[SciPy-User] Speeding things up - how to use more than one computer core

Troels Emtekær Linnet tlinnet@gmail....
Sat Apr 6 10:40:25 CDT 2013


Dear Scipy users.

I am doing analysis of some NMR data, where I repeatability are doing
leastsq fitting.
But I get a little impatient for the time-consumption. For a run of my
data, it takes
approx 3-5 min, but it in this testing phase, it is to slow.

A look in my  task manager, show that I only consume 25%=1 core on my
computer.
And I have access to a computer with 24 cores, so I would like to speed
things up.
------------------------------------------------
I have been looking at the descriptions of multithreading/Multiprocess
http://www.scipy.org/Cookbook/Multithreading
http://stackoverflow.com/questions/4598339/parallelism-with-scipy-optimize
http://www.scipy.org/ParallelProgramming


But I hope someone can guide me, which of these two methods I should go
for, and how to implement it?
I am little unsure about GIL, synchronisation?, and such things, which I
know none about.

For the real data, I can see that I am always waiting for the call of the
leastsq fitting.
How can start a pool of cores when I go through fitting?

I have this test script, which exemplifies my problem:
*Fitting single peaks N=300 0:00:00.045000*
*Done with fitting single peaks 0:00:01.146000*
*
*
*Make a test on chisqr 0:00:01.147000*
*Done with test on chisqr 0:00:01.148000*
*
*
*Prepare for global fit 0:00:01.148000*
*Doing global fit 0:00:01.152000*
*Done with global fit 0:00:17.288000*
*global fit unpacked 0:00:17.301000 *
*
*
*Making figure 0:00:17.301000*
--------------------------------------
import pylab as pl
#import matplotlib.pyplot as pl
import numpy as np
import scipy.optimize
import lmfit
from datetime import datetime
startTime = datetime.now()
#
############# Fitting functions ################
def sim(pars,x,data=None,eps=None):
    a = pars['a'].value
    b = pars['b'].value
    c = pars['c'].value
    model = a*np.exp(-b*x)+c
    if data is None:
        return model
    if eps is None:
        return (model - data)
    return (model-data)/eps
#
def err_global(pars,x_arr,y_arr,sel_p):
    toterr = np.array([])
    for i in range(len(sel_p)):
        p = sel_p[i]
        par = lmfit.Parameters()
        par.add('b', value=pars['b'].value, vary=True, min=0.0)
        par.add('a', value=pars['a%s'%p].value, vary=True)
        par.add('c', value=pars['c%s'%p].value, vary=True)
        x = x_arr[i]
        y = y_arr[i]
        Yfit = sim(par,x)
        erri = Yfit - y
        toterr = np.concatenate((toterr, erri))
    #print len(toterr), type(toterr)
    return toterr
#
def unpack_global(dic, p_list):
    for i in range(len(p_list)):
        p = p_list[i]
        par = lmfit.Parameters()
        b = dic['gfit']['par']['b']
        a = dic['gfit']['par']['a%s'%p]
        c = dic['gfit']['par']['c%s'%p]
        par['b'] = b; par['a'] = a; par['c'] = c
        dic[str(p)]['gfit']['par'] = par
        # Calc other parameters for the fit
        Yfit = sim(par, dic[str(p)]['X'])
        dic[str(p)]['gfit']['Yfit'] = Yfit
        residual = Yfit - dic[str(p)]['Yran']
        dic[str(p)]['gfit']['residual'] = residual
        chisq = sum(residual**2)
        dic[str(p)]['gfit']['chisq'] = chisq
        NDF = len(residual)-len(par)
        dic[str(p)]['gfit']['NDF'] = NDF
        dic[str(p)]['gfit']['what_is_this_called'] = np.sqrt(chisq/NDF)
        dic[str(p)]['gfit']['redchisq'] = chisq/NDF
    return()
################ Random peak data generator ###########################
def gendat(nr):
    pd = {}
    for i in range(1,nr+1):
        b = 0.15
        a = np.random.random_integers(1, 80)/10.
        c = np.random.random_integers(1, 80)/100.
        par = lmfit.Parameters(); par.add('b', value=b, vary=True);
par.add('a', value=a, vary=True); par.add('c', value=c, vary=True)
        pd[str(i)] = par
    return(pd)
#############################################################################
## Start
#############################################################################
limit = 0.6   # Limit set for chisq test, to select peaks
#############################################################################
# set up the data
data_x = np.linspace(0, 20, 50)
pd = {} # Parameter dictionary, the "true" values of the data sets
par = lmfit.Parameters(); par.add('b', value=0.15, vary=True); par.add('a',
value=2.5, vary=True); par.add('c', value=0.5, vary=True)
pd['1'] = par # parameters for the first trajectory
par = lmfit.Parameters(); par.add('b', value=0.15, vary=True); par.add('a',
value=4.2, vary=True); par.add('c', value=0.2, vary=True)
pd['2'] = par       # parameters for the second trajectory, same b
par = lmfit.Parameters(); par.add('b', value=0.15, vary=True); par.add('a',
value=1.2, vary=True); par.add('c', value=0.3, vary=True)
pd['3'] = par       # parameters for the third trajectory, same b
pd = gendat(300)  # You can generate a large number of peaks to test
#
#Start making a dictionary, which holds all data
dic = {}; dic['peaks']=range(1,len(pd)+1)
for p in dic['peaks']:
    dic['%s'%p] = {}
    dic[str(p)]['X'] = data_x
    dic[str(p)]['Y'] = sim(pd[str(p)],data_x)
    dic[str(p)]['Yran'] = dic[str(p)]['Y'] +
np.random.normal(size=len(dic[str(p)]['Y']), scale=0.12)
    dic[str(p)]['fit'] = {}  # Make space for future fit results
    dic[str(p)]['gfit'] = {}  # Male space for future global fit results
#print "keys for start dictionary:", dic.keys()
#
# independent fitting of the trajectories
print "Fitting single peaks N=%s %s"%(len(pd),(datetime.now()-startTime))
for p in dic['peaks']:
    par = lmfit.Parameters(); par.add('b', value=2.0, vary=True, min=0.0);
par.add('a', value=2.0, vary=True); par.add('c', value=2.0, vary=True)
    lmf = lmfit.minimize(sim, par, args=(dic[str(p)]['X'],
dic[str(p)]['Yran']),method='leastsq')
    dic[str(p)]['fit']['par']= par
    dic[str(p)]['fit']['lmf']= lmf
    Yfit = sim(par,dic[str(p)]['X'])
    #Yfit2 = dic[str(p)]['Yran']+lmf.residual
    #print sum(Yfit-Yfit2), "Test for difference in two ways to get the
fitted Y-values "
    dic[str(p)]['fit']['Yfit'] = Yfit
    #print "Best fit parameter for peak %s. %3.2f %3.2f
%3.2f."%(p,par['b'].value,par['a'].value,par['c'].value),
    #print "Compare to real paramaters. %3.2f %3.2f
%3.2f."%(pd[str(p)]['b'].value,pd[str(p)]['a'].value,pd[str(p)]['c'].value)
print "Done with fitting single peaks %s\n"%(datetime.now()-startTime)
#
# Make a selection flag, based on some test. Now a chisq value, but could
be a Ftest between a simple and advanced model fit.
print "Make a test on chisqr %s"%(datetime.now()-startTime)
sel_p = []
for p in dic['peaks']:
    chisq = dic[str(p)]['fit']['lmf'].chisqr
    #chisq2 = sum((dic[str(p)]['fit']['Yfit']-dic[str(p)]['Yran'])**2)
    #print chisq - chisq2 "Test for difference in two ways to get chisqr"
    if chisq < limit:
        dic[str(p)]['Pval'] = 1.0
        #print "Peak %s passed test"%p
        sel_p.append(p)
    else:
        dic[str(p)]['Pval'] = False
print 'Done with test on chisqr %s\n'%(datetime.now()-startTime)
#print sel_p
#
# Global fitting
# Pick up x,y-values and parameters that passed the test
X_arr = []
Y_arr = []
P_arr = lmfit.Parameters(); P_arr.add('b', value=1.0, vary=True, min=0.0)
dic['gfit'] = {} # Make room for globat fit result
print "Prepare for global fit %s"%(datetime.now()-startTime)
for p in sel_p:
    par = dic[str(p)]['fit']['par']
    X_arr.append(dic[str(p)]['X'])
    Y_arr.append(dic[str(p)]['Yran'])
    P_arr.add('a%s'%p, value=par['a'].value, vary=True)
    P_arr.add('c%s'%p, value=par['c'].value, vary=True)
print "Doing global fit %s"%(datetime.now()-startTime)
lmf = lmfit.minimize(err_global, P_arr, args=(X_arr, Y_arr,
sel_p),method='leastsq')
print "Done with global fit %s"%(datetime.now()-startTime)
dic['gfit']['par']= P_arr
dic['gfit']['lmf']= lmf
unpack_global(dic, sel_p) # Unpack the paramerts into the selected peaks
print "global fit unpacked %s \n"%(datetime.now()-startTime)
#
# Check result
#for p in sel_p:
#    ip= pd[str(p)]; sp = dic[str(p)]['fit']['par']; gp =
dic[str(p)]['gfit']['par']
    #print p, "Single fit. %3.2f %3.2f
%3.2f"%(sp['b'].value,sp['a'].value,sp['c'].value),
    #print "Global fit. %3.2f %3.2f
%3.2f"%(gp['b'].value,gp['a'].value,gp['c'].value)
    #print p, "Single fit. %3.2f %3.2f
%3.2f"%(sp['b'].value-ip['b'].value,sp['a'].value-ip['a'].value,sp['c'].value-ip['c'].value),
    #print "Global fit. %3.2f %3.2f
%3.2f"%(gp['b'].value-ip['b'].value,gp['a'].value-ip['a'].value,gp['c'].value-ip['c'].value)##
#
# Start plotting
print "Making figure %s"%(datetime.now()-startTime)
fig = pl.figure()
sel_p = sel_p[:9]
for i in range(len(sel_p)):
    p = sel_p[i]
    # Create figure
    ax = fig.add_subplot('%s1%s'%(len(sel_p),i+1))
    X = dic[str(p)]['X']
    Y = dic[str(p)]['Y']
    Ymeas = dic[str(p)]['Yran']
    Yfit = dic[str(p)]['fit']['Yfit']
    Yfit_global = dic[str(p)]['gfit']['Yfit']
    rpar = pd[str(p)]
    fpar = dic[str(p)]['fit']['par']
    gpar = dic[str(p)]['gfit']['par']
    fchisq = dic[str(p)]['fit']['lmf'].chisqr
    gchisq = dic[str(p)]['gfit']['chisq']
    # plot
    ax.plot(X,Y,".-",label='real. Peak: %s'%p)
    ax.plot(X,Ymeas,'o',label='Measured (real+noise)')
    ax.plot(X,Yfit,'.-',label='leastsq fit. chisq:%3.3f'%fchisq)
    ax.plot(X,Yfit_global,'.-',label='global fit. chisq:%3.3f'%gchisq)
    # annotate
    ax.annotate('p%s. real    par: %1.3f %1.3f %1.3f'%(p,
rpar['b'].value,rpar['a'].value,rpar['c'].value), xy=(1,1),
xycoords='data', xytext=(0.4, 0.8), textcoords='axes fraction')
    ax.annotate('p%s. single  par: %1.3f %1.3f %1.3f'%(p,
fpar['b'].value,fpar['a'].value,fpar['c'].value), xy=(1,1),
xycoords='data', xytext=(0.4, 0.6), textcoords='axes fraction')
    ax.annotate('p%s. global  par: %1.3f %1.3f %1.3f'%(p,
gpar['b'].value,gpar['a'].value,gpar['c'].value), xy=(1,1),
xycoords='data', xytext=(0.4, 0.4), textcoords='axes fraction')
    # set title and axis name
    #ax.set_title('Fitting for peak %s'%p)
    ax.set_ylabel('Decay')
    # Put legend to the right
    box = ax.get_position()
    ax.set_position([box.x0, box.y0, box.width * 0.8, box.height]) # Shink
current axis by 20%
    ax.legend(loc='center left', bbox_to_anchor=(1, 0.5),prop={'size':8}) #
Put a legend to the right of the current axis
    ax.grid('on')
ax.set_xlabel('Time')
#
print "ready to show figure %s"%(datetime.now()-startTime)
pl.show()
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