SpectralShapeSkewedGaussian

class glotaran.builtin.models.spectral.shape.SpectralShapeSkewedGaussian[source]

Bases: object

A (skewed) Gaussian spectral shape

Attributes Summary

`amplitude`
`label`
`location`
`skewness`
`type`
`width`

Methods Summary

`calculate`	Calculate a (skewed) Gaussian shape for a given `axis`.
`calculate_gaussian`	Calculate a normal Gaussian shape for a given `axis`.
`calculate_skewed_gaussian`	Calculate the skewed Gaussian shape for `axis`.
`fill`	Returns a copy of the {cls._name} instance with all members which are Parameters are replaced by the value of the corresponding parameter in the parameter group.
`from_dict`
`from_list`
`mprint`
`validate`

Methods Documentation

property amplitude: glotaran.parameter.parameter.Parameter

calculate(axis: numpy.ndarray) → numpy.ndarray[source]

Calculate a (skewed) Gaussian shape for a given axis.

If a non-zero skewness parameter was added calculate_skewed_gaussian() will be used. Otherwise it will use calculate_gaussian().

Parameters: axis (np.ndarray) – The axis to calculate the shape for.
Returns: shape – A Gaussian shape.
Return type: numpy.ndarray

Note

Internally axis is converted from $\mbox{nm}$ to $1/\mbox{cm}$ , thus location and width also need to be provided in $1/\mbox{cm}$ (1e7/value_in_nm).

calculate_gaussian(axis: numpy.ndarray) → numpy.ndarray[source]

Calculate a normal Gaussian shape for a given axis.

The following equation is used for the calculation:

$f(x, A, x_0, \Delta) = A \exp \left({- \frac{ \log{\left(2 \right) \left(2(x - x_{0})\right)^{2} }}{\Delta^{2}}}\right)$

The parameters of the equation represent the following attributes of the shape:

$x$ : axis
$A$ : amplitude
$x_0$ : location
$\Delta$ : width

In this formalism, $\Delta$ represents the full width at half maximum (FWHM). Compared to the more common definition $\exp \left(- (x-\mu )^{2}/(2\sigma^{2})\right)$ we have $\sigma = \Delta/(2\sqrt{2\ln(2)})=\Delta/2.35482$

Parameters: axis (np.ndarray) – The axis to calculate the shape for.
Returns: An array representing a Gaussian shape.
Return type: np.ndarray

calculate_skewed_gaussian(axis: numpy.ndarray) → numpy.ndarray[source]

Calculate the skewed Gaussian shape for axis.

The following equation is used for the calculation:

$f(x, x_0, A, \Delta, b) = \left\{ \begin{array}{ll} 0 & \mbox{if } \theta \leq 0 \\ A \exp \left({- \dfrac{\log{\left(2 \right)} \log{\left(\theta(x, x_0, \Delta, b) \right)}^{2}}{b^{2}}}\right) & \mbox{if } \theta > 0 \end{array} \right.$

With:

$\theta(x, x_0, \Delta, b) = \frac{2 b \left(x - x_{0}\right) + \Delta}{\Delta}$

The parameters of the equation represent the following attributes of the shape:

$x$ : axis
$A$ : amplitude
$x_0$ : location
$\Delta$ : width
$b$ : skewness

Where $\Delta$ represents the full width at half maximum (FWHM), see calculate_gaussian().

Note that in the limit of skewness parameter $b$ equal to zero $f(x, x_0, A, \Delta, b)$ simplifies to a normal gaussian (since $\lim_{b \to 0} \frac{\ln(1+bx)}{b}=x$ ), see the definition in calculate_gaussian().

Parameters: axis (np.ndarray) – The axis to calculate the shape for.
Returns: An array representing a skewed Gaussian shape.
Return type: np.ndarray

fill(model: Model, parameters: ParameterGroup) → cls

Returns a copy of the {cls._name} instance with all members which are Parameters are replaced by the value of the corresponding parameter in the parameter group.

Parameters

model – A glotaran model.
parameter (ParameterGroup) – The parameter group to fill from.

classmethod from_dict(values: dict) → cls

classmethod from_list(values: list) → cls

property label: str

property location: glotaran.parameter.parameter.Parameter

mprint(parameters: ParameterGroup = None, initial_parameters: ParameterGroup = None) → str

property skewness: glotaran.parameter.parameter.Parameter

property type: str

validate(model: Model, parameters=None) → list[str]

property width: glotaran.parameter.parameter.Parameter