exojax.spec package

Submodules

exojax.spec.api module

Molecular database API class using a common API w/ RADIS = (CAPI)

  • MdbExomol is the MDB for ExoMol

  • MdbHitran is the MDB for HITRAN

  • MdbHitemp is the MDB for HITEMP

  • MdbCommonHitempHitran is the common MDB for HITEMP and HITRAN

Notes

If you use vaex as radis engine, hdf5 files are saved while pytables uses .h5 files.

class exojax.spec.api.MdbExomol(path, nurange=[- inf, inf], crit=0.0, elower_max=None, Ttyp=1000.0, bkgdatm='H2', broadf=True, broadf_download=True, gpu_transfer=True, inherit_dataframe=False, optional_quantum_states=False, activation=True, local_databases='./', engine=None)

Bases: MdbExomol

molecular database of ExoMol form.

MdbExomol is a class for ExoMol database. It inherits the CAPI class MdbExomol and adds some additional features.

simple_molecule_name

simple molecule name

nurange

nu range [min,max] (cm-1)

nu_lines

line center (cm-1)

Type:

nd array

Sij0

line strength at T=Tref (cm)

Type:

nd array

logsij0

log line strength at T=Tref

Type:

jnp array

A

Einstein A coeeficient

Type:

jnp array

gamma_natural

gamma factor of the natural broadening

Type:

DataFrame or jnp array

elower

the lower state energy (cm-1)

Type:

DataFrame or jnp array

gpp

statistical weight

Type:

DataFrame or jnp array

jlower

J_lower

Type:

DataFrame or jnp array

jupper

J_upper

Type:

DataFrame or jnp array

n_Texp

temperature exponent

Type:

DataFrame or jnp array

dev_nu_lines

line center in device (cm-1)

Type:

jnp array

alpha_ref

alpha_ref (gamma0), Lorentzian half-width at reference temperature and pressure in cm-1/bar

Type:

jnp array

n_Texp_def

default temperature exponent in .def file, used for jlower not given in .broad

alpha_ref_def

default alpha_ref (gamma0) in .def file, used for jlower not given in .broad

QT_interp(T)

interpolated partition function.

Parameters:

T – temperature

Returns:

Q(T) interpolated in jnp.array

activate(df, mask=None)

Activates of moldb for Exomol, including making attributes, computing broadening parameters, natural width, and transfering attributes to gpu arrays when self.gpu_transfer = True

Notes

activation includes, making attributes, computing broadening parameters, natural width, and transfering attributes to gpu arrays when self.gpu_transfer = True

Parameters:

  • df – DataFrame

  • mask – mask of DataFrame to be used for the activation, if None, no additional mask is applied.

Note

self.df_load_mask is always applied when the activation.

Examples

>>> # we would extract the line with delta nu = 2 here
>>> mdb = api.MdbExomol(emf, nus, optional_quantum_states=True, activation=False)
>>> load_mask = (mdb.df["v_u"] - mdb.df["v_l"] == 2)
>>> mdb.activate(mdb.df, load_mask)
apply_mask_mdb(mask)

Applys mask for mdb class for Exomol

Parameters:

mask – mask to be applied

Examples

>>> mdb = api.MdbExomol(emf, nus)
>>> # we would extract the lines with elower > 100.
>>> mask = mdb.elower > 100.
>>> mdb.apply_mask_mdb(mask)
attributes_from_dataframes(df_masked)

Generates attributes from (usually masked) data frame for Exomol

Parameters:

df_masked (DataFrame) – (masked) data frame

Raises:

ValueError – _description_

compute_load_mask(df)
generate_jnp_arrays()

(re)generates jnp.arrays.

Note

We have nd arrays and jnp arrays. We usually apply the mask to nd arrays and then generate jnp array from the corresponding nd array. For instance, self._A is nd array and self.A is jnp array. logsij0 is computed assuming Tref=Tref_original because it is not used for PreMODIT.

line_strength(T)

line strength at T

Parameters:

T (float) – temperature

Returns:

line strength at T

Return type:

float

qr_interp(T, Tref)

interpolated partition function ratio.

Parameters:

  • T – temperature

  • Tref – reference temperature

Returns:

qr(T)=Q(T)/Q(Tref) interpolated

set_wavenum(nurange)
class exojax.spec.api.MdbHitemp(molecule_path, nurange=[- inf, inf], crit=0.0, elower_max=None, Ttyp=1000.0, isotope=1, gpu_transfer=False, inherit_dataframe=False, activation=True, parfile=None, with_error=False, engine=None)

Bases: MdbCommonHitempHitran, HITEMPDatabaseManager

molecular database of HITEMP.

simple_molecule_name

simple molecule name

nurange

nu range [min,max] (cm-1)

nu_lines

line center (cm-1)

Type:

nd array

Sij0

line strength at T=Tref (cm)

Type:

nd array

dev_nu_lines

line center in device (cm-1)

Type:

jnp array

logsij0

log line strength at T=Tref

Type:

jnp array

A

Einstein A coeeficient

Type:

jnp array

gamma_natural

gamma factor of the natural broadening

Type:

jnp array

gamma_air

gamma factor of air pressure broadening

Type:

jnp array

gamma_self

gamma factor of self pressure broadening

Type:

jnp array

elower

the lower state energy (cm-1)

Type:

jnp array

gpp

statistical weight

Type:

jnp array

n_air

air temperature exponent

Type:

jnp array

attributes_from_dataframes(df_masked)

generate attributes from (usually masked) data farame

Parameters:

df_load_mask (DataFrame) – (masked) data frame

generate_jnp_arrays()

(re)generate jnp.arrays.

Note

We have nd arrays and jnp arrays. We usually apply the mask to nd arrays and then generate jnp array from the corresponding nd array. For attributes, self._A is nd array and self.A is jnp array.

class exojax.spec.api.MdbHitran(molecule_path, nurange=[- inf, inf], crit=0.0, elower_max=None, Ttyp=1000.0, isotope=0, gpu_transfer=False, inherit_dataframe=False, activation=True, parfile=None, nonair_broadening=False, with_error=False, engine=None)

Bases: MdbCommonHitempHitran, HITRANDatabaseManager

molecular database of HITRAN

simple_molecule_name

simple molecule name

nurange

nu range [min,max] (cm-1)

nu_lines

line center (cm-1)

Type:

nd array

Sij0

line strength at T=Tref (cm)

Type:

nd array

dev_nu_lines

line center in device (cm-1)

Type:

jnp array

logsij0

log line strength at T=Tref

Type:

jnp array

A

Einstein A coeeficient

Type:

jnp array

gamma_natural

gamma factor of the natural broadening

Type:

jnp array

gamma_air

gamma factor of air pressure broadening

Type:

jnp array

gamma_self

gamma factor of self pressure broadening

Type:

jnp array

elower

the lower state energy (cm-1)

Type:

jnp array

gpp

statistical weight

Type:

jnp array

n_air

air temperature exponent

Type:

jnp array

attributes_from_dataframes(df_load_mask)

generate attributes from (usually masked) data farame

Parameters:

df_load_mask (DataFrame) – (masked) data frame

Raises:

ValueError – _description_

generate_jnp_arrays()

(re)generate jnp.arrays.

Note

We have nd arrays and jnp arrays. We usually apply the mask to nd arrays and then generate jnp array from the corresponding nd array. For instance, self._A is nd array and self.A is jnp array.

exojax.spec.atmrt module

Atmospheric Radiative Transfer (art) class

Notes

The opacity is computed in art because it uses planet physical quantities such as gravity, mmr. β€œrun” method computes a spectrum.

class exojax.spec.atmrt.ArtAbsPure(pressure_top=1e-08, pressure_btm=100.0, nlayer=100, nu_grid=None)

Bases: ArtCommon

run(dtau, pressure_surface, incoming_flux, mu_in, mu_out)

run radiative transfer

Parameters:

  • dtau (2D array) – optical depth matrix, dtau (N_layer, N_nus)

  • pressure_surface – pressure at the surface (bar)

  • flux (incoming) – incoming flux (x reflectivity) (N_nus)

  • mu_in (float>0) – cosine of the viewing angle for incoming ray (>0.0)

  • mu_out (float>0 or None) – cosine of the viewing angle for outgoing ray, (>0.0) when mu_out is given (is not None), the observer is located at the top of the atmosphere if None, the observe is located at the ground.

Notes

We include the reflectivity by surface in β€œincoming flux” for the simplicity when the obserber is located at the top of atmosphere (mu_out is not None).

Returns:

spectrum

Return type:

1D array

class exojax.spec.atmrt.ArtCommon(pressure_top, pressure_btm, nlayer, nu_grid=None)

Bases: object

Common Atmospheric Radiative Transfer

atmosphere_height(temperature, mean_molecular_weight, radius_btm, gravity_btm)

atmosphere height and radius

Parameters:

  • temperature (1D array) – temparature profile (Nlayer)

  • mean_molecular_weight (float/1D array) – mean molecular weight profile (float/Nlayer)

  • radius_btm (float) – the bottom radius of the atmospheric layer

  • gravity_btm (float) – the bottom gravity cm2/s at radius_btm, i.e. G M_p/radius_btm

Returns:

height normalized by radius_btm (Nlayer) 1D array: layer radius r_n normalized by radius_btm (Nlayer)

Return type:

1D array

Notes

Our definitions of the radius_lower, radius_layer, and height are as follows: n=0,1,…,N-1 radius_lower[N-1] = radius_btm (i.e. R0) radius_lower[n-1] = radius_lower[n] + height[n] β€œnormalized” means physical length divided by radius_btm

change_temperature_range(Tlow, Thigh)

temperature range to be assumed.

Note

The default temperature range is self.Tlow = 0 K, self.Thigh = jnp.inf.

Parameters:

  • Tlow (float) – lower temperature

  • Thigh (float) – higher temperature

check_pressure()
clip_temperature(temperature)

temperature clipping

Parameters:

temperature (array) – temperature profile

Returns:

temperature profile clipped in the range of (self.Tlow-self.Thigh)

Return type:

array

constant_gravity_profile(value)
constant_mmr_profile(value)
constant_profile(value)
custom_temperature(np_temperature)

custom temperature profile from numpy ndarray

Notes: this function is equivalen to jnp.array(np_temperature), but it is necessary for the compatibility.

Parameters:

np_temperature (numpy nd array) – temperature profile

Returns:

jnp.array temperature profile

Return type:

array

gravity_profile(temperature, mean_molecular_weight, radius_btm, gravity_btm)

gravity layer profile assuming hydrostatic equilibrium

Parameters:

  • temperature (1D array) – temparature profile (Nlayer)

  • mean_molecular_weight (float/1D array) – mean molecular weight profile (float/Nlayer)

  • radius_btm (float) – the bottom radius of the atmospheric layer

  • gravity_btm (float) – the bottom gravity cm2/s at radius_btm, i.e. G M_p/radius_btm

Returns:

gravity in cm2/s (Nlayer, 1), suitable for the input of opacity_profile_lines

Return type:

2D array

gray_temperature(gravity, kappa, Tint)

gray temperature profile

Parameters:

  • gravity – gravity (cm/s2)

  • kappa – infrared opacity

  • Tint – temperature equivalence of the intrinsic energy flow in K

Returns:

temperature profile

Return type:

array

guillot_temperature(gravity, kappa, gamma, Tint, Tirr)

Guillot tempearture profile

Notes

Set self.fguillot (default 0.25) to change the assumption of irradiation. self.fguillot = 1. at the substellar point, self.fguillot = 0.5 for a day-side average and self.fguillot = 0.25 for an averaging over the whole planetary surface See Guillot (2010) Equation (29) for details.

Parameters:

  • gravity – gravity (cm/s2)

  • kappa – thermal/IR opacity (kappa_th in Guillot 2010)

  • gamma – ratio of optical and IR opacity (kappa_v/kappa_th), gamma > 1 means thermal inversion

  • Tint – temperature equivalence of the intrinsic energy flow in K

  • Tirr – temperature equivalence of the irradiation in K

Returns:

temperature profile

Return type:

array

init_pressure_profile()
opacity_profile_cia(logacia_matrix, temperature, vmr1, vmr2, mmw, gravity)

opacity profile (delta tau) from collision-induced absorption

Parameters:

  • logacia_matrix (_type_) – _description_

  • temperature (_type_) – _description_

  • vmr1 (_type_) – _description_

  • vmr2 (_type_) – _description_

  • mmw (_type_) – _description_

  • gravity (_type_) – _description_

Returns:

_description_

Return type:

_type_

opacity_profile_cloud_lognormal(extinction_coefficient, condensate_substance_density, mmr_condensate, rg, sigmag, gravity)

opacity profile (delta tau) from extinction coefficient assuming the AM cloud model with a lognormal cloud distribution :param extinction coefficient: extinction coefficient in cgs (cm-1) [N_layer, N_nus] :param condensate_substance_density: condensate substance density (g/cm3) :param mmr_condensate: Mass mixing ratio (array) of condensate [Nlayer] :param rg: rg parameter in the lognormal distribution of condensate size, defined by (9) in AM01 :param sigmag: sigmag parameter (geometric standard deviation) in the lognormal distribution of condensate size, defined by (9) in AM01, must be sigmag > 1 :param gravity: gravity (cm/s2)

Returns:

optical depth matrix, dtau [N_layer, N_nus]

Return type:

2D array

opacity_profile_lines(xs, mixing_ratio, molmass, gravity)
opacity_profile_xs(xs, mixing_ratio, molmass, gravity)

opacity profile (delta tau) from cross section matrix or vector, molecular line/Rayleigh scattering

Parameters:

  • xs (2D array/1D array) – cross section matrix i.e. xsmatrix (Nlayer, N_wavenumber) or vector i.e. xsvector (N_wavenumber)

  • mixing_ratio (1D array) – mass mixing ratio, Nlayer, (or volume mixing ratio profile)

  • molmass (float) – molecular mass (or mean molecular weight)

  • gravity (float/1D profile) – constant or 1d profile of gravity in cgs

Returns:

opacity profile, whose element is optical depth in each layer.

Return type:

dtau

powerlaw_temperature(T0, alpha)

powerlaw temperature profile

Parameters:

  • T0 (float) – T at P=1 bar in K

  • alpha (float) – powerlaw index

Returns:

temperature profile

Return type:

array

powerlaw_temperature_boundary(T0, alpha)

powerlaw temperature at the upper point (overline{T}) + TB profile

Parameters:

  • T0 (float) – T at P=1 bar in K

  • alpha (float) – powerlaw index

Returns:

layer boundary temperature profile (Nlayer + 1)

Return type:

array

class exojax.spec.atmrt.ArtEmisPure(pressure_top=1e-08, pressure_btm=100.0, nlayer=100, nu_grid=None, rtsolver='ibased', nstream=8)

Bases: ArtCommon

Atmospheric RT for emission w/ pure absorption

Notes

The default radiative transfer scheme has been the intensity-based transfer since version 1.5

pressure_layer

pressure profile in bar

run(dtau, temperature, nu_grid=None)

run radiative transfer

Parameters:

  • dtau (2D array) – optical depth matrix, dtau (N_layer, N_nus)

  • temperature (1D array) – temperature profile (Nlayer)

  • nu_grid (1D array) – if nu_grid is not initialized, provide it.

Returns:

emission spectrum

Return type:

1D array

set_capable_rtsolvers()
validate_rtsolver(rtsolver, nstream)

validates rtsolver

Parameters:

  • rtsolver (str) – rtsolver

  • nstream (int) – the number of streams

class exojax.spec.atmrt.ArtEmisScat(pressure_top=1e-08, pressure_btm=100.0, nlayer=100, nu_grid=None, rtsolver='fluxadding_toon_hemispheric_mean')

Bases: ArtCommon

Atmospheric RT for emission w/ scattering

pressure_layer

pressure profile in bar

run(dtau, single_scattering_albedo, asymmetric_parameter, temperature, nu_grid=None, show=False)

run radiative transfer

Parameters:

  • dtau (2D array) – optical depth matrix, dtau (N_layer, N_nus)

  • temperature (1D array) – temperature profile (Nlayer)

  • nu_grid (1D array) – if nu_grid is not initialized, provide it.

  • show – plot intermediate results

Returns:

spectrum

Return type:

1D array

class exojax.spec.atmrt.ArtReflectEmis(pressure_top=1e-08, pressure_btm=100.0, nlayer=100, nu_grid=None, rtsolver='fluxadding_toon_hemispheric_mean')

Bases: ArtCommon

Atmospheric RT for Reflected light with Source Term

pressure_layer

pressure profile in bar

run(dtau, single_scattering_albedo, asymmetric_parameter, temperature, source_surface, reflectivity_surface, incoming_flux, nu_grid=None)

run radiative transfer

Parameters:

  • dtau (2D array) – optical depth matrix, dtau (N_layer, N_nus)

  • single_scattering_albedo – single scattering albedo (Nlayer, N_nus)

  • asymmetric_parameter – assymetric parameter (Nlayer, N_nus)

  • temperature (1D array) – temperature profile (Nlayer)

  • source_surface – source from the surface (N_nus)

  • reflectivity_surface – reflectivity from the surface (N_nus)

  • flux (incoming) – incoming flux F_0^- (N_nus)

  • nu_grid (1D array) – if nu_grid is not initialized, provide it.

Returns:

spectrum

Return type:

1D array

class exojax.spec.atmrt.ArtReflectPure(pressure_top=1e-08, pressure_btm=100.0, nlayer=100, nu_grid=None, rtsolver='fluxadding_toon_hemispheric_mean')

Bases: ArtCommon

Atmospheric RT for Pure Reflected light (no source term)

pressure_layer

pressure profile in bar

run(dtau, single_scattering_albedo, asymmetric_parameter, reflectivity_surface, incoming_flux)

run radiative transfer

Parameters:

  • dtau (2D array) – optical depth matrix, dtau (N_layer, N_nus)

  • single_scattering_albedo – single scattering albedo (Nlayer, N_nus)

  • asymmetric_parameter – assymetric parameter (Nlayer, N_nus)

  • reflectivity_surface – reflectivity from the surface (N_nus)

  • flux (incoming) – incoming flux F_0^- (N_nus)

Returns:

spectrum

Return type:

1D array

class exojax.spec.atmrt.ArtTransPure(pressure_top=1e-08, pressure_btm=100.0, nlayer=100, integration='simpson')

Bases: ArtCommon

Atmospheric Radiative Transfer for transmission spectroscopy

Parameters:

ArtCommon – ArtCommon class

run(dtau, temperature, mean_molecular_weight, radius_btm, gravity_btm)

run radiative transfer

Parameters:

  • dtau (2D array) – optical depth matrix, dtau (N_layer, N_nus)

  • temperature (1D array) – temperature profile (Nlayer)

  • mean_molecular_weight (1D array) – mean molecular weight profile, (Nlayer, from atmospheric top to bottom)

  • radius_btm (float) – radius (cm) at the lower boundary of the bottom layer, R0 or r_N

  • gravity_btm (float) – gravity (cm/s2) at the lower boundary of the bottom layer, g_N

Returns:

transit squared radius normalized by radius_btm**2, i.e. it returns (radius/radius_btm)**2

Return type:

1D array

Notes

This function gives the sqaure of the transit radius. If you would like to obtain the transit radius, take sqaure root of the output and multiply radius_btm. If you would like to compute the transit depth, divide the output by (stellar radius/radius_btm)**2

set_capable_integration()

sets integration scheme directory

set_integration_scheme(integration)

sets and validates integration

Parameters:

integration (str) – integration scheme, i.e. β€œtrapezoid” or β€œsimpson”

exojax.spec.atomll module

exojax.spec.atomll.Sij0(A, gupper, nu_lines, elower, QTref_284, QTmask, Irwin=False)

Reference Line Strength in Tref=296K, S0.

Parameters:

  • A – Einstein coefficient (s-1)

  • gupper – the upper state statistical weight

  • nu_lines – line center wavenumber (cm-1)

  • elower – elower

  • QTref_284 – partition function Q(Tref)

  • QTmask – mask to identify a rows of QTref_284 to apply for each line

  • Irwin – if True(1), the partition functions of Irwin1981 is used, otherwise those of Barklem&Collet2016

Returns:

Line strength (cm)

Return type:

Sij(T)

exojax.spec.atomll.gamma_KA3(T, PH, PHH, PHe, ielem, iion, nu_lines, elower, eupper, atomicmass, ionE, gamRad, gamSta, vdWdamp, enh_damp=1.0, Nelec=0.0)

HWHM of Lorentzian (cm-1) caluculated with the 3rd equation in p.4 of Kurucz&Avrett1981.

Parameters:

  • T – temperature (K)

  • PH – hydrogen pressure (bar) #1 bar = 1e6 dyn/cm2

  • PHH – H2 molecule pressure (bar)

  • PHe – helium pressure (bar)

  • ielem – atomic number (e.g., Fe=26)

  • iion – ionized level (e.g., neutral=1, singly ionized=2, etc.)

  • nu_lines – transition waveNUMBER in [cm-1] (NOT frequency in [s-1])

  • elower – excitation potential (lower level) [cm-1]

  • eupper – excitation potential (upper level) [cm-1]

  • atomicmass – atomic mass [amu]

  • ionE – ionization potential [eV]

  • gamRad – log of gamma of radiation damping (s-1) #(https://www.astro.uu.se/valdwiki/Vald3Format)

  • gamSta – log of gamma of Stark damping ((s * Nelec)^-1)

  • vdWdamp – log of (van der Waals damping constant / neutral hydrogen number) (s-1)

  • enh_damp – empirical β€œenhancement factor” for classical Unsoeld’s damping constant cf.) This coefficient (enh_damp) depends on each species in some codes such as Turbospectrum. #tako210917

  • Nelec – number density of electron

  • chi_lam (=h*nu=1.2398e4/wvl[AA]) – energy of a photon in the line (computed)

  • C6 – interaction constant (Eq.11.17 in Gray2005) (computed)

  • logg6 – log(gamma6) (Eq.11.29 in Gray2005) (computed)

  • gam6H – 17*v**(0.6)*C6**(0.4)*N (v:relative velocity, N:number density of neutral perturber) (computed)

  • Texp – temperature dependency (gamma6 sim T**((1-Ξ±)/2) ranging 0.3–0.4) (computed)

Returns: gamma: pressure gamma factor (cm-1)

Note: β€œ/(4*np.pi*ccgs)” means: damping constant -> HWHM of Lorentzian in [cm^-1]

exojax.spec.atomll.gamma_KA3s(T, PH, PHH, PHe, ielem, iion, nu_lines, elower, eupper, atomicmass, ionE, gamRad, gamSta, vdWdamp, enh_damp=1.0, Nelec=0.0)

(supplemetary:) HWHM of Lorentzian (cm-1) caluculated with the 3rd equation in p.4 of Kurucz&Avrett1981 but without discriminating iron group elements.

Parameters:

  • T – temperature (K)

  • PH – hydrogen pressure (bar) #1 bar = 1e6 dyn/cm2

  • PHH – H2 molecule pressure (bar)

  • PHe – helium pressure (bar)

  • ielem – atomic number (e.g., Fe=26)

  • iion – ionized level (e.g., neutral=1, singly ionized=2, etc.)

  • nu_lines – transition waveNUMBER in [cm-1] (NOT frequency in [s-1])

  • elower – excitation potential (lower level) [cm-1]

  • eupper – excitation potential (upper level) [cm-1]

  • atomicmass – atomic mass [amu]

  • ionE – ionization potential [eV]

  • gamRad – log of gamma of radiation damping (s-1) #(https://www.astro.uu.se/valdwiki/Vald3Format)

  • gamSta – log of gamma of Stark damping ((s * Nelec)^-1)

  • vdWdamp – log of (van der Waals damping constant / neutral hydrogen number) (s-1)

  • enh_damp – empirical β€œenhancement factor” for classical Unsoeld’s damping constant cf.) This coefficient (enh_damp) depends on each species in some codes such as Turbospectrum. #tako210917

  • Nelec – number density of electron

  • chi_lam (=h*nu=1.2398e4/wvl[AA]) – energy of a photon in the line (computed)

  • C6 – interaction constant (Eq.11.17 in Gray2005) (computed)

  • logg6 – log(gamma6) (Eq.11.29 in Gray2005) (computed)

  • gam6H – 17*v**(0.6)*C6**(0.4)*N (v:relative velocity, N:number density of neutral perturber) (computed)

  • Texp – temperature dependency (gamma6 sim T**((1-Ξ±)/2) ranging 0.3–0.4)(computed)

Returns:

pressure gamma factor (cm-1)

Return type:

gamma

Note

β€œ/(4*np.pi*ccgs)” means: damping constant -> HWHM of Lorentzian in [cm^-1]

exojax.spec.atomll.gamma_KA4(T, PH, PHH, PHe, ielem, iion, nu_lines, elower, eupper, atomicmass, ionE, gamRad, gamSta, vdWdamp, enh_damp=1.0, Nelec=0.0)

HWHM of Lorentzian (cm-1) caluculated with the 4rd equation in p.4 of Kurucz&Avrett1981.

Parameters:

  • T – temperature (K)

  • PH – hydrogen pressure (bar) #1 bar = 1e6 dyn/cm2

  • PHH – H2 molecule pressure (bar)

  • PHe – helium pressure (bar)

  • ielem – atomic number (e.g., Fe=26)

  • iion – ionized level (e.g., neutral=1, singly ionized=2, etc.)

  • nu_lines – transition waveNUMBER in [cm-1] (NOT frequency in [s-1])

  • elower – excitation potential (lower level) [cm-1]

  • eupper – excitation potential (upper level) [cm-1]

  • atomicmass – atomic mass [amu]

  • ionE – ionization potential [eV]

  • gamRad – log of gamma of radiation damping (s-1) #(https://www.astro.uu.se/valdwiki/Vald3Format)

  • gamSta – log of gamma of Stark damping ((s * Nelec)^-1)

  • vdWdamp – log of (van der Waals damping constant / neutral hydrogen number) (s-1)

  • enh_damp – empirical β€œenhancement factor” for classical Unsoeld’s damping constant #cf.) This coefficient (enh_damp) depends on each species in some codes such as Turbospectrum. #tako210917

  • Nelec – number density of electron

  • chi_lam (=h*nu=1.2398e4/wvl[AA]) – energy of a photon in the line (computed)

  • C6 – interaction constant (Eq.11.17 in Gray2005) (computed)

  • logg6 – log(gamma6) (Eq.11.29 in Gray2005) (computed)

  • gam6H – 17*v**(0.6)*C6**(0.4)*N (v:relative velocity, N:number density of neutral perturber) (computed)

  • Texp – temperature dependency (gamma6 sim T**((1-Ξ±)/2) ranging 0.3–0.4) (computed)

Returns:

pressure gamma factor (cm-1)

Return type:

gamma

Note

Approximation of case4 assume β€œthat the atomic weight A is much greater than 4, and that the mean-square-radius of the lower level <r^2>_lo is small compared to <r^2>_up”.

β€œ/(4*np.pi*ccgs)” means: damping constant -> HWHM of Lorentzian in [cm^-1]

exojax.spec.atomll.gamma_uns(T, PH, PHH, PHe, ielem, iion, nu_lines, elower, eupper, atomicmass, ionE, gamRad, gamSta, vdWdamp, enh_damp=1.0, Nelec=0.0)

HWHM of Lorentzian (cm-1) estimated with the classical approximation by Unsoeld (1955)

Parameters:

  • T – temperature (K)

  • PH – hydrogen pressure (bar) #1 bar = 1e6 dyn/cm2

  • PHH – H2 molecule pressure (bar)

  • PHe – helium pressure (bar)

  • ielem – atomic number (e.g., Fe=26)

  • iion – ionized level (e.g., neutral=1, singly ionized=2, etc.)

  • nu_lines – transition waveNUMBER in [cm-1] (NOT frequency in [s-1])

  • elower – excitation potential (lower level) [cm-1]

  • eupper – excitation potential (upper level) [cm-1]

  • atomicmass – atomic mass [amu]

  • ionE – ionization potential [eV]

  • gamRad – log of gamma of radiation damping (s-1) #(https://www.astro.uu.se/valdwiki/Vald3Format)

  • gamSta – log of gamma of Stark damping ((s * Nelec)^-1)

  • vdWdamp – log of (van der Waals damping constant / neutral hydrogen number) (s-1)

  • enh_damp – empirical β€œenhancement factor” for classical Unsoeld’s damping constant cf.) This coefficient (enh_damp) depends on each species in some codes such as Turbospectrum. #tako210917

  • Nelec – number density of electron

  • chi_lam (=h*nu=1.2398e4/wvl[AA]) – energy of a photon in the line (computed)

  • C6 – interaction constant (Eq.11.17 in Gray2005) (computed)

  • logg6 – log(gamma6) (Eq.11.29 in Gray2005) (computed)

  • gam6H – 17*v**(0.6)*C6**(0.4)*N (v:relative velocity, N:number density of neutral perturber) (computed)

  • Texp – temperature dependency (gamma6 sim T**((1-Ξ±)/2) ranging 0.3–0.4)(computed)

Returns:

pressure gamma factor (cm-1)

Return type:

gamma

Note

β€œ/(4*np.pi*ccgs)” means: damping constant -> HWHM of Lorentzian in [cm^-1]

exojax.spec.atomll.gamma_vald3(T, PH, PHH, PHe, ielem, iion, nu_lines, elower, eupper, atomicmass, ionE, gamRad, gamSta, vdWdamp, enh_damp=1.0, Nelec=0.0)

HWHM of Lorentzian (cm-1) caluculated as gamma/(4*pi*c) [cm-1] for lines with the van der Waals gamma in the line list (VALD or Kurucz), otherwise estimated according to the Unsoeld (1955)

Parameters:

  • T – temperature (K)

  • PH – hydrogen pressure (bar) #1 bar = 1e6 dyn/cm2

  • PHH – H2 molecule pressure (bar)

  • PHe – helium pressure (bar)

  • ielem – atomic number (e.g., Fe=26)

  • iion – ionized level (e.g., neutral=1, singly ionized=2, etc.)

  • nu_lines – transition waveNUMBER in [cm-1] (NOT frequency in [s-1])

  • elower – excitation potential (lower level) [cm-1]

  • eupper – excitation potential (upper level) [cm-1]

  • atomicmass – atomic mass [amu]

  • ionE – ionization potential [eV]

  • gamRad – log of gamma of radiation damping (s-1) (https://www.astro.uu.se/valdwiki/Vald3Format)

  • gamSta – log of gamma of Stark damping ((s * Nelec)^-1)

  • vdWdamp – log of (van der Waals damping constant / neutral hydrogen number) (s-1)

  • enh_damp – empirical β€œenhancement factor” for classical Unsoeld’s damping constant cf.) This coefficient (enh_damp) depends on each species in some codes such as Turbospectrum. #tako210917

  • Nelec – number density of electron

  • chi_lam (=h*nu=1.2398e4/wvl[AA]) – energy of a photon in the line (computed)

  • C6 – interaction constant (Eq.11.17 in Gray2005) (computed)

  • logg6 – log(gamma6) (Eq.11.29 in Gray2005) (computed)

  • gam6H – 17*v**(0.6)*C6**(0.4)*N (computed) (v:relative velocity, N:number density of neutral perturber)

  • Texp – temperature dependency (gamma6 sim T**((1-Ξ±)/2) ranging 0.3–0.4) (computed)

Returns:

pressure gamma factor (cm-1)

Return type:

gamma

Note

β€œ/(4*np.pi*ccgs)” means: damping constant -> HWHM of Lorentzian in [cm^-1]

exojax.spec.atomll.get_VMR_uspecies(uspecies, mods_ID=Array([[0, 0]], dtype=int32), mods=Array([0], dtype=int32))

Extract VMR arrays of the species that contribute the opacity (β€œuspecies” made with β€œget_unique_species”)

Parameters:

  • uspecies – jnp.array of unique list of the species contributing the opacity [N_species x 2(ielem and iion)]

  • mods_ID – jnp.array listing the species whose abundances are different from the solar [N_modified_species x 2(ielem and iion)]

  • mods – jnp.array of each abundance deviation from the Sun [dex] for each modified species listed in mods_ID [N_modified_species]

Returns:

jnp.array of volume mixing ratio [N_species]

Return type:

VMR_uspecies

exojax.spec.atomll.get_VMR_uspecies_FC(FCSpIndex_uspecies, mixing_ratios)

By using FastChem, extract volume mixing ratio (VMR) of the species that contribute the opacity (β€œuspecies” made with β€œget_unique_species”)

Parameters:

  • FCSpIndex_uspecies – SpeciesIndex in FastChem for each species of interest [N_species]

  • mixing_ratios – volume mixing ratios of all available gases calculated using fastchem2_call.run_fastchem [N_layer x N_species]

Returns:

VMR of each species in each atmospheric layer [N_species x N_layer]

Return type:

VMR_uspecies

exojax.spec.atomll.get_unique_species(adb)

Extract a unique list of line contributing species from VALD atomic database (adb)

Parameters:

adb – adb instance made by the AdbVald class in moldb.py

Returns:

unique elements of the combination of ielem and iion (jnp.array with a shape of N_UniqueSpecies x 2(ielem and iion))

Return type:

uspecies

exojax.spec.atomll.ielemion_to_FastChemSymbol(ielem, iion)

Translate atomic number and ionization level into SpeciesSymbol in FastChem.

Parameters:

  • ielem – atomic number (int) (e.g., Fe=26)

  • iion – ionized level (int) (e.g., neutral=1, singly)

Returns:

//github.com/exoclime/FastChem/blob/master/input/logK_ext.dat)

Return type:

SpeciesSymbol in FastChem (str) (cf. https

exojax.spec.atomll.interp_QT_284(T, T_gQT, gQT_284species)

interpolated partition function of all 284 species.

Parameters:

  • T – temperature

  • T_gQT – temperature in the grid obtained from the adb instance [N_grid(42)]

  • gQT_284species – partition function in the grid from the adb instance [N_species(284) x N_grid(42)]

Returns:

interpolated partition function at T Q(T) for all 284 Atomic Species [284]

Return type:

QT_284

exojax.spec.atomll.padding_2Darray_for_each_atom(orig_arr, adb, sp)

Extract only data of the species of interest from 2D-array and pad with zeros to adjust the length.

Parameters:

  • orig_arr – array [N_any (e.g., N_nu or N_layer), N_line] Note that if your ARRAY is 1D, it must be broadcasted with ARRAY[None,:], and the output must be also reshaped with OUTPUTARRAY.reshape(ARRAY.shape)

  • adb – adb instance made by the AdbVald class in moldb.py

  • sp – array of [ielem, iion]

Returns:

padded_valid_arr

exojax.spec.atomll.sep_arr_of_sp(arr, adb, trans_jnp=True, inttype=False)

Separate by species (atoms or ions) the jnp.array stored as an instance variable in adb, and pad with zeros to adjust the length

Parameters:

  • arr – array of a parameter (one of the attributes of adb below) to be separated [N_line]

  • adb – adb instance made by the AdbVald class in moldb.py

  • trans_jnp – if True, the output is converted to jnp.array (dtype=’float32’)

  • inttype – if True (along with trans_jnp = True), the output is converted to jnp.array of dtype=’int32’

Returns:

species-separated array [N_species x N_line_max]

Return type:

arr_stacksp

exojax.spec.atomll.uspecies_info(uspecies, ielem_to_index_of_ipccd, mods_ID=Array([[0, 0]], dtype=int32), mods=Array([0], dtype=int32), mods_id_trans=Array([], shape=(0,), dtype=float32))

Provide arrays of information of the species that contribute the opacity (β€œuspecies” made with β€œget_unique_species”)

Parameters:

  • uspecies – jnp.array of unique list of the species contributing the opacity

  • ielem_to_index_of_ipccd – jnp.array for conversion from ielem to the index of ipccd

  • mods_ID – jnp.array listing the species whose abundances are different from the solar

  • mods – jnp.array of each abundance deviation from the Sun [dex] for each modified species in mods_ID

  • mods_id_trans – jnp.array for converting index in β€œmods_ID” of each species into index in uspecies

Returns:

jnp.array of mass mixing ratio in the Sun of each species in β€œuspecies” atomicmass_uspecies_list: jnp.array of atomic mass [amu] of each species in β€œuspecies” mods_uspecies_list: jnp.array of abundance deviation from the Sun [dex] for each species in β€œuspecies”

Return type:

MMR_uspecies_list

exojax.spec.atomllapi module

API for VALD 3.

exojax.spec.atomllapi.air_to_vac(wlair)

Convert wavelengths [AA] in air into those in vacuum.

Parameters:

  • wlair – wavelengthe in air [Angstrom]

  • n – Refractive Index in dry air at 1 atm pressure and 15ΒΊC with 0.045% CO2 by volume (Birch and Downs, 1994, Metrologia, 31, 315)

Returns:

wavelength in vacuum [Angstrom]

Return type:

wlvac

exojax.spec.atomllapi.load_atomicdata()

load atomic data and solar composition.

  • See Asplund et al. 2009, Gerevesse et al. 1996

Returns:

table of atomic data

Return type:

ipccd (pd.DataFrame)

Note

atomic.txt is in data/atom

exojax.spec.atomllapi.load_ionization_energies()

Load atomic ionization energies.

Returns:

table of ionization energies

Return type:

df_ionE (pd.DataFrame)

Note

NIST_Atomic_Ionization_Energies.txt is in data/atom

exojax.spec.atomllapi.load_pf_Barklem2016()

load a table of the partition functions for 284 atomic species.

Returns:

steps of temperature (K) pfdat (pd.DataFrame): partition functions for 284 atomic species

Return type:

pfTdat (pd.DataFrame)

exojax.spec.atomllapi.make_ielem_to_index_of_ipccd()

index conversion for atomll.uspecies_info (Preparation for LPF)

Returns:

jnp.array to convert ielem into index of ipccd

Return type:

ielem_to_index_of_ipccd

exojax.spec.atomllapi.partfn_Fe(T)

Partition function of Fe I from Irwin_1981.

Parameters:

T – temperature

Returns:

partition function Q

exojax.spec.atomllapi.pick_ionE(ielem, iion, df_ionE)

Pick up ionization energy of a specific atomic species.

Parameters:

  • ielem (int) – atomic number (e.g., Fe=26)

  • iion (int) – ionized level (e.g., neutral=1, singly ionized=2, etc.)

  • df_ionE (pd.DataFrame) – table of ionization energies

Returns:

ionization energy

Return type:

ionE (float)

Note

NIST_Atomic_Ionization_Energies.txt is in data/atom

exojax.spec.atomllapi.pickup_param(ExAll)

extract transition parameters from VALD3 line list and insert the same DataFrame.

Parameters:

ExAll – VALD3 line list as pandas DataFrame (Output of read_ExAll)

Returns:

Einstein coefficient in [s-1] nu_lines: transition waveNUMBER in [cm-1] (#NOT frequency in [s-1]) elower: lower excitation potential [cm-1] (#converted from eV) eupper: upper excitation potential [cm-1] (#converted from eV) gupper: upper statistical weight jlower: lower J (rotational quantum number, total angular momentum) jupper: upper J ielem: atomic number (e.g., Fe=26) iion: ionized level (e.g., neutral=1, singly) gamRad: log of gamma of radiation damping (s-1) #(https://www.astro.uu.se/valdwiki/Vald3Format) gamSta: log of gamma of Stark damping (s-1) vdWdamp: log of (van der Waals damping constant / neutral hydrogen number) (s-1)

Return type:

A

exojax.spec.atomllapi.read_ExAll(allf, engine='vaex')

IO for linelists downloaded from VALD3 with a query of β€œLong format” in the format of β€œExtract All” or β€œExtract Element”.

Note

About input linelists obtained from VALD3 (http://vald.astro.uu.se/). VALD data access is free but requires registration through the Contact form (http://vald.astro.uu.se/~vald/php/vald.php?docpage=contact.html). After the registration, you can login and choose the β€œExtract Element” mode. For example, if you want the Fe I linelist, the request form should be filled as

>>> Starting wavelength :    1500
>>> Ending wavelength :    100000
>>> Element [ + ionization ] :    Fe 1
>>> Extraction format :    Long format
>>> Retrieve data via :    FTP
>>> Linelist configuration :    Default
>>> Unit selection:    Energy unit: eV - Medium: vacuum - Wavelength unit: angstrom - VdW syntax: default

Please assign the fullpath of the output file sent by VALD ([user_name_at_VALD].[request_number_at_VALD].gz) to the variable β€œallf”. See https://www.astro.uu.se/valdwiki/presformat_output for the detail of the format.

Parameters:

  • allf – fullpath to the input VALD linelist (See Notes above for more details.)

  • Ion (Elm) –

  • WL_vac (AA) –

  • gf* (log) –

  • E_low (eV) – lower excitation potential

  • lo (J) – lower rotational quantum number

  • E_up (eV) – upper excitation potential

  • up (J) – upper rotational quantum number

  • lower (Lande) –

  • upper (Lande) –

  • mean (Lande) –

  • Rad. (Damping) –

  • Stark (Damping) –

  • Waals (Damping) –

  • engine – β€œvaex” or β€œpytables” (default: β€œvaex”)

Returns:

line data in vaex/pytables DataFrame

exojax.spec.atomllapi.read_kurucz(kuruczf)

Input Kurucz line list (http://kurucz.harvard.edu/linelists/)

Parameters:

kuruczf – file path

Returns:

Einstein coefficient in [s-1] nu_lines: transition waveNUMBER in [cm-1] (#NOT frequency in [s-1]) elower: lower excitation potential [cm-1] (#converted from eV) eupper: upper excitation potential [cm-1] (#converted from eV) gupper: upper statistical weight jlower: lower J (rotational quantum number, total angular momentum) jupper: upper J ielem: atomic number (e.g., Fe=26) iion: ionized level (e.g., neutral=1, singly) gamRad: log of gamma of radiation damping (s-1) #(https://www.astro.uu.se/valdwiki/Vald3Format) gamSta: log of gamma of Stark damping (s-1) gamvdW: log of (van der Waals damping constant / neutral hydrogen number) (s-1)

Return type:

A

exojax.spec.atomllapi.vac_to_air(wlvac)

Convert wavelengths [AA] in vacuum into those in air.

Parameters:

  • wlvac – wavelength in vacuum [Angstrom]

  • n – Refractive Index in dry air at 1 atm pressure and 15ΒΊC with 0.045% CO2 by volume (Birch and Downs, 1994, Metrologia, 31, 315)

Returns:

wavelengthe in air [Angstrom]

Return type:

wlair

exojax.spec.contdb module

Continuum database (CDB) class.

  • CdbCIA is the CDB for CIA

class exojax.spec.contdb.CdbCIA(path, nurange=[- inf, inf], margin=10.0)

Bases: object

download()

Downloading HITRAN cia file.

Note

The download URL is written in exojax.utils.url.

exojax.spec.customapi module

exojax.spec.customapi.Einstein_coeff_from_line_strength(nu_lines, Sij, elower, g, Q, T)

Einstein coefficient from line strength

Parameters:

  • nu_lines (float) – line center wavenumber (cm-1)

  • Sij (float) – line strength (cm)

  • elower (float) – elower

  • g (float) – upper state statistical weight

  • Q (float) – partition function

  • T (float) – temperature

Returns:

Einstein coefficient (s-1)

class exojax.spec.customapi.MdbHargreaves(path, nurange=[- inf, inf], QTref_original=215.3488, QTref_raw=11691.1386, scale_intensity=0.3333333333333333, engine=None, verbose=True, download=False, cache=True)

Bases: HargreavesDatabaseManager

molecular database of Hargreaves et al. (2010) in ExoMol form.

path

Path to the local database file

Type:

str

database

Name of the database

Type:

str

exact_molecule_name

Exact name of the molecule

Type:

str

simple_molecule_name

Simple name of the molecule

Type:

str

engine

Computational engine to use

Type:

str

QTref_original

Original partition function at reference temperature

Type:

float

QTref_raw

Raw partition function at reference temperature

Type:

float

df

Dataframe containing the converted data

Type:

pd.DataFrame

activate_with_exomol(mdb_exomol, extend=True)

Activate the Hargreaves database with an existing ExoMol database. :param mdb_exomol: An existing ExoMol database to extend :type mdb_exomol: MdbExomol :param extend: If True, extend the existing database with Hargreaves data :type extend: bool

Returns:

A new ExoMol database with Hargreaves data activated

Return type:

MdbExomol

convert_to_exomol(df_raw)

Convert the raw (original) dataframe to ExoMol format.

exojax.spec.customapi.set_wavenum(nurange)

Set the wavenumber range for the database.

Parameters:

nurange (list) – Wavenumber range for the database

Returns:

Minimum and maximum wavenumber

Return type:

tuple

exojax.spec.dbmanager module

class exojax.spec.dbmanager.CustomDatabaseManager(name, molecule, local_databases, url, engine='default', verbose=True, parallel=True)

Bases: DatabaseManager

common base class for custom database managers

download(urlname)

download the data file from the given URL

Parameters:

urlname (str) – URL of the data file

Returns:

Response object containing the downloaded data

Return type:

response (requests.Response)

fetch_urlnames()

fetch the URL names of the data files

Returns:

List of URL names

Return type:

list

class exojax.spec.dbmanager.HargreavesDatabaseManager(name, molecule, local_databases, url, engine='default', verbose=True, parallel=True)

Bases: CustomDatabaseManager

database manager for the line list of the transition of FeH (Hargreaves et al., 2010)

parse_to_local_file(urlname, local_file)

download and parse the data file to a local file

Parameters:

  • urlname (str) – URL of the data file

  • local_file (str) – Local file path to save the data

Returns:

Number of lines in the downloaded data

Return type:

int

exojax.spec.dit module

Line profile computation using Discrete Integral Transform.

  • Line profile computation of Discrete Integral Transform for rapid spectral synthesis, originally proposed by D.C.M van den Bekerom and E.Pannier.

  • This module consists of selected functions in addit package.

  • The concept of β€œfolding” can be understood by reading the discussion by D.C.M van den Bekerom.

exojax.spec.dit.dgmatrix(x, dit_grid_resolution=0.1, adopt=True)

DIT GRID MATRIX (alias)

Parameters:

  • x – simgaD or gammaL matrix (Nlayer x Nline)

  • dit_grid_resolution – grid resolution. dit_grid_resolution=0.1 (defaut) means a grid point per digit

  • adopt – if True, min, max grid points are used at min and max values of x. In this case, the grid width does not need to be dit_grid_resolution exactly.

Returns:

grid for DIT (Nlayer x NDITgrid)

exojax.spec.dit.ditgrid(x, dit_grid_resolution=0.1, adopt=True)

DIT GRID (deplicated).

Parameters:

  • x – simgaD or gammaL array (Nline)

  • dit_grid_resolution – grid resolution. res=0.1 (defaut) means a grid point per digit

  • adopt – if True, min, max grid points are used at min and max values of x. In this case, the grid width does not need to be res exactly.

Returns:

grid for DIT

exojax.spec.dit.dtauM_vald(dParr, g, adb, nus, cnu, indexnu, pmarray, SijM, gammaLM, sigmaDM, uspecies, mods_uspecies_list, MMR_uspecies_list, atomicmass_uspecies_list, dgm_sigmaD, dgm_gammaL)

Compute dtau caused by VALD lines from cross section xs (DIT)

Parameters:

  • dParr – delta pressure profile (bar) [N_layer]

  • g – gravity (cm/s^2)

  • adb – adb instance made by the AdbVald class in moldb.py

  • nus – wavenumber matrix (cm-1) [N_nus]

  • cnu – cont (contribution) jnp.array [N_line]

  • indexnu – index (index) jnp.array [N_line]

  • pmarray – (+1,-1) array [len(nu_grid)+1,]

  • SijM – line intensity matrix [N_layer x N_line]

  • gammaLM – gammaL matrix [N_layer x N_line]

  • sigmaDM – sigmaD matrix [N_layer x N_line]

  • uspecies – unique elements of the combination of ielem and iion [N_UniqueSpecies x 2(ielem and iion)]

  • mods_uspecies_list – jnp.array of abundance deviation from the Sun [dex] for each species in β€œuspecies” [N_UniqueSpecies]

  • MMR_uspecies_list – jnp.array of mass mixing ratio in the Sun of each species in β€œuspecies” [N_UniqueSpecies]

  • atomicmass_uspecies_list – jnp.array of atomic mass [amu] of each species in β€œuspecies” [N_UniqueSpecies]

Returns:

optical depth matrix [N_layer, N_nus]

Return type:

dtauatom

exojax.spec.dit.sigma_voigt(dgm_sigmaD, dgm_gammaL)

compute sigma of the Voigt profile.

Parameters:

  • dgm_sigmaD – DIT grid matrix for sigmaD

  • dgm_gammaL – DIT grid matrix for gammaL

Returns:

sigma

exojax.spec.dit.vald(adb, Tarr, PH, PHe, PHH)

(alias of lpf.vald)

Parameters:

  • adb – adb instance made by the AdbVald class in moldb.py

  • Tarr – Temperature array

  • PH – Partial pressure array of neutral hydrogen (H)

  • PHe – Partial pressure array of neutral helium (He)

  • PHH – Partial pressure array of molecular hydrogen (H2)

Returns:

line intensity matrix gammaLM: gammaL matrix sigmaDM: sigmaD matrix

Return type:

SijM

exojax.spec.dit.xsmatrix(cnu, indexnu, pmarray, sigmaDM, gammaLM, SijM, nu_grid, dgm_sigmaD, dgm_gammaL)

Cross section matrix (DIT/2D+ version)

Parameters:

  • cnu – contribution by npgetix for wavenumber

  • indexnu – index by npgetix for wavenumber

  • pmarray – (+1,-1) array whose length of len(nu_grid)+1

  • sigmaDM – doppler sigma matrix in R^(Nlayer x Nline)

  • gammaLM – gamma factor matrix in R^(Nlayer x Nline)

  • SijM – line strength matrix in R^(Nlayer x Nline)

  • nu_grid – linear wavenumber grid

  • dgm_sigmaD – DIT Grid Matrix for sigmaD R^(Nlayer, NDITgrid)

  • dgm_gammaL – DIT Grid Matrix for gammaL R^(Nlayer, NDITgrid)

Returns:

cross section matrix in R^(Nlayer x Nwav)

Warning

This function have not been well tested.

exojax.spec.dit.xsvector(cnu, indexnu, pmarray, sigmaD, gammaL, S, nu_grid, sigmaD_grid, gammaL_grid)

Cross section vector (DIT/2D+ version; default)

The original code is rundit in [addit package](https://github.com/HajimeKawahara/addit)

Parameters:

  • cnu – contribution by npgetix for wavenumber

  • indexnu – index by npgetix for wavenumber

  • pmarray – (+1,-1) array whose length of len(nu_grid)+1

  • sigmaD – Gaussian STD (Nlines)

  • gammaL – Lorentzian half width (Nlines)

  • S – line strength (Nlines)

  • nu_grid – linear wavenumber grid

  • sigmaD_grid – sigmaD grid

  • gammaL_grid – gammaL grid

Returns:

Cross section in the linear nu grid

Note

This function uses the precomputed neibouring contribution function for wavenumber (nu_ncf). Use npnc1D to compute nu_ncf in float64 precision.

exojax.spec.ditkernel module

Kernels for Discrete Integral Transform.

exojax.spec.ditkernel.fold_voigt_kernel(k, beta, gammaL, vmax, pmarray)

Fourier Kernel of the Voigt Profile.

Parameters:

  • k – conjugated of wavenumber

  • beta – Gaussian standard deviation

  • gammaL – Lorentian Half Width

  • vmax – Nnu x dq

  • pmarray – (+1,-1) array whose length of len(nu_grid)+1

Returns:

kernel (N_x,N_beta,N_gammaL)

Note

Conversions to the (full) width, wG and wL are as follows: wG=2*sqrt(2*ln2) beta wL=2*gamma

exojax.spec.ditkernel.fold_voigt_kernel_logst(k, beta, log_ngammaL, vmax, pmarray)

Folded Fourier Kernel of the Voigt Profile for a common normalized beta. See https://github.com/dcmvdbekerom/discrete-integral- transform/blob/master/demo/discrete_integral_transform_log.py for the alias correction.

Parameters:

  • k – conjugate wavenumber

  • beta – normalized Gaussian standard deviation (scalar, not log)

  • log_ngammaL – log normalized Lorentian Half Width (Nlines)

  • vmax – vmax

  • pmarray – (+1,-1) array whose length of len(nu_grid)+1

Returns:

kernel (N_x,N_gammaL)

Note

Conversions to the (full) width, wG and wL are as follows: wG=2*sqrt(2*ln2) beta wL=2*gamma

exojax.spec.ditkernel.voigt_kernel(k, beta, gammaL)

Fourier Kernel of the Voigt Profile.

Parameters:

  • k – conjugated of wavenumber

  • beta – Gaussian standard deviation

  • gammaL – Lorentzian Half Width

Returns:

kernel (N_x,N_beta,N_gammaL)

Note

Conversions to the (full) width, wG and wL are as follows: wG=2*sqrt(2*ln2) beta wL=2*gamma

exojax.spec.ditkernel.voigt_kernel_logst(k, beta, log_ngammaL)

Fourier Kernel of the Voigt Profile for a common normalized beta.

Parameters:

  • k – conjugate wavenumber

  • beta – normalized Gaussian standard deviation (scalar)

  • log_ngammaL – log normalized Lorentian Half Width (Nlines)

Returns:

kernel (N_x,N_gammaL)

Note

Conversions to the (full) width, wG and wL are as follows: wG=2*sqrt(2*ln2) beta wL=2*gamma

exojax.spec.dtau_mmwl module

compute dtau (opacity difference in atmospheric layers) using mean molecular weight

exojax.spec.dtau_mmwl.dtauCIA_mmwl(nus, Tarr, Parr, dParr, vmr1, vmr2, mmw, g, nucia, tcia, logac)
dtau of the CIA continuum.

(for the case where mmw is given for each atmospheric layer)

Parameters:

  • nus – wavenumber matrix (cm-1)

  • Tarr – temperature array (K)

  • Parr – temperature array (bar)

  • dParr – delta temperature array (bar)

  • vmr1 – volume mixing ratio (VMR) for molecules 1 [N_layer]

  • vmr2 – volume mixing ratio (VMR) for molecules 2 [N_layer]

  • mmw – mean molecular weight of atmosphere [N_layer]

  • g – gravity (cm2/s)

  • nucia – wavenumber array for CIA

  • tcia – temperature array for CIA

  • logac – log10(absorption coefficient of CIA)

Returns:

optical depth matrix [N_layer, N_nus]

exojax.spec.dtau_mmwl.dtauHminus_mmwl(nus, Tarr, Parr, dParr, vmre, vmrh, mmw, g)
dtau of the H- continuum.

(for the case where mmw is given for each atmospheric layer)

Parameters:

  • nus – wavenumber matrix (cm-1)

  • Tarr – temperature array (K)

  • Parr – temperature array (bar)

  • dParr – delta temperature array (bar)

  • vmre – volume mixing ratio (VMR) for e- [N_layer]

  • vmrH – volume mixing ratio (VMR) for H atoms [N_layer]

  • mmw – mean molecular weight of atmosphere [N_layer]

  • g – gravity (cm2/s)

Returns:

optical depth matrix [N_layer, N_nus]

exojax.spec.dtau_mmwl.dtauM_mmwl(dParr, xsm, MR, mass, g)
dtau of the molecular cross section.

(for the case where mmw is given for each atmospheric layer)

Note

opfac=bar_cgs/(m_u (g)). m_u: atomic mass unit. It can be obtained by fac=1.e3/m_u, where m_u = scipy.constants.m_u.

Parameters:

  • dParr – delta pressure profile (bar) [N_layer]

  • xsm – cross section matrix (cm2) [N_layer, N_nus]

  • MR – volume mixing ratio (VMR) or mass mixing ratio (MMR) [N_layer]

  • mass – mean molecular weight for VMR or molecular mass for MMR [N_layer]

  • g – gravity (cm/s2)

Returns:

optical depth matrix [N_layer, N_nus]

exojax.spec.exomol module

exojax.spec.exomol.gamma_exomol(P, T, n_air, alpha_ref)

gamma factor by a pressure broadening.

Parameters:

  • P – pressure (bar)

  • T – temperature (K)

  • n_air – coefficient of the temperature dependence of the air-broadened halfwidth

  • alpha_ref – broadening parameter

Returns:

pressure gamma factor (cm-1)

Return type:

gamma

exojax.spec.exomol.gamma_natural(A)

gamma factor by natural broadning.

1/(4 pi c) = 2.6544188e-12 (cm-1 s)

Parameters:

A – Einstein A-factor (1/s)

Returns:

natural width (cm-1)

Return type:

gamma_natural

exojax.spec.exomol.line_strength_from_Einstein_coeff(A, g, nu_lines, elower, QTref)

Reference Line Strength in Tref=296K, S0 from Einstein coefficient.

Note

This function is not used in other codes in ExoJAX. But it can be used for the conversion of the line strength from the original ExoMol form into HITRAN form.

Parameters:

  • A – Einstein coefficient (s-1)

  • g – the upper state statistical weight

  • nu_lines – line center wavenumber (cm-1)

  • elower – elower

  • QTref – partition function Q(Tref)

  • Mmol – molecular mass (normalized by m_u)

Returns:

Line strength (cm)

exojax.spec.exomolhr module

class exojax.spec.exomolhr.XdbExomolHR(exact_molecule_name, nurange, temperature, crit=1e-40, gpu_transfer=True, activation=True, inherit_dataframe=False, local_databases='./opacity_zips')

Bases: object

XdbExomolHR class for ExomolHR database

Warning

XdbExomolHR is not MDB.

Notes

The ExomolHR database (eXtra db) is emprical high-res line strengths/info for a given single temperature. Xdb is a database that does not belong to regular types of ExoJAX databases.

simple_molecule_name

simple molecule name

nurange

nu range [min,max] (cm-1)

nu_lines

line center (cm-1)

Type:

nd array

Sij0

line strength at T=Tref (cm)

Type:

nd array

logsij0

log line strength at T=Tref

Type:

jnp array

A

Einstein A coeeficient

Type:

jnp array

gamma_natural

gamma factor of the natural broadening

Type:

DataFrame or jnp array

elower

the lower state energy (cm-1)

Type:

DataFrame or jnp array

gpp

statistical weight

Type:

DataFrame or jnp array

jlower

J_lower

Type:

DataFrame or jnp array

jupper

J_upper

Type:

DataFrame or jnp array

n_Texp

temperature exponent

Type:

DataFrame or jnp array

dev_nu_lines

line center in device (cm-1)

Type:

jnp array

activate(df, mask=None)

Activates of moldb for Exomol, including making attributes, computing broadening parameters, natural width, and transfering attributes to gpu arrays when self.gpu_transfer = True

Notes

activation includes, making attributes, computing broadening parameters, natural width, and transfering attributes to gpu arrays when self.gpu_transfer = True

Parameters:

  • df – DataFrame

  • mask – mask of DataFrame to be used for the activation, if None, no additional mask is applied.

Note

self.df_load_mask is always applied when the activation.

Examples

>>> # we would extract the line with delta nu = 2 here
>>> mdb = api.MdbExomolHR(emf, nus, optional_quantum_states=True, activation=False)
>>> load_mask = (mdb.df["v_u"] - mdb.df["v_l"] == 2)
>>> mdb.activate(mdb.df, load_mask)
attributes_from_dataframes(df_masked)

Generates attributes from (usually masked) data frame for Exomol

Parameters:

df_masked (DataFrame) – (masked) data frame

Raises:

ValueError – _description_

fetch_data()
exojax.spec.exomolhr.fetch_opacity_zip(*, wvmin: float, wvmax: float | None, numin: float, numax: float, T: int, Smin: float, iso: str, out_dir: str | os.PathLike = '.', session: Optional[Session] = None, chunk: int = 524288) → Path

Return a local ExoMolHR CSVβ€”downloaded only if necessary.

The function skips the network step when a file with the same physics (identical iso and T) is already present in out_dir; only the timestamp differs between downloads.

Parameters:

  • wvmax (wvmin /) – float | None Viewer wavenumber limits (nm). Pass None to omit wvmax.

  • numax (numin /) – float Line‑list limits in cm⁻¹ requested from the service.

  • T – int Temperature [K].

  • Smin – float Lower cut‑off for line strength (cmβ€―molecule⁻¹).

  • iso – str Isotopologue tag, e.g. "12C-16O2".

  • out_dir – str | os.PathLike, optional Directory for ZIP/CSV files (default ".").

  • session – requests.Session | None, optional Re‑use a requests.Session if supplied.

  • chunk – int, optional Streaming block size in bytes (default 512Β kB).

Returns:

pathlib.Path

Path to the local CSV file.

Raises:

RuntimeError – When the expected download link is missing or HTTP fails.

exojax.spec.exomolhr.list_exomolhr_molecules(html_source: Optional[Union[str, bytes, Path]] = None, *, session: Optional[Session] = None) → Sequence[str]

Return the list of molecule formulas shown on the ExoMolHR landing page.

The function can work in three modes:

  1. Online html_source is None β†’ download https://www.exomol.com/exomolhr/ live.

  2. From file html_source is a pathlib.Path or filename β†’ read the saved HTML.

  3. From string/bytes html_source is raw HTML content β†’ parse directly.

Parameters:

  • html_source – str | bytes | pathlib.Path | None, optional Where to get the HTML. Pass None (default) to fetch online.

  • session – requests.Session | None, optional Re-use a session if you call repeatedly.

Returns: Sequence[str]

Formulas in the order they appear in the table (duplicates are removed).

Raises:

RuntimeError – If the molecule table cannot be located in the HTML.

exojax.spec.exomolhr.list_isotopologues(simple_molecule_list: Iterable[str], *, max_workers: Optional[int] = None) → dict[str, list[str]]

Return {molecule: [iso₁, isoβ‚‚, …]} for the given molecules.

Parameters:

  • simple_molecule_list – list of simple molecule names, e.g. [AlCl, AlH, AlO, C2, C2H2, CaH, CH4, CN, CO2]

  • max_workers – number of workers for parallel processing

Returns:

dictionary of isotopologues (simple_molecule_name:[list of exact_molecule_name]) for each molecule e.g. {β€˜H2O’: [β€˜1H2-16O’], β€˜C2H2’: [β€˜12C2-1H2’], β€˜H3O+’: [β€˜1H3-16O_p’]}

Return type:

dict[str, list[str]]

exojax.spec.exomolhr.load_exomolhr_csv(csv_path: str | pathlib.Path) → DataFrame

Load a CSV file from an ExoMolHR ZIP archive into a DataFrame.

exojax.spec.generate_elower_grid_trange module

elower grid trange file

exojax.spec.generate_elower_grid_trange.generate_elower_grid_trange(N_Twt, N_Tref, N_Trange, N_dE, Treflow, Trefhigh, Twtlow, Twthigh, Tsearchl, Tsearchh, dErangel, dErangeh, filename, precision_criterion=0.01)

generates β€œelower_grid_trange” file, i.e. robust temperature range (Tlow, Thigh) as a function of dE, Tre, Twt, (and diffmode)

Parameters:

  • N_Twt (int) – the number of Twt grid

  • N_Tref (int) – the number of Tref grid

  • N_Trange (int) – the number of Trange to serach for Tlow and Thigh

  • N_dE (int) – the number of dE grid

  • Treflow (float) – lower limit of Tref grid

  • Trefhigh (float) – upper limit of Tref grid

  • Twtlow (float) – lower limit of Twt grid

  • Twthigh (float) – upper limit of Twt grid

  • Tsearchl (float) – lower limit of Trange grid

  • Tsearchh (float) – upper limit of Trange grid

  • dErangel (float) – lower limit of dE grid

  • dErangeh (float) – upper limit of dE grid

  • filename (str) – output filename

  • precision_criterion (float, optional) – _description_. Defaults to 0.01.

Raises:

  • ValueError – _description_

  • ValueError – _description_

exojax.spec.generate_elower_grid_trange.params_version1()

parameters for the defaut elower grid trange version 1

Returns:

params for generate_elower_grid_trange

exojax.spec.generate_elower_grid_trange.params_version2()

parameters for the defaut elower grid trange version 2

Returns:

params for generate_elower_grid_trange

exojax.spec.hitran module

exojax.spec.hitran.doppler_sigma(nu_lines, T, M)

Dopper width (sigmaD)

Note

c3 is sqrt(kB/m_u)/c

Parameters:

  • nu_lines – line center wavenumber (cm-1)

  • T – temperature (K)

  • M – atom/molecular mass

Returns:

doppler width (standard deviation) (cm-1)

Return type:

sigma

exojax.spec.hitran.gamma_hitran(P, T, Pself, n_air, gamma_air_ref, gamma_self_ref)

gamma factor by a pressure broadening.

Parameters:

  • P – pressure (bar)

  • T – temperature (K)

  • Pself – partial pressure (bar)

  • n_air – coefficient of the temperature dependence of the air-broadened halfwidth

  • gamma_air_ref – gamma air

  • gamma_self_ref – gamma self

Returns:

pressure gamma factor (cm-1)

Return type:

gamma

exojax.spec.hitran.gamma_natural(A)

gamma factor by natural broadning.

1/(4 pi c) = 2.6544188e-12 (cm-1 s)

Parameters:

A – Einstein A-factor (1/s)

Returns:

natural width (cm-1)

Return type:

gamma_natural

exojax.spec.hitran.line_strength(T, logsij0, nu_lines, elower, qr, Tref)

Line strength as a function of temperature, JAX/XLA compatible

Notes

Tref=296.0 (default) in moldb, but it might have been changed by OpaPremodit.

Parameters:

  • T – temperature (K)

  • logsij0 – log(Sij(Tref)) (Tref=296K)

  • nu_lines – line center wavenumber (cm-1)

  • elower – elower

  • qr – partition function ratio qr(T) = Q(T)/Q(Tref)

  • Tref – reference temperature

Returns:

Line strength (cm)

Return type:

Sij(T)

exojax.spec.hitran.line_strength_numpy(T, Sij0, nu_lines, elower, qr, Tref=296.0)

Line strength as a function of temperature, numpy version

Parameters:

  • T – temperature (K)

  • Sij0 – line strength at Tref=296K

  • elower – elower

  • nu_lines – line center wavenumber

  • qr – partition function ratio qr(T) = Q(T)/Q(Tref)

  • Tref – reference temeparture

Returns:

line strength at Ttyp

exojax.spec.hitran.normalized_doppler_sigma(T, M, R)

Normalized Dopper width (nsigmaD) by wavenumber difference at line centers.

Note

This quantity is used in MODIT. c3 is sqrt(kB/m_u)/c

Parameters:

  • T – temperature (K)

  • M – atom/molecular mass

  • R – spectral resolution

Returns:

normalized Doppler width (standard deviation)

Return type:

nsigma

exojax.spec.hitranapi module

API for HITRAN and HITEMP outside HAPI.

exojax.spec.hitranapi.make_partition_function_grid_hitran(M, I_list)

HITRAN/HITEMP IO for partition function

Parameters:

  • M – HITRAN molecule number

  • I_list – HITRAN isotopologue number list

Returns:

jnp array of partition function grid T_gQT: jnp array of temperature grid for gQT

Return type:

gQT

exojax.spec.hitranapi.molecid_hitran(molec)

molec id from Hitran/Hitemp filename or molecule name or molecid itself.

Parameters:

molec – Hitran/Hitemp filename or molecule name or molec id itself.

Returns:

molecid (HITRAN molecular id)

Return type:

int

exojax.spec.hitrancia module

exojax.spec.hitrancia.interp_logacia_matrix(Tarr, nu_grid, nucia, tcia, logac)

interpolated function of log10(alpha_CIA)

Parameters:

  • Tarr (1D array) – temperature array (K) [Nlayer]

  • nu_grid (1D array) – wavenumber array (cm-1) [Nnus]

  • nucia – CIA wavenumber (cm-1)

  • tcia – CIA temperature (K)

  • logac – log10 cia coefficient

Returns:

logarithm of absorption coefficient [Nlayer, Nnus] in the unit of cm5

Example

nucia,tcia,ac=read_cia(β€œ../../data/CIA/H2-H2_2011.cia”,nus[0]-1.0,nus[-1]+1.0) logac=jnp.array(np.log10(ac)) interp_logacia_matrix(Tarr,nus,nucia,tcia,logac)

exojax.spec.hitrancia.interp_logacia_vector(T, nu_grid, nucia, tcia, logac)

interpolated function of log10(alpha_CIA)

Parameters:

  • T (float) – temperature (K)

  • nu_grid – wavenumber array (cm-1)

  • nucia – CIA wavenumber (cm-1)

  • tcia – CIA temperature (K)

  • logac – log10 cia coefficient

Returns:

logarithm of absorption coefficient [Nnus] at T in the unit of cm5

exojax.spec.hitrancia.read_cia(filename, nus, nue)

READ HITRAN CIA data.

Parameters:

  • filename – HITRAN CIA file name (_2011.cia)

  • nus – wavenumber min (cm-1)

  • nue – wavenumber max (cm-1)

Returns:

wavenumber (cm-1) tcia: temperature (K) ac: cia coefficient

Return type:

nucia

exojax.spec.hminus module

H minus opacity by John (1988)

exojax.spec.hminus.bound_free_absorption(wavelength_um, temperature)

bound free absorption of H-

Note

alpha has a value of 1.439e4 micron-1 K-1, the value stated in John (1988) is wrong

Parameters:

  • wavelength_um – wavelength in the unit of micron

  • temperature – temperature in the unit of Kelvin

Returns:

absorption coefficient [cm4/dyne]

exojax.spec.hminus.free_free_absorption(wavelength_um, temperature)

free free absorption of H- (coefficients from John (1988))

Note

to follow his notation (which starts at an index of 1), the 0-index components are 0 for wavelengths larger than 0.3645 micron

Parameters:

  • wavelength_um – wavelength in the unit of micron

  • temperature – temperature in the unit of Kelvin

Returns:

absorption coefficient [cm4/dyne]

exojax.spec.hminus.log_hminus_continuum(nu_grid, temperatures, number_density_e, number_density_h)

John (1988) H- continuum opacity.

Parameters:

  • nu_grid – wavenumber grid (cm-1) [Nnu]

  • temperature – gas temperature array [K] [Nlayer]

  • number_density_e – electron number density array [Nlayer]

  • number_density_h – H atom number density array [Nlayer]

Returns:

log10(absorption coefficient in cm-1) [Nlayer,Nnu]

exojax.spec.hminus.log_hminus_continuum_single(nu_grid, temperature, number_density_e, number_density_h)

John (1988) H- continuum opacity for single temperature, number_density_e, number_density_h. used in single_layer_optical_depth_Hminus

Parameters:

  • nu_grid – wavenumber grid (cm-1) [Nnu]

  • temperature (float) – gas temperature [K]

  • number_density_e (float) – electron number density

  • number_density_h (float) – H atom number density

Returns:

log10(absorption coefficient in cm-1) [Nnu]

exojax.spec.initspec module

Initialization for opacity computation.

The functions in this module are a wrapper for initialization processes for opacity computation.

exojax.spec.initspec.broadening_grid_for_single_broadening_mode(nu_lines, gamma_ref, n_Texp, single_broadening_parameters, R)
exojax.spec.initspec.init_dit(nu_lines, nu_grid, warning=False)
Initialization for DIT. i.e. Generate nu contribution and index for the

line shape density (actually, this is a numpy version of getix)

Parameters:

  • nu_lines – wavenumber list of lines [Nline] (should be numpy F64)

  • nu_grid – wavenumenr grid [Nnugrid] (should be numpy F64)

Returns:

cont (contribution) jnp.array index (index) jnp.array pmarray: (+1.,-1.) array whose length of len(nu_grid)+1

Note

cont is the contribution for i=index+1. 1 - cont is the contribution for i=index. For other i, the contribution should be zero.

exojax.spec.initspec.init_lpf(nu_lines, nu_grid)

Initialization for LPF.

Parameters:

  • nu_lines – wavenumber list of lines [Nline] (should be numpy F64)

  • nu_grid – wavenumenr grid [Nnugrid] (should be numpy F64)

Returns:

numatrix [Nline,Nnu]

exojax.spec.initspec.init_modit(nu_lines, nu_grid, warning=False)

Initialization for MODIT. i.e. Generate nu contribution and index for the line shape density (actually, this is a numpy version of getix)

Parameters:

  • nu_lines – wavenumber list of lines [Nline] (should be numpy F64)

  • nu_grid – wavenumenr grid [Nnugrid] (should be numpy F64)

Returns:

(contribution for q) jnp.array index: (index for q) jnp.array spectral_resolution: spectral resolution (R) pmarray: (+1.,-1.) array whose length of len(nu_grid)+1

Return type:

cont

Note

cont is the contribution for i=index+1. 1 - cont is the contribution for i=index. For other i, the contribution should be zero. dq is computed using numpy not jnp.numpy. If you use jnp, you might observe a significant residual because of the float32 truncation error.

exojax.spec.initspec.init_modit_vald(nu_linesM, nus, N_usp)

Initialization for MODIT for asdb from VALD

Parameters:

  • nu_linesM – wavenumbers of lines for each species [N_species x N_line] (should be numpy F64)

  • nu_grid – wavenumenr grid [Nnugrid] (should be numpy F64)

  • N_usp – number of species

Returns:

(contribution) jnp.array [N_species x N_line] indexS: (index) jnp.array [N_species x N_line] R: spectral resolution

pmarray: (+1,-1) array whose length of len(nu_grid)+1

Return type:

contS

exojax.spec.initspec.init_premodit(nu_lines, nu_grid, elower, gamma_ref, n_Texp, line_strength_ref, Twt, Tref, Tref_broadening, Tmax=None, Tmin=None, dE=160.0, dit_grid_resolution=0.2, diffmode=0, single_broadening=False, single_broadening_parameters=None, warning=False)

Initialization for PreMODIT.

Parameters:

  • nu_lines – wavenumber list of lines [Nline] (should be numpy F64)

  • nu_grid – wavenumenr grid [Nnugrid] (should be numpy F64)

  • elower – elower of lines

  • gamma_ref – half-width at reference (alpha_ref for ExoMol, gamma_air for HITRAN/HITEMP etc)

  • n_Texp – temperature exponent (n_Texp for ExoMol, n_air for HITRAN/HITEMP)

  • line_strength_ref – line strength at reference Tref

  • Twt – temperature for weight in Kelvin

  • Tref – reference temperature of premodit grid

  • Tref_broadening – reference temperature for broadening.

  • Tmax – max temperature to construct n_Texp grid, if None, max(Twt and Tref) is used

  • Tmin – min temperature to construct n_Texp grid, if None, max(Twt and Tref) is used

  • dE – Elower grid interval

  • dit_grid_resolution (float) – DIT grid resolution. when np.inf, the minmax simplex is used

  • diffmode (int) – i-th Taylor expansion is used for the weight, default is 1.

  • single_broadening (optional) – if True, single_braodening_parameters is used. Defaults to False.

  • single_broadening_parameters (optional) – [gamma_ref, n_Texp] at 296K for single broadening. When None, the median is used.

Returns:

contribution for wavenumber jnp.array index_nu: index for wavenumber jnp.array elower_grid: elower grid cont_broadpar: contribution for broadening parmaeters index_broadpar: index for broadening parmaeters R: spectral resolution pmarray: (+1,-1) array whose length of len(nu_grid)+1

Return type:

cont_nu

Note

cont is the contribution for i=index+1. 1 - cont is the contribution for i=index. For other i, the contribution should be zero. dq is computed using numpy not jnp.numpy. If you use jnp, you might observe a significant residual because of the float32 truncation error.

exojax.spec.initspec.warn_dtype64(arr, warning, tag='')

check arr’s dtype.

Parameters:

  • arr – input array

  • warning – True/False

  • tag –

exojax.spec.initspec.warn_out_of_nu_grid(nu_lines, nu_grid)

warning for out-of-nu grid

Note

See Issue 341, https://github.com/HajimeKawahara/exojax/issues/341 Only for DIT and MODIT. For PreMODIT or newer Opacalc, this issue is automatically fixed.

Parameters:

  • nu_lines (_type_) – line center

  • nu_grid (_type_) – wavenumber grid

exojax.spec.initspec.warn_outside_wavenumber_grid(nu_lines, nu_grid)

Check if all the line centers are in the wavenumber grid.

Parameters:

  • nu_lines – line center

  • nu_grid – wavenumber grid

Note

For MODIT/DIT, if the lines whose center are outside of the wavenumber grid, they contribute the edges of the wavenumber grid. This function is to check it. This warning often occurs when you set non-negative value to margin in MdbExomol, MdbHit, AdbVALD, and AdbKurucz in moldb. See #190 for the details.

exojax.spec.layeropacity module

compute opacity difference in atmospheric layers

exojax.spec.layeropacity.layer_optical_depth(dParr, xsmatrix, mixing_ratio, mass, gravity)

dtau matrix from the cross section matrix/vector.

Note

opfac=bar_cgs/(m_u (g)). m_u: atomic mass unit. It can be obtained by fac=1.e3/m_u, where m_u = scipy.constants.m_u.

Parameters:

  • dParr (array) – delta pressure profile (bar) [N_layer]

  • xsmatrix (2D or 1D array) – cross section matrix (cm2) [N_layer, N_nus] or cross section vector (cm2) [N_nus]

  • mixing_ratio (array) – volume mixing ratio (VMR) or mass mixing ratio (MMR) [N_layer]

  • mass – mean molecular weight for VMR or molecular mass for MMR

  • gravity – gravity (cm/s2)

Returns:

optical depth matrix, dtau [N_layer, N_nus]

Return type:

2D array

exojax.spec.layeropacity.layer_optical_depth_CIA(nu_grid, temperature, pressure, dParr, vmr1arr, vmr2arr, mmw, g, nucia, tcia, logac)

dtau of the CIA continuum.

Warning

Not used in art.

Parameters:

  • nu_grid (array) – wavenumber matrix (cm-1)

  • temperature (array) – temperature array (K)

  • pressure (array) – pressure array (bar)

  • dParr (array) – delta temperature array (bar)

  • vmr1arr (array) – volume mixing ratio (VMR) for molecules 1 [N_layer]

  • vmr2arr (array) – volume mixing ratio (VMR) for molecules 2 [N_layer]

  • mmw – mean molecular weight of atmosphere

  • g – gravity (cm2/s)

  • nucia (array) – wavenumber array for CIA

  • tcia (array) – temperature array for CIA

  • logac – log10(absorption coefficient of CIA)

Returns:

optical depth matrix, dtau [N_layer, N_nus]

Return type:

2D array

exojax.spec.layeropacity.layer_optical_depth_Hminus(nu_grid, temperature, pressure, dParr, vmre, vmrh, mmw, gravity)

dtau of the H- continuum.

Parameters:

  • nu_grid (array) – wavenumber matrix (cm-1) [N_nus]

  • temperature (array) – temperature array (K) [N_layer]

  • pressure (array) – pressure array (bar) [N_layer]

  • dParr (array) – delta temperature array (bar) [N_layer]

  • vmre (array) – volume mixing ratio (VMR) for e- [N_layer]

  • vmrH – volume mixing ratio (VMR) for H atoms [N_layer]

  • mmw – mean molecular weight of atmosphere

  • gravity – gravity (cm2/s)

Returns:

optical depth matrix [N_layer, N_nus]

exojax.spec.layeropacity.layer_optical_depth_VALD(dParr, xsm, VMR, mean_molecular_weight, gravity)

dtau of the atomic (+ionic) cross section from VALD.

Parameters:

  • dParr – delta pressure profile (bar) [N_layer]

  • xsm – cross section matrix (cm2) [N_species x N_layer x N_wav]

  • VMR – volume mixing ratio [N_species x N_layer]

  • mean_molecular_weight – mean molecular weight [N_layer]

  • gravity – gravity (cm/s2)

Returns:

optical depth matrix, dtau [N_layer, N_nus]

Return type:

2D array

exojax.spec.layeropacity.layer_optical_depth_cloudgeo(dParr, condensate_substance_density, mmr_condensate, rg, sigmag, gravity)

the optical depth using a geometric cross-section approximation, based on (16) in AM01.

Parameters:

  • dParr – delta pressure profile (bar)

  • condensate_substance_density – condensate substance density (g/cm3)

  • mmr_condensate – Mass mixing ratio (array) of condensate [Nlayer]

  • rg – rg parameter in the lognormal distribution of condensate size, defined by (9) in AM01

  • sigmag – sigmag parameter (geometric standard deviation) in the lognormal distribution of condensate size, defined by (9) in AM01, must be sigmag > 1

  • gravity – gravity (cm/s2)

exojax.spec.layeropacity.layer_optical_depth_clouds_lognormal(dParr, extinction_coefficient, condensate_substance_density, mmr_condensate, rg, sigmag, gravity, N0=1.0)

dtau matrix from the cross section matrix/vector for the lognormal particulate distribution.

Parameters:

  • dParr (array) – delta pressure profile (bar) [N_layer]

  • coefficient (extinction) – extinction coefficient in cgs (cm-1) [N_layer, N_nus]

  • condensate_substance_density (float) – condensate substance density (g/cm3)

  • mmr_condensate (array) – Mass mixing ratio (array) of condensate [Nlayer]

  • rg (float) – rg parameter in the lognormal distribution of condensate size, defined by (9) in AM01

  • sigmag (float) – sigmag parameter (geometric standard deviation) in the lognormal distribution of condensate size, defined by (9) in AM01, must be sigmag > 1

  • gravity (float) – gravity (cm/s2)

  • N0 (float, optional) – the normalization of the lognormal distribution ($N_0$). Defaults to 1.0.

Returns:

optical depth matrix, dtau [N_layer, N_nus]

Return type:

2D array

exojax.spec.layeropacity.single_layer_optical_depth(dpressure, xsv, mixing_ratio, mass, gravity)

opacity for a single layer (delta tau) from cross section vector, molecular line/Rayleigh scattering (for opart)

Parameters:

  • dpressure (float) – pressure difference (dP) of the layer in bar

  • xsv (array) – cross section vector i.e. xsvector (N_wavenumber)

  • mixing_ratio (float) – mass mixing ratio, (or volume mixing ratio profile)

  • mass (float) – molecular mass (or mean molecular weight)

  • gravity (float) – constant or 1d profile of gravity in cgs

Returns:

opacity whose element is optical depth in a single layer [N_wavenumber].

Return type:

dtau (array)

exojax.spec.layeropacity.single_layer_optical_depth_CIA(temperature, pressure, dpressure, vmr1, vmr2, mmw, g, logacia_vector)

dtau of the CIA continuum for a single layer (for opart).

Parameters:

  • temperature (float) – layer temperature (K)

  • pressure (float) – layer pressure (bar)

  • dpressure (float) – delta temperature (bar)

  • vmr1 (float) – volume mixing ratio (VMR) for molecules 1

  • vmr2 (float) – volume mixing ratio (VMR) for molecules 2

  • mmw – mean molecular weight of atmosphere

  • g – gravity (cm2/s)

  • logacia_vector – log CIA coefficient vector [N_nus], usually obtained by opacont.OpaCIA.logacia_vector(temperature)

Returns:

optical depth matrix, dtau [N_nus]

Return type:

1D array

exojax.spec.layeropacity.single_layer_optical_depth_Hminus(nu_grid, temperature, pressure, dpressure, vmre, vmrh, mmw, g)

dtau of the H- continuum for a single layer (e.g. for opart).

Parameters:

  • nu_grid (array) – wavenumber matrix (cm-1) [N_nus]

  • temperature (float) – temperature (K)

  • pressure (float) – pressure (bar)

  • dpressure (float) – delta pressure (bar)

  • vmre – volume mixing ratio (VMR) for e- [N_layer]

  • vmrH – volume mixing ratio (VMR) for H atoms [N_layer]

  • mmw – mean molecular weight of atmosphere

  • g – gravity (cm2/s)

Returns:

optical depth matrix [N_layer, N_nus]

exojax.spec.layeropacity.single_layer_optical_depth_clouds_lognormal(dpressure, extinction_coefficient, condensate_substance_density, mmr_condensate, rg, sigmag, gravity, N0=1.0)

dtau matrix from the cross section matrix/vector for the lognormal particulate distribution, for a single layer.

Parameters:

  • dpressure (float) – delta pressure (bar)

  • coefficient (extinction) – extinction coefficient in cgs (cm-1) [N_nus]

  • condensate_substance_density (float) – condensate substance density (g/cm3)

  • mmr_condensate (float) – Mass mixing ratio of condensate

  • rg (float) – rg parameter in the lognormal distribution of condensate size, defined by (9) in AM01

  • sigmag (float) – sigmag parameter (geometric standard deviation) in the lognormal distribution of condensate size, defined by (9) in AM01, must be sigmag > 1

  • gravity (float) – gravity (cm/s2)

  • N0 (float, optional) – the normalization of the lognormal distribution ($N_0$). Defaults to 1.0.

Returns:

optical depth matrix, dtau [N_nus]

Return type:

1D array

exojax.spec.lbd module

exojax.spec.lbd.lbd_coefficients(elower_lines, elower_grid, Tref, Twt, diffmode=2, conversion_dtype=<class 'numpy.float64'>)

compute the LBD zeroth and first coefficients

Parameters:

  • elower_lines – Line’s Elower

  • elower_grid – Elower grid for LBD

  • Tref – reference tempreature to be used for the line strength S0

  • Twt – temperature used for the weight coefficient computation

  • diffmode (int) – i-th Taylor expansion is used for the weight, default is 2.

  • converted_dtype – data type for conversion. Needs enough large because this code uses exp.

Returns:

the zeroth coefficient at Point 2 the first coefficient at Point 2 index

Note

Twp (Temperature at the weight point) corresponds to Ttyp, but not typical temparture at all. zeroth and first coefficients are at Point 2, i.e. for i=index+1. 1 - zeroth_coefficient gives the zeroth coefficient at Point 1, i.e. for i=index. - first_coefficient gives the first coefficient at Point 1.

exojax.spec.lbd.weight(T, Twt, zeroth_coeff, first_coeff)

construct lbd from zeroth and first terms in the first Taylor approximation

Parameters:

  • Tref – reference tempreature to be used for the line strength S0

  • Twt (float) – temperature used for the weight coefficient computation

  • T (float) – _description_

  • Twt – _description_

  • zeroth_coeff (ndarray) – zeroth coefficient of the Taylor expansion of the weight at Twt

  • first_coeff (ndarray) – first coefficient of the Taylor expansion of the weight at Twt

Returns:

weight at the points 1 and 2

Return type:

ndarray

exojax.spec.lbderror module

exojax.spec.lbderror.default_elower_grid_trange_file(version)

default elower_grid_trange filename

Parameters:

version (int) – version of default elower_grid_trange file, 1 or 2

Returns:

default_elower_grid_trange (degt) filename

Note

This file assumes 1 % precision of line strength within [Tl, Tu] default_elower_grid_trange_file generated by spec/generate_elower_grid_trange.py. Version 1 The original one when premodit was implemented Version 2 a wider temperature range (Jan 2024)

exojax.spec.lbderror.evaluate_trange(Tarr, tlide_line_strength, crit, Twt)

evaluate robust temperature range

Parameters:

  • Tarr (ndarray) – temperature array, shape = (N,)

  • tlide_line_strength (ndarray) – line strength error, shape = (N,)

  • crit (float) – criterion of line strength error (0.01=1%)

  • Twt (float) – weight temperature

Returns:

Tl, Tu. The line strength error is below crit within [Tl, Tu]

Return type:

float, float

exojax.spec.lbderror.optimal_params(Tl, Tu, diffmode=2, version=2, makefig=False, filename=None)

derive the optimal parameters for a given Tu and Tl, which satisfies x % (1% if filename=None) precision within [Tl, Tu]

Parameters:

  • Tl (float) – lower temperature

  • Tu (float) – upper temperature

  • diffmode (int, optional) – diff mode. Defaults to 2.

  • version (int, optional) – version of the default_elower_grid_trange_file, 1 or 2 (default)

  • makefig (bool, optional) – if you wanna make a fig. Defaults to False.

  • filename – grid_trange file, if None default_elower_grid_trange_file is used.

Returns:

dE, Tref, Twt (optimal ones)

Return type:

float

exojax.spec.lbderror.single_tilde_line_strength(t, w1, w2, tref, dE, p=0.5)
Parameters:

  • t (float) – inverse temperature

  • w1 (_type_) – weight at point 1

  • w2 (_type_) – weight at point 2

  • tref (_type_) – reference temperature

  • dE (_type_) – energy interval in cm-1

  • p (float, optional) – between 0 to 1 Defaults to 0.5.

Returns:

_description_

Return type:

_type_

exojax.spec.lbderror.single_tilde_line_strength_first(t, twp, tref, dE, p=0.5)

Single Line Line strength prediction for Premodit/diffmode=1

Parameters:

  • t (_type_) – inverse temperature

  • twp (_type_) – inverse weight temperature

  • tref (_type_) – inverse reference temperature

  • dE (_type_) – Elower interval

  • p (float, optional) – fraction of the line point. Defaults to 0.5.

Returns:

_description_

Return type:

_type_

exojax.spec.lbderror.single_tilde_line_strength_second(t, twp, tref, dE, p=0.5)

Single Line Line strength prediction for Premodit/diffmode=1

Parameters:

  • t (_type_) – inverse temperature

  • twp (_type_) – inverse weight temperature

  • tref (_type_) – inverse reference temperature

  • dE (_type_) – Elower interval

  • p (float, optional) – fraction of the line point. Defaults to 0.5.

Returns:

_description_

Return type:

_type_

exojax.spec.lbderror.single_tilde_line_strength_zeroth(t, twp, tref, dE, p=0.5)
exojax.spec.lbderror.weight_point1_dE(t, tref, dE, p=0.5)

dE version of the weight at point 1 for PreMODIT

Parameters:

  • t (float) – inverse temperature

  • tref (float) – reference inverse temperature

  • dE (float) – envergy interval between points 1 nad 2 (cm-1)

  • p (float) – between 0 to 1

Returns:

weight at point 1

exojax.spec.lbderror.weight_point2_dE(t, tref, dE, p=0.5)

dE version of the weight at point 2 for PreMODIT

Parameters:

  • t (float) – inverse temperature

  • tref (float) – reference inverse temperature

  • dE (float) – envergy interval between points 1 nad 2 (cm-1)

  • p (float) – between 0 to 1

Returns:

weight at point 2

exojax.spec.lbderror.worst_tilde_line_strength_first(T, Ttyp, Tref, dE)

worst deviation of single tilde line search first in terms of p

Parameters:

  • T (float, ndarray) – temperature (array) K

  • Twp (float) – weight temperature K

  • Tref (float) – reference tempearture K

  • dE (float) – Elower interval cm-1

Returns:

worst value of single_tilde_line_strength_first in terms of p

exojax.spec.lbderror.worst_tilde_line_strength_second(T, Ttyp, Tref, dE)

worst deviation of single tilde line search first in terms of p

Parameters:

  • T (float, ndarray) – temperature (array) K

  • Twp (float) – weight temperature K

  • Tref (float) – reference tempearture K

  • dE (float) – Elower interval cm-1

Returns:

worst value of single_tilde_line_strength_first in terms of p

exojax.spec.limb_darkening module

Limb darkening functions.

exojax.spec.limb_darkening.ld_kipping(q1, q2)

Uninformative prior conversion of the limb darkening by Kipping (arxiv:1308.0009)

Parameters:

  • q1 – U(0,1)

  • q2 – U(0,1)

Returns:

quadratic LD coefficient u1 u2: quadratic LD coefficient u2

Return type:

u1

exojax.spec.lpf module

Line Profile Functions method for opacity calculation.

exojax.spec.lpf.exomol(mdb, Tarr, Parr, molmass)

Computes molecular line information required for MODIT using Exomol mdb.

Parameters:

  • mdb – mdb instance

  • Tarr – Temperature array

  • Parr – Pressure array

  • molmass – molecular mass

Returns:

line intensity matrix, gammaL matrix, sigmaD matrix

exojax.spec.lpf.hjert_jvp(primals, tangents)
exojax.spec.lpf.ljert(x, a)

ljert function, consisting of a combination of imwofz and imag(asymptiotic wofz).

Parameters:

  • x –

  • a –

Returns:

L(x,a) or Imag(wofz(x+ia))

Note

ljert provides a L(x,a) function. This function accepts a scalar value as an input. Use jax.vmap to use a vector as an input.

exojax.spec.lpf.vald(adb, Tarr, PH, PHe, PHH)

Computes VALD line information required for LPF using VALD atomic database (adb)

Parameters:

  • adb – adb instance made by the AdbVald class in moldb.py

  • Tarr – Temperature array

  • PH – Partial pressure array of neutral hydrogen (H)

  • PHe – Partial pressure array of neutral helium (He)

  • PHH – Partial pressure array of molecular hydrogen (H2)

Returns:

line intensity matrix gammaLM: gammaL matrix sigmaDM: sigmaD matrix

Return type:

SijM

exojax.spec.lpf.vald_each(Tarr, PH, PHe, PHH, qt_284_T, QTmask, QTref_284, logsij0, nu_lines, ielem, iion, dev_nu_lines, elower, eupper, atomicmass, ionE, gamRad, gamSta, vdWdamp, Tref)

Compute VALD line information required for LPF for separated each species

Parameters:

  • Tarr – temperature array [N_layer]

  • PH – partial pressure array of neutral hydrogen (H) [N_layer]

  • PHe – partial pressure array of neutral helium (He) [N_layer]

  • PHH – partial pressure array of molecular hydrogen (H2) [N_layer]

  • qt_284_T – partition function at the temperature T Q(T), for 284 species

  • QTmask – array of index of Q(Tref) grid (gQT) for each line

  • QTref_284 – partition function at the reference temperature Q(Tref), for 284 species

  • logsij0 – log line strength at T=Tref

  • nu_lines – line center (cm-1) in np.array (float64)

  • ielem – atomic number (e.g., Fe=26)

  • iion – ionized level (e.g., neutral=1, singly ionized=2, etc.)

  • dev_nu_lines – line center (cm-1) in device (float32)

  • elower – the lower state energy (cm-1)

  • eupper – the upper state energy (cm-1)

  • atomicmass – atomic mass (amu)

  • ionE – ionization potential (eV)

  • gamRad – log of gamma of radiation damping (s-1)

  • gamSta – log of gamma of Stark damping (s-1)

  • vdWdamp – log of (van der Waals damping constant / neutral hydrogen number) (s-1)

Returns:

line intensity matrix [N_layer x N_line] gammaLM: gammaL matrix [N_layer x N_line] sigmaDM: sigmaD matrix [N_layer x N_line]

Return type:

SijM

exojax.spec.lpf.voigt(nuvector, sigmaD, gammaL)

Custom JVP version of Voigt profile using Voigt-Hjerting function.

Parameters:

  • nu – wavenumber array

  • sigmaD – sigma parameter in Doppler profile

  • gammaL – broadening coefficient in Lorentz profile

Returns:

Voigt profile

Return type:

v

exojax.spec.lpf.voigtone(nu, sigmaD, gammaL)

Custom JVP version of (non-vmapped) Voigt function using Voigt-Hjerting function.

Parameters:

  • nu – wavenumber

  • sigmaD – sigma parameter in Doppler profile

  • gammaL – broadening coefficient in Lorentz profile

Returns:

Voigt funtion

Return type:

v

exojax.spec.lpf.vvoigt(numatrix, sigmaD, gammaL)

Custom JVP version of vmaped voigt profile.

Parameters:

  • numatrix – wavenumber matrix in R^(Nline x Nwav)

  • sigmaD – doppler sigma vector in R^Nline

  • gammaL – gamma factor vector in R^Nline

Returns:

Voigt profile vector in R^Nwav

exojax.spec.lpf.xsmatrix(numatrix, sigmaDM, gammaLM, SijM)

Custom JVP version of cross section matrix.

Parameters:

  • numatrix – wavenumber matrix in R^(Nline x Nwav)

  • sigmaDM – doppler sigma matrix in R^(Nlayer x Nline)

  • gammaLM – gamma factor matrix in R^(Nlayer x Nline)

  • SijM – line strength matrix in R^(Nlayer x Nline)

Returns:

cross section matrix in R^(Nlayer x Nwav)

exojax.spec.lpf.xsvector(numatrix, sigmaD, gammaL, Sij)

Custom JVP version of cross section vector.

Parameters:

  • numatrix – wavenumber matrix in R^(Nline x Nwav)

  • sigmaD – doppler sigma vector in R^Nline

  • gammaL – gamma factor vector in R^Nline

  • Sij – line strength vector in R^Nline

Returns:

cross section vector in R^Nwav

exojax.spec.lpffilter module

exojax.spec.lpffilter.compute_filter_length(wavenumber_halfwidth, representative_wavenumber, spectral_resolution)

compute the length of the FIR line shape filter

Parameters:

  • wavenumber_halfwidth (float) – half width at representative wavenumber (cm-1)

  • representative_wavenumber (float) – representative wavenumber (cm-1)

  • spectral_resolution (float) – spectral resolution R0

Returns:

filter length

Return type:

int

Examples

from exojax.utils.instfunc import resolution_eslog spectral_resolution = resolution_eslog(nu_grid) filter_length = compute_filter_length(50.0, 4000.0, spectral_resolution)

exojax.spec.lpffilter.generate_closed_lpffilter(filter_length_oneside, nsigmaD, ngammaL)

Generates the closed form LPF filter

Parameters:

  • filter_length (int) – length of the wavenumber grid of lpffilter

  • nsigmaD (float) – normalized gaussian standard deviation, resolution*betaT/nu betaT is the STD of Doppler broadening

  • ngammaL (float) – normalized Lorentzian half width

Notes

The filter structure is filter[1:M] = vkfilter[M+1:][::-1]m where M=N/2 filter[0] is the DC component, Nyquist component. filter[M] is the Nyquist component. The dimension of the closed lpf filter is even number.

Returns:

closed lpf filter [2*filter_length_oneside]

Return type:

array

exojax.spec.lpffilter.generate_open_lpffilter(filter_length_oneside, nsigmaD, ngammaL)

Generates the open form LPF filter

Notes

The dimension of the open lpf filter is odd number to ensure asymmetry. This forces fft_length to be even number when the dimension of signal is even number.

Parameters:

  • filter_length_oneside (int) – length of the wavenumber grid of lpffilter

  • nsigmaD (float) – normalized gaussian standard deviation, resolution*betaT/nu betaT is the STD of Doppler broadening

  • ngammaL (float) – normalized Lorentzian half width

Returns:

open lpf filter [2*filter_length_oneside+1]

Return type:

array

exojax.spec.lsd module

functions for computation of line shape density (LSD)

  • there are both numpy and jnp versions. (np)*** is numpy version.

  • (np)add(x)D constructs the (x)Dimensional LSD array given the contribution and index.

exojax.spec.lsd.add2D(a, w, cx, ix, cy, iy)

Add into an array when contirbutions and indices are given (2D).

Parameters:

  • a – lineshape density (LSD) array (np.array)

  • w – weight (N)

  • cx – given contribution for x

  • ix – given index for x

  • cy – given contribution for y

  • iy – given index for y

Returns:

a

exojax.spec.lsd.add3D(a, w, cx, ix, cy, iy, cz, iz)

Add into an array when contirbutions and indices are given (3D).

Parameters:

  • a – lineshape density (LSD) array (np.array)

  • w – weight (N)

  • cx – given contribution for x

  • ix – given index for x

  • cy – given contribution for y

  • iy – given index for y

  • cz – given contribution for z

  • iz – given index for z

Returns:

a

exojax.spec.lsd.inc2D_givenx(a, w, cx, ix, y, yv)

Compute integrated neighbouring contribution for 2D LSD (memory reduced sum) but using given contribution and index for x .

Parameters:

  • a – lineshape density (LSD) array (jnp.array)

  • w – weight (N)

  • cx – given contribution for x

  • ix – given index for x

  • y – y values (N)

  • yv – y grid

Returns:

lineshape distribution matrix (integrated neighbouring contribution for 2D)

Note

This function computes sum_n w_n fx_n otimes fy_n, where w_n is the weight, fx_n, fy_n, are the n-th NCFs for 1D. A direct sum uses huge RAM.

exojax.spec.lsd.inc3D_givenx(a, w, cx, ix, y, z, xv, yv, zv)

Compute integrated neighbouring contribution for the 3D lineshape distribution (LSD) matrix (memory reduced sum) but using given contribution and index for x .

Parameters:

  • a – lineshape density (LSD) array (jnp.array)

  • w – weight (N)

  • cx – given contribution for x

  • ix – given index for x

  • y – y values (N)

  • z – z values (N)

  • xv – x grid

  • yv – y grid

  • zv – z grid

Returns:

lineshape distribution matrix (integrated neighbouring contribution for 3D)

Note

This function computes sum_n w_n fx_n otimes fy_n otimes fz_n, where w_n is the weight, fx_n, fy_n, and fz_n are the n-th NCFs for 1D. A direct sum uses huge RAM.

exojax.spec.lsd.npadd3D_direct1D(a, w, cx, ix, direct_cy, direct_iy, cz, iz, sumx=1.0, sumz=1.0)

numpy version: Add into an array when contirbutions and indices are given (2D+direct).

Parameters:

  • a – lineshape density (LSD) array (np.array)

  • w – weight (N)

  • cx – given contribution for x

  • ix – given index for x

  • direct_cy – direct contribution for y

  • direct_iy – direct index for y

  • cz – given contribution for z

  • iz – given index for z

  • sumx – a sum of contribution for x at point 1 and point 2, default=1.0

  • sumz – a sum of contribution for z at point 1 and point 2, default=1.0

Returns:

lineshape density a(nx,ny,nz)

Note

sumx or sumz gives a sum of contribution at point 1 and point 2. For the zeroth coeeficient, it should be 1.0 while it should be 0.0 for the first coefficient.

exojax.spec.lsd.npadd3D_multi_index(a, w, cx, ix, cz, iz, uidx, multi_cont_lines, neighbor_uidx, sumx=1.0, sumz=1.0)

numpy version: Add into an array using multi_index system in y :param a: lineshape density (LSD) array (np.array) :param w: weight (N) :param cx: given contribution for x :param ix: given index for x :param cz: given contribution for z :param iz: given index for z :param sumx: a sum of contribution for x at point 1 and point 2, default=1.0 :param sumz: a sum of contribution for z at point 1 and point 2, default=1.0

Returns:

lineshape density a(nx,ny,nz)

Note

sumx or sumz gives a sum of contribution at point 1 and point 2. For the zeroth coeeficient, it should be 1.0 while it should be 0.0 for the first coefficient.

exojax.spec.make_numatrix module

exojax.spec.make_numatrix.add_nu(dd, fnu, fhatnu, Nz)

re-adding an interger part w/JIT.

Parameters:

  • dd – difference matrix

  • fnu – integer part of wavenumber

  • fhatnu – residual wavenumber

  • Nz – boost factor

Returns:

an integer part readded value

exojax.spec.make_numatrix.divwavnum(nu, Nz=1)

separate an integer part from a residual.

Parameters:

  • nu – wavenumber array

  • Nz – boost factor (default=1)

Returns:

integer part of wavenumber, residual wavenumber, boost factor

exojax.spec.make_numatrix.make_numatrix0(nu, hatnu, warning=True)

Generate numatrix0.

Note

Use float64 as inputs.

Parameters:

  • nu – wavenumber matrix (Nnu,)

  • hatnu – line center wavenumber vector (Nline,), where Nm is the number of lines

  • warning – True=warning on for nu.dtype=float32

Returns:

numatrix (Nline,Nnu)

exojax.spec.make_numatrix.make_numatrix0_subtract(nu, hatnu, Nz=1, warning=True)

Generate numatrix0 using gpu.

Note

This function computes a wavenumber matrix using XLA. Because XLA does not support float64, a direct computation sometimes results in large uncertainity. For instace, let’s assume nu=2000.0396123 cm-1 and hatnu=2000.0396122 cm-1. If applying float32, we get np.float32(2000.0396123)-np.float32(2000.0396122) = 0.0. But, after subtracting 2000 from both nu and hatnu, we get np.float32(0.0396123)-np.float32(0.0396122)=1.0058284e-07. make_numatrix0 does such computation. Nz=1 means we subtract a integer part (i.e. 2000), Nz=10 means we subtract 2000.0, and Nz=10 means we subtract 2000.00.

Parameters:

  • nu – wavenumber matrix (Nnu,)

  • hatnu – line center wavenumber vector (Nline,), where Nm is the number of lines

  • Nz – boost factor (default=1)

  • warning – True=warning on for nu.dtype=float32

Returns:

wavenumber matrix w/ no shift

Return type:

numatrix0

exojax.spec.make_numatrix.subtract_nu(dnu, dhatnu)

compute nu - hatnu by subtracting an integer part w/JIT

Parameters:

  • dnu – residual wavenumber array

  • dhatnu – residual line center array

Returns:

difference matrix

exojax.spec.mie module

Mie scattering calculation using PyMieScatt

exojax.spec.mie.auto_rgrid(rg, sigmag, nrgrid=1500)

sets the automatic rgrid (particulate radius grid).

Note

This method optimizes the sampling grid of the particulate radius (rgrid). The basic strategy is as follows. 1. if the cube-weighted lognormal distribution q(x) is enough compact, the sampling points is given by the linear within the range of [mean - m sigma, mean + n sigma] where sigma is the STD of q(x). 2. else, i.e., the distribution starts from close to 0 (large sigmag), the range is [0 + dr, n*mean]. Currently sigmag = 1.0001 to 4 is within 1 % error for the defalut setting. See tests/unittests/spec/clouds/mie_test.py

Parameters:

  • rg (float) – rg parameter in lognormal distribution in cgs

  • sigmag (float) – sigma_g parameter in lognormal distribution

  • nrgrid (int, optional) – the number of rgrid. Defaults to 1500.

Returns:

rgrid (the particulate radius grid)

Return type:

array

exojax.spec.mie.compute_mie_coeff_lognormal_grid(refractive_indices, refractive_wavenm, sigmag_arr, rg_arr, N0=1.0)

computes miegrid for lognomal distribution parameters rg and sigmag

Args:

refractive_indices (_type_): refractive indices (m = n + ik) refractive_wavenm (_type_): wavenlenth in nm for refractive indices sigmag_arr (1d array): sigmag ($sigma_g$) array rg_arr (1d array): rg ($r_g$) array N0 (_type_, optional): the normalization of the lognormal distribution ($N_0$). Defaults to 1.0.

Note:

N0 ($N_0$) is defined as the normalization of the cloud distribution, $n(r) pr = N_0 p(r) pr where $r$ is the particulate radius and $p(r) =

rac{1}{sqrt{2 pi}} rac{1}{r log{sigma_g}} exp{- rac{(log{r} - log{r_g})^2}{2 log^2{sigma_g}}}$$

is the lognormal distribution. See also https://pymiescatt.readthedocs.io/en/latest/forward.html they use the diameter instead (but p(d) ) $p(d) pd =

rac{N_0}{sqrt{2 pi}} rac{1}{d log{sigma_g}} exp{- rac{(log{d} - log{d_g})^2}{2 log^2{sigma_g}}}$ pd

where and $d = 2 r$ and $d_g = 2 r_g$. In ExoJAX Ackerman and Marley cloud model, $N_0$ can be evaluated by atm.amclouds.normalization_lognormal.

Returns:

_type_: miegrid (N_rg, N_sigmag, N_refractive_indices, 7), 7 is the number of the mie coefficients

exojax.spec.mie.compute_mieparams_cgs_from_miegrid(rg, sigmag, miegrid, rg_arr, sigmag_arr, N0)

computes Mie parameters i.e. extinction coeff, sinigle scattering albedo, asymmetric factor using miegrid. This process also convert the unit to cgs

Args:

rg_layer (1d array): layer wise rg parameters sigmag_layer (1d array): layer wise sigmag parameters miegrid (5d array): Mie grid (lognormal) rg_arr (1d array): rg array used for computing miegrid sigmag_arr (1d array): sigma_g array used for computing miegrid N0 (float, optional): the normalization of the lognormal distribution ($N_0$). Defaults to 1.0.

Note:

N0 ($N_0$) is defined as the normalization of the cloud distribution, $n(r) pr = N_0 p(r) pr where $r$ is the particulate radius and $p(r) =

rac{1}{sqrt{2 pi}} rac{1}{r log{sigma_g}} exp{- rac{(log{r} - log{r_g})^2}{2 log^2{sigma_g}}}$$

is the lognormal distribution. See also https://pymiescatt.readthedocs.io/en/latest/forward.html they use the diameter instead (but p(d) ) $p(d) pd =

rac{N_0}{sqrt{2 pi}} rac{1}{d log{sigma_g}} exp{- rac{(log{d} - log{d_g})^2}{2 log^2{sigma_g}}}$ pd

where and $d = 2 r$ and $d_g = 2 r_g$. In ExoJAX Ackerman and Marley cloud model, $N_0$ can be evaluated by atm.amclouds.normalization_lognormal.

Note:

Volume extinction coefficient (1/cm) for the number density N can be computed by beta_extinction = N*sigma0_extinction The original extinction coefficient (beta) from PyMieScat has the unit of 1/Mm (Mega meter) for diameter. Therefore, this method multiplies 1.e-8 to beta for conversion to 1/cm for radius.

Returns:

sigma_extinction, extinction cross section (cm2) = volume extinction coefficient (1/cm) normalized by the reference numbver density N0. sigma_scattering, scattering cross section (cm2) = volume extinction coefficient (1/cm) normalized by the reference numbver density N0. g, asymmetric factor (mean g)

exojax.spec.mie.cubeweighted_integral_checker(rgrid, rg, sigmag, accuracy=0.01)

checks if the trapezoid integral of the cube-weighted lognormal distribution agrees with 1 within prec given rgrid, rg, sigmag

Parameters:

  • rgrid (array) – the particulate radius grid

  • rg (float) – rg parameter in lognormal distribution in cgs

  • sigmag (float) – sigma_g parameter in lognormal distribution

  • accuracy (float, optional) – _description_. Defaults to 1.e-2, i.e. 1% accuracy.

Returns:

True or False

Return type:

bool

exojax.spec.mie.evaluate_miegrid(rg, sigmag, miegrid, rg_arr, sigmag_arr)

evaluates the value at rg and sigmag by interpolating miegrid

Parameters:

  • rg (float) – rg parameter in lognormal distribution

  • sigmag (float) – sigma_g parameter in lognormal distribution

  • miegrid (5d array) – Mie grid (lognormal)

  • sigmag_arr (1d array) – sigma_g array

  • rg_arr (1d array) – rg array

Note

beta derived here is in the unit of 1/Mm (Mega meter) for diameter multiply 1.e-8 to convert to 1/cm for radius.

Returns:

evaluated values of miegrid, output of MieQ_lognormal Bext (1/Mm), Bsca, Babs, G, Bpr, Bback, Bratio (wavenumber, number of mieparams)

Return type:

_type_

exojax.spec.mie.make_miegrid_lognormal(refraction_index, refraction_index_wavelength_nm, filename, sigmagmin=1.0001, sigmagmax=4.0, Nsigmag=10, log_rg_min=- 7.0, log_rg_max=- 3.0, Nrg=40, N0=1.0)

generates miegrid assuming lognormal size distribution

Args:

refraction_index: complex refracion (refractive) index refraction_index_wavelength_nm: wavelength grid in nm filename (str): filename sigmagmin (float, optional): sigma_g minimum. Defaults to 1.0001. sigmagmax (float, optional): sigma_g maximum. Defaults to 4.0. Nsigmag (int, optional): the number of the sigmag grid. Defaults to 10. log_rg_min (float, optional): log r_g (cm) minimum . Defaults to -7.0. log_rg_max (float, optional): log r_g (cm) minimum. Defaults to -3.0. Nrg (int, optional): the number of the rg grid. Defaults to 40. N0 (float, optional): the normalization of the lognormal distribution ($N_0$). Defaults to 1.0.

Note:

N0 ($N_0$) is defined as the normalization of the cloud distribution, $n(r) pr = N_0 p(r) pr where $r$ is the particulate radius and $p(r) =

rac{1}{sqrt{2 pi}} rac{1}{r log{sigma_g}} exp{- rac{(log{r} - log{r_g})^2}{2 log^2{sigma_g}}}$$

is the lognormal distribution. See also https://pymiescatt.readthedocs.io/en/latest/forward.html they use the diameter instead (but p(d) ) $p(d) pd =

rac{N_0}{sqrt{2 pi}} rac{1}{d log{sigma_g}} exp{- rac{(log{d} - log{d_g})^2}{2 log^2{sigma_g}}}$ pd

where and $d = 2 r$ and $d_g = 2 r_g$. In ExoJAX Ackerman and Marley cloud model, $N_0$ can be evaluated by atm.amclouds.normalization_lognormal.

exojax.spec.mie.mie_lognormal_pymiescatt(m, wavelength, sigmag, rg, N0, rgrid, nMedium=1.0)

Mie parameters assuming a lognormal distribution

Parameters:

  • m (_type_) – _description_

  • wavelength (_type_) – _description_

  • sigmag (float) – sigma_g parameter in lognormal distribution

  • rg (float) – rg parameter in lognormal distribution in cgs

  • N0 (_type_) –

  • rgrid – grid of the particulate radius

  • nMedium (float, optional) – _description_. Defaults to 1.0.

Returns:

_description_

Return type:

_type_

exojax.spec.mie.read_miegrid(filename)

read miegrid file

Parameters:

filename (str) – file name

Returns:

miegrid jnp 1d array: array for rg jnp 1d array: array for sigmag

Return type:

jnp Nd array

exojax.spec.mie.save_miegrid(filename, miegrid, rg_arr, sigmag_arr)

save miegrid file

Parameters:

  • filename (str) – file name

  • array (jnp 1d) – miegrid

  • array – array for rg

  • array – array for sigmag

exojax.spec.modit module

Line profile computation using Discrete Integral Transform.

exojax.spec.modit.dgmatrix(x, dit_grid_resolution=0.1, adopt=True)

DIT GRID MATRIX (alias)

Parameters:

  • x – simgaD or gammaL matrix (Nlayer x Nline)

  • dit_grid_resolution – grid resolution. dit_grid_resolution=0.1 (defaut) means a grid point per digit

  • adopt – if True, min, max grid points are used at min and max values of x. In this case, the grid width does not need to be dit_grid_resolution exactly.

Returns:

grid for DIT (Nlayer x NDITgrid)

exojax.spec.modit.ditgrid(x, dit_grid_resolution=0.1, adopt=True)

DIT GRID (deprecated).

Parameters:

  • x – simgaD or gammaL array (Nline)

  • dit_grid_resolution – grid resolution. res=0.1 (defaut) means a grid point per digit

  • adopt – if True, min, max grid points are used at min and max values of x. In this case, the grid width does not need to be res exactly.

Returns:

grid for DIT

exojax.spec.modit.exomol(mdb, Tarr, Parr, R, molmass)

compute molecular line information required for MODIT using Exomol mdb.

Parameters:

  • mdb – mdb instance

  • Tarr – Temperature array

  • Parr – Pressure array

  • R – spectral resolution

  • molmass – molecular mass

  • wavmask – mask for wavenumber #Issue 341

Returns:

line intensity matrix, normalized gammaL matrix, normalized sigmaD matrix

exojax.spec.modit.hitran(mdb, Tarr, Parr, Pself, R, molmass)

compute molecular line information required for MODIT using HITRAN/HITEMP mdb.

Parameters:

  • mdb – mdb instance

  • Tarr – Temperature array

  • Parr – Pressure array

  • Pself – Partial pressure array

  • R – spectral resolution

  • molmass – molecular mass

Returns:

line intensity matrix, normalized gammaL matrix, normalized sigmaD matrix

exojax.spec.modit.minmax_dgmatrix(x, dit_grid_resolution=0.1, adopt=True)

compute MIN and MAX DIT GRID MATRIX.

Parameters:

  • x – gammaL matrix (Nlayer x Nline)

  • dit_grid_resolution – grid resolution. dit_grid_resolution=0.1 (defaut) means a grid point per digit

  • adopt – if True, min, max grid points are used at min and max values of x. In this case, the grid width does not need to be dit_grid_resolution exactly.

Returns:

minimum and maximum for DIT (dgm_minmax)

exojax.spec.modit.precompute_dgmatrix(set_gm_minmax, dit_grid_resolution=0.1, adopt=True)

Precomputing MODIT GRID MATRIX for normalized GammaL.

Parameters:

  • set_gm_minmax – set of gm_minmax for different parameters [Nsample, Nlayers, 2], 2=min,max

  • dit_grid_resolution – grid resolution. dit_grid_resolution=0.1 (defaut) means a grid point per digit

  • adopt – if True, min, max grid points are used at min and max values of x. In this case, the grid width does not need to be dit_grid_resolution exactly.

Returns:

grid for DIT (Nlayer x NDITgrid)

exojax.spec.modit.set_ditgrid_matrix_exomol(mdb, fT, Parr, R, molmass, dit_grid_resolution, *kargs)

Easy Setting of DIT Grid Matrix (dgm) using Exomol.

Parameters:

  • mdb – mdb instance

  • fT – function of temperature array

  • Parr – pressure array

  • R – spectral resolution

  • molmass – molecular mass

  • dit_grid_resolution –

    resolution of dgm

    *kargs: arguments for fT

Returns:

DIT Grid Matrix (dgm) of normalized gammaL

Example

>>> fT = lambda T0,alpha: T0[:,None]*(Parr[None,:]/Pref)**alpha[:,None]
>>> T0_test=np.array([1100.0,1500.0,1100.0,1500.0])
>>> alpha_test=np.array([0.2,0.2,0.05,0.05])
>>> dit_grid_resolution=0.2
>>> dgm_ngammaL=setdgm_exomol(mdbCH4,fT,Parr,R,molmassCH4,dit_grid_resolution,T0_test,alpha_test)
exojax.spec.modit.set_ditgrid_matrix_hitran(mdb, fT, Parr, Pself_ref, R, molmass, dit_grid_resolution, *kargs)

Easy Setting of DIT Grid Matrix (dgm) using HITRAN/HITEMP.

Parameters:

  • mdb – mdb instance

  • fT – function of temperature array

  • Parr – pressure array

  • Pself_ref – reference partial pressure array

  • R – spectral resolution

  • molmass – molecular mass

  • dit_grid_resolution –

    resolution of dgm

    *kargs: arguments for fT

Returns:

DIT Grid Matrix (dgm) of normalized gammaL

Example

>>> fT = lambda T0,alpha: T0[:,None]*(Parr[None,:]/Pref)**alpha[:,None]
>>> T0_test=np.array([1100.0,1500.0,1100.0,1500.0])
>>> alpha_test=np.array([0.2,0.2,0.05,0.05])
>>> dit_grid_resolution=0.2
>>> dgm_ngammaL=setdgm_hitran(mdbCH4,fT,Parr,Pself,R,molmassCH4,dit_grid_resolution,T0_test,alpha_test)
exojax.spec.modit.set_ditgrid_matrix_vald_all(asdb, PH, PHe, PHH, R, fT, dit_grid_resolution, *kargs)

Easy Setting of DIT Grid Matrix (dgm) using VALD.

Parameters:

  • asdb – asdb instance made by the AdbSepVald class in moldb.py

  • PH – partial pressure array of neutral hydrogen (H) [N_layer]

  • PHe – partial pressure array of neutral helium (He) [N_layer]

  • PHH – partial pressure array of molecular hydrogen (H2) [N_layer]

  • R – spectral resolution

  • fT – function of temperature array

  • dit_grid_resolution – resolution of dgm

  • *kargs – arguments for fT

Returns:

DIT Grid Matrix (dgm) of normalized gammaL [N_species x N_layer x N_DITgrid]

Return type:

dgm_ngammaLS

Example

>>> fT = lambda T0,alpha:  T0[:,None]*(Parr[None,:]/Pref)**alpha[:,None]
>>> T0_test=np.array([3000.0,4000.0,3000.0,4000.0])
>>> alpha_test=np.array([0.2,0.2,0.05,0.05])
>>> dit_grid_resolution=0.2
>>> dgm_ngammaLS = setdgm_vald_all(asdb, PH, PHe, PHH, R, fT, dit_grid_resolution, T0_test, alpha_test)
exojax.spec.modit.set_ditgrid_matrix_vald_each(ielem, iion, atomicmass, ionE, dev_nu_lines, logsij0, elower, eupper, gamRad, gamSta, vdWdamp, Tref, QTmask, T_gQT, gQT_284species, PH, PHe, PHH, R, fT, dit_grid_resolution, *kargs)

Easy Setting of DIT Grid Matrix (dgm) using VALD.

Parameters:

  • ielem – atomic number (e.g., Fe=26)

  • iion – ionized level (e.g., neutral=1, singly ionized=2, etc.)

  • atomicmass – atomic mass (amu)

  • ionE – ionization potential (eV)

  • dev_nu_lines – line center (cm-1) in device

  • logsij0 – log line strength at T=Tref

  • elower – the lower state energy (cm-1)

  • eupper – the upper state energy (cm-1)

  • gamRad – log of gamma of radiation damping (s-1)

  • gamSta – log of gamma of Stark damping (s-1)

  • vdWdamp – log of (van der Waals damping constant / neutral hydrogen number) (s-1)

  • Tref – reference temperature

  • T_gQT – temperature in the grid obtained from the adb instance

  • gQT_284species – partition function in the grid from the adb instance

  • QTmask – array of index of Q(Tref) grid (gQT) for each line

  • PH – partial pressure array of neutral hydrogen (H) [N_layer]

  • PHe – partial pressure array of neutral helium (He) [N_layer]

  • PHH – partial pressure array of molecular hydrogen (H2) [N_layer]

  • R – spectral resolution

  • fT – function of temperature array

  • dit_grid_resolution – resolution of dgm

  • *kargs – arguments for fT

Returns:

DIT Grid Matrix (dgm) of normalized gammaL [N_layer x N_DITgrid]

Return type:

dgm_ngammaL

exojax.spec.modit.setdgm_exomol(mdb, fT, Parr, R, molmass, dit_grid_resolution, *kargs)
exojax.spec.modit.setdgm_hitran(mdb, fT, Parr, Pself_ref, R, molmass, dit_grid_resolution, *kargs)
exojax.spec.modit.setdgm_vald_all(asdb, PH, PHe, PHH, R, fT, dit_grid_resolution, *kargs)
exojax.spec.modit.setdgm_vald_each(ielem, iion, atomicmass, ionE, dev_nu_lines, logsij0, elower, eupper, gamRad, gamSta, vdWdamp, Tref, QTmask, T_gQT, gQT_284species, PH, PHe, PHH, R, fT, dit_grid_resolution, *kargs)
exojax.spec.modit.vald_all(asdb, Tarr, PH, PHe, PHH, R)

Compute atomic line information required for MODIT for separated ALL species, using VALD separated atomic database (asdb).

Parameters:

  • asdb – asdb instance made by the AdbSepVald class in moldb.py

  • Tarr – temperature array [N_layer]

  • PH – partial pressure array of neutral hydrogen (H) [N_layer]

  • PHe – partial pressure array of neutral helium (He) [N_layer]

  • PHH – partial pressure array of molecular hydrogen (H2) [N_layer]

  • R – spectral resolution [scalar]

Returns:

line intensity matrix [N_species x N_layer x N_line] ngammaLMS: normalized gammaL matrix [N_species x N_layer x N_line] nsigmaDlS: normalized sigmaD matrix [N_species x N_layer x 1]

Return type:

SijMS

exojax.spec.modit.vald_each(Tarr, PH, PHe, PHH, R, qt_284_T, QTmask, QTref_284, ielem, iion, atomicmass, ionE, dev_nu_lines, logsij0, elower, eupper, gamRad, gamSta, vdWdamp, Tref)

Compute atomic line information required for MODIT for separated EACH species, using parameters attributed in VALD separated atomic database (asdb).

Parameters:

  • Tarr – temperature array [N_layer]

  • PH – partial pressure array of neutral hydrogen (H) [N_layer]

  • PHe – partial pressure array of neutral helium (He) [N_layer]

  • PHH – partial pressure array of molecular hydrogen (H2) [N_layer]

  • R – spectral resolution [scalar]

  • qt_284_T – partition function at the temperature T Q(T), for 284 species

  • QTmask – array of index of Q(Tref) grid (gQT) for each line

  • QTref_284 – partition function at the reference temperature Q(Tref), for 284 species

  • ielem – atomic number (e.g., Fe=26)

  • iion – ionized level (e.g., neutral=1, singly ionized=2, etc.)

  • atomicmass – atomic mass (amu)

  • ionE – ionization potential (eV)

  • dev_nu_lines – line center (cm-1) in device

  • logsij0 – log line strength at T=Tref

  • elower – the lower state energy (cm-1)

  • eupper – the upper state energy (cm-1)

  • gamRad – log of gamma of radiation damping (s-1)

  • gamSta – log of gamma of Stark damping (s-1)

  • vdWdamp – log of (van der Waals damping constant / neutral hydrogen number) (s-1)

  • Tref – reference temperature

Returns:

line intensity matrix [N_layer x N_line] ngammaLM: normalized gammaL matrix [N_layer x N_line] nsigmaDl: normalized sigmaD matrix [N_layer x 1]

Return type:

SijM

exojax.spec.modit.xsmatrix_open_zeroscan(cnu, indexnu, R, nsigmaDl, ngammaLM, SijM, nu_grid, dgm_ngammaL, nu_grid_extended, filter_length_oneside)

Cross section matrix for xsvector (MODIT/open/zeroscan)

Notes

The aliasing part is closed and thereby can’t be used in OLA. #277

Parameters:

  • cnu – contribution by npgetix for wavenumber

  • indexnu – index by npgetix for wavenumber

  • R – spectral resolution

  • nu_lines – line center (Nlines)

  • nsigmaDl – normalized doppler sigma in layers in R^(Nlayer x 1)

  • ngammaLM – gamma factor matrix in R^(Nlayer x Nline)

  • SijM – line strength matrix in R^(Nlayer x Nline)

  • nu_grid – wavenumber grid (ESLOG)

  • dgm_ngammaL – DIT Grid Matrix for normalized gammaL R^(Nlayer, NDITgrid)

  • nu_grid_extended – extended wavenumber grid (ESLOG)

  • filter_length_oneside – filter length for the convolution

Returns:

cross section matrix in R^(Nlayer x Nwav)

exojax.spec.modit.xsmatrix_scanfft(cnu, indexnu, R, pmarray, nsigmaDl, ngammaLM, SijM, nu_grid, dgm_ngammaL)

Cross section matrix for xsvector (MODIT), scan+fft

Notes

This function is deprecated. Use xsmatrix_zeroscan instead. The aliasing part is closed and thereby can’t be used in OLA.

Parameters:

  • cnu – contribution by npgetix for wavenumber

  • indexnu – index by npgetix for wavenumber

  • R – spectral resolution

  • pmarray – (+1,-1) array whose length of len(nu_grid)+1

  • nu_lines – line center (Nlines)

  • nsigmaDl – normalized doppler sigma in layers in R^(Nlayer x 1)

  • ngammaLM – gamma factor matrix in R^(Nlayer x Nline)

  • SijM – line strength matrix in R^(Nlayer x Nline)

  • nu_grid – linear wavenumber grid

  • dgm_ngammaL – DIT Grid Matrix for normalized gammaL R^(Nlayer, NDITgrid)

Returns:

cross section matrix in R^(Nlayer x Nwav)

exojax.spec.modit.xsmatrix_vald(cnuS, indexnuS, R, pmarray, nsigmaDlS, ngammaLMS, SijMS, nu_grid, dgm_ngammaLS)

Cross section matrix for xsvector (MODIT) for VALD lines (asdb)

Parameters:

  • cnuS – contribution by npgetix for wavenumber [N_species x N_line]

  • indexnuS – index by npgetix for wavenumber [N_species x N_line]

  • R – spectral resolution

  • pmarray – (+1,-1) array whose length of len(nu_grid)+1

  • nsigmaDlS – normalized sigmaD matrix [N_species x N_layer x 1]

  • ngammaLMS – normalized gammaL matrix [N_species x N_layer x N_line]

  • SijMS – line intensity matrix [N_species x N_layer x N_line]

  • nu_grid – linear wavenumber grid

  • dgm_ngammaLS – DIT Grid Matrix (dgm) of normalized gammaL [N_species x N_layer x N_DITgrid]

Returns:

cross section matrix [N_species x N_layer x N_wav]

Return type:

xsmS

exojax.spec.modit.xsmatrix_vald_scanfft(cnuS, indexnuS, R, pmarray, nsigmaDlS, ngammaLMS, SijMS, nu_grid, dgm_ngammaLS)

Cross section matrix for xsvector (MODIT) with scan+fft, for VALD lines (asdb)

Parameters:

  • cnuS – contribution by npgetix for wavenumber [N_species x N_line]

  • indexnuS – index by npgetix for wavenumber [N_species x N_line]

  • R – spectral resolution

  • pmarray – (+1,-1) array whose length of len(nu_grid)+1

  • nsigmaDlS – normalized sigmaD matrix [N_species x N_layer x 1]

  • ngammaLMS – normalized gammaL matrix [N_species x N_layer x N_line]

  • SijMS – line intensity matrix [N_species x N_layer x N_line]

  • nu_grid – linear wavenumber grid

  • dgm_ngammaLS – DIT Grid Matrix (dgm) of normalized gammaL [N_species x N_layer x N_DITgrid]

Returns:

cross section matrix [N_species x N_layer x N_wav]

Return type:

xsmS

exojax.spec.modit.xsmatrix_zeroscan(cnu, indexnu, R, pmarray, nsigmaDl, ngammaLM, SijM, nu_grid, dgm_ngammaL)

Cross section matrix for xsvector (MODIT), zeroscan

Notes

The aliasing part is closed and thereby can’t be used in OLA. #277

Parameters:

  • cnu – contribution by npgetix for wavenumber

  • indexnu – index by npgetix for wavenumber

  • R – spectral resolution

  • pmarray – (+1,-1) array whose length of len(nu_grid)+1

  • nu_lines – line center (Nlines)

  • nsigmaDl – normalized doppler sigma in layers in R^(Nlayer x 1)

  • ngammaLM – gamma factor matrix in R^(Nlayer x Nline)

  • SijM – line strength matrix in R^(Nlayer x Nline)

  • nu_grid – wavenumber grid (ESLOG)

  • dgm_ngammaL – DIT Grid Matrix for normalized gammaL R^(Nlayer, NDITgrid)

Returns:

cross section matrix in R^(Nlayer x Nwav)

exojax.spec.modit.xsvector_open_zeroscan(cnu, indexnu, R, nsigmaD, ngammaL, S, nu_grid, ngammaL_grid, nu_grid_extended, filter_length_oneside)

Cross section vector (MODIT/open/zeroscan)

Notes

The aliasing part is closed and thereby can’t be used in OLA. #277

Parameters:

  • cnu – contribution by npgetix for wavenumber

  • indexnu – index by npgetix for wavenumber

  • R – spectral resolution

  • nsigmaD – normaized Gaussian STD

  • gammaL – Lorentzian half width (Nlines)

  • S – line strength (Nlines)

  • nu_grid – wavenumber grid (ESLOG)

  • ngammaL_grid – normalized gammaL grid

  • nu_grid_extended – extended wavenumber grid (ESLOG)

  • filter_length_oneside – filter length for the convolution

Returns:

Cross section in the log nu grid

exojax.spec.modit.xsvector_scanfft(cnu, indexnu, R, pmarray, nsigmaD, ngammaL, S, nu_grid, ngammaL_grid)

Cross section vector (MODIT scanfft), deprecated

Notes

This function is deprecated. Use xsvector_zeroscan instead. The aliasing part is closed and thereby can’t be used in OLA.

Parameters:

  • cnu – contribution by npgetix for wavenumber

  • indexnu – index by npgetix for wavenumber

  • R – spectral resolution

  • pmarray – (+1,-1) array whose length of len(nu_grid)+1

  • nsigmaD – normaized Gaussian STD

  • gammaL – Lorentzian half width (Nlines)

  • S – line strength (Nlines)

  • nu_grid – linear wavenumber grid

  • gammaL_grid – gammaL grid

Returns:

Cross section in the log nu grid

exojax.spec.modit.xsvector_zeroscan(cnu, indexnu, R, pmarray, nsigmaD, ngammaL, S, nu_grid, ngammaL_grid)

Cross section vector (MODIT/close/zeroscan)

Notes

The aliasing part is closed and thereby can’t be used in OLA. #277

Parameters:

  • cnu – contribution by npgetix for wavenumber

  • indexnu – index by npgetix for wavenumber

  • R – spectral resolution

  • pmarray – (+1,-1) array whose length of len(nu_grid)+1

  • nsigmaD – normaized Gaussian STD

  • gammaL – Lorentzian half width (Nlines)

  • S – line strength (Nlines)

  • nu_grid – wavenumber grid (ESLOG)

  • gammaL_grid – gammaL grid

Returns:

Cross section in the log nu grid

exojax.spec.moldb module

Atomic database (MDB) class.

class exojax.spec.moldb.AdbKurucz(path, nurange=[- inf, inf], margin=0.0, crit=0.0, Irwin=False, gpu_transfer=True, vmr_fraction=None)

Bases: object

atomic database from Kurucz (http://kurucz.harvard.edu/linelists/)

AdbKurucz is a class for Kurucz line list.

nurange

nu range [min,max] (cm-1)

nu_lines

line center (cm-1) (#NOT frequency in (s-1))

Type:

nd array

dev_nu_lines

line center (cm-1) in device

Type:

jnp array

Sij0

line strength at T=Tref (cm)

Type:

nd array

logsij0

log line strength at T=Tref

Type:

jnp array

A

Einstein A coeeficient in (s-1)

Type:

jnp array

elower

the lower state energy (cm-1)

Type:

jnp array

eupper

the upper state energy (cm-1)

Type:

jnp array

gupper

(jnp array): upper statistical weight

jlower

lower J (rotational quantum number, total angular momentum)

Type:

jnp array

jupper

upper J

Type:

jnp array

QTmask

identifier of species for Q(T)

Type:

jnp array

ielem

atomic number (e.g., Fe=26)

Type:

jnp array

iion

ionized level (e.g., neutral=1, singly ionized=2, etc.)

Type:

jnp array

gamRad

log of gamma of radiation damping (s-1) #(https://www.astro.uu.se/valdwiki/Vald3Format)

Type:

jnp array

gamSta

log of gamma of Stark damping (s-1)

Type:

jnp array

vdWdamp

log of (van der Waals damping constant / neutral hydrogen number) (s-1)

Type:

jnp array

Atomic_gQT(atomspecies)

Select grid of partition function especially for the species of interest.

Parameters:

atomspecies – species e.g., β€œFe 1”, β€œSr 2”, etc.

Returns:

grid Q(T) for the species

Return type:

gQT

QT_interp(atomspecies, T)

interpolated partition function The partition functions of Barklem & Collet (2016) are adopted.

Parameters:

  • atomspecies – species e.g., β€œFe 1”

  • T – temperature

Returns:

interpolated in jnp.array for the Atomic Species

Return type:

Q(T)

QT_interp_284(T)

(DEPRECATED) interpolated partition function of all 284 species.

Parameters:

T – temperature

Returns:

interpolated in jnp.array for all 284 Atomic Species

Return type:

Q(T)*284

QT_interp_Irwin_Fe(T, atomspecies='Fe 1')

interpolated partition function This function is for the exceptional case where you want to adopt partition functions of Irwin (1981) for Fe I (Other species are not yet implemented).

Parameters:

  • atomspecies – species e.g., β€œFe 1”

  • T – temperature

Returns:

interpolated in jnp.array for the Atomic Species

Return type:

Q(T)

generate_jnp_arrays()

(re)generate jnp.arrays.

Note

We have nd arrays and jnp arrays. We usually apply the mask to nd arrays and then generate jnp array from the corresponding nd array. For instance, self._A is nd array and self.A is jnp array.

make_QTmask(ielem, iion)

Convert the species identifier to the index for Q(Tref) grid (gQT) for each line.

Parameters:

  • ielem – atomic number (e.g., Fe=26)

  • iion – ionized level (e.g., neutral=1, singly)

Returns:

array of index of Q(Tref) grid (gQT) for each line

Return type:

QTmask_sp

masking(mask)

applying mask

Parameters:

mask – mask to be applied. self.mask is updated.

qr_interp(atomspecies, T)

interpolated partition function ratio The partition functions of Barklem & Collet (2016) are adopted.

Parameters:

  • T – temperature

  • atomspecies – species e.g., β€œFe 1”

Returns:

interpolated in jnp.array

Return type:

qr(T)=Q(T)/Q(Tref)

qr_interp_Irwin_Fe(T, atomspecies='Fe 1')

interpolated partition function ratio This function is for the exceptional case where you want to adopt partition functions of Irwin (1981) for Fe I (Other species are not yet implemented).

Parameters:

  • T – temperature

  • atomspecies – species e.g., β€œFe 1”

Returns:

interpolated in jnp.array

Return type:

qr(T)=Q(T)/Q(Tref)

class exojax.spec.moldb.AdbSepVald(adb)

Bases: object

atomic database from VALD3 with an additional axis for separating each species (atom or ion)

AdbSepVald is a class for VALD3.

nu_lines

line center (cm-1) (#NOT frequency in (s-1))

Type:

nd array

dev_nu_lines

line center (cm-1) in device

Type:

jnp array

logsij0

log line strength at T=Tref

Type:

jnp array

elower

the lower state energy (cm-1)

Type:

jnp array

eupper

the upper state energy (cm-1)

Type:

jnp array

QTmask

identifier of species for Q(T)

Type:

jnp array

ielem

atomic number (e.g., Fe=26)

Type:

jnp array

iion

ionized level (e.g., neutral=1, singly ionized=2, etc.)

Type:

jnp array

atomicmass

atomic mass (amu)

Type:

jnp array

ionE

ionization potential (eV)

Type:

jnp array

gamRad

log of gamma of radiation damping (s-1) #(https://www.astro.uu.se/valdwiki/Vald3Format)

Type:

jnp array

gamSta

log of gamma of Stark damping (s-1)

Type:

jnp array

vdWdamp

log of (van der Waals damping constant / neutral hydrogen number) (s-1)

Type:

jnp array

uspecies

unique combinations of ielem and iion [N_species x 2(ielem and iion)]

Type:

jnp array

N_usp

number of species (atoms and ions)

Type:

int

L_max

maximum number of spectral lines for a single species

Type:

int

gQT_284species

partition function grid of 284 species

Type:

jnp array

T_gQT

temperatures in the partition function grid

Type:

jnp array

QTref_284

partition function at the reference temperature Q(Tref), for 284 species

Type:

jnp array

class exojax.spec.moldb.AdbVald(path, nurange=[- inf, inf], margin=0.0, crit=0.0, Irwin=False, gpu_transfer=True, vmr_fraction=None, engine='vaex')

Bases: object

atomic database from VALD3 (http://vald.astro.uu.se/)

AdbVald is a class for VALD3.

nurange

nu range [min,max] (cm-1)

nu_lines

line center (cm-1) (#NOT frequency in (s-1))

Type:

nd array

dev_nu_lines

line center (cm-1) in device

Type:

jnp array

Sij0

line strength at T=Tref (cm)

Type:

nd array

logsij0

log line strength at T=Tref

Type:

jnp array

A

Einstein A coeeficient in (s-1)

Type:

jnp array

elower

the lower state energy (cm-1)

Type:

jnp array

eupper

the upper state energy (cm-1)

Type:

jnp array

gupper

(jnp array): upper statistical weight

jlower

lower J (rotational quantum number, total angular momentum)

Type:

jnp array

jupper

upper J

Type:

jnp array

QTmask

identifier of species for Q(T)

Type:

jnp array

ielem

atomic number (e.g., Fe=26)

Type:

jnp array

iion

ionized level (e.g., neutral=1, singly ionized=2, etc.)

Type:

jnp array

solarA

solar abundance (log10 of number density in the Sun)

Type:

jnp array

atomicmass

atomic mass (amu)

Type:

jnp array

ionE

ionization potential (eV)

Type:

jnp array

gamRad

log of gamma of radiation damping (s-1) #(https://www.astro.uu.se/valdwiki/Vald3Format)

Type:

jnp array

gamSta

log of gamma of Stark damping (s-1)

Type:

jnp array

vdWdamp

log of (van der Waals damping constant / neutral hydrogen number) (s-1)

Type:

jnp array

gQT_284species

partition function grid of 284 species

Type:

jnp array

T_gQT

temperatures in the partition function grid

Type:

jnp array

QTref_284

partition function at the reference temperature Q(Tref), for 284 species

Type:

jnp array

Note

For the first time to read the VALD line list, it is converted to HDF/vaex. After the second-time, we use the HDF5 format with vaex instead.

Atomic_gQT(atomspecies)

Select grid of partition function especially for the species of interest.

Parameters:

atomspecies – species e.g., β€œFe 1”, β€œSr 2”, etc.

Returns:

grid Q(T) for the species

Return type:

gQT

QT_interp(atomspecies, T)

interpolated partition function The partition functions of Barklem & Collet (2016) are adopted.

Parameters:

  • atomspecies – species e.g., β€œFe 1”

  • T – temperature

Returns:

interpolated in jnp.array for the Atomic Species

Return type:

Q(T)

QT_interp_284(T)

(DEPRECATED) interpolated partition function of all 284 species.

Parameters:

T – temperature

Returns:

interpolated in jnp.array for all 284 Atomic Species

Return type:

Q(T)*284

QT_interp_Irwin_Fe(T, atomspecies='Fe 1')

interpolated partition function This function is for the exceptional case where you want to adopt partition functions of Irwin (1981) for Fe I (Other species are not yet implemented).

Parameters:

  • atomspecies – species e.g., β€œFe 1”

  • T – temperature

Returns:

interpolated in jnp.array for the Atomic Species

Return type:

Q(T)

generate_jnp_arrays()

(re)generate jnp.arrays.

Note

We have nd arrays and jnp arrays. We usually apply the mask to nd arrays and then generate jnp array from the corresponding nd array. For instance, self._A is nd array and self.A is jnp array.

make_QTmask(ielem, iion)

Convert the species identifier to the index for Q(Tref) grid (gQT) for each line.

Parameters:

  • ielem – atomic number (e.g., Fe=26)

  • iion – ionized level (e.g., neutral=1, singly ionized=2, etc.)

Returns:

array of index of Q(Tref) grid (gQT) for each line

Return type:

QTmask_sp

masking(mask)

applying mask.

Parameters:

mask – mask to be applied. self.mask is updated.

qr_interp(atomspecies, T)

interpolated partition function ratio The partition functions of Barklem & Collet (2016) are adopted.

Parameters:

  • T – temperature

  • atomspecies – species e.g., β€œFe 1”

Returns:

interpolated in jnp.array

Return type:

qr(T)=Q(T)/Q(Tref)

qr_interp_Irwin_Fe(T, atomspecies='Fe 1')

interpolated partition function ratio This function is for the exceptional case where you want to adopt partition functions of Irwin (1981) for Fe I (Other species are not yet implemented).

Parameters:

  • T – temperature

  • atomspecies – species e.g., β€œFe 1”

Returns:

interpolated in jnp.array

Return type:

qr(T)=Q(T)/Q(Tref)

exojax.spec.molinfo module

exojax.spec.molinfo.isotope_molmass(exact_molecule_name)

isotope molecular mass

Parameters:

exact_molecule_name (str) – exact exomol, hitran, molecule name such as 12C-16O, (12C)(16O)

Returns:

molecular mass g/mol

Return type:

float or None

exojax.spec.molinfo.mean_molmass_manual(simple_molecule_name)

molecular mass for major isotope given manually

Parameters:

simple_molecule_name (_type_) – _description_

Returns:

_description_

Return type:

_type_

exojax.spec.molinfo.molmass(simple_molecule_name, db_HIT=True)

provide molecular mass for the major isotope from the simple molecular name.

Parameters:

  • molecule – molecular name e.g. CO2, He

  • db_HIT – if True, use the molecular mass considering the natural terrestrial abundance and mass of each isotopologue provided by HITRAN (https://hitran.org/docs/iso-meta/)

Returns:

molecular mass

Example

>>> from exojax.spec.molinfo import molmass
>>> print(molmass("H2"))
>>> 2.01588
>>> print(molmass("CO2"))
>>> 44.0095
>>> print(molmass("He"))
>>> 4.002602
>>> print(molmass("air"))
>>> 28.97
exojax.spec.molinfo.molmass_isotope(simple_molecule_name, db_HIT=True)

provide molecular mass for the major isotope from the simple molecular name.

Parameters:

  • molecule – molecular name e.g. CO2, He

  • db_HIT – if True, use the molecular mass considering the natural terrestrial abundance and mass of each isotopologue provided by HITRAN (https://hitran.org/docs/iso-meta/)

Returns:

molecular mass

Example

>>> from exojax.spec.molinfo import molmass
>>> print(molmass("H2"))
>>> 2.01588
>>> print(molmass("CO2"))
>>> 44.0095
>>> print(molmass("He"))
>>> 4.002602
>>> print(molmass("air"))
>>> 28.97

exojax.spec.multimol module

class exojax.spec.multimol.MultiMol(molmulti, dbmulti, database_root_path='.database')

Bases: object

multiple molecular database and opacity calculator handler (multi Mdb/Opa Listing)

Notes

MultiMol provides an easy way to generate multiple mdb (multimdb) and multiple opa (multiopa) for multiple molecules/wavenumber segments/stitching.

molmulti

multiple simple molecule names [n_wavenumber_segments, n_molecules], such as [[β€œH2O”,”CO”],[β€œH2O”],[β€œCO”]]

dbmulti

multiple database names, such as [[β€œHITEMP”,”EXOMOL”],[β€œHITEMP”,”HITRAN12”]]]

masked_molmulti

masked multiple simple molecule names [n_wavenumber_segments, n_molecules], such as [[β€œH2O”,”CO”],[β€œH2O”],[False]] Note that β€œFalse” is assigned when the code fails to get mdb because, for example, there are no transition lines for the specified condition.

database_root_path

database root path

db_dirs

database directories

mols_unique

the list of the unique molecules,

mols_num

the same shape as self.masked_molmulti but gives indices of mols_unique

multimdb()

return multiple mdb

multiopa_premodit()

return multiple opa for premodit

molmass()

return molecular mass list

derive_unique_molecules()

derive unique molecules in masked_molmulti and set self.mols_unique and self.mols_num

Notes

self.mols_unique is the list of the unique molecules, and self.mols_num has the same shape as self.masked_molmulti but gives indices of self.mols_unique

generate_database_directories()

generate database directory array

molmass()

return molecular mass list and H and He

Returns:

molecular mass list for self.mols_unique molmassH2: molecular mass for hydorogen molmassHe: molecular mass for helium

Return type:

molmass_list

multimdb(nu_grid_list, crit=0.0, Ttyp=1000.0)

select current multimols from wavenumber grid

Notes

multimdb() also generates self.masked_molmulti (masked molmulti), self.mols_unique (unique molecules), and self.mols_num (same shape as self.masked_molmulti but gives indices of self.mols_unique)

Parameters:

  • nu_grid_list (list) – list of wavelength grids

  • crit (float, optional) – line strength criterion. Defaults to 0..

  • Ttyp (float, optional) – Typical temperature. Defaults to 1000..

Returns:

multi mdb

Return type:

lists of mdb

multiopa_premodit(multimdb, nu_grid_list, auto_trange, nstitch_list=None, diffmode=0, dit_grid_resolution=0.2, allow_32bit=False)

multiple opa for PreMODIT

Parameters:

  • () (nu_grid_list) – multimdb

  • () – wavenumber grid list

  • auto_trange (list) – temperature range [Tl, Tu], in which line strength is within 1 % prescision. Defaults to None.

  • nstitch_list (list) – The list of the number of nu-stitching segments for nu_grid_list (same structure). If None, no nu-stitching.

  • diffmode (int, optional) – _description_. Defaults to 0.

  • dit_grid_resolution (float, optional) – force to set broadening_parameter_resolution={mode:manual, value: dit_grid_resolution}), ignores broadening_parameter_resolution.

Returns:

_description_

Return type:

_type_

store_single_opa(multimdb_each, nu_grid_list_seg, auto_trange, diffmode, dit_grid_resolution, allow_32bit, nstitch)
exojax.spec.multimol.database_path_exomol(simple_molecule_name)

default ExoMol path

Parameters:

simple_molecule_name (str) – simple molecule name β€œH2O”

Returns:

Exomol default data path

Return type:

str

exojax.spec.multimol.database_path_hitemp(simple_molname)

default HITEMP path based on https://hitran.org/hitemp/

Parameters:

simple_molecule_name (str) – simple molecule name β€œH2O”

Returns:

HITEMP default data path, such as β€œH2O/01_HITEMP2010” for β€œH2O”

Return type:

str

exojax.spec.multimol.database_path_hitran12(simple_molecule_name)

HITRAN12 default data path

Parameters:

simple_molecule_name (str) – simple molecule name β€œH2O”

Returns:

HITRAN12 default data path, such as β€œH2O/01_hit12.par” for β€œH2O”

Return type:

str

exojax.spec.multimol.database_path_sample(simple_molname)

default SAMPLE (emulated mdb)

Parameters:

simple_molecule_name (str) – simple molecule name β€œCO” or β€œH2O”

Returns:

HITEMP default data path, such as β€œH2O/01_HITEMP2010” for β€œH2O”

Return type:

str

exojax.spec.nonair module

exojax.spec.nonair.gamma_nonair(m, coeff)

non air gamma (Lorentian width at reference)

Parameters:

  • m (int array) – m transition state

  • coeff (array) – nonair coefficient (a,b,a’,b’)

Returns:

nonair Lorentian width at reference (cm-1)

Return type:

float array

exojax.spec.nonair.nonair_polynomial(m, a_coeff, b_coeff)

nonair polynomial

Notes

value = ((a0 + a1 * x + a2 * x**2 + a3 * x**3) / (1 + b1 * x + b2 * x**2 + b3 * x**3 + b4 * x**4)) where x = m

Parameters:

  • m (int array) – m transition state

  • a_coeff (array) – nonair coefficient a

  • b_coeff (array) – nonair coefficient b

Returns:

nonair value

Return type:

float array

exojax.spec.nonair.temperature_exponent_nonair(m, coeff)

non air temperature exponent

Parameters:

  • m (int array) – m transition state

  • coeff (array) – nonair coefficient (a,b,a’,b’)

Returns:

nonair tempearure exponent

Return type:

float array

exojax.spec.opacalc module

opacity calculator class

Notes

Opa does not assume any T-P structure, no fixed T, P, mmr grids.

class exojax.spec.opacalc.OpaDirect(mdb, nu_grid, wavelength_order='descending')

Bases: OpaCalc

apply_params()
xsmatrix(Tarr, Parr)

cross section matrix

Notes

Currently Pself is regarded to be zero for HITEMP/HITRAN

Parameters:

  • () (Parr) – tempearture array in K

  • () – pressure array in bar

Raises:

ValueError – _description_

Returns:

cross section matrix (Nlayer, N_wavenumber)

Return type:

jnp.array

xsvector(T, P, Pself=0.0)

cross section vector

Parameters:

  • T (float) – temperature

  • P (float) – pressure in bar

  • Pself (float, optional) – self pressure for HITEMP/HITRAN. Defaults to 0.0.

Returns:

cross section in cm2

Return type:

1D array

class exojax.spec.opacalc.OpaModit(mdb, nu_grid, Tarr_list=None, Parr=None, Pself_ref=None, dit_grid_resolution=0.2, allow_32bit=False, alias='close', cutwing=1.0, wavelength_order='descending')

Bases: OpaCalc

Opacity Calculator Class for MODIT

opainfo

information set used in MODIT: cont_nu, index_nu, R, pmarray

apply_params()
setdgm(Tarr_list, Parr, Pself_ref=None)

_summary_

Parameters:

  • Tarr_list (1d or 2d array) – tempearture array to be tested such as [Tarr_1, Tarr_2, …, Tarr_n]

  • Parr (1d array) – pressure array in bar

  • Pself_ref (1d array, optional) – self pressure array in bar. Defaults to None. If None Pself = 0.0.

Returns:

dgm (DIT grid matrix) for gammaL

Return type:

_type_

xsmatrix(Tarr, Parr)

cross section matrix

Notes

Currently Pself is regarded to be zero for HITEMP/HITRAN

Parameters:

  • () (Parr) – tempearture array in K

  • () – pressure array in bar

Raises:

ValueError – _description_

Returns:

cross section matrix (Nlayer, N_wavenumber)

Return type:

jnp.array

xsvector(T, P, Pself=0.0)

cross section vector

Parameters:

  • T (float) – temperature

  • P (float) – pressure in bar

  • Pself (float, optional) – self pressure for HITEMP/HITRAN. Defaults to 0.0.

Returns:

cross section in cm2

Return type:

1D array

class exojax.spec.opacalc.OpaPremodit(mdb, nu_grid, diffmode=0, broadening_resolution={'mode': 'manual', 'value': 0.2}, auto_trange=None, manual_params=None, dit_grid_resolution=None, allow_32bit=False, nstitch=1, cutwing=1.0, wavelength_order='descending', version_auto_trange=2)

Bases: OpaCalc

Opacity Calculator Class for PreMODIT

opainfo

information set used in PreMODIT

apply_params()

apply the parameters to the class define self.lbd_coeff and self.opainfo

auto_setting(Tl, Tu)
broadening_parameters_setting()
compute_gamma_ref_and_n_Texp()

convert gamma_ref to the regular formalization and noramlize it for Tref_braodening

Notes

gamma (T) = (gamma at Tref_original) * (Tref_original/Tref_broadening)**n * (T/Tref_broadening)**-n * (P/1bar)

Parameters:

mdb (_type_) – mdb instance

determine_broadening_parameter_resolution(broadening_parameter_resolution, dit_grid_resolution)
manual_setting(dE, Tref, Twt, Tmax=None, Tmin=None)

setting PreMODIT parameters by manual

Parameters:

  • dE (float) – E lower grid interval (cm-1)

  • Tref (float) – reference temperature (K)

  • Twt (float) – Temperature for weight (K)

  • Tmax (float/None) – max temperature (K) for braodening grid

  • Tmin (float/None) – min temperature (K) for braodening grid

plot_broadening_parameters(figname='broadpar_grid.png', crit=300000)

plot broadening parameters and grids

Parameters:

  • figname (str, optional) – output image file. Defaults to β€œbroadpar_grid.png”.

  • crit (int, optional) – sampling criterion. Defaults to 300000. when the number of lines is huge and if it exceeded ~ crit, we sample the lines to reduce the computation.

reshape_lbd_coeff()

reshape lbd_coeff for stitching mode this method deletes self.lbd_coeff and creates self.lbd_coeff_reshaped self.lbd_coeff_reshaped has a dimension of (self.nstitch, diffmode+1, self.div_length, N_broadening, len(elower_grid))

set_Tref_broadening_to_midpoint()

Set self.Tref_broadening using log midpoint of Tmax and Tmin

set_nu_grid(x0, x1, unit, resolution=700000, Nx=None)
xsmatrix(Tarr, Parr)

cross section matrix

Parameters:

  • () (Parr) – tempearture array in K

  • () – pressure array in bar

Raises:

ValueError – _description_

Returns:

cross section matrix (Nlayer, N_wavenumber)

Return type:

jnp.array

xsvector(T, P)

exojax.spec.opachord module

exojax.spec.opachord.chord_geometric_matrix(height, radius_lower)

compute chord geometric matrix

Parameters:

  • height (1D array) – (normalized) height of the layers from top atmosphere, Nlayer

  • radius_lower (1D array) – (normalized) radius at the lower boundary from top to bottom (R0), (Nlayer)

Returns:

chord geometric matrix (Nlayer, Nlayer), lower triangle matrix

Return type:

2D array

Notes

Our definitions of the radius_lower and height (and radius_top, internally defined) are as follows: n=0,1,…,N-1 radius_lower[N-1] = radius_btm (i.e. R0) radius_lower[n-1] = radius_lower[n] + height[n] radius_top = radius_lower[0] + height[0]

exojax.spec.opachord.chord_geometric_matrix_lower(height, radius_lower)

compute chord geometric matrix

Parameters:

  • height (1D array) – (normalized) height of the layers from top atmosphere, Nlayer

  • radius_lower (1D array) – (normalized) radius at the lower boundary from top to bottom (R0), (Nlayer)

Returns:

chord geometric matrix (Nlayer, Nlayer), lower triangle matrix

Return type:

2D array

Notes

Our definitions of the radius_lower and height (and radius_top, internally defined) are as follows: n=0,1,…,N-1 radius_lower[N-1] = radius_btm (i.e. R0) radius_lower[n-1] = radius_lower[n] + height[n]

exojax.spec.opachord.chord_optical_depth(chord_geometric_matrix, dtau)

chord optical depth vector from a chord geometric matrix and dtau

Parameters:

  • chord_geometric_matrix (jnp array) – chord geometric matrix (Nlayer, Nlayer), lower triangle matrix

  • dtau (jnp array) – layer optical depth matrix, dtau (Nlayer, N_wavenumber)

Returns: chord optical depth (tauchord) matrix (Nlayer, N_wavenumber)

exojax.spec.opacitytools module

Extract tau=1 height pressure at different wavelengths

exojax.spec.opacitytools.pressure_at_given_opacity(dtau, Parr, tauextracted=1.0)

Extract pressure of tau=1(or a given value) at different wavelengths

Parameters:

  • dtau – delta tau for each layer [N_layer x N_nu]

  • Parr – pressure at each layer [N_layer]

  • tauextracted – the tau value at which pressure is extracted

Returns:

[N_nu]

Return type:

P_tauone

Note

Return 0 if tau is too optically thin and does not reach tauextracted.

exojax.spec.opacont module

opacity continuum calculator class

Notes

Opa does not assume any T-P structure, no fixed T, P, mmr grids.

class exojax.spec.opacont.OpaCIA(cdb, nu_grid)

Bases: OpaCont

Opacity Continuum Calculator Class for CIA

logacia_matrix(temperatures)

computes absorption coefficient matrix of CIA

Parameters:

temperatures (array) – temperature array (K) [Nlayer]

Returns:

logarithm of absorption coefficient [Nlayer, Nnus] in the unit of cm5

Return type:

2D array

logacia_vector(T)

computes absorption coefficient vector of CIA

Parameters:

T (float) – temperature (K)

Returns:

logarithm of absorption coefficient [Nnus] at T in the unit of cm5

Return type:

1D array

opainfo
class exojax.spec.opacont.OpaCont

Bases: object

Common Opacity Calculator Class

opainfo
class exojax.spec.opacont.OpaHminus(nu_grid)

Bases: OpaCont

Opacity Continuum Calculator Class for H-

logahminus_matrix(temperatures, number_density_e, number_density_h)

absorption coefficient (cm-1) matrix of H- continuum

Parameters:

  • temperatures (_type_) – temperature array

  • number_density_e (_type_) – number density of electron in cgs

  • number_density_h (_type_) – number density of H in cgs

Returns:

log10(absorption coefficient in cm-1 ) [Nlayer,Nnu]

opainfo
class exojax.spec.opacont.OpaMie(pdb, nu_grid)

Bases: OpaCont

mieparams_matrix(rg_layer, sigmag_layer)

interpolate the Mie parameters matrix (Nlayer x Nnu) from Miegrid :param rg_layer: layer rg parameters in the lognormal distribution of condensate size, defined by (9) in AM01 :type rg_layer: 1d array :param sigmag_layer: layer sigmag parameters in the lognormal distribution of condensate size, defined by (9) in AM01 :type sigmag_layer: 1d array

Notes

AM01 = Ackerman and Marley 2001 Volume extinction coefficient (1/cm) for the number density N can be computed by beta_extinction = N*beta0_extinction/N0

Returns:

sigma_extinction matrix, extinction cross section (cm2) = volume extinction coefficient (1/cm) normalized by the reference number density N0 omega0 matrix, single scattering albedo g matrix, asymmetric factor (mean g)

mieparams_matrix_direct_from_pymiescatt(rg_layer, sigmag_layer)

compute the Mie parameters matrix (Nlayer x Nnu) from pymiescatt direclty (slow), i.e. no need of Miegrid :param rg_layer: layer rg parameters in the lognormal distribution of condensate size, defined by (9) in AM01 :type rg_layer: 1d array :param sigmag_layer: layer sigmag parameters in the lognormal distribution of condensate size, defined by (9) in AM01 :type sigmag_layer: 1d array

Notes

AM01 = Ackerman and Marley 2001 Volume extinction coefficient (1/cm) for the number density N can be computed by beta_extinction = N*beta0_extinction/N0

Returns:

sigma_extinction matrix, extinction cross section (cm2) = volume extinction coefficient (1/cm) normalized by the reference number density N0 omega0 matrix, single scattering albedo g matrix, asymmetric factor (mean g)

mieparams_vector(rg, sigmag)

interpolate the Mie parameters vector (Nnu: wavenumber direction) from Miegrid

Parameters:

  • rg (float) – rg parameter in the lognormal distribution of condensate size, defined by (9) in AM01

  • sigmag (float) – sigmag parameter in the lognormal distribution of condensate size, defined by (9) in AM01

Notes

AM01 = Ackerman and Marley 2001 Volume extinction coefficient (1/cm) for the number density N can be computed by beta_extinction = N*beta0_extinction/N0

Returns:

sigma_extinction, extinction cross section (cm2) = volume extinction coefficient (1/cm) normalized by the reference numbver density N0. sigma_scattering, scattering cross section (cm2) = volume extinction coefficient (1/cm) normalized by the reference numbver density N0. asymmetric factor, (mean g)

mieparams_vector_direct_from_pymiescatt(rg, sigmag)

compute the Mie parameters vector (Nnu: wavenumber direction) from pymiescatt direclty (slow), i.e. no need of Miegrid, the unit is in cgs

Parameters:

  • rg (float) – rg parameter in the lognormal distribution of condensate size, defined by (9) in AM01

  • sigmag (float) – sigmag parameter in the lognormal distribution of condensate size, defined by (9) in AM01

Notes

AM01 = Ackerman and Marley 2001 Volume extinction coefficient (1/cm) for the number density N can be computed by beta_extinction = N*beta0_extinction/N0

Returns:

sigma_extinction, extinction cross section (cm2) = volume extinction coefficient (1/cm) normalized by the reference numbver density N0. sigma_scattering, scattering cross section (cm2) = volume extinction coefficient (1/cm) normalized by the reference numbver density N0. asymmetric factor, (mean g)

opainfo
class exojax.spec.opacont.OpaRayleigh(nu_grid, molname)

Bases: OpaCont

check_ready()
opainfo
set_auto_king_factor()
set_auto_polarizability()
xsvector()

computes cross section vector of the Rayleigh scattering

Returns:

Rayleigh scattring cross section vector [Nnus] in cm2

Return type:

float, array

exojax.spec.opart module

class exojax.spec.opart.OpartEmisPure(opalayer, pressure_top=1e-08, pressure_btm=100.0, nlayer=100, nstream=8)

Bases: ArtCommon

run(opalayer, layer_params, flbl)
update_layer(carry_tauflux, params)

updates the layer opacity and flux

Parameters:

  • carry_tauflux (list) – carry for the tau and flux

  • params (list) – layer parameters for this layer, params[0] should be temperature

Returns:

updated carry_tauflux

Return type:

list

update_layerflux(temperature, tauup, taulow, flux)

updates the flux of the layer

Parameters:

  • temperature (float) – temperature of the layer, usually params[0] is used

  • tauup (array) – optical depth at the upper layer [Nnus]

  • taulow (array) – optical depth at the lower layer [Nnus]

  • flux (array) – flux array to be updated

Returns:

updated flux [Nnus]

Return type:

array

update_layeropacity(tauup, params)

updates the optical depth of the layer

Notes

up = n, low = n+1 in (44) of Paper II

Parameters:

  • tauup (array) – optical depth at the upper layer [Nnus]

  • params – layer parameters for this layer, params[0] should be temperature

Returns:

taulow (optical depth at the lower layer, [Nnus])

Return type:

array

class exojax.spec.opart.OpartEmisScat(opalayer, pressure_top=1e-08, pressure_btm=100.0, nlayer=100)

Bases: ArtCommon

Opart verision of ArtEmisScat.

This class computes the outgoing emission flux of the atmosphere with scattering in the atmospheric layers. Radiative transfer scheme: flux-based two-stream method, using flux-adding treatment, Toon-type hemispheric mean approximation

run(opalayer, layer_params, flbl)
update_layer(carry_rs, params)

updates the layer opacity and effective reflectivity (Rphat) and source (Sphat)

Parameters:

  • carry_rs (list) – carry for the Rphat and Sphat

  • params (list) – layer parameters for this layer

Returns:

updated carry_rs

Return type:

list

class exojax.spec.opart.OpartReflectEmis(opalayer, pressure_top=1e-08, pressure_btm=100.0, nlayer=100)

Bases: ArtCommon

Opart verision of ArtReflectEmis.

This class computes the outgoing flux of the atmosphere with reflection, with emission from atmospheric layers. Radiative transfer scheme: flux-based two-stream method, using flux-adding treatment, Toon-type hemispheric mean approximation

run(opalayer, layer_params, flbl)
update_layer(carry_rs, params)

updates the layer opacity and effective reflectivity (Rphat) and source (Sphat)

Parameters:

  • carry_rs (list) – carry for the Rphat and Sphat

  • params (list) – layer parameters for this layer

Returns:

updated carry_rs

Return type:

list

class exojax.spec.opart.OpartReflectPure(opalayer, pressure_top=1e-08, pressure_btm=100.0, nlayer=100)

Bases: ArtCommon

Opart verision of ArtReflectPure.

This class computes the outgoing flux of the atmosphere with reflection, no emission from atmospheric layers nor surface. Radiative transfer scheme: flux-based two-stream method, using flux-adding treatment, Toon-type hemispheric mean approximation

run(opalayer, layer_params, flbl)
update_layer(carry_rs, params)

updates the layer opacity and effective reflectivity (Rphat) and source (Sphat)

Parameters:

  • carry_rs (list) – carry for the Rphat and Sphat

  • params (list) – layer parameters for this layer

Returns:

updated carry_rs

Return type:

list

exojax.spec.optgrid module

exojax.spec.optgrid.optelower(mdb, nu_grid, Tmax, Pmin, accuracy=0.01, dE=100.0, isotope=1, display=False)

look for the value of the optimal maximum Elower

Note

The memory use of PreModit depends on the maximum Elower of mdb. This function determine the optimal maximum Elower that does not change the cross section within the accuracy.

Parameters:

  • mdb (mdb) – molecular db

  • nu_grid (array) – wavenumber array cm-1

  • Tmax (float) – maximum temperature in your use (K)

  • Pmin (float) – minimum temperature in your use (bar)

  • accuracy (float, optional) – accuracy allowed. Defaults to 0.01.

  • dE (float, optional) – E grid to search for the optimal Elower. Defaults to 100.0.

  • isotope – isotope number for HITRAN/HITEMP default to 1

  • display (bool, optional) – if you want to compare the cross section using Eopt w/ ground truth, set True. Defaults to False.

Returns:

optimal maximum Elower (Eopt) in cm-1

Return type:

float

exojax.spec.pardb module

Particulates Database

  • Cloud

  • Haze (in future)

class exojax.spec.pardb.PdbCloud(condensate, nurange=None, margin=10.0, path='./.database/particulates/virga', download=True, refrind_path=None)

Bases: object

download_and_unzip()

Downloading virga refractive index data

Note

The download URL is written in exojax.utils.url.

generate_miegrid(sigmagmin=1.0001, sigmagmax=4.0, Nsigmag=10, log_rg_min=- 7.0, log_rg_max=- 3.0, Nrg=40)

generates miegrid assuming lognormal size distribution

Parameters:

  • sigmagmin (float, optional) – sigma_g minimum. Defaults to 1.0001.

  • sigmagmax (float, optional) – sigma_g maximum. Defaults to 4.0.

  • Nsigmag (int, optional) – the number of the sigmag grid. Defaults to 10.

  • log_rg_min (float, optional) – log r_g (cm) minimum . Defaults to -7.0.

  • log_rg_max (float, optional) – log r_g (cm) minimum. Defaults to -3.0.

  • Nrg (int, optional) – the number of the rg grid. Defaults to 40.

Note

it will take a bit long time. See src/exojax/tests/generate_pdb.py as a sample code.

load_miegrid()

loads Miegrid

Raises:

ValueError – _description_

load_virga()

loads VIRGA refraction index

Notes

self.refraction_index_wavenumber is in ascending and self.refraction_index_wavelength_nm is in descending. Each component of both corresponds to that of self.refraction_index. (no need to put [::-1])

miegrid_interpolated_values(rg, sigmag)

evaluates the value at rg and sigmag by interpolating miegrid

Parameters:

  • rg (float) – rg parameter in lognormal distribution

  • sigmag (float) – sigma_g parameter in lognormal distribution

Note

beta derived here is in the unit of 1/Mm (Mega meter) for diameter multiply 1.e-8 to convert to 1/cm for radius.

Returns:

evaluated values of miegrid, output of MieQ_lognormal Bext (1/Mm), Bsca, Babs, G, Bpr, Bback, Bratio (wavenumber, number of mieparams)

Return type:

_type_

mieparams_cgs_at_refraction_index_wavenumber_from_miegrid(rg, sigmag)

computes Mie parameters in the original refraction index wavenumber, i.e. extinction coeff, sinigle scattering albedo, asymmetric factor from miegrid

Parameters:

  • rg (float) – rg parameter in lognormal distribution

  • sigmag (float) – sigma_g parameter in lognormal distribution

Note

Volume extinction coefficient (1/cm) for the number density N can be computed by beta_extinction = N*beta0_extinction The output returns are computed at self.refraction_index_wavenumber

Returns:

sigma_extinction, extinction cross section (cm2) = volume extinction coefficient (1/cm) normalized by the reference numbver density N0. sigma_scattering, scattering cross section (cm2) = volume extinction coefficient (1/cm) normalized by the reference numbver density N0. g, asymmetric factor (mean g)

reset_miegrid_for_nurange()

Resets wavenumber indices of miegrid, refraction_index_wavenumber, refraction_index_wavelength_nm, refraction_index :raises ValueError: _description_

saturation_pressure(temperatures)
set_condensate_substance_density()

sets condensate density

Note

β€œcondensate substance density” means the mass substance density of the condensate matter itself. For instance, in the room temperature, for liquid water clouds, condensate_substance_density ~ 1 g/cm3 Notice that the mass density of the condensates in the atmosphere is the different quantity.

set_miegrid_filename(miegrid_filename=None)
set_miegrid_path(miegrid_path=None)
set_saturation_pressure_list()

exojax.spec.planck module

planck functions.

  • The units are nu [1/cm], f [1/s], wav [cm]. In this module, the input variable is always wavenumber [cm].

  • nu = f/c = 1/lambda.

  • Recall nu B_nu = lambda B_lambda = f B_f.

  • B_f (erg/s/cm2/Hz) = B_nu/c (erg/s/cm2/cm-1)

exojax.spec.planck.piB(T, nu_grid)

pi B_nu (Planck Function)

Parameters:

  • T (float) – temperature in the unit of K

  • nu_grid (array) – wavenumber grid in the unit of cm-1 [Nnu]

Returns:

pi B_nu (erg/s/cm2/cm-1) [Nnu]

Note

hcperk = hc/k in cgs, fac = 2*h*c*c*pi in cgs

exojax.spec.planck.piBarr(Tarr, nu_grid)

pi B_nu (Planck Function)

Parameters:

  • Tarr (array) – temperature in the unit of K [Nlayer]

  • nu_grid (array) – wavenumber grid in the unit of cm-1 [Nnu]

Returns:

pi B_nu (erg/s/cm2/cm-1) [Nlayer, Nnu]

Note

hcperk = hc/k in cgs, fac = 2*h*c*c*pi in cgs

exojax.spec.premodit module

Line profile computation using PremoDIT = Precomputation of LSD version of MODIT

Notes

calc_xsection_from_lsd_scanfft has been replace to calc_xsection_from_lsd_zeroscan since 2.0 #577

exojax.spec.premodit.broadpar_getix(ngamma_ref, ngamma_ref_grid, n_Texp, n_Texp_grid)

get indices and contribution of broadpar

Parameters:

  • ngamma_ref – normalized half-width at reference

  • ngamma_ref_grid – grid of normalized half-width at reference

  • n_Texp – temperature exponent (n_Texp, n_air, etc)

  • n_Texp_grid – grid of temperature exponent (n_Texp, n_air, etc)

Returns:

multi_index_lines multi_cont_lines uidx_lines neighbor_uidx multi_index_uniqgrid number of broadpar grid

Examples

>>> multi_index_lines, multi_cont_lines, uidx_lines, neighbor_uidx, multi_index_uniqgrid, Ng = broadpar_getix(
>>> ngamma_ref, ngamma_ref_grid, n_Texp, n_Texp_grid)
>>> iline_interest = 1 # we wanna investiget this line
>>> print(multi_index_lines[iline_interest]) # multi index from a line
>>> print(multi_cont_lines[iline_interest]) # multi contribution from a line
>>> print(uidx_lines[iline_interest]) # uniq index of a line
>>> print(multi_index_uniqgrid[uniq_index]) # multi index from uniq_index
>>> ui,uj,uk=neighbor_uidx[uniq_index, :] # neighbour uniq index
exojax.spec.premodit.check_multi_index_uniqgrid_shape(ngamma_ref_grid, n_Texp_grid, multi_index_uniqgrid)

checks the shape of multi_index_uniqgrid. See #586

Parameters:

  • ngamma_ref_grid (array) – normalized half-width at reference grid

  • n_Texp_grid (array) – temperature exponent grid

  • multi_index_uniqgrid (array) – multi index of unique broadening parameter grid [nbroad,2]

Returns:

0=pass, 1=ngamma_ref_grid error, 2=n_Texp_grid error

Return type:

status (int)

exojax.spec.premodit.compute_dElower(T, interval_contrast=0.1)

compute a grid interval of Elower given the grid interval of line strength

Parameters:

  • T – temperature in Kelvin

  • interval_contrast – putting c = grid_interval_line_strength, then, the contrast of line strength between the upper and lower of the grid becomes c-order of magnitude.

Returns:

Required dElower

exojax.spec.premodit.convert_to_jnplog(lbd_nth)

compute log and convert to jnp

Notes

This function is used to avoid an overflow when using FP32 in JAX

Parameters:

lbd_nth (ndarray) – n-th coefficient (non-log) LBD

Returns:

log form of n-th coefficient LBD

Return type:

jnp.array

exojax.spec.premodit.error_diagnositcs(status, multi_index_uniqgrid, val, val_grid)
exojax.spec.premodit.g_bias(nu_in, T, Tref)
Parameters:

  • nu_in – wavenumber in cm-1

  • T – temperature for unbiasing in Kelvin

  • Tref – reference temperature in Kelvin

Returns:

bias g function

exojax.spec.premodit.generate_lbd(line_strength_ref, nu_lines, nu_grid, ngamma_ref, ngamma_ref_grid, n_Texp, n_Texp_grid, elower, elower_grid, Twt, Tref=296.0, diffmode=0)

generate log-biased line shape density (LBD)

Parameters:

  • line_strength_ref – line strength at reference temperature 296K, Sij0

  • nu_lines (_type_) – _description_

  • nu_grid (_type_) – _description_

  • ngamma_ref (_type_) – _description_

  • ngamma_ref_grid (_type_) – normalized gamma at reference grid

  • n_Texp (_type_) –

  • n_Texp_grid (_type_) – normalized temperature exponent grid

  • elower (_type_) – _description_

  • elower_grid (_type_) – _description_

  • Twt – temperature used for the weight coefficient computation

  • Tref – reference temperature in Kelvin, default is 296.0 K

  • diffmode (int) – i-th Taylor expansion is used for the weight, default is 1.

Notes

When len(ngamma_ref_grid) = 1 and len(n_Texp_grid) = 1, the single broadening parameter mode is applied.

Returns:

the list of the n-th coeffs of line shape density (LBD) jnp.array: multi_index_uniqgrid (number of unique broadpar, 2)

Return type:

[jnp array]

Examples

>>> lbd_coeff, multi_index_uniqgrid = generate_lbd(mdb.Sij0, mdb.nu_lines, nu_grid, ngamma_ref,
>>>               ngamma_ref_grid, mdb.n_Texp, n_Texp_grid, mdb.elower,
>>>               elower_grid, Twp)
>>> ngamma_ref = ngamma_ref_grid[multi_index_uniqgrid[:,0]] # ngamma ref for the unique broad par
>>> n_Texp = n_Texp_grid[multi_index_uniqgrid[:,0]] # temperature exponent for the unique broad par
exojax.spec.premodit.logf_bias(elower_in, T, Tref)

logarithm f bias function

Parameters:

  • elower_in – Elower in cm-1

  • T – temperature for unbiasing in Kelvin

  • Tref – reference temperature in Kelvin

Returns:

logarithm of bias f function

exojax.spec.premodit.make_broadpar_grid(ngamma_ref, n_Texp, Tmax, Tmin, Tref_broadening, dit_grid_resolution=0.2, twod_factor=1.3333333333333333, adopt=True)

make grids of normalized half-width at reference and temperature exoponent

Parameters:

  • ngamma_ref (nd array) – n_Texp: temperature exponent (n_Texp, n_air, etc)

  • n_Texp (nd array) – temperature exponent (n_Texp, n_air, etc)

  • Tmax – maximum temperature in Kelvin (NOT weight temperature)

  • Tmin – minimum temperature in Kelvin (NOT weight temperature)

  • Tref_broadening – reference temperature for broadening in Kelvin

  • dit_grid_resolution (float, optional) – DIT grid resolution. Defaults to 0.2.

  • twod_factor – conversion factor of the grid resolution from 1D to 2D. default 3.0/4.0. See Issue #366.

  • adopt (bool, optional) – if True, min, max grid points are used at min and max values of x. In this case, the grid width does not need to be dit_grid_resolution exactly. Defaults to True.

Returns:

ngamma_ref_grid, grid of normalized half-width at reference nd array: n_Texp_grid, grid of temperature exponent (n_Texp, n_air, etc)

Return type:

nd array

exojax.spec.premodit.make_elower_grid(elower, dE)

compute E_lower grid given dE or interval_contrast of line strength

Parameters:

  • elower – E_lower

  • dE – elower interval in cm-1

Returns:

grid of E_lower given interval_contrast

exojax.spec.premodit.parallel_merge_grids(grid1, grid2)

Merge two different grids into one grid in parallel, in a C-contiguous RAM mapping.

Parameters:

  • grid1 – grid 1

  • grid2 – grid 2

Returns:

merged grid (len(grid1),2)

exojax.spec.premodit.reference_temperature_broadening_at_midpoint(Tmin, Tmax)

compute Tref_broadening at the logarithmic midpoint of Tmin and Tmax

Parameters:

  • Tmin (float) – minimum temperature

  • Tmax (float) – maximum temperature

Returns:

Tref_broadening at the logarithmic midpoint of Tmin and Tmax

Return type:

float

exojax.spec.premodit.unbiased_lsd_first(lbd_coeff, T, Tref, Twt, nu_grid, elower_grid, qt)

unbias the biased LSD, first order

Parameters:

  • lbd_coeff – the zeroth/first coeff of log-biased line shape density (LBD)

  • T – temperature for unbiasing in Kelvin

  • Tref – reference temperature in Kelvin

  • Twt – Temperature at the weight point

  • nu_grid – wavenumber grid in cm-1

  • elower_grid – Elower grid in cm-1

  • qt – partition function ratio Q(T)/Q(Tref)

Returns:

LSD, shape = (number_of_wavenumber_bin, number_of_broadening_parameters)

exojax.spec.premodit.unbiased_lsd_second(lbd_coeff, T, Tref, Twt, nu_grid, elower_grid, qt)

unbias the biased LSD, second order

Parameters:

  • lbd_coeff – the zeroth/first/second coeff of log-biased line shape density (LBD)

  • T – temperature for unbiasing in Kelvin

  • Tref – reference temperature in Kelvin

  • Twt – Temperature at the weight point

  • nu_grid – wavenumber grid in cm-1

  • elower_grid – Elower grid in cm-1

  • qt – partition function ratio Q(T)/Q(Tref)

Returns:

LSD, shape = (number_of_wavenumber_bin, number_of_broadening_parameters)

exojax.spec.premodit.unbiased_lsd_zeroth(lbd_zeroth, T, Tref, nu_grid, elower_grid, qt)

unbias the biased LSD

Parameters:

  • lbd_zeroth – the zeroth coeff of log-biased line shape density (LBD)

  • T – temperature for unbiasing in Kelvin

  • Tref – reference temperature in Kelvin

  • nu_grid – wavenumber grid in cm-1

  • elower_grid – Elower grid in cm-1

  • qt – partition function ratio Q(T)/Q(Tref)

Returns:

LSD (0th), shape = (number_of_wavenumber_bin, number_of_broadening_parameters)

exojax.spec.premodit.unbiased_ngamma_grid(T, P, ngamma_ref_grid, n_Texp_grid, multi_index_uniqgrid, Tref_broadening)

compute unbiased ngamma grid

Parameters:

  • T – temperature in Kelvin

  • P – pressure in bar

  • ngamma_ref_grid – pressure broadening half width at Tref_broadening

  • n_Texp_grid – temperature exponent at reference

  • multi_index_uniqgrid – multi index of unique broadening parameter

  • Tref_broadening – reference temperature in Kelvin for broadening

Returns:

pressure broadening half width at temperature T and pressure P

Notes

It should be noted that the gamma is not affected by changing Tref.

exojax.spec.premodit.xsmatrix_first(Tarr, Parr, Tref, R, pmarray, lbd_coeff, nu_grid, ngamma_ref_grid, n_Texp_grid, multi_index_uniqgrid, elower_grid, Mmol, qtarr, Tref_broadening, Twt)

compute cross section matrix given atmospheric layers, for diffmode=1, with scan+fft

Parameters:

  • Tarr (_type_) – temperature layers

  • Parr (_type_) – pressure layers

  • Tref – reference temperature in K

  • R (float) – spectral resolution

  • pmarray (_type_) – pmarray

  • lbd_coeff (_type_) – LBD coefficient

  • nu_grid (_type_) – wavenumber grid

  • ngamma_ref_grid (_type_) – normalized half-width grid

  • n_Texp_grid (_type_) – temperature exponent grid

  • multi_index_uniqgrid (_type_) – multi index for uniq broadpar grid

  • elower_grid (_type_) – Elower grid

  • Mmol (_type_) – molecular mass

  • qtarr (_type_) – partition function ratio layers

  • Tref_broadening – reference temperature for broadening in Kelvin

  • Twt – weight temperature in K

Returns:

cross section matrix (Nlayer, N_wavenumber)

Return type:

jnp.array

exojax.spec.premodit.xsmatrix_nu_open_first(Tarr, Parr, Tref, R, lbd_coeff, nu_grid, ngamma_ref_grid, n_Texp_grid, multi_index_uniqgrid, elower_grid, Mmol, qtarr, Tref_broadening, filter_length_oneside, Twt)

compute nu sigma (wavenumber x cross section) matrix, with scan+fft, using the first Taylor expansion

Parameters:

  • Tarr (array) – temperature layers

  • Parr (array) – pressure layers

  • Tref – reference temperature in K

  • R (float) – spectral resolution

  • lbd_coeff (arrau) –

  • nu_grid (array) – wavenumber grid

  • ngamma_ref_grid (array) – normalized half-width grid

  • n_Texp_grid (array) – temperature exponent grid

  • multi_index_uniqgrid (array) – multi index for uniq broadpar grid

  • elower_grid (array) – Elower grid

  • Mmol (float) – molecular mass

  • qtarr (array) – partition function ratio layers

  • Tref_broadening – reference temperature for broadening in Kelvin

  • nu_grid_extended – extended wavenumber grid to aliasing parts

  • filter_length_oneside – one side length of the wavenumber grid of lpffilter

  • Twt – temperature used in the weight point

Returns:

nu sigma (nu_grid_extended x cross section) in cgs matrix

Return type:

jnp.array

exojax.spec.premodit.xsmatrix_nu_open_second(Tarr, Parr, Tref, R, lbd_coeff, nu_grid, ngamma_ref_grid, n_Texp_grid, multi_index_uniqgrid, elower_grid, Mmol, qtarr, Tref_broadening, filter_length_oneside, Twt)

compute nu sigma (wavenumber x cross section) matrix, with scan+fft, using the second Taylor expansion

Parameters:

  • Tarr (array) – temperature layers

  • Parr (array) – pressure layers

  • Tref – reference temperature in K

  • R (float) – spectral resolution

  • lbd_coeff (arrau) –

  • nu_grid (array) – wavenumber grid

  • ngamma_ref_grid (array) – normalized half-width grid

  • n_Texp_grid (array) – temperature exponent grid

  • multi_index_uniqgrid (array) – multi index for uniq broadpar grid

  • elower_grid (array) – Elower grid

  • Mmol (float) – molecular mass

  • qtarr (array) – partition function ratio layers

  • Tref_broadening – reference temperature for broadening in Kelvin

  • nu_grid_extended – extended wavenumber grid to aliasing parts

  • filter_length_oneside – one side length of the wavenumber grid of lpffilter

  • Twt – temperature used in the weight point

Returns:

nu sigma (nu_grid_extended x cross section) in cgs matrix

Return type:

jnp.array

exojax.spec.premodit.xsmatrix_nu_open_zeroth(Tarr, Parr, Tref, R, lbd_coeff, nu_grid, ngamma_ref_grid, n_Texp_grid, multi_index_uniqgrid, elower_grid, Mmol, qtarr, Tref_broadening, filter_length_oneside, Twt=None)

compute nu sigma (wavenumber x cross section) matrix, with scan+fft, using the zero-th Taylor expansion

Parameters:

  • Tarr (array) – temperature layers

  • Parr (array) – pressure layers

  • Tref – reference temperature in K

  • R (float) – spectral resolution

  • lbd_coeff (arrau) –

  • nu_grid (array) – wavenumber grid

  • ngamma_ref_grid (array) – normalized half-width grid

  • n_Texp_grid (array) – temperature exponent grid

  • multi_index_uniqgrid (array) – multi index for uniq broadpar grid

  • elower_grid (array) – Elower grid

  • Mmol (float) – molecular mass

  • qtarr (array) – partition function ratio layers

  • Tref_broadening – reference temperature for broadening in Kelvin

  • nu_grid_extended – extended wavenumber grid to aliasing parts

  • filter_length_oneside – one side length of the wavenumber grid of lpffilter

  • Twt – not used

Returns:

nu sigma (nu_grid_extended x cross section) in cgs matrix

Return type:

jnp.array

exojax.spec.premodit.xsmatrix_open_first(Tarr, Parr, Tref, R, lbd_coeff, nu_grid, ngamma_ref_grid, n_Texp_grid, multi_index_uniqgrid, elower_grid, Mmol, qtarr, Tref_broadening, nu_grid_extended, filter_length_oneside, Twt)

compute open cross section matrix given atmospheric layers, for diffmode=1, with scan+fft

Parameters:

  • Tarr (_type_) – temperature layers

  • Parr (_type_) – pressure layers

  • Tref – reference temperature in K

  • R (float) – spectral resolution

  • lbd_coeff (_type_) – LBD coefficient

  • nu_grid (_type_) – wavenumber grid

  • ngamma_ref_grid (_type_) – normalized half-width grid

  • n_Texp_grid (_type_) – temperature exponent grid

  • multi_index_uniqgrid (_type_) – multi index for uniq broadpar grid

  • elower_grid (_type_) – Elower grid

  • Mmol (_type_) – molecular mass

  • qtarr (_type_) – partition function ratio layers

  • Tref_broadening – reference temperature for broadening in Kelvin

  • nu_grid_extended – extended wavenumber grid to aliasing parts

  • filter_length_oneside – one side length of the wavenumber grid of lpffilter

  • Twt – weight temperature in K

Returns:

cross section matrix (Nlayer, N_wavenumber)

Return type:

jnp.array

exojax.spec.premodit.xsmatrix_open_second(Tarr, Parr, Tref, R, lbd_coeff, nu_grid, ngamma_ref_grid, n_Texp_grid, multi_index_uniqgrid, elower_grid, Mmol, qtarr, Tref_broadening, nu_grid_extended, filter_length_oneside, Twt)

compute open cross section matrix given atmospheric layers, for diffmode=1, with scan+fft

Parameters:

  • Tarr (_type_) – temperature layers

  • Parr (_type_) – pressure layers

  • Tref – reference temperature in K

  • R (float) – spectral resolution

  • pmarray (_type_) – pmarray

  • lbd_coeff (_type_) – LBD coefficient

  • nu_grid (_type_) – wavenumber grid

  • ngamma_ref_grid (_type_) – normalized half-width grid

  • n_Texp_grid (_type_) – temperature exponent grid

  • multi_index_uniqgrid (_type_) – multi index for uniq broadpar grid

  • elower_grid (_type_) – Elower grid

  • Mmol (_type_) – molecular mass

  • qtarr (_type_) – partition function ratio layers

  • Tref_broadening – reference temperature for broadening in Kelvin

  • nu_grid_extended – extended wavenumber grid to aliasing parts

  • filter_length_oneside – one side length of the wavenumber grid of lpffilter

  • Twt – weight temperature in K

Returns:

cross section matrix (Nlayer, N_wavenumber)

Return type:

jnp.array

exojax.spec.premodit.xsmatrix_open_zeroth(Tarr, Parr, Tref, R, lbd_coeff, nu_grid, ngamma_ref_grid, n_Texp_grid, multi_index_uniqgrid, elower_grid, Mmol, qtarr, Tref_broadening, nu_grid_extended, filter_length_oneside, Twt=None)

compute open cross section matrix given atmospheric layers, for diffmode=0, with scan+fft

Parameters:

  • Tarr (array) – temperature layers

  • Parr (array) – pressure layers

  • Tref – reference temperature in K

  • R (float) – spectral resolution

  • lbd_coeff (arrau) –

  • nu_grid (array) – wavenumber grid

  • ngamma_ref_grid (array) – normalized half-width grid

  • n_Texp_grid (array) – temperature exponent grid

  • multi_index_uniqgrid (array) – multi index for uniq broadpar grid

  • elower_grid (array) – Elower grid

  • Mmol (float) – molecular mass

  • qtarr (array) – partition function ratio layers

  • Tref_broadening – reference temperature for broadening in Kelvin

  • nu_grid_extended – extended wavenumber grid to aliasing parts

  • filter_length_oneside – one side length of the wavenumber grid of lpffilter

  • Twt – not used

Returns:

cross section matrix (Nlayer, N_wavenumber)

Return type:

jnp.array

exojax.spec.premodit.xsmatrix_second(Tarr, Parr, Tref, R, pmarray, lbd_coeff, nu_grid, ngamma_ref_grid, n_Texp_grid, multi_index_uniqgrid, elower_grid, Mmol, qtarr, Tref_broadening, Twt)

compute cross section matrix given atmospheric layers, for diffmode=1, with scan+fft

Parameters:

  • Tarr (_type_) – temperature layers

  • Parr (_type_) – pressure layers

  • Tref – reference temperature in K

  • R (float) – spectral resolution

  • pmarray (_type_) – pmarray

  • lbd_coeff (_type_) – LBD coefficient

  • nu_grid (_type_) – wavenumber grid

  • ngamma_ref_grid (_type_) – normalized half-width grid

  • n_Texp_grid (_type_) – temperature exponent grid

  • multi_index_uniqgrid (_type_) – multi index for uniq broadpar grid

  • elower_grid (_type_) – Elower grid

  • Mmol (_type_) – molecular mass

  • qtarr (_type_) – partition function ratio layers

  • Tref_broadening – reference temperature for broadening in Kelvin

  • Twt – weight temperature in K

Returns:

cross section matrix (Nlayer, N_wavenumber)

Return type:

jnp.array

exojax.spec.premodit.xsmatrix_zeroth(Tarr, Parr, Tref, R, pmarray, lbd_coeff, nu_grid, ngamma_ref_grid, n_Texp_grid, multi_index_uniqgrid, elower_grid, Mmol, qtarr, Tref_broadening, Twt=None)

compute cross section matrix given atmospheric layers, for diffmode=0, with scan+fft

Parameters:

  • Tarr (_type_) – temperature layers

  • Parr (_type_) – pressure layers

  • Tref – reference temperature in K

  • R (float) – spectral resolution

  • pmarray (_type_) – pmarray

  • lbd_coeff (_type_) –

  • nu_grid (_type_) – wavenumber grid

  • ngamma_ref_grid (_type_) – normalized half-width grid

  • n_Texp_grid (_type_) – temperature exponent grid

  • multi_index_uniqgrid (_type_) – multi index for uniq broadpar grid

  • elower_grid (_type_) – Elower grid

  • Mmol (_type_) – molecular mass

  • qtarr (_type_) – partition function ratio layers

  • Tref_broadening – reference temperature for broadening in Kelvin

  • Twt – not used

Returns:

cross section matrix (Nlayer, N_wavenumber)

Return type:

jnp.array

exojax.spec.premodit.xsvector_first(T, P, nsigmaD, lbd_coeff, Tref, R, pmarray, nu_grid, elower_grid, multi_index_uniqgrid, ngamma_ref_grid, n_Texp_grid, qt, Tref_broadening, Twt)

compute cross section vector, with scan+fft, using the first Taylor expansion

Parameters:

  • T (_type_) – temperature in Kelvin

  • P (_type_) – pressure in bar

  • nsigmaD – normalized doplar STD

  • lbd_zeroth (_type_) – log biased line shape density (LBD), zeroth coefficient

  • lbd_first (_type_) – log biased line shape density (LBD), first coefficient

  • Tref – reference temperature used to compute lbd_zeroth and lbd_first in Kelvin

  • R (_type_) – spectral resolution

  • pmarray (_type_) – (+1,-1) array whose length of len(nu_grid)+1

  • nu_grid (_type_) – wavenumber grid

  • elower_grid (_type_) – E lower grid

  • multi_index_uniqgrid (_type_) – multi index of unique broadening parameter grid

  • ngamma_ref_grid (_type_) – normalized pressure broadening half-width

  • n_Texp_grid (_type_) – temperature exponent grid

  • qt (_type_) – partirion function ratio

  • Tref_broadening – reference temperature for broadening in Kelvin

  • Twt – temperature used in the weight point

Returns:

cross section in cgs vector

Return type:

jnp.array

exojax.spec.premodit.xsvector_nu_open_first(T, P, nsigmaD, lbd_coeff, Tref, R, nu_grid, elower_grid, multi_index_uniqgrid, ngamma_ref_grid, n_Texp_grid, qt, Tref_broadening, filter_length_oneside, Twt)

compute nu sigma (wavenumber x cross section) vector, with scan+fft, using the first Taylor expansion

Parameters:

  • T (_type_) – temperature in Kelvin

  • P (_type_) – pressure in bar

  • nsigmaD – normalized doplar STD

  • lbd_coeff (_type_) – log biased line shape density (LBD) coefficient

  • Tref – reference temperature used to compute lbd_zeroth in Kelvin

  • R (_type_) – spectral resolution

  • nu_grid (_type_) – wavenumber grid

  • elower_grid (_type_) – E lower grid

  • multi_index_uniqgrid (_type_) – multi index of unique broadening parameter grid

  • ngamma_ref_grid (_type_) – normalized pressure broadening half-width

  • n_Texp_grid (_type_) – temperature exponent grid

  • qt (_type_) – partirion function ratio

  • Tref_broadening – reference temperature for broadening in Kelvin

  • filter_length_oneside – one side length of the wavenumber grid of lpffilter

  • Twt – temperature used in the weight point

Returns:

nu sigma (nu_grid_extended x cross section) in cgs vector

Return type:

jnp.array

exojax.spec.premodit.xsvector_nu_open_second(T, P, nsigmaD, lbd_coeff, Tref, R, nu_grid, elower_grid, multi_index_uniqgrid, ngamma_ref_grid, n_Texp_grid, qt, Tref_broadening, filter_length_oneside, Twt)

compute nu sigma (wavenumber x cross section) vector, with scan+fft, using the second Taylor expansion

Parameters:

  • T (_type_) – temperature in Kelvin

  • P (_type_) – pressure in bar

  • nsigmaD – normalized doplar STD

  • lbd_coeff (_type_) – log biased line shape density (LBD) coefficient

  • Tref – reference temperature used to compute lbd_zeroth in Kelvin

  • R (_type_) – spectral resolution

  • nu_grid (_type_) – wavenumber grid

  • elower_grid (_type_) – E lower grid

  • multi_index_uniqgrid (_type_) – multi index of unique broadening parameter grid

  • ngamma_ref_grid (_type_) – normalized pressure broadening half-width

  • n_Texp_grid (_type_) – temperature exponent grid

  • qt (_type_) – partirion function ratio

  • Tref_broadening – reference temperature for broadening in Kelvin

  • filter_length_oneside – one side length of the wavenumber grid of lpffilter

  • Twt – temperature used in the weight point

Returns:

nu sigma (nu_grid_extended x cross section) in cgs vector

Return type:

jnp.array

exojax.spec.premodit.xsvector_nu_open_zeroth(T, P, nsigmaD, lbd_coeff, Tref, R, nu_grid, elower_grid, multi_index_uniqgrid, ngamma_ref_grid, n_Texp_grid, qt, Tref_broadening, filter_length_oneside, Twt=None)

compute nu sigma (wavenumber x cross section) vector, with scan+fft, using the zero-th Taylor expansion

Parameters:

  • T (_type_) – temperature in Kelvin

  • P (_type_) – pressure in bar

  • nsigmaD – normalized doplar STD

  • lbd_coeff (_type_) – log biased line shape density (LBD) coefficient

  • Tref – reference temperature used to compute lbd_zeroth in Kelvin

  • R (_type_) – spectral resolution

  • nu_grid (_type_) – wavenumber grid

  • elower_grid (_type_) – E lower grid

  • multi_index_uniqgrid (_type_) – multi index of unique broadening parameter grid

  • ngamma_ref_grid (_type_) – normalized pressure broadening half-width

  • n_Texp_grid (_type_) – temperature exponent grid

  • qt (_type_) – partirion function ratio

  • Tref_broadening – reference temperature for broadening in Kelvin

  • filter_length_oneside – one side length of the wavenumber grid of lpffilter

  • Twt – not used

Returns:

nu sigma (nu_grid_extended x cross section) in cgs vector

Return type:

jnp.array

exojax.spec.premodit.xsvector_open_first(T, P, nsigmaD, lbd_coeff, Tref, R, nu_grid, elower_grid, multi_index_uniqgrid, ngamma_ref_grid, n_Texp_grid, qt, Tref_broadening, nu_grid_extended, filter_length_oneside, Twt)

compute cross section vector, with scan+fft, using the first Taylor expansion

Parameters:

  • T (_type_) – temperature in Kelvin

  • P (_type_) – pressure in bar

  • nsigmaD – normalized doplar STD

  • lbd_zeroth (_type_) – log biased line shape density (LBD), zeroth coefficient

  • lbd_first (_type_) – log biased line shape density (LBD), first coefficient

  • Tref – reference temperature used to compute lbd_zeroth and lbd_first in Kelvin

  • R (_type_) – spectral resolution

  • nu_grid (_type_) – wavenumber grid

  • elower_grid (_type_) – E lower grid

  • multi_index_uniqgrid (_type_) – multi index of unique broadening parameter grid

  • ngamma_ref_grid (_type_) – normalized pressure broadening half-width

  • n_Texp_grid (_type_) – temperature exponent grid

  • qt (_type_) – partirion function ratio

  • Tref_broadening – reference temperature for broadening in Kelvin

  • nu_grid_extended – extended wavenumber grid to aliasing parts

  • filter_length_oneside – one side length of the wavenumber grid of lpffilter

  • Twt – temperature used in the weight point

Returns:

cross section in cgs vector

Return type:

jnp.array

exojax.spec.premodit.xsvector_open_second(T, P, nsigmaD, lbd_coeff, Tref, R, nu_grid, elower_grid, multi_index_uniqgrid, ngamma_ref_grid, n_Texp_grid, qt, Tref_broadening, nu_grid_extended, filter_length_oneside, Twt)

compute open cross section vector, with scan+fft, using the second Taylor expansion

Parameters:

  • T (_type_) – temperature in Kelvin

  • P (_type_) – pressure in bar

  • nsigmaD – normalized doplar STD

  • lbd_coeff (_type_) – log biased line shape density (LBD), coefficient

  • Tref – reference temperature used to compute lbd_zeroth and lbd_first in Kelvin

  • R (_type_) – spectral resolution

  • nu_grid (_type_) – wavenumber grid

  • elower_grid (_type_) – E lower grid

  • multi_index_uniqgrid (_type_) – multi index of unique broadening parameter grid

  • ngamma_ref_grid (_type_) – normalized pressure broadening half-width

  • n_Texp_grid (_type_) – temperature exponent grid

  • qt (_type_) – partirion function ratio

  • Tref_broadening – reference temperature for broadening in Kelvin

  • nu_grid_extended – extended wavenumber grid to aliasing parts

  • filter_length_oneside – one side length of the wavenumber grid of lpffilter

  • Twt – temperature used in the weight point

Returns:

cross section in cgs vector

Return type:

jnp.array

exojax.spec.premodit.xsvector_open_zeroth(T, P, nsigmaD, lbd_coeff, Tref, R, nu_grid, elower_grid, multi_index_uniqgrid, ngamma_ref_grid, n_Texp_grid, qt, Tref_broadening, nu_grid_extended, filter_length_oneside, Twt=None)

compute cross section vector, with scan+fft, using the zero-th Taylor expansion

Parameters:

  • T (_type_) – temperature in Kelvin

  • P (_type_) – pressure in bar

  • nsigmaD – normalized doplar STD

  • lbd_coeff (_type_) – log biased line shape density (LBD) coefficient

  • Tref – reference temperature used to compute lbd_zeroth in Kelvin

  • R (_type_) – spectral resolution

  • nu_grid (_type_) – wavenumber grid

  • elower_grid (_type_) – E lower grid

  • multi_index_uniqgrid (_type_) – multi index of unique broadening parameter grid

  • ngamma_ref_grid (_type_) – normalized pressure broadening half-width

  • n_Texp_grid (_type_) – temperature exponent grid

  • qt (_type_) – partirion function ratio

  • Tref_broadening – reference temperature for broadening in Kelvin

  • nu_grid_extended – extended wavenumber grid to aliasing parts

  • filter_length_oneside – one side length of the wavenumber grid of lpffilter

  • Twt – not used

Returns:

cross section in cgs vector

Return type:

jnp.array

exojax.spec.premodit.xsvector_second(T, P, nsigmaD, lbd_coeff, Tref, R, pmarray, nu_grid, elower_grid, multi_index_uniqgrid, ngamma_ref_grid, n_Texp_grid, qt, Tref_broadening, Twt)

compute cross section vector, with scan+fft, using the second Taylor expansion

Parameters:

  • T (_type_) – temperature in Kelvin

  • P (_type_) – pressure in bar

  • nsigmaD – normalized doplar STD

  • lbd_coeff (_type_) – log biased line shape density (LBD), coefficient

  • Tref – reference temperature used to compute lbd_zeroth and lbd_first in Kelvin

  • R (_type_) – spectral resolution

  • pmarray (_type_) – (+1,-1) array whose length of len(nu_grid)+1

  • nu_grid (_type_) – wavenumber grid

  • elower_grid (_type_) – E lower grid

  • multi_index_uniqgrid (_type_) – multi index of unique broadening parameter grid

  • ngamma_ref_grid (_type_) – normalized pressure broadening half-width

  • n_Texp_grid (_type_) – temperature exponent grid

  • qt (_type_) – partirion function ratio

  • Tref_broadening – reference temperature for broadening in Kelvin

  • Twt – temperature used in the weight point

Returns:

cross section in cgs vector

Return type:

jnp.array

exojax.spec.premodit.xsvector_zeroth(T, P, nsigmaD, lbd_coeff, Tref, R, pmarray, nu_grid, elower_grid, multi_index_uniqgrid, ngamma_ref_grid, n_Texp_grid, qt, Tref_broadening, Twt=None)

compute cross section vector, with scan+fft, using the zero-th Taylor expansion

Parameters:

  • T (_type_) – temperature in Kelvin

  • P (_type_) – pressure in bar

  • nsigmaD – normalized doplar STD

  • lbd_coeff (_type_) – log biased line shape density (LBD) coefficient

  • Tref – reference temperature used to compute lbd_zeroth in Kelvin

  • R (_type_) – spectral resolution

  • pmarray – (+1,-1) array whose length of len(nu_grid)+1

  • nu_grid (_type_) – wavenumber grid

  • elower_grid (_type_) – E lower grid

  • multi_index_uniqgrid (_type_) – multi index of unique broadening parameter grid

  • ngamma_ref_grid (_type_) – normalized pressure broadening half-width

  • n_Texp_grid (_type_) – temperature exponent grid

  • qt (_type_) – partirion function ratio

  • Tref_broadening – reference temperature for broadening in Kelvin

  • Twt – not used

Returns:

cross section in cgs vector

Return type:

jnp.array

exojax.spec.profconv module

line profile convolution with LSD

  • calc_open_xsection_from_lsd_zeroscan: compute open cross section from LSD in MODIT algorithm using scan+fft to avoid 4GB memory limit in fft and zero padding in scan

  • calc_xsection_from_lsd_zeroscan: compute cross section from LSD in MODIT algorithm using scan+fft to avoid 4GB memory limit in fft and zero padding in scan

  • calc_xsection_from_lsd_scanfft: compute cross section from LSD in MODIT algorithm using scan+fft to avoid 4GB memory limit in fft (see #277), deprecated

exojax.spec.profconv.calc_open_nu_xsection_from_lsd_zeroscan(Slsd, R, nsigmaD, log_ngammaL_grid, filter_length_oneside)

Compute (wavenumber x open cross section9 from LSD in MODIT algorithm using scan+fft to avoid 4GB memory limit in fft and zero padding in scan

Notes

The aliasing part is closed and thereby can’t be used in OLA. #277 Why the output is not cross section, but (nu_grid_extended x Cross section)? This is related to the scan in OpaPremoditStitch. I (@HajimeKawahara) did not want to use wavenumber_grid_extended in the scan in OpaPremoditStitch.xsvector/xsmatrix 2/28 2025

Parameters:

  • Slsd (array) – line shape density [Nnus, Ngamma]

  • R (float) – spectral resolution

  • nsigmaD (float) – normaized Gaussian STD

  • log_gammaL_grid (array) – logarithm of gammaL grid [Ngamma]

  • filter_length_oneside (int) – one side length of the wavenumber grid of lpffilter, Nfilter = 2*filter_length_oneside + 1

Returns:

Open (nu_grid_extended x Cross section) in the log nu grid [Nnus]

exojax.spec.profconv.calc_xsection_from_lsd_scanfft(Slsd, R, pmarray, nsigmaD, nu_grid, log_ngammaL_grid)

Compute cross section from LSD in MODIT algorithm using scan+fft to avoid 4GB memory limit in fft (see #277), deprecated

Notes

This function is deprecated. Use calc_xsection_from_lsd_zeroscan instead. The aliasing part is closed and thereby can’t be used in OLA.

Parameters:

  • Slsd (array) – line shape density [Nnus, Ngamma]

  • R (float) – spectral resolution

  • pmarray – (+1,-1) array whose length of len(nu_grid)+1

  • nsigmaD (float) – normaized Gaussian STD

  • nu_grid (array) – wavenumber grid [Nnus]

  • log_gammaL_grid (array) – logarithm of gammaL grid [Ngamma]

Returns:

Closed Cross section in the log nu grid [Mnus]

exojax.spec.profconv.calc_xsection_from_lsd_zeroscan(Slsd, R, pmarray, nsigmaD, nu_grid, log_ngammaL_grid)

Compute cross section from LSD in MODIT algorithm using scan+fft to avoid 4GB memory limit in fft and zero padding in scan

Notes

The aliasing part is closed and thereby can’t be used in OLA. #277

Parameters:

  • Slsd (array) – line shape density [Nnus, Ngamma]

  • R (float) – spectral resolution

  • pmarray – (+1,-1) array whose length of len(nu_grid)+1

  • nsigmaD (float) – normaized Gaussian STD

  • nu_grid (array) – wavenumber grid [Nnus]

  • log_gammaL_grid (array) – logarithm of gammaL grid [Ngamma]

Returns:

Closed Cross section in the log nu grid [Nnus]

exojax.spec.qstate module

Quantum States Module

exojax.spec.qstate.branch_to_number(branch_str, fillvalue=None)

convert branch: object to number (float) :param branch_str: Branch type (R, P, Q) :type branch_str: np.ndarray

Returns:

jupper - jlower

Return type:

np.ndarray

exojax.spec.qstate.m_transition_state(jlower, branch)

compute m-value of the transition from rotational state

Parameters:

  • jlower (int) – lower rotational quantum state

  • branch (int) – jupper - jlower

Returns:

m

Return type:

int

Notes

m = Jlower + 1 for R-branch (branch=1) m = Jlower for P- and Q- branch (branch=-1 and 0)

exojax.spec.rayleigh module

exojax.spec.rayleigh.xsvector_rayleigh_gas(wavenumber, polarizability, king_factor=1.0)

Computes Rayleigh scattering cross-section of gas from polarizability

Parameters:

  • wavenumber – wavenumber (cm-1)

  • polarizability – alpha (cm3)

  • king_factor – King correction factor which accounts for the depolarization effect (default=1.0)

Returns:

cross section (cm2) for Rayleigh scattering

exojax.spec.rayleigh.xsvector_rayleigh_gas_from_refractive_index(wavenumber, refractive_index, number_density, king_factor=1.0)

Computes Rayleigh scattering cross-section of gas from real refractive index

Parameters:

  • wavenumber – wavenumber (cm-1)

  • refractive_index – real refractive index (use atm.lorentz_lorenz to compute this)

  • number_density – gas number density (cm-2)

  • king_factor – King correction factor which accounts for the depolarization effect (default=1.0)

Returns:

cross section (cm2) for Rayleigh scattering

Notes

This function uses the exact form of the gas Rayleigh scattering, which depends on the number density of the gas

exojax.spec.response module

Response

  • input nus/wav should be spaced evenly on a log scale (ESLOG).

  • response is a response operation for the wavenumber grid spaced evenly on a log scale.

exojax.spec.response.ipgauss(spectrum, varr_kernel, beta)

Apply the Gaussian IP response to a spectrum F.

Parameters:

  • spectrum – original spectrum (F0)

  • varr_kernel – velocity array for the rotational kernel

  • beta – STD of a Gaussian broadening (IP+microturbulence)

Returns:

response-applied spectrum (F)

exojax.spec.response.ipgauss_ola(folded_spectrum, varr_kernel, beta)

Apply the Gaussian IP response to a spectrum F using OLA.

Parameters:

  • folded_spectrum – original spectrum (F0) folded to (ndiv, div_length) form

  • varr_kernel – velocity array for the rotational kernel

  • beta – STD of a Gaussian broadening (IP+microturbulence)

Returns:

response-applied spectrum (F)

exojax.spec.response.ipgauss_ola_sampling(nusd, nus, folded_spectrum, beta, RV, varr_kernel)

Apply the Gaussian IP response using OLA + sampling to a spectrum F.

Parameters:

  • nusd – sampling wavenumber

  • nus – input wavenumber, evenly log-spaced

  • folded_spectrum – original spectrum (F0) folded to (ndiv, div_length) form

  • beta – STD of a Gaussian broadening (IP+microturbulence)

  • RV – radial velocity (km/s)

  • varr_kernel – velocity array for the rotational kernel

Returns:

response-applied spectrum (F)

exojax.spec.response.ipgauss_sampling(nusd, nus, spectrum, beta, RV, varr_kernel)

Apply the Gaussian IP response + sampling to a spectrum F.

Parameters:

  • nusd – sampling wavenumber

  • nus – input wavenumber, evenly log-spaced

  • spectrum – original spectrum (F0)

  • beta – STD of a Gaussian broadening (IP+microturbulence)

  • RV – radial velocity (km/s)

  • varr_kernel – velocity array for the rotational kernel

Returns:

response-applied spectrum (F)

exojax.spec.response.ipgauss_variable_sampling(nusd, nus, spectrum, beta_variable, RV)

Apply the variable Gaussian IP response + sampling to a spectrum F.

Notes

STD is a function of nusd

Parameters:

  • nusd – sampling wavenumber

  • nus – input wavenumber, evenly log-spaced

  • spectrum – original spectrum (F0)

  • beta_variable (1D array) – STD of a Gaussian broadening, shape=(len(nusd),)

  • RV – radial velocity (km/s)

Returns:

response-applied spectrum (F)

exojax.spec.response.sampling(nusd, nus, F, RV)

Sampling w/ RV.

Parameters:

  • nusd – sampling wavenumber

  • nus – input wavenumber

  • F – input spectrum

  • RV – radial velocity (km/s)

Returns:

sampled spectrum

exojax.spec.rtlayer module

layer by layer radiative transfer module

exojax.spec.rtlayer.fluxsum_scan(tauup, taulow, mus, weights)

flux sum using jax.lax.scan (but unrolling)

Parameters:

  • tauup (array) – optical depth at the top of the layer [N_wavenumber]

  • taulow (array) – optical depth at the bottom of the layer [N_wavenumber]

  • mus (array) – array of cosine of zenith angles [N_stream]

  • weights (array) – array of weights for each zenith angle [N_stream]

Returns:

flux sum for each wavenumber [N_wavenumber]

Return type:

array

exojax.spec.rtlayer.fluxsum_vector(tauup, taulow, mus, weights)

flux sum for vectorized calculation

Parameters:

  • tauup (array) – optical depth at the top of the layer [N_wavenumber]

  • taulow (array) – optical depth at the bottom of the layer [N_wavenumber]

  • mus (array) – array of cosine of zenith angles [N_stream]

  • weights (array) – array of weights for each zenith angle [N_stream]

Returns:

flux sum for each wavenumber [N_wavenumber]

Return type:

array

exojax.spec.rtransfer module

Runs radiative transfer

The classification of rtrun(s):

  • flux-based emission

– pure absoprtion β€” 2stream: rtrun_emis_pureabs_flux2st, rtrun_emis_pureabs_flux2st_surface – scattering β€” 2stream β€”- LART: rtrun_emis_scat_lart_toonhm β€”- flux-adding: rtrun_emis_scat_fluxadding_toonhm – relfection β€” 2stream β€”- flux-adding: rtrun_reflect_fluxadding_toonhm

  • intensity-based emission

– pure absorption β€” isothermal: rtrun_emis_pureabs_ibased β€” linear source approximation: rtrun_emis_pureabs_ibased_linsap

  • transmision:

– trapezoid integration: rtrun_trans_pureabs_trapezoid – simpson integration: rtrun_trans_pureabs_simpson

exojax.spec.rtransfer.coeffs_linsap(dtau_per_mu, trans)

coefficients of the linsap

Parameters:

  • dtau_per_mu (_type_) – opacity difference divided by mu (cos theta)

  • trans – transmission of the layers

Returns:

beta coefficient, gamma coefficient

Return type:

_type_

exojax.spec.rtransfer.initialize_gaussian_quadrature(nstream)

Initialization of Gaussian Quadrature

Parameters:

nstream (int) – the number of the stream

Raises:

ValueError – odd nstream error

Returns:

cosine angle array (mu), weight array

Return type:

array, array

exojax.spec.rtransfer.rtrun_emis_pureabs_fbased2st(dtau, source_matrix)

Radiative Transfer for emission spectrum using flux-based two-stream pure absorption with no surface :param dtau: optical depth matrix, dtau (N_layer, N_nus) :type dtau: 2D array :param source_matrix: source matrix (N_layer, N_nus) :type source_matrix: 2D array

Returns:

flux in the unit of [erg/cm2/s/cm-1] if using piBarr as a source function.

exojax.spec.rtransfer.rtrun_emis_pureabs_fbased2st_surface(dtau, source_matrix, source_surface)

Radiative Transfer for emission spectrum using flux-based two-stream pure absorption with a planetary surface.

Parameters:

  • dtau (2D array) – optical depth matrix, dtau (N_layer, N_nus)

  • source_matrix (2D array) – source matrix (N_layer, N_nus)

  • source_surface – source from the surface [N_nus]

Returns:

flux in the unit of [erg/cm2/s/cm-1] if using piBarr as a source function.

exojax.spec.rtransfer.rtrun_emis_pureabs_ibased(dtau, source_matrix, mus, weights)

Radiative Transfer for emission spectrum using intensity-based n-stream pure absorption with no surface (NEMESIS, pRT-like) :param dtau: optical depth matrix, dtau (N_layer, N_nus) :type dtau: 2D array :param source_matrix: source matrix (N_layer, N_nus) :type source_matrix: 2D array :param mus: mu (cos theta) list for integration :type mus: list :param weights: weight list for mu :type weights: list

Returns:

flux in the unit of [erg/cm2/s/cm-1] if using piBarr as a source function.

exojax.spec.rtransfer.rtrun_emis_pureabs_ibased_linsap(dtau, source_matrix_boundary, mus, weights)

Radiative Transfer for emission spectrum using intensity-based n-stream pure absorption with no surface w/ linear source approximation = linsap (HELIOS-R2 like)

Parameters:

  • dtau (2D array) – optical depth matrix, dtau (N_layer, N_nus)

  • source_matrix_booundary (2D array) – source matrix at the layer upper boundary (N_layer + 1, N_nus)

  • mus (list) – mu (cos theta) list for integration

  • weights (list) – weight list for mu

Returns:

flux in the unit of [erg/cm2/s/cm-1] if using piBarr as a source function.

Notes

See Olson and Kunasz as well as HELIOS-R2 paper (Kitzmann+) for the derivation.

exojax.spec.rtransfer.rtrun_emis_scat_fluxadding_toonhm(dtau, single_scattering_albedo, asymmetric_parameter, source_matrix)

Radiative Transfer for emission spectrum (w/ scattering) using flux-based two-stream scattering the flux adding solver w/ Toon Hemispheric Mean with surface.

Parameters:

  • dtau (2D array) – Optical depth matrix, dtau (N_layer, N_nus)

  • single_scattering_albedo (2D array) – Single scattering albedo (N_layer, N_nus)

  • asymmetric_parameter (2D array) – Asymmetric parameter (N_layer, N_nus)

  • source_matrix (2D array) – Source matrix (N_layer, N_nus)

Returns:

Emission spectrum in the unit of [erg/cm2/s/cm-1] if using piBarr as a source function.

Return type:

1D array

exojax.spec.rtransfer.rtrun_emis_scat_lart_toonhm(dtau, single_scattering_albedo, asymmetric_parameter, source_matrix)

Radiative Transfer for emission spectrum using flux-based two-stream scattering LART solver w/ Toon Hemispheric Mean with no surface.

Parameters:

  • dtau (2D array) – Optical depth matrix, dtau (N_layer, N_nus)

  • single_scattering_albedo (2D array) – Single scattering albedo (N_layer, N_nus)

  • asymmetric_parameter (2D array) – Asymmetric parameter (N_layer, N_nus)

  • source_matrix (2D array) – Source matrix (N_layer, N_nus)

Returns:

A tuple containing:

  • spectrum (1D array): Emission spectrum in the unit of [erg/cm2/s/cm-1] if using piBarr as a source function.

  • cumTtilde (2D array): Cumulative transmission function.

  • Qtilde (2D array): Scattering source function.

  • trans_coeff (2D array): Transmission coefficients.

  • scat_coeff (2D array): Scattering coefficients.

  • reduced_piB (2D array): Reduced source function.

Return type:

tuple

exojax.spec.rtransfer.rtrun_emis_scat_lart_toonhm_surface(dtau, single_scattering_albedo, asymmetric_parameter, source_matrix, source_surface)

Radiative Transfer for emission spectrum using flux-based two-stream scattering LART solver w/ Toon Hemispheric Mean with surface.

Parameters:

  • dtau (2D array) – Optical depth matrix, dtau (N_layer, N_nus)

  • single_scattering_albedo (2D array) – Single scattering albedo (N_layer, N_nus)

  • asymmetric_parameter (2D array) – Asymmetric parameter (N_layer, N_nus)

  • source_matrix (2D array) – Source matrix (N_layer, N_nus)

  • source_surface (1D array) – Source from the surface (N_nus)

Returns:

A tuple containing:

  • spectrum (1D array): Emission spectrum in the unit of [erg/cm2/s/cm-1] if using piBarr as a source function.

  • cumTtilde (2D array): Cumulative transmission function.

  • Qtilde (2D array): Scattering source function.

  • trans_coeff (2D array): Transmission coefficients.

  • scat_coeff (2D array): Scattering coefficients.

  • piB (2D array): Reduced source function.

Return type:

tuple

exojax.spec.rtransfer.rtrun_reflect_fluxadding_toonhm(dtau, single_scattering_albedo, asymmetric_parameter, source_matrix, source_surface, reflectivity_surface, incoming_flux)

Radiative Transfer for reflected spectrum using the flux adding solver w/ Toon Hemispheric Mean with surface.

Parameters:

  • dtau (2D array) – Layer optical depth (N_layer, N_nus)

  • single_scattering_albedo (2D array) – Single scattering albedo (N_layer, N_nus)

  • asymmetric_parameter (2D array) – Asymmetric parameter (N_layer, N_nus)

  • source_matrix (2D array) – Source term (N_layer, N_nus)

  • source_surface (1D array) – Source from the surface (N_nus)

  • reflectivity_surface (1D array) – Reflectivity from the surface (N_nus)

  • incoming_flux (1D array) – Incoming flux F_0^- (N_nus)

Returns:

Reflected spectrum in the unit of [erg/cm2/s/cm-1] if using piBarr as a source function.

Return type:

1D array

exojax.spec.rtransfer.rtrun_trans_pureabs_simpson(dtau_chord_modpoint, dtau_chord_lower, radius_lower, height)

Radiative transfer for transmission spectrum assuming pure absorption with the Simpson integration (signals.integration.simpson)

Parameters:

  • dtau_chord_midpoint (2D array) – chord opatical depth at the midpoint (Nlayer, N_wavenumber)

  • dtau_chord_lower (2D array) – chord opatical depth at the lower boundary (Nlayer, N_wavenumber)

  • radius_lower (1D array) – (normalized) radius at the lower boundary, underline(r) (Nlayer). R0 = radius_lower[-1] corresponds to the most bottom of the layers.

  • height (1D array) – (normalized) height of the layers

Returns:

transit squared radius normalized by radius_lower[-1], i.e. it returns (radius/radius_lower[-1])**2

Return type:

1D array

Notes

This function gives the sqaure of the transit radius. If you would like to obtain the transit radius, take sqaure root of the output. If you would like to compute the transit depth, devide the output by the square of stellar radius

Notes

We need the edge correction because the trapezoid integration with radius_lower lacks the edge point integration. i.e. the integration of the 0-th layer from radius_lower[0] to radius_top. We assume tau = 0 at the radius_top. then, the edge correction should be (1-T_0)*(delta r_0), but usually negligible though.

exojax.spec.rtransfer.rtrun_trans_pureabs_trapezoid(dtau_chord, radius_lower, radius_top)

Radiative transfer for transmission spectrum assuming pure absorption with the trapezoid integration (jax.scipy.integrate.trapezoid)

Parameters:

  • dtau_chord (2D array) – chord optical depth (Nlayer, N_wavenumber)

  • radius_lower (1D array) – (normalized) radius at the lower boundary, underline(r) (Nlayer). R0 = radius_lower[-1] corresponds to the most bottom of the layers.

  • radius_top (float) – (normalized) radius at the ToA, i.e. the radius at the most top of the layers

Returns:

transit squared radius normalized by radius_lower[-1], i.e. it returns (radius/radius_lower[-1])**2

Return type:

1D array

Notes

This function gives the sqaure of the transit radius. If you would like to obtain the transit radius, take sqaure root of the output. If you would like to compute the transit depth, devide the output by the square of stellar radius

Notes

We need the edge correction because the trapezoid integration with radius_lower lacks the edge point integration. i.e. the integration of the 0-th layer from radius_lower[0] to radius_top. We assume tau = 0 at the radius_top. then, the edge correction should be (1-T_0)*(delta r_0), but usually negligible though.

exojax.spec.rtransfer.setrt_toonhm(dtau, single_scattering_albedo, asymmetric_parameter, source_matrix)

Sets some coefficients for radiative transfer assuming Toon Hemispheric Mean.

Parameters:

  • dtau (2D array) – Optical depth matrix, dtau (N_layer, N_nus)

  • single_scattering_albedo (2D array) – Single scattering albedo (N_layer, N_nus)

  • asymmetric_parameter (2D array) – Asymmetric parameter (N_layer, N_nus)

  • source_matrix (2D array) – Source matrix (N_layer, N_nus)

Returns:

Transmission coefficients. scat_coeff (2D array): Scattering coefficients. reduced_piB (2D array): Reduced source function. zeta_plus (2D array): Zeta plus coefficients. zeta_minus (2D array): Zeta minus coefficients. lambdan (2D array): Lambda coefficients.

Return type:

trans_coeff (2D array)

exojax.spec.rtransfer.settridiag_toohm(dtau, zeta_plus, zeta_minus, lambdan, trans_coeff, scat_coeff, reduced_piB)
exojax.spec.rtransfer.trans2E3(x)

transmission function 2E3 (two-stream approximation with no scattering) expressed by 2 E3(x)

Note

The exponetial integral of the third order E3(x) is computed using Abramowitz Stegun (1970) approximation of E1 (exojax.special.E1).

Parameters:

x – input variable

Returns:

Transmission function T=2 E3(x)

exojax.spec.set_ditgrid module

set DIT

  • This module provides functions to generate the grid used in DIT/MODIT/PreMODIT.

exojax.spec.set_ditgrid.ditgrid_linear_interval(input_variable, dit_grid_resolution=0.1, weight=None, adopt=True)

generate DIT GRID with constant interval in linear scale

Parameters:

  • input_variable – input array, e.g. n_Texp (temperature exponent) array (Nline)

  • dit_grid_resolution – grid resolution. dit_grid_resolution=0.1 (defaut) means a grid point per digit

  • weight – weight, e.g. np.abs(ln(T)-ln(Tref))

  • adopt – if True, min, max grid points are used at min and max values of x.

  • case (In this) –

  • exactly. (the grid width does not need to be dit_grid_resolution) –

Returns:

grid for DIT

exojax.spec.set_ditgrid.ditgrid_log_interval(input_variable, dit_grid_resolution=0.1, adopt=True)

generate DIT GRID with constant interval in logarithm scale

Parameters:

  • input_variable – simgaD or gammaL array (Nline)

  • dit_grid_resolution – grid resolution. dit_grid_resolution=0.1 (defaut) means a grid point per digit

  • adopt – if True, min, max grid points are used at min and max values of x.

  • case (In this) –

  • exactly. (the grid width does not need to be dit_grid_resolution) –

Returns:

grid for DIT

exojax.spec.set_ditgrid.ditgrid_matrix(x, res=0.1, adopt=True)

DIT GRID MATRIX.

Parameters:

  • x – simgaD or gammaL matrix (Nlayer x Nline)

  • res – grid resolution. res=0.1 (defaut) means a grid point per digit

  • adopt – if True, min, max grid points are used at min and max values of x. In this case, the grid width does not need to be res exactly.

Returns:

grid for DIT (Nlayer x NDITgrid)

exojax.spec.set_ditgrid.minmax_ditgrid_matrix(x, dit_grid_resolution=0.1, adopt=True)

compute MIN and MAX DIT GRID MATRIX.

Parameters:

  • x – gammaL matrix (Nlayer x Nline)

  • dit_grid_resolution – grid resolution. dit_grid_resolution=0.1 (defaut) means a grid point per digit

  • adopt – if True, min, max grid points are used at min and max values of x. In this case, the grid width does not need to be dit_grid_resolution exactly.

Returns:

minimum and maximum for DIT (dgm_minmax)

exojax.spec.set_ditgrid.precompute_modit_ditgrid_matrix(set_gm_minmax, dit_grid_resolution=0.1, adopt=True)

Precomputing MODIT GRID MATRIX for normalized GammaL.

Parameters:

  • set_gm_minmax – set of minmax of ditgrid matrix for different parameters [Nsample, Nlayers, 2], 2=min,max

  • dit_grid_resolution – grid resolution. dit_grid_resolution=0.1 (defaut) means a grid point per digit

  • adopt – if True, min, max grid points are used at min and max values of x. In this case, the grid width does not need to be dit_grid_resolution exactly.

Returns:

grid for DIT (Nlayer x NDITgrid)

exojax.spec.specop module

Spectral Operators (Sop)

The role of SOP is to apply various operators (essentially convolution) to a single spectrum, such as spin rotation, gaussian IP, RV shift etc. There are several convolution methods: - β€œexojax.signal.convolve”: regular FFT-based convolution - β€œexojax.signal.ola”: Overlap-and-Add based convolution

class exojax.spec.specop.SopCommonConv(nu_grid, vrmax, convolution_method)

Bases: object

Common Spectral Operator for convloution type operators

check_ola_reducible(spectrum)
generate_vrarray()
class exojax.spec.specop.SopInstProfile(nu_grid, vrmax=100.0, convolution_method='exojax.signal.convolve')

Bases: SopCommonConv

Spectral operator on Instrumental profile and sampling

ipgauss(spectrum, standard_deviation)

Gaussian Instrumental Profile

Parameters:

  • spectrum (nd array) – 1D spectrum

  • standard_deviation (float) – standard deviation of Gaussian in km/s

Raises:

ValueError – _description_

Returns:

IP applied spectrum

Return type:

array

sampling(spectrum, radial_velocity, nu_grid_sampling)

sampling to instrumental wavenumber grid (not necessary ESLOG nor ESLIN)

Parameters:

  • spectrum (nd array) – 1D spectrum

  • radial_velocity (float) – radial velocity in km/s

  • nu_grid_sampling (array) – instrumental wavenumber grid

Returns:

inst sampled spectrum

Return type:

array

class exojax.spec.specop.SopPhoto(filter_id, filter_bank='svo', path='.database/filter', download=True, up_resolution_factor=32.0, factor=1e+20)

Bases: object

Spectral Operator for photometry

apparent_magnitude(flux)

computes apparent magnitude

Parameters:

flux (array) – flux in the unit of erg/s/cm2/cm-1, the same dimension as self.transmission_filter

Returns:

apparent magnitude

Return type:

float

computes_interpolated_transmission_filter(xsmode='premodit')

computes

Parameters:

xsmode (str, optional) – xsmode for wavenumber_grid. Defaults to β€œpremodit”.

download_filter()

downloads the filter

Raises:

ValueError – No filter bank

download_filter_svo()

downloads the filter from SVO

load_filter()

loads the filter from the saved dataset

Raises:

ValueError – datasets not found

save_filter()

save the filter dataset

class exojax.spec.specop.SopRotation(nu_grid, vsini_max=100.0, convolution_method='exojax.signal.convolve')

Bases: SopCommonConv

Spectral operator on rotation

rigid_rotation(spectrum, vsini, u1, u2)

apply a rigid rotation

Parameters:

  • spectrum (nd array) – 1D spectrum

  • vsini (float) – V sini in km/s

  • u1 (float) – Limb darkening parameter u1

  • u2 (float) – Limb darkening parameter u2

Raises:

ValueError – _description_

Returns:

rotationally broaden spectrum

Return type:

nd array

exojax.spec.spin_rotation module

exojax.spec.spin_rotation.convolve_rigid_rotation(F0, vr_array, vsini, u1=0.0, u2=0.0)

Apply the Rotation response to a spectrum F (No OLA and No cuDNN).

Parameters:

  • F0 – original spectrum (F0)

  • vr_array – fix-sized vr array for kernel, see utils.dvgrid_rigid_rotation

  • vsini – V sini for rotation (km/s)

  • RV – radial velocity

  • u1 – Limb-darkening coefficient 1

  • u2 – Limb-darkening coefficient 2

Returns:

response-applied spectrum (F)

exojax.spec.spin_rotation.convolve_rigid_rotation_ola(folded_F0, vr_array, vsini, u1=0.0, u2=0.0)

Apply the Rotation response to a spectrum F (No OLA and No cuDNN).

Parameters:

  • folded_F0 – original spectrum (F0) folded to (ndiv, div_length) form

  • vr_array – fix-sized vr array for kernel, see utils.dvgrid_rigid_rotation

  • vsini – V sini for rotation (km/s)

  • RV – radial velocity

  • u1 – Limb-darkening coefficient 1

  • u2 – Limb-darkening coefficient 2

Returns:

response-applied spectrum (F)

exojax.spec.spin_rotation.rotkernel_jvp(primals, tangents)

exojax.spec.toon module

Methods for Toon et al. 1989

  • gamma_1, gamma_2, (gamma_3,) and mu1 are the fundamental parameters of Toon+89 (Table 1), called toon_params.

  • gamma_1, gamma_2 can be converted to the fundamental parameters of the twostream solver, zeta and lambda.

  • one can choose Eddington, Quadrature, Hemispheric_Mean to compute toon_params from single_scattering_albedo and asymmetric_parameter (and mu0 for the former two cases)

exojax.spec.toon.params_eddington(single_scattering_albedo, asymmetric_parameter, mu0)

computes Toon+89 parameters for Eddington approximation

Parameters:

  • single_scattering_albedo (_type_) – single scattering albedo

  • asymmetric_parameter (_type_) – asymmetric parameter

  • mu0 (_type_) – cosine of the incident angle

Returns:

gamma_1, gamma_2, gamma_3, mu1

Return type:

_type_

exojax.spec.toon.params_hemispheric_mean(single_scattering_albedo, asymmetric_parameter)

computes Toon+89 parameters for Hemispheric Mean approximation

Parameters:

  • single_scattering_albedo (_type_) – single scattering albedo

  • asymmetric_parameter (_type_) – asymmetric parameter

Returns:

gamma_1, gamma_2, mu1

Return type:

_type_

exojax.spec.toon.params_quadrature(single_scattering_albedo, asymmetric_parameter, mu0)

computes Toon+89 parameters for Quadrature approximation

Parameters:

  • single_scattering_albedo (_type_) – single scattering albedo

  • asymmetric_parameter (_type_) – asymmetric parameter

  • mu0 (_type_) – cosine of the incident angle

Returns:

gamma_1, gamma_2, gamma_3, mu1

Return type:

_type_

exojax.spec.toon.reduced_source_function(single_scattering_albedo, gamma_1, gamma_2, source_function, source_function_derivative, sign=1.0)

computes reduced source functions (pi mathcal{B}^+ or -)

Parameters:

  • single_scattering_albedo (_type_) – single scattering albedo

  • gamma_1 (_type_) – Toon+89 gamma_1 coefficient

  • gamma_2 (_type_) – Toon+89 gamma_2 coefficient

  • source_function (_type_) – pi B(tau)

  • source_function_derivative (_type_) – pi dB(tau)/dtau

  • sign (float) – 1.0 gives pi mathcal{B}^+ or -1.0 gives pi mathcal{B}^-, defaults to 1.0

Returns:

reduced_source_function

Return type:

_type_

exojax.spec.toon.reduced_source_function_isothermal_layer(single_scattering_albedo, gamma_1, gamma_2, source_function)

computes reduced source functions (pi mathcal{B}) for the isothermal layer

Parameters:

  • single_scattering_albedo (_type_) – single scattering albedo

  • gamma_1 (_type_) – Toon+89 gamma_1 coefficient

  • gamma_2 (_type_) – Toon+89 gamma_2 coefficient

  • source_function (_type_) – pi B(tau)

Returns:

reduced source function for the isothermal layer

Return type:

_type_

exojax.spec.toon.zetalambda_coeffs(gamma_1, gamma_2)

computes coupling coefficients zeta and lambda coefficients for Toon-type two stream approximation

Parameters:

  • gamma_1 (_type_) – Toon+89 gamma_1 coefficient

  • gamma_2 (_type_) – Toon+89 gamma_2 coefficient

Returns:

coupling zeta (+), coupling zeta (-), lambda coefficients

Return type:

_type_

exojax.spec.twostream module

Two-stream solvers and related methods

Note

ExoJAX has two types of the flux-based two-stream solvers for scattering/reflection. - fluxadding - LART

exojax.spec.twostream.compute_tridiag_diagonals_and_vector(scat_coeff, trans_coeff, piB, upper_diagonal_top, diagonal_top, vector_top)

computes the diagonals and right-handside vector from scattering and transmission coefficients for the tridiagonal system

Parameters:

  • scat_coeff (_type_) – scattering coefficient of the n-th layer, S_n

  • trans_coeff (_type_) – transmission coefficient of the n-th layer, T_n

  • () (piB) – Planck source function, piB

  • upper_diagonal_top (_type_) – a[0] upper diagonal top boundary

  • diagonal_top (_type_) – b[0] diagonal top boundary

  • vector_top (_type_) – vector top boundary

Notes

In ExoJAX 2 paper, we assume the tridiagonal form as -an F_{n+1}^+ + b_n F_n^+ - cn F_{n-1}^+ = dn

Returns:

diagonal (bn) [Nlayer], lower dianoals (cn) [Nlayer], upper diagonal (an) [Nlayer], vector (dn) [Nlayer],

Return type:

jnp arrays

exojax.spec.twostream.contribution_function_lart(cumT, Q)

computes the contribution function from LART cumlative transmission and generalized source

Parameters:

  • cumT (_type_) – cumlative transmission

  • Q (_type_) – generalized source

Returns:

contribution fnction in a vector form

Return type:

_type_

exojax.spec.twostream.set_scat_trans_coeffs(zeta_plus, zeta_minus, lambdan, dtau)

sets scattering and transmission coefficients from zeta and lambda coefficient and dtau

Parameters:

  • zeta_plus (_type_) – coupling zeta (+) coefficient (e.g. Heng 2017)

  • zeta_minus (_type_) – coupling zeta (-) coefficient (e.g. Heng 2017)

  • lambdan (_type_) – lambda coefficient

  • dtau (_type_) – optical depth interval of the layers

Returns:

transmission coefficient, scattering coeffcient

Return type:

_type_

exojax.spec.twostream.solve_fluxadding_twostream(trans_coeff, scat_coeff, reduced_source_function, reflectivity_bottom, source_bottom)

Two-stream RT solver using flux adding

Parameters:

  • trans_coeff (_type_) – Transmission coefficient

  • scat_coeff (_type_) – Scattering coefficient

  • reduced_source_function – pi mathcal{B} (Nlayer, Nnus)

  • reflectivity_bottom (_type_) – R^+_N (Nnus)

  • source_bottom (_type_) – S^+_N (Nnus)

Returns:

Effective reflectivity (hat(R^plus)), Effective source (hat(S^plus))

exojax.spec.twostream.solve_lart_twostream(diagonal, lower_diagonal, upper_diagonal, vector, flux_bottom)

Two-stream RT solver given tridiagonal system components (LART form)

Parameters:

  • diagonal (_type_) – diagonal component of the tridiagonal system (bn)

  • lower_diagonal (_type_) – lower diagonal component of the tridiagonal system (cn)

  • upper_diagonal (_type_) – upper diagonal component of the tridiagonal system (an)

  • vector (_type_) – right-hand side vector (dn)

  • flux_bottom – bottom flux FB

Note

Our definition of the tridiagonal components is an F+_(n+1) + bn F+_n + c_(n-1) F+_(n-1) = dn Notice that c_(n-1) is not cn

Returns:

cumlative hat{T}, hat{Q}, spectrum

Return type:

_type_

exojax.spec.twostream.solve_twostream_pure_absorption_numpy(trans_coeff, scat_coeff, piB)

solves pure absorption limit for two stream

Parameters:

  • trans_coeff (_type_) – transmission coefficient

  • scat_coeff (_type_) – scattering coefficient

  • piB (_type_) – pi x Planck function

Returns:

cumlative transmission, generalized source, spectrum

Return type:

_type_

exojax.spec.unitconvert module

unit conversion for spectrum.

exojax.spec.unitconvert.nu2wav(nus, wavelength_order='descending', unit='AA', values=None)

wavenumber to wavelength (AA)

Parameters:

  • nus – wavenumber (cm-1)

  • order (wavlength) – wavelength order: β€œascending” or β€œdescending”, default to β€œdescending”

  • unit – the unit of the output wavelength, β€œAA”, β€œnm”, or β€œum”

  • values – corresponding values, e.g. f(nus) for nus

Returns:

wavelength (unit) values (optional): corresponding values in the same order as wavelength, if values is not None.

exojax.spec.unitconvert.wav2nu(wav, unit, values=None)

wavelength to wavenumber.

Parameters:

  • wav – wavelength array in ascending/descending order

  • unit – the unit of the output wavelength, β€œAA”, β€œnm”, or β€œum”

  • values – corresponding values, e.g. f(wav) for wav

Returns:

wavenumber (cm-1) in ascending order values (optional): corresponding values in the same order as wavenumber, if values is not None.

Module contents