rtd_sensor.fitting

The public fitting API was introduced in rtd-sensor 0.6.0. rtd-sensor 0.7.0 adds characterized IEC 60751 R0 fitting, selected custom Callendar–Van Dusen parameter fitting, fitted-parameter covariance/diagnostics, calibration provenance, and explicit reference-temperature uncertainty handling.

CalibrationObservation

Introduced in: rtd-sensor 0.6.0

CalibrationObservation(
    temperature_c: float,
    resistance_ohms: float,
    weight: float | None = None,
    standard_uncertainty_ohms: float | None = None,
    standard_uncertainty_temperature_c: float | None = None,
)

weight and standard_uncertainty_ohms are mutually exclusive on one observation. standard_uncertainty_temperature_c records uncertainty in the calibration/reference temperature coordinate; current fitters do not use it as a weight. Fits reject it by default unless the caller explicitly chooses temperature_uncertainty_handling="retain_not_used". The standard_uncertainty_temperature_c field was added in rtd-sensor 0.7.0.

Type aliases added in rtd-sensor 0.7.0

CalibrationTemperatureUncertaintyHandling = Literal["reject", "retain_not_used"]
CallendarVanDusenFitParameter = Literal["r0_ohms", "a", "b", "c"]

CalibrationProvenance

Introduced in: rtd-sensor 0.7.0

Immutable application-neutral calibration context retained only with fit evidence. Optional fields are certificate_identifier, calibration_date, laboratory, reference_standard, source_document, and notes. These values do not alter the fit or numerical model and are not automatically copied into portable-model metadata.

fit_iec60751_r0

Introduced in: rtd-sensor 0.7.0

fit_iec60751_r0(
    observations: Iterable[CalibrationObservation],
    *,
    minimum_temperature_c: float | None = None,
    maximum_temperature_c: float | None = None,
    name: str = "Fitted IEC 60751 RTD",
    temperature_uncertainty_handling: Literal["reject", "retain_not_used"] = "reject",
    provenance: CalibrationProvenance | None = None,
) -> IEC60751R0FitResult

Fits only the reference resistance R0 while retaining the package's verified IEC 60751 PT-385 characteristic. With two or more distinct temperatures, an omitted model range defaults to the observation span. A single-temperature fit requires an explicit minimum and maximum model temperature.

Explicit range limits describe intended model applicability, not the span of calibration evidence. With an independent basis they may be broader, narrower, or disjoint from the observation span, but they must remain within the supported IEC characteristic range. The evidence retains the observation span separately so this assumption remains visible.

fit_callendar_van_dusen

Introduced in: rtd-sensor 0.7.0

fit_callendar_van_dusen(
    observations: Iterable[CalibrationObservation],
    *,
    fit_parameters: Iterable[CallendarVanDusenFitParameter],
    r0_ohms: float | None = None,
    a: float | None = None,
    b: float | None = None,
    c: float | None = None,
    minimum_temperature_c: float | None = None,
    maximum_temperature_c: float | None = None,
    name: str = "Fitted Callendar-Van Dusen RTD",
    coefficient_source: str | None = None,
    temperature_uncertainty_handling: Literal["reject", "retain_not_used"] = "reject",
    provenance: CalibrationProvenance | None = None,
) -> CallendarVanDusenFitResult

Fits an explicitly requested subset of r0_ohms, a, b, and c. Any parameter not fitted must be supplied as a fixed value, except c may be omitted for a wholly non-negative model range. The fitting system is algebraically linearized and column-scaled before Householder QR. Rank deficiency and severe scaled-system ill-conditioning are rejected as non-identifiable parameter fits.

Fitting c requires at least one negative-temperature observation because the CVD C term is zero at and above 0 °C. When any shape coefficient (a, b, or c) is fitted, the declared model range may be narrowed but not extended beyond the calibration-observation span. An R0-only CVD fit with fixed shape coefficients may use an independently justified explicit applicability range.

CallendarVanDusenFitResult / CallendarVanDusenFitEvidence

Introduced in: rtd-sensor 0.7.0

The result contains a validated CallendarVanDusenRTDModel plus immutable fit evidence. Evidence identifies the fitted parameters, residuals, observation span separately from the declared model range, weighting method, chi-square diagnostics when absolute resistance uncertainties are supplied, parameter covariance, scaled-system condition diagnostic, linearized parameter names, and design-column scales used for identifiability/stability.

IEC60751R0FitResult

Introduced in: rtd-sensor 0.7.0

Fields:

model: IEC60751RTDModel
evidence: IEC60751R0FitEvidence

IEC60751R0FitEvidence

Introduced in: rtd-sensor 0.7.0

Key fields include observations, calibration/reference-temperature uncertainty treatment, optional CalibrationProvenance, resistance residuals, counts/degrees of freedom, observation span, declared model range, RMS/max residuals, weighting diagnostics, fitted-parameter covariance when available, and the fitting method.

FitParameterCovariance

Introduced in: rtd-sensor 0.7.0

Immutable fit evidence describing a fitted-parameter covariance matrix. Key fields:

parameter_names: tuple[str, ...]
covariance_matrix: tuple[tuple[float, ...], ...]
estimation_method: str
parameterization: str
parameter_transformation: str | None

standard_uncertainties and correlation_matrix are derived read-only properties. The correlation matrix is particularly useful for spotting strongly coupled fitted CVD or polynomial parameters; entries involving a zero-variance parameter are None because the correlation coefficient is undefined.

For fits that supply an absolute standard_uncertainty_ohms on every observation, fit evidence also reports chi_squared; reduced_chi_squared is reported when residual degrees of freedom are positive. These are residual-consistency diagnostics under the stated resistance-uncertainty model, not automatic acceptance criteria.

For an IEC R0 fit the single parameter is r0_ohms. Custom CVD fits expose covariance in the actual fitted subset of the public r0_ohms, a, b, c parameter basis after transforming out of the internal linearized product basis. When R0 and a shape coefficient are fitted jointly, parameter_transformation records that this public-parameter covariance uses a first-order ratio/Jacobian transformation from the exact linearized-fit covariance. For polynomial fits the parameterization is the unnormalized resistance power series at the returned model's reference temperature, with parameter names a0, a1, and so on. a0 equals the model reference resistance; higher a values are the corresponding resistance-space coefficients rather than the model's normalized coefficients.

Unweighted and relative-weighted fits require positive residual degrees of freedom to estimate the common residual-variance scale. When covariance cannot be estimated for that reason, parameter_covariance is None and the fit evidence records parameter_covariance_unavailable_reason. The same field reports the rare case where covariance arithmetic is numerically invalid, including non-finite values or a negative diagonal variance produced by floating-point error. When every observation supplies an absolute resistance standard uncertainty, covariance comes directly from those uncertainties and can be available even for a saturated fit.

fit_polynomial

Introduced in: rtd-sensor 0.6.0. The temperature_uncertainty_handling and provenance arguments were added in rtd-sensor 0.7.0.

fit_polynomial(
    observations: Iterable[CalibrationObservation],
    *,
    degree: int,
    minimum_temperature_c: float | None = None,
    maximum_temperature_c: float | None = None,
    name: str = "Fitted polynomial RTD",
    coefficient_source: str | None = None,
    temperature_uncertainty_handling: Literal["reject", "retain_not_used"] = "reject",
    provenance: CalibrationProvenance | None = None,
) -> PolynomialFitResult

Returns a validated polynomial model plus immutable evidence. Raises RTDFitError when observations cannot produce an acceptable deployable model.

PolynomialFitResult

Introduced in: rtd-sensor 0.6.0

Fields:

model: PolynomialRTDModel
evidence: PolynomialFitEvidence

PolynomialFitEvidence

Introduced in: rtd-sensor 0.6.0; covariance, chi-square diagnostics, reference-temperature uncertainty treatment, and calibration provenance were added in rtd-sensor 0.7.0.

Key fields include observations, calibration/reference-temperature uncertainty treatment, optional CalibrationProvenance, residuals, degree, counts/degrees of freedom, fit range, RMS/max residuals, weighting diagnostics, chi-square diagnostics when absolute resistance uncertainties are supplied, fitted-parameter covariance when available, condition number, solver, and scaling information.

See Calibration fitting.