optmat.solid.fitting#

Fitting a solid’s universal dispersion model to the curated data.

A fit starts from a published UDM formula of a source record (its newAD2 parameter file’s values) and frees a chosen set of its parameters. It adjusts them, by least squares, to curated n and k at their stated uncertainties:

n: refractive_index, or a refractive_index_deviation from a named formula, which the fit adds back to that formula; an index relative to room air (parameters.index_medium = "air") is taken to vacuum with the index of that air (TC-398);
k: extinction_coefficient, compared in log k, since k spans many decades;
offsets: each fitted n dataset may carry a free additive offset with a prior (its grade and temperature: silica grades differ by ~1e-5 in n, and dn/dT is ~1e-5 per kelvin);
priors: free parameters may carry priors.

The model stays causal, passive and sum-rule normalised whatever the parameters, so the fitted dielectric function is analytic like the published one. The configuration is data/solid/fits/<name>.toml; the result is stored as data/solid/models/fitted/<name>.json with its covariance (TC-322).

Module Attributes

FIT_DIRECTORY

The solid fit configurations.

Functions

`dumps`(result)	Serialise a fit result as JSON text.
`fit`(config)	Fit the configuration's free UDM parameters to its datasets.
`load_config`(name)	Load a solid fit configuration.
`validation`(result)	Compare the fitted model with each validator dataset.

Classes

`DatasetOptions`(key[, range_nm, sigma, ...])	How one curated dataset enters a fit.
`FitConfig`(name, material, description, ...)	A solid fit's configuration.
`FitResult`(config, attributes, values, ...)	A fitted model with its statistics.

class optmat.solid.fitting.DatasetOptions(key, range_nm=(0.0, inf), sigma=None, extra=0.0, offset_sigma=None, offset_group='', reference='', thermo_optic='', temperature_k=None)[source]#

Bases: object

How one curated dataset enters a fit.

Attributes:

keystr: source/dataset.
range_nmtuple of float: The vacuum-wavelength window used, nm.
sigmafloat or None: Uncertainty used where the dataset states none (n: absolute; k: relative).
extrafloat: Added in quadrature to every point’s uncertainty (same units as sigma).
offset_sigmafloat or None: The prior (one sigma) of a free additive offset in n; None for no offset.
offset_groupstr: Datasets naming the same group share one offset (a common reference level, such as whether a source’s n is relative to air); empty for the dataset’s own.
referencestr: For a refractive_index_deviation, the formula model it is relative to.
thermo_opticstr: A thermo_optic_coefficient dataset (source/dataset) that takes the values from their sample temperature to temperature_k, interpolated in wavelength; empty for none.
temperature_kfloat or None: The temperature the fit refers to, K, for thermo_optic.

extra: float = 0.0#

key: str#

offset_group: str = ''#

offset_sigma: float | None = None#

range_nm: tuple[float, float] = (0.0, inf)#

reference: str = ''#

sigma: float | None = None#

temperature_k: float | None = None#

thermo_optic: str = ''#

optmat.solid.fitting.FIT_DIRECTORY: Final = PosixPath('/home/docs/checkouts/optmat/checkouts/7/src/optmat/data/solid/fits')#: The solid fit configurations.

class optmat.solid.fitting.FitConfig(name, material, description, range_nm, start, free, scales=<factory>, added_attributes=(), added_values=<factory>, priors=<factory>, fitted=(), validators=(), digest='')[source]#

Bases: object

A solid fit’s configuration.

Attributes:

namestr: The configuration’s name (its file stem).
materialstr: The material’s id.
descriptionstr: What the fit is and why.
range_nmtuple of float: The range the fitted model supports, nm.
startstr: The starting UDM formula, <source>/<formula id> of a curated source whose formula holds a newAD2 parameter file’s values as its terms.
freetuple of str: The freed parameters, in newAD2’s names.
scalesdict of str to tuple of str: Groups of parameters multiplied by one fitted factor each (the OH bands of a grade, say), by the group’s name.
added_attributestuple of str: Terms added to the start model (loc=1 adds one Gaussian peak).
added_valuesdict of str to float: The added terms’ starting parameters.
priorsdict of str to tuple of float: Priors (value, sigma) on free parameters.
fitted, validatorstuple of DatasetOptions: The fitted datasets and the datasets only compared.
digeststr: The configuration file’s SHA-256.

added_attributes: tuple[str, ...] = ()#

added_values: Mapping[str, float]#

description: str#

digest: str = ''#

fitted: tuple[DatasetOptions, ...] = ()#

free: tuple[str, ...]#

material: str#

name: str#

priors: Mapping[str, tuple[float, float]]#

range_nm: tuple[float, float]#

scales: Mapping[str, tuple[str, ...]]#

start: str#

validators: tuple[DatasetOptions, ...] = ()#

class optmat.solid.fitting.FitResult(config, attributes, values, covariance, offsets, chi2, dof, dataset_chi2)[source]#

Bases: object

A fitted model with its statistics.

Attributes:

configFitConfig: The configuration.
attributestuple of str: The UDM’s attributes.
valuesdict of str to float: Every UDM parameter, fitted or fixed.
covariancenumpy.ndarray: The covariance of the free parameters, then of the group scales, then of the offsets (in their own units), Birge-scaled when the reduced chi-squared exceeds 1.
offsetsdict of str to float: The fitted n offset of each dataset that has one.
chi2float: The total chi-squared, priors included.
dofint: Degrees of freedom.
dataset_chi2dict of str to tuple: Points and chi-squared of each fitted dataset.

attributes: tuple[str, ...]#

chi2: float#

config: FitConfig#

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

dataset_chi2: Mapping[str, tuple[int, float]]#

dof: int#

property model: UniversalDispersionModel#

The fitted UDM.

Returns:

UniversalDispersionModel: The model at the fitted parameters.

offsets: Mapping[str, float]#

values: Mapping[str, float]#

optmat.solid.fitting.dumps(result)[source]#

Serialise a fit result as JSON text.

Parameters:

resultFitResult: The result.

Returns:

str: Indented JSON: the full parameter set, the covariance of the free parameters, the statistics and the configuration’s digest.

optmat.solid.fitting.fit(config)[source]#

Fit the configuration’s free UDM parameters to its datasets.

Parameters:

configFitConfig: The configuration.

Returns:

FitResult: The fitted model, covariance and statistics.

optmat.solid.fitting.load_config(name)[source]#

Load a solid fit configuration.

Parameters:

namestr or pathlib.Path: The name (data/solid/fits/<name>.toml) or a path.

Returns:

FitConfig: The configuration.

Raises:

DataError: If it is malformed or names an unknown dataset.

optmat.solid.fitting.validation(result)[source]#

Compare the fitted model with each validator dataset.

Parameters:

resultFitResult: The fit.

Returns:

dict of str to dict: Per validator: the points, chi-squared and mean deviation (n: absolute; log k: relative).