def lbfgs_example(verbose):
if (exgauss):
fit = lbfgs_exgauss(x_obs=x_obs,y_obs=y_obs,w_obs=w_obs,initial=initial)
else:
fit = lbfgs_gauss(x_obs=x_obs,y_obs=y_obs,w_obs=w_obs,initial=initial)
print "------------------------------------------------------------------------- "
print " Initial and fitted coeffcients, and inverse-curvature e.s.d.'s"
print "------------------------------------------------------------------------- "
for i in range(initial.size()):
print "%2d %10.4f %10.4f %10.4f"%(
i, initial[i], fit.a[i], fit.a[i])
X1 = x_obs.as_numpy_array()
plt.figure(1)
plt.plot(x_obs,y_obs,'o')#, facecolors='None',edgecolors='b')
# fout = open('exgauss_simulated.dat','w')
# for i in range(len(X1)):
# fout.write("%12.4f" %X1[i])
# fout.write("%12.4f\n" %y_obs[i])
if (exgauss):
F0 = fit.exgauss_cdf_nparray(X1, initial[0], initial[1], initial[2])
F1 = fit.exgauss_cdf_nparray(X1,fit.a[0],fit.a[1], fit.a[2])
F2 = fit.exgauss_cdf_nparray(X1,-4000.0,4000.0, 25000.0)
else:
F0 = gauss_cdf_nparray(X1, initial[0], initial[1])
F1 = gauss_cdf_nparray(X1, fit.a[0], fit.a[1])
plt.plot(X1, F0, 'r*', linewidth=2.0)
plt.plot(X1,F1,'g+',linewidth=2)
# plt.plot(X1,F2,'k-',linewidth=2)
import os
seed = os.path.split(sys.argv[1])[-1].split('.')[0].split('_')[-1]
from construct_random_datapt import ExGauss
EXG= ExGauss(10000, -200000, 200000, fit.a[0], fit.a[1], fit.a[2])
cdf_cutoff = 0.95
I_fit = EXG.interpolate_x_value(cdf_cutoff)
print I_fit
fout = open('intensity_cdf.dat','a')
fout.write("%12.5f %12.5f %12.5f %12.5f\n"%(I_fit, fit.a[0], fit.a[1], fit.a[2]))
fout.close()
plt.plot(X1, [cdf_cutoff]*len(X1), 'r--')
plt.plot([I_fit]*100, np.linspace(0,1,100),'r--' )
plt.savefig('fit_intensities_%s.pdf'%seed)
plt.figure(2)
plt.plot(X1, F2-np.array(y_obs), 'o')
plt.plot(X1, [0.0]*len(X1), 'r--')
plt.ylabel('$\Delta(CDF_{Theory}-CDF_{Calc})$', fontsize=18)
plt.xlabel('$ Intensity $', fontsize=18)
plt.hist(x_obs, normed=True,bins=100)
plt.show()
def run(self):
"""
Runs the mcmc_exgauss class and returns the I_ideal average and variance
"""
import matplotlib.pyplot as plt
print '--------------------- Minimization ----------------------------------'
intensities = exgauss_fit(self.datasource)
exercise_levenberg_marquardt(intensities)
initial = intensities.x_0
mu0, sigma0, tau0 = intensities.x
self.error_diagonal = [1., 1., 1.]
self.bootstrap_errors = intensities.bootstrap_errors
# Get the covariance matrix
get_covar_from_LM = False
if get_covar_from_LM:
intensities.build_up()
upper = intensities.step_equations().normal_matrix_packed_u()
nm_elem = flex.double(9)
self.c = flex.double(3)
ctr = 0
for x in xrange(3):
x_0 = ctr
for y in xrange(2, x - 1, -1):
nm_elem[3 * x + y] = upper[x_0 + (y - x)]
ctr += 1
if x != y:
nm_elem[3 * y + x] = upper[x_0 + (y - x)]
else:
self.c[x] = upper[x_0 + (y - x)]
NM = sqr(nm_elem)
#from IPython import embed; embed(); exit()
# self.helper.solve()
#print list(self.helper.step_equations().cholesky_factor_packed_u())
# from IPython import embed; embed()
error_matrix = NM.inverse()
#from IPython import embed; embed(); exit()
#print 'stdev from covariance matrix ', self.error_diagonal
# Make sure sigma and tau are sensible after minimization. Should not blow up !!
# This is highly controversial # FIXME
if sigma0 < 0.0 or tau0 < 0.0:
print 'Negative sigma or tau values not acceptable'
# mu0,sigma0,tau0=intensities.initial_guess(wiki_method=True)
print 'OK'
print 'Initial Values of params = %10.4f, %10.4f, %10.4f' % (
initial[0], initial[1], initial[2])
print 'Final Values of parameters = %10.4f, %10.4f, %10.4f\n' % (
mu0, sigma0, tau0)
X1 = intensities.t.as_numpy_array()
Y1 = intensities.y.as_numpy_array()
from construct_random_datapt import ExGauss
EXG = ExGauss(len(X1), np.min(X1), np.max(X1), mu0, sigma0, tau0)
I_fit0 = EXG.find_x_from_iter(self.cdf_cutoff)
print 'Initial from fit I_%.2f value = ' % self.cdf_cutoff, I_fit0
if self.plot:
plt.figure(1)
plt.plot(X1, Y1, '.')
if (1):
F0 = intensities.exgauss_cdf_array(X1, initial[0], initial[1],
initial[2])
F1 = intensities.exgauss_cdf_array(X1, mu0, sigma0, tau0)
F2 = intensities.exgauss_cdf_array(X1, -4000.0, 4000.0, 25000.0)
# print 'Initial Sum Squared Difference = ',sum(map(lambda x:x*x,F0-Y1))
residual = sum(map(lambda x: x * x, F1 - Y1))
if get_covar_from_LM:
self.error_diagonal = [
math.sqrt(residual * error_matrix(a, a)) for a in xrange(3)
]
print ' From LevMar: 1./(df/da)*sqrt(residual) = ', self.error_diagonal
print 'Final Sum Squared Difference = ', residual
if self.plot:
# plt.plot(X1, F0, 'r*', linewidth=2.0) # Initial guess
plt.plot(X1, F1, 'g+', linewidth=2) # Best fit
plt.ylabel('CDF value')
plt.xlabel('Intensities')
# Plot difference between obs and calc values
plt.figure(2)
plt.plot(X1, (F1 - Y1), 'o')
plt.ylabel('$\Delta(CDF_{calc}-CDF_{obs})$', fontsize=18)
plt.xlabel('Intensities', fontsize=18)
# Now do the MCMC stuff
print '======================= MCMC stuff beginning ============================'
# nsteps = 5
# t_start = 5
# dt = 1000
maxI = np.max(X1) #+np.max(X1)/2.
minI = np.min(X1) #-np.min(X1)/2.
proposal_width = 0.001 * np.abs(maxI - minI)
# print 'initial guesses and proposal width = ',mu0, sigma0, tau0, proposal_width
mcmc_helper = mcmc()
# I_exp, cdf_exp = mcmc_helper.find_x_from_expdata_annlib(X1,self.cdf_cutoff)
# fitted_cdf = intensities.exgauss_cdf(I_exp, mu0, sigma0, tau0)
# print 'Experimental value of I_%.2f and corresponding cdf %.2f= %12.3f'%(self.cdf_cutoff, fitted_cdf,I_exp)
I_avg_ideal, I_var_ideal, accept_rate = mcmc_helper.sampler(
X1,
samples=self.nsteps,
mu_init=mu0,
sigma_init=sigma0,
tau_init=tau0,
proposal_width=proposal_width,
t_start=self.t_start,
dt=self.dt,
cdf_cutoff=self.cdf_cutoff,
plot=False,
analyse_mcmc=False,
seed=self.mcmc_seed,
prior_errors=self.bootstrap_errors,
residual=residual)
# mu,sigma, tau = params[-1]
mu, sigma, tau = [mu0, sigma0, tau0]
# plt.figure(3)
# plt.plot(X1, F1, '-*g', linewidth=3.0)
# for count in range(len(posterior)):
# F1 = intensities.exgauss_cdf_array(X1,posterior[count][0], posterior[count][1], posterior[count][2])
# plt.plot(X1, F1, 'grey')
# EXG = ExGauss(10000,minI,maxI,posterior[count][0], posterior[count][1], posterior[count][2])
# I_95 = EXG.find_x_from_iter(self.cdf_cutoff)
# plt.plot(I_95,0.05,'r*')
# F1 = intensities.exgauss_cdf_array(X1, mu,sigma,tau)
# plt.plot(X1,F1,'grey')
# Take MCMC averages
# I_mcmc = []
# thinned_params = []
# for count in range(self.t_start, self.nsteps,self.dt):
# mu,sigma, tau = params[count]
# thinned_params.append(params[count])
# EXG= ExGauss(10000, minI, maxI, mu,sigma,tau)
# I_mcmc.append(EXG.interpolate_x_value(self.cdf_cutoff))
# print_I_to_file = False
# if print_I_to_file:
# fout = open('intensity_mcmc_%.2f.dat'%self.cdf_cutoff, 'a')
# if isinstance(self.datasource,str):
# fout.write('Mean and Stdev of I_mcmc = %12.7f, %12.7f in file %s %d\n'%(np.mean(I_mcmc), np.std(I_mcmc), self.datasource,self.mcmc_seed))
# else:
# fout.write('Mean and Stdev of I_mcmc = %12.7f, %12.7f in file %s %d\n'%(np.mean(I_mcmc), np.std(I_mcmc), 'CXI_MERGE',self.mcmc_seed))
# fout.close()
if self.plot:
plt.show()
# if np.isnan(np.mean(I_mcmc)):
# from IPython import embed; embed(); exit()
del (X1)
del (F1)
del (F2)
del (F0)
del (mcmc_helper)
# return thinned_params
return I_avg_ideal, I_var_ideal, accept_rate
def mcmc_lbfgs_example(verbose):
if (exgauss):
fit = lbfgs_exgauss(x_obs=x_obs,y_obs=y_obs,w_obs=w_obs,initial=initial)
else:
fit = lbfgs_gauss(x_obs=x_obs,y_obs=y_obs,w_obs=w_obs,initial=initial)
print "------------------------------------------------------------------------- "
print " Initial and fitted coeffcients, and inverse-curvature e.s.d.'s"
print "------------------------------------------------------------------------- "
for i in range(initial.size()):
print "%2d %10.4f %10.4f %10.4f"%(
i, initial[i], fit.a[i], fit.a[i])
X1 = x_obs.as_numpy_array()
plt.figure(1)
plt.plot(x_obs,y_obs,'o')#, facecolors='None',edgecolors='b')
# fout = open('exgauss_simulated.dat','w')
# for i in range(len(X1)):
# fout.write("%12.4f" %X1[i])
# fout.write("%12.4f\n" %y_obs[i])
if (exgauss):
F0 = fit.exgauss_cdf_nparray(X1, initial[0], initial[1], initial[2])
F1 = fit.exgauss_cdf_nparray(X1,fit.a[0],fit.a[1], fit.a[2])
F2 = fit.exgauss_cdf_nparray(X1,-4000.0,4000.0, 25000.0)
else:
F0 = gauss_cdf_nparray(X1, initial[0], initial[1])
F1 = gauss_cdf_nparray(X1, fit.a[0], fit.a[1])
plt.plot(X1, F0, 'r*', linewidth=2.0)
plt.plot(X1,F1,'g+',linewidth=2)
# plt.plot(X1,F2,'k-',linewidth=2)
import os
seed = os.path.split(sys.argv[1])[-1].split('.')[0].split('_')[-1]
from construct_random_datapt import ExGauss
EXG= ExGauss(10000, -200000, 200000, fit.a[0], fit.a[1], fit.a[2])
cdf_cutoff = 0.95
I_fit = EXG.interpolate_x_value(cdf_cutoff)
print I_fit
fout = open('intensity_cdf.dat','a')
fout.write("%12.5f\n"%I_fit)
fout.close()
plt.plot(X1, [cdf_cutoff]*len(X1), 'r--')
plt.plot([I_fit]*100, np.linspace(0,1,100),'r--' )
plt.savefig('fit_intensities_%s.pdf'%seed)
# plt.figure(2)
# plt.plot(X1, F2-np.array(y_obs), 'o')
# plt.plot(X1, [0.0]*len(X1), 'r--')
# plt.ylabel('$\Delta(CDF_{Theory}-CDF_{Calc})$', fontsize=18)
# plt.xlabel('$ Intensity $', fontsize=18)
# plt.hist(x_obs, normed=True,bins=100)
# plt.show()
# =========== NOW DO THE MCMC bit here below ==========
print '======================= MCMC stuff beginning ============================'
nsteps = 50000
# x_obs = x_obs.as_numpy_array()
maxI = np.max(x_obs)
minI = np.min(x_obs)
proposal_width = 0.01*np.abs(maxI-minI)
print 'initial guesses and proposal width = ',fit.a[0], fit.a[1], fit.a[2], proposal_width
params = sampler(x_obs, samples=nsteps, mu_init= fit.a[0],sigma_init = fit.a[1],tau_init = fit.a[2],
proposal_width = proposal_width,plot=False)
mu,sigma, tau = params[-1]
print 'final parameter values ',mu,sigma, tau
# X1 = np.arange(min(x_obs), max(x_obs),100.0)
t_start = 0
dt = 50
plt.figure(2)
plt.plot(X1, F1, 'green')
F1 = exgauss_cdf(X1, mu,sigma,tau)
plt.plot(X1,F1,'grey')
I_mcmc = []
fout = open('params_mcmc_dummy_%s.dat'%seed, 'w')
for count in range(t_start,nsteps):
fout.write("%14.6f %14.6f %14.6f\n" %(params[count][0],params[count][1], params[count][2]))
fout.close()
exit()
for count in range(t_start, nsteps,dt):
mu,sigma, tau = params[count]
EXG= ExGauss(10000, -200000, 200000, mu,sigma,tau)
I_mcmc.append(EXG.interpolate_x_value(cdf_cutoff))
# Get CDFs
# F1 = exgauss_cdf(X1,mu,sigma,tau)
# plt.plot(X1,F1,'grey',linewidth=1.0)
print 'Mean and Stdev of I_mcmc = %12.7f, %12.7f'%(np.mean(I_mcmc), np.std(I_mcmc))
X2 = np.sort(x_obs)
F2 = np.array(range(len(x_obs)))/float(len(x_obs))
plt.plot(X2,F2,'o')
plt.show()
def run(self):
import matplotlib.pyplot as plt
print '--------------------- Minimization ----------------------------------'
intensities = exgauss_fit(self.filename)
exercise_levenberg_marquardt(intensities)
initial = intensities.x_0
mu0,sigma0,tau0 = intensities.x
print 'OK'
print 'Initial Values of params = %10.4f, %10.4f, %10.4f'%(initial[0], initial[1], initial[2])
print 'Final Values of parameters = %10.4f, %10.4f, %10.4f\n'%(mu0,sigma0,tau0)
X1 = intensities.t.as_numpy_array()
Y1 = intensities.y.as_numpy_array()
from construct_random_datapt import ExGauss
EXG= ExGauss(10000, np.min(X1), np.max(X1), mu0, sigma0, tau0)
I_fit0 = EXG.interpolate_x_value(self.cdf_cutoff)
print 'Initial I_%.2f value = '%self.cdf_cutoff, I_fit0
plt.figure(1)
plt.plot(X1,Y1,'.')
if (1):
F0 = intensities.exgauss_cdf_array(X1, initial[0], initial[1], initial[2])
F1 = intensities.exgauss_cdf_array(X1,mu0, sigma0, tau0)
F2 = intensities.exgauss_cdf_array(X1,-4000.0,4000.0, 25000.0)
print 'Sum Squared Difference = ',sum(map(lambda x:x*x,F1-Y1))
plt.plot(X1, F0, 'r*', linewidth=2.0)
plt.plot(X1,F1,'g+',linewidth=2)
plt.ylabel('CDF value')
plt.xlabel('Intensities')
# Plot difference between obs and calc values
plt.figure(2)
plt.plot(X1, (F1-Y1), 'o')
plt.ylabel('$\Delta(CDF_{calc}-CDF_{obs})$', fontsize=18)
plt.xlabel('Intensities', fontsize=18)
# Now do the MCMC stuff
print '======================= MCMC stuff beginning ============================'
# nsteps = 5
# t_start = 5
# dt = 1000
maxI = np.max(X1)+np.max(X1)/5.
minI = np.min(X1)-np.min(X1)/5.
proposal_width = 0.01*np.abs(maxI-minI)
print 'initial guesses and proposal width = ',mu0, sigma0, tau0, proposal_width
mcmc_helper = mcmc()
params = mcmc_helper.sampler(X1, samples=self.nsteps, mu_init= mu0,sigma_init = sigma0, tau_init = tau0,
proposal_width = proposal_width,plot=False, seed=self.mcmc_seed)
mu,sigma, tau = params[-1]
print 'final parameter values ',mu,sigma, tau
plt.figure(3)
plt.plot(X1, F1, 'green')
F1 = intensities.exgauss_cdf_array(X1, mu,sigma,tau)
plt.plot(X1,F1,'grey')
I_mcmc = []
# fout = open('params_mcmc_%s.dat'%seed, 'a')
# for count in range(t_start,nsteps):
# fout.write("%14.6f %14.6f %14.6f\n" %(params[count][0],params[count][1], params[count][2]))
# fout.close()
# exit()
for count in range(self.t_start, self.nsteps,self.dt):
mu,sigma, tau = params[count]
EXG= ExGauss(10000, minI, maxI, mu,sigma,tau)
I_mcmc.append(EXG.interpolate_x_value(self.cdf_cutoff))
# Get CDFs
# F1 = exgauss_cdf(X1,mu,sigma,tau)
# plt.plot(X1,F1,'grey',linewidth=1.0)
# print 'Mean and Stdev of I_mcmc = %12.7f, %12.7f'%(np.mean(I_mcmc), np.std(I_mcmc))
import os
seed = os.path.split(self.filename)[-1].split('.')[0].split('_')[-1]
# fout = open('intensity_mcmc_%s.dat'%seed, 'a')
fout = open('intensity_mcmc_%.2f.dat'%self.cdf_cutoff, 'a')
fout.write('Mean and Stdev of I_mcmc = %12.7f, %12.7f in file %s %d\n'%(np.mean(I_mcmc), np.std(I_mcmc), self.filename,self.mcmc_seed))
fout.close()
# X2 = np.sort(x_obs)
# F2 = np.array(range(len(x_obs)))/float(len(x_obs))
# plt.plot(X2,F2,'o')
if self.plot:
plt.show()
def mcmc_statistics(self, posterior, I_mcmc, data, cdf_cutoff):
''' Get statistics from the ensemble of curves generated using MCMC
The following statistics are going to be calculated
a. I_95_avg
b. I_95_avg - I_95_exp
c. P(I_95_mcmc) vs delta(I_95_mcmc-I_95_exp)
d. I_95_mcmc vs t
e. RMSD(CDF) vs t
f. RMSF(CDF) vs i (data point)
Note that here 95 stands for 95 percentile. In effect it is the cdf cutoff value used my mcmc.sampler.
So don't take the variable name too literally
'''
print 'Printing MCMC summary statistics'
rmsd_flag = False
# a.
I_95_avg = np.mean(I_mcmc)
print 'I_95_avg = ', I_95_avg, '+/-', np.std(I_mcmc)
# b.
I_95_exp, cdf_exp = self.find_x_from_expdata_annlib(data, cdf_cutoff)
d_I_95_avg = I_95_avg - I_95_exp
print 'Experimental I_95 = ', I_95_exp
print 'Deviation of average I_95 from experimental I_95 = ', d_I_95_avg
#exit()
plt.figure(3)
data = np.sort(data)
fake_pts = np.linspace(np.min(data), np.max(data), 100)
F1 = np.array(range(1, len(data) + 1)) / float(len(data))
F1[:] = [z - 0.5 / len(F1) for z in F1] # Actual Data
#F1 = self.exgauss_cdf_array(data,posterior[0][0], posterior[0][1], posterior[0][2]) # Best fit from minimization
plt.plot(data, F1, '.', linewidth=3.0)
for count in range(1, len(posterior)):
F1 = self.exgauss_cdf_array(fake_pts, posterior[count][0],
posterior[count][1],
posterior[count][2])
plt.plot(fake_pts, F1, 'grey')
EXG = ExGauss(10000, np.min(data), np.max(data),
posterior[count][0], posterior[count][1],
posterior[count][2])
I_95 = EXG.find_x_from_iter(cdf_cutoff)
plt.plot(I_95, 0.05, 'r*')
F1 = self.exgauss_cdf_array(data, posterior[0][0], posterior[0][1],
posterior[0][2])
plt.plot(data, F1, 'g+', linewidth=3.0)
# c.
d_I_95_mcmc = [np.abs(x - I_95_exp) for x in I_mcmc]
print 'Average absolute deviation I_95 mcmc from experimental I_95', np.mean(
d_I_95_mcmc)
hist, bin_edges = np.histogram(d_I_95_mcmc, density=True)
plt.figure(4)
# plt.hist(d_I_95_mcmc)
plt.plot(bin_edges[:-1], hist * np.diff(bin_edges), '-*r')
plt.xlabel('$\Delta(I_{95_calc}-I_{95_obs})$', fontsize=18)
plt.ylabel('Probability', fontsize=18)
# d.
plt.figure(5)
plt.plot(range(len(I_mcmc)), I_mcmc, 'b')
plt.plot(range(len(I_mcmc)), [I_95_exp] * len(I_mcmc), '-*r')
plt.xlabel('time', fontsize=18)
plt.ylabel('I_95_mcmc', fontsize=18)
# e.
if (rmsd_flag):
rmsd = self.calc_rmsd(posterior, data, cdf_exp)
print 'Average RMSD of datapoints', np.mean(rmsd)
plt.figure(6)
plt.plot(range(len(rmsd)), rmsd, '-*r')
plt.xlabel('time', fontsize=18)
plt.ylabel('RMSD', fontsize=18)
plt.show()
def run_sampler(self,
samples,
data,
t_start,
dt,
mu_current,
sigma_current,
tau_current,
cdf_cutoff,
analyse_mcmc=False,
exploratory_run=False):
maxI = np.max(data) #+np.max(data)/2.
minI = np.min(data) #-np.min(data)/2.
accept_counter = 0
posterior = [[mu_current, sigma_current, tau_current]]
I_mcmc = []
for i in range(samples):
accept = False
inf_flag = False
# trial move
mu_proposal = np.random.normal(
mu_current, self.proposal_factor * self.mu_prior_sd)
sigma_proposal = np.abs(
np.random.normal(sigma_current,
self.proposal_factor * self.sd_prior_sd)) #
tau_proposal = np.abs(
np.random.normal(tau_current,
self.proposal_factor * self.tau_prior_sd))
likelihood_current = self.exgauss(
data, mu_current, sigma_current,
tau_current) # multiply the probabilties
likelihood_proposal = self.exgauss(data, mu_proposal,
sigma_proposal,
tau_proposal) # multiply
prior_current = self.gauss_pdf(mu_current, self.mu_prior_mu, self.mu_prior_sd)+self.gauss_pdf(sigma_current, self.sd_prior_mu, self.sd_prior_sd)+ \
self.gauss_pdf(tau_current, self.tau_prior_mu, self.tau_prior_sd)
prior_proposal = self.gauss_pdf(mu_proposal, self.mu_prior_mu, self.mu_prior_sd)+self.gauss_pdf(sigma_proposal, self.sd_prior_mu, self.sd_prior_sd)+ \
self.gauss_pdf(tau_proposal, self.tau_prior_mu, self.tau_prior_sd)
if likelihood_proposal == -np.inf:
accept = False
inf_flag = True
if not accept and not inf_flag:
p_current = likelihood_current + prior_current
p_proposal = likelihood_proposal + prior_proposal
p_accept = p_proposal - p_current
accept = np.log(np.random.rand()) < p_accept
if accept:
mu_current = mu_proposal
sigma_current = sigma_proposal
tau_current = tau_proposal
accept_counter += 1
if i > t_start and i % dt == 0:
EXG = ExGauss(10000, minI, maxI, mu_current, sigma_current,
tau_current)
I_ideal_temp = EXG.find_x_from_iter(cdf_cutoff)
I_mcmc.append(I_ideal_temp)
del (EXG)
if analyse_mcmc:
posterior.append([mu_current, sigma_current, tau_current])
# print 'acceptance rate',accept_counter*1.0/samples
I_mcmc_avg = np.mean(I_mcmc)
I_mcmc_var = np.var(I_mcmc)
if analyse_mcmc:
self.mcmc_statistics(posterior, I_mcmc, data, cdf_cutoff)
del (I_mcmc)
return I_mcmc_avg, I_mcmc_var, accept_counter * 1.0 / samples
from construct_random_datapt import ExGauss
import matplotlib.pyplot as plt
import numpy as np
import sys
seed = int(sys.argv[1])
exgauss= ExGauss(20, -200000, 200000, -4000.0, 4000.0, 25000.0)
#exgauss_random_array = p.map(exgauss.rand())
#exgauss_random_array = exgauss.rand(seed)
exgauss_random_array = exgauss.rand_annlib(seed)
print 'created numbers'
X2 = np.sort(exgauss_random_array)
F2 = np.array(range(1,len(exgauss_random_array)+1))/float(len(exgauss_random_array))
# Nick's suggestion on using (n-0.5)/N for cdf to create a buffer region
F2[:] = [x-0.5/len(exgauss_random_array) for x in F2]
fout = open('exgauss_simulated_intensities_'+sys.argv[1]+'.dat', 'w')
for i in range(len(X2)):
fout.write("%12.7f"%X2[i])
fout.write("%12.7f\n"%F2[i])
print exgauss.interpolate_x_value(0.95)
#plt.plot(X2,F2,'o')