How to locally run parallel code with mpi4py in an IPython notebook:

The prerequisite for this is a working installation of some MPI distribution.

Using Ubuntu or some derivative, I recommend using OpenMPI which can be istalled from the repository by means of the following packages: libopenmpi-dev, openmpi-bin, openmpi-doc.

Now, you can already run MPI enabled code from you shell by calling

$mpirun -n [numbmer_of_threads] python [script_to_run.py]

To use MPI with iPython, one has to install ipyparallel:

via pip: $pip install ipyparallel

via conda: $conda install ipyparallel

and then enable the Clusters tab in ipython via

$ ipcluster nbextension enable

To make MPI acessable via mpi4py in an ipython notebook, one has to do the following: open one shell and start the ipcontroller:

$ipcontroller

open another shell and start a number of engines:

$mpirun -n [number of engines] ipengine --mpi=mpi4py

and then connect to the engines via the following fragment of code:


In [11]:
from ipyparallel import Client
import os
c = Client()
view = c[:]
print(c.ids)


[0, 1, 2, 3]

In [5]:
%%px

def find(name, path):
    for root, dirs, files in os.walk(path):
        if name in files:
            return root
path = find('02_LocalParallelization.ipynb', '/home/')
print(path)
os.chdir(path)


[stdout:0] /home/jakob/Project_PyMofa/tutorial
[stdout:1] /home/jakob/Project_PyMofa/tutorial
[stdout:2] /home/jakob/Project_PyMofa/tutorial
[stdout:3] /home/jakob/Project_PyMofa/tutorial

Now, to make the code run on all of our engines (and not just on one), the following cells have to start with the parallel magic command %%px


In [6]:
%%px
from mpi4py import MPI
com = MPI.COMM_WORLD
print(com.Get_rank())


[stdout:0] 3
[stdout:1] 1
[stdout:2] 0
[stdout:3] 2

Now, that we have MPI running, and mpi4py recognizing the nodes and their ranks, we can continue with the predator prey exercise, that we know from the first tutorial.

First, define the model:


In [7]:
%%px
import numpy as np
import matplotlib.pyplot as plt

def predprey_model(prey_birth_rate=0.1, prey_mortality=0.1, 
                   predator_efficiency=0.1, predator_death_rate=0.01,
                   initial_prey=1., initial_predators=1.,
                   time_length=1000):
    """Discrete predetor prey model."""
    A = -1 * np.ones(time_length)
    B = -1 * np.ones(time_length)
    A[0] = initial_prey
    B[0] = initial_predators
    for t in range(1, time_length):
        A[t] = A[t-1] + prey_birth_rate * A[t-1] - prey_mortality * B[t-1]*A[t-1]
        B[t] = B[t-1] + predator_efficiency * B[t-1]*A[t-1] - predator_death_rate * B[t-1] +\
            0.02 * (0.5 - np.random.rand())
    return A, B

#preys, predators = predprey_model()
#plt.plot(preys, label="preys") 
#plt.plot(predators, label="predators")
#plt.legend()
#plt.show()

Then import the experiment_handling class from pymofa and define a run function:


In [8]:
%%px
# imports
from pymofa.experiment_handling import experiment_handling as eh
import itertools as it
import pandas as pd
# import cPickle


#Definingh the experiment execution function
#      it gets paramater you want to investigate, plus `filename` as the last parameter
def RUN_FUNC(prey_birth_rate=0.1, prey_mortality=0.1, 
                   predator_efficiency=0.1, predator_death_rate=0.01,
                   initial_prey=1., initial_predators=1.,
                   time_length=1000, filename='./'):
    """Insightful docstring."""
    print(prey_birth_rate, prey_mortality, 
                   predator_efficiency, predator_death_rate,
                   initial_prey, initial_predators,
                   time_length)
    # one could also do more complicated stuff here, e.g. drawing something from a random distribution
    
    # running the model
    # TO DO: there seems to be a problem passing arguments to function
    #preys, predators = predprey_model(prey_birth_rate, prey_mortality, 
    #                                  predator_efficiency, predator_death_rate,
    #                                  initial_prey, initial_predators,
    #                                  time_length)
    preys, predators = predprey_model(
    )
    print(preys)
    # preparing the data
    res = pd.DataFrame({"preys": np.array(preys),
                        "predators": np.array(predators)})
    
    # Save Result
    res.to_pickle(filename)
    
    # determine exit status (if something went wrong)
    # if exit status > 0 == run passen
    # if exit status < 0 == Run Failed
    exit_status = 1
    
    # RUN_FUNC needs to return exit_status
    return exit_status

Specify the necessary parameters, generate their combinations and feed them to an experiment handle:


In [9]:
%%px
# Path where to Store the simulated Data
SAVE_PATH_RAW = "./dummy/pymofatutorial"

# Parameter combinations to investiage

prey_birth_rate = [0.1]
predator_death_rate = [0.1]
initial_pop = [1.]
            
PARAM_COMBS = list(it.product(prey_birth_rate, predator_death_rate, initial_pop))

# Sample Size
SAMPLE_SIZE = 5

# INDEX 
INDEX = {0: 'prey_birth_rate', 1: 'predator_death_rate', 2: 'initial_prey'}

# initiate handle instance with experiment variables
handle = eh(SAMPLE_SIZE, PARAM_COMBS, INDEX, SAVE_PATH_RAW)


[stdout:0] initializing pymofa experiment handle
[stdout:1] initializing pymofa experiment handle
[stdout:2] 
initializing pymofa experiment handle
detected 4 nodes in MPI environment
[stdout:3] initializing pymofa experiment handle

And finally run the model - now in parallel:


In [10]:
%%px
# Compute experiemnts raw data
handle.compute(RUN_FUNC)


[stdout:0] 
0.1 0.1 1.0 0.01 1.0 1.0 1000
[  1.00000000e+00   1.00000000e+00   9.91674642e-01   9.73540145e-01
   9.45090242e-01   9.06516153e-01   8.58956476e-01   8.03209299e-01
   7.40500972e-01   6.73276286e-01   6.03923016e-01   5.34879696e-01
   4.67860021e-01   4.04240508e-01   3.45855404e-01   2.93634338e-01
   2.47716789e-01   2.07957307e-01   1.73900593e-01   1.44821540e-01
   1.20421287e-01   1.00028709e-01   8.30345959e-02   6.89912691e-02
   5.73557909e-02   4.77819148e-02   3.98866282e-02   3.33716112e-02
   2.79524338e-02   2.34557856e-02   1.97212527e-02   1.66081283e-02
   1.40159792e-02   1.18713541e-02   1.00916056e-02   8.60402157e-03
   7.35643709e-03   6.30050854e-03   5.41390236e-03   4.65902474e-03
   4.02238618e-03   3.48041695e-03   3.01922654e-03   2.62515644e-03
   2.29038567e-03   2.00356994e-03   1.75774133e-03   1.54593341e-03
   1.36245664e-03   1.20336766e-03   1.06546355e-03   9.45430119e-04
   8.40980551e-04   7.50490760e-04   6.71864232e-04   6.02504027e-04
   5.41709378e-04   4.88244203e-04   4.41312952e-04   3.99586866e-04
   3.62361410e-04   3.29010229e-04   2.99628424e-04   2.73515467e-04
   2.49944163e-04   2.29109288e-04   2.10514374e-04   1.94018503e-04
   1.79003322e-04   1.65478122e-04   1.53229745e-04   1.42291871e-04
   1.32409283e-04   1.23411626e-04   1.15193849e-04   1.07767987e-04
   1.01012701e-04   9.48186732e-05   8.92152391e-05   8.40118455e-05
   7.93040981e-05   7.49669167e-05   7.09960041e-05   6.73830970e-05
   6.40914431e-05   6.10676263e-05   5.83295479e-05   5.58365198e-05
   5.35235090e-05   5.13797838e-05   4.94081696e-05   4.75347172e-05
   4.58226488e-05   4.42383870e-05   4.28089820e-05   4.14712326e-05
   4.02276190e-05   3.90609312e-05   3.79857394e-05   3.69542841e-05
   3.59818708e-05   3.50473381e-05   3.42022357e-05   3.34056597e-05
   3.26699687e-05   3.19713119e-05   3.13506765e-05   3.07597194e-05
   3.02011008e-05   2.96840674e-05   2.92226166e-05   2.87870468e-05
   2.84053109e-05   2.80699359e-05   2.77964991e-05   2.75655064e-05
   2.73918021e-05   2.72254528e-05   2.70977640e-05   2.70070877e-05
   2.69245418e-05   2.68687031e-05   2.68463717e-05   2.68626504e-05
   2.69143581e-05   2.69703824e-05   2.70386833e-05   2.71249054e-05
   2.72167621e-05   2.73422300e-05   2.75172449e-05   2.77168257e-05
   2.79257445e-05   2.81518847e-05   2.84007790e-05   2.87047091e-05
   2.90419768e-05   2.93940365e-05   2.97788984e-05   3.01800048e-05
   3.06123113e-05   3.10485564e-05   3.15372182e-05   3.20584776e-05
   3.25965236e-05   3.31865393e-05   3.38073995e-05   3.44640887e-05
   3.51620047e-05   3.59283564e-05   3.67059720e-05   3.75518937e-05
   3.84411913e-05   3.93726017e-05   4.03336583e-05   4.13750905e-05
   4.24760944e-05   4.36205396e-05   4.47979307e-05   4.60109463e-05
   4.73304501e-05   4.86824051e-05   5.01559565e-05   5.17573097e-05
   5.34167898e-05   5.51374414e-05   5.69964580e-05   5.90067908e-05
   6.11098233e-05   6.33415195e-05   6.56624097e-05   6.80488829e-05
   7.05550589e-05   7.31530430e-05   7.59137120e-05   7.88106195e-05
   8.17970729e-05   8.49482286e-05   8.83169207e-05   9.17936074e-05
   9.54314703e-05   9.93049239e-05   1.03440494e-04   1.07842263e-04
   1.12423492e-04   1.17374854e-04   1.22602950e-04   1.28062870e-04
   1.33833579e-04   1.39930747e-04   1.46291772e-04   1.52954027e-04
   1.59989871e-04   1.67583056e-04   1.75670129e-04   1.84089275e-04
   1.92959637e-04   2.02340753e-04   2.12258212e-04   2.22752358e-04
   2.33933533e-04   2.45703380e-04   2.57994689e-04   2.71134847e-04
   2.84916983e-04   2.99719888e-04   3.15309851e-04   3.31937880e-04
   3.49757903e-04   3.68926256e-04   3.89491901e-04   4.11301248e-04
   4.34882404e-04   4.59667785e-04   4.85653266e-04   5.13164090e-04
   5.42806938e-04   5.74328020e-04   6.07568234e-04   6.42936748e-04
   6.80213780e-04   7.20040256e-04   7.63061564e-04   8.08666090e-04
   8.58068108e-04   9.09999521e-04   9.66308641e-04   1.02633193e-03
   1.09101444e-03   1.15925633e-03   1.23204940e-03   1.30946301e-03
   1.39349106e-03   1.48438018e-03   1.58055474e-03   1.68501095e-03
   1.79719924e-03   1.91812112e-03   2.04747041e-03   2.18729178e-03
   2.33760151e-03   2.49863861e-03   2.67046672e-03   2.85622909e-03
   3.05551610e-03   3.27050207e-03   3.49950935e-03   3.74533958e-03
   4.01120152e-03   4.30095074e-03   4.60856267e-03   4.94000333e-03
   5.30008354e-03   5.68474902e-03   6.10172960e-03   6.54582631e-03
   7.02233836e-03   7.53719784e-03   8.09734069e-03   8.70578050e-03
   9.36672133e-03   1.00829455e-02   1.08590349e-02   1.17007467e-02
   1.26146720e-02   1.36054825e-02   1.46839814e-02   1.58587235e-02
   1.71423030e-02   1.85330996e-02   2.00538188e-02   2.16824452e-02
   2.34632863e-02   2.53820424e-02   2.74434977e-02   2.96877034e-02
   3.20977106e-02   3.47189816e-02   3.75692743e-02   4.06599460e-02
   4.40403666e-02   4.76904434e-02   5.16121925e-02   5.58699132e-02
   6.04656283e-02   6.54041623e-02   7.07523128e-02   7.65300337e-02
   8.28026612e-02   8.96207059e-02   9.70722722e-02   1.05114020e-01
   1.13743252e-01   1.23053439e-01   1.33060999e-01   1.43988867e-01
   1.55902283e-01   1.68659098e-01   1.82606625e-01   1.97650899e-01
   2.13937699e-01   2.31554020e-01   2.50688145e-01   2.71578641e-01
   2.93974061e-01   3.18106253e-01   3.44349707e-01   3.72877997e-01
   4.03822095e-01   4.37493169e-01   4.73430402e-01   5.12085935e-01
   5.53283621e-01   5.97387777e-01   6.44684138e-01   6.95543139e-01
   7.49038018e-01   8.05235480e-01   8.63657214e-01   9.25208094e-01
   9.89249316e-01   1.05605743e+00   1.12388420e+00   1.19280404e+00
   1.26205765e+00   1.32948822e+00   1.39217956e+00   1.44769371e+00
   1.49284347e+00   1.52450992e+00   1.54015433e+00   1.53767854e+00
   1.51141473e+00   1.45941976e+00   1.38265181e+00   1.28063620e+00
   1.15664149e+00   1.01705528e+00   8.70808490e-01   7.26770642e-01
   5.92215270e-01   4.72090615e-01   3.69679462e-01   2.84906177e-01
   2.16837767e-01   1.63504868e-01   1.22518812e-01   9.16089393e-02
   6.83563974e-02   5.09996280e-02   3.81569681e-02   2.86173179e-02
   2.15475214e-02   1.62788529e-02   1.23471411e-02   9.39016293e-03
   7.17312333e-03   5.50404412e-03   4.24081124e-03   3.28388543e-03
   2.55546971e-03   1.99583619e-03   1.56516183e-03   1.23258974e-03
   9.74866162e-04   7.73948977e-04   6.16448301e-04   4.92280594e-04
   3.94896149e-04   3.18181699e-04   2.57138435e-04   2.08335493e-04
   1.69345214e-04   1.38214483e-04   1.13335484e-04   9.31643023e-05
   7.68104866e-05   6.35703310e-05   5.27484171e-05   4.38653112e-05
   3.65867192e-05   3.05936383e-05   2.56382131e-05   2.15461212e-05
   1.81589168e-05   1.53625364e-05   1.30466670e-05   1.11145774e-05
   9.49451522e-06   8.13895991e-06   6.99393521e-06   6.02920968e-06
   5.20918685e-06   4.51107698e-06   3.91880973e-06   3.41676511e-06
   2.98945955e-06   2.62470247e-06   2.31201811e-06   2.04301648e-06
   1.80977522e-06   1.60689113e-06   1.42892460e-06   1.27309729e-06
   1.13742447e-06   1.01853532e-06   9.13995097e-07   8.21341059e-07
   7.40052181e-07   6.67669140e-07   6.03748501e-07   5.47230371e-07
   4.96695660e-07   4.51830384e-07   4.11753893e-07   3.75872926e-07
   3.44144662e-07   3.15752270e-07   2.90575154e-07   2.68214092e-07
   2.47976693e-07   2.29666753e-07   2.12879246e-07   1.97490476e-07
   1.83692435e-07   1.71172307e-07   1.59663971e-07   1.49333660e-07
   1.39922638e-07   1.31253613e-07   1.23411413e-07   1.16253711e-07
   1.09746688e-07   1.03837133e-07   9.83989317e-08   9.34414346e-08
   8.88454665e-08   8.46954478e-08   8.08963833e-08   7.73783724e-08
   7.40548367e-08   7.09824854e-08   6.81379500e-08   6.55076694e-08
   6.30167798e-08   6.07296971e-08   5.86135662e-08   5.66771482e-08
   5.48785902e-08   5.32275782e-08   5.16485056e-08   5.02030141e-08
   4.88670211e-08   4.75814352e-08   4.64298926e-08   4.53980745e-08
   4.44392404e-08   4.35762367e-08   4.27811784e-08   4.20629632e-08
   4.13909602e-08   4.07544215e-08   4.02133050e-08   3.96855554e-08
   3.92327636e-08   3.88489074e-08   3.85040907e-08   3.82071553e-08
   3.79858166e-08   3.77818791e-08   3.75996266e-08   3.74617907e-08
   3.73763809e-08   3.73184571e-08   3.72641271e-08   3.72234599e-08
   3.72371651e-08   3.72536131e-08   3.72948914e-08   3.73551984e-08
   3.74374398e-08   3.75737279e-08   3.77423990e-08   3.79190314e-08
   3.81576750e-08   3.83993413e-08   3.86715722e-08   3.89879709e-08
   3.93428591e-08   3.97450103e-08   4.01609518e-08   4.06258907e-08
   4.11309614e-08   4.17076886e-08   4.23234761e-08   4.29714644e-08
   4.36235965e-08   4.43300676e-08   4.50968886e-08   4.59426300e-08
   4.68586820e-08   4.77867010e-08   4.88063714e-08   4.98873869e-08
   5.10014243e-08   5.21385402e-08   5.33910787e-08   5.47492953e-08
   5.61551734e-08   5.76796645e-08   5.92804663e-08   6.09806120e-08
   6.28046596e-08   6.46688084e-08   6.66540042e-08   6.87016681e-08
   7.08119331e-08   7.30622529e-08   7.54933124e-08   7.80555212e-08
   8.08145317e-08   8.36856184e-08   8.67401722e-08   8.99587644e-08
   9.32889387e-08   9.67274824e-08   1.00388064e-07   1.04314772e-07
   1.08372088e-07   1.12605818e-07   1.17006294e-07   1.21640118e-07
   1.26593852e-07   1.31700974e-07   1.37069578e-07   1.42731379e-07
   1.48645332e-07   1.55033453e-07   1.61907494e-07   1.69015371e-07
   1.76638730e-07   1.84646948e-07   1.93292951e-07   2.02258745e-07
   2.11794189e-07   2.21938560e-07   2.32614034e-07   2.43782410e-07
   2.55643803e-07   2.68229908e-07   2.81504600e-07   2.95471724e-07
   3.10136574e-07   3.25942355e-07   3.42925342e-07   3.60657525e-07
   3.79550746e-07   3.99953456e-07   4.21716182e-07   4.45244717e-07
   4.70488596e-07   4.97668462e-07   5.26863976e-07   5.57676873e-07
   5.90303317e-07   6.24808710e-07   6.61123452e-07   6.99991342e-07
   7.42099963e-07   7.87247561e-07   8.36083960e-07   8.88982546e-07
   9.46360590e-07   1.00801226e-06   1.07487568e-06   1.14588588e-06
   1.22128967e-06   1.30158939e-06   1.38783354e-06   1.47923668e-06
   1.57802793e-06   1.68497830e-06   1.79816985e-06   1.91943688e-06
   2.04937259e-06   2.19030361e-06   2.34086112e-06   2.50303524e-06
   2.67756095e-06   2.86416643e-06   3.06707395e-06   3.28350243e-06
   3.51347655e-06   3.75813191e-06   4.01873692e-06   4.29909139e-06
   4.59823550e-06   4.91816134e-06   5.26184751e-06   5.63168541e-06
   6.03126883e-06   6.46591873e-06   6.93066231e-06   7.43640644e-06
   7.98840920e-06   8.57570440e-06   9.20712623e-06   9.88349526e-06
   1.06140948e-05   1.14078194e-05   1.22560551e-05   1.31593288e-05
   1.41310649e-05   1.51848046e-05   1.63174002e-05   1.75289949e-05
   1.88520914e-05   2.02619126e-05   2.17632307e-05   2.33832858e-05
   2.51074816e-05   2.69419134e-05   2.89269741e-05   3.10729736e-05
   3.33727870e-05   3.58562068e-05   3.85577387e-05   4.15088639e-05
   4.46734165e-05   4.80734423e-05   5.17445622e-05   5.57437226e-05
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[stdout:1] 
0.1 0.1 1.0 0.01 1.0 1.0 1000
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   1.48537969e-07   1.40987415e-07   1.34146433e-07   1.27852361e-07
   1.21983656e-07   1.16662907e-07   1.11799217e-07   1.07225518e-07
   1.02953618e-07   9.90985939e-08   9.55705104e-08   9.22384395e-08
   8.91304326e-08   8.61927710e-08   8.35486997e-08   8.10672502e-08
   7.88237679e-08   7.66995427e-08   7.47793050e-08   7.30723112e-08
   7.15127340e-08   7.01113765e-08   6.88443216e-08   6.76247751e-08
   6.65635350e-08   6.56583245e-08   6.48623912e-08   6.41994596e-08
   6.36449323e-08   6.31117611e-08   6.26631727e-08   6.23453118e-08
   6.20866405e-08   6.19125393e-08   6.17650226e-08   6.16606648e-08
   6.15768112e-08   6.15528009e-08   6.15423783e-08   6.16521583e-08
   6.18122507e-08   6.19831879e-08   6.21731187e-08   6.24291090e-08
   6.28066098e-08   6.32138956e-08   6.36876999e-08   6.42033251e-08
   6.48387051e-08   6.55117797e-08   6.62467755e-08   6.69992652e-08
   6.77795844e-08   6.85945417e-08   6.94195264e-08   7.03539504e-08
   7.13469295e-08   7.24776252e-08   7.36265701e-08   7.49236076e-08
   7.63284676e-08   7.78325765e-08   7.93938118e-08   8.09905492e-08
   8.26283215e-08   8.44372874e-08   8.63434802e-08   8.83311815e-08
   9.03959591e-08   9.25315917e-08   9.47342284e-08   9.70153710e-08
   9.94251221e-08   1.02008340e-07   1.04727353e-07   1.07569891e-07
   1.10547563e-07   1.13711262e-07   1.16934889e-07   1.20365735e-07
   1.23893484e-07   1.27711543e-07   1.31747255e-07   1.36062854e-07
   1.40688297e-07   1.45626025e-07   1.50802015e-07   1.56316380e-07
   1.62128350e-07   1.68282962e-07   1.74757317e-07   1.81646898e-07
   1.88867901e-07   1.96349835e-07   2.04117819e-07   2.12347781e-07
   2.20835465e-07   2.29951238e-07   2.39744908e-07   2.50079751e-07
   2.60766025e-07   2.71917115e-07   2.83444877e-07   2.95555570e-07
   3.08397986e-07   3.21930790e-07   3.36075111e-07   3.51200093e-07
   3.67542265e-07   3.84792007e-07   4.03333932e-07   4.22699586e-07
   4.43258907e-07   4.64706508e-07   4.87826006e-07   5.12019005e-07
   5.37903698e-07   5.65231673e-07   5.94452470e-07   6.25108273e-07
   6.57422205e-07   6.91748146e-07   7.28307336e-07   7.66910689e-07
   8.07886367e-07   8.51238156e-07   8.97909787e-07   9.47354439e-07
   9.99345035e-07   1.05524054e-06   1.11474434e-06   1.17760000e-06
   1.24424260e-06   1.31586683e-06   1.39112686e-06   1.47001388e-06
   1.55455822e-06   1.64375159e-06   1.73886740e-06   1.84195422e-06
   1.95245702e-06   2.07101695e-06   2.19815987e-06   2.33333555e-06
   2.47983733e-06   2.63523345e-06   2.80014108e-06   2.97472412e-06
   3.16131076e-06   3.35995834e-06   3.57284584e-06   3.79901697e-06
   4.03972957e-06   4.30111520e-06   4.58476743e-06   4.89044852e-06
   5.21639455e-06   5.57065163e-06   5.95180738e-06   6.36601375e-06
   6.80534505e-06   7.27416702e-06   7.78358675e-06   8.33331892e-06
   8.92842358e-06   9.57295528e-06   1.02622291e-05   1.10033791e-05
   1.18063687e-05   1.26690610e-05   1.36062876e-05   1.46225057e-05
   1.57295746e-05   1.69323500e-05   1.82449061e-05   1.96689562e-05
   2.12154320e-05   2.28977455e-05   2.47021394e-05   2.66694502e-05
   2.87864165e-05   3.10614828e-05   3.35428614e-05   3.62316123e-05
   3.91543591e-05   4.22851481e-05   4.56447073e-05   4.92773385e-05
   5.31757927e-05   5.73466338e-05   6.19103957e-05   6.68549546e-05
   7.22432462e-05   7.80490820e-05   8.43235369e-05   9.10574206e-05
   9.84126744e-05   1.06471105e-04   1.15120323e-04   1.24433917e-04
   1.34447890e-04   1.45190110e-04   1.56798207e-04   1.69359829e-04
   1.83062760e-04   1.98043547e-04   2.14281099e-04   2.31819571e-04
   2.51029140e-04   2.71889480e-04   2.94760079e-04   3.19429969e-04
   3.46067953e-04   3.74729827e-04   4.05495639e-04   4.39259206e-04
   4.75591399e-04   5.15144176e-04   5.57606540e-04   6.03815971e-04
   6.53478586e-04   7.07899176e-04   7.67593910e-04   8.32799781e-04
   9.03353138e-04   9.79765961e-04   1.06293400e-03   1.15295267e-03
   1.25153858e-03   1.35854689e-03   1.47564432e-03   1.60365912e-03
   1.74167647e-03   1.89198765e-03   2.05390190e-03   2.22936844e-03
   2.42052913e-03   2.63060572e-03   2.85736593e-03   3.10349284e-03
   3.37089315e-03   3.65901096e-03   3.97428697e-03   4.31898086e-03
   4.69612928e-03   5.10392198e-03   5.54940173e-03   6.03086495e-03
   6.55705612e-03   7.12848470e-03   7.75573852e-03   8.43648034e-03
   9.17623447e-03   9.97881419e-03   1.08585344e-02   1.18081002e-02
   1.28341086e-02   1.39493710e-02   1.51698798e-02   1.64902539e-02
   1.79185058e-02   1.94792761e-02   2.11814401e-02   2.30496111e-02
   2.50738605e-02   2.72841533e-02   2.96971960e-02   3.23438714e-02
   3.52380867e-02   3.83641240e-02   4.17898166e-02   4.54864318e-02
   4.95132721e-02   5.38512006e-02   5.85570458e-02   6.37091514e-02
   6.92741852e-02   7.53565999e-02   8.19589417e-02   8.91718674e-02
   9.70059909e-02   1.05551844e-01   1.14757567e-01   1.24857270e-01
   1.35794830e-01   1.47563152e-01   1.60346482e-01   1.74214037e-01
   1.89199389e-01   2.05585834e-01   2.23230330e-01   2.42239374e-01
   2.62689225e-01   2.84895541e-01   3.08887475e-01   3.35017434e-01
   3.63544168e-01   3.94452580e-01   4.28050504e-01   4.63994819e-01
   5.03054737e-01   5.45120351e-01   5.90263556e-01   6.38925495e-01
   6.90867532e-01   7.46760068e-01   8.06333943e-01   8.68829044e-01
   9.34693020e-01   1.00434128e+00   1.07797328e+00   1.15413135e+00
   1.23306016e+00   1.31249448e+00   1.39164124e+00   1.46998903e+00
   1.54304490e+00   1.61058970e+00   1.66657489e+00   1.70706764e+00
   1.72875479e+00   1.72545351e+00   1.69511467e+00   1.63180104e+00
   1.53552336e+00   1.40822931e+00   1.25485801e+00   1.08364900e+00
   9.05488201e-01   7.32611297e-01   5.76068852e-01   4.41844046e-01
   3.31693410e-01   2.45124716e-01   1.79225890e-01   1.29960512e-01
   9.38522407e-02   6.76752557e-02   4.87882884e-02   3.52710925e-02
   2.55940143e-02   1.86471159e-02   1.36452211e-02   1.00344911e-02
   7.40430679e-03   5.48972217e-03   4.08919443e-03   3.05633105e-03
   2.29464438e-03   1.73150459e-03   1.31319222e-03   1.00090565e-03
   7.65864793e-04   5.87808804e-04   4.53597195e-04   3.51322394e-04
   2.73461272e-04   2.13727462e-04   1.67563698e-04   1.31808412e-04
   1.04223743e-04   8.27496403e-05   6.59993381e-05   5.28049435e-05
   4.24099036e-05   3.42101824e-05   2.77273686e-05   2.25399837e-05
   1.83736978e-05   1.50200855e-05   1.23156763e-05   1.01325681e-05
   8.36894271e-06   6.93951440e-06   5.76855324e-06   4.80894200e-06
   4.01871034e-06   3.37167752e-06   2.83834730e-06   2.39717519e-06
   2.02951616e-06   1.72224303e-06   1.46432090e-06   1.24993094e-06
   1.07102619e-06   9.20845990e-07   7.93091045e-07   6.84559955e-07
   5.92981996e-07   5.15576154e-07   4.49412426e-07   3.93076546e-07
   3.44654823e-07   3.02734684e-07   2.66398143e-07   2.34815421e-07
   2.07535595e-07   1.83830470e-07   1.63095733e-07   1.45153810e-07
   1.29442549e-07   1.15790840e-07   1.03912113e-07   9.35612260e-08
   8.44218276e-08   7.63087334e-08   6.91275067e-08   6.27750020e-08
   5.70731755e-08   5.19575592e-08   4.73816420e-08   4.32628061e-08
   3.96098372e-08   3.63493343e-08   3.34192043e-08   3.08136485e-08
   2.84588230e-08   2.63264110e-08   2.44039956e-08   2.26544648e-08
   2.10601985e-08   1.96056367e-08   1.82928320e-08   1.71139088e-08
   1.60537702e-08   1.50762864e-08   1.41862841e-08   1.33603564e-08
   1.26022429e-08   1.19112689e-08   1.12802225e-08   1.07045766e-08
   1.01699579e-08   9.67430419e-09   9.22291983e-09   8.80282071e-09
   8.42096045e-09   8.06510172e-09   7.72972162e-09   7.41250219e-09
   7.11964792e-09   6.85395666e-09   6.61067190e-09   6.39087878e-09
   6.19267386e-09   6.00383642e-09   5.82440546e-09   5.65346797e-09
   5.49168423e-09   5.34561688e-09   5.21071647e-09   5.08779660e-09
   4.97080457e-09   4.86227868e-09   4.76451318e-09   4.67003770e-09
   4.58703879e-09   4.51265099e-09   4.44880975e-09   4.38951780e-09
   4.33348195e-09   4.28193489e-09   4.23460814e-09   4.19440854e-09
   4.15718750e-09   4.12725158e-09   4.10516606e-09   4.08513724e-09
   4.07292133e-09   4.06110739e-09   4.05662093e-09   4.05357045e-09
   4.05391168e-09   4.05509872e-09   4.06075126e-09   4.06863836e-09
   4.07819717e-09   4.08918970e-09   4.10741931e-09   4.12614902e-09
   4.14704390e-09   4.17571644e-09   4.20693581e-09   4.24387620e-09
   4.28169018e-09   4.32607344e-09   4.37446493e-09   4.42962664e-09
   4.48857882e-09   4.55320313e-09   4.62582966e-09   4.70442212e-09
   4.78602071e-09   4.87732158e-09   4.96994471e-09   5.07021182e-09
   5.17762251e-09   5.29389252e-09   5.41164905e-09   5.53845206e-09
   5.67661662e-09   5.81753083e-09   5.96831264e-09   6.12886514e-09
   6.29476115e-09   6.47569973e-09   6.66643635e-09   6.86510432e-09
   7.08040074e-09   7.30092385e-09   7.52797840e-09   7.76742371e-09
   8.01357742e-09   8.27132475e-09   8.54996008e-09   8.83976545e-09
   9.14384923e-09   9.46936256e-09   9.80912612e-09   1.01713129e-08
   1.05632278e-08   1.09805532e-08   1.14190874e-08   1.18725271e-08
   1.23424359e-08   1.28274710e-08   1.33332437e-08   1.38606736e-08
   1.44125563e-08   1.49848755e-08   1.56007454e-08   1.62619350e-08
   1.69764322e-08   1.77203361e-08   1.85116015e-08   1.93601075e-08
   2.02430990e-08   2.11699212e-08   2.21675536e-08   2.32270896e-08
   2.43396823e-08   2.55388055e-08   2.67872614e-08   2.81040545e-08
   2.95095960e-08   3.09860929e-08   3.25594295e-08   3.42060771e-08
   3.59860533e-08   3.78652041e-08   3.98555691e-08   4.19512250e-08
   4.41699649e-08   4.65066529e-08   4.89682106e-08   5.16289777e-08
   5.44067621e-08   5.74023742e-08   6.05318152e-08   6.38557144e-08
   6.73343662e-08   7.10306308e-08   7.50169723e-08   7.92272352e-08]
0.1 0.1 1.0 0.01 1.0 1.0 1000
[  1.00000000e+00   1.00000000e+00   9.91355174e-01   9.73354372e-01
   9.46189366e-01   9.09211879e-01   8.63716456e-01   8.10346988e-01
   7.50033163e-01   6.84668173e-01   6.17046530e-01   5.48334670e-01
   4.81704657e-01   4.18065071e-01   3.59143068e-01   3.05893590e-01
   2.58679926e-01   2.17312321e-01   1.81834391e-01   1.51652406e-01
   1.26038363e-01   1.04504491e-01   8.65167011e-02   7.16851498e-02
   5.94722297e-02   4.93293562e-02   4.09781017e-02   3.40676558e-02
   2.83880134e-02   2.36853655e-02   1.98218602e-02   1.66454754e-02
   1.40047322e-02   1.18091133e-02   9.98033834e-03   8.45415758e-03
   7.17564924e-03   6.10140819e-03   5.20017107e-03   4.44441867e-03
   3.80892094e-03   3.27061919e-03   2.81558010e-03   2.42910571e-03
   2.10218182e-03   1.82543790e-03   1.58992507e-03   1.38863125e-03
   1.21685815e-03   1.06789006e-03   9.39482691e-04   8.29229112e-04
   7.33811773e-04   6.50358688e-04   5.77946717e-04   5.15138559e-04
   4.60715057e-04   4.12922290e-04   3.71012947e-04   3.34379831e-04
   3.01824549e-04   2.73169532e-04   2.47522007e-04   2.24704383e-04
   2.04514429e-04   1.86482379e-04   1.70564466e-04   1.56353343e-04
   1.43478131e-04   1.32062354e-04   1.21872021e-04   1.12652690e-04
   1.04393658e-04   9.70018123e-05   9.03333219e-05   8.42538297e-05
   7.87790525e-05   7.38040459e-05   6.92892518e-05   6.51016866e-05
   6.12632535e-05   5.76881295e-05   5.44098117e-05   5.13534134e-05
   4.85181038e-05   4.58860862e-05   4.34533276e-05   4.11773274e-05
   3.91053077e-05   3.71810674e-05   3.54340728e-05   3.37910324e-05
   3.22901774e-05   3.08863625e-05   2.95704304e-05   2.83635833e-05
   2.72528289e-05   2.62102349e-05   2.52592376e-05   2.43736628e-05
   2.35716352e-05   2.28472052e-05   2.21811459e-05   2.15766135e-05
   2.09989146e-05   2.04736976e-05   1.99840308e-05   1.95253377e-05
   1.91107383e-05   1.87469685e-05   1.84304478e-05   1.81417839e-05
   1.78808047e-05   1.76422907e-05   1.74107007e-05   1.72110037e-05
   1.70357838e-05   1.68682264e-05   1.67356116e-05   1.66354504e-05
   1.65547219e-05   1.65058843e-05   1.64720673e-05   1.64712287e-05
   1.64876766e-05   1.65275276e-05   1.65788422e-05   1.66493628e-05
   1.67509823e-05   1.68774135e-05   1.70122433e-05   1.71545209e-05
   1.73109024e-05   1.74994009e-05   1.76881060e-05   1.79026087e-05
   1.81384228e-05   1.84048775e-05   1.87057273e-05   1.90221313e-05
   1.93469790e-05   1.96875111e-05   2.00654906e-05   2.04504321e-05
   2.08409101e-05   2.12490653e-05   2.16819561e-05   2.21264941e-05
   2.25980158e-05   2.31012200e-05   2.36390254e-05   2.41870560e-05
   2.47807645e-05   2.54185964e-05   2.61070418e-05   2.68123247e-05
   2.75321189e-05   2.82844393e-05   2.90950211e-05   2.99700069e-05
   3.08945084e-05   3.18866795e-05   3.29364402e-05   3.40439789e-05
   3.52085477e-05   3.64621927e-05   3.77819462e-05   3.91618104e-05
   4.06156806e-05   4.21647565e-05   4.38083382e-05   4.55444652e-05
   4.73573295e-05   4.92501610e-05   5.12624475e-05   5.33470154e-05
   5.55240347e-05   5.78756314e-05   6.03816070e-05   6.30454031e-05
   6.58514645e-05   6.88733100e-05   7.20231347e-05   7.53768880e-05
   7.89182969e-05   8.26263036e-05   8.65216630e-05   9.05619986e-05
   9.48456221e-05   9.94328915e-05   1.04231997e-04   1.09271868e-04
   1.14583316e-04   1.20201848e-04   1.26115736e-04   1.32438869e-04
   1.39182782e-04   1.46380363e-04   1.54043686e-04   1.62236764e-04
   1.70857462e-04   1.79938528e-04   1.89407462e-04   1.99459401e-04
   2.10109648e-04   2.21622060e-04   2.33706269e-04   2.46357117e-04
   2.59897207e-04   2.74382502e-04   2.89963499e-04   3.06367204e-04
   3.23909901e-04   3.42530694e-04   3.62476157e-04   3.83683475e-04
   4.06158895e-04   4.29880497e-04   4.54744771e-04   4.81156929e-04
   5.09262465e-04   5.39642884e-04   5.72094921e-04   6.07263610e-04
   6.45101342e-04   6.85768769e-04   7.29894528e-04   7.76868891e-04
   8.26449432e-04   8.78730149e-04   9.33927503e-04   9.92933171e-04
   1.05522565e-03   1.12259751e-03   1.19356794e-03   1.27022778e-03
   1.35188926e-03   1.43972133e-03   1.53395365e-03   1.63444276e-03
   1.74299612e-03   1.85852221e-03   1.98408440e-03   2.11808756e-03
   2.26246807e-03   2.41798240e-03   2.58252100e-03   2.75753249e-03
   2.94419553e-03   3.14269060e-03   3.35574278e-03   3.58348394e-03
   3.82711036e-03   4.09204454e-03   4.37446246e-03   4.67520256e-03
   4.99765231e-03   5.34386268e-03   5.72052590e-03   6.12986267e-03
   6.56829633e-03   7.04004777e-03   7.54260499e-03   8.08320762e-03
   8.67188638e-03   9.29859044e-03   9.97931915e-03   1.07121780e-02
   1.15097610e-02   1.23617219e-02   1.32912189e-02   1.43008421e-02
   1.53954743e-02   1.65700268e-02   1.78388605e-02   1.92022180e-02
   2.06778710e-02   2.22742369e-02   2.40187527e-02   2.58862117e-02
   2.78844313e-02   3.00153748e-02   3.22918326e-02   3.47690151e-02
   3.74157654e-02   4.02728918e-02   4.33200997e-02   4.65807166e-02
   5.01182708e-02   5.39663672e-02   5.81621620e-02   6.26930393e-02
   6.75335931e-02   7.27913267e-02   7.84359293e-02   8.45405187e-02
   9.11543680e-02   9.82229558e-02   1.05834481e-01   1.13979496e-01
   1.22796303e-01   1.32355062e-01   1.42593127e-01   1.53641543e-01
   1.65609980e-01   1.78458378e-01   1.92427628e-01   2.07556782e-01
   2.23803810e-01   2.41308070e-01   2.60062030e-01   2.80295165e-01
   3.01889106e-01   3.24927846e-01   3.49602871e-01   3.76221490e-01
   4.04911037e-01   4.35752333e-01   4.68594964e-01   5.03100487e-01
   5.39853549e-01   5.78465964e-01   6.19466440e-01   6.62195848e-01
   7.06589020e-01   7.52089901e-01   7.99590534e-01   8.47544872e-01
   8.95799902e-01   9.43740791e-01   9.90229727e-01   1.03485317e+00
   1.07711462e+00   1.11465618e+00   1.14614479e+00   1.16930188e+00
   1.18204392e+00   1.18290204e+00   1.17174970e+00   1.14605351e+00
   1.10553367e+00   1.05130041e+00   9.84352786e-01   9.07311929e-01
   8.21985757e-01   7.31385925e-01   6.39841629e-01   5.51093552e-01
   4.67374658e-01   3.90962495e-01   3.23154648e-01   2.64583175e-01
   2.14744772e-01   1.73417246e-01   1.39553006e-01   1.11881434e-01
   8.95996170e-02   7.17016461e-02   5.74615346e-02   4.60448410e-02
   3.69531765e-02   2.97220838e-02   2.39642679e-02   1.93665670e-02
   1.57019624e-02   1.27582563e-02   1.04011519e-02   8.49723633e-03
   6.95965789e-03   5.71236700e-03   4.69818509e-03   3.87825480e-03
   3.20846820e-03   2.66313589e-03   2.21973814e-03   1.85371690e-03
   1.55463138e-03   1.30785961e-03   1.10488197e-03   9.36844164e-04
   7.96987802e-04   6.79589086e-04   5.80613275e-04   4.97531699e-04
   4.27631980e-04   3.68323507e-04   3.17771326e-04   2.75076602e-04
   2.38529224e-04   2.07328420e-04   1.80767092e-04   1.58118894e-04
   1.38818686e-04   1.22294721e-04   1.08080769e-04   9.58024474e-05
   8.50706507e-05   7.56795844e-05   6.74796397e-05   6.02828210e-05
   5.39774714e-05   4.84278590e-05   4.35431257e-05   3.92507263e-05
   3.54476340e-05   3.20712510e-05   2.90653053e-05   2.64034910e-05
   2.40460546e-05   2.19669556e-05   2.00974756e-05   1.84255838e-05
   1.69279856e-05   1.55790401e-05   1.43715418e-05   1.32949162e-05
   1.23210473e-05   1.14363636e-05   1.06383606e-05   9.92326282e-06
   9.27167102e-06   8.67560091e-06   8.12364694e-06   7.62806542e-06
   7.16919958e-06   6.74269342e-06   6.35029723e-06   5.99025538e-06
   5.66140884e-06   5.36360176e-06   5.08444901e-06   4.83108521e-06
   4.59581510e-06   4.38049643e-06   4.18098399e-06   3.99295691e-06
   3.81740388e-06   3.65799811e-06   3.50826223e-06   3.36690764e-06
   3.23569660e-06   3.11356395e-06   3.00307122e-06   2.90207388e-06
   2.80678440e-06   2.71584951e-06   2.62922282e-06   2.55111499e-06
   2.47892818e-06   2.41341012e-06   2.35077416e-06   2.29125863e-06
   2.23787273e-06   2.18924819e-06   2.14337596e-06   2.10065709e-06
   2.05937270e-06   2.02249742e-06   1.99030816e-06   1.95930758e-06
   1.93098881e-06   1.90371018e-06   1.88017465e-06   1.86084815e-06
   1.84280668e-06   1.82628252e-06   1.81028575e-06   1.79579742e-06
   1.78167849e-06   1.76824715e-06   1.75822254e-06   1.75129066e-06
   1.74512372e-06   1.74122161e-06   1.73821510e-06   1.73836887e-06
   1.74075390e-06   1.74403069e-06   1.74889779e-06   1.75548132e-06
   1.76340780e-06   1.77363534e-06   1.78713868e-06   1.80135324e-06
   1.81615416e-06   1.83365918e-06   1.85282762e-06   1.87276801e-06
   1.89573166e-06   1.92195054e-06   1.95118848e-06   1.98161898e-06
   2.01236529e-06   2.04630102e-06   2.08108189e-06   2.11973806e-06
   2.15966871e-06   2.20030153e-06   2.24432803e-06   2.29004865e-06
   2.33643380e-06   2.38771403e-06   2.44054753e-06   2.49785011e-06
   2.55781508e-06   2.62204022e-06   2.69188029e-06   2.76515695e-06
   2.84182207e-06   2.92500096e-06   3.01416852e-06   3.10898346e-06
   3.20793411e-06   3.31474449e-06   3.42722376e-06   3.54811779e-06
   3.67891534e-06   3.82023274e-06   3.97267075e-06   4.13726646e-06
   4.30869050e-06   4.48782086e-06   4.67694720e-06   4.88106446e-06
   5.09197555e-06   5.31520004e-06   5.55241231e-06   5.80742151e-06
   6.07231982e-06   6.35027431e-06   6.64023219e-06   6.94979611e-06
   7.27154249e-06   7.60987697e-06   7.96954564e-06   8.34748461e-06
   8.74177161e-06   9.16429563e-06   9.61261715e-06   1.00824124e-05
   1.05794682e-05   1.10974904e-05   1.16417245e-05   1.22080594e-05
   1.28011861e-05   1.34189937e-05   1.40719487e-05   1.47642595e-05
   1.54892588e-05   1.62708121e-05   1.71036592e-05   1.79939541e-05
   1.89229415e-05   1.99038463e-05   2.09648931e-05   2.20938433e-05
   2.33031184e-05   2.46040759e-05   2.60002769e-05   2.74615095e-05
   2.90248992e-05   3.06781535e-05   3.24642158e-05   3.43628511e-05
   3.63838434e-05   3.85722704e-05   4.08838313e-05   4.33219081e-05
   4.59567430e-05   4.87772990e-05   5.18116728e-05   5.50150898e-05
   5.84007613e-05   6.20172448e-05   6.58877727e-05   7.00531206e-05
   7.44733356e-05   7.92123892e-05   8.42197103e-05   8.96089406e-05
   9.54068038e-05   1.01646108e-04   1.08408616e-04   1.15654143e-04
   1.23421364e-04   1.31834321e-04   1.40902098e-04   1.50711202e-04
   1.61098280e-04   1.72102139e-04   1.84046292e-04   1.96784501e-04
   2.10591455e-04   2.25358076e-04   2.41420615e-04   2.58739121e-04
   2.77522686e-04   2.97823854e-04   3.19559074e-04   3.42858549e-04
   3.67645145e-04   3.94507204e-04   4.23805633e-04   4.55012229e-04
   4.89077549e-04   5.25692749e-04   5.64806361e-04   6.06732862e-04
   6.51421048e-04   6.99867952e-04   7.52512364e-04   8.08584786e-04
   8.68360637e-04   9.33091130e-04   1.00263559e-03   1.07681885e-03
   1.15579786e-03   1.24064518e-03   1.33158903e-03   1.42918799e-03
   1.53524974e-03   1.64997790e-03   1.77384295e-03   1.90727976e-03
   2.05268515e-03   2.21115006e-03   2.38230988e-03   2.56747901e-03
   2.76977031e-03   2.99097283e-03   3.23070551e-03   3.48792317e-03
   3.76750196e-03   4.06793984e-03   4.39263089e-03   4.74175932e-03
   5.11760622e-03   5.52321632e-03   5.96280887e-03   6.43736374e-03
   6.95436148e-03   7.51372927e-03   8.12149238e-03   8.78619892e-03
   9.50704303e-03   1.02950200e-02   1.11555976e-02   1.20797546e-02
   1.30848488e-02   1.41666751e-02   1.53400571e-02   1.66257431e-02
   1.80377627e-02   1.95711405e-02   2.12353377e-02   2.30273417e-02
   2.49514332e-02   2.70175228e-02   2.92706258e-02   3.16938790e-02
   3.43071297e-02   3.71543638e-02   4.02196851e-02   4.35694611e-02
   4.71593321e-02   5.10769116e-02   5.53406264e-02   5.99991653e-02
   6.50551176e-02   7.05457198e-02   7.64914322e-02   8.29486153e-02
   8.98780471e-02   9.74058913e-02   1.05644660e-01   1.14502595e-01
   1.24213049e-01   1.34723091e-01   1.46141013e-01   1.58633111e-01
   1.72060032e-01   1.86560550e-01   2.02396708e-01   2.19631108e-01
   2.38085903e-01   2.58057030e-01   2.79725812e-01   3.02974558e-01
   3.28176300e-01   3.55440100e-01   3.84981205e-01   4.16617019e-01
   4.50920575e-01   4.88174232e-01   5.27971500e-01   5.70615083e-01
   6.16338607e-01   6.64540217e-01   7.16388928e-01   7.70743054e-01
   8.27784836e-01   8.87959628e-01   9.51185242e-01   1.01749083e+00
   1.08559324e+00   1.15549683e+00   1.22593566e+00   1.29664530e+00
   1.36579273e+00   1.43171690e+00   1.49054088e+00   1.53990890e+00
   1.57636345e+00   1.59780327e+00   1.59951253e+00   1.57657829e+00
   1.52846076e+00   1.45200610e+00   1.34845619e+00   1.22220734e+00
   1.07827835e+00   9.25358096e-01   7.71912414e-01   6.26258754e-01
   4.96393604e-01   3.85735280e-01   2.95175500e-01   2.23099118e-01
   1.67123168e-01   1.24408502e-01   9.23723789e-02   6.84486256e-02
   5.08026626e-02   3.77880174e-02   2.81555557e-02   2.10659068e-02
   1.58321331e-02   1.19347707e-02   9.03923679e-03   6.88164224e-03
   5.26590316e-03   4.04303622e-03   3.11638964e-03   2.41463859e-03
   1.87615099e-03   1.46179832e-03   1.14398591e-03   8.98974995e-04
   7.09005023e-04   5.61662178e-04   4.46415446e-04   3.56545430e-04
   2.86070458e-04   2.30649881e-04   1.86812747e-04   1.51815015e-04
   1.23847617e-04   1.01506114e-04   8.35080770e-05   6.89730592e-05
   5.71902311e-05   4.76211399e-05   3.98202756e-05   3.34152334e-05
   2.81563665e-05   2.38195464e-05   2.02094694e-05   1.71901660e-05
   1.46519537e-05   1.25224452e-05   1.07441073e-05   9.24367518e-06
   7.97108600e-06   6.89189224e-06   5.97558189e-06   5.18930943e-06
   4.52011377e-06   3.95129557e-06   3.46345996e-06   3.04452447e-06
   2.68429844e-06   2.37251295e-06   2.10427112e-06   1.87178232e-06
   1.66753386e-06   1.49037934e-06   1.33452932e-06   1.19738622e-06
   1.07598262e-06   9.69112139e-07   8.75748010e-07   7.93720152e-07
   7.21622664e-07   6.56732097e-07   5.98645291e-07   5.46940295e-07
   5.00699262e-07   4.58794039e-07   4.21035352e-07   3.87292461e-07
   3.57229900e-07   3.30114009e-07   3.05391713e-07   2.82751790e-07
   2.62168403e-07   2.43469782e-07   2.26656734e-07   2.11237749e-07
   1.97051886e-07   1.84266587e-07   1.72691670e-07   1.61967521e-07
   1.52072667e-07   1.42911501e-07   1.34470811e-07   1.26690172e-07
   1.19649488e-07   1.13237116e-07   1.07313176e-07   1.01766581e-07
   9.67068075e-08   9.20306435e-08   8.77764709e-08   8.39185232e-08
   8.03277213e-08   7.70552862e-08   7.40394860e-08   7.11972869e-08
   6.85027390e-08   6.60416650e-08   6.37416045e-08   6.15610981e-08
   5.95057900e-08   5.76308815e-08   5.58533654e-08   5.42142796e-08
   5.27349419e-08   5.13103635e-08   5.00235051e-08   4.87834522e-08
   4.76248580e-08   4.65483213e-08   4.55607754e-08   4.46831275e-08
   4.38838052e-08   4.31331256e-08   4.24316217e-08   4.17973978e-08
   4.12104744e-08   4.06527635e-08   4.01769430e-08   3.97299132e-08
   3.93039375e-08   3.88871187e-08   3.84945958e-08   3.81530549e-08
   3.78659832e-08   3.76506980e-08   3.74504751e-08   3.73200984e-08
   3.72307189e-08   3.71840465e-08   3.71845143e-08   3.72399805e-08
   3.73082426e-08   3.73803529e-08   3.74690940e-08   3.75832919e-08
   3.77673932e-08   3.79873118e-08   3.82297841e-08   3.84935636e-08
   3.87777383e-08   3.91337163e-08   3.95625367e-08   4.00124018e-08
   4.04802355e-08   4.10083976e-08   4.15613175e-08   4.21177847e-08
   4.27406552e-08   4.34294333e-08   4.41921783e-08   4.49664336e-08
   4.58348937e-08   4.67358718e-08   4.77376517e-08   4.87749554e-08
   4.98532291e-08   5.09732982e-08   5.21785176e-08   5.34380114e-08
   5.47816377e-08   5.62479957e-08   5.78357392e-08   5.95562838e-08
   6.13733008e-08   6.33213837e-08   6.54309799e-08   6.77189753e-08
   7.01276847e-08   7.26382788e-08   7.52291029e-08   7.79967109e-08
   8.09291183e-08   8.39901497e-08   8.72771565e-08   9.08192004e-08
   9.45250501e-08   9.84912872e-08   1.02638718e-07   1.06932629e-07
   1.11495309e-07   1.16207827e-07   1.21133481e-07   1.26243031e-07
   1.31722156e-07   1.37394561e-07   1.43259999e-07   1.49512211e-07
   1.56235863e-07   1.63239310e-07   1.70640025e-07   1.78427609e-07
   1.86530528e-07   1.95159476e-07   2.04148776e-07   2.13495274e-07
   2.23544855e-07   2.34068602e-07   2.45063566e-07   2.56764951e-07
   2.68942956e-07   2.81760516e-07   2.95096801e-07   3.08957838e-07
   3.23430548e-07   3.38682927e-07   3.54888585e-07   3.72164327e-07
   3.90787853e-07   4.10490490e-07   4.31358600e-07   4.53894000e-07
   4.77706899e-07   5.02669655e-07   5.29035623e-07   5.57243851e-07
   5.87324360e-07   6.19101033e-07   6.53105949e-07   6.89715288e-07
   7.28251469e-07   7.69805883e-07   8.14434447e-07   8.61594712e-07
   9.11607229e-07   9.64782074e-07   1.02128675e-06   1.08184658e-06
   1.14715766e-06   1.21656413e-06   1.29064200e-06   1.36945323e-06
   1.45354424e-06   1.54366377e-06   1.63896354e-06   1.74168214e-06
   1.85028962e-06   1.96537051e-06   2.08999599e-06   2.22342739e-06
   2.36767879e-06   2.52363979e-06   2.69208206e-06   2.87010509e-06
   3.05806849e-06   3.25889547e-06   3.47641794e-06   3.71037685e-06
   3.95804934e-06   4.22575839e-06   4.50950499e-06   4.81041961e-06
   5.13361436e-06   5.48022055e-06   5.84956206e-06   6.25077379e-06
   6.67999306e-06   7.13962606e-06   7.62851043e-06   8.16069268e-06
   8.74062508e-06   9.36987120e-06   1.00497950e-05   1.07722455e-05
   1.15450836e-05   1.23663353e-05   1.32485107e-05   1.41995626e-05]
[stdout:2] 
5 of 5 single computations left
Splitting calculations to 3 nodes.
Calculating... 80.00%
Calculating... 100.00%Calculating 0 ...done.
[stdout:3] 
0.1 0.1 1.0 0.01 1.0 1.0 1000
[  1.00000000e+00   1.00000000e+00   9.91109859e-01   9.72500958e-01
   9.43401415e-01   9.05045126e-01   8.57327864e-01   8.02129237e-01
   7.41087023e-01   6.75325137e-01   6.07598712e-01   5.39387719e-01
   4.73138982e-01   4.10506121e-01   3.52588399e-01   3.00492976e-01
   2.54495809e-01   2.14066942e-01   1.79349562e-01   1.49843293e-01
   1.24990953e-01   1.04152231e-01   8.68093724e-02   7.24312766e-02
   6.04827451e-02   5.05046596e-02   4.22471559e-02   3.53763276e-02
   2.97029833e-02   2.49778221e-02   2.10341669e-02   1.77532585e-02
   1.50122744e-02   1.27158554e-02   1.08073789e-02   9.19888521e-03
   7.85140670e-03   6.72565381e-03   5.77788286e-03   4.97657416e-03
   4.29601075e-03   3.71586969e-03   3.21919371e-03   2.79591178e-03
   2.43479675e-03   2.12610127e-03   1.86097779e-03   1.63270689e-03
   1.43548545e-03   1.26547869e-03   1.11949869e-03   9.92307924e-04
   8.81485228e-04   7.85183731e-04   7.01132753e-04   6.27381712e-04
   5.62564334e-04   5.05943131e-04   4.55873236e-04   4.11858444e-04
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   6.34961379e-06   6.54404006e-06   6.74671326e-06   6.95960631e-06
   7.18876096e-06   7.42583574e-06   7.68024702e-06   7.95529828e-06
   8.25226103e-06   8.56502143e-06   8.90248413e-06   9.26227377e-06
   9.64377504e-06   1.00373322e-05   1.04543586e-05   1.08977535e-05
   1.13680494e-05   1.18736048e-05   1.24085687e-05   1.29803883e-05
   1.35948861e-05   1.42365824e-05   1.49234380e-05   1.56459228e-05
   1.64179508e-05   1.72396786e-05   1.80977971e-05   1.90060405e-05
   1.99651012e-05   2.09783719e-05   2.20705389e-05   2.32425685e-05
   2.45014043e-05   2.58453647e-05   2.72990442e-05   2.88335729e-05
   3.04956213e-05   3.22555330e-05   3.41252980e-05   3.60838167e-05
   3.81441949e-05   4.03428944e-05   4.27121702e-05   4.52530941e-05
   4.80004949e-05   5.08975284e-05   5.39756822e-05   5.72127256e-05
   6.06545379e-05   6.43318765e-05   6.82746012e-05   7.24357698e-05
   7.68783148e-05   8.15977717e-05   8.66339413e-05   9.19649510e-05
   9.76093981e-05   1.03731728e-04   1.10355976e-04   1.17511154e-04
   1.25079419e-04   1.33129597e-04   1.41740608e-04   1.50930679e-04
   1.60832813e-04   1.71547511e-04   1.83197301e-04   1.95769624e-04
   2.09368124e-04   2.24103715e-04   2.39863063e-04   2.56854539e-04
   2.75245609e-04   2.95214893e-04   3.16922879e-04   3.40276937e-04
   3.65126975e-04   3.92040401e-04   4.21025169e-04   4.52584225e-04
   4.86580074e-04   5.23101282e-04   5.62080846e-04   6.03914594e-04
   6.48451974e-04   6.96218065e-04   7.48036104e-04   8.03168282e-04
   8.62399923e-04   9.26112993e-04   9.93886529e-04   1.06661162e-03
   1.14582411e-03   1.23138554e-03   1.32352726e-03   1.42282163e-03
   1.53025194e-03   1.64499178e-03   1.76872119e-03   1.90130860e-03
   2.04542224e-03   2.20256214e-03   2.37102136e-03   2.55214874e-03
   2.74964535e-03   2.96399377e-03   3.19503198e-03   3.44312028e-03
   3.71110155e-03   4.00151920e-03   4.31507050e-03   4.65620551e-03
   5.02111122e-03   5.41351182e-03   5.83338760e-03   6.28307897e-03
   6.77140316e-03   7.29742109e-03   7.86954337e-03   8.49230598e-03
   9.16166985e-03   9.88593444e-03   1.06607173e-02   1.14928286e-02
   1.23882089e-02   1.33598318e-02   1.44208903e-02   1.55570248e-02
   1.67974145e-02   1.81469022e-02   1.95943152e-02   2.11696157e-02]
0.1 0.1 1.0 0.01 1.0 1.0 1000
[  1.00000000e+00   1.00000000e+00   9.90627562e-01   9.70786868e-01
   9.40317675e-01   9.00548642e-01   8.51934894e-01   7.94829732e-01
   7.30875781e-01   6.62907162e-01   5.93284641e-01   5.24672086e-01
   4.57914823e-01   3.95471292e-01   3.37975974e-01   2.86072574e-01
   2.40199495e-01   2.00546200e-01   1.66798920e-01   1.38258561e-01
   1.14397923e-01   9.45881199e-02   7.81548810e-02   6.46241820e-02
   5.35298955e-02   4.44353137e-02   3.69450167e-02   3.07875514e-02
   2.57173187e-02   2.15105222e-02   1.80472757e-02   1.51823374e-02
   1.28015543e-02   1.08126845e-02   9.15371528e-03   7.77151893e-03
   6.61189269e-03   5.63499813e-03   4.81675848e-03   4.13043327e-03
   3.55147848e-03   3.06323205e-03   2.64844660e-03   2.29529380e-03
   1.99245612e-03   1.73231855e-03   1.50895137e-03   1.31817601e-03
   1.15335513e-03   1.01197501e-03   8.89182204e-04   7.82397548e-04
   6.90057650e-04   6.09742014e-04   5.39494656e-04   4.78884070e-04
   4.25994145e-04   3.79834429e-04   3.39663369e-04   3.04535525e-04
   2.73746080e-04   2.46834842e-04   2.23167041e-04   2.02046611e-04
   1.83194125e-04   1.66519388e-04   1.51627519e-04   1.38285549e-04
   1.26335888e-04   1.15749679e-04   1.06315942e-04   9.79368883e-05
   9.04523552e-05   8.36511682e-05   7.75068288e-05   7.19237582e-05
   6.69065232e-05   6.22937491e-05   5.81010195e-05   5.43426078e-05
   5.09587892e-05   4.79093285e-05   4.50961531e-05   4.25200024e-05
   4.01787604e-05   3.80273419e-05   3.60335965e-05   3.41973416e-05
   3.24735920e-05   3.08935939e-05   2.94535760e-05   2.81325469e-05
   2.69366085e-05   2.58397651e-05   2.48262217e-05   2.39064613e-05
   2.30730399e-05   2.22782386e-05   2.15607056e-05   2.09122182e-05
   2.03278875e-05   1.97734763e-05   1.92641402e-05   1.88075169e-05
   1.84016599e-05   1.80372436e-05   1.76980782e-05   1.73750834e-05
   1.70829789e-05   1.68209533e-05   1.65761965e-05   1.63580234e-05
   1.61613741e-05   1.59953517e-05   1.58524442e-05   1.57309538e-05
   1.56142747e-05   1.55291415e-05   1.54737173e-05   1.54296766e-05
   1.54015599e-05   1.53923315e-05   1.54098042e-05   1.54414793e-05
   1.54764141e-05   1.55198354e-05   1.55748292e-05   1.56575936e-05
   1.57602662e-05   1.58756339e-05   1.60145005e-05   1.61778289e-05
   1.63488275e-05   1.65352077e-05   1.67285560e-05   1.69454899e-05
   1.71680393e-05   1.74042024e-05   1.76506617e-05   1.79225306e-05
   1.82035986e-05   1.85163926e-05   1.88653629e-05   1.92415870e-05
   1.96574908e-05   2.00828505e-05   2.05440852e-05   2.10294496e-05
   2.15432513e-05   2.20950003e-05   2.26819279e-05   2.33150259e-05
   2.39975368e-05   2.47217103e-05   2.54959499e-05   2.63329451e-05
   2.72243091e-05   2.81670755e-05   2.91773321e-05   3.02460246e-05
   3.13558313e-05   3.25058486e-05   3.37085347e-05   3.49603497e-05
   3.62928199e-05   3.77113759e-05   3.92155310e-05   4.07837630e-05
   4.24225354e-05   4.41251219e-05   4.59640775e-05   4.79203433e-05
   4.99910398e-05   5.21817351e-05   5.45140699e-05   5.69597034e-05
   5.95711413e-05   6.22895865e-05   6.51680727e-05   6.82506431e-05
   7.15033356e-05   7.48812990e-05   7.85325249e-05   8.24156083e-05
   8.64794159e-05   9.08123399e-05   9.54481579e-05   1.00448077e-04
   1.05768868e-04   1.11504424e-04   1.17699903e-04   1.24292165e-04
   1.31252077e-04   1.38649865e-04   1.46402235e-04   1.54521973e-04
   1.63015811e-04   1.72086966e-04   1.81696642e-04   1.91879640e-04
   2.02568255e-04   2.13940187e-04   2.26105763e-04   2.38941852e-04
   2.52513559e-04   2.66730703e-04   2.81949251e-04   2.98240019e-04
   3.15645089e-04   3.33980549e-04   3.53522435e-04   3.74331965e-04
   3.96318124e-04   4.19991830e-04   4.45161923e-04   4.72395277e-04
   5.01109403e-04   5.31997871e-04   5.64713467e-04   6.00006951e-04
   6.37218052e-04   6.77509615e-04   7.20417874e-04   7.66623910e-04
   8.16740012e-04   8.71037284e-04   9.28601634e-04   9.90946491e-04
   1.05680936e-03   1.12749694e-03   1.20288743e-03   1.28307925e-03
   1.36880441e-03   1.46161291e-03   1.56176267e-03   1.66974969e-03
   1.78549952e-03   1.90987081e-03   2.04421093e-03   2.18791221e-03
   2.34327214e-03   2.51177450e-03   2.69395062e-03   2.88966376e-03
   3.10127399e-03   3.33225102e-03   3.57947667e-03   3.84266110e-03
   4.12573762e-03   4.43074667e-03   4.75923635e-03   5.10972499e-03
   5.48929369e-03   5.89578367e-03   6.33503341e-03   6.81143049e-03
   7.31987972e-03   7.87135790e-03   8.46085774e-03   9.10287520e-03
   9.80426786e-03   1.05583508e-02   1.13757396e-02   1.22642477e-02
   1.32165702e-02   1.42436802e-02   1.53538544e-02   1.65465325e-02
   1.78481503e-02   1.92639257e-02   2.07838553e-02   2.24410407e-02
   2.42538818e-02   2.62187042e-02   2.83410300e-02   3.06146941e-02
   3.30510070e-02   3.57053215e-02   3.86111468e-02   4.17234100e-02
   4.50840218e-02   4.87076401e-02   5.26685997e-02   5.69898823e-02
   6.16646545e-02   6.67579828e-02   7.22749933e-02   7.83027044e-02
   8.48043206e-02   9.17701110e-02   9.92525785e-02   1.07429697e-01
   1.16286162e-01   1.25869751e-01   1.36118484e-01   1.47228761e-01
   1.59303012e-01   1.72466321e-01   1.86661972e-01   2.01936023e-01
   2.18621355e-01   2.36724071e-01   2.56397764e-01   2.77815633e-01
   3.01176231e-01   3.26604300e-01   3.54247296e-01   3.84373801e-01
   4.16917401e-01   4.51942609e-01   4.89444286e-01   5.29292689e-01
   5.72511751e-01   6.19110173e-01   6.68498247e-01   7.21763380e-01
   7.77986847e-01   8.38150259e-01   9.01182101e-01   9.67809724e-01
   1.03741239e+00   1.11017089e+00   1.18393098e+00   1.25956074e+00
   1.33587466e+00   1.41068019e+00   1.48266756e+00   1.55015252e+00
   1.61036932e+00   1.65825913e+00   1.68889236e+00   1.69740719e+00
   1.68192131e+00   1.63863818e+00   1.56544449e+00   1.45918588e+00
   1.32448197e+00   1.16738599e+00   9.97167489e-01   8.26316062e-01
   6.64168424e-01   5.19065570e-01   3.96324725e-01   2.96663953e-01
   2.19258611e-01   1.60577843e-01   1.16855721e-01   8.48458886e-02
   6.15348109e-02   4.46575141e-02   3.24755613e-02   2.36931692e-02
   1.73245200e-02   1.27146819e-02   9.36957838e-03   6.94228521e-03
   5.17267305e-03   3.87547896e-03   2.91563954e-03   2.20535217e-03
   1.67690233e-03   1.28225752e-03   9.84118158e-04   7.59004063e-04
   5.88482081e-04   4.57785780e-04   3.57800682e-04   2.80727806e-04
   2.20874374e-04   1.74515335e-04   1.38490279e-04   1.10222122e-04
   8.79810220e-05   7.05164042e-05   5.67367923e-05   4.58372387e-05
   3.71856516e-05   3.02417953e-05   2.47102035e-05   2.02711687e-05
   1.66686291e-05   1.37378290e-05   1.13690696e-05   9.44818109e-06
   7.86913030e-06   6.57364082e-06   5.50889124e-06   4.62940815e-06
   3.90642090e-06   3.30870006e-06   2.80885195e-06   2.39075901e-06
   2.04132921e-06   1.74701191e-06   1.49845212e-06   1.28891373e-06
   1.11093865e-06   9.60700556e-07   8.33817587e-07   7.26394154e-07
   6.34033130e-07   5.55247425e-07   4.87246006e-07   4.28527661e-07
   3.77428028e-07   3.32940205e-07   2.94381206e-07   2.60710803e-07
   2.31358724e-07   2.05901139e-07   1.83797767e-07   1.64311257e-07
   1.47351991e-07   1.32464837e-07   1.19244931e-07   1.07581963e-07
   9.72790815e-08   8.81201881e-08   8.00457347e-08   7.29053791e-08
   6.64738445e-08   6.07186473e-08   5.55367440e-08   5.08663543e-08
   4.67116470e-08   4.30232725e-08   3.96752881e-08   3.66342300e-08
   3.38677363e-08   3.13613600e-08   2.91023661e-08   2.70340890e-08
   2.51711582e-08   2.34901123e-08   2.19513574e-08   2.05364538e-08
   1.92584423e-08   1.80746328e-08   1.69988496e-08   1.60171814e-08
   1.51207792e-08   1.42867665e-08   1.35339662e-08   1.28487385e-08
   1.22182614e-08   1.16456947e-08   1.11271172e-08   1.06373212e-08
   1.01888072e-08   9.76503576e-09   9.37677306e-09   9.00801155e-09
   8.66830094e-09   8.35732620e-09   8.06155668e-09   7.78444069e-09
   7.52928077e-09   7.29250019e-09   7.07941871e-09   6.88041533e-09
   6.69484540e-09   6.52802231e-09   6.37738200e-09   6.24012111e-09
   6.11455767e-09   6.00183579e-09   5.89868384e-09   5.80409008e-09
   5.72192335e-09   5.65154826e-09   5.58888325e-09   5.53231421e-09
   5.47777578e-09   5.42514505e-09   5.38085929e-09   5.34284094e-09
   5.30954732e-09   5.28522905e-09   5.26326051e-09   5.24579200e-09
   5.23421867e-09   5.23123815e-09   5.23135867e-09   5.23214809e-09
   5.23342116e-09   5.23984736e-09   5.24856220e-09   5.26093381e-09
   5.27845889e-09   5.30467054e-09   5.33210491e-09   5.36403031e-09
   5.40567527e-09   5.45617755e-09   5.51162270e-09   5.57490296e-09
   5.63946100e-09   5.71471729e-09   5.79594012e-09   5.87969809e-09
   5.97020712e-09   6.06443456e-09   6.16381165e-09   6.27284718e-09
   6.38911266e-09   6.50724387e-09   6.63723025e-09   6.77751574e-09
   6.93149969e-09   7.08756475e-09   7.25063818e-09   7.42796734e-09
   7.61474740e-09   7.81409399e-09   8.02477333e-09   8.24195810e-09
   8.47556176e-09   8.71860955e-09   8.96711918e-09   9.22408562e-09
   9.49034948e-09   9.76403111e-09   1.00482713e-08   1.03577837e-08
   1.06851925e-08   1.10265389e-08   1.13957175e-08   1.17805657e-08
   1.21892579e-08   1.26100354e-08   1.30621972e-08   1.35390504e-08
   1.40351758e-08   1.45578337e-08   1.51024288e-08   1.56704353e-08
   1.62668446e-08   1.69120482e-08   1.75815408e-08   1.82827137e-08
   1.90305078e-08   1.98301779e-08   2.06625780e-08   2.15402723e-08
   2.24601630e-08   2.34510329e-08   2.44910789e-08   2.55791726e-08
   2.67260697e-08   2.79300205e-08   2.92209593e-08   3.05739108e-08
   3.20057547e-08   3.35199857e-08   3.51479571e-08   3.68917439e-08
   3.87055047e-08   4.06543796e-08   4.26972610e-08   4.48738809e-08
   4.71967166e-08   4.96368101e-08   5.21793445e-08   5.48591171e-08
   5.77103366e-08   6.07013820e-08   6.38439498e-08   6.72340289e-08
   7.08892668e-08   7.47325124e-08   7.88469453e-08   8.32944580e-08
   8.80246458e-08   9.31304509e-08   9.85916094e-08   1.04493896e-07
   1.10875751e-07   1.17678617e-07   1.25010743e-07   1.32843912e-07
   1.41187673e-07   1.50094770e-07   1.59691630e-07   1.69859509e-07
   1.80891767e-07   1.92539050e-07   2.05170601e-07   2.18753653e-07
   2.33189776e-07   2.48607260e-07   2.65127302e-07   2.83098149e-07
   3.02119920e-07   3.22581539e-07   3.44264102e-07   3.67540864e-07
   3.92606887e-07   4.19717900e-07   4.48591647e-07   4.79339938e-07
   5.12497129e-07   5.48003929e-07   5.85655530e-07   6.26044852e-07
   6.69098734e-07   7.15365786e-07   7.65338009e-07   8.18564912e-07
   8.75705739e-07   9.37847935e-07   1.00441271e-06   1.07572041e-06
   1.15184577e-06   1.23466355e-06   1.32459297e-06   1.42197089e-06
   1.52716146e-06   1.64144508e-06   1.76331382e-06   1.89546186e-06
   2.03879268e-06   2.19251583e-06   2.35718545e-06   2.53545259e-06
   2.72989225e-06   2.94077959e-06   3.17007651e-06   3.41597178e-06
   3.68218268e-06   3.97072281e-06   4.28028105e-06   4.61338292e-06
   4.97563148e-06   5.36886999e-06   5.79427648e-06   6.25766337e-06
   6.76041451e-06   7.30057915e-06   7.89012448e-06   8.53533876e-06
   9.23991526e-06   9.99886067e-06   1.08305223e-05   1.17415525e-05
   1.27385562e-05   1.38157044e-05   1.49985487e-05   1.62864149e-05
   1.76827829e-05   1.92122519e-05   2.08855984e-05   2.26988334e-05
   2.46669343e-05   2.68098973e-05   2.91491752e-05   3.16803550e-05
   3.44066263e-05   3.73995055e-05   4.06652502e-05   4.42409711e-05
   4.81720035e-05   5.24454881e-05   5.70891929e-05   6.21117044e-05
   6.75956515e-05   7.35720555e-05   8.01326791e-05   8.73117368e-05
   9.51510338e-05   1.03679694e-04   1.13059276e-04   1.23321191e-04
   1.34454492e-04   1.46535209e-04   1.59665350e-04   1.73924461e-04
   1.89486446e-04   2.06367313e-04   2.24942112e-04   2.45380019e-04
   2.67719050e-04   2.91892953e-04   3.18418169e-04   3.47271054e-04
   3.78557712e-04   4.12440931e-04   4.49758275e-04   4.90415719e-04
   5.34906793e-04   5.83978629e-04   6.37722807e-04   6.95876910e-04
   7.58961610e-04   8.27878290e-04   9.03825437e-04   9.86689200e-04
   1.07657025e-03   1.17417000e-03   1.27980814e-03   1.39572602e-03
   1.52200996e-03   1.65891359e-03   1.80991103e-03   1.97567095e-03
   2.15525808e-03   2.35290354e-03   2.56691879e-03   2.80263050e-03
   3.06193678e-03   3.34682585e-03   3.66004581e-03   4.00607897e-03
   4.38142240e-03   4.79393971e-03   5.24970000e-03   5.74893543e-03
   6.29436233e-03   6.88786594e-03   7.53990321e-03   8.25554157e-03
   9.04607146e-03   9.90547680e-03   1.08545683e-02   1.18843524e-02
   1.30211623e-02   1.42548629e-02   1.55970711e-02   1.70760729e-02
   1.86815846e-02   2.04385190e-02   2.23727843e-02   2.45027347e-02
   2.68522625e-02   2.94033116e-02   3.21942137e-02   3.52774201e-02
   3.86811069e-02   4.24509930e-02   4.66304434e-02   5.12447408e-02
   5.63160975e-02   6.18879155e-02   6.80159661e-02   7.47406809e-02
   8.21697997e-02   9.03439653e-02   9.93858256e-02   1.09286108e-01
   1.20220539e-01   1.32178032e-01   1.45218060e-01   1.59497470e-01
   1.75239972e-01   1.92601794e-01   2.11737023e-01   2.32919219e-01
   2.56030202e-01   2.81302548e-01   3.09301370e-01   3.40166034e-01
   3.73894293e-01   4.11203090e-01   4.52110172e-01   4.97038410e-01
   5.45940309e-01   5.99768453e-01   6.59151292e-01   7.23820181e-01
   7.95166128e-01   8.72949792e-01   9.57843220e-01   1.05085735e+00
   1.15205154e+00   1.26145540e+00   1.37962910e+00   1.50697109e+00
   1.64582056e+00   1.79699611e+00   1.95980172e+00   2.13359912e+00
   2.31846241e+00   2.51108758e+00   2.70944065e+00   2.91042614e+00
   3.10735572e+00   3.29093534e+00   3.44794800e+00   3.55206072e+00
   3.57897266e+00   3.49139586e+00   3.25516205e+00   2.85025164e+00
   2.29409507e+00   1.65804271e+00   1.06132874e+00   6.04067909e-01
   3.12503289e-01   1.52350183e-01   7.22011298e-02   3.39689204e-02
   1.60483685e-02   7.65601564e-03   3.69286882e-03   1.80135322e-03
   8.89158844e-04   4.44566463e-04   2.24747792e-04   1.14913779e-04
   5.93819448e-05   3.10852434e-05   1.64259074e-05   8.76702487e-06
   4.73115255e-06   2.57819174e-06   1.41981269e-06   7.89248671e-07
   4.42351760e-07   2.49947903e-07   1.42542017e-07   8.21062893e-08
   4.77041697e-08   2.79505924e-08   1.64980832e-08   9.83462370e-09
   5.91649340e-09   3.58767133e-09   2.19458298e-09   1.35096217e-09
   8.39120119e-10   5.25951272e-10   3.31629700e-10   2.10529449e-10
   1.34433349e-10   8.63317866e-11   5.57504863e-11   3.62083481e-11
   2.37037849e-11   1.56468785e-11   1.03826076e-11   6.93598929e-12
   4.66363199e-12   3.15626646e-12   2.15028507e-12   1.47564268e-12
   1.01770232e-12   7.07053932e-13   4.94677952e-13   3.48535703e-13
   2.46980090e-13   1.75955513e-13   1.26143913e-13   9.09777264e-14
   6.59297805e-14   4.80480020e-14   3.51508825e-14   2.58222200e-14
   1.90674165e-14   1.41400927e-14   1.05259000e-14   7.87656861e-15
   5.91739842e-15   4.46643723e-15   3.38360347e-15   2.57515086e-15
   1.96828019e-15   1.50921368e-15   1.16134120e-15   8.98642042e-16
   6.98514731e-16   5.44574160e-16   4.26138883e-16   3.34925827e-16
   2.64457178e-16   2.09427461e-16   1.66378979e-16   1.32742318e-16
   1.06298244e-16   8.55123648e-17   6.90123364e-17   5.59078564e-17
   4.54121075e-17   3.70159581e-17   3.02423580e-17   2.47995183e-17
   2.04206050e-17   1.68751074e-17   1.39956982e-17   1.16449764e-17
   9.73023839e-18   8.16276774e-18   6.87678021e-18   5.80428502e-18
   4.91904621e-18   4.17937244e-18   3.56142462e-18   3.04546278e-18
   2.61094099e-18   2.24361328e-18   1.93211657e-18   1.66843302e-18
   1.44374796e-18   1.25174608e-18   1.08909791e-18   9.49748461e-19
   8.30584348e-19   7.28614687e-19   6.40219461e-19   5.64367156e-19
   4.99224019e-19   4.43115104e-19   3.94280762e-19   3.51601485e-19
   3.14000769e-19   2.81028884e-19   2.52081336e-19   2.26852350e-19
   2.04650002e-19   1.84994555e-19   1.67573377e-19   1.52166384e-19
   1.38604166e-19   1.26589737e-19   1.15812903e-19   1.06278799e-19
   9.77950626e-20   9.00855312e-20   8.31413496e-20   7.68972616e-20
   7.13226703e-20   6.62337722e-20   6.16633664e-20   5.75201962e-20
   5.37891574e-20   5.03870269e-20   4.72669611e-20   4.44586340e-20
   4.18814753e-20   3.95064528e-20   3.73612781e-20   3.53857362e-20
   3.36006579e-20   3.19252027e-20   3.04057819e-20   2.90219854e-20
   2.77454944e-20   2.65656222e-20   2.54676064e-20   2.44340038e-20
   2.35001367e-20   2.26267412e-20   2.18225211e-20   2.10644171e-20
   2.03800803e-20   1.97306550e-20   1.91300183e-20   1.85802756e-20
   1.80596076e-20   1.75728785e-20   1.71077744e-20   1.66877088e-20
   1.62923092e-20   1.59365304e-20   1.56138813e-20   1.53293818e-20
   1.50706025e-20   1.48332947e-20   1.46282642e-20   1.44457772e-20
   1.42892263e-20   1.41446197e-20   1.40295585e-20   1.39420528e-20
   1.38825253e-20   1.38483279e-20   1.38272964e-20   1.38175205e-20
   1.38205421e-20   1.38288785e-20   1.38617009e-20   1.38972916e-20
   1.39591682e-20   1.40284547e-20   1.40996271e-20   1.41811825e-20
   1.42785592e-20   1.43808907e-20   1.44950202e-20   1.46362734e-20
   1.48044514e-20   1.49945617e-20   1.51930450e-20   1.54172872e-20
   1.56555695e-20   1.59212008e-20   1.62110797e-20   1.65177527e-20
   1.68358410e-20   1.71744594e-20   1.75240091e-20   1.78852406e-20]

And if everyting whent well, the calculations should have been splitted between all the engines that you've started in the beginning.

To run you experiments in scripts outside of an IPython notebook, simply run you experiment script (defining a run function, an experiment handle and calling the compute routine of that handle) with mpirun in a terminal