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#!/usr/bin/env python
# Author: Samuel Ponc\'e
# Date: 30/04/2013 -- 11/09/2014
# Version: 1.3
# Script to compute the ZPR
import sys
import os
import copy
try:
from rf_mods_seq import system
except ImportError:
import warnings
warnings.warn("The system module is missing!")
raise
from rf_mods_seq import zpm
import multiprocessing
from datetime import datetime
try:
import numpy as N
except ImportError:
import warnings
warnings.warn("The numpy module is missing!")
raise
from numpy import zeros
try:
import netCDF4 as nc
except ImportError:
import warnings
warnings.warn("The netCDF4 module is missing!")
raise
start = datetime.now()
print 'Start on %s/%s/%s at %sh%s ' %(start.day,start.month,start.year,start.hour,start.minute)
#############
# Constants #
#############
tol6 = 1E-6
tol8 = 1E-8
Ha2eV = 27.21138386
kb_HaK = 3.1668154267112283e-06
######################################################################################
# Interaction with the user
print """
____ ____ _ _
| _ \| _ \ | |_ ___ _ __ ___ _ __ ___ _ __ __ _| |_ _ _ _ __ ___
| |_) | |_) |____| __/ _ \ '_ ` _ \| '_ \ / _ \ '__/ _` | __| | | | '__/ _ \
| __/| __/_____| || __/ | | | | | |_) | __/ | | (_| | |_| |_| | | | __/
|_| |_| \__\___|_| |_| |_| .__/ \___|_| \__,_|\__|\__,_|_| \___|
|_| Version 1.3
"""
print '\nThis script compute the static/dynamic zero-point motion \n\
and the temperature dependance of eigenenergies due to electron-phonon interaction.\n\
The static electronic lifetime can also be computed. \n\n\
WARNING: The first Q-point MUST be the Gamma point.\n'
# Enter the number of cpu on which you want to multi-thread
user_input = raw_input('Enter the number of cpu on which you want to multi-thread\n')
nb_cpus = user_input
try:
nb_cpus = int(user_input)
except ValueError:
raise Exception('The value you enter is not an integer!')
# Type of calculation the user want to perform
user_input = raw_input('Define the type of calculation you want to perform. Type:\n\
1 if you want to run a static AHC calculation\n \
2 if you want to run a dynamic AHC calculation\n \
3 if you want to run a static AHC calculation with control over active space\n\
Note that option 2 and 3 requires _FAN.nc files obtained through ABINIT option "ieig2rf 4\n')
type = N.int(user_input)
# Define the output file name
user_input = raw_input('Enter name of the output file\n')
output = user_input.strip()
# Enter the value of the smearing parameter for dynamic AHC
if (type == 2 or type == 3 ):
user_input = raw_input('Enter value of the smearing parameter (in eV)\n')
smearing = N.float(user_input)
smearing = smearing/Ha2eV
else:
smearing = None
# Temperature dependence analysis?
user_input = raw_input('Do you want to compute the change of eigenergies with temperature? [y/n]\n')
temperature =user_input.split()[0]
if temperature == 'y':
temperature = True
user_input = raw_input('Introduce the starting temperature, max temperature and steps. e.g. 0 2000 100\n')
temp_info = user_input.split()
else:
temperature = False
temp_info = None
# Broadening lifetime of the electron
user_input = raw_input('Do you want to compute the lifetime of the electrons? [y/n]\n')
tmp =user_input.split()[0]
if tmp == 'y':
lifetime = True
else:
lifetime = False
# Get the nb of random Q-points from user
user_input = raw_input('Enter the number of random Q-points you have\n')
try:
nbQ = int(user_input)
except ValueError:
raise Exception('The value you enter is not an integer!')
# Get the path of the DDB files from user
DDB_files = []
for ii in N.arange(nbQ):
user_input = raw_input('Enter the name of the %s DDB file\n' %ii)
if len(user_input.split()) != 1:
raise Exception("You should provide only 1 file")
else: # Append and TRIM the input string with STRIP
DDB_files.append(user_input.strip(' \t\n\r'))
# Test if the first file is at the Gamma point
DDBtmp = system(directory='.',filename=DDB_files[0])
if N.allclose(DDBtmp.iqpt,[0.0,0.0,0.0]) == False:
raise Exception('The first Q-point is not Gamma!')
# Get the path of the eigq files from user
eigq_files = []
for ii in N.arange(nbQ):
user_input = raw_input('Enter the name of the %s eigq file\n' %ii)
if len(user_input.split()) != 1:
raise Exception("You should provide only 1 file")
else:
eigq_files.append(user_input.strip(' \t\n\r'))
# Get the path of the EIGR2D files from user
EIGR2D_files = []
for ii in N.arange(nbQ):
user_input = raw_input('Enter the name of the %s EIGR2D file\n' %ii)
if len(user_input.split()) != 1:
raise Exception("You should provide only 1 file")
else:
EIGR2D_files.append(user_input.strip(' \t\n\r'))
# Get the path of the EIGI2D files from user
if lifetime:
EIGI2D_files = []
for ii in N.arange(nbQ):
user_input = raw_input('Enter the name of the %s EIGI2D file\n' %ii)
if len(user_input.split()) != 1:
raise Exception("You should provide only 1 file")
else:
EIGI2D_files.append(user_input.strip(' \t\n\r'))
# Get the path of the FAN files from user if dynamical calculation
if (type == 2 or type == 3):
FAN_files = []
for ii in N.arange(nbQ):
user_input = raw_input('Enter the name of the %s FAN file\n' %ii)
if len(user_input.split()) != 1:
raise Exception("You should provide only 1 file")
else:
FAN_files.append(user_input.strip(' \t\n\r'))
# Take the EIG at Gamma
user_input = raw_input('Enter the name of the unperturbed EIG.nc file at Gamma\n')
if len(user_input.split()) != 1:
raise Exception("You sould only provide 1 file")
else:
eig0 = system(directory='.',filename=user_input.strip(' \t\n\r'))
# Read the EIGR2D file at Gamma and save it in ddw_save
EIGR2D = system(directory='.',filename=EIGR2D_files[0])
ddw_save = zeros((EIGR2D.nkpt,EIGR2D.nband,3,EIGR2D.natom,3,EIGR2D.natom),dtype=complex)
ddw_save = copy.deepcopy(EIGR2D.EIG2D)
if (type == 2 or type == 3):
FAN = system(directory='.',filename=FAN_files[0])
ddw_save2 = zeros((FAN.nkpt,FAN.nband,3,FAN.natom,3,FAN.natom,FAN.nband),dtype=complex)
ddw_save2 = copy.deepcopy(FAN.FAN)
if (type == 1):
# We put dummy argument
ddw_save2 = 0.0
# Find the degenerate eigenstates
degen = zeros((EIGR2D.nkpt,EIGR2D.nband),dtype=int)
for ikpt in N.arange(EIGR2D.nkpt):
count = 0
for iband in N.arange(EIGR2D.nband):
if iband != EIGR2D.nband-1:
if N.allclose(eig0.EIG[0,ikpt,iband+1], eig0.EIG[0,ikpt,iband]):
degen[ikpt,iband] = count
else:
degen[ikpt,iband] = count
count += 1
continue
else:
if N.allclose(eig0.EIG[0,ikpt,iband-1], eig0.EIG[0,ikpt,iband]):
degen[ikpt,iband] = count
if iband != 0:
if N.allclose(eig0.EIG[0,ikpt,iband-1], eig0.EIG[0,ikpt,iband]):
degen[ikpt,iband] = count
else:
if N.allclose(eig0.EIG[0,ikpt,iband+1], eig0.EIG[0,ikpt,iband]):
degen[ikpt,iband] = count
# Create the random Q-integration (wtq=1/nqpt):
if (EIGR2D.wtq == 0):
wtq = N.ones((nbQ))
wtq = wtq*(1.0/nbQ)
else:
wtq = N.zeros((nbQ))
#DBSP
#wtq = N.ones((nbQ))
#END
nbqpt = N.arange(nbQ)
# Compute phonon freq. and eigenvector for each Q-point
# from each DDB (1 qpt per DDB file)
vkpt = EIGR2D.nkpt
vband = EIGR2D.nband
tkpt = zeros((EIGR2D.nkpt,3))
tkpt = EIGR2D.kpt[:,:]
eig0_pass = copy.deepcopy(eig0.EIG)
if temperature:
temp_info = N.arange(N.float(temp_info[0]),N.float(temp_info[1]),N.float(temp_info[2]))
if (type == 1):
total = zpm(zip(nbqpt,wtq,eigq_files,DDB_files,EIGR2D_files),ddw_save,ddw_save2,nb_cpus,type,temperature,\
temp_info,smearing,eig0_pass,degen,lifetime=False)
if lifetime:
print "Now compute broadening ..."
broadening = zpm(zip(nbqpt,wtq,eigq_files,DDB_files,EIGI2D_files),ddw_save,ddw_save2,nb_cpus,type,temperature,\
temp_info,smearing,eig0_pass,degen,lifetime)
if (type == 2):
if ((FAN.nkpt*FAN.nband*3*FAN.natom*3*FAN.natom*FAN.nband)*8.0)/(1024**2) < 1000: # If FAN file is smaller than 1000MB
total = zpm(zip(nbqpt,wtq,eigq_files,DDB_files,EIGR2D_files,FAN_files),ddw_save,ddw_save2,nb_cpus,type,temperature,\
temp_info,smearing,eig0_pass,degen,lifetime=False)
else: # Use sequential version without multiprocess threading ==> otherwise it breaks down
total = zpm(zip(nbqpt,wtq,eigq_files,DDB_files,EIGR2D_files,FAN_files),ddw_save,ddw_save2,1,type,temperature,\
temp_info,smearing,eig0_pass,degen,lifetime=False)
if lifetime:
#raise Exception("Dynamical lifetime is not yet implemented.")
print "WARNING:"
print "Dynamical lifetime is not yet implemented...proceed with static lifetime"
print "Now compute broadening ..."
broadening = zpm(zip(nbqpt,wtq,eigq_files,DDB_files,EIGI2D_files),ddw_save,ddw_save2,nb_cpus,type,temperature,\
temp_info,smearing,eig0_pass,degen,lifetime)
if (type == 3):
if ((FAN.nkpt*FAN.nband*3*FAN.natom*3*FAN.natom*FAN.nband)*8.0)/(1024**2) < 1000: # If FAN file is smaller than 1000MB
total = zpm(zip(nbqpt,wtq,eigq_files,DDB_files,EIGR2D_files,FAN_files),ddw_save,ddw_save2,nb_cpus,type,temperature,\
temp_info,smearing,eig0_pass,degen,lifetime=False)
else: # Use sequential version without multiprocess threading ==> otherwise it breaks down
total = zpm(zip(nbqpt,wtq,eigq_files,DDB_files,EIGR2D_files,FAN_files),ddw_save,ddw_save2,1,type,temperature,\
temp_info,smearing,eig0_pass,degen,lifetime=False)
if lifetime:
print "Now compute broadening ..."
broadening = zpm(zip(nbqpt,wtq,eigq_files,DDB_files,EIGI2D_files),ddw_save,ddw_save2,nb_cpus,type,temperature,\
temp_info,smearing,eig0_pass,degen,lifetime)
total_corr = total.total_corr
if lifetime:
brd_total = broadening.broadening
if (EIGR2D.wtq != 0):
total_wtq = total.total_wtq
print "Total weigth is ",total_wtq
if (total_wtq < 0.9 or total_wtq > 1.1):
raise Exception("The total weigth is not equal to 1.0. Check that you provide all the q-points.")
# Report wall time (before writing final result to be able to include it)
end = datetime.now()
print 'End on %s/%s/%s at %s h %s ' %(end.day,end.month,end.year,end.hour,end.minute)
runtime = end - start
print "Runtime: %s seconds (or %s minutes)" %(runtime.seconds,float(runtime.seconds)/60.0)
if temperature:
if lifetime:
# Write on a NC files with etsf-io name convention
ncfile = nc.Dataset(str(output)+'_EP.nc','w')
# Read dim from first EIGR2D file
root = nc.Dataset(EIGR2D_files[0],'r')
# Determine nsppol from reading occ
nsppol = len(root.variables['occupations'][:,0,0])
if nsppol > 1:
print "WARNING: nsppol > 1 has not been tested."
mband = len(root.dimensions['product_mband_nsppol'])/nsppol
# Create dimension
ncfile.createDimension('number_of_atoms',len(root.dimensions['number_of_atoms']))
ncfile.createDimension('number_of_kpoints',len(root.dimensions['number_of_kpoints']))
ncfile.createDimension('product_mband_nsppol',len(root.dimensions['product_mband_nsppol']))
ncfile.createDimension('cartesian',3)
ncfile.createDimension('cplex',2)
ncfile.createDimension('number_of_qpoints',nbQ)
ncfile.createDimension('number_of_spins',len(root.dimensions['number_of_spins']))
ncfile.createDimension('max_number_of_states',mband)
ncfile.createDimension('number_of_temperature',len(temp_info))
# Create variable
data = ncfile.createVariable('reduced_coordinates_of_kpoints','d',('number_of_kpoints','cartesian'))
data[:,:] = root.variables['reduced_coordinates_of_kpoints'][:,:]
data = ncfile.createVariable('eigenvalues','d',('number_of_spins','number_of_kpoints','max_number_of_states'))
data[:,:,:] = root.variables['eigenvalues'][:,:,:]
data = ncfile.createVariable('occupations','i',('number_of_spins','number_of_kpoints','max_number_of_states'))
data[:,:,:] = root.variables['occupations'][:,:,:]
data = ncfile.createVariable('primitive_vectors','d',('cartesian','cartesian'))
data[:,:] = root.variables['primitive_vectors'][:,:]
data = ncfile.createVariable('temperature','d',('number_of_temperature'))
data[:] = temp_info
data = ncfile.createVariable('zero_point_motion','d',('number_of_spins','number_of_temperature','number_of_kpoints',\
'max_number_of_states','cplex'))
data[0,:,:,:,0] = total_corr[0,:,:,:].real
data[0,:,:,:,1] = brd_total[:,:,:].real
# Close the file
ncfile.close()
else:
# Write on a NC files with etsf-io name convention
ncfile = nc.Dataset(str(output)+'_EP.nc','w')
# Read dim from first EIGR2D file
root = nc.Dataset(EIGR2D_files[0],'r')
# Determine nsppol from reading occ
nsppol = len(root.variables['occupations'][:,0,0])
if nsppol > 1:
print "WARNING: nsppol > 1 has not been tested."
mband = len(root.dimensions['product_mband_nsppol'])/nsppol
# Create dimension
ncfile.createDimension('number_of_atoms',len(root.dimensions['number_of_atoms']))
ncfile.createDimension('number_of_kpoints',len(root.dimensions['number_of_kpoints']))
ncfile.createDimension('product_mband_nsppol',len(root.dimensions['product_mband_nsppol']))
ncfile.createDimension('cartesian',3)
ncfile.createDimension('cplex',2)
ncfile.createDimension('number_of_qpoints',nbQ)
ncfile.createDimension('number_of_spins',len(root.dimensions['number_of_spins']))
ncfile.createDimension('max_number_of_states',mband)
ncfile.createDimension('number_of_temperature',len(temp_info))
# Create variable
data = ncfile.createVariable('reduced_coordinates_of_kpoints','d',('number_of_kpoints','cartesian'))
data[:,:] = root.variables['reduced_coordinates_of_kpoints'][:,:]
data = ncfile.createVariable('eigenvalues','d',('number_of_spins','number_of_kpoints','max_number_of_states'))
data[:,:,:] = root.variables['eigenvalues'][:,:,:]
data = ncfile.createVariable('occupations','i',('number_of_spins','number_of_kpoints','max_number_of_states'))
data[:,:,:] = root.variables['occupations'][:,:,:]
data = ncfile.createVariable('primitive_vectors','d',('cartesian','cartesian'))
data[:,:] = root.variables['primitive_vectors'][:,:]
data = ncfile.createVariable('temperature','d',('number_of_temperature'))
data[:] = temp_info
data = ncfile.createVariable('zero_point_motion','d',('number_of_spins','number_of_temperature','number_of_kpoints',\
'max_number_of_states','cplex'))
data[0,:,:,:,0] = total_corr[0,:,:,:].real
data[0,:,:,:,1] = 0.0
# Close the file
ncfile.close()
else:
if lifetime:
# Write on a NC files with etsf-io name convention
ncfile = nc.Dataset(str(output)+'_EP.nc','w')
# Read dim from first EIGR2D file
root = nc.Dataset(EIGR2D_files[0],'r')
# Determine nsppol from reading occ
nsppol = len(root.variables['occupations'][:,0,0])
if nsppol > 1:
print "WARNING: nsppol > 1 has not been tested."
mband = len(root.dimensions['product_mband_nsppol'])/nsppol
# Create dimension
ncfile.createDimension('number_of_atoms',len(root.dimensions['number_of_atoms']))
ncfile.createDimension('number_of_kpoints',len(root.dimensions['number_of_kpoints']))
ncfile.createDimension('product_mband_nsppol',len(root.dimensions['product_mband_nsppol']))
ncfile.createDimension('cartesian',3)
ncfile.createDimension('cplex',2)
ncfile.createDimension('number_of_qpoints',nbQ)
ncfile.createDimension('number_of_spins',len(root.dimensions['number_of_spins']))
ncfile.createDimension('max_number_of_states',mband)
ncfile.createDimension('number_of_temperature',1)
# Create variable
data = ncfile.createVariable('reduced_coordinates_of_kpoints','d',('number_of_kpoints','cartesian'))
data[:,:] = root.variables['reduced_coordinates_of_kpoints'][:,:]
data = ncfile.createVariable('eigenvalues','d',('number_of_spins','number_of_kpoints','max_number_of_states'))
data[:,:,:] = root.variables['eigenvalues'][:,:,:]
data = ncfile.createVariable('occupations','i',('number_of_spins','number_of_kpoints','max_number_of_states'))
data[:,:,:] = root.variables['occupations'][:,:,:]
data = ncfile.createVariable('primitive_vectors','d',('cartesian','cartesian'))
data[:,:] = root.variables['primitive_vectors'][:,:]
data = ncfile.createVariable('temperature','d',('number_of_temperature'))
data[:] = 0.0
data = ncfile.createVariable('zero_point_motion','d',('number_of_spins','number_of_temperature','number_of_kpoints',\
'max_number_of_states','cplex'))
data[0,0,:,:,0] = total_corr[0,:,:].real
data[0,0,:,:,1] = brd_total[:,:].real
# Close the file
ncfile.close()
else:
# Write on a NC files with etsf-io name convention
ncfile = nc.Dataset(str(output)+'_EP.nc','w')
# Read dim from first EIGR2D file
root = nc.Dataset(EIGR2D_files[0],'r')
# Determine nsppol from reading occ
nsppol = len(root.variables['occupations'][:,0,0])
if nsppol > 1:
print "WARNING: nsppol > 1 has not been tested."
mband = len(root.dimensions['product_mband_nsppol'])/nsppol
# Create dimension
ncfile.createDimension('number_of_atoms',len(root.dimensions['number_of_atoms']))
ncfile.createDimension('number_of_kpoints',len(root.dimensions['number_of_kpoints']))
ncfile.createDimension('product_mband_nsppol',len(root.dimensions['product_mband_nsppol']))
ncfile.createDimension('cartesian',3)
ncfile.createDimension('cplex',2)
ncfile.createDimension('number_of_qpoints',nbQ)
ncfile.createDimension('number_of_spins',len(root.dimensions['number_of_spins']))
ncfile.createDimension('max_number_of_states',mband)
ncfile.createDimension('number_of_temperature',1)
# Create variable
data = ncfile.createVariable('reduced_coordinates_of_kpoints','d',('number_of_kpoints','cartesian'))
data[:,:] = root.variables['reduced_coordinates_of_kpoints'][:,:]
data = ncfile.createVariable('eigenvalues','d',('number_of_spins','number_of_kpoints','max_number_of_states'))
data[:,:,:] = root.variables['eigenvalues'][:,:,:]
data = ncfile.createVariable('occupations','i',('number_of_spins','number_of_kpoints','max_number_of_states'))
data[:,:,:] = root.variables['occupations'][:,:,:]
data = ncfile.createVariable('primitive_vectors','d',('cartesian','cartesian'))
data[:,:] = root.variables['primitive_vectors'][:,:]
data = ncfile.createVariable('temperature','d',('number_of_temperature'))
data[:] = 0.0
data = ncfile.createVariable('zero_point_motion','d',('number_of_spins','number_of_temperature','number_of_kpoints',\
'max_number_of_states','cplex'))
data[0,0,:,:,0] = total_corr[0,:,:].real
data[0,0,:,:,1] = 0.0
# Close the file
ncfile.close()
# Write the results into the output file
if temperature:
with open(str(output)+".txt","w") as O:
O.write("Total correction of the ZPM (eV) for "+str(nbQ)+" Q points\n")
for ikpt in N.arange(vkpt):
O.write('Kpt: '+str(tkpt[ikpt,:])+"\n")
j = 1
for ii in (total_corr[0,0,ikpt,:].real*Ha2eV):
# Create a new line every 6 values
if (j%6 == 0 and j !=0):
O.write(str(ii)+'\n')
j += 1
elif j == vband:
O.write(str(ii)+'\n')
else:
O.write(str(ii)+' ')
j += 1
O.write("Temperature dependence at Gamma\n")
for iband in N.arange(vband):
O.write('Band: '+str(iband)+"\n")
tt = 0
for T in temp_info:
O.write(str(T)+" "+str(total_corr[0,tt,0,iband].real*Ha2eV)+"\n")
tt += 1
O.write("Fan/DDW contribution at Gamma:\n")
for iband in N.arange(vband):
O.write('Band: '+str(iband)+" FAN: "+str(total_corr[1,0,0,iband].real*Ha2eV)+"\n")
O.write(' '+ " DDW: "+str(-total_corr[2,0,0,iband].real*Ha2eV)+"\n")
O.write(' '+ " TOTAL: "+str(total_corr[0,0,0,iband].real*Ha2eV)+"\n")
O.write("Runtime: "+str(runtime.seconds)+' seconds (or '+str(float(runtime.seconds)/60.0)+' minutes)')
if lifetime:
with open(str(output)+"_BRD.txt","w") as O:
O.write("Total correction of the ZPM (eV) for "+str(nbQ)+" Q points\n")
for ikpt in N.arange(vkpt):
O.write('Kpt: '+str(tkpt[ikpt,:])+"\n")
j = 1
for ii in (brd_total[0,ikpt,:].real*Ha2eV):
# Create a new line every 6 values
if (j%6 == 0 and j !=0):
O.write(str(ii)+'\n')
j += 1
elif j == vband:
O.write(str(ii)+'\n')
else:
O.write(str(ii)+' ')
j += 1
O.write("Temperature dependence at Gamma\n")
for iband in N.arange(vband):
O.write('Band: '+str(iband)+"\n")
tt = 0
for T in temp_info:
O.write(str(T)+" "+str(brd_total[tt,0,iband].real*Ha2eV)+"\n")
tt += 1
O.write("Runtime: "+str(runtime.seconds)+' seconds (or '+str(float(runtime.seconds)/60.0)+' minutes)')
else:
with open(str(output)+".txt","w") as O:
O.write("Total correction of the ZPM (eV) for "+str(nbQ)+" Q points\n")
for ikpt in N.arange(vkpt):
O.write('Kpt: '+str(tkpt[ikpt,:])+"\n")
j = 1
for ii in (total_corr[0,ikpt,:].real*Ha2eV):
# Create a new line every 6 values
if (j%6 == 0 and j !=0):
O.write(str(ii)+'\n')
j += 1
elif j == vband:
O.write(str(ii)+'\n')
else:
O.write(str(ii)+' ')
j += 1
O.write("Fan/DDW contribution at Gamma:\n")
for iband in N.arange(vband):
O.write('Band: '+str(iband)+" FAN: "+str(total_corr[1,0,iband].real*Ha2eV)+"\n")
O.write(' '+ " DDW: "+str(-total_corr[2,0,iband].real*Ha2eV)+"\n")
O.write(' '+ " TOTAL: "+str(total_corr[0,0,iband].real*Ha2eV)+"\n")
O.write("Runtime: "+str(runtime.seconds)+' seconds (or '+str(float(runtime.seconds)/60.0)+' minutes)')
if lifetime:
with open(str(output)+"_BRD.txt","w") as O:
O.write("Total correction of the ZPM (eV) for "+str(nbQ)+" Q points\n")
for ikpt in N.arange(vkpt):
O.write('Kpt: '+str(tkpt[ikpt,:])+"\n")
j = 1
for ii in (brd_total[ikpt,:].real*Ha2eV):
# Create a new line every 6 values
if (j%6 == 0 and j !=0):
O.write(str(ii)+'\n')
j += 1
elif j == vband:
O.write(str(ii)+'\n')
else:
O.write(str(ii)+' ')
j += 1
O.write("Runtime: "+str(runtime.seconds)+' seconds (or '+str(float(runtime.seconds)/60.0)+' minutes)')
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