random.random(len(x1))-0.5)
y2=a*x2**2+b*x2+c
y2+=y2*0.35*(numpy.random.random(len(x2))-0.5)
X0=[0.5,2.5,1.5]
f1=TFitFuncComplex(X0,x1,y1,1)
f2=TFitFuncComplex(X0,x2,y2,2)
fitfuncs=[f1,f2]
calcErrorSum(X0,fitfuncs)
def main_single_complex():
"""
Same a main_complex but now serial evaluation (for time comparison purposes)
"""
a=1.0
b=2.0
c=3.0
x1=numpy.r_[0:10:-1000000j]
x2=numpy.r_[0:10:-1000000j]
y1=a*x1**2+b*x1+c
y1+=y1*0.35*(numpy.random.random(len(x1))-0.5)
y2=a*x2**2+b*x2+c
y2+=y2*0.35*(numpy.random.random(len(x2))-0.5)
X0=[0.5,2.5,1.5]
f1=TFitFuncComplex(X0,x1,y1,1)
f2=TFitFuncComplex(X0,x2,y2,2)
errSum=f(f1,X0)
errSum+=f(f2,X0)
print "Total errsum: %e"%(errSum)
def main_single():
"""
Same a main but now serial evaluation (for time comparison purposes)
"""
a=1.0
b=2.0
c=3.0
x1=numpy.r_[0:10:-10000000j]
x2=numpy.r_[0:10:-10000000j]
y1=a*x1**2+b*x1+c
y1+=y1*0.35*(numpy.random.random(len(x1))-0.5)
y2=a*x2**2+b*x2+c
y2+=y2*0.35*(numpy.random.random(len(x2))-0.5)
X0=[0.5,2.5,1.5]
f1=TFitFunc(X0,x1,y1,1)
f2=TFitFunc(X0,x2,y2,2)
f(f1,X0)
f(f2,X0)
if __name__=='__main__':
#~ main_single()
#~ main()
#~ main_complex2()
main_complex()
#~ main_single_complex()
The code in TFitFunctions.pyx shows that the trick for an extension type is to add the __reduce__ method to make it pickable. This is only needed on windows.
