Parametric fit features

`light_curve.BazinFit`

Bases: light_curve.light_curve_ext._FeatureEvaluator

Bazin function fit

Five fit parameters and goodness of fit (reduced $\chi^2$) of the Bazin function developed for core-collapsed supernovae:

\[ f(t) = A \frac{ \mathrm{e}^{ -(t-t_0)/\tau_\mathrm{fall} } }{ 1 + \mathrm{e}^{ -(t - t_0) / \tau_\mathrm{rise} } } + B. \]

Note, that the Bazin function is developed to be used with fluxes, not magnitudes. Also note a typo in the Eq. (1) of the original paper, the minus sign is missed in the "rise" exponent.

Depends on: time, magnitude, magnitude error
Minimum number of observations: 6
Number of features: 6

Bazin et al. 2009 DOI:10.1051/0004-6361/200911847

Names and description of the output features: - bazin_fit_amplitude: half amplitude of the Bazin function (A) - bazin_fit_baseline: baseline of the Bazin function (B) - bazin_fit_reference_time: reference time of the Bazin fit (t0) - bazin_fit_rise_time: rise time of the Bazin function (tau_rise) - bazin_fit_fall_time: fall time of the Bazin function (tau_fall) - bazin_fit_reduced_chi2: Bazin fit quality (reduced chi2)

Parameters:

Name	Type	Description	Default
`algorithm`	`str`	Non-linear least-square algorithm, supported values are: mcmc, ceres, mcmc-ceres, lmsder, mcmc-lmsder, nuts, nuts-ceres, nuts-lmsder.	required
`mcmc_niter`	`int`	Number of MCMC iterations, default is 128	required
`ceres_niter`	`int`	Number of Ceres iterations, default is 10	required
`ceres_loss_reg`	`float`	Ceres loss regularization, default is to use square norm as is, if set to a number, the loss function is regularized to descriminate outlier residuals larger than this value. Default is None which means no regularization.	required
`lmsder_niter`	`int`	Number of LMSDER iterations, default is 10	required
`init`	`list or None`	Initial conditions, must be `None` or a `list` of `float`s or `None`s. The length of the list must be 5, `None` values will be replaced with some defauls values. It is supported by MCMC only	required
`bounds`	`list of tuples or None`	Boundary conditions, must be `None` or a `list` of `tuple`s of `float`s or `None`s. The length of the list must be 5, boundary conditions must include initial conditions, `None` values will be replaced with some broad defaults. It is supported by MCMC only	required
`ln_prior`	`str or list of ln_prior.LnPrior1D or None`	Prior for MCMC, None means no prior. It is specified by a string literal or a list of 5 `ln_prior.LnPrior1D` objects, see `ln_prior` submodule for corresponding functions. Available string literals are: 'no': no prior	required
`transform`	`bool or None`	If `False` or `None` (default) output is not transformed. If `True` output is transformed as following: - Half-amplitude A is transformed as `zp - 2.5 lg(2*A)`, zp = 8.9, so that the amplitude is assumed to be the object peak flux in Jy. - baseline flux is normalised by A: baseline -> baseline / A - reference time is removed - goodness of fit is transformed as `ln(reduced chi^2 + 1)` to reduce its spread - other parameters are not transformed See `names` and `descriptions` attributes an object for the list and order of features.	required

Attributes:

Name	Type	Description
`names`	`list of str`	Feature names
`descriptions`	`list of str`	Feature descriptions
`supported_algorithms`	`list of str`	Available argument values for the constructor

Methods:

Name	Description
`__call__`	Extract features and return them as a numpy array Parameters t : numpy.ndarray of np.float32 or np.float64 dtype Time moments m : numpy.ndarray Signal in magnitude or fluxes. Refer to the feature description to decide which would work better in your case sigma : numpy.ndarray, optional Observation error, if None it is assumed to be unity fill_value : float or None, optional Value to fill invalid feature values, for example if count of observations is not enough to find a proper value. None causes exception for invalid features sorted : bool or None, optional Specifies if input array are sorted by time moments. True is for certainly sorted, False is for unsorted. If None is specified than sorting is checked and an exception is raised for unsorted `t` check : bool, optional Check all input arrays for NaNs, `t` and `m` for infinite values cast : bool, optional Allows non-numpy input and casting of arrays to a common dtype. If `False`, inputs must be `np.ndarray` instances with matched dtypes. Casting provides more flexibility with input types at the cost of performance. Returns ndarray of np.float32 or np.float64 Extracted feature array
`many`	Parallel light curve feature extraction It is a parallel executed equivalent of def many(self, lcs, , fill_value=None, sorted=None, check=True): ... return np.stack( ... [ ... self( ... lc, ... fill_value=fill_value, ... sorted=sorted, ... check=check, ... cast=False, ... ) ... for lc in lcs ... ] ... ) Parameters lcs : list of (t, m, sigma) or Arrow array Either a list of light curves packed into three-tuples (all numpy.ndarray of the same dtype), or an Arrow array/chunked array of type List<Struct<...>> where the selected fields share the same float dtype (float32 or float64). Arrow input is auto-detected via the arrow_c_array / arrow_c_stream protocol and enables zero-copy data access from pyarrow, polars, and other Arrow-compatible libraries. arrow_fields : list of (str or int) Required when lcs is an Arrow array. Field names or indices specifying which struct fields to use as t, m, and optionally sigma. Must contain 2 elements [t, m] or 3 elements [t, m, sigma]. Each element may be a field name (str) or a zero-based positional index (int); all elements must be of the same type. Ignored for non-Arrow input. fill_value : float or None, optional Fill invalid values by this or raise an exception if None sorted : bool or None, optional Specifies if input array are sorted by time moments, see call documentation for details check : bool, optional Check all input arrays for NaNs, `t` and `m` for infinite values n_jobs : int Number of tasks to run in paralell. Default is -1 which means run as many jobs as CPU count. See rayon rust crate documentation for details
`model`	Underlying parametric model function Parameters t : np.ndarray of np.float32 or np.float64 Time moments, can be unsorted params : np.ndaarray of np.float32 or np.float64 Parameters of the model, this array can be longer than actual parameter list, the beginning part of the array will be used in this case, see Examples section in the class documentation. cast : bool, optional Cast inputs to np.ndarray of the same dtype Returns np.ndarray of np.float32 or np.float64 Array of model values corresponded to the given time moments

Examples:

>>> import numpy as np
>>> from light_curve import BazinFit
>>>
>>> fit = BazinFit('mcmc')
>>> t = np.linspace(0, 10, 101)
>>> flux = 1 + (t - 3) ** 2
>>> fluxerr = np.sqrt(flux)
>>> result = fit(t, flux, fluxerr, sorted=True)
>>> # Result is built from a model parameters and reduced chi^2
>>> # So we can use as a `params` array of the static `.model()` method
>>> model = BazinFit.model(t, result)

`supported_algorithms = ['mcmc', 'ceres', 'mcmc-ceres', 'lmsder', 'mcmc-lmsder', 'nuts', 'nuts-ceres', 'nuts-lmsder']` `class-attribute`

Built-in mutable sequence.

If no argument is given, the constructor creates a new empty list. The argument must be an iterable if specified.

`model` `staticmethod`

model(t, params, *, cast=False) Underlying parametric model function

Parameters:

Name	Type	Description	Default
`t`	`np.ndarray of np.float32 or np.float64`	Time moments, can be unsorted	required
`params`	`np.ndaarray of np.float32 or np.float64`	Parameters of the model, this array can be longer than actual parameter list, the beginning part of the array will be used in this case, see Examples section in the class documentation.	required
`cast`	`bool`	Cast inputs to np.ndarray of the same dtype	`False`

Returns:

Type	Description
`np.ndarray of np.float32 or np.float64`	Array of model values corresponded to the given time moments

`light_curve.LinexpFit`

Bases: light_curve.light_curve_ext._FeatureEvaluator

Linexp function fit

Four fit parameters and goodness of fit (reduced $\chi^2$) of the Linexp function developed for core-collapsed supernovae:

\[ f(t) = A \frac{(t-t_0)}{\tau} \times \exp{\left(\frac{(t-t_0)}{\tau}\right)} + B. \]

Note, that the Linexp function is developed to be used with fluxes, not magnitudes.

Depends on: time, flux, flux error
Minimum number of observations: 5
Number of features: 5

Names and description of the output features: - linexp_fit_amplitude: Amplitude of the Linexp function (A) - linexp_fit_reference_time: reference time of the Linexp fit (t0) - linexp_fit_fall_time: fall time of the Linexp function (tau) - linexp_fit_baseline: baseline of the Linexp function (B) - linexp_fit_reduced_chi2: Linexp fit quality (reduced chi2)

Parameters:

Name	Type	Description	Default
`algorithm`	`str`	Non-linear least-square algorithm, supported values are: mcmc, ceres, mcmc-ceres, lmsder, mcmc-lmsder, nuts, nuts-ceres, nuts-lmsder.	required
`mcmc_niter`	`int`	Number of MCMC iterations, default is 128	required
`ceres_niter`	`int`	Number of Ceres iterations, default is 10	required
`ceres_loss_reg`	`float`	Ceres loss regularization, default is to use square norm as is, if set to a number, the loss function is regularized to descriminate outlier residuals larger than this value. Default is None which means no regularization.	required
`lmsder_niter`	`int`	Number of LMSDER iterations, default is 10	required
`init`	`list or None`	Initial conditions, must be `None` or a `list` of `float`s or `None`s. The length of the list must be 4, `None` values will be replaced with some defauls values. It is supported by MCMC only	required
`bounds`	`list of tuples or None`	Boundary conditions, must be `None` or a `list` of `tuple`s of `float`s or `None`s. The length of the list must be 4, boundary conditions must include initial conditions, `None` values will be replaced with some broad defaults. It is supported by MCMC only	required
`ln_prior`	`str or list of ln_prior.LnPrior1D or None`	Prior for MCMC, None means no prior. It is specified by a string literal or a list of 4 `ln_prior.LnPrior1D` objects, see `ln_prior` submodule for corresponding functions. Available string literals are: 'no': no prior	required
`transform`	`bool or None`	If `False` or `None` (default) output is not transformed. If `True` output is transformed as following: - Half-amplitude A is transformed as `zp - 2.5 lg(2*A)`, zp = 8.9, so that the amplitude is assumed to be the object peak flux in Jy. - baseline flux is normalised by A: baseline -> baseline / A - reference time is removed - goodness of fit is transformed as `ln(reduced chi^2 + 1)` to reduce its spread - other parameters are not transformed See `names` and `descriptions` attributes an object for the list and order of features.	required

Attributes:

Name	Type	Description
`names`	`list of str`	Feature names
`descriptions`	`list of str`	Feature descriptions
`supported_algorithms`	`list of str`	Available argument values for the constructor

Methods:

Name	Description
`__call__`	Extract features and return them as a numpy array Parameters t : numpy.ndarray of np.float32 or np.float64 dtype Time moments m : numpy.ndarray Signal in magnitude or fluxes. Refer to the feature description to decide which would work better in your case sigma : numpy.ndarray, optional Observation error, if None it is assumed to be unity fill_value : float or None, optional Value to fill invalid feature values, for example if count of observations is not enough to find a proper value. None causes exception for invalid features sorted : bool or None, optional Specifies if input array are sorted by time moments. True is for certainly sorted, False is for unsorted. If None is specified than sorting is checked and an exception is raised for unsorted `t` check : bool, optional Check all input arrays for NaNs, `t` and `m` for infinite values cast : bool, optional Allows non-numpy input and casting of arrays to a common dtype. If `False`, inputs must be `np.ndarray` instances with matched dtypes. Casting provides more flexibility with input types at the cost of performance. Returns ndarray of np.float32 or np.float64 Extracted feature array
`many`	Parallel light curve feature extraction It is a parallel executed equivalent of def many(self, lcs, , fill_value=None, sorted=None, check=True): ... return np.stack( ... [ ... self( ... lc, ... fill_value=fill_value, ... sorted=sorted, ... check=check, ... cast=False, ... ) ... for lc in lcs ... ] ... ) Parameters lcs : list of (t, m, sigma) or Arrow array Either a list of light curves packed into three-tuples (all numpy.ndarray of the same dtype), or an Arrow array/chunked array of type List<Struct<...>> where the selected fields share the same float dtype (float32 or float64). Arrow input is auto-detected via the arrow_c_array / arrow_c_stream protocol and enables zero-copy data access from pyarrow, polars, and other Arrow-compatible libraries. arrow_fields : list of (str or int) Required when lcs is an Arrow array. Field names or indices specifying which struct fields to use as t, m, and optionally sigma. Must contain 2 elements [t, m] or 3 elements [t, m, sigma]. Each element may be a field name (str) or a zero-based positional index (int); all elements must be of the same type. Ignored for non-Arrow input. fill_value : float or None, optional Fill invalid values by this or raise an exception if None sorted : bool or None, optional Specifies if input array are sorted by time moments, see call documentation for details check : bool, optional Check all input arrays for NaNs, `t` and `m` for infinite values n_jobs : int Number of tasks to run in paralell. Default is -1 which means run as many jobs as CPU count. See rayon rust crate documentation for details
`model`	Underlying parametric model function Parameters t : np.ndarray of np.float32 or np.float64 Time moments, can be unsorted params : np.ndaarray of np.float32 or np.float64 Parameters of the model, this array can be longer than actual parameter list, the beginning part of the array will be used in this case, see Examples section in the class documentation. cast : bool, optional Cast inputs to np.ndarray of the same dtype Returns np.ndarray of np.float32 or np.float64 Array of model values corresponded to the given time moments

Examples:

>>> import numpy as np
>>> from light_curve import LinexpFit
>>>
>>> fit = LinexpFit('mcmc')
>>> t = np.linspace(0, 10, 101)
>>> flux = 1 + (t - 3) ** 2
>>> fluxerr = np.sqrt(flux)
>>> result = fit(t, flux, fluxerr, sorted=True)
>>> # Result is built from a model parameters and reduced chi^2
>>> # So we can use as a `params` array of the static `.model()` method
>>> model = LinexpFit.model(t, result)

`supported_algorithms = ['mcmc', 'ceres', 'mcmc-ceres', 'lmsder', 'mcmc-lmsder', 'nuts', 'nuts-ceres', 'nuts-lmsder']` `class-attribute`

Built-in mutable sequence.

If no argument is given, the constructor creates a new empty list. The argument must be an iterable if specified.

`model` `staticmethod`

model(t, params, *, cast=False) Underlying parametric model function

Parameters:

Name	Type	Description	Default
`t`	`np.ndarray of np.float32 or np.float64`	Time moments, can be unsorted	required
`params`	`np.ndaarray of np.float32 or np.float64`	Parameters of the model, this array can be longer than actual parameter list, the beginning part of the array will be used in this case, see Examples section in the class documentation.	required
`cast`	`bool`	Cast inputs to np.ndarray of the same dtype	`False`

Returns:

Type	Description
`np.ndarray of np.float32 or np.float64`	Array of model values corresponded to the given time moments

`light_curve.VillarFit`

Bases: light_curve.light_curve_ext._FeatureEvaluator

Villar function fit

Seven fit parameters and goodness of fit (reduced $\chi^2$) of the Villar function developed for supernovae classification:

$$ f(t) = c + \frac{A}{ 1 + \exp{\frac{-(t - t_0)}{\tau_\mathrm{rise}}}} \left{ \begin{array}{ll} 1 - \frac{\nu (t - t_0)}{\gamma}, &t < t_0 + \gamma \ (1 - \nu) \exp{\frac{-(t-t_0-\gamma)}{\tau_\mathrm{fall}}}, &t \geq t_0 + \gamma \end{array} \right. $$ where $A, \gamma, \tau_\mathrm{rise}, \tau_\mathrm{fall} > 0$, $\nu \in [0; 1)$.

Here we introduce a new dimensionless parameter $\nu$ instead of the plateau slope $\beta$ from the orioginal paper: $\nu \equiv -\beta \gamma / A$.

Note, that the Villar function is developed to be used with fluxes, not magnitudes.

Depends on: time, magnitude, magnitude error
Minimum number of observations: 8
Number of features: 8

Villar et al. 2019 DOI:10.3847/1538-4357/ab418c

Names and description of the output features: - villar_fit_amplitude: half amplitude of the Villar function (A) - villar_fit_baseline: baseline of the Villar function (c) - villar_fit_reference_time: reference time of the Villar function (t_0) - villar_fit_rise_time: rise time of the Villar function (tau_rise) - villar_fit_fall_time: decline time of the Villar function (tau_fall) - villar_fit_plateau_rel_amplitude: relative plateau amplitude of the Villar function (nu = beta gamma / A) - villar_fit_plateau_duration: plateau duration of the Villar function (gamma) - villar_fit_reduced_chi2: Villar fit quality (reduced chi2)

Parameters:

Name	Type	Description	Default
`algorithm`	`str`	Non-linear least-square algorithm, supported values are: mcmc, ceres, mcmc-ceres, lmsder, mcmc-lmsder, nuts, nuts-ceres, nuts-lmsder.	required
`mcmc_niter`	`int`	Number of MCMC iterations, default is 128	required
`ceres_niter`	`int`	Number of Ceres iterations, default is 10	required
`ceres_loss_reg`	`float`	Ceres loss regularization, default is to use square norm as is, if set to a number, the loss function is regularized to descriminate outlier residuals larger than this value. Default is None which means no regularization.	required
`lmsder_niter`	`int`	Number of LMSDER iterations, default is 10	required
`init`	`list or None`	Initial conditions, must be `None` or a `list` of `float`s or `None`s. The length of the list must be 7, `None` values will be replaced with some defauls values. It is supported by MCMC only	required
`bounds`	`list of tuples or None`	Boundary conditions, must be `None` or a `list` of `tuple`s of `float`s or `None`s. The length of the list must be 7, boundary conditions must include initial conditions, `None` values will be replaced with some broad defaults. It is supported by MCMC only	required
`ln_prior`	`str or list of ln_prior.LnPrior1D or None`	Prior for MCMC, None means no prior. It is specified by a string literal or a list of 7 `ln_prior.LnPrior1D` objects, see `ln_prior` submodule for corresponding functions. Available string literals are: - 'no': no prior,\ - 'hosseinzadeh2020': prior addopted from Hosseinzadeh et al. 2020, it assumes that `t` is in days	required
`transform`	`bool or None`	If `False` or `None` (default) output is not transformed. If `True` output is transformed as following: - Half-amplitude A is transformed as `zp - 2.5 lg(2*A)`, zp = 8.9, so that the amplitude is assumed to be the object peak flux in Jy. - baseline flux is normalised by A: baseline -> baseline / A - reference time is removed - goodness of fit is transformed as `ln(reduced chi^2 + 1)` to reduce its spread - other parameters are not transformed See `names` and `descriptions` attributes an object for the list and order of features.	required

Attributes:

Name	Type	Description
`names`	`list of str`	Feature names
`descriptions`	`list of str`	Feature descriptions
`supported_algorithms`	`list of str`	Available argument values for the constructor

Methods:

Name	Description
`__call__`	Extract features and return them as a numpy array Parameters t : numpy.ndarray of np.float32 or np.float64 dtype Time moments m : numpy.ndarray Signal in magnitude or fluxes. Refer to the feature description to decide which would work better in your case sigma : numpy.ndarray, optional Observation error, if None it is assumed to be unity fill_value : float or None, optional Value to fill invalid feature values, for example if count of observations is not enough to find a proper value. None causes exception for invalid features sorted : bool or None, optional Specifies if input array are sorted by time moments. True is for certainly sorted, False is for unsorted. If None is specified than sorting is checked and an exception is raised for unsorted `t` check : bool, optional Check all input arrays for NaNs, `t` and `m` for infinite values cast : bool, optional Allows non-numpy input and casting of arrays to a common dtype. If `False`, inputs must be `np.ndarray` instances with matched dtypes. Casting provides more flexibility with input types at the cost of performance. Returns ndarray of np.float32 or np.float64 Extracted feature array
`many`	Parallel light curve feature extraction It is a parallel executed equivalent of def many(self, lcs, , fill_value=None, sorted=None, check=True): ... return np.stack( ... [ ... self( ... lc, ... fill_value=fill_value, ... sorted=sorted, ... check=check, ... cast=False, ... ) ... for lc in lcs ... ] ... ) Parameters lcs : list of (t, m, sigma) or Arrow array Either a list of light curves packed into three-tuples (all numpy.ndarray of the same dtype), or an Arrow array/chunked array of type List<Struct<...>> where the selected fields share the same float dtype (float32 or float64). Arrow input is auto-detected via the arrow_c_array / arrow_c_stream protocol and enables zero-copy data access from pyarrow, polars, and other Arrow-compatible libraries. arrow_fields : list of (str or int) Required when lcs is an Arrow array. Field names or indices specifying which struct fields to use as t, m, and optionally sigma. Must contain 2 elements [t, m] or 3 elements [t, m, sigma]. Each element may be a field name (str) or a zero-based positional index (int); all elements must be of the same type. Ignored for non-Arrow input. fill_value : float or None, optional Fill invalid values by this or raise an exception if None sorted : bool or None, optional Specifies if input array are sorted by time moments, see call documentation for details check : bool, optional Check all input arrays for NaNs, `t` and `m` for infinite values n_jobs : int Number of tasks to run in paralell. Default is -1 which means run as many jobs as CPU count. See rayon rust crate documentation for details
`model`	Underlying parametric model function Parameters t : np.ndarray of np.float32 or np.float64 Time moments, can be unsorted params : np.ndaarray of np.float32 or np.float64 Parameters of the model, this array can be longer than actual parameter list, the beginning part of the array will be used in this case, see Examples section in the class documentation. cast : bool, optional Cast inputs to np.ndarray of the same dtype Returns np.ndarray of np.float32 or np.float64 Array of model values corresponded to the given time moments

Examples:

>>> import numpy as np
>>> from light_curve import VillarFit
>>>
>>> fit = VillarFit('mcmc')
>>> t = np.linspace(0, 10, 101)
>>> flux = 1 + (t - 3) ** 2
>>> fluxerr = np.sqrt(flux)
>>> result = fit(t, flux, fluxerr, sorted=True)
>>> # Result is built from a model parameters and reduced chi^2
>>> # So we can use as a `params` array of the static `.model()` method
>>> model = VillarFit.model(t, result)

`supported_algorithms = ['mcmc', 'ceres', 'mcmc-ceres', 'lmsder', 'mcmc-lmsder', 'nuts', 'nuts-ceres', 'nuts-lmsder']` `class-attribute`

Built-in mutable sequence.

If no argument is given, the constructor creates a new empty list. The argument must be an iterable if specified.

`model` `staticmethod`

model(t, params, *, cast=False) Underlying parametric model function

Parameters:

Name	Type	Description	Default
`t`	`np.ndarray of np.float32 or np.float64`	Time moments, can be unsorted	required
`params`	`np.ndaarray of np.float32 or np.float64`	Parameters of the model, this array can be longer than actual parameter list, the beginning part of the array will be used in this case, see Examples section in the class documentation.	required
`cast`	`bool`	Cast inputs to np.ndarray of the same dtype	`False`

Returns:

Type	Description
`np.ndarray of np.float32 or np.float64`	Array of model values corresponded to the given time moments

Parametric fit features

light_curve.BazinFit

Parameters

Parameters

Parameters

Returns

supported_algorithms = ['mcmc', 'ceres', 'mcmc-ceres', 'lmsder', 'mcmc-lmsder', 'nuts', 'nuts-ceres', 'nuts-lmsder'] class-attribute

model staticmethod

light_curve.LinexpFit

Parameters

Parameters

Parameters

Returns

supported_algorithms = ['mcmc', 'ceres', 'mcmc-ceres', 'lmsder', 'mcmc-lmsder', 'nuts', 'nuts-ceres', 'nuts-lmsder'] class-attribute

model staticmethod

light_curve.VillarFit

Parameters

Parameters

Parameters

Returns

supported_algorithms = ['mcmc', 'ceres', 'mcmc-ceres', 'lmsder', 'mcmc-lmsder', 'nuts', 'nuts-ceres', 'nuts-lmsder'] class-attribute

model staticmethod

`light_curve.BazinFit`

`supported_algorithms = ['mcmc', 'ceres', 'mcmc-ceres', 'lmsder', 'mcmc-lmsder', 'nuts', 'nuts-ceres', 'nuts-lmsder']` `class-attribute`

`model` `staticmethod`

`light_curve.LinexpFit`

`supported_algorithms = ['mcmc', 'ceres', 'mcmc-ceres', 'lmsder', 'mcmc-lmsder', 'nuts', 'nuts-ceres', 'nuts-lmsder']` `class-attribute`

`model` `staticmethod`

`light_curve.VillarFit`

`supported_algorithms = ['mcmc', 'ceres', 'mcmc-ceres', 'lmsder', 'mcmc-lmsder', 'nuts', 'nuts-ceres', 'nuts-lmsder']` `class-attribute`

`model` `staticmethod`