Fit a non-LTE spectrum with multiple fit parameters using new fitting module

With the new fitting module introduced in fit_spectrum() function, and in the example of Tgas fitting using new fitting module, we can see its 1-temperature fitting performance for equilibrium condition.

This example features how new fitting module can fit non-equilibrium spectrum, with multiple fit parameters, such as vibrational/rotational temperatures, or mole fraction, etc.

This is a real fitting case introduced by Mr. Corentin Grimaldi, a scientist and member of RADIS community. This case features CO molecule emitting on a wide range of spectrum. This case also includes a user-defined trapezoid slit function, which is accounted by the distortion (dispersion) of the slit, as a result of the influences from experimental parameters and spectrometer dispersion parameters during the experiment.

• 
• 

======================= COMMENCE FITTING PROCESS =======================

Successfully retrieved the experimental data in 0.0009868144989013672s.

Acquired spectral quantity 'radiance' from the spectrum.
NaN values successfully purged.Number of data points left: 1479 points.
Successfully refined the experimental data in 0.0003924369812011719s.

Commence fitting process for non-LTE spectrum!
/home/docs/checkouts/readthedocs.org/user_builds/radis/checkouts/latest/radis/misc/warning.py:427: PerformanceWarning:

'gu' was recomputed although 'gp' already in DataFrame. All values are equal

[[Fit Statistics]]
    # fitting method   = L-BFGS-B
    # function evals   = 188
    # data points      = 1
    # variables        = 3
    chi-square         = 1.1070e-21
    reduced chi-square = 1.1070e-21
    Akaike info crit   = -42.2526499
    Bayesian info crit = -48.2526499
##  Warning: uncertainties could not be estimated:
    this fitting method does not natively calculate uncertainties
    and numdifftools is not installed for lmfit to do this. Use
    `pip install numdifftools` for lmfit to estimate uncertainties
    with this fitting method.
[[Variables]]
    Tvib:           4193.06781 (init = 6000)
    Trot:           4033.49909 (init = 4000)
    mole_fraction:  0.07216532 (init = 0.05)

Successfully finished the fitting process in 17.85886573791504s.
/home/docs/checkouts/readthedocs.org/user_builds/radis/checkouts/latest/radis/misc/curve.py:241: UserWarning:

Presence of NaN in curve_divide!
Think about interpolation=2


======================== END OF FITTING PROCESS ========================


Residual history:

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Fitted values history:

[6000.0, 4000.0, 0.05]
[6000.0000199999995, 4000.0, 0.05]
[6000.0, 4000.0000244948974, 0.05]
[6000.0, 4000.0, 0.0500000005]
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[4193.075748371061, 4033.5396151784685, 0.07216563527843067]
[4193.064833074306, 4033.4839235763793, 0.07216520060677879]
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[4193.064833074306, 4033.4839481372483, 0.07216520060677879]
[4193.064833074306, 4033.4839235763793, 0.07216520105496446]
[4193.070735604103, 4033.514039208062, 0.07216543541671189]
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[4193.067780217645, 4033.4989192011826, 0.07216531659048499]
[4193.067780217645, 4033.4988946402855, 0.07216531703867007]
[4193.067798971513, 4033.499038534105, 0.07216531825895041]
[4193.067823782383, 4033.499038534105, 0.07216531825895041]
[4193.067798971513, 4033.4990630950024, 0.07216531825895041]
[4193.067798971513, 4033.499038534105, 0.07216531870713548]
[4193.067805027136, 4033.49908499741, 0.07216531879769776]
[4193.067829838006, 4033.49908499741, 0.07216531879769776]
[4193.067805027136, 4033.4991095583073, 0.07216531879769776]
[4193.067805027136, 4033.49908499741, 0.07216531924588286]
[4193.067805763854, 4033.4990906500616, 0.07216531886324092]
[4193.067830574724, 4033.4990906500616, 0.07216531886324092]
[4193.067805763854, 4033.499115210959, 0.07216531886324092]
[4193.067805763854, 4033.4990906500616, 0.07216531931142599]
[4193.067805736285, 4033.499090438532, 0.07216531886078821]
[4193.067830547155, 4033.499090438532, 0.07216531886078821]
[4193.067805736285, 4033.4991149994294, 0.07216531886078821]
[4193.067805736285, 4033.499090438532, 0.07216531930897328]
[4193.067805763589, 4033.4990906480252, 0.07216531886321731]
[4193.067830574459, 4033.4990906480252, 0.07216531886321731]
[4193.067805763589, 4033.4991152089233, 0.07216531886321731]
[4193.067805763589, 4033.4990906480252, 0.07216531931140238]
[4193.067805763854, 4033.4990906500616, 0.07216531886324092]
[4193.067830574724, 4033.4990906500616, 0.07216531886324092]
[4193.067805763854, 4033.499115210959, 0.07216531886324092]
[4193.067805763854, 4033.4990906500616, 0.07216531931142599]
[4193.067805763854, 4033.4990906500616, 0.07216531886324092]

Total fitting time:
17.85886573791504 s

import astropy.units as u
import numpy as np

from radis import load_spec
from radis.test.utils import getTestFile
from radis.tools.new_fitting import fit_spectrum

# The following script is for Mr. Correnti Grimaldi's cases, used for his own slit settings.
# This is not native to current fitting modules.

# ----------------------- Begin of Mr. Grimaldi's script ----------------------- #


def slit_dispersion(w):
    phi = -6.33
    f = 750
    gr = 300
    m = 1
    phi *= -2 * np.pi / 360
    d = 1e-3 / gr
    disp = (
        w
        / (2 * f)
        * (-np.tan(phi) + np.sqrt((2 * d / m / (w * 1e-9) * np.cos(phi)) ** 2 - 1))
    )
    return disp  # nm/mm


slit = 1500  # µm
pitch = 20  # µm
top_slit_um = slit - pitch  # µm
base_slit_um = slit + pitch  # µm
center_slit = 5090
dispersion = slit_dispersion(center_slit)
top_slit_nm = top_slit_um * 1e-3 * dispersion
base_slit_nm = base_slit_um * 1e-3 * dispersion * 1.33

# ------------------------ End of Mr. Grimaldi's script ------------------------ #


# ------------------------------------ Step 1. Load experimental spectrum ------------------------------------ #


specName = (
    "Corentin_0_100cm_DownSampled_20cm_10pctCO2_1-wc-gw450-gr300-sl1500-acc5000-.spec"
)
s_experimental = load_spec(getTestFile(specName)).offset(-0.6, "nm")


# ------------------------------------ Step 2. Fill ground-truths and data ------------------------------------ #


# Experimental conditions which will be used for spectrum modeling. Basically, these are known ground-truths.
experimental_conditions = {
    "molecule": "CO",  # Molecule ID
    "isotope": "1,2,3",  # Isotope ID, can have multiple at once
    "wmin": 2270
    * u.nm,  # Starting wavelength/wavenumber to be cropped out from the original experimental spectrum.
    "wmax": 2400 * u.nm,  # Ending wavelength/wavenumber for the cropping range.
    "pressure": 1.01325
    * u.bar,  # Total pressure of gas, in "bar" unit by default, but you can also use Astropy units.
    "path_length": 1
    / 195
    * u.cm,  # Experimental path length, in "cm" unit by default, but you can also use Astropy units.
    "slit": {  # Experimental slit. In simple form: "[value] [unit]", i.e. "-0.2 nm". In complex form: a dict with parameters of apply_slit()
        "slit_function": (top_slit_nm, base_slit_nm),
        "unit": "nm",
        "shape": "trapezoidal",
        "center_wavespace": center_slit,
        "slit_dispersion": slit_dispersion,
        "inplace": False,
    },
    "cutoff": 0,  # (RADIS native) Discard linestrengths that are lower that this to reduce calculation time, in cm-1.
    "databank": "hitemp",  # Databank used for calculation. Must be stated.
}

# List of parameters to be fitted, accompanied by its initial value
fit_parameters = {
    "Tvib": 6000,  # Vibrational temperature, in K.
    "Trot": 4000,  # Rotational temperature, in K.
    "mole_fraction": 0.05,  # Species mole fraction, from 0 to 1.
}

# List of bounding ranges applied for those fit parameters above.
# You can skip this step and let it use default bounding ranges, but this is not recommended.
# Bounding range must be at format [<lower bound>, <upper bound>].
bounding_ranges = {
    "Tvib": [2000, 7000],
    "Trot": [2000, 7000],
    "mole_fraction": [0, 0.1],
}

# Fitting pipeline setups.
fit_properties = {
    "method": "lbfgsb",  # Preferred fitting method. By default, "leastsq".
    "fit_var": "radiance",  # Spectral quantity to be extracted for fitting process, such as "radiance", "absorbance", etc.
    "normalize": False,  # Either applying normalization on both spectra or not.
    "max_loop": 300,  # Max number of loops allowed. By default, 200.
    "tol": 1e-20,  # Fitting tolerance, only applicable for "lbfgsb" method.
}

"""

For the fitting method, you can try one among 17 different fitting methods and algorithms of LMFIT,
introduced in `LMFIT method list <https://lmfit.github.io/lmfit-py/fitting.html#choosing-different-fitting-methods>`.

You can see the benchmark result of these algorithms here:
`RADIS Newfitting Algorithm Benchmark <https://github.com/radis/radis-benchmark/blob/master/manual_benchmarks/plot_newfitting_comparison_algorithm.py>`.

"""


# ------------------------------------ Step 3. Run the fitting and retrieve results ------------------------------------ #


# Conduct the fitting process!
s_best, result, log = fit_spectrum(
    s_exp=s_experimental,  # Experimental spectrum.
    fit_params=fit_parameters,  # Fit parameters.
    bounds=bounding_ranges,  # Bounding ranges for those fit parameters.
    model=experimental_conditions,  # Experimental ground-truths conditions.
    pipeline=fit_properties,  # # Fitting pipeline references.
)


# Now investigate the result logs for additional information about what's going on during the fitting process

print("\nResidual history: \n")
print(log["residual"])

print("\nFitted values history: \n")
for fit_val in log["fit_vals"]:
    print(fit_val)

print("\nTotal fitting time: ")
print(log["time_fitting"], end=" s\n")