CNRatioModel Tutorial

Trey V. Wenger (c) April 2025

CNRatioModel models both \({\rm CN}\) and \(^{13}{\rm CN}\) spectral simultaneously in order to constrain the isotopic ratio \(^{12}{\rm C}/^{13}{\rm C}\).

The ratio parameter 12C_13C_ratio is only equivalent to the “true” isotopic ratio under the assumption that both species have the same excitation conditions (i.e., the same population fraction in the \(N=0\) and \(N=1\) states). This parameter is equivalent to the total column density ratio of all \(N=0\) and \(N=1\) states, \(N_{\rm tot, CN}/N_{{\rm tot}, ^{13}\rm CN}\) where \(N_{\rm tot} = \sum N_{N=0} + N_{N=1}\).

[1]:

# General imports
import os
import pickle
import time

import matplotlib.pyplot as plt
import arviz as az
import pandas as pd
import numpy as np
import pymc as pm

print("arviz version:", az.__version__)

print("pymc version:", pm.__version__)

import bayes_spec
print("bayes_spec version:", bayes_spec.__version__)

import bayes_cn_hfs
print("bayes_cn_hfs version:", bayes_cn_hfs.__version__)

# Notebook configuration
pd.options.display.max_rows = None

arviz version: 0.22.0dev
pymc version: 5.21.1
bayes_spec version: 1.7.8
bayes_cn_hfs version: 2.0.0-staging+0.g7afe3a8.dirty

Simulate Data

[2]:

from bayes_spec import SpecData
from bayes_cn_hfs.cn_ratio_model import CNRatioModel

# spectral axis definition
freq_axis_12CN_1 = np.arange(113110.0, 113200.0, 0.2) # MHz
freq_axis_12CN_2 = np.arange(113470.0, 113530.0, 0.2) # MHz
freq_axis_13CN_1 = np.arange(108620.0, 108670.0, 0.2) # MHz
freq_axis_13CN_2 = np.arange(108760.0, 108810.0, 0.2) # MHz

# data noise can either be a scalar (assumed constant noise across the spectrum)
# or an array of the same length as the data
noise = 0.005 # K

# brightness data. In this case, we just throw in some random data for now
# since we are only doing this in order to simulate some actual data.
brightness_data_12CN_1 = noise * np.random.randn(len(freq_axis_12CN_1)) # K
brightness_data_12CN_2 = noise * np.random.randn(len(freq_axis_12CN_2)) # K
brightness_data_13CN_1 = noise * np.random.randn(len(freq_axis_13CN_1)) # K
brightness_data_13CN_2 = noise * np.random.randn(len(freq_axis_13CN_2)) # K

# CNRatioModel expects observation names to contain either "12CN" or "13CN"
observation_12CN_1 = SpecData(
    freq_axis_12CN_1,
    brightness_data_12CN_1,
    noise,
    xlabel=r"LSRK Frequency (MHz)",
    ylabel=r"CN $T_B$ (K)",
)
observation_12CN_2 = SpecData(
    freq_axis_12CN_2,
    brightness_data_12CN_2,
    noise,
    xlabel=r"LSRK Frequency (MHz)",
    ylabel=r"CN $T_B$ (K)",
)
observation_13CN_1 = SpecData(
    freq_axis_13CN_1,
    brightness_data_13CN_1,
    noise,
    xlabel=r"LSRK Frequency (MHz)",
    ylabel=r"$^{13}$CN $T_B$ (K)",
)
observation_13CN_2 = SpecData(
    freq_axis_13CN_2,
    brightness_data_13CN_2,
    noise,
    xlabel=r"LSRK Frequency (MHz)",
    ylabel=r"$^{13}$CN $T_B$ (K)",
)
dummy_data = {
    "12CN-1": observation_12CN_1,
    "12CN-2": observation_12CN_2,
    "13CN-1": observation_13CN_1,
    "13CN-2": observation_13CN_2,
}

# Initialize and define the model
n_clouds = 2 # number of cloud components
baseline_degree = 0 # polynomial baseline degree
model = CNRatioModel(
    dummy_data,
    bg_temp = 2.7, # assumed background temperature (K)
    Beff = 1.0, # beam efficiency
    Feff = 1.0, # forward efficiency
    n_clouds=n_clouds,
    baseline_degree=baseline_degree,
    seed=1234,
    verbose=True
)
model.add_priors(
    prior_log10_N_12CN = [13.5, 1.0], # mean and width of log10 12CN total column density prior (cm-2)
    prior_ratio_13C_12C = 0.1, # width of 13C/12C ratio prior
    prior_log10_Tkin = [1.0, 0.5], # mean and width of log10 kinetic temperature prior (K)
    prior_velocity = [0.0, 3.0], # mean and width of velocity prior (km/s)
    prior_fwhm_nonthermal = 1.0, # width of non-thermal broadening prior (km/s)
    prior_fwhm_L = None, # assume Gaussian line profile
    prior_rms = None, # do not infer spectral rms
    prior_baseline_coeffs = None, # use default baseline priors
    assume_LTE = True, # assume LTE
    prior_log10_Tex = None, # ignored for this LTE model
    assume_CTEX_12CN = True, # implied for this LTE model
    prior_log10_LTE_precision = None, # ignored for this LTE model
    assume_CTEX_13CN = True, # implied for this LTE model
    fix_log10_Tkin = None, # do not fix the kinetic temperature
    clip_weights = 1.0e-9, # clip statistical weights between [clip_weights, 1-clip_weights]
    clip_tau = -10.0, # clip optical depths below to prevent masers
    ordered = False, # do not assume optically-thin
)
model.add_likelihood()

sim_params = {
    "log10_N_12CN": [13.9, 13.8],
    "ratio_13C_12C": [1.0/65.0, 1.0/55.0],
    "log10_Tkin": [0.6, 0.7],
    "velocity": [-0.5, 1.5],
    "fwhm_nonthermal": [0.5, 0.75],
    "fwhm_L": 0.0,
    "baseline_12CN_norm": [0.0],
    "baseline_13CN_norm": [0.0],
}

# add derived quantities to sim_params
for key in model.cloud_deterministics:
    if key not in sim_params.keys():
        sim_params[key] = model.model[key].eval(sim_params, on_unused_input="ignore")

# Evaluate and save simulated observations
sim_12CN_1 = model.model["12CN-1"].eval(sim_params, on_unused_input="ignore")
sim_12CN_2 = model.model["12CN-2"].eval(sim_params, on_unused_input="ignore")
sim_13CN_1 = model.model["13CN-1"].eval(sim_params, on_unused_input="ignore")
sim_13CN_2 = model.model["13CN-2"].eval(sim_params, on_unused_input="ignore")

# pack simulated data
observation_12CN_1 = SpecData(
    freq_axis_12CN_1,
    sim_12CN_1,
    noise,
    xlabel=r"LSRK Frequency (MHz)",
    ylabel=r"$T_B$ (K)",
)
observation_12CN_2 = SpecData(
    freq_axis_12CN_2,
    sim_12CN_2,
    noise,
    xlabel=r"LSRK Frequency (MHz)",
    ylabel=r"$T_B$ (K)",
)
observation_13CN_1 = SpecData(
    freq_axis_13CN_1,
    sim_13CN_1,
    noise,
    xlabel=r"LSRK Frequency (MHz)",
    ylabel=r"$T_B$ (K)",
)
observation_13CN_2 = SpecData(
    freq_axis_13CN_2,
    sim_13CN_2,
    noise,
    xlabel=r"LSRK Frequency (MHz)",
    ylabel=r"$T_B$ (K)",
)
data = {
    "12CN-1": observation_12CN_1,
    "12CN-2": observation_12CN_2,
    "13CN-1": observation_13CN_1,
    "13CN-2": observation_13CN_2,
}

# Plot the simulated data
fig, axes = plt.subplots(4, layout="constrained", figsize=(8, 12))
for i, dataset in enumerate(data.values()):
    axes[i].plot(dataset.spectral, dataset.brightness, 'k-')
    axes[i].set_ylabel(dataset.ylabel)
    _ = axes[i].set_xlabel(dataset.xlabel)
../_images/notebooks_cn_ratio_model_3_0.png 
[3]:

sim_params

[3]:

{'log10_N_12CN': [13.9, 13.8],
 'ratio_13C_12C': [0.015384615384615385, 0.01818181818181818],
 'log10_Tkin': [0.6, 0.7],
 'velocity': [-0.5, 1.5],
 'fwhm_nonthermal': [0.5, 0.75],
 'fwhm_L': 0.0,
 'baseline_12CN_norm': [0.0],
 'baseline_13CN_norm': [0.0],
 'fwhm_thermal_12CN': array([0.08371703, 0.09393205]),
 'fwhm_thermal_13CN': array([0.08215209, 0.09217616]),
 'fwhm_12CN': array([0.5069601 , 0.75585927]),
 'fwhm_13CN': array([0.50670402, 0.75564307]),
 'N_13CN': array([1.22204344e+12, 1.14719517e+12]),
 'log10_Tex_ul': array([0.6, 0.7]),
 'Tex_12CN': array([[3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234]]),
 'tau_12CN': array([[0.03961643, 0.02451991],
        [0.32429648, 0.20071051],
        [0.31672379, 0.19603779],
        [0.41128963, 0.25456059],
        [0.41280405, 0.25556863],
        [1.09659601, 0.67887309],
        [0.32570236, 0.20164538],
        [0.31820796, 0.19699669],
        [0.03980962, 0.02464562]]),
 'tau_total_12CN': array([3.28504631, 2.03355822]),
 'TR_12CN': array([[1.86520154, 2.77809747],
        [1.86491585, 2.77777149],
        [1.86455441, 2.77735907],
        [1.86426923, 2.77703365],
        [1.86020143, 2.77239079],
        [1.8601625 , 2.77234635],
        [1.86004396, 2.77221102],
        [1.85991675, 2.77206579],
        [1.85975948, 2.77188624]]),
 'Tex_13CN': array([[3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234],
        [3.98107171, 5.01187234]]),
 'tau_13CN': array([[8.24496577e-05, 6.02192983e-05],
        [1.07530913e-04, 7.85363678e-05],
        [4.19011486e-05, 3.06031489e-05],
        [1.86018175e-04, 1.35858466e-04],
        [1.12614014e-04, 8.22501549e-05],
        [3.01871348e-04, 2.20473967e-04],
        [3.48079688e-04, 2.54298411e-04],
        [1.15988719e-03, 8.47371921e-04],
        [2.31496962e-03, 1.69119911e-03],
        [1.18392499e-03, 8.63849880e-04],
        [3.56464846e-03, 2.60095895e-03],
        [1.32375606e-03, 9.67277682e-04],
        [1.56871308e-03, 1.14624869e-03],
        [1.17609379e-03, 8.59364781e-04],
        [1.01005419e-03, 7.38042257e-04],
        [6.04620985e-03, 4.41168091e-03],
        [4.43581042e-03, 3.24115230e-03],
        [1.22652051e-03, 8.96194954e-04],
        [9.01007799e-03, 6.58410847e-03],
        [4.74856292e-03, 3.47011820e-03],
        [2.10090491e-03, 1.53532281e-03],
        [1.64113167e-03, 1.19930619e-03],
        [1.68613286e-03, 1.23215399e-03],
        [1.18979719e-04, 8.69462211e-05],
        [2.03848497e-05, 1.48779157e-05],
        [4.23970801e-04, 3.09490503e-04],
        [1.09934607e-04, 8.02501891e-05],
        [2.96918708e-04, 2.16745533e-04]]),
 'tau_total_13CN': array([0.04634805, 0.0338549 ]),
 'TR_13CN': array([[1.93577105, 2.85831292],
        [1.93575722, 2.85829726],
        [1.93567541, 2.85820461],
        [1.93547703, 2.85797995],
        [1.93547258, 2.85797491],
        [1.93527423, 2.85775027],
        [1.93083047, 2.8527165 ],
        [1.93073508, 2.85260841],
        [1.93053726, 2.85238427],
        [1.92765886, 2.84912234],
        [1.92757714, 2.84902971],
        [1.92755898, 2.84900914],
        [1.92748323, 2.84892328],
        [1.92747238, 2.84891099],
        [1.92746247, 2.84889975],
        [1.92737469, 2.84880025],
        [1.92728527, 2.8486989 ],
        [1.92726693, 2.84867812],
        [1.9255599 , 2.84674309],
        [1.92552932, 2.84670843],
        [1.92546447, 2.84663491],
        [1.92536919, 2.84652689],
        [1.92533194, 2.84648466],
        [1.92517152, 2.84630279],
        [1.92265315, 2.84344732],
        [1.91941201, 2.83977121],
        [1.91940133, 2.8397591 ],
        [1.91939307, 2.83974973]])}

Model Definition

[4]:

# Initialize and define the model
model = CNRatioModel(
    data,
    bg_temp = 2.7, # assumed background temperature (K)
    Beff = 1.0, # beam efficiency
    Feff = 1.0, # forward efficiency
    n_clouds=n_clouds,
    baseline_degree=baseline_degree,
    seed=1234,
    verbose=True
)
model.add_priors(
    prior_log10_N_12CN = [13.5, 1.0], # mean and width of log10 12CN total column density prior (cm-2)
    prior_ratio_13C_12C = 0.1, # width of 13C/12C ratio prior
    prior_log10_Tkin = [1.0, 0.5], # mean and width of log10 kinetic temperature prior (K)
    prior_velocity = [0.0, 3.0], # mean and width of velocity prior (km/s)
    prior_fwhm_nonthermal = 1.0, # width of non-thermal broadening prior (km/s)
    prior_fwhm_L = None, # assume Gaussian line profile
    prior_rms = None, # do not infer spectral rms
    prior_baseline_coeffs = None, # use default baseline priors
    assume_LTE = True, # assume LTE
    prior_log10_Tex = None, # ignored for this LTE model
    assume_CTEX_12CN = True, # implied for this LTE model
    prior_log10_LTE_precision = None, # ignored for this LTE model
    assume_CTEX_13CN = True, # implied for this LTE model
    fix_log10_Tkin = None, # do not fix the kinetic temperature
    clip_weights = 1.0e-9, # clip statistical weights between [clip_weights, 1-clip_weights]
    clip_tau = -10.0, # clip optical depths below to prevent masers
    ordered = False, # do not assume optically-thin
)
model.add_likelihood()

[5]:

# Plot model graph
model.graph().render('cn_ratio_model', format='png')
model.graph()

[5]:
../_images/notebooks_cn_ratio_model_7_0.svg 
[6]:

# model string representation
print(model.model.str_repr())

baseline_12CN-1_norm ~ Normal(0, 1)
baseline_12CN-2_norm ~ Normal(0, 1)
baseline_13CN-1_norm ~ Normal(0, 1)
baseline_13CN-2_norm ~ Normal(0, 1)
       velocity_norm ~ Normal(0, 1)
     log10_Tkin_norm ~ Normal(0, 1)
fwhm_nonthermal_norm ~ HalfNormal(0, 1)
   log10_N_12CN_norm ~ Normal(0, 1)
  ratio_13C_12C_norm ~ HalfNormal(0, 1)
            velocity ~ Deterministic(f(velocity_norm))
          log10_Tkin ~ Deterministic(f(log10_Tkin_norm))
   fwhm_thermal_12CN ~ Deterministic(f(log10_Tkin_norm))
   fwhm_thermal_13CN ~ Deterministic(f(log10_Tkin_norm))
     fwhm_nonthermal ~ Deterministic(f(fwhm_nonthermal_norm))
           fwhm_12CN ~ Deterministic(f(fwhm_nonthermal_norm, log10_Tkin_norm))
           fwhm_13CN ~ Deterministic(f(fwhm_nonthermal_norm, log10_Tkin_norm))
        log10_N_12CN ~ Deterministic(f(log10_N_12CN_norm))
       ratio_13C_12C ~ Deterministic(f(ratio_13C_12C_norm))
              N_13CN ~ Deterministic(f(ratio_13C_12C_norm, log10_N_12CN_norm))
        log10_Tex_ul ~ Deterministic(f(log10_Tkin_norm))
            Tex_12CN ~ Deterministic(f(log10_Tkin_norm))
            tau_12CN ~ Deterministic(f(log10_N_12CN_norm, log10_Tkin_norm))
      tau_total_12CN ~ Deterministic(f(log10_N_12CN_norm, log10_Tkin_norm))
             TR_12CN ~ Deterministic(f(log10_Tkin_norm))
            Tex_13CN ~ Deterministic(f(log10_Tkin_norm))
            tau_13CN ~ Deterministic(f(ratio_13C_12C_norm, log10_N_12CN_norm, log10_Tkin_norm))
      tau_total_13CN ~ Deterministic(f(ratio_13C_12C_norm, log10_N_12CN_norm, log10_Tkin_norm))
             TR_13CN ~ Deterministic(f(log10_Tkin_norm))
              12CN-1 ~ Normal(f(baseline_12CN-1_norm, log10_Tkin_norm, velocity_norm, log10_N_12CN_norm, fwhm_nonthermal_norm), <constant>)
              12CN-2 ~ Normal(f(baseline_12CN-2_norm, log10_Tkin_norm, velocity_norm, log10_N_12CN_norm, fwhm_nonthermal_norm), <constant>)
              13CN-1 ~ Normal(f(baseline_13CN-1_norm, log10_Tkin_norm, velocity_norm, ratio_13C_12C_norm, fwhm_nonthermal_norm, log10_N_12CN_norm), <constant>)
              13CN-2 ~ Normal(f(baseline_13CN-2_norm, log10_Tkin_norm, velocity_norm, ratio_13C_12C_norm, fwhm_nonthermal_norm, log10_N_12CN_norm), <constant>)

[7]:

from bayes_spec.plots import plot_predictive

# prior predictive check
prior = model.sample_prior_predictive(
    samples=1000,  # prior predictive samples
)
_ = plot_predictive(model.data, prior.prior_predictive)

Sampling: [12CN-1, 12CN-2, 13CN-1, 13CN-2, baseline_12CN-1_norm, baseline_12CN-2_norm, baseline_13CN-1_norm, baseline_13CN-2_norm, fwhm_nonthermal_norm, log10_N_12CN_norm, log10_Tkin_norm, ratio_13C_12C_norm, velocity_norm]
../_images/notebooks_cn_ratio_model_9_1.png 
[8]:

from bayes_spec.plots import plot_pair

# available parameter attributes:
print("baseline_freeRVs", model.baseline_freeRVs)
print("baseline_deterministics", model.baseline_deterministics)
print("cloud_freeRVs", model.cloud_freeRVs)
print("cloud_deterministics", model.cloud_deterministics)
print("hyper_freeRVs", model.hyper_freeRVs)
print("hyper_deterministics", model.hyper_deterministics)

# ignore transition and state dependent parameters
var_names = [
    param for param in model.cloud_deterministics
    if not set(model.model.named_vars_to_dims[param]).intersection(set(
        ["transition_12CN", "state_12CN", "transition_13CN", "state_13CN"]
    ))
]
print(var_names)
_ = plot_pair(
    prior.prior, # samples
    var_names, # var_names to plot
    labeller=model.labeller, # label manager
    kind="scatter", # plot type
    reference_values=sim_params, # truths
)

baseline_freeRVs ['baseline_12CN-1_norm', 'baseline_12CN-2_norm', 'baseline_13CN-1_norm', 'baseline_13CN-2_norm']
baseline_deterministics []
cloud_freeRVs ['velocity_norm', 'log10_Tkin_norm', 'fwhm_nonthermal_norm', 'log10_N_12CN_norm', 'ratio_13C_12C_norm']
cloud_deterministics ['velocity', 'log10_Tkin', 'fwhm_thermal_12CN', 'fwhm_thermal_13CN', 'fwhm_nonthermal', 'fwhm_12CN', 'fwhm_13CN', 'log10_N_12CN', 'ratio_13C_12C', 'N_13CN', 'log10_Tex_ul', 'Tex_12CN', 'tau_12CN', 'tau_total_12CN', 'TR_12CN', 'Tex_13CN', 'tau_13CN', 'tau_total_13CN', 'TR_13CN']
hyper_freeRVs []
hyper_deterministics []
['velocity', 'log10_Tkin', 'fwhm_thermal_12CN', 'fwhm_thermal_13CN', 'fwhm_nonthermal', 'fwhm_12CN', 'fwhm_13CN', 'log10_N_12CN', 'ratio_13C_12C', 'N_13CN', 'log10_Tex_ul', 'tau_total_12CN', 'tau_total_13CN']
../_images/notebooks_cn_ratio_model_10_1.png

Variational Inference

[9]:

start = time.time()
model.fit(
    n = 100_000, # maximum number of VI iterations
    draws = 1_000, # number of posterior samples
    rel_tolerance = 0.05, # VI relative convergence threshold
    abs_tolerance = 0.05, # VI absolute convergence threshold
    learning_rate = 0.01, # VI learning rate
)
end = time.time()
print(f"Runtime: {(end-start)/60.0:.2f} minutes")













Convergence achieved at 6300
Interrupted at 6,299 [6%]: Average Loss = 1.4302e+05





































Runtime: 0.44 minutes







[10]:





posterior = model.sample_posterior_predictive(
    thin=10, # keep one in {thin} posterior samples
)
_ = plot_predictive(model.data, posterior.posterior_predictive)















Sampling: [12CN-1, 12CN-2, 13CN-1, 13CN-2]




































../_images/notebooks_cn_ratio_model_13_3.png









Posterior Sampling: MCMC




[11]:





start = time.time()
init_kwargs = {
    "rel_tolerance": 0.05,
    "abs_tolerance": 0.05,
    "learning_rate": 0.01,
}
model.sample(
    init = "advi+adapt_diag", # initialization strategy
    tune = 1000, # tuning samples
    draws = 1000, # posterior samples
    chains = 8, # number of independent chains
    cores = 8, # number of parallel chains
    init_kwargs = init_kwargs, # VI initialization arguments
    nuts_kwargs = {"target_accept": 0.8}, # NUTS arguments
)
end = time.time()
print(f"Runtime: {(end-start)/60.0:.2f} minutes")















Initializing NUTS using custom advi+adapt_diag strategy





































Convergence achieved at 6300
Interrupted at 6,299 [6%]: Average Loss = 1.4302e+05
Multiprocess sampling (8 chains in 8 jobs)
NUTS: [baseline_12CN-1_norm, baseline_12CN-2_norm, baseline_13CN-1_norm, baseline_13CN-2_norm, velocity_norm, log10_Tkin_norm, fwhm_nonthermal_norm, log10_N_12CN_norm, ratio_13C_12C_norm]





































Sampling 8 chains for 1_000 tune and 1_000 draw iterations (8_000 + 8_000 draws total) took 68 seconds.













Adding log-likelihood to trace





































Runtime: 1.82 minutes







[12]:





model.solve(kl_div_threshold=0.1)















GMM converged to unique solution







[13]:





print("solutions:", model.solutions)

pm.summary(model.trace.solution_0)















solutions: [0]







[13]:











  
    

      
      mean
      sd
      hdi_3%
      hdi_97%
      mcse_mean
      mcse_sd
      ess_bulk
      ess_tail
      r_hat
    

  
  
    

      baseline_12CN-1_norm[0]
      -2.020000e-01
      4.700000e-02
      -2.890000e-01
      -1.130000e-01
      0.000000e+00
      1.000000e-03
      11161.0
      5772.0
      1.0
    

    

      baseline_12CN-2_norm[0]
      -2.550000e-01
      6.000000e-02
      -3.630000e-01
      -1.400000e-01
      1.000000e-03
      1.000000e-03
      10346.0
      5718.0
      1.0
    

    

      baseline_13CN-1_norm[0]
      -1.020000e-01
      6.500000e-02
      -2.260000e-01
      1.500000e-02
      1.000000e-03
      1.000000e-03
      10616.0
      6478.0
      1.0
    

    

      baseline_13CN-2_norm[0]
      -8.200000e-02
      6.400000e-02
      -2.030000e-01
      3.700000e-02
      1.000000e-03
      1.000000e-03
      11413.0
      5918.0
      1.0
    

    

      velocity_norm[0]
      -1.670000e-01
      0.000000e+00
      -1.670000e-01
      -1.660000e-01
      0.000000e+00
      0.000000e+00
      11225.0
      6395.0
      1.0
    

    

      velocity_norm[1]
      5.000000e-01
      0.000000e+00
      4.990000e-01
      5.010000e-01
      0.000000e+00
      0.000000e+00
      11070.0
      6152.0
      1.0
    

    

      log10_Tkin_norm[0]
      -8.020000e-01
      1.000000e-03
      -8.040000e-01
      -7.990000e-01
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      log10_Tkin_norm[1]
      -6.020000e-01
      2.000000e-03
      -6.060000e-01
      -5.980000e-01
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      log10_N_12CN_norm[0]
      4.050000e-01
      4.000000e-03
      3.980000e-01
      4.120000e-01
      0.000000e+00
      0.000000e+00
      7722.0
      6351.0
      1.0
    

    

      log10_N_12CN_norm[1]
      3.000000e-01
      2.000000e-03
      2.950000e-01
      3.050000e-01
      0.000000e+00
      0.000000e+00
      7570.0
      5873.0
      1.0
    

    

      fwhm_nonthermal_norm[0]
      5.010000e-01
      3.000000e-03
      4.950000e-01
      5.060000e-01
      0.000000e+00
      0.000000e+00
      10781.0
      6085.0
      1.0
    

    

      fwhm_nonthermal_norm[1]
      7.460000e-01
      2.000000e-03
      7.420000e-01
      7.510000e-01
      0.000000e+00
      0.000000e+00
      10446.0
      6487.0
      1.0
    

    

      ratio_13C_12C_norm[0]
      1.700000e-01
      1.500000e-02
      1.410000e-01
      1.990000e-01
      0.000000e+00
      0.000000e+00
      10279.0
      5823.0
      1.0
    

    

      ratio_13C_12C_norm[1]
      1.720000e-01
      1.500000e-02
      1.460000e-01
      2.010000e-01
      0.000000e+00
      0.000000e+00
      10356.0
      5761.0
      1.0
    

    

      velocity[0]
      -5.000000e-01
      1.000000e-03
      -5.020000e-01
      -4.980000e-01
      0.000000e+00
      0.000000e+00
      11225.0
      6395.0
      1.0
    

    

      velocity[1]
      1.500000e+00
      1.000000e-03
      1.498000e+00
      1.502000e+00
      0.000000e+00
      0.000000e+00
      11070.0
      6152.0
      1.0
    

    

      log10_Tkin[0]
      5.990000e-01
      1.000000e-03
      5.980000e-01
      6.000000e-01
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      log10_Tkin[1]
      6.990000e-01
      1.000000e-03
      6.970000e-01
      7.010000e-01
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      fwhm_thermal_12CN[0]
      8.400000e-02
      0.000000e+00
      8.400000e-02
      8.400000e-02
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      fwhm_thermal_12CN[1]
      9.400000e-02
      0.000000e+00
      9.400000e-02
      9.400000e-02
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      fwhm_thermal_13CN[0]
      8.200000e-02
      0.000000e+00
      8.200000e-02
      8.200000e-02
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      fwhm_thermal_13CN[1]
      9.200000e-02
      0.000000e+00
      9.200000e-02
      9.200000e-02
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      fwhm_nonthermal[0]
      5.010000e-01
      3.000000e-03
      4.950000e-01
      5.060000e-01
      0.000000e+00
      0.000000e+00
      10781.0
      6085.0
      1.0
    

    

      fwhm_nonthermal[1]
      7.460000e-01
      2.000000e-03
      7.420000e-01
      7.510000e-01
      0.000000e+00
      0.000000e+00
      10446.0
      6487.0
      1.0
    

    

      fwhm_12CN[0]
      5.080000e-01
      3.000000e-03
      5.020000e-01
      5.130000e-01
      0.000000e+00
      0.000000e+00
      10764.0
      6133.0
      1.0
    

    

      fwhm_12CN[1]
      7.520000e-01
      2.000000e-03
      7.480000e-01
      7.560000e-01
      0.000000e+00
      0.000000e+00
      10415.0
      6487.0
      1.0
    

    

      fwhm_13CN[0]
      5.070000e-01
      3.000000e-03
      5.020000e-01
      5.130000e-01
      0.000000e+00
      0.000000e+00
      10765.0
      6133.0
      1.0
    

    

      fwhm_13CN[1]
      7.520000e-01
      2.000000e-03
      7.470000e-01
      7.560000e-01
      0.000000e+00
      0.000000e+00
      10417.0
      6487.0
      1.0
    

    

      log10_N_12CN[0]
      1.390500e+01
      4.000000e-03
      1.389800e+01
      1.391200e+01
      0.000000e+00
      0.000000e+00
      7722.0
      6351.0
      1.0
    

    

      log10_N_12CN[1]
      1.380000e+01
      2.000000e-03
      1.379500e+01
      1.380500e+01
      0.000000e+00
      0.000000e+00
      7570.0
      5873.0
      1.0
    

    

      ratio_13C_12C[0]
      1.700000e-02
      2.000000e-03
      1.400000e-02
      2.000000e-02
      0.000000e+00
      0.000000e+00
      10279.0
      5823.0
      1.0
    

    

      ratio_13C_12C[1]
      1.700000e-02
      1.000000e-03
      1.500000e-02
      2.000000e-02
      0.000000e+00
      0.000000e+00
      10356.0
      5761.0
      1.0
    

    

      N_13CN[0]
      1.361780e+12
      1.221311e+11
      1.137075e+12
      1.593363e+12
      1.197683e+09
      1.430151e+09
      10396.0
      5667.0
      1.0
    

    

      N_13CN[1]
      1.086187e+12
      9.311752e+10
      9.165948e+11
      1.263586e+12
      9.165776e+08
      1.101186e+09
      10327.0
      5822.0
      1.0
    

    

      log10_Tex_ul[0]
      5.990000e-01
      1.000000e-03
      5.980000e-01
      6.000000e-01
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      log10_Tex_ul[1]
      6.990000e-01
      1.000000e-03
      6.970000e-01
      7.010000e-01
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      Tex_12CN[113123.3687, 0]
      3.973000e+00
      7.000000e-03
      3.961000e+00
      3.986000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      Tex_12CN[113123.3687, 1]
      5.001000e+00
      1.200000e-02
      4.979000e+00
      5.024000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      Tex_12CN[113144.19, 0]
      3.973000e+00
      7.000000e-03
      3.961000e+00
      3.986000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      Tex_12CN[113144.19, 1]
      5.001000e+00
      1.200000e-02
      4.979000e+00
      5.024000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      Tex_12CN[113170.535, 0]
      3.973000e+00
      7.000000e-03
      3.961000e+00
      3.986000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      Tex_12CN[113170.535, 1]
      5.001000e+00
      1.200000e-02
      4.979000e+00
      5.024000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      Tex_12CN[113191.325, 0]
      3.973000e+00
      7.000000e-03
      3.961000e+00
      3.986000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      Tex_12CN[113191.325, 1]
      5.001000e+00
      1.200000e-02
      4.979000e+00
      5.024000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      Tex_12CN[113488.142, 0]
      3.973000e+00
      7.000000e-03
      3.961000e+00
      3.986000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      Tex_12CN[113488.142, 1]
      5.001000e+00
      1.200000e-02
      4.979000e+00
      5.024000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      Tex_12CN[113490.985, 0]
      3.973000e+00
      7.000000e-03
      3.961000e+00
      3.986000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      Tex_12CN[113490.985, 1]
      5.001000e+00
      1.200000e-02
      4.979000e+00
      5.024000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      Tex_12CN[113499.643, 0]
      3.973000e+00
      7.000000e-03
      3.961000e+00
      3.986000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      Tex_12CN[113499.643, 1]
      5.001000e+00
      1.200000e-02
      4.979000e+00
      5.024000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      Tex_12CN[113508.934, 0]
      3.973000e+00
      7.000000e-03
      3.961000e+00
      3.986000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      Tex_12CN[113508.934, 1]
      5.001000e+00
      1.200000e-02
      4.979000e+00
      5.024000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      Tex_12CN[113520.4215, 0]
      3.973000e+00
      7.000000e-03
      3.961000e+00
      3.986000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      Tex_12CN[113520.4215, 1]
      5.001000e+00
      1.200000e-02
      4.979000e+00
      5.024000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      tau_12CN[113123.3687, 0]
      4.000000e-02
      0.000000e+00
      3.900000e-02
      4.100000e-02
      0.000000e+00
      0.000000e+00
      7666.0
      6023.0
      1.0
    

    

      tau_12CN[113123.3687, 1]
      2.500000e-02
      0.000000e+00
      2.400000e-02
      2.500000e-02
      0.000000e+00
      0.000000e+00
      7458.0
      5355.0
      1.0
    

    

      tau_12CN[113144.19, 0]
      3.290000e-01
      3.000000e-03
      3.230000e-01
      3.350000e-01
      0.000000e+00
      0.000000e+00
      7666.0
      6023.0
      1.0
    

    

      tau_12CN[113144.19, 1]
      2.010000e-01
      2.000000e-03
      1.980000e-01
      2.040000e-01
      0.000000e+00
      0.000000e+00
      7458.0
      5355.0
      1.0
    

    

      tau_12CN[113170.535, 0]
      3.210000e-01
      3.000000e-03
      3.150000e-01
      3.270000e-01
      0.000000e+00
      0.000000e+00
      7666.0
      6023.0
      1.0
    

    

      tau_12CN[113170.535, 1]
      1.960000e-01
      2.000000e-03
      1.930000e-01
      1.990000e-01
      0.000000e+00
      0.000000e+00
      7458.0
      5355.0
      1.0
    

    

      tau_12CN[113191.325, 0]
      4.170000e-01
      4.000000e-03
      4.090000e-01
      4.250000e-01
      0.000000e+00
      0.000000e+00
      7666.0
      6023.0
      1.0
    

    

      tau_12CN[113191.325, 1]
      2.550000e-01
      2.000000e-03
      2.510000e-01
      2.590000e-01
      0.000000e+00
      0.000000e+00
      7458.0
      5355.0
      1.0
    

    

      tau_12CN[113488.142, 0]
      4.180000e-01
      4.000000e-03
      4.110000e-01
      4.260000e-01
      0.000000e+00
      0.000000e+00
      7666.0
      6023.0
      1.0
    

    

      tau_12CN[113488.142, 1]
      2.560000e-01
      2.000000e-03
      2.520000e-01
      2.600000e-01
      0.000000e+00
      0.000000e+00
      7458.0
      5355.0
      1.0
    

    

      tau_12CN[113490.985, 0]
      1.111000e+00
      1.100000e-02
      1.091000e+00
      1.133000e+00
      0.000000e+00
      0.000000e+00
      7666.0
      6023.0
      1.0
    

    

      tau_12CN[113490.985, 1]
      6.800000e-01
      6.000000e-03
      6.690000e-01
      6.900000e-01
      0.000000e+00
      0.000000e+00
      7458.0
      5355.0
      1.0
    

    

      tau_12CN[113499.643, 0]
      3.300000e-01
      3.000000e-03
      3.240000e-01
      3.360000e-01
      0.000000e+00
      0.000000e+00
      7666.0
      6023.0
      1.0
    

    

      tau_12CN[113499.643, 1]
      2.020000e-01
      2.000000e-03
      1.990000e-01
      2.050000e-01
      0.000000e+00
      0.000000e+00
      7458.0
      5355.0
      1.0
    

    

      tau_12CN[113508.934, 0]
      3.220000e-01
      3.000000e-03
      3.170000e-01
      3.290000e-01
      0.000000e+00
      0.000000e+00
      7666.0
      6023.0
      1.0
    

    

      tau_12CN[113508.934, 1]
      1.970000e-01
      2.000000e-03
      1.940000e-01
      2.000000e-01
      0.000000e+00
      0.000000e+00
      7458.0
      5355.0
      1.0
    

    

      tau_12CN[113520.4215, 0]
      4.000000e-02
      0.000000e+00
      4.000000e-02
      4.100000e-02
      0.000000e+00
      0.000000e+00
      7666.0
      6023.0
      1.0
    

    

      tau_12CN[113520.4215, 1]
      2.500000e-02
      0.000000e+00
      2.400000e-02
      2.500000e-02
      0.000000e+00
      0.000000e+00
      7458.0
      5355.0
      1.0
    

    

      tau_total_12CN[0]
      3.329000e+00
      3.400000e-02
      3.268000e+00
      3.393000e+00
      0.000000e+00
      0.000000e+00
      7666.0
      6023.0
      1.0
    

    

      tau_total_12CN[1]
      2.038000e+00
      1.700000e-02
      2.005000e+00
      2.068000e+00
      0.000000e+00
      0.000000e+00
      7458.0
      5355.0
      1.0
    

    

      TR_12CN[113123.3687, 0]
      1.858000e+00
      6.000000e-03
      1.848000e+00
      1.869000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_12CN[113123.3687, 1]
      2.768000e+00
      1.100000e-02
      2.748000e+00
      2.789000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_12CN[113144.19, 0]
      1.858000e+00
      6.000000e-03
      1.848000e+00
      1.869000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_12CN[113144.19, 1]
      2.768000e+00
      1.100000e-02
      2.748000e+00
      2.789000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_12CN[113170.535, 0]
      1.858000e+00
      6.000000e-03
      1.847000e+00
      1.868000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_12CN[113170.535, 1]
      2.767000e+00
      1.100000e-02
      2.747000e+00
      2.788000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_12CN[113191.325, 0]
      1.857000e+00
      6.000000e-03
      1.847000e+00
      1.868000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_12CN[113191.325, 1]
      2.767000e+00
      1.100000e-02
      2.747000e+00
      2.788000e+00
      0.000000e+00
      0.000000e+00
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      5553.0
      1.0
    

    

      tau_13CN[108426.889, 1]
      2.000000e-03
      0.000000e+00
      1.000000e-03
      2.000000e-03
      0.000000e+00
      0.000000e+00
      10280.0
      5664.0
      1.0
    

    

      tau_13CN[108631.121, 0]
      1.000000e-03
      0.000000e+00
      1.000000e-03
      2.000000e-03
      0.000000e+00
      0.000000e+00
      10418.0
      5553.0
      1.0
    

    

      tau_13CN[108631.121, 1]
      1.000000e-03
      0.000000e+00
      1.000000e-03
      1.000000e-03
      0.000000e+00
      0.000000e+00
      10279.0
      5664.0
      1.0
    

    

      tau_13CN[108636.923, 0]
      4.000000e-03
      0.000000e+00
      3.000000e-03
      5.000000e-03
      0.000000e+00
      0.000000e+00
      10418.0
      5553.0
      1.0
    

    

      tau_13CN[108636.923, 1]
      2.000000e-03
      0.000000e+00
      2.000000e-03
      3.000000e-03
      0.000000e+00
      0.000000e+00
      10279.0
      5664.0
      1.0
    

    

      tau_13CN[108638.212, 0]
      1.000000e-03
      0.000000e+00
      1.000000e-03
      2.000000e-03
      0.000000e+00
      0.000000e+00
      10419.0
      5553.0
      1.0
    

    

      tau_13CN[108638.212, 1]
      1.000000e-03
      0.000000e+00
      1.000000e-03
      1.000000e-03
      0.000000e+00
      0.000000e+00
      10280.0
      5664.0
      1.0
    

    

      tau_13CN[108643.59, 0]
      2.000000e-03
      0.000000e+00
      1.000000e-03
      2.000000e-03
      0.000000e+00
      0.000000e+00
      10419.0
      5553.0
      1.0
    

    

      tau_13CN[108643.59, 1]
      1.000000e-03
      0.000000e+00
      1.000000e-03
      1.000000e-03
      0.000000e+00
      0.000000e+00
      10280.0
      5664.0
      1.0
    

    

      tau_13CN[108644.3602, 0]
      1.000000e-03
      0.000000e+00
      1.000000e-03
      2.000000e-03
      0.000000e+00
      0.000000e+00
      10419.0
      5553.0
      1.0
    

    

      tau_13CN[108644.3602, 1]
      1.000000e-03
      0.000000e+00
      1.000000e-03
      1.000000e-03
      0.000000e+00
      0.000000e+00
      10280.0
      5664.0
      1.0
    

    

      tau_13CN[108645.064, 0]
      1.000000e-03
      0.000000e+00
      1.000000e-03
      1.000000e-03
      0.000000e+00
      0.000000e+00
      10419.0
      5553.0
      1.0
    

    

      tau_13CN[108645.064, 1]
      1.000000e-03
      0.000000e+00
      1.000000e-03
      1.000000e-03
      0.000000e+00
      0.000000e+00
      10280.0
      5664.0
      1.0
    

    

      tau_13CN[108651.297, 0]
      7.000000e-03
      1.000000e-03
      6.000000e-03
      8.000000e-03
      0.000000e+00
      0.000000e+00
      10418.0
      5553.0
      1.0
    

    

      tau_13CN[108651.297, 1]
      4.000000e-03
      0.000000e+00
      4.000000e-03
      5.000000e-03
      0.000000e+00
      0.000000e+00
      10279.0
      5664.0
      1.0
    

    

      tau_13CN[108657.646, 0]
      5.000000e-03
      0.000000e+00
      4.000000e-03
      6.000000e-03
      0.000000e+00
      0.000000e+00
      10419.0
      5553.0
      1.0
    

    

      tau_13CN[108657.646, 1]
      3.000000e-03
      0.000000e+00
      3.000000e-03
      4.000000e-03
      0.000000e+00
      0.000000e+00
      10280.0
      5664.0
      1.0
    

    

      tau_13CN[108658.948, 0]
      1.000000e-03
      0.000000e+00
      1.000000e-03
      2.000000e-03
      0.000000e+00
      0.000000e+00
      10419.0
      5553.0
      1.0
    

    

      tau_13CN[108658.948, 1]
      1.000000e-03
      0.000000e+00
      1.000000e-03
      1.000000e-03
      0.000000e+00
      0.000000e+00
      10280.0
      5664.0
      1.0
    

    

      tau_13CN[108780.201, 0]
      1.000000e-02
      1.000000e-03
      8.000000e-03
      1.200000e-02
      0.000000e+00
      0.000000e+00
      10418.0
      5553.0
      1.0
    

    

      tau_13CN[108780.201, 1]
      6.000000e-03
      1.000000e-03
      5.000000e-03
      7.000000e-03
      0.000000e+00
      0.000000e+00
      10280.0
      5664.0
      1.0
    

    

      tau_13CN[108782.374, 0]
      5.000000e-03
      0.000000e+00
      4.000000e-03
      6.000000e-03
      0.000000e+00
      0.000000e+00
      10418.0
      5553.0
      1.0
    

    

      tau_13CN[108782.374, 1]
      3.000000e-03
      0.000000e+00
      3.000000e-03
      4.000000e-03
      0.000000e+00
      0.000000e+00
      10280.0
      5664.0
      1.0
    

    

      tau_13CN[108786.982, 0]
      2.000000e-03
      0.000000e+00
      2.000000e-03
      3.000000e-03
      0.000000e+00
      0.000000e+00
      10418.0
      5553.0
      1.0
    

    

      tau_13CN[108786.982, 1]
      1.000000e-03
      0.000000e+00
      1.000000e-03
      2.000000e-03
      0.000000e+00
      0.000000e+00
      10280.0
      5664.0
      1.0
    

    

      tau_13CN[108793.753, 0]
      2.000000e-03
      0.000000e+00
      2.000000e-03
      2.000000e-03
      0.000000e+00
      0.000000e+00
      10418.0
      5553.0
      1.0
    

    

      tau_13CN[108793.753, 1]
      1.000000e-03
      0.000000e+00
      1.000000e-03
      1.000000e-03
      0.000000e+00
      0.000000e+00
      10280.0
      5664.0
      1.0
    

    

      tau_13CN[108796.4, 0]
      2.000000e-03
      0.000000e+00
      2.000000e-03
      2.000000e-03
      0.000000e+00
      0.000000e+00
      10418.0
      5553.0
      1.0
    

    

      tau_13CN[108796.4, 1]
      1.000000e-03
      0.000000e+00
      1.000000e-03
      1.000000e-03
      0.000000e+00
      0.000000e+00
      10280.0
      5664.0
      1.0
    

    

      tau_13CN[108807.8006, 0]
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      10418.0
      5553.0
      1.0
    

    

      tau_13CN[108807.8006, 1]
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      10280.0
      5664.0
      1.0
    

    

      tau_13CN[108986.8678, 0]
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      10418.0
      5553.0
      1.0
    

    

      tau_13CN[108986.8678, 1]
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      10279.0
      5664.0
      1.0
    

    

      tau_13CN[109217.6017, 0]
      0.000000e+00
      0.000000e+00
      0.000000e+00
      1.000000e-03
      0.000000e+00
      0.000000e+00
      10418.0
      5553.0
      1.0
    

    

      tau_13CN[109217.6017, 1]
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      10279.0
      5664.0
      1.0
    

    

      tau_13CN[109218.3621, 0]
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      10418.0
      5553.0
      1.0
    

    

      tau_13CN[109218.3621, 1]
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      10279.0
      5664.0
      1.0
    

    

      tau_13CN[109218.9506, 0]
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      10418.0
      5553.0
      1.0
    

    

      tau_13CN[109218.9506, 1]
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      0.000000e+00
      10279.0
      5664.0
      1.0
    

    

      tau_total_13CN[0]
      5.200000e-02
      5.000000e-03
      4.300000e-02
      6.100000e-02
      0.000000e+00
      0.000000e+00
      10418.0
      5553.0
      1.0
    

    

      tau_total_13CN[1]
      3.200000e-02
      3.000000e-03
      2.700000e-02
      3.700000e-02
      0.000000e+00
      0.000000e+00
      10280.0
      5664.0
      1.0
    

    

      TR_13CN[108056.1506, 0]
      1.929000e+00
      6.000000e-03
      1.918000e+00
      1.940000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108056.1506, 1]
      2.848000e+00
      1.100000e-02
      2.828000e+00
      2.869000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[108057.1294, 0]
      1.929000e+00
      6.000000e-03
      1.918000e+00
      1.940000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108057.1294, 1]
      2.848000e+00
      1.100000e-02
      2.828000e+00
      2.869000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[108062.9185, 0]
      1.929000e+00
      6.000000e-03
      1.918000e+00
      1.940000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108062.9185, 1]
      2.848000e+00
      1.100000e-02
      2.828000e+00
      2.869000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[108076.9565, 0]
      1.929000e+00
      6.000000e-03
      1.918000e+00
      1.939000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108076.9565, 1]
      2.848000e+00
      1.100000e-02
      2.828000e+00
      2.869000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[108077.2715, 0]
      1.929000e+00
      6.000000e-03
      1.918000e+00
      1.939000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108077.2715, 1]
      2.848000e+00
      1.100000e-02
      2.828000e+00
      2.869000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[108091.3095, 0]
      1.928000e+00
      6.000000e-03
      1.918000e+00
      1.939000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108091.3095, 1]
      2.848000e+00
      1.100000e-02
      2.828000e+00
      2.869000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[108406.0979, 0]
      1.924000e+00
      6.000000e-03
      1.913000e+00
      1.935000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108406.0979, 1]
      2.843000e+00
      1.100000e-02
      2.823000e+00
      2.864000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[108412.862, 0]
      1.924000e+00
      6.000000e-03
      1.913000e+00
      1.935000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108412.862, 1]
      2.843000e+00
      1.100000e-02
      2.822000e+00
      2.864000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[108426.889, 0]
      1.924000e+00
      6.000000e-03
      1.913000e+00
      1.934000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108426.889, 1]
      2.842000e+00
      1.100000e-02
      2.822000e+00
      2.863000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[108631.121, 0]
      1.921000e+00
      6.000000e-03
      1.910000e+00
      1.932000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108631.121, 1]
      2.839000e+00
      1.100000e-02
      2.819000e+00
      2.860000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[108636.923, 0]
      1.921000e+00
      6.000000e-03
      1.910000e+00
      1.931000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108636.923, 1]
      2.839000e+00
      1.100000e-02
      2.819000e+00
      2.860000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[108638.212, 0]
      1.921000e+00
      6.000000e-03
      1.910000e+00
      1.931000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108638.212, 1]
      2.839000e+00
      1.100000e-02
      2.819000e+00
      2.860000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[108643.59, 0]
      1.921000e+00
      6.000000e-03
      1.910000e+00
      1.931000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108643.59, 1]
      2.839000e+00
      1.100000e-02
      2.819000e+00
      2.860000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[108644.3602, 0]
      1.921000e+00
      6.000000e-03
      1.910000e+00
      1.931000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108644.3602, 1]
      2.839000e+00
      1.100000e-02
      2.819000e+00
      2.860000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[108645.064, 0]
      1.921000e+00
      6.000000e-03
      1.910000e+00
      1.931000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108645.064, 1]
      2.839000e+00
      1.100000e-02
      2.819000e+00
      2.860000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[108651.297, 0]
      1.920000e+00
      6.000000e-03
      1.910000e+00
      1.931000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108651.297, 1]
      2.839000e+00
      1.100000e-02
      2.819000e+00
      2.860000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[108657.646, 0]
      1.920000e+00
      6.000000e-03
      1.910000e+00
      1.931000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108657.646, 1]
      2.839000e+00
      1.100000e-02
      2.819000e+00
      2.860000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[108658.948, 0]
      1.920000e+00
      6.000000e-03
      1.910000e+00
      1.931000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108658.948, 1]
      2.839000e+00
      1.100000e-02
      2.819000e+00
      2.860000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[108780.201, 0]
      1.919000e+00
      6.000000e-03
      1.908000e+00
      1.929000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108780.201, 1]
      2.837000e+00
      1.100000e-02
      2.817000e+00
      2.858000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[108782.374, 0]
      1.919000e+00
      6.000000e-03
      1.908000e+00
      1.929000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108782.374, 1]
      2.837000e+00
      1.100000e-02
      2.817000e+00
      2.858000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[108786.982, 0]
      1.919000e+00
      6.000000e-03
      1.908000e+00
      1.929000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108786.982, 1]
      2.837000e+00
      1.100000e-02
      2.816000e+00
      2.858000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[108793.753, 0]
      1.918000e+00
      6.000000e-03
      1.908000e+00
      1.929000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108793.753, 1]
      2.836000e+00
      1.100000e-02
      2.816000e+00
      2.858000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[108796.4, 0]
      1.918000e+00
      6.000000e-03
      1.908000e+00
      1.929000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108796.4, 1]
      2.836000e+00
      1.100000e-02
      2.816000e+00
      2.857000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[108807.8006, 0]
      1.918000e+00
      6.000000e-03
      1.908000e+00
      1.929000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108807.8006, 1]
      2.836000e+00
      1.100000e-02
      2.816000e+00
      2.857000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[108986.8678, 0]
      1.916000e+00
      6.000000e-03
      1.905000e+00
      1.927000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[108986.8678, 1]
      2.833000e+00
      1.100000e-02
      2.813000e+00
      2.854000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[109217.6017, 0]
      1.912000e+00
      6.000000e-03
      1.902000e+00
      1.923000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[109217.6017, 1]
      2.830000e+00
      1.100000e-02
      2.810000e+00
      2.851000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[109218.3621, 0]
      1.912000e+00
      6.000000e-03
      1.902000e+00
      1.923000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[109218.3621, 1]
      2.830000e+00
      1.100000e-02
      2.810000e+00
      2.851000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

    

      TR_13CN[109218.9506, 0]
      1.912000e+00
      6.000000e-03
      1.902000e+00
      1.923000e+00
      0.000000e+00
      0.000000e+00
      7582.0
      5864.0
      1.0
    

    

      TR_13CN[109218.9506, 1]
      2.830000e+00
      1.100000e-02
      2.810000e+00
      2.851000e+00
      0.000000e+00
      0.000000e+00
      7265.0
      5703.0
      1.0
    

  









[14]:





posterior = model.sample_posterior_predictive(
    thin=10, # keep one in {thin} posterior samples
)
_ = plot_predictive(model.data, posterior.posterior_predictive)















Sampling: [12CN-1, 12CN-2, 13CN-1, 13CN-2]




































../_images/notebooks_cn_ratio_model_18_3.png







[15]:





from bayes_spec.plots import plot_traces

axes = plot_traces(model.trace.solution_0, model.cloud_freeRVs + model.baseline_freeRVs + model.hyper_freeRVs)
fig = axes.ravel()[0].figure
fig.tight_layout()














../_images/notebooks_cn_ratio_model_19_0.png





We can inspect the posterior distribution pair plots. First, the normalized, free cloud parameters.




[16]:





from bayes_spec.plots import plot_pair

var_names = [
    param for param in model.cloud_deterministics
    if not set(model.model.named_vars_to_dims[param]).intersection(set(
        ["transition_12CN", "state_12CN", "transition_13CN", "state_13CN"]
    ))
]
_ = plot_pair(
    model.trace.solution_0, # samples
    var_names, # var_names to plot
    labeller=model.labeller, # label manager
    kind="scatter", # plot type
    reference_values=sim_params, # truths
)














../_images/notebooks_cn_ratio_model_21_0.png







[17]:





# identify simulation cloud corresponding to each posterior cloud
sim_cloud_map = {}
for i in range(n_clouds):
    posterior_velocity = model.trace.solution_0['velocity'].sel(cloud=i).data.mean()
    match = np.argmin(np.abs(sim_params["velocity"] - posterior_velocity))
    sim_cloud_map[i] = match
sim_cloud_map









[17]:







{0: np.int64(0), 1: np.int64(1)}







[18]:





cloud = 0

# subset of sim_params
my_sim_params = {}
for var_name in model.cloud_deterministics:
    my_sim_params[var_name] = sim_params[var_name][sim_cloud_map[cloud]]

# ignore transition and state dependent parameters
var_names = [
    param for param in model.cloud_deterministics
    if not set(model.model.named_vars_to_dims[param]).intersection(set(
        ["transition_12CN", "state_12CN", "transition_13CN", "state_13CN"]
    ))
]
print(var_names)
_ = plot_pair(
    model.trace.solution_0.sel(cloud=cloud), # samples
    var_names, # var_names to plot
    labeller=model.labeller, # label manager
    kind="kde", # plot type
    reference_values=my_sim_params, # truths
)















['velocity', 'log10_Tkin', 'fwhm_thermal_12CN', 'fwhm_thermal_13CN', 'fwhm_nonthermal', 'fwhm_12CN', 'fwhm_13CN', 'log10_N_12CN', 'ratio_13C_12C', 'N_13CN', 'log10_Tex_ul', 'tau_total_12CN', 'tau_total_13CN']












../_images/notebooks_cn_ratio_model_23_1.png







[19]:





cloud = 1

# subset of sim_params
my_sim_params = {}
for var_name in model.cloud_deterministics:
    my_sim_params[var_name] = sim_params[var_name][sim_cloud_map[cloud]]

# ignore transition and state dependent parameters
var_names = [
    param for param in model.cloud_deterministics
    if not set(model.model.named_vars_to_dims[param]).intersection(set(
        ["transition_12CN", "state_12CN", "transition_13CN", "state_13CN"]
    ))
]
print(var_names)
_ = plot_pair(
    model.trace.solution_0.sel(cloud=cloud), # samples
    var_names, # var_names to plot
    labeller=model.labeller, # label manager
    kind="kde", # plot type
    reference_values=my_sim_params, # truths
)















['velocity', 'log10_Tkin', 'fwhm_thermal_12CN', 'fwhm_thermal_13CN', 'fwhm_nonthermal', 'fwhm_12CN', 'fwhm_13CN', 'log10_N_12CN', 'ratio_13C_12C', 'N_13CN', 'log10_Tex_ul', 'tau_total_12CN', 'tau_total_13CN']












../_images/notebooks_cn_ratio_model_24_1.png







[20]:





var_names=model.cloud_deterministics + model.baseline_freeRVs
point_stats = az.summary(model.trace.solution_0, var_names=var_names, kind='stats', hdi_prob=0.68)
print("BIC:", model.bic())
display(point_stats)















BIC: -9571.68263464707

















  
    

      
      mean
      sd
      hdi_16%
      hdi_84%
    

  
  
    

      velocity[0]
      -5.000000e-01
      1.000000e-03
      -5.010000e-01
      -4.990000e-01
    

    

      velocity[1]
      1.500000e+00
      1.000000e-03
      1.499000e+00
      1.501000e+00
    

    

      log10_Tkin[0]
      5.990000e-01
      1.000000e-03
      5.980000e-01
      6.000000e-01
    

    

      log10_Tkin[1]
      6.990000e-01
      1.000000e-03
      6.980000e-01
      7.000000e-01
    

    

      fwhm_thermal_12CN[0]
      8.400000e-02
      0.000000e+00
      8.400000e-02
      8.400000e-02
    

    

      fwhm_thermal_12CN[1]
      9.400000e-02
      0.000000e+00
      9.400000e-02
      9.400000e-02
    

    

      fwhm_thermal_13CN[0]
      8.200000e-02
      0.000000e+00
      8.200000e-02
      8.200000e-02
    

    

      fwhm_thermal_13CN[1]
      9.200000e-02
      0.000000e+00
      9.200000e-02
      9.200000e-02
    

    

      fwhm_nonthermal[0]
      5.010000e-01
      3.000000e-03
      4.980000e-01
      5.040000e-01
    

    

      fwhm_nonthermal[1]
      7.460000e-01
      2.000000e-03
      7.440000e-01
      7.490000e-01
    

    

      fwhm_12CN[0]
      5.080000e-01
      3.000000e-03
      5.050000e-01
      5.110000e-01
    

    

      fwhm_12CN[1]
      7.520000e-01
      2.000000e-03
      7.500000e-01
      7.550000e-01
    

    

      fwhm_13CN[0]
      5.070000e-01
      3.000000e-03
      5.040000e-01
      5.100000e-01
    

    

      fwhm_13CN[1]
      7.520000e-01
      2.000000e-03
      7.500000e-01
      7.540000e-01
    

    

      log10_N_12CN[0]
      1.390500e+01
      4.000000e-03
      1.390100e+01
      1.390900e+01
    

    

      log10_N_12CN[1]
      1.380000e+01
      2.000000e-03
      1.379700e+01
      1.380200e+01
    

    

      ratio_13C_12C[0]
      1.700000e-02
      2.000000e-03
      1.500000e-02
      1.800000e-02
    

    

      ratio_13C_12C[1]
      1.700000e-02
      1.000000e-03
      1.600000e-02
      1.900000e-02
    

    

      N_13CN[0]
      1.361780e+12
      1.221311e+11
      1.245871e+12
      1.487733e+12
    

    

      N_13CN[1]
      1.086187e+12
      9.311752e+10
      9.974303e+11
      1.183039e+12
    

    

      log10_Tex_ul[0]
      5.990000e-01
      1.000000e-03
      5.980000e-01
      6.000000e-01
    

    

      log10_Tex_ul[1]
      6.990000e-01
      1.000000e-03
      6.980000e-01
      7.000000e-01
    

    

      Tex_12CN[113123.3687, 0]
      3.973000e+00
      7.000000e-03
      3.966000e+00
      3.979000e+00
    

    

      Tex_12CN[113123.3687, 1]
      5.001000e+00
      1.200000e-02
      4.988000e+00
      5.012000e+00
    

    

      Tex_12CN[113144.19, 0]
      3.973000e+00
      7.000000e-03
      3.966000e+00
      3.979000e+00
    

    

      Tex_12CN[113144.19, 1]
      5.001000e+00
      1.200000e-02
      4.988000e+00
      5.012000e+00
    

    

      Tex_12CN[113170.535, 0]
      3.973000e+00
      7.000000e-03
      3.966000e+00
      3.979000e+00
    

    

      Tex_12CN[113170.535, 1]
      5.001000e+00
      1.200000e-02
      4.988000e+00
      5.012000e+00
    

    

      Tex_12CN[113191.325, 0]
      3.973000e+00
      7.000000e-03
      3.966000e+00
      3.979000e+00
    

    

      Tex_12CN[113191.325, 1]
      5.001000e+00
      1.200000e-02
      4.988000e+00
      5.012000e+00
    

    

      Tex_12CN[113488.142, 0]
      3.973000e+00
      7.000000e-03
      3.966000e+00
      3.979000e+00
    

    

      Tex_12CN[113488.142, 1]
      5.001000e+00
      1.200000e-02
      4.988000e+00
      5.012000e+00
    

    

      Tex_12CN[113490.985, 0]
      3.973000e+00
      7.000000e-03
      3.966000e+00
      3.979000e+00
    

    

      Tex_12CN[113490.985, 1]
      5.001000e+00
      1.200000e-02
      4.988000e+00
      5.012000e+00
    

    

      Tex_12CN[113499.643, 0]
      3.973000e+00
      7.000000e-03
      3.966000e+00
      3.979000e+00
    

    

      Tex_12CN[113499.643, 1]
      5.001000e+00
      1.200000e-02
      4.988000e+00
      5.012000e+00
    

    

      Tex_12CN[113508.934, 0]
      3.973000e+00
      7.000000e-03
      3.966000e+00
      3.979000e+00
    

    

      Tex_12CN[113508.934, 1]
      5.001000e+00
      1.200000e-02
      4.988000e+00
      5.012000e+00
    

    

      Tex_12CN[113520.4215, 0]
      3.973000e+00
      7.000000e-03
      3.966000e+00
      3.979000e+00
    

    

      Tex_12CN[113520.4215, 1]
      5.001000e+00
      1.200000e-02
      4.988000e+00
      5.012000e+00
    

    

      tau_12CN[113123.3687, 0]
      4.000000e-02
      0.000000e+00
      4.000000e-02
      4.100000e-02
    

    

      tau_12CN[113123.3687, 1]
      2.500000e-02
      0.000000e+00
      2.400000e-02
      2.500000e-02
    

    

      tau_12CN[113144.19, 0]
      3.290000e-01
      3.000000e-03
      3.250000e-01
      3.320000e-01
    

    

      tau_12CN[113144.19, 1]
      2.010000e-01
      2.000000e-03
      2.000000e-01
      2.030000e-01
    

    

      tau_12CN[113170.535, 0]
      3.210000e-01
      3.000000e-03
      3.180000e-01
      3.240000e-01
    

    

      tau_12CN[113170.535, 1]
      1.960000e-01
      2.000000e-03
      1.950000e-01
      1.980000e-01
    

    

      tau_12CN[113191.325, 0]
      4.170000e-01
      4.000000e-03
      4.120000e-01
      4.210000e-01
    

    

      tau_12CN[113191.325, 1]
      2.550000e-01
      2.000000e-03
      2.530000e-01
      2.570000e-01
    

    

      tau_12CN[113488.142, 0]
      4.180000e-01
      4.000000e-03
      4.140000e-01
      4.220000e-01
    

    

      tau_12CN[113488.142, 1]
      2.560000e-01
      2.000000e-03
      2.540000e-01
      2.580000e-01
    

    

      tau_12CN[113490.985, 0]
      1.111000e+00
      1.100000e-02
      1.100000e+00
      1.122000e+00
    

    

      tau_12CN[113490.985, 1]
      6.800000e-01
      6.000000e-03
      6.750000e-01
      6.860000e-01
    

    

      tau_12CN[113499.643, 0]
      3.300000e-01
      3.000000e-03
      3.270000e-01
      3.330000e-01
    

    

      tau_12CN[113499.643, 1]
      2.020000e-01
      2.000000e-03
      2.000000e-01
      2.040000e-01
    

    

      tau_12CN[113508.934, 0]
      3.220000e-01
      3.000000e-03
      3.190000e-01
      3.260000e-01
    

    

      tau_12CN[113508.934, 1]
      1.970000e-01
      2.000000e-03
      1.960000e-01
      1.990000e-01
    

    

      tau_12CN[113520.4215, 0]
      4.000000e-02
      0.000000e+00
      4.000000e-02
      4.100000e-02
    

    

      tau_12CN[113520.4215, 1]
      2.500000e-02
      0.000000e+00
      2.500000e-02
      2.500000e-02
    

    

      tau_total_12CN[0]
      3.329000e+00
      3.400000e-02
      3.294000e+00
      3.361000e+00
    

    

      tau_total_12CN[1]
      2.038000e+00
      1.700000e-02
      2.022000e+00
      2.055000e+00
    

    

      TR_12CN[113123.3687, 0]
      1.858000e+00
      6.000000e-03
      1.852000e+00
      1.864000e+00
    

    

      TR_12CN[113123.3687, 1]
      2.768000e+00
      1.100000e-02
      2.757000e+00
      2.779000e+00
    

    

      TR_12CN[113144.19, 0]
      1.858000e+00
      6.000000e-03
      1.852000e+00
      1.863000e+00
    

    

      TR_12CN[113144.19, 1]
      2.768000e+00
      1.100000e-02
      2.756000e+00
      2.778000e+00
    

    

      TR_12CN[113170.535, 0]
      1.858000e+00
      6.000000e-03
      1.852000e+00
      1.863000e+00
    

    

      TR_12CN[113170.535, 1]
      2.767000e+00
      1.100000e-02
      2.756000e+00
      2.778000e+00
    

    

      TR_12CN[113191.325, 0]
      1.857000e+00
      6.000000e-03
      1.851000e+00
      1.863000e+00
    

    

      TR_12CN[113191.325, 1]
      2.767000e+00
      1.100000e-02
      2.756000e+00
      2.777000e+00
    

    

      TR_12CN[113488.142, 0]
      1.853000e+00
      6.000000e-03
      1.847000e+00
      1.859000e+00
    

    

      TR_12CN[113488.142, 1]
      2.762000e+00
      1.100000e-02
      2.751000e+00
      2.773000e+00
    

    

      TR_12CN[113490.985, 0]
      1.853000e+00
      6.000000e-03
      1.847000e+00
      1.859000e+00
    

    

      TR_12CN[113490.985, 1]
      2.762000e+00
      1.100000e-02
      2.751000e+00
      2.773000e+00
    

    

      TR_12CN[113499.643, 0]
      1.853000e+00
      6.000000e-03
      1.847000e+00
      1.858000e+00
    

    

      TR_12CN[113499.643, 1]
      2.762000e+00
      1.100000e-02
      2.751000e+00
      2.773000e+00
    

    

      TR_12CN[113508.934, 0]
      1.853000e+00
      6.000000e-03
      1.847000e+00
      1.858000e+00
    

    

      TR_12CN[113508.934, 1]
      2.762000e+00
      1.100000e-02
      2.751000e+00
      2.772000e+00
    

    

      TR_12CN[113520.4215, 0]
      1.853000e+00
      6.000000e-03
      1.847000e+00
      1.858000e+00
    

    

      TR_12CN[113520.4215, 1]
      2.762000e+00
      1.100000e-02
      2.751000e+00
      2.772000e+00
    

    

      Tex_13CN[108056.1506, 0]
      3.973000e+00
      7.000000e-03
      3.966000e+00
      3.979000e+00
    

    

      Tex_13CN[108056.1506, 1]
      5.001000e+00
      1.200000e-02
      4.988000e+00
      5.012000e+00
    

    

      Tex_13CN[108057.1294, 0]
      3.973000e+00
      7.000000e-03
      3.966000e+00
      3.979000e+00
    

    

      Tex_13CN[108057.1294, 1]
      5.001000e+00
      1.200000e-02
      4.988000e+00
      5.012000e+00
    

    

      Tex_13CN[108062.9185, 0]
      3.973000e+00
      7.000000e-03
      3.966000e+00
      3.979000e+00
    

    

      Tex_13CN[108062.9185, 1]
      5.001000e+00
      1.200000e-02
      4.988000e+00
      5.012000e+00
    

    

      Tex_13CN[108076.9565, 0]
      3.973000e+00
      7.000000e-03
      3.966000e+00
      3.979000e+00
    

    

      Tex_13CN[108076.9565, 1]
      5.001000e+00
      1.200000e-02
      4.988000e+00
      5.012000e+00
    

    

      Tex_13CN[108077.2715, 0]
      3.973000e+00
      7.000000e-03
      3.966000e+00
      3.979000e+00
    

    

      Tex_13CN[108077.2715, 1]
      5.001000e+00
      1.200000e-02
      4.988000e+00
      5.012000e+00
    

    

      Tex_13CN[108091.3095, 0]
      3.973000e+00
      7.000000e-03
      3.966000e+00
      3.979000e+00
    

    

      Tex_13CN[108091.3095, 1]
      5.001000e+00
      1.200000e-02
      4.988000e+00
      5.012000e+00
    

    

      Tex_13CN[108406.0979, 0]
      3.973000e+00
      7.000000e-03
      3.966000e+00
      3.979000e+00
    

    

      Tex_13CN[108406.0979, 1]
      5.001000e+00
      1.200000e-02
      4.988000e+00
      5.012000e+00
    

    

      Tex_13CN[108412.862, 0]
      3.973000e+00
      7.000000e-03
      3.966000e+00
      3.979000e+00
    

    

      Tex_13CN[108412.862, 1]
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      Tex_13CN[108426.889, 0]
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      Tex_13CN[108426.889, 1]
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      Tex_13CN[108631.121, 0]
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      Tex_13CN[108631.121, 1]
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      Tex_13CN[108636.923, 0]
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      Tex_13CN[108636.923, 1]
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      Tex_13CN[108638.212, 0]
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      Tex_13CN[108638.212, 1]
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      Tex_13CN[108643.59, 0]
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      Tex_13CN[108643.59, 1]
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      Tex_13CN[108644.3602, 0]
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      Tex_13CN[108644.3602, 1]
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      Tex_13CN[108645.064, 0]
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      Tex_13CN[108645.064, 1]
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      Tex_13CN[108651.297, 0]
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      Tex_13CN[108651.297, 1]
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      Tex_13CN[108657.646, 0]
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      Tex_13CN[108657.646, 1]
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      Tex_13CN[108658.948, 0]
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      Tex_13CN[108658.948, 1]
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      Tex_13CN[108780.201, 0]
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      Tex_13CN[108780.201, 1]
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      Tex_13CN[108782.374, 0]
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      Tex_13CN[108782.374, 1]
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      Tex_13CN[108786.982, 0]
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      Tex_13CN[108786.982, 1]
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      Tex_13CN[108793.753, 0]
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      Tex_13CN[108793.753, 1]
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      Tex_13CN[108796.4, 0]
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      Tex_13CN[108796.4, 1]
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      Tex_13CN[108807.8006, 0]
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      Tex_13CN[108807.8006, 1]
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      Tex_13CN[108986.8678, 0]
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      Tex_13CN[108986.8678, 1]
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      Tex_13CN[109217.6017, 0]
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      Tex_13CN[109217.6017, 1]
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      Tex_13CN[109218.3621, 0]
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      Tex_13CN[109218.3621, 1]
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      Tex_13CN[109218.9506, 0]
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      Tex_13CN[109218.9506, 1]
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      tau_13CN[108412.862, 1]
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      tau_13CN[108426.889, 1]
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      tau_13CN[108638.212, 1]
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      tau_13CN[108644.3602, 0]
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      tau_13CN[108644.3602, 1]
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      tau_13CN[108645.064, 1]
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      tau_13CN[108780.201, 1]
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      tau_13CN[108782.374, 0]
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      TR_13CN[108780.201, 1]
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      2.837000e+00
      1.100000e-02
      2.825000e+00
      2.847000e+00
    

    

      TR_13CN[108786.982, 0]
      1.919000e+00
      6.000000e-03
      1.912000e+00
      1.924000e+00
    

    

      TR_13CN[108786.982, 1]
      2.837000e+00
      1.100000e-02
      2.825000e+00
      2.847000e+00
    

    

      TR_13CN[108793.753, 0]
      1.918000e+00
      6.000000e-03
      1.912000e+00
      1.924000e+00
    

    

      TR_13CN[108793.753, 1]
      2.836000e+00
      1.100000e-02
      2.825000e+00
      2.847000e+00
    

    

      TR_13CN[108796.4, 0]
      1.918000e+00
      6.000000e-03
      1.912000e+00
      1.924000e+00
    

    

      TR_13CN[108796.4, 1]
      2.836000e+00
      1.100000e-02
      2.825000e+00
      2.847000e+00
    

    

      TR_13CN[108807.8006, 0]
      1.918000e+00
      6.000000e-03
      1.912000e+00
      1.924000e+00
    

    

      TR_13CN[108807.8006, 1]
      2.836000e+00
      1.100000e-02
      2.825000e+00
      2.847000e+00
    

    

      TR_13CN[108986.8678, 0]
      1.916000e+00
      6.000000e-03
      1.910000e+00
      1.921000e+00
    

    

      TR_13CN[108986.8678, 1]
      2.833000e+00
      1.100000e-02
      2.822000e+00
      2.844000e+00
    

    

      TR_13CN[109217.6017, 0]
      1.912000e+00
      6.000000e-03
      1.906000e+00
      1.918000e+00
    

    

      TR_13CN[109217.6017, 1]
      2.830000e+00
      1.100000e-02
      2.818000e+00
      2.840000e+00
    

    

      TR_13CN[109218.3621, 0]
      1.912000e+00
      6.000000e-03
      1.906000e+00
      1.918000e+00
    

    

      TR_13CN[109218.3621, 1]
      2.830000e+00
      1.100000e-02
      2.818000e+00
      2.840000e+00
    

    

      TR_13CN[109218.9506, 0]
      1.912000e+00
      6.000000e-03
      1.906000e+00
      1.918000e+00
    

    

      TR_13CN[109218.9506, 1]
      2.830000e+00
      1.100000e-02
      2.818000e+00
      2.840000e+00
    

    

      baseline_12CN-1_norm[0]
      -2.020000e-01
      4.700000e-02
      -2.440000e-01
      -1.500000e-01
    

    

      baseline_12CN-2_norm[0]
      -2.550000e-01
      6.000000e-02
      -3.120000e-01
      -1.920000e-01
    

    

      baseline_13CN-1_norm[0]
      -1.020000e-01
      6.500000e-02
      -1.620000e-01
      -3.400000e-02
    

    

      baseline_13CN-2_norm[0]
      -8.200000e-02
      6.400000e-02
      -1.480000e-01
      -2.100000e-02
    

  









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