Variability & trend features

`light_curve.Eta`

Bases: light_curve.light_curve_ext._FeatureEvaluator

Von Neummann $\eta$

$$ \eta \equiv \frac1{(N - 1)\,\sigma_m^2} \sum_{i=0}^{N-2}(m_{i+1} - m_i)^2, $$ where $N$ is the number of observations, $\sigma_m = \sqrt{\sum_i (m_i - \langle m \rangle)^2 / (N-1)}$ is the magnitude standard deviation.

Depends on: magnitude
Minimum number of observations: 2
Number of features: 1

Kim et al. 2014, DOI:10.1051/0004-6361/201323252

Parameters:

Name	Type	Description	Default
`transform`	`str or bool or None`	Transformer to apply to the feature values. If str, must be one of: - 'default' - use default transformer for the feature, it same as giving True. The default for this feature is 'identity' - 'arcsinh' - Hyperbolic arcsine feature transformer - 'clipped_lg' - Decimal logarithm of a value clipped to a minimum value - 'identity' - Identity feature transformer - 'lg' - Decimal logarithm feature transformer - 'ln1p' - ln(1+x) feature transformer - 'sqrt' - Square root feature transformer If bool, must be True to use default transformer or False to disable. If None, no transformation is applied	required

Attributes:

Name	Type	Description
`names`	`list of str`	Feature names
`descriptions`	`list of str`	Feature descriptions

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

`default_transform = 'identity'` `class-attribute`

str(object='') -> str str(bytes_or_buffer[, encoding[, errors]]) -> str

Create a new string object from the given object. If encoding or errors is specified, then the object must expose a data buffer that will be decoded using the given encoding and error handler. Otherwise, returns the result of object.str() (if defined) or repr(object). encoding defaults to sys.getdefaultencoding(). errors defaults to 'strict'.

`supported_transforms = ['arcsinh', 'clipped_lg', 'identity', 'lg', 'ln1p', 'sqrt']` `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.

`light_curve.EtaE`

Bases: light_curve.light_curve_ext._FeatureEvaluator

$\eta^e$ — modification of Eta for unevenly time series

$$ \eta^e \equiv \frac{(t_{N-1} - t_0)^2}{(N - 1)^3} \frac{\sum_{i=0}^{N-2} \left(\frac{m_{i+1} - m_i}{t_{i+1} - t_i}\right)^2}{\sigma_m^2} $$ where $N$ is the number of observations, $\sigma_m = \sqrt{\sum_i (m_i - \langle m \rangle)^2 / (N-1)}$ is the magnitude standard deviation. Note that this definition is a bit different from both Kim et al. 2014 and feets

Note that this feature can have very high values and be highly cadence-dependent in the case of large range of time lags. In this case consider to use this feature with Bins.

Depends on: time, magnitude
Minimum number of observations: 2
Number of features: 1

Kim et al. 2014, DOI:10.1051/0004-6361/201323252

Parameters:

Name	Type	Description	Default
`transform`	`str or bool or None`	Transformer to apply to the feature values. If str, must be one of: - 'default' - use default transformer for the feature, it same as giving True. The default for this feature is 'lg' - 'arcsinh' - Hyperbolic arcsine feature transformer - 'clipped_lg' - Decimal logarithm of a value clipped to a minimum value - 'identity' - Identity feature transformer - 'lg' - Decimal logarithm feature transformer - 'ln1p' - ln(1+x) feature transformer - 'sqrt' - Square root feature transformer If bool, must be True to use default transformer or False to disable. If None, no transformation is applied	required

Attributes:

Name	Type	Description
`names`	`list of str`	Feature names
`descriptions`	`list of str`	Feature descriptions

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

`default_transform = 'lg'` `class-attribute`

str(object='') -> str str(bytes_or_buffer[, encoding[, errors]]) -> str

Create a new string object from the given object. If encoding or errors is specified, then the object must expose a data buffer that will be decoded using the given encoding and error handler. Otherwise, returns the result of object.str() (if defined) or repr(object). encoding defaults to sys.getdefaultencoding(). errors defaults to 'strict'.

`supported_transforms = ['arcsinh', 'clipped_lg', 'identity', 'lg', 'ln1p', 'sqrt']` `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.

`light_curve.LinearFit`

Bases: light_curve.light_curve_ext._FeatureEvaluator

Slope, its error and reduced $\chi^2$ of the light curve in the linear fit

Least squares fit of the linear stochastic model with Gaussian noise described by observation errors $\{\delta_i\}$: $$ m_i = c + \mathrm{slope} t_i + \delta_i \varepsilon_i $$ where $c$ is a constant, $\{\varepsilon_i\}$ are standard distributed random variables.

Feature values are $\mathrm{slope}$, $\sigma_\mathrm{slope}$ and $\frac{\sum{((m_i - c - \mathrm{slope} t_i) / \delta_i)^2}}{N - 2}$.

Depends on: time, magnitude, magnitude error
Minimum number of observations: 3
Number of features: 3

Parameters:

Name	Type	Description	Default
`transform`	`str or bool or None`	Transformer to apply to the feature values. If str, must be one of: - 'default' - use default transformer for the feature, it same as giving True. The default for this feature is 'identity' - 'arcsinh' - Hyperbolic arcsine feature transformer - 'clipped_lg' - Decimal logarithm of a value clipped to a minimum value - 'identity' - Identity feature transformer - 'lg' - Decimal logarithm feature transformer - 'ln1p' - ln(1+x) feature transformer - 'sqrt' - Square root feature transformer If bool, must be True to use default transformer or False to disable. If None, no transformation is applied	required

Attributes:

Name	Type	Description
`names`	`list of str`	Feature names
`descriptions`	`list of str`	Feature descriptions

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

`default_transform = 'identity'` `class-attribute`

str(object='') -> str str(bytes_or_buffer[, encoding[, errors]]) -> str

Create a new string object from the given object. If encoding or errors is specified, then the object must expose a data buffer that will be decoded using the given encoding and error handler. Otherwise, returns the result of object.str() (if defined) or repr(object). encoding defaults to sys.getdefaultencoding(). errors defaults to 'strict'.

`supported_transforms = ['arcsinh', 'clipped_lg', 'identity', 'lg', 'ln1p', 'sqrt']` `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.

`light_curve.LinearTrend`

Bases: light_curve.light_curve_ext._FeatureEvaluator

The slope, its error and noise level of the light curve in the linear fit

Least squares fit of the linear stochastic model with constant Gaussian noise $\Sigma$ assuming observation errors to be zero: $$ m_i = c + \mathrm{slope} t_i + \Sigma \varepsilon_i, $$ where $c$ is a constant, $\{\varepsilon_i\}$ are standard distributed random variables. $\mathrm{slope}$, $\sigma_\mathrm{slope}$ and $\Sigma$ are returned.

Depends on: time, magnitude
Minimum number of observations: 3
Number of features: 3

Parameters:

Name	Type	Description	Default
`transform`	`str or bool or None`	Transformer to apply to the feature values. If str, must be one of: - 'default' - use default transformer for the feature, it same as giving True. The default for this feature is 'identity' - 'arcsinh' - Hyperbolic arcsine feature transformer - 'clipped_lg' - Decimal logarithm of a value clipped to a minimum value - 'identity' - Identity feature transformer - 'lg' - Decimal logarithm feature transformer - 'ln1p' - ln(1+x) feature transformer - 'sqrt' - Square root feature transformer If bool, must be True to use default transformer or False to disable. If None, no transformation is applied	required

Attributes:

Name	Type	Description
`names`	`list of str`	Feature names
`descriptions`	`list of str`	Feature descriptions

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

`default_transform = 'identity'` `class-attribute`

str(object='') -> str str(bytes_or_buffer[, encoding[, errors]]) -> str

Create a new string object from the given object. If encoding or errors is specified, then the object must expose a data buffer that will be decoded using the given encoding and error handler. Otherwise, returns the result of object.str() (if defined) or repr(object). encoding defaults to sys.getdefaultencoding(). errors defaults to 'strict'.

`supported_transforms = ['arcsinh', 'clipped_lg', 'identity', 'lg', 'ln1p', 'sqrt']` `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.

`light_curve.MaximumSlope`

Bases: light_curve.light_curve_ext._FeatureEvaluator

Maximum slope between two sub-sequential observations

\[ \mathrm{maximum~slope} \equiv \max_{i=0..N-2}\left|\frac{m_{i+1} - m_i}{t_{i+1} - t_i}\right| \]

Note that this feature can have high values and be cadence-dependent in the case of large range of time lags. In this case consider to use this feature with Bins.

Depends on: time, magnitude
Minimum number of observations: 2
Number of features: 1

D’Isanto et al. 2016 DOI:10.1093/mnras/stw157

Parameters:

Name	Type	Description	Default
`transform`	`str or bool or None`	Transformer to apply to the feature values. If str, must be one of: - 'default' - use default transformer for the feature, it same as giving True. The default for this feature is 'clipped_lg' - 'arcsinh' - Hyperbolic arcsine feature transformer - 'clipped_lg' - Decimal logarithm of a value clipped to a minimum value - 'identity' - Identity feature transformer - 'lg' - Decimal logarithm feature transformer - 'ln1p' - ln(1+x) feature transformer - 'sqrt' - Square root feature transformer If bool, must be True to use default transformer or False to disable. If None, no transformation is applied	required

Attributes:

Name	Type	Description
`names`	`list of str`	Feature names
`descriptions`	`list of str`	Feature descriptions

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

`default_transform = 'clipped_lg'` `class-attribute`

str(object='') -> str str(bytes_or_buffer[, encoding[, errors]]) -> str

Create a new string object from the given object. If encoding or errors is specified, then the object must expose a data buffer that will be decoded using the given encoding and error handler. Otherwise, returns the result of object.str() (if defined) or repr(object). encoding defaults to sys.getdefaultencoding(). errors defaults to 'strict'.

`supported_transforms = ['arcsinh', 'clipped_lg', 'identity', 'lg', 'ln1p', 'sqrt']` `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.

Variability & trend features

light_curve.Eta

Parameters

Parameters

default_transform = 'identity' class-attribute

supported_transforms = ['arcsinh', 'clipped_lg', 'identity', 'lg', 'ln1p', 'sqrt'] class-attribute

light_curve.EtaE

Parameters

Parameters

default_transform = 'lg' class-attribute

supported_transforms = ['arcsinh', 'clipped_lg', 'identity', 'lg', 'ln1p', 'sqrt'] class-attribute

light_curve.LinearFit

Parameters

Parameters

default_transform = 'identity' class-attribute

supported_transforms = ['arcsinh', 'clipped_lg', 'identity', 'lg', 'ln1p', 'sqrt'] class-attribute

light_curve.LinearTrend

Parameters

Parameters

default_transform = 'identity' class-attribute

supported_transforms = ['arcsinh', 'clipped_lg', 'identity', 'lg', 'ln1p', 'sqrt'] class-attribute

light_curve.MaximumSlope

Parameters

Parameters

default_transform = 'clipped_lg' class-attribute

supported_transforms = ['arcsinh', 'clipped_lg', 'identity', 'lg', 'ln1p', 'sqrt'] class-attribute

`light_curve.Eta`

`default_transform = 'identity'` `class-attribute`

`supported_transforms = ['arcsinh', 'clipped_lg', 'identity', 'lg', 'ln1p', 'sqrt']` `class-attribute`

`light_curve.EtaE`

`default_transform = 'lg'` `class-attribute`

`supported_transforms = ['arcsinh', 'clipped_lg', 'identity', 'lg', 'ln1p', 'sqrt']` `class-attribute`

`light_curve.LinearFit`

`default_transform = 'identity'` `class-attribute`

`supported_transforms = ['arcsinh', 'clipped_lg', 'identity', 'lg', 'ln1p', 'sqrt']` `class-attribute`

`light_curve.LinearTrend`

`default_transform = 'identity'` `class-attribute`

`supported_transforms = ['arcsinh', 'clipped_lg', 'identity', 'lg', 'ln1p', 'sqrt']` `class-attribute`

`light_curve.MaximumSlope`

`default_transform = 'clipped_lg'` `class-attribute`

`supported_transforms = ['arcsinh', 'clipped_lg', 'identity', 'lg', 'ln1p', 'sqrt']` `class-attribute`