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[1D] Try harder to find non-extinct diffusion flames when using 'auto'

Browse source 
Increasing the density of grid points is more likely to lead to a non-extinct
solution, but takes longer to solve. To give good average-case performance,
first try solving on a grid with few points, then increase the number of points
until a reacting solution is found, if possible.
This commit is contained in:
Ray Speth 2016-03-25 19:13:21 -04:00
parent b56094b183
commit 77c744204e
5 changed files with 230 additions and 26 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

2
interfaces/cython/cantera/_cantera.pxd
View file

@ -999,6 +999,8 @@ cdef class Sim1D:
cdef CxxSim1D* sim
cdef readonly object domains
cdef object _initialized
cdef object _initial_guess_args
cdef object _initial_guess_kwargs
cdef Func1 interrupt
cdef class ReactionPathDiagram:

9
interfaces/cython/cantera/onedim.py
View file

@ -623,6 +623,9 @@ class CounterflowDiffusionFlame(FlameBase):
for k,spec in enumerate(self.gas.species_names):
self.set_profile(spec, zrel, Y[:,k])
def extinct(self):
return max(self.T) - max(self.fuel_inlet.T, self.oxidizer_inlet.T) < 10
def solve(self, loglevel=1, refine_grid=True, auto=False):
"""
Solve the problem.
@ -644,10 +647,8 @@ class CounterflowDiffusionFlame(FlameBase):
super(CounterflowDiffusionFlame, self).solve(loglevel, refine_grid, auto)
# Do some checks if loglevel is set
if loglevel > 0:
# Check if flame is extinct
if max(self.T) - max(self.fuel_inlet.T, self.oxidizer_inlet.T) < 1.0:
if self.extinct():
print('WARNING: Flame is extinct.')
return
# Check if the flame is very thick
# crude width estimate based on temperature
@ -835,7 +836,7 @@ class ImpingingJet(FlameBase):
used to form the initial guess. Otherwise the inlet composition will
be used.
"""
super(ImpingingJet, self).set_initial_guess()
super(ImpingingJet, self).set_initial_guess(products=products)
Y0 = self.inlet.Y
T0 = self.inlet.T

92
interfaces/cython/cantera/onedim.pyx
View file

@ -533,6 +533,8 @@ cdef class Sim1D:
self.domains = tuple(domains)
self.set_interrupt(interrupts.no_op)
self._initialized = False
self._initial_guess_args = ()
self._initial_guess_kwargs = {}
def set_interrupt(self, f):
"""
@ -722,12 +724,14 @@ cdef class Sim1D:
def __set__(self, nmax):
self.sim.setMaxTimeStepCount(nmax)
def set_initial_guess(self):
def set_initial_guess(self, *args, **kwargs):
"""
Set the initial guess for the solution. Derived classes extend this
function to set approximations for the temperature and composition
profiles.
"""
self._initial_guess_args = args
self._initial_guess_kwargs = kwargs
self._get_initial_solution()
self._initialized = True
@ -739,6 +743,13 @@ cdef class Sim1D:
self.sim.resize()
self.sim.getInitialSoln()
def extinct(self):
"""
Method overloaded for some flame types to indicate if the flame has been
extinguished. Base class method always returns 'False'
"""
return False
def solve(self, loglevel=1, refine_grid=True, auto=False):
"""
Solve the problem.
@ -757,10 +768,10 @@ cdef class Sim1D:
transport is enabled, an additional solution using these options
will be calculated.
"""
if not self._initialized:
self.set_initial_guess()
if not auto:
if not self._initialized:
self.set_initial_guess()
self.sim.solve(loglevel, <cbool>refine_grid)
return
@ -784,28 +795,65 @@ cdef class Sim1D:
if isinstance(dom, _FlowBase):
dom.set_transport(self.gas)
def log(msg):
def log(msg, *args):
if loglevel:
print('\n{:*^78s}'.format(' ' + msg + ' '))
print('\n{:*^78s}'.format(' ' + msg.format(*args) + ' '))
try:
# Try solving with energy enabled, which usually works
log('Solving on initial grid with energy equation enabled')
self.energy_enabled = True
self.sim.solve(loglevel, <cbool>False)
except Exception:
# If initial solve using energy equation fails, fall back on the
# traditional fixed temperature solve followed by solving the energy
# equation
log('Initial solve failed; Retrying with energy equation disabled')
self.energy_enabled = False
self.sim.solve(loglevel, <cbool>False)
log('Solving on initial grid with energy equation re-enabled')
self.energy_enabled = True
self.sim.solve(loglevel, <cbool>False)
flow_domains = [D for D in self.domains if isinstance(D, _FlowBase)]
zmin = [D.grid[0] for D in flow_domains]
zmax = [D.grid[-1] for D in flow_domains]
nPoints = [len(flow_domains[0].grid), 12, 24, 48]
log('Solving with grid refinement enabled')
self.sim.solve(loglevel, <cbool>True)
for N in nPoints:
for i,D in enumerate(flow_domains):
if N != len(D.grid):
D.grid = np.linspace(zmin[i], zmax[i], N)
self.set_initial_guess(*self._initial_guess_args,
**self._initial_guess_kwargs)
try:
# Try solving with energy enabled, which usually works
log('Solving on {} point grid with energy equation enabled', N)
self.energy_enabled = True
self.sim.solve(loglevel, <cbool>False)
solved = True
except Exception:
solved = False
if not solved:
# If initial solve using energy equation fails, fall back on the
# traditional fixed temperature solve followed by solving the energy
# equation
log('Initial solve failed; Retrying with energy equation disabled')
try:
self.energy_enabled = False
self.sim.solve(loglevel, <cbool>False)
log('Solving on {} point grid with energy equation re-enabled', N)
self.energy_enabled = True
self.sim.solve(loglevel, <cbool>False)
solved = True
except Exception:
pass
if solved and not self.extinct():
# Found a non-extinct solution on the fixed grid
log('Solving with grid refinement enabled')
try:
self.sim.solve(loglevel, <cbool>True)
solved = True
except Exception:
solved = False
if solved and not self.extinct():
# Found a non-extinct solution on the refined grid
break
if self.extinct():
log('Flame is extinct on {} point grid', N)
if not solved:
raise Exception('Could not find a solution for the 1D problem')
if solve_multi:
log('Solving with multicomponent transport')

22
interfaces/cython/cantera/test/test_onedim.py
View file

@ -515,6 +515,28 @@ class TestDiffusionFlame(utilities.CanteraTest):
rtol=1e-2, atol=1e-8, xtol=1e-2)
self.assertFalse(bad, bad)
def test_auto(self, saveReference=False):
referenceFile = '../data/DiffusionFlameTest-h2-auto.csv'
self.create_sim(p=ct.one_atm, mdot_fuel=2, mdot_ox=3)
self.sim.set_refine_criteria(ratio=3.0, slope=0.1, curve=0.12, prune=0.0)
self.sim.solve(loglevel=0, auto=True)
data = np.empty((self.sim.flame.n_points, self.gas.n_species + 4))
data[:,0] = self.sim.grid
data[:,1] = self.sim.u
data[:,2] = self.sim.V
data[:,3] = self.sim.T
data[:,4:] = self.sim.Y.T
if saveReference:
np.savetxt(referenceFile, data, '%11.6e', ', ')
else:
bad = utilities.compareProfiles(referenceFile, data,
rtol=1e-2, atol=1e-8, xtol=1e-2)
self.assertFalse(bad, bad)
def test_mixture_averaged_rad(self, saveReference=False):
referenceFile = '../data/DiffusionFlameTest-h2-mix-rad.csv'
self.create_sim(p=ct.one_atm)

131
test/data/DiffusionFlameTest-h2-auto.csv Normal file
View file

@ -0,0 +1,131 @@
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2.727273e-03, 2.107956e+00, 8.747110e+01, 3.000000e+02, 4.803846e-02, 3.076615e-12, -9.206271e-18, 3.648117e-17, -1.356760e-20, 1.357178e-16, -6.185646e-22, -1.611992e-18, 9.519615e-01
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1.136364e-02, -3.493912e-01, 1.861885e+02, 3.151847e+02, 1.143125e-05, 2.604979e-12, 1.190406e-07, 1.663805e-01, 4.309122e-07, 7.373645e-04, 3.255774e-07, 5.112003e-07, 8.328693e-01
1.147727e-02, -3.792007e-01, 1.827507e+02, 3.050536e+02, 7.274235e-06, 4.030020e-13, 4.705999e-08, 1.666839e-01, 1.681183e-07, 2.514269e-04, 9.843571e-08, 1.619801e-07, 8.330569e-01
1.159091e-02, -4.157647e-01, 1.799630e+02, 3.015719e+02, 4.527040e-06, 6.599135e-14, 1.851056e-08, 1.667907e-01, 6.523427e-08, 8.063071e-05, 2.906551e-08, 4.782429e-08, 8.331240e-01
1.170455e-02, -4.547509e-01, 1.774209e+02, 3.004745e+02, 2.783584e-06, 1.130824e-14, 7.245806e-09, 1.668256e-01, 2.518603e-08, 2.517051e-05, 8.428804e-09, 1.366978e-08, 8.331464e-01
1.181818e-02, -4.942675e-01, 1.749588e+02, 3.001523e+02, 1.716513e-06, 2.178611e-15, 2.958722e-09, 1.668364e-01, 1.015651e-08, 8.335471e-06, 2.620153e-09, 4.175857e-09, 8.331535e-01
1.204545e-02, -5.724405e-01, 1.700852e+02, 3.000218e+02, 6.678999e-07, 1.245207e-16, 5.989042e-10, 1.668412e-01, 2.019752e-09, 1.247001e-06, 3.563961e-10, 5.584310e-10, 8.331569e-01
1.227273e-02, -6.486045e-01, 1.652237e+02, 3.000034e+02, 2.645695e-07, 8.645795e-18, 1.300687e-10, 1.668420e-01, 4.315529e-10, 2.040442e-07, 5.322297e-11, 8.217212e-11, 8.331575e-01
1.272727e-02, -7.943791e-01, 1.555042e+02, 3.000002e+02, 4.767898e-08, 1.075811e-19, 1.057214e-11, 1.668422e-01, 3.440013e-11, 1.184686e-08, 2.759980e-12, 4.220606e-12, 8.331578e-01
1.318182e-02, -9.313276e-01, 1.457852e+02, 3.000000e+02, 7.813133e-09, 1.146736e-21, 7.572754e-13, 1.668422e-01, 2.415269e-12, 6.009059e-10, 1.245276e-13, 1.888831e-13, 8.331578e-01
1.363636e-02, -1.059442e+00, 1.360661e+02, 3.000000e+02, 1.389403e-09, 1.944693e-23, 6.124242e-14, 1.668422e-01, 1.915919e-13, 3.476772e-11, 6.426039e-15, 9.671323e-15, 8.331578e-01
1.454545e-02, -1.289164e+00, 1.166281e+02, 3.000000e+02, 8.948169e-11, 6.380816e-27, 1.637773e-15, 1.668422e-01, 5.018671e-15, 6.516802e-13, 1.068082e-16, 1.594839e-16, 8.331578e-01
1.545455e-02, -1.483544e+00, 9.719011e+01, 3.000000e+02, 5.140146e-12, 4.167863e-29, 3.849461e-17, 1.668422e-01, 1.155173e-16, 1.070030e-14, 1.553757e-18, 2.301627e-18, 8.331578e-01
1.636364e-02, -1.642582e+00, 7.775208e+01, 3.000000e+02, 3.441215e-13, 6.222340e-32, 1.074486e-18, 1.668422e-01, 3.158513e-18, 2.095085e-16, 2.698246e-20, 3.965305e-20, 8.331578e-01
1.818182e-02, -1.854633e+00, 3.887604e+01, 3.000000e+02, 8.096075e-15, 1.405620e-35, 1.019494e-20, 1.668422e-01, 2.934225e-20, 1.384712e-18, 1.578809e-22, 2.301441e-22, 8.331578e-01
2.000000e-02, -1.925317e+00, 0.000000e+00, 3.000000e+02, 1.837957e-16, 4.948927e-37, 9.324517e-23, 1.668422e-01, 2.627569e-22, 8.820295e-21, 8.902653e-25, 1.287438e-24, 8.331578e-01
1 0.000000e+00 2.346514e+00 -1.016622e-19 3.000000e+02 4.803846e-02 1.106492e-15 -1.044084e-17 3.646972e-17 -9.486255e-19 8.829205e-19 -1.732232e-21 -1.613005e-18 9.519615e-01
2 9.090909e-04 2.320008e+00 2.915703e+01 3.000000e+02 4.803846e-02 1.587564e-14 -1.003015e-17 3.647355e-17 -4.548035e-20 -5.083179e-19 -1.387481e-21 -1.613170e-18 9.519615e-01
3 1.818182e-03 2.240488e+00 5.831406e+01 3.000000e+02 4.803846e-02 2.244657e-13 -9.621839e-18 3.647734e-17 -1.513487e-20 1.301516e-18 -1.028654e-21 -1.612512e-18 9.519615e-01
4 2.727273e-03 2.107956e+00 8.747110e+01 3.000000e+02 4.803846e-02 3.076615e-12 -9.206271e-18 3.648117e-17 -1.356760e-20 1.357178e-16 -6.185646e-22 -1.611992e-18 9.519615e-01
5 3.636364e-03 1.922412e+00 1.166281e+02 3.000000e+02 4.803846e-02 3.993721e-11 -8.770397e-18 3.648478e-17 -1.289792e-20 7.563010e-15 2.385253e-22 -1.611465e-18 9.519615e-01
6 4.545455e-03 1.683854e+00 1.457852e+02 3.000000e+02 4.803845e-02 4.776304e-10 -8.253035e-18 3.648465e-17 -1.213900e-20 3.812263e-13 6.472221e-21 -1.610916e-18 9.519615e-01
7 5.454545e-03 1.392284e+00 1.749422e+02 3.000001e+02 4.803841e-02 5.084477e-09 -6.147613e-18 3.648921e-17 -8.966477e-21 1.689255e-11 6.564647e-20 -1.609878e-18 9.519616e-01
8 5.909091e-03 1.226619e+00 1.895207e+02 3.000008e+02 4.803818e-02 2.100198e-08 1.103190e-17 3.733130e-17 1.772683e-20 2.462511e-10 1.856237e-19 -1.608934e-18 9.519618e-01
9 6.363636e-03 1.047708e+00 2.040994e+02 3.000074e+02 4.803646e-02 9.223605e-08 2.262732e-16 5.516455e-17 3.750898e-19 4.083332e-09 6.909946e-19 -1.604081e-18 9.519634e-01
10 6.590909e-03 9.533054e-01 2.113894e+02 3.000278e+02 4.803197e-02 2.077003e-07 1.148578e-15 1.691033e-16 2.132805e-18 2.533190e-08 2.586525e-18 -1.583046e-18 9.519678e-01
11 6.818182e-03 8.556801e-01 2.186823e+02 3.001132e+02 4.801583e-02 4.810641e-07 6.242559e-15 1.080162e-15 1.518364e-17 1.763845e-07 1.695742e-17 -1.427011e-18 9.519835e-01
12 7.045455e-03 7.550768e-01 2.259872e+02 3.004401e+02 4.796187e-02 1.096771e-06 3.218764e-14 7.869029e-15 1.257710e-16 1.154231e-06 1.232936e-16 -3.167907e-19 9.520359e-01
13 7.159091e-03 7.039403e-01 2.296545e+02 3.009050e+02 4.789304e-02 1.673816e-06 8.102352e-14 2.693029e-14 4.733658e-16 3.409138e-06 4.194889e-16 2.506200e-18 9.521019e-01
14 7.272727e-03 6.526849e-01 2.333533e+02 3.019041e+02 4.775828e-02 2.570097e-06 2.125937e-13 1.003296e-13 1.991833e-15 1.069395e-05 1.545487e-15 1.248983e-17 9.522285e-01
15 7.386364e-03 6.019264e-01 2.371195e+02 3.039559e+02 4.750570e-02 3.950053e-06 5.524984e-13 3.800492e-13 8.661555e-15 3.285558e-05 5.729947e-15 4.583971e-17 9.524575e-01
16 7.443182e-03 5.771169e-01 2.390513e+02 3.057162e+02 4.730432e-02 4.921955e-06 9.127856e-13 8.207747e-13 1.997307e-14 5.938965e-05 1.213704e-14 8.949258e-17 9.526314e-01
17 7.500000e-03 5.530320e-01 2.410472e+02 3.082765e+02 4.702877e-02 6.147103e-06 1.524316e-12 1.837818e-12 4.706623e-14 1.091076e-04 2.645624e-14 1.775220e-16 9.528560e-01
18 7.556818e-03 5.299541e-01 2.431410e+02 3.119319e+02 4.665949e-02 7.689688e-06 2.542459e-12 4.177351e-12 1.113306e-13 1.994089e-04 5.793858e-14 3.500930e-16 9.531334e-01
19 7.613636e-03 5.081954e-01 2.453803e+02 3.170480e+02 4.617576e-02 9.629703e-06 4.203187e-12 9.558539e-12 2.607858e-13 3.578852e-04 1.260652e-13 6.785742e-16 9.534567e-01
20 7.670455e-03 4.880730e-01 2.478298e+02 3.240584e+02 4.555792e-02 1.206542e-05 6.851452e-12 2.194036e-11 5.991184e-13 6.256955e-04 2.708360e-13 1.285299e-15 9.538043e-01
21 7.727273e-03 4.698711e-01 2.505736e+02 3.334511e+02 4.479008e-02 1.511478e-05 1.096647e-11 5.038060e-11 1.338188e-12 1.059986e-03 5.716754e-13 2.373580e-15 9.541348e-01
22 7.784091e-03 4.537957e-01 2.537147e+02 3.457433e+02 4.386321e-02 1.891455e-05 1.716808e-11 1.152933e-10 2.879542e-12 1.733712e-03 1.179671e-12 4.275366e-15 9.543842e-01
23 7.840909e-03 4.399290e-01 2.573713e+02 3.614455e+02 4.277741e-02 2.361627e-05 2.617802e-11 2.615310e-10 5.914000e-12 2.731289e-03 2.367664e-12 7.536316e-15 9.544677e-01
24 7.897727e-03 4.281946e-01 2.616689e+02 3.810203e+02 4.154286e-02 2.937860e-05 3.870999e-11 5.841017e-10 1.150782e-11 4.139665e-03 4.599879e-12 1.309066e-14 9.542881e-01
25 7.954545e-03 4.183436e-01 2.667284e+02 4.048439e+02 4.017864e-02 3.635644e-05 5.530246e-11 1.274996e-09 2.120558e-11 6.036329e-03 8.617170e-12 2.265797e-14 9.537487e-01
26 8.011364e-03 4.099639e-01 2.726514e+02 4.331766e+02 3.871004e-02 4.468856e-05 7.623736e-11 2.701172e-09 3.768713e-11 8.477549e-03 1.552751e-11 3.968852e-14 9.527677e-01
27 8.068182e-03 4.025114e-01 2.795063e+02 4.661468e+02 3.716497e-02 5.448594e-05 1.019548e-10 5.522266e-09 6.906180e-11 1.149030e-02 2.688766e-11 7.168974e-14 9.512902e-01
28 8.125000e-03 3.953546e-01 2.873178e+02 5.037491e+02 3.557062e-02 6.582275e-05 1.348531e-10 1.085074e-08 1.514591e-10 1.506987e-02 4.476300e-11 1.361934e-13 9.492937e-01
29 8.181818e-03 3.878229e-01 2.960608e+02 5.458553e+02 3.395118e-02 7.873145e-05 1.844868e-10 2.044787e-08 4.508717e-10 1.918285e-02 7.175688e-11 2.769326e-13 9.467872e-01
30 8.238636e-03 3.792529e-01 3.056599e+02 5.922338e+02 3.232654e-02 9.320245e-05 2.820676e-10 3.694000e-08 1.662892e-09 2.377364e-02 1.110070e-10 6.105165e-13 9.438066e-01
31 8.295455e-03 3.690267e-01 3.159950e+02 6.425739e+02 3.071213e-02 1.091877e-04 5.244051e-10 6.403584e-08 6.519750e-09 2.877220e-02 1.661180e-10 1.469317e-12 9.404064e-01
32 8.409091e-03 3.418774e-01 3.383157e+02 7.536436e+02 2.768207e-02 1.437418e-04 2.231956e-09 1.590863e-07 7.042887e-08 3.923180e-02 3.149816e-10 7.354554e-12 9.329421e-01
33 8.522727e-03 3.024618e-01 3.613466e+02 8.752902e+02 2.477749e-02 1.827831e-04 1.335250e-08 3.545834e-07 5.244761e-07 5.028152e-02 5.561366e-10 4.853066e-11 9.247573e-01
34 8.636364e-03 2.492918e-01 3.836266e+02 1.004727e+03 2.201771e-02 2.252821e-04 7.285181e-08 7.320831e-07 2.753646e-06 6.146915e-02 9.417260e-10 3.134054e-10 9.162843e-01
35 8.750000e-03 1.820505e-01 4.038325e+02 1.139232e+03 1.940868e-02 2.702367e-04 3.288939e-07 1.488810e-06 1.088617e-05 7.242836e-02 1.631533e-09 1.658488e-09 9.078800e-01
36 8.863636e-03 1.014207e-01 4.209234e+02 1.276422e+03 1.695025e-02 3.167148e-04 1.237366e-06 3.210746e-06 3.443748e-05 8.287933e-02 3.146302e-09 6.628903e-09 8.998148e-01
37 8.977273e-03 8.796660e-03 4.341996e+02 1.414122e+03 1.463959e-02 3.638341e-04 4.003598e-06 7.658258e-06 9.161439e-05 9.261750e-02 7.019284e-09 1.895414e-08 8.922758e-01
38 9.090909e-03 -9.393661e-02 4.432964e+02 1.550299e+03 1.247315e-02 4.106768e-04 1.152264e-05 1.997234e-05 2.131802e-04 1.014943e-01 1.744113e-08 3.743718e-08 8.853771e-01
39 9.204545e-03 -2.045760e-01 4.482735e+02 1.682775e+03 1.044702e-02 4.560807e-04 3.037121e-05 5.452855e-05 4.472404e-04 1.094066e-01 4.537060e-08 5.493210e-08 8.791580e-01
40 9.318182e-03 -3.207256e-01 4.493729e+02 1.809355e+03 8.560018e-03 4.982275e-04 7.515563e-05 1.514121e-04 8.661874e-04 1.162381e-01 1.181083e-07 6.978120e-08 8.736107e-01
41 9.431818e-03 -4.398045e-01 4.469301e+02 1.927395e+03 6.817207e-03 5.338266e-04 1.772930e-04 4.185889e-04 1.573397e-03 1.217925e-01 2.955944e-07 8.637315e-08 8.686868e-01
42 9.488636e-03 -4.994228e-01 4.444800e+02 1.981915e+03 5.994411e-03 5.474032e-04 2.704667e-04 7.221946e-04 2.080978e-03 1.239913e-01 4.710032e-07 9.777094e-08 8.663927e-01
43 9.545455e-03 -5.586209e-01 4.412675e+02 2.032811e+03 5.218936e-03 5.564546e-04 4.064382e-04 1.218532e-03 2.708947e-03 1.256762e-01 7.268900e-07 1.115831e-07 8.642137e-01
44 9.602273e-03 -6.169219e-01 4.373408e+02 2.079354e+03 4.497214e-03 5.594173e-04 5.995332e-04 2.019934e-03 3.462973e-03 1.267422e-01 1.088469e-06 1.280921e-07 8.621176e-01
45 9.630682e-03 -6.455377e-01 4.351225e+02 2.100690e+03 4.157485e-03 5.580308e-04 7.225606e-04 2.594550e-03 3.885463e-03 1.270008e-01 1.320351e-06 1.374642e-07 8.610796e-01
46 9.659091e-03 -6.737238e-01 4.327404e+02 2.120628e+03 3.834218e-03 5.545400e-04 8.640760e-04 3.305775e-03 4.332516e-03 1.270604e-01 1.585007e-06 1.473418e-07 8.600468e-01
47 9.687500e-03 -7.014059e-01 4.302001e+02 2.139065e+03 3.528254e-03 5.488050e-04 1.024335e-03 4.176742e-03 4.798185e-03 1.269089e-01 1.882429e-06 1.575896e-07 8.590128e-01
48 9.715909e-03 -7.285084e-01 4.275070e+02 2.155901e+03 3.240221e-03 5.407522e-04 1.202585e-03 5.229618e-03 5.274736e-03 1.265379e-01 2.211062e-06 1.680399e-07 8.579718e-01
49 9.744318e-03 -7.549558e-01 4.246667e+02 2.171043e+03 2.970473e-03 5.303832e-04 1.397012e-03 6.484352e-03 5.753014e-03 1.259434e-01 2.567815e-06 1.785063e-07 8.569186e-01
50 9.772727e-03 -7.806726e-01 4.216841e+02 2.184405e+03 2.719063e-03 5.177777e-04 1.604770e-03 7.957458e-03 6.222981e-03 1.251260e-01 2.948303e-06 1.888008e-07 8.558488e-01
51 9.801136e-03 -8.055845e-01 4.185644e+02 2.195908e+03 2.485734e-03 5.030899e-04 1.822128e-03 9.661053e-03 6.674347e-03 1.240906e-01 3.347248e-06 1.987497e-07 8.547595e-01
52 9.829545e-03 -8.296181e-01 4.153125e+02 2.205481e+03 2.269943e-03 4.865361e-04 2.044721e-03 1.160230e-02 7.097217e-03 1.228464e-01 3.758959e-06 2.082069e-07 8.536489e-01
53 9.857955e-03 -8.527015e-01 4.119329e+02 2.213054e+03 2.070915e-03 4.683787e-04 2.267850e-03 1.378332e-02 7.482632e-03 1.214057e-01 4.177821e-06 2.170616e-07 8.525168e-01
54 9.886364e-03 -8.747639e-01 4.084304e+02 2.218565e+03 1.887707e-03 4.489070e-04 2.486791e-03 1.620160e-02 7.822954e-03 1.197829e-01 4.598713e-06 2.252422e-07 8.513643e-01
55 9.914773e-03 -8.957359e-01 4.048092e+02 2.221950e+03 1.719272e-03 4.284190e-04 2.697052e-03 1.885061e-02 8.112074e-03 1.179938e-01 5.017330e-06 2.327164e-07 8.501936e-01
56 9.943182e-03 -9.155494e-01 4.010738e+02 2.223151e+03 1.564525e-03 4.072064e-04 2.894574e-03 2.172065e-02 8.345457e-03 1.160543e-01 5.430396e-06 2.394883e-07 8.490076e-01
57 9.971591e-03 -9.341377e-01 3.972281e+02 2.222108e+03 1.422393e-03 3.855433e-04 3.075846e-03 2.479968e-02 8.520075e-03 1.139802e-01 5.835781e-06 2.455958e-07 8.478102e-01
58 1.000000e-02 -9.514356e-01 3.932763e+02 2.218766e+03 1.291845e-03 3.636788e-04 3.237960e-03 2.807410e-02 8.634274e-03 1.117862e-01 6.232567e-06 2.511071e-07 8.466055e-01
59 1.002841e-02 -9.673798e-01 3.892222e+02 2.213071e+03 1.171921e-03 3.418334e-04 3.378616e-03 3.152926e-02 8.687606e-03 1.094860e-01 6.621074e-06 2.561192e-07 8.453979e-01
60 1.005682e-02 -9.819090e-01 3.850697e+02 2.204973e+03 1.061737e-03 3.201977e-04 3.496092e-03 3.515000e-02 8.680664e-03 1.070919e-01 7.002900e-06 2.607565e-07 8.441921e-01
61 1.008523e-02 -9.949643e-01 3.808224e+02 2.194424e+03 9.604883e-04 2.989338e-04 3.589187e-03 3.892086e-02 8.614934e-03 1.046152e-01 7.380955e-06 2.651711e-07 8.429928e-01
62 1.011364e-02 -1.006489e+00 3.764839e+02 2.181381e+03 8.674430e-04 2.781783e-04 3.657106e-03 4.282635e-02 8.492688e-03 1.020658e-01 7.759594e-06 2.695455e-07 8.418044e-01
63 1.017045e-02 -1.024737e+00 3.675461e+02 2.147717e+03 7.031502e-04 2.383739e-04 3.716480e-03 5.101404e-02 8.088814e-03 9.676004e-02 8.541836e-06 2.789513e-07 8.394703e-01
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101 1.098011e-02 -5.040561e-01 2.215577e+02 6.727675e+02 3.738939e-05 3.258694e-07 1.611885e-05 1.558484e-01 4.585900e-05 1.549649e-02 5.650515e-05 1.149118e-05 8.284874e-01
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128 1.545455e-02 -1.483544e+00 9.719011e+01 3.000000e+02 5.140146e-12 4.167863e-29 3.849461e-17 1.668422e-01 1.155173e-16 1.070030e-14 1.553757e-18 2.301627e-18 8.331578e-01
129 1.636364e-02 -1.642582e+00 7.775208e+01 3.000000e+02 3.441215e-13 6.222340e-32 1.074486e-18 1.668422e-01 3.158513e-18 2.095085e-16 2.698246e-20 3.965305e-20 8.331578e-01
130 1.818182e-02 -1.854633e+00 3.887604e+01 3.000000e+02 8.096075e-15 1.405620e-35 1.019494e-20 1.668422e-01 2.934225e-20 1.384712e-18 1.578809e-22 2.301441e-22 8.331578e-01
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