resins.models.polynomial module

Collection of models based off polynomials.

All classes within are exposed for reference only and should not be instantiated directly. For obtaining the resolution function of an instrument, please use the resins.instrument.Instrument.get_resolution_function method.

class resins.models.polynomial.DiscontinuousPolynomialModel1D(model_data: DiscontinuousPolynomialModelData, **_)

Bases: GaussianKernel1DMixin, SimpleBroaden1DMixin, InstrumentModel

Model using a 1D polynomial to model an instrument, but with values above and below certain energy transfer set to constant values.

Models the resolution as a function of energy transfer (frequencies) only, with the output model being a Gaussian. This is done by fitting a single power-series polynomial (see numpy.polynomial.polynomial.Polynomial) to the resolution curve, where the result of the polynomial is the width (sigma) of the Gaussian. The polynomial can be of any degree and is given via the PolynomialModelData. However, all sigma values below DiscontinuousPolynomialModelData.low_energy_cutoff are set to the value of DiscontinuousPolynomialModelData.low_energy_resolution and similarly all sigma values above DiscontinuousPolynomialModelData.high_energy_cutoff are set to the value of DiscontinuousPolynomialModelData.high_energy_resolution.

Parameters:

model_data: The data associated with the model for a given version of a given instrument.

Attributes:

input: The names of the columns in the omega_q array expected by all computation methods, i.e. the names of the independent variables ([Q, w]) that the model models.
data_class: Data for the DiscontinuousPolynomialModel1D model.
polynomialnumpy.polynomial.polynomial.Polynomial: The polynomial representing the resolution function.
low_energy_cutoff: The lower bound (in meV) for the energy transfer (frequencies), below which the sigma values are set to the value of low_energy_resolution.
low_energy_resolution: The value (in meV) to which sigma is set when the energy transfer is lower than low_energy_cutoff.
high_energy_cutoff: The upper bound (in meV) for the energy transfer (frequencies), above which the sigma values are set to the value of high_energy_resolution.
high_energy_resolution: The value (in meV) to which sigma is set when the energy transfer is higher than high_energy_cutoff.
citation: The citation for this model.

Methods

`__call__`(points, data, *meshes)	Broadens the `data` on the `meshes`.
`broaden`(points, data, mesh)	Broadens the `data` on the full `mesh` using the straightforward scheme.
`data_class`
`get_characteristics`(points)	Computes the broadening width at each value of energy transfer given by `points`.
`get_kernel`(points, mesh)	Computes the Gaussian kernel centered on zero on the provided `mesh` at each (energy transfer or momentum scalar) point in `points`.
`get_peak`(points, mesh)	Computes the Gaussian broadening peak on the provided `mesh` at each (energy transfer or momentum scalar) point in `points`.

data_class: alias of DiscontinuousPolynomialModelData

get_characteristics(points: Float[np.ndarray, 'energy_transfer dimension=1']) → dict[str, Float[np.ndarray, 'sigma']]

Computes the broadening width at each value of energy transfer given by points.

The model approximates the broadening using the Gaussian distribution, so the returned widths are in the form of the standard deviation (sigma).

Parameters:

points: The energy transfer in meV at which to compute the width in sigma of the kernel. This must be a sample x 1 2D array where sample is the number of energy transfers.

Returns:

characteristics: The characteristics of the broadening function, i.e. the Gaussian width as sigma in meV.

class resins.models.polynomial.DiscontinuousPolynomialModelData(*, function: str, citation: list[str], defaults: dict[str, int | float], restrictions: dict[str, list[int | float], set[int | float]], fit: list[float], low_energy_cutoff: float = -inf, low_energy_resolution: float = 0.0, high_energy_cutoff: float = inf, high_energy_resolution: float = 0.0)

Bases: ModelData

Data for the DiscontinuousPolynomialModel1D model.

Attributes:

function: The name of the function, i.e. the alias for DiscontinuousPolynomialModel1D.
citation: The citation for the model. Please use this to look up more details and cite the model.
restrictions: All constraints that the model places on the settings. If the value is a list, this signifies the range style (start, stop, step) tuple, and if it is a set, it is a set of explicitly allowed values.
defaults: The default values for the settings, used when a value is not provided when creating the model.
fit: Polynomial coefficients.
low_energy_cutoff: The lower bound (in meV) for the energy transfer (frequencies), below which the sigma values are set to the value of low_energy_resolution.
low_energy_resolution: The value (in meV) to which sigma is set when the energy transfer is lower than low_energy_cutoff.
high_energy_cutoff: The upper bound (in meV) for the energy transfer (frequencies), above which the sigma values are set to the value of high_energy_resolution.
high_energy_resolution: The value (in meV) to which sigma is set when the energy transfer is higher than high_energy_cutoff.

class resins.models.polynomial.PolynomialModel1D(model_data: PolynomialModelData, **_)

Bases: GaussianKernel1DMixin, SimpleBroaden1DMixin, InstrumentModel

Model using a 1D polynomial to model an instrument.

Models the resolution as a function of energy transfer (frequencies) only, with the output model being a Gaussian. This is done by fitting a single power-series polynomial (see numpy.polynomial.polynomial.Polynomial) to the resolution curve, where the result of the polynomial is the width (sigma) of the Gaussian. The polynomial can be of any degree and is given via the PolynomialModelData.

Parameters:

model_data: The data associated with the model for a given version of a given instrument.

Attributes:

input: The names of the columns in the omega_q array expected by all computation methods, i.e. the names of the independent variables ([Q, w]) that the model models.
data_class: Data for the PolynomialModel1D model.
polynomialnumpy.polynomial.polynomial.Polynomial: The polynomial representing the resolution function.
citation: The citation for this model.

Methods

`__call__`(points, data, *meshes)	Broadens the `data` on the `meshes`.
`broaden`(points, data, mesh)	Broadens the `data` on the full `mesh` using the straightforward scheme.
`data_class`
`get_characteristics`(points)	Computes the broadening width at each value of energy transfer (`points`).
`get_kernel`(points, mesh)	Computes the Gaussian kernel centered on zero on the provided `mesh` at each (energy transfer or momentum scalar) point in `points`.
`get_peak`(points, mesh)	Computes the Gaussian broadening peak on the provided `mesh` at each (energy transfer or momentum scalar) point in `points`.

data_class: alias of PolynomialModelData

get_characteristics(points: Float[np.ndarray, 'energy_transfer dimension=1']) → dict[str, Float[np.ndarray, 'sigma']]

Computes the broadening width at each value of energy transfer (points).

The model approximates the broadening using the Gaussian distribution, so the returned widths are in the form of the standard deviation (sigma).

Parameters:

points: The energy transfer in meV at which to compute the width in sigma of the kernel. This must be a sample x 1 2D array where sample is the number of energy transfers.

Returns:

characteristics: The characteristics of the broadening function, i.e. the Gaussian width as sigma.

class resins.models.polynomial.PolynomialModelData(*, function: str, citation: list[str], defaults: dict[str, int | float], restrictions: dict[str, list[int | float], set[int | float]], fit: list[float])

Bases: ModelData

Data for the PolynomialModel1D model.

Attributes:

function: The name of the function, i.e. the alias for PolynomialModel1D.
citation: The citation for the model. Please use this to look up more details and cite the model.
restrictions: All constraints that the model places on the settings. If the value is a list, this signifies the range style (start, stop, step) tuple, and if it is a set, it is a set of explicitly allowed values.
defaults: The default values for the settings, used when a value is not provided when creating the model.
fit: Polynomial coefficients.