License
LRTvsFisher
Mon Jun 01 09:20:00 2020\ Copyright 2020\ Sandro Dias Pinto Vitenti vitenti@uel.br
LRTvsFisher\ Copyright (C) 2020 Sandro Dias Pinto Vitenti vitenti@uel.br
numcosmo is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
numcosmo is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.
Example to compare the results from Likelihood ratio test (profile likelihood) and Fisher matrix methods. For this, we obtain constraints (68.27% contour) on the cold dark matter density $\Omega_c$ and the dark energy equation of state $w$ parameters, where $w =$ constant, using type Ia supernova (SNeIa) and baryon acoustic oscillations (BAO) data.
The first step is to load both NumCosmo and NumCosmoMath libraries. We also load some Python packages.
In [1]:
try:
import gi
gi.require_version('NumCosmo', '1.0')
gi.require_version('NumCosmoMath', '1.0')
except:
pass
from gi.repository import GObject
from gi.repository import NumCosmo as Nc
from gi.repository import NumCosmoMath as Ncm
import sys
import math
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
In [2]:
__name__ = "NcContext"
Ncm.cfg_init ()
Ncm.cfg_set_log_handler (lambda msg: sys.stdout.write (msg) and sys.stdout.flush ())
We first initialize the NcHICosmo object. It describes a cosmological model assuming a homogeneous and isotropic metric of the background.
In particular, we initialize a NcHICosmo child whose Dark Energy (DE) component is described by a barotropic fluid with constant equation of state, NcHICosmoDEXcdm.
One choice we make here is to parametrize the problem considering the curvature density parameter, $\Omega_k$, instead of the DE density parameter $\Omega_{DE}$. We then set the values for the others cosmological parameters:
The parameters that are not set here kepp the default values.
In [3]:
cosmo = Nc.HICosmo.new_from_name (Nc.HICosmo, "NcHICosmoDEXcdm{'massnu-length':<1>}")
cosmo.omega_x2omega_k ()
cosmo.param_set_by_name ("H0", 67.66)
cosmo.param_set_by_name ("Omegak", 0.0)
cosmo.param_set_by_name ("w", -0.8)
cosmo.param_set_by_name ("Omegab", 0.049)
cosmo.param_set_by_name ("Omegac", 0.2621)
cosmo.param_set_by_name ("massnu_0", 0.0)
cosmo.param_set_by_name ("ENnu", 3.046)
cosmo.param_set_by_name ("Tgamma0", 2.7255)
In [4]:
mset = Ncm.MSet ()
mset.set (cosmo)
Setting $\Omega_c$ and $w$ parameters to be fitted.
In [5]:
cosmo.props.Omegac_fit = True
cosmo.props.Omegax_fit = True
cosmo.props.w_fit = True
At this step we initialize the NcDistance object. This object computes the cosmological distances using an interpolation method (spline) as a matter of optimization.
The argument of the new function corresponds to the maximum redshift $z_{max}$ up to which the spline of the comoving distance will be prepared. The cosmological distances depend on the cosmological model.
Note that if the user calls a distance function at a redshift $z^\prime$ bigger than $z_{max}$, then the computation between $z_{max}$ and $z^\prime$ is performed by numerical integration.
In [6]:
zmax = 2.5
dist = Nc.Distance.new (zmax)
A new Data object NcmData from Type Ia supernovae (snia) catalogs. Distance modulus $\mu(z)$: $$\mu(z) = 5\log_{10}[c/H_0 * D_l(z)/(1\,\text{Mpc})] + 25,$$ where $c$ is the speed of light and $D_l(z) = (1 + z) D_M(z)$ is the luminosity distance.
New data objects from baryon acoustic oscillations (BAO). $$D_V(z) \equiv \left[ z D_M(z)^2 D_H(z) \right]^{1/3},$$ and $r_d$, i.e., the sound horizon at the drag redshift, $$r_d \equiv r_s (z_d) = \frac{1}{H_0} \int_{z_d}^{\infty} dz \frac{c_s(z)}{E(z)},$$ where $c_s(z)$ is the sound wave speed in the photon-baryon fluid.
The transverse distances is
$$ D_M(z) = \left\{ \begin{array}{ll} K^{-1} \sin\left(K \chi (z)\right) &\mbox{for $\Omega_k < 0$,} \\ \chi (z) &\mbox{for $\Omega_k = 0$,} \\ K^{-1} \sinh\left(K \chi (z)\right) &\mbox{for $\Omega_k > 0$,} \end{array} \right. $$where $K = \frac{H_0 \sqrt{\vert\Omega^0_k\vert}}{c}$, and the comoving distance is $$ \chi (z) = \frac{c}{H_0} \int_0^z \frac{dz^\prime}{E(z^\prime)},$$ $E(z) = \frac{H(z)}{H_0}$ is the normalized Hubble function.
In [7]:
snia = Nc.DataDistMu.new_from_id (dist, Nc.DataSNIAId.SIMPLE_UNION2_1)
bao1 = Nc.data_bao_create (dist, Nc.DataBaoId.RDV_BEUTLER2011)
bao2 = Nc.data_bao_create (dist, Nc.DataBaoId.RDV_BOSS_QSO_ATA2017)
In [8]:
dset = Ncm.Dataset ()
dset.append_data (snia)
dset.append_data (bao1)
dset.append_data (bao2)
In [9]:
lh = Ncm.Likelihood (dataset = dset)
In [10]:
fit = Ncm.Fit.new (Ncm.FitType.NLOPT, "ln-neldermead", lh, mset, Ncm.FitGradType.NUMDIFF_FORWARD)
In [11]:
fit.run (Ncm.FitRunMsgs.SIMPLE)
fit.log_info ()
fit.numdiff_m2lnL_covar ()
fit.log_covar ()
#----------------------------------------------------------------------------------
# Model fitting. Interating using:
# - solver: NLOpt:ln-neldermead
# - differentiation: Numerical differentiantion (forward)
#............................
# Minimum found with precision: |df|/f = 1.00000e-08 and |dx| = 1.00000e-05
# Elapsed time: 00 days, 00:00:00.3275360
# iteration [000192]
# function evaluations [000194]
# gradient evaluations [000000]
# degrees of freedom [000578]
# m2lnL = 562.232483109849 ( 562.2132 0.01203794 0.0072416001 )
# Fit parameters:
# 0.22879852589591 0.166425955933339 -1.25244635950561
#----------------------------------------------------------------------------------
# Data used:
# - Union2.1 sample
# - 6dFGRS -- Beutler (2011), BAO Sample R-Dv
# - BOSS DR14 QSO -- Ata et al. (2017), BAO Sample Dv_r
#----------------------------------------------------------------------------------
# Model[01000]:
# - NcHICosmo : XCDM - Constant EOS
#----------------------------------------------------------------------------------
# Model parameters
# - H0[00]: 67.66 [FIXED]
# - Omegac[01]: 0.22879852589591 [FREE]
# - Omegak[02]: 0.166425955933339 [FREE]
# - Tgamma0[03]: 2.7255 [FIXED]
# - Yp[04]: 0.24 [FIXED]
# - ENnu[05]: 3.046 [FIXED]
# - Omegab[06]: 0.049 [FIXED]
# - w[07]: -1.25244635950561 [FREE]
# - massnu_0[08]: 0 [FIXED]
# - Tnu_0[09]: 0.71611 [FIXED]
# - munu_0[10]: 0 [FIXED]
# - gnu_0[11]: 1 [FIXED]
#----------------------------------------------------------------------------------
# NcmMSet parameters covariance matrix
# ----------------------------------------------
# Omegac[01000:01] = 0.2288 +/- 0.03506 | 1 | -0.3509 | -0.03835 |
# Omegak[01000:02] = 0.1664 +/- 0.1743 | -0.3509 | 1 | -0.897 |
# w[01000:07] = -1.252 +/- 0.3728 | -0.03835 | -0.897 | 1 |
# ----------------------------------------------
In [12]:
p1 = Ncm.MSetPIndex.new (cosmo.id (), Nc.HICosmoDESParams.OMEGA_C)
p2 = Ncm.MSetPIndex.new (cosmo.id (), Nc.HICosmoDEXCDMSParams.W)
lhr2d = Ncm.LHRatio2d.new (fit, p1, p2, 1.0e-3)
Calculating the confidence region using the Likelihood ratio test. Also using the Fisher matrix approach.
In [13]:
cr_rg = lhr2d.conf_region (0.6827, 300.0, Ncm.FitRunMsgs.SIMPLE)
fisher_rg = lhr2d.fisher_border (0.6827, 300.0, Ncm.FitRunMsgs.SIMPLE)
cr_p1array = cr_rg.p1.dup_array ()
cr_p2array = cr_rg.p2.dup_array ()
fisher_p1array = fisher_rg.p1.dup_array ()
fisher_p2array = fisher_rg.p2.dup_array ()
#----------------------------------------------------------------------------------
# Likelihood ratio confidence region at 68.270%, bestfit [ 0.22879853 -1.2524464]:
#
# looking root in interval [ 0 1.5151948]:
#........
# root found at 1.4057724 with precision 1.00000000e-03.
# border found at 1.4057724.
#.
# looking root in interval [ 7.0669608 8.6377572]:
#...
# root found at 8.0281606 with precision 1.00000000e-03.
# looking root in interval [ 7.2427624 8.8135588]:
#....
# root found at 8.0329703 with precision 1.00000000e-03.
# looking root in interval [ 7.2475721 8.8183684]:
#...
# root found at 8.0382076 with precision 1.00000000e-03.
# looking root in interval [ 7.2528094 8.8236057]:
#...
# root found at 8.0434138 with precision 1.00000000e-03.
# looking root in interval [ 7.2580157 8.828812]:
#...
# root found at 8.0488754 with precision 1.00000000e-03.
# looking root in interval [ 7.2634772 8.8342735]:
#...
# root found at 8.0545137 with precision 1.00000000e-03.
# looking root in interval [ 7.2691155 8.8399118]:
#...
# root found at 8.0602835 with precision 1.00000000e-03.
# looking root in interval [ 7.2748854 8.8456817]:
#...
# root found at 8.0662812 with precision 1.00000000e-03.
# looking root in interval [ 7.280883 8.8516794]:
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# root found at 8.0724892 with precision 1.00000000e-03.
# looking root in interval [ 7.2870911 8.8578874]:
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# root found at 8.079074 with precision 1.00000000e-03.
# looking root in interval [ 7.2936758 8.8644721]:
#...
# root found at 8.0853375 with precision 1.00000000e-03.
# looking root in interval [ 7.2999393 8.8707356]:
#...
# root found at 8.0924051 with precision 1.00000000e-03.
# looking root in interval [ 7.307007 8.8778033]:
#...
# root found at 8.0995406 with precision 1.00000000e-03.
# looking root in interval [ 7.3141425 8.8849388]:
#...
# root found at 8.1069144 with precision 1.00000000e-03.
# looking root in interval [ 7.3215162 8.8923125]:
#...
# root found at 8.114591 with precision 1.00000000e-03.
# looking root in interval [ 7.3291928 8.8999892]:
#...
# root found at 8.1225598 with precision 1.00000000e-03.
# looking root in interval [ 7.3371616 8.9079579]:
#...
# root found at 8.1308277 with precision 1.00000000e-03.
# looking root in interval [ 7.3454295 8.9162259]:
#....
# root found at 8.139423 with precision 1.00000000e-03.
# looking root in interval [ 7.3540248 8.9248211]:
#...
# root found at 8.1483595 with precision 1.00000000e-03.
# looking root in interval [ 7.3629613 8.9337576]:
#...
# root found at 8.158764 with precision 1.00000000e-03.
# looking root in interval [ 7.3733659 8.9441622]:
#...
# root found at 8.1662178 with precision 1.00000000e-03.
# looking root in interval [ 7.3808196 8.9516159]:
#......
# root found at 8.1773612 with precision 1.00000000e-03.
# looking root in interval [ 7.391963 8.9627594]:
#...
# root found at 8.1878846 with precision 1.00000000e-03.
# looking root in interval [ 7.4024864 8.9732828]:
#....
# root found at 8.198706 with precision 1.00000000e-03.
# looking root in interval [ 7.4133078 8.9841041]:
#...
# root found at 8.2100825 with precision 1.00000000e-03.
# looking root in interval [ 7.4246843 8.9954806]:
#...
# root found at 8.2219038 with precision 1.00000000e-03.
# looking root in interval [ 7.4365056 9.0073019]:
#...
# root found at 8.2341939 with precision 1.00000000e-03.
# looking root in interval [ 7.4487957 9.019592]:
#....
# root found at 8.2470312 with precision 1.00000000e-03.
# looking root in interval [ 7.461633 9.0324294]:
#...
# root found at 8.2603562 with precision 1.00000000e-03.
# looking root in interval [ 7.4749581 9.0457544]:
#...
# root found at 8.2742663 with precision 1.00000000e-03.
# looking root in interval [ 7.4888681 9.0596645]:
#...
# root found at 8.288746 with precision 1.00000000e-03.
# looking root in interval [ 7.5033478 9.0741442]:
#....
# root found at 8.3038175 with precision 1.00000000e-03.
# looking root in interval [ 7.5184193 9.0892156]:
#...
# root found at 8.3195007 with precision 1.00000000e-03.
# looking root in interval [ 7.5341025 9.1048988]:
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# root found at 8.3358315 with precision 1.00000000e-03.
# looking root in interval [ 7.5504333 9.1212296]:
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# root found at 8.3528219 with precision 1.00000000e-03.
# looking root in interval [ 7.5674237 9.1382201]:
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# root found at 8.3705003 with precision 1.00000000e-03.
# looking root in interval [ 7.5851022 9.1558985]:
#....
# root found at 8.3888696 with precision 1.00000000e-03.
# looking root in interval [ 7.6034714 9.1742677]:
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# root found at 8.4079613 with precision 1.00000000e-03.
# looking root in interval [ 7.6225631 9.1933595]:
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# root found at 8.4284975 with precision 1.00000000e-03.
# looking root in interval [ 7.6430993 9.2138957]:
#...
# root found at 8.4476884 with precision 1.00000000e-03.
# looking root in interval [ 7.6622903 9.2330866]:
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# root found at 8.4697262 with precision 1.00000000e-03.
# looking root in interval [ 7.684328 9.2551243]:
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# root found at 8.4918437 with precision 1.00000000e-03.
# looking root in interval [ 7.7064456 9.2772419]:
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# root found at 8.5147966 with precision 1.00000000e-03.
# looking root in interval [ 7.7293985 9.3001948]:
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# root found at 8.5385144 with precision 1.00000000e-03.
# looking root in interval [ 7.7531162 9.3239125]:
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# root found at 8.5630993 with precision 1.00000000e-03.
# looking root in interval [ 7.7777012 9.3484975]:
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# root found at 8.5883041 with precision 1.00000000e-03.
# looking root in interval [ 7.8029059 9.3737022]:
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# root found at 8.6145097 with precision 1.00000000e-03.
# looking root in interval [ 7.8291115 9.3999078]:
#..
# root found at 8.6408441 with precision 1.00000000e-03.
# looking root in interval [ 7.8554459 9.4262423]:
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# root found at 8.6692244 with precision 1.00000000e-03.
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# root found at 8.7269299 with precision 1.00000000e-03.
# looking root in interval [ 7.9415317 9.5123281]:
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# root found at 8.7566446 with precision 1.00000000e-03.
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# root found at 8.7872692 with precision 1.00000000e-03.
# looking root in interval [ 8.001871 9.5726673]:
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# root found at 8.8184056 with precision 1.00000000e-03.
# looking root in interval [ 8.0330075 9.6038038]:
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# root found at 8.8500846 with precision 1.00000000e-03.
# looking root in interval [ 8.0646865 9.6354828]:
#..
# root found at 8.8822181 with precision 1.00000000e-03.
# looking root in interval [ 8.09682 9.6676163]:
#..
# root found at 8.9153085 with precision 1.00000000e-03.
# looking root in interval [ 8.1299104 9.7007067]:
#..
# root found at 8.9471911 with precision 1.00000000e-03.
# looking root in interval [ 8.1617929 9.7325893]:
#..
# root found at 8.9808657 with precision 1.00000000e-03.
# looking root in interval [ 8.1954676 9.7662639]:
#..
# root found at 9.0141421 with precision 1.00000000e-03.
# looking root in interval [ 8.2287439 9.7995403]:
#..
# root found at 9.0474844 with precision 1.00000000e-03.
# looking root in interval [ 8.2620863 9.8328826]:
#..
# root found at 9.0807893 with precision 1.00000000e-03.
# looking root in interval [ 8.2953911 9.8661874]:
#..
# root found at 9.1140585 with precision 1.00000000e-03.
# looking root in interval [ 8.3286604 9.8994567]:
#..
# root found at 9.1468882 with precision 1.00000000e-03.
# looking root in interval [ 8.36149 9.9322863]:
#..
# root found at 9.1794566 with precision 1.00000000e-03.
# looking root in interval [ 8.3940585 9.9648548]:
#..
# root found at 9.2114644 with precision 1.00000000e-03.
# looking root in interval [ 8.4260662 9.9968625]:
#..
# root found at 9.2433562 with precision 1.00000000e-03.
# looking root in interval [ 8.457958 10.028754]:
#..
# root found at 9.2744095 with precision 1.00000000e-03.
# looking root in interval [ 8.4890113 10.059808]:
#..
# root found at 9.3048467 with precision 1.00000000e-03.
# looking root in interval [ 8.5194485 10.090245]:
#..
# root found at 9.3345479 with precision 1.00000000e-03.
# looking root in interval [ 8.5491497 10.119946]:
#..
# root found at 9.3636358 with precision 1.00000000e-03.
# looking root in interval [ 8.5782376 10.149034]:
#..
# root found at 9.391753 with precision 1.00000000e-03.
# looking root in interval [ 8.6063548 10.177151]:
#..
# root found at 9.4192513 with precision 1.00000000e-03.
# looking root in interval [ 8.6338532 10.204649]:
#..
# root found at 9.4457023 with precision 1.00000000e-03.
# looking root in interval [ 8.6603041 10.2311]:
#..
# root found at 9.4716358 with precision 1.00000000e-03.
# looking root in interval [ 8.6862376 10.257034]:
#..
# root found at 9.4961398 with precision 1.00000000e-03.
# looking root in interval [ 8.7107416 10.281538]:
#..
# root found at 9.520454 with precision 1.00000000e-03.
# looking root in interval [ 8.7350558 10.305852]:
#..
# root found at 9.5432105 with precision 1.00000000e-03.
# looking root in interval [ 8.7578124 10.328609]:
#..
# root found at 9.5657384 with precision 1.00000000e-03.
# looking root in interval [ 8.7803402 10.351137]:
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# root found at 9.5872464 with precision 1.00000000e-03.
# looking root in interval [ 8.8018482 10.372645]:
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# root found at 9.6076824 with precision 1.00000000e-03.
# looking root in interval [ 8.8222843 10.393081]:
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# root found at 9.6280778 with precision 1.00000000e-03.
# looking root in interval [ 8.8426796 10.413476]:
#..
# root found at 9.6468752 with precision 1.00000000e-03.
# looking root in interval [ 8.861477 10.432273]:
#..
# root found at 9.6653689 with precision 1.00000000e-03.
# looking root in interval [ 8.8799708 10.450767]:
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# root found at 9.6830586 with precision 1.00000000e-03.
# looking root in interval [ 8.8976604 10.468457]:
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# root found at 9.70013 with precision 1.00000000e-03.
# looking root in interval [ 8.9147319 10.485528]:
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# root found at 9.716667 with precision 1.00000000e-03.
# looking root in interval [ 8.9312688 10.502065]:
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# root found at 9.7319658 with precision 1.00000000e-03.
# looking root in interval [ 8.9465677 10.517364]:
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# root found at 9.7473486 with precision 1.00000000e-03.
# looking root in interval [ 8.9619504 10.532747]:
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# root found at 9.7619452 with precision 1.00000000e-03.
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# root found at 9.7760553 with precision 1.00000000e-03.
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# root found at 9.7895062 with precision 1.00000000e-03.
# looking root in interval [ 9.0041081 10.574904]:
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# looking root in interval [ 9.0170366 10.587833]:
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# root found at 9.8151193 with precision 1.00000000e-03.
# looking root in interval [ 9.0297212 10.600517]:
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# root found at 9.827197 with precision 1.00000000e-03.
# looking root in interval [ 9.0417989 10.612595]:
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# root found at 9.8388724 with precision 1.00000000e-03.
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# root found at 9.850172 with precision 1.00000000e-03.
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# looking root in interval [ 9.1339118 10.704708]:
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# root found at 9.9752594 with precision 1.00000000e-03.
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# looking root in interval [ 9.2242184 10.795015]:
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# root found at 10.058054 with precision 1.00000000e-03.
# looking root in interval [ 9.2726555 10.843452]:
#..
# root found at 10.06376 with precision 1.00000000e-03.
# looking root in interval [ 9.2783619 10.849158]:
#..
# root found at 10.069306 with precision 1.00000000e-03.
# looking root in interval [ 9.283908 10.854704]:
#..
# root found at 10.07471 with precision 1.00000000e-03.
# looking root in interval [ 9.2893119 10.860108]:
#..
# root found at 10.080603 with precision 1.00000000e-03.
# looking root in interval [ 9.2952048 10.866001]:
#..
# root found at 10.085365 with precision 1.00000000e-03.
# looking root in interval [ 9.2999664 10.870763]:
#..
# root found at 10.091385 with precision 1.00000000e-03.
# looking root in interval [ 9.3059868 10.876783]:
#..
# root found at 10.096065 with precision 1.00000000e-03.
# looking root in interval [ 9.3106672 10.881464]:
#..
# root found at 10.101692 with precision 1.00000000e-03.
# looking root in interval [ 9.3162943 10.887091]:
#..
# root found at 10.106989 with precision 1.00000000e-03.
# looking root in interval [ 9.3215908 10.892387]:
#..
# root found at 10.112298 with precision 1.00000000e-03.
# looking root in interval [ 9.3268997 10.897696]:
#..
# root found at 10.117598 with precision 1.00000000e-03.
# looking root in interval [ 9.3321997 10.902996]:
#..
# root found at 10.122671 with precision 1.00000000e-03.
# looking root in interval [ 9.337273 10.908069]:
#..
# root found at 10.128051 with precision 1.00000000e-03.
# looking root in interval [ 9.3426529 10.913449]:
#..
# root found at 10.133365 with precision 1.00000000e-03.
# looking root in interval [ 9.3479664 10.918763]:
#..
# root found at 10.138486 with precision 1.00000000e-03.
# looking root in interval [ 9.3530883 10.923885]:
#..
# root found at 10.143825 with precision 1.00000000e-03.
# looking root in interval [ 9.3584272 10.929224]:
#..
# root found at 10.149199 with precision 1.00000000e-03.
# looking root in interval [ 9.3638008 10.934597]:
#..
# root found at 10.154504 with precision 1.00000000e-03.
# looking root in interval [ 9.3691055 10.939902]:
#..
# root found at 10.160042 with precision 1.00000000e-03.
# looking root in interval [ 9.3746437 10.94544]:
#..
# root found at 10.165279 with precision 1.00000000e-03.
# looking root in interval [ 9.3798807 10.950677]:
#..
# root found at 10.170875 with precision 1.00000000e-03.
# looking root in interval [ 9.3854768 10.956273]:
#..
# root found at 10.176348 with precision 1.00000000e-03.
# looking root in interval [ 9.3909503 10.961747]:
#..
# root found at 10.181987 with precision 1.00000000e-03.
# looking root in interval [ 9.3965892 10.967386]:
#..
# root found at 10.187735 with precision 1.00000000e-03.
# looking root in interval [ 9.4023369 10.973133]:
#..
# root found at 10.193461 with precision 1.00000000e-03.
# looking root in interval [ 9.4080628 10.978859]:
#..
# root found at 10.19935 with precision 1.00000000e-03.
# looking root in interval [ 9.4139522 10.984749]:
#..
# root found at 10.205324 with precision 1.00000000e-03.
# looking root in interval [ 9.4199256 10.990722]:
#..
# root found at 10.211809 with precision 1.00000000e-03.
# looking root in interval [ 9.426411 10.997207]:
#..
# root found at 10.21726 with precision 1.00000000e-03.
# looking root in interval [ 9.4318615 11.002658]:
#..
# root found at 10.223842 with precision 1.00000000e-03.
# looking root in interval [ 9.4384438 11.00924]:
#..
# root found at 10.230413 with precision 1.00000000e-03.
# looking root in interval [ 9.445015 11.015811]:
#..
# root found at 10.237068 with precision 1.00000000e-03.
# looking root in interval [ 9.45167 11.022466]:
#..
# root found at 10.243778 with precision 1.00000000e-03.
# looking root in interval [ 9.45838 11.029176]:
#..
# root found at 10.250845 with precision 1.00000000e-03.
# looking root in interval [ 9.4654472 11.036244]:
#..
# root found at 10.257936 with precision 1.00000000e-03.
# looking root in interval [ 9.472538 11.043334]:
#..
# root found at 10.265744 with precision 1.00000000e-03.
# looking root in interval [ 9.480346 11.051142]:
#..
# root found at 10.272533 with precision 1.00000000e-03.
# looking root in interval [ 9.4871349 11.057931]:
#..
# root found at 10.280634 with precision 1.00000000e-03.
# looking root in interval [ 9.4952357 11.066032]:
#..
# root found at 10.288882 with precision 1.00000000e-03.
# looking root in interval [ 9.503484 11.07428]:
#..
# root found at 10.297177 with precision 1.00000000e-03.
# looking root in interval [ 9.511779 11.082575]:
#..
# root found at 10.305905 with precision 1.00000000e-03.
# looking root in interval [ 9.520507 11.091303]:
#..
# root found at 10.314882 with precision 1.00000000e-03.
# looking root in interval [ 9.5294837 11.10028]:
#..
# root found at 10.324356 with precision 1.00000000e-03.
# looking root in interval [ 9.5389575 11.109754]:
#..
# root found at 10.333815 with precision 1.00000000e-03.
# looking root in interval [ 9.5484166 11.119213]:
#..
# root found at 10.344116 with precision 1.00000000e-03.
# looking root in interval [ 9.5587177 11.129514]:
#..
# root found at 10.354625 with precision 1.00000000e-03.
# looking root in interval [ 9.5692272 11.140024]:
#..
# root found at 10.365677 with precision 1.00000000e-03.
# looking root in interval [ 9.5802786 11.151075]:
#..
# root found at 10.377253 with precision 1.00000000e-03.
# looking root in interval [ 9.5918552 11.162651]:
#..
# root found at 10.389303 with precision 1.00000000e-03.
# looking root in interval [ 9.6039051 11.174701]:
#..
# root found at 10.402023 with precision 1.00000000e-03.
# looking root in interval [ 9.616625 11.187421]:
#..
# root found at 10.415978 with precision 1.00000000e-03.
# looking root in interval [ 9.6305801 11.201376]:
#..
# root found at 10.428834 with precision 1.00000000e-03.
# looking root in interval [ 9.6434355 11.214232]:
#..
# root found at 10.444344 with precision 1.00000000e-03.
# looking root in interval [ 9.6589461 11.229742]:
#..
# root found at 10.459811 with precision 1.00000000e-03.
# looking root in interval [ 9.6744133 11.24521]:
#..
# root found at 10.476586 with precision 1.00000000e-03.
# looking root in interval [ 9.691188 11.261984]:
#..
# root found at 10.494085 with precision 1.00000000e-03.
# looking root in interval [ 9.7086865 11.279483]:
#..
# root found at 10.512706 with precision 1.00000000e-03.
# looking root in interval [ 9.7273079 11.298104]:
#...
# root found at 10.532542 with precision 1.00000000e-03.
# looking root in interval [ 9.7471435 11.31794]:
#..
# root found at 10.553785 with precision 1.00000000e-03.
# looking root in interval [ 9.7683864 11.339183]:
#..
# root found at 10.576159 with precision 1.00000000e-03.
# looking root in interval [ 9.7907605 11.361557]:
#..
# root found at 10.600092 with precision 1.00000000e-03.
# looking root in interval [ 9.8146943 11.385491]:
#..
# root found at 10.626045 with precision 1.00000000e-03.
# looking root in interval [ 9.8406473 11.411444]:
#..
# root found at 10.653374 with precision 1.00000000e-03.
# looking root in interval [ 9.8679754 11.438772]:
#..
# root found at 10.68297 with precision 1.00000000e-03.
# looking root in interval [ 9.8975714 11.468368]:
#..
# root found at 10.714675 with precision 1.00000000e-03.
# looking root in interval [ 9.9292765 11.500073]:
#..
# root found at 10.748541 with precision 1.00000000e-03.
# looking root in interval [ 9.9631432 11.53394]:
#..
# root found at 10.785304 with precision 1.00000000e-03.
# looking root in interval [ 9.9999057 11.570702]:
#..
# root found at 10.824025 with precision 1.00000000e-03.
# looking root in interval [ 10.038627 11.609423]:
#...
# root found at 10.865869 with precision 1.00000000e-03.
# looking root in interval [ 10.080471 11.651267]:
#...
# root found at 10.909705 with precision 1.00000000e-03.
# looking root in interval [ 10.124307 11.695104]:
#...
# root found at 10.958239 with precision 1.00000000e-03.
# looking root in interval [ 10.17284 11.743637]:
#....
# root found at 11.008309 with precision 1.00000000e-03.
# looking root in interval [ 10.222911 11.793707]:
#...
# root found at 11.061541 with precision 1.00000000e-03.
# looking root in interval [ 10.276143 11.84694]:
#.....
# root found at 11.109383 with precision 1.00000000e-03.
# looking root in interval [ 10.323985 11.894781]:
#....
# root found at 11.182773 with precision 1.00000000e-03.
# looking root in interval [ 10.397375 11.968171]:
#.....
# root found at 11.226088 with precision 1.00000000e-03.
# looking root in interval [ 10.44069 12.011487]:
#...
# root found at 11.302961 with precision 1.00000000e-03.
# looking root in interval [ 10.517563 12.088359]:
#...
# root found at 11.35576 with precision 1.00000000e-03.
# looking root in interval [ 10.570362 12.141158]:
#...
# root found at 11.416552 with precision 1.00000000e-03.
# looking root in interval [ 10.631154 12.20195]:
#...
# root found at 11.476441 with precision 1.00000000e-03.
# looking root in interval [ 10.691042 12.261839]:
#....
# root found at 11.534979 with precision 1.00000000e-03.
# looking root in interval [ 10.749581 12.320377]:
#...
# root found at 11.591529 with precision 1.00000000e-03.
# looking root in interval [ 10.80613 12.376927]:
#....
# root found at 11.645763 with precision 1.00000000e-03.
# looking root in interval [ 10.860365 12.431161]:
#....
# root found at 11.69742 with precision 1.00000000e-03.
# looking root in interval [ 10.912021 12.482818]:
#...
# root found at 11.746251 with precision 1.00000000e-03.
# looking root in interval [ 10.960853 12.53165]:
#...
# root found at 11.792443 with precision 1.00000000e-03.
# looking root in interval [ 11.007045 12.577841]:
#..
# root found at 11.836446 with precision 1.00000000e-03.
# looking root in interval [ 11.051048 12.621844]:
#..
# root found at 11.876009 with precision 1.00000000e-03.
# looking root in interval [ 11.090611 12.661407]:
#..
# root found at 11.913904 with precision 1.00000000e-03.
# looking root in interval [ 11.128506 12.699302]:
#..
# root found at 11.949289 with precision 1.00000000e-03.
# looking root in interval [ 11.163891 12.734687]:
#..
# root found at 11.982584 with precision 1.00000000e-03.
# looking root in interval [ 11.197186 12.767982]:
#..
# root found at 12.01319 with precision 1.00000000e-03.
# looking root in interval [ 11.227792 12.798588]:
#..
# root found at 12.04241 with precision 1.00000000e-03.
# looking root in interval [ 11.257011 12.827808]:
#..
# root found at 12.070022 with precision 1.00000000e-03.
# looking root in interval [ 11.284623 12.85542]:
#..
# root found at 12.094108 with precision 1.00000000e-03.
# looking root in interval [ 11.308709 12.879506]:
#..
# root found at 12.118898 with precision 1.00000000e-03.
# looking root in interval [ 11.3335 12.904296]:
#..
# root found at 12.14099 with precision 1.00000000e-03.
# looking root in interval [ 11.355592 12.926388]:
#..
# root found at 12.162237 with precision 1.00000000e-03.
# looking root in interval [ 11.376839 12.947635]:
#..
# root found at 12.182193 with precision 1.00000000e-03.
# looking root in interval [ 11.396795 12.967592]:
#..
# root found at 12.200857 with precision 1.00000000e-03.
# looking root in interval [ 11.415459 12.986256]:
#..
# root found at 12.218907 with precision 1.00000000e-03.
# looking root in interval [ 11.433509 13.004305]:
#..
# root found at 12.235743 with precision 1.00000000e-03.
# looking root in interval [ 11.450345 13.021141]:
#..
# root found at 12.25174 with precision 1.00000000e-03.
# looking root in interval [ 11.466342 13.037138]:
#..
# root found at 12.266945 with precision 1.00000000e-03.
# looking root in interval [ 11.481546 13.052343]:
#..
# root found at 12.281422 with precision 1.00000000e-03.
# looking root in interval [ 11.496024 13.06682]:
#..
# root found at 12.295291 with precision 1.00000000e-03.
# looking root in interval [ 11.509893 13.080689]:
#..
# root found at 12.308596 with precision 1.00000000e-03.
# looking root in interval [ 11.523198 13.093994]:
#..
# root found at 12.32107 with precision 1.00000000e-03.
# looking root in interval [ 11.535672 13.106468]:
#..
# root found at 12.33327 with precision 1.00000000e-03.
# looking root in interval [ 11.547872 13.118668]:
#..
# root found at 12.344968 with precision 1.00000000e-03.
# looking root in interval [ 11.55957 13.130366]:
#..
# root found at 12.356394 with precision 1.00000000e-03.
# looking root in interval [ 11.570996 13.141792]:
#..
# root found at 12.366239 with precision 1.00000000e-03.
# looking root in interval [ 11.580841 13.151637]:
#..
# root found at 12.37714 with precision 1.00000000e-03.
# looking root in interval [ 11.591742 13.162539]:
#..
# root found at 12.386879 with precision 1.00000000e-03.
# looking root in interval [ 11.601481 13.172277]:
#..
# root found at 12.396559 with precision 1.00000000e-03.
# looking root in interval [ 11.611161 13.181957]:
#..
# root found at 12.405713 with precision 1.00000000e-03.
# looking root in interval [ 11.620315 13.191112]:
#..
# root found at 12.414983 with precision 1.00000000e-03.
# looking root in interval [ 11.629585 13.200381]:
#..
# root found at 12.423334 with precision 1.00000000e-03.
# looking root in interval [ 11.637936 13.208732]:
#..
# root found at 12.431779 with precision 1.00000000e-03.
# looking root in interval [ 11.646381 13.217178]:
#..
# root found at 12.439901 with precision 1.00000000e-03.
# looking root in interval [ 11.654503 13.225299]:
#..
# root found at 12.4477 with precision 1.00000000e-03.
# looking root in interval [ 11.662302 13.233098]:
#..
# root found at 12.455585 with precision 1.00000000e-03.
# looking root in interval [ 11.670187 13.240983]:
#..
# root found at 12.462854 with precision 1.00000000e-03.
# looking root in interval [ 11.677456 13.248252]:
#..
# root found at 12.47 with precision 1.00000000e-03.
# looking root in interval [ 11.684601 13.255398]:
#..
# root found at 12.477074 with precision 1.00000000e-03.
# looking root in interval [ 11.691676 13.262472]:
#..
# root found at 12.483984 with precision 1.00000000e-03.
# looking root in interval [ 11.698586 13.269382]:
#..
# root found at 12.490478 with precision 1.00000000e-03.
# looking root in interval [ 11.705079 13.275876]:
#..
# root found at 12.497023 with precision 1.00000000e-03.
# looking root in interval [ 11.711625 13.282421]:
#...
# root found at 12.503805 with precision 1.00000000e-03.
# looking root in interval [ 11.718407 13.289203]:
#..
# root found at 12.509047 with precision 1.00000000e-03.
# looking root in interval [ 11.723649 13.294445]:
#..
# root found at 12.515426 with precision 1.00000000e-03.
# looking root in interval [ 11.730028 13.300824]:
#..
# root found at 12.52129 with precision 1.00000000e-03.
# looking root in interval [ 11.735892 13.306688]:
#..
# root found at 12.527031 with precision 1.00000000e-03.
# looking root in interval [ 11.741633 13.312429]:
#..
# root found at 12.5329 with precision 1.00000000e-03.
# looking root in interval [ 11.747502 13.318298]:
#..
# root found at 12.537704 with precision 1.00000000e-03.
# looking root in interval [ 11.752306 13.323102]:
#..
# root found at 12.543369 with precision 1.00000000e-03.
# looking root in interval [ 11.757971 13.328767]:
#..
# root found at 12.548416 with precision 1.00000000e-03.
# looking root in interval [ 11.763017 13.333814]:
#..
# root found at 12.553519 with precision 1.00000000e-03.
# looking root in interval [ 11.768121 13.338918]:
#..
# root found at 12.558488 with precision 1.00000000e-03.
# looking root in interval [ 11.77309 13.343886]:
#..
# root found at 12.563485 with precision 1.00000000e-03.
# looking root in interval [ 11.778087 13.348883]:
#..
# root found at 12.567663 with precision 1.00000000e-03.
# looking root in interval [ 11.782265 13.353062]:
#..
# root found at 12.572431 with precision 1.00000000e-03.
# looking root in interval [ 11.787033 13.35783]:
#..
# root found at 12.576997 with precision 1.00000000e-03.
# looking root in interval [ 11.791598 13.362395]:
#..
# root found at 12.581307 with precision 1.00000000e-03.
# looking root in interval [ 11.795909 13.366705]:
#..
# root found at 12.585355 with precision 1.00000000e-03.
# looking root in interval [ 11.799957 13.370753]:
#..
# root found at 12.589619 with precision 1.00000000e-03.
# looking root in interval [ 11.804221 13.375017]:
#..
# root found at 12.593594 with precision 1.00000000e-03.
# looking root in interval [ 11.808196 13.378992]:
#..
# root found at 12.597327 with precision 1.00000000e-03.
# looking root in interval [ 11.811929 13.382725]:
#..
# root found at 12.601152 with precision 1.00000000e-03.
# looking root in interval [ 11.815754 13.386551]:
#..
# root found at 12.604713 with precision 1.00000000e-03.
# looking root in interval [ 11.819315 13.390111]:
#..
# root found at 12.608171 with precision 1.00000000e-03.
# looking root in interval [ 11.822773 13.393569]:
#..
# root found at 12.6115 with precision 1.00000000e-03.
# looking root in interval [ 11.826102 13.396898]:
#..
# root found at 12.614728 with precision 1.00000000e-03.
# looking root in interval [ 11.82933 13.400126]:
#..
# root found at 12.617821 with precision 1.00000000e-03.
# looking root in interval [ 11.832423 13.40322]:
#..
# root found at 12.620695 with precision 1.00000000e-03.
# looking root in interval [ 11.835297 13.406093]:
#..
# root found at 12.623487 with precision 1.00000000e-03.
# looking root in interval [ 11.838089 13.408886]:
#..
# root found at 12.626088 with precision 1.00000000e-03.
# looking root in interval [ 11.84069 13.411486]:
#..
# root found at 12.62858 with precision 1.00000000e-03.
# looking root in interval [ 11.843182 13.413978]:
#..
# root found at 12.63081 with precision 1.00000000e-03.
# looking root in interval [ 11.845412 13.416209]:
#..
# root found at 12.632959 with precision 1.00000000e-03.
# looking root in interval [ 11.847561 13.418357]:
#....
# root found at 12.635666 with precision 1.00000000e-03.
# looking root in interval [ 11.850267 13.421064]:
#..
# root found at 12.635841 with precision 1.00000000e-03.
# looking root in interval [ 11.850443 13.42124]:
#..
# root found at 12.638104 with precision 1.00000000e-03.
# looking root in interval [ 11.852706 13.423502]:
#..
# root found at 12.63944 with precision 1.00000000e-03.
# looking root in interval [ 11.854042 13.424838]:
#..
# root found at 12.640476 with precision 1.00000000e-03.
# looking root in interval [ 11.855078 13.425874]:
#..
# root found at 12.641328 with precision 1.00000000e-03.
# looking root in interval [ 11.85593 13.426726]:
#..
# root found at 12.642054 with precision 1.00000000e-03.
# looking root in interval [ 11.856656 13.427452]:
#..
# root found at 12.642017 with precision 1.00000000e-03.
# looking root in interval [ 11.856619 13.427415]:
#..
# root found at 12.642203 with precision 1.00000000e-03.
# looking root in interval [ 11.856805 13.427602]:
#..
# root found at 12.641838 with precision 1.00000000e-03.
# looking root in interval [ 11.856439 13.427236]:
#..
# root found at 12.641278 with precision 1.00000000e-03.
# looking root in interval [ 11.85588 13.426676]:
#..
# root found at 12.640168 with precision 1.00000000e-03.
# looking root in interval [ 11.85477 13.425566]:
#..
# root found at 12.638846 with precision 1.00000000e-03.
# looking root in interval [ 11.853447 13.424244]:
#..
# root found at 12.63707 with precision 1.00000000e-03.
# looking root in interval [ 11.851671 13.422468]:
#..
# root found at 12.634765 with precision 1.00000000e-03.
# looking root in interval [ 11.849367 13.420163]:
#..
# root found at 12.632125 with precision 1.00000000e-03.
# looking root in interval [ 11.846726 13.417523]:
#..
# root found at 12.628863 with precision 1.00000000e-03.
# looking root in interval [ 11.843465 13.414261]:
#..
# root found at 12.625189 with precision 1.00000000e-03.
# looking root in interval [ 11.839791 13.410587]:
#..
# root found at 12.620839 with precision 1.00000000e-03.
# looking root in interval [ 11.83544 13.406237]:
#..
# root found at 12.615949 with precision 1.00000000e-03.
# looking root in interval [ 11.830551 13.401347]:
#..
# root found at 12.610282 with precision 1.00000000e-03.
# looking root in interval [ 11.824883 13.39568]:
#..
# root found at 12.603982 with precision 1.00000000e-03.
# looking root in interval [ 11.818584 13.38938]:
#..
# root found at 12.596936 with precision 1.00000000e-03.
# looking root in interval [ 11.811538 13.382335]:
#..
# root found at 12.589013 with precision 1.00000000e-03.
# looking root in interval [ 11.803615 13.374411]:
#..
# root found at 12.580255 with precision 1.00000000e-03.
# looking root in interval [ 11.794857 13.365653]:
#..
# root found at 12.570562 with precision 1.00000000e-03.
# looking root in interval [ 11.785164 13.35596]:
#..
# root found at 12.559862 with precision 1.00000000e-03.
# looking root in interval [ 11.774464 13.34526]:
#...
# root found at 12.549394 with precision 1.00000000e-03.
# looking root in interval [ 11.763996 13.334793]:
#...
# root found at 12.535319 with precision 1.00000000e-03.
# looking root in interval [ 11.749921 13.320717]:
#...
# root found at 12.521306 with precision 1.00000000e-03.
# looking root in interval [ 11.735908 13.306704]:
#...
# root found at 12.506035 with precision 1.00000000e-03.
# looking root in interval [ 11.720637 13.291433]:
#....
# root found at 12.489559 with precision 1.00000000e-03.
# looking root in interval [ 11.704161 13.274957]:
#....
# root found at 12.471778 with precision 1.00000000e-03.
# looking root in interval [ 11.68638 13.257176]:
#.....
# root found at 12.459824 with precision 1.00000000e-03.
# looking root in interval [ 11.674426 13.245222]:
#.....
# root found at 12.425065 with precision 1.00000000e-03.
# looking root in interval [ 11.639667 13.210463]:
#...
# root found at 12.410502 with precision 1.00000000e-03.
# looking root in interval [ 11.625104 13.195901]:
#.....
# root found at 12.39563 with precision 1.00000000e-03.
# looking root in interval [ 11.610232 13.181029]:
#...
# root found at 12.355801 with precision 1.00000000e-03.
# looking root in interval [ 11.570403 13.141199]:
#....
# root found at 12.338703 with precision 1.00000000e-03.
# looking root in interval [ 11.553305 13.124101]:
#...
# root found at 12.31315 with precision 1.00000000e-03.
# looking root in interval [ 11.527752 13.098548]:
#....
# root found at 12.287147 with precision 1.00000000e-03.
# looking root in interval [ 11.501748 13.072545]:
#...
# root found at 12.261131 with precision 1.00000000e-03.
# looking root in interval [ 11.475733 13.046529]:
#...
# root found at 12.235603 with precision 1.00000000e-03.
# looking root in interval [ 11.450204 13.021001]:
#...
# root found at 12.211024 with precision 1.00000000e-03.
# looking root in interval [ 11.425626 12.996422]:
#.....
# root found at 12.188447 with precision 1.00000000e-03.
# looking root in interval [ 11.403049 12.973845]:
#...
# root found at 12.168686 with precision 1.00000000e-03.
# looking root in interval [ 11.383287 12.954084]:
#...
# root found at 12.153141 with precision 1.00000000e-03.
# looking root in interval [ 11.367743 12.93854]:
#....
# root found at 12.143756 with precision 1.00000000e-03.
# looking root in interval [ 11.358358 12.929154]:
#.....
# root found at 12.143394 with precision 1.00000000e-03.
# looking root in interval [ 11.357996 12.928792]:
#...
# root found at 12.157099 with precision 1.00000000e-03.
# looking root in interval [ 11.371701 12.942497]:
#..
# root found at 12.193113 with precision 1.00000000e-03.
# looking root in interval [ 11.407715 12.978511]:
#..
# root found at 12.27298 with precision 1.00000000e-03.
# looking root in interval [ 11.487582 13.058378]:
#...
# root found at 12.431785 with precision 1.00000000e-03.
# looking root in interval [ 11.646387 13.217183]:
#...
# root found at 12.746048 with precision 1.00000000e-03.
# looking root in interval [ 11.96065 13.531446]:
#...
# root found at 13.191635 with precision 1.00000000e-03.
# looking root in interval [ 12.406237 13.977034]:
#.....
# root found at 13.544104 with precision 1.00000000e-03.
# looking root in interval [ 12.758706 14.329502]:
#...
# root found at 13.744702 with precision 1.00000000e-03.
# looking root in interval [ 12.959303 14.5301]:
#...
# root found at 13.856798 with precision 1.00000000e-03.
# looking root in interval [ 13.0714 14.642196]:
#......
# root found at 13.929896 with precision 1.00000000e-03.
# looking root in interval [ 13.144498 14.715294]:
#......
# root found at 13.979652 with precision 1.00000000e-03.
# looking root in interval [ 13.194254 14.76505]:
#......
# root found at 14.015762 with precision 1.00000000e-03.
# looking root in interval [ 13.230364 14.80116]:
#.....
# root found at 14.04475 with precision 1.00000000e-03.
# looking root in interval [ 13.259352 14.830148]:
#.....
# root found at 14.089401 with precision 1.00000000e-03.
# looking root in interval [ 13.304003 14.874799]:
#.....
# root found at 14.118048 with precision 1.00000000e-03.
# looking root in interval [ 13.33265 14.903446]:
#.....
# root found at 14.134484 with precision 1.00000000e-03.
# looking root in interval [ 13.349086 14.919882]:
#.....
# root found at 14.145749 with precision 1.00000000e-03.
# looking root in interval [ 13.360351 14.931147]:
#.....
# root found at 14.154241 with precision 1.00000000e-03.
# looking root in interval [ 13.368843 14.939639]:
#.....
# root found at 14.161018 with precision 1.00000000e-03.
# looking root in interval [ 13.37562 14.946416]:
#.....
# root found at 14.166663 with precision 1.00000000e-03.
# looking root in interval [ 13.381265 14.952061]:
#.....
# root found at 14.171516 with precision 1.00000000e-03.
# looking root in interval [ 13.386118 14.956915]:
#.....
# root found at 14.175794 with precision 1.00000000e-03.
# looking root in interval [ 13.390396 14.961192]:
#.....
# root found at 14.179635 with precision 1.00000000e-03.
# looking root in interval [ 13.394237 14.965033]:
#.....
# root found at 14.18314 with precision 1.00000000e-03.
# looking root in interval [ 13.397742 14.968538]:
#.....
# root found at 14.186379 with precision 1.00000000e-03.
# looking root in interval [ 13.400981 14.971778]:
#.....
# root found at 14.189407 with precision 1.00000000e-03.
# looking root in interval [ 13.404009 14.974805]:
#.....
# root found at 14.192266 with precision 1.00000000e-03.
# looking root in interval [ 13.406868 14.977664]:
#.....
# root found at 14.194987 with precision 1.00000000e-03.
# looking root in interval [ 13.409589 14.980385]:
#.....
# root found at 14.197598 with precision 1.00000000e-03.
# looking root in interval [ 13.412199 14.982996]:
#.....
# root found at 14.200119 with precision 1.00000000e-03.
# looking root in interval [ 13.414721 14.985517]:
#.....
# root found at 14.202571 with precision 1.00000000e-03.
# looking root in interval [ 13.417173 14.987969]:
#.....
# root found at 14.204969 with precision 1.00000000e-03.
# looking root in interval [ 13.419571 14.990367]:
#.....
# root found at 14.207327 with precision 1.00000000e-03.
# looking root in interval [ 13.421929 14.992725]:
#.....
# root found at 14.20966 with precision 1.00000000e-03.
# looking root in interval [ 13.424262 14.995058]:
#.....
# root found at 14.211977 with precision 1.00000000e-03.
# looking root in interval [ 13.426578 14.997375]:
#.....
# root found at 14.214291 with precision 1.00000000e-03.
# looking root in interval [ 13.428893 14.99969]:
#.....
# root found at 14.216615 with precision 1.00000000e-03.
# looking root in interval [ 13.431217 15.002013]:
#.....
# root found at 14.218959 with precision 1.00000000e-03.
# looking root in interval [ 13.433561 15.004357]:
#.....
# root found at 14.221335 with precision 1.00000000e-03.
# looking root in interval [ 13.435937 15.006733]:
#.....
# root found at 14.223757 with precision 1.00000000e-03.
# looking root in interval [ 13.438359 15.009155]:
#.....
# root found at 14.226237 with precision 1.00000000e-03.
# looking root in interval [ 13.440839 15.011635]:
#.....
# root found at 14.228793 with precision 1.00000000e-03.
# looking root in interval [ 13.443394 15.014191]:
#.....
# root found at 14.231441 with precision 1.00000000e-03.
# looking root in interval [ 13.446043 15.016839]:
#.....
# root found at 14.234204 with precision 1.00000000e-03.
# looking root in interval [ 13.448806 15.019602]:
#.....
# root found at 14.237106 with precision 1.00000000e-03.
# looking root in interval [ 13.451708 15.022504]:
#.....
# root found at 14.240179 with precision 1.00000000e-03.
# looking root in interval [ 13.454781 15.025577]:
#.....
# root found at 14.243462 with precision 1.00000000e-03.
# looking root in interval [ 13.458064 15.02886]:
#.....
# root found at 14.247003 with precision 1.00000000e-03.
# looking root in interval [ 13.461605 15.032402]:
#.....
# root found at 14.25087 with precision 1.00000000e-03.
# looking root in interval [ 13.465472 15.036268]:
#.....
# root found at 14.255151 with precision 1.00000000e-03.
# looking root in interval [ 13.469753 15.040549]:
#......
# root found at 14.25997 with precision 1.00000000e-03.
# looking root in interval [ 13.474572 15.045368]:
#.....
# root found at 14.265509 with precision 1.00000000e-03.
# looking root in interval [ 13.480111 15.050908]:
#.....
# root found at 14.272049 with precision 1.00000000e-03.
# looking root in interval [ 13.48665 15.057447]:
#.....
# root found at 14.280045 with precision 1.00000000e-03.
# looking root in interval [ 13.494647 15.065443]:
#...
# root found at 14.290945 with precision 1.00000000e-03.
# looking root in interval [ 13.505547 15.076344]:
#...
# root found at 14.300759 with precision 1.00000000e-03.
# looking root in interval [ 13.515361 15.086158]:
#...
# root found at 14.306163 with precision 1.00000000e-03.
# Start found at [389], ending...
In [14]:
plt.figure (figsize=(14, 7))
plt.title ("Confidence regions (%.2f)" % (cr_rg.clevel * 100.0))
plt.plot (cr_p1array, cr_p2array, 'r', label="Likelihood Ratio")
plt.plot (fisher_p1array, fisher_p2array, 'b-', label="Fisher Matrix")
plt.xlabel(r'$\Omega_c$')
plt.ylabel(r'$w$')
plt.legend(loc=4)
plt.savefig ("snia_bao_rg_omegac_w.svg")
Content source: NumCosmo/NumCosmo
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