optmat.gas.models.fitted#

The models fitted here, loaded from data/gas/models/fitted/<name>.json.

Each file is written by tools/fit/run.py from a fit configuration (data/gas/fits/<name>.toml) and records the model’s terms, their covariance, the fitted dataset scales, the chi-squared per dataset and the configuration’s SHA-256.

Functions

`fitted_model`(name)	Return one stored fitted model, reading only its record.
`fitted_models`()	Return every stored fitted model, by name.

Classes

`FittedModel`(gas, name, citation, ...[, ...])	An oscillator model fitted here, with its covariance and statistics.
`TemperatureCoefficient`(coefficient_per_k, ...)	A measured temperature coefficient of a gas polarizability (OEP 1, section 4.9).

class optmat.gas.models.fitted.FittedModel(gas, name, citation, wavelength_range, kind, strengths=(), energies=(), labels=(), offset_au=0.0, retardation_au=0.0, absorption=None, n_lines=0, n_fixed=0, covariance=<factory>, reduced_chi2=0.0, record=<factory>, *, status='user', status_reason='', modified=(), base='', intervals=())[source]#

Bases: OscillatorModel

An oscillator model fitted here, with its covariance and statistics.

Its overrides add two inputs to the oscillator model’s: infrared, a pair of sequences (strengths, energies in hartree) that replaces the fixed infrared terms whole, and infrared_scale, a factor on their strengths. The term counts are fixed otherwise. An override drops the covariance and the chi-squared (NaN): the fit’s uncertainty does not carry over.

Attributes:

n_linesint: How many leading terms are resonance lines at fixed energies.
n_fixedint: How many trailing terms are fixed (the infrared bands), outside the covariance.
covariancenumpy.ndarray: Covariance of the strengths and of the effective terms’ energies.
reduced_chi2float: Chi-squared per degree of freedom of the fit.
recorddict: The stored record, for reports.

DERIVED: ClassVar[tuple[str, ...]] = ('wavelength_range', 'covariance', 'n_fixed', 'n_lines', 'reduced_chi2')#: Fields derived from the inputs, which an override may not name.

EVALUATION_VERSION: ClassVar[int] = 1#

INPUTS: ClassVar[tuple[str, ...]] = ('energies', 'intervals', 'labels', 'offset_au', 'retardation_au', 'strengths', 'infrared', 'infrared_scale')#: The parameters with_parameters() may change.

covariance: Float[ndarray, 'q q']#

property derived_sha256: str#

The SHA-256 of the derived tables the fit read, or empty (OEP 3).

Returns:

str: optmat.gas.infrared.derived_digest() when the fit was made.

dispersion_sigma_au(omega, order, *, birge=True)[source]#

Return the absolute one-sigma uncertainty of a dispersion derivative.

sqrt(g^T Sigma g), with g the gradient of d^k (omega alpha) / d omega^k (dispersion_au()) with respect to the fitted parameters and Sigma their covariance. It stays finite where the derivative crosses zero (OEP 2, section 4). The fixed terms carry none.

Parameters:

omeganumpy.ndarray: Photon energies, hartree.
orderint: The order k >= 2.
birgebool, optional: Scale the covariance by the reduced chi-squared when it exceeds one.

Returns:

numpy.ndarray: One-sigma uncertainty, atomic units (those of alpha times E_h^(1 - k)).

Raises:

ValueError: If order is below 2.

dispersion_sigma_relative(omega, order, *, birge=True)[source]#

Return the relative one-sigma uncertainty of a dispersion coefficient.

In the dilute limit the propagation constant is beta = (omega / c) [1 + N alpha / (2 epsilon_0)], so for k >= 2 each beta_k = d^k beta / d omega^k is proportional to d^k (omega alpha) / d omega^k and its relative uncertainty is that of the derivative, independent of the density (k = 2 is the group-velocity dispersion, k = 3 the third-order dispersion). Lorentz-Lorenz changes the relative uncertainty only at the order of the susceptibility (below 1e-3 of itself at a few bar). The magnetic term is frequency-independent and drops out.

Parameters:

omeganumpy.ndarray: Photon energies, hartree, below the lowest term’s energy.
orderint: The order k >= 2 of the coefficient.
birgebool, optional: Scale the covariance by the reduced chi-squared when it exceeds one.

Returns:

numpy.ndarray: sigma(beta_k) / |beta_k|: dispersion_sigma_au() over |dispersion_au|.

Raises:

ValueError: If order is below 2.

property gap_reasons: tuple[str, ...]#

The reason of each gap between two qualified intervals (OEP 3).

Returns:

tuple of str: absorption, representation, representation: kept band or width; empty for a fit with one interval.

property infrared_temperature: float | None#

The temperature of the fit’s fixed infrared terms, K.

Returns:

float or None: 296 K for HITRAN’s line intensities (298.1 K for SF6’s cross-section); None for a fit without infrared terms.

n_fixed: int = 0#

n_lines: int = 0#

property n_rotational: int#

How many of the fixed terms are the rotational system (OEP 3).

Returns:

int: They follow the fitted terms; 0 for a fit without the derived rules.

polarizability_sigma_au(omega, *, birge=True)[source]#

Return the one-sigma uncertainty of the polarizability.

Parameters:

omeganumpy.ndarray: Photon energies, hartree.
birgebool, optional: Scale the covariance by the reduced chi-squared when it exceeds one.

Returns:

numpy.ndarray: One-sigma uncertainty, atomic units.

record: Mapping[str, object]#

reduced_chi2: float = 0.0#

property reference_temperature: float | None#

The temperature the fit’s polarizability refers to, K, where it declares one.

Returns:

float or None: 293.15 K for N2, O2, CO2, N2O, H2 and D2; None for the atoms and for CH4, CO and SF6, whose levels rest on data at other temperatures without a curated coefficient (TC-730). Evaluation does not depend on it.

representation_bound_au(omega, order)[source]#

Return the bound on the representation error of the fixed infrared terms.

B_m(omega) >= |D_m[model] - D_m[reference]| (OEP 3, section 4) from the gas’s derived tables: order 0 bounds the polarizability, 2 and 3 the dispersion d^m (omega alpha) / d omega^m. It is defined in every qualified interval.

Parameters:

omeganumpy.ndarray: Photon energies, hartree.
orderint: 0, 2 or 3.

Returns:

numpy.ndarray: The bound, atomic units (those of alpha times E_h^(1 - m) for order m), NaN outside every qualified interval.

Raises:

ValueError: For another order.
DataError: For a fit that read no derived tables.

Warns:

ModelRangeWarning: Outside every qualified interval.

property temperature_coefficient: TemperatureCoefficient | None#

The measured temperature coefficient of the polarizability, if curated.

Returns:

TemperatureCoefficient or None: For N2, O2 and CO2 (TC-730); None otherwise.

class optmat.gas.models.fitted.TemperatureCoefficient(coefficient_per_k, sigma_per_k, wavelength, dataset, reason)[source]#

Bases: object

A measured temperature coefficient of a gas polarizability (OEP 1, section 4.9).

Attributes:

coefficient_per_kfloat: A_theta, per K, in A_R(T) = A_R(T0) [1 + A_theta (T - T0)].
sigma_per_kfloat: Its standard uncertainty, per K.
wavelengthfloat: The vacuum wavelength it is measured at, m.
datasetstr: The curated dataset it comes with.
reasonstr: Where it is printed.

coefficient_per_k: float#

dataset: str#

reason: str#

sigma_per_k: float#

wavelength: float#

optmat.gas.models.fitted.fitted_model(name)[source]#

Return one stored fitted model, reading only its record.

Parameters:

namestr: The model’s name, fit/<name>.

Returns:

FittedModel: The model.

Raises:

KeyError: If no fit is stored under that name.
DataError: If the stored record names another fit.

optmat.gas.models.fitted.fitted_models()[source]#

Return every stored fitted model, by name.

Returns:

dict of str to FittedModel: Models named fit/<name>.