Variability features

light_curve.Amplitude

Bases: _FeatureEvaluator

Half amplitude of magnitude

\[ \mathrm{amplitude} \equiv \frac{\left( \max{(m)} - \min{(m)} \right)}{2} \]

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

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, 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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.AndersonDarlingNormal

Bases: _FeatureEvaluator

Unbiased Anderson–Darling normality test statistic

\[ A^2 \equiv \left(1 + \frac4{N} - \frac{25}{N^2}\right) \left(-N - \frac1{N} \sum_{i=0}^{N-1} {(2i + 1)\ln\Phi_i + (2(N - i) - 1)\ln(1 - \Phi_i)}\right), \]

where \(\Phi_i \equiv \Phi((m_i - \langle m \rangle) / \sigma_m)\) is the standard cumulative distribution, \(N\) is the number of observations, \(\langle m \rangle\) is the mean magnitude and \(\sigma_m = \sqrt{\sum_i (m_i - \langle m \rangle)^2 / (N-1)}\) is the magnitude standard deviation.

• Depends on: magnitude
• Minimum number of observations: 4
• Number of features: 1

Wikipedia

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, 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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.BeyondNStd

Bases: _FeatureEvaluator

Fraction of observations beyond \(n\,\sigma\_m\) from the mean magnitude \(\langle m \rangle\)

\[ \mathrm{beyond}~n\,\sigma\_m \equiv \frac{\sum\_i I\_{|m - \langle m \rangle| > n\,\sigma\_m}(m_i)}{N}, \]

where \(I\) is the indicator function, \(N\) is the number of observations, \(\langle m \rangle\) is the mean magnitude and \(\sigma_m = \sqrt{\sum_i (m_i - \langle m \rangle)^2 / (N-1)}\) is the magnitude standard deviation.

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

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

Parameters:

Name	Type	Description	Default
nstd	positive float	N — how many standard deviations from the mean	1.0
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, 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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.Chi2Pvar

Bases: _FeatureEvaluator

Probability of variability based on \(\chi^2\) distribution

\[ p_{\rm var} \equiv Q\!\left(\frac{N-1}{2},\,\frac{\chi^2}{2}\right), \]

where \(Q(a, x)\) is the regularized upper incomplete gamma function, \(N\) is the number of observations, and

\[ \chi^2 \equiv \sum_i\left(\frac{m_i - \bar{m}}{\delta_i}\right)^2 \]

is the chi-squared statistic with \(N-1\) degrees of freedom. The weighted mean \(\bar{m}\) is computed as described in [WeightedMean].

\(p_{\rm var}\) is the probability that the observed scatter exceeds what is expected from measurement uncertainties alone, i.e.\ the probability that the source is intrinsically variable.

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

Kim et al. 2014

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, 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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.Cusum

Bases: _FeatureEvaluator

Cusum — a range of cumulative sums

\[ \mathrm{cusum} \equiv \max(S) - \min(S), \]

where

\[ S_j \equiv \frac1{N\sigma_m} \sum_{i=0}^j{\left(m\_i - \langle m \rangle\right)}, \]

\(N\) is the number of observations, \(\langle m \rangle\) is the mean magnitude and \(\sigma_m = \sqrt{\sum_i (m_i - \langle m \rangle)^2 / (N-1)}\) 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, 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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.Eta

Bases: _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, 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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.EtaE

Bases: _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, 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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.ExcessVariance

Bases: _FeatureEvaluator

Measure of the variability amplitude

\[ \frac{\sigma_m^2 - \langle \delta^2 \rangle}{\langle m \rangle^2}, \]

where \(\langle \delta^2 \rangle\) is the mean of squared error, \(\sigma_m\) is the magnitude standard deviation. Note that this definition differs from Sánchez et al. 2017

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

Sánchez et al. 2017 DOI:10.3847/1538-4357/aa9188

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, 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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.InterPercentileRange

Bases: _FeatureEvaluator

Inter-percentile range

\[ Q(1 - p) - Q(p), \]

where \(Q(p)\) is the \(p\)th quantile of the magnitude distribution.

Special cases are the interquartile range which is inter-percentile range for \(p = 0.25\) and the interdecile range which is inter-percentile range for \(p = 0.1\).

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

Parameters:

Name	Type	Description	Default
quantile	positive float	Range is (100% × quantile, 100% × (1 - quantile))	0.25
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, 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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.Kurtosis

Bases: _FeatureEvaluator

Excess kurtosis of magnitude

\[ G_2 \equiv \frac{N\,(N + 1)}{(N - 1)(N - 2)(N - 3)} \frac{\sum_i(m_i - \langle m \rangle)^4}{\sigma_m^4} \- 3\frac{(N - 1)^2}{(N - 2)(N - 3)}, \]

where \(N\) is the number of observations, \(\langle m \rangle\) is the mean magnitude, \(\sigma_m = \sqrt{\sum_i (m_i - \langle m \rangle)^2 / (N-1)}\) is the magnitude standard deviation.

• Depends on: magnitude
• Minimum number of observations: 4
• Number of features: 1

Wikipedia

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, same as giving True. The default for this feature is 'arcsinh' '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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.LaflerKinmanStringLength

Bases: _FeatureEvaluator

Lafler–Kinman string-length statistic

A smoothness measure for a light curve. The normalised sum of squared successive magnitude differences is computed:

\[ \theta = \frac{\sum_{i=0}^{N-1} \bigl(m_{\pi(i+1 \bmod N)} - m_{\pi(i)}\bigr)^2}{2 (N-1) s^2}, \]

where \(s^2 = (N-1)^{-1}\sum_i(m_i-\bar m)^2\) is the sample variance, and the sum wraps around (last observation is followed by the first).

With this normalisation \(\langle\theta\rangle \approx 1\) for observations in random magnitude order; a smooth curve yields \(\theta \ll 1\).

One natural use case is applying it to a phase-folded light curve; see [Periodogram] for details.

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

Lafler, J. & Kinman, T. D. 1965, ApJS 11, 216 ADS:1965ApJS...11..216L

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, 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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.MagnitudePercentageRatio

Bases: _FeatureEvaluator

Magnitude percentage ratio

\[ \mathrm{magnitude~}q\mathrm{~to~}n\mathrm{~ratio} \equiv \frac{Q(1-n) - Q(n)}{Q(1-d) - Q(d)}, \]

where \(n\) and \(d\) denotes user defined percentage, \(Q\) is the quantile function of magnitude distribution.

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

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

Parameters:

Name	Type	Description	Default
quantile_numerator	positive float	Numerator inter-percentile range is (100% × q, 100% × (1 - q))	0.40
quantile_denominator	positive float	Denominator inter-percentile range is (100% × q, 100% × (1 - q))	0.05
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, 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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.MaximumSlope

Bases: _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, 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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.Mean

Bases: _FeatureEvaluator

Mean magnitude

\[ \langle m \rangle \equiv \frac1{N} \sum_i m_i. \]

This is non-weighted mean, see WeightedMean for weighted mean.

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

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, 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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.MeanVariance

Bases: _FeatureEvaluator

Standard deviation to mean ratio

\[ \frac{\sigma_m}{\langle m \rangle} \]

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

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, 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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.Median

Bases: _FeatureEvaluator

Median magnitude

\[ \mathrm{Median}(m_i) \]

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

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, 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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.MedianAbsoluteDeviation

Bases: _FeatureEvaluator

Median of the absolute value of the difference between magnitude and its median

\[ \mathrm{median~absolute~deviation} \equiv \mathrm{Median}\left(|m_i - \mathrm{Median}(m)|\right). \]

• Depends on: magnitude
• Minimum number of observations: 1
• 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, 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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.MedianBufferRangePercentage

Bases: _FeatureEvaluator

Fraction of observations inside \(\mathrm{Median}(m) \pm q \times (\max(m) - \min(m)) / 2\) interval

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

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

Parameters:

Name	Type	Description	Default
quantile	positive float	Relative range size	0.10
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, 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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.OtsuSplit

Bases: _FeatureEvaluator

Otsu threshholding algorithm

Difference of subset means, standard deviation of the lower subset, standard deviation of the upper subset and lower-to-all observation count ratio for two subsets of magnitudes obtained by Otsu's method split. Otsu's method is used to perform automatic thresholding. The algorithm returns a single threshold that separate values into two classes. This threshold is determined by minimizing intra-class intensity variance, or equivalently, by maximizing inter-class variance. The algorithm returns the minimum threshold which corresponds to the absolute maximum of the inter-class variance.

• Depends on: magnitude
• Minimum number of observations: 2
• Number of features: 4

Otsu, Nobuyuki 1979. DOI:10.1109/tsmc.1979.4310076

Parameters:

Name	Type	Description	Default
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.PercentAmplitude

Bases: _FeatureEvaluator

Maximum deviation of magnitude from its median

\[ \mathrm{percent~amplitude} \equiv \max_i\left|m_i - \mathrm{Median}(m)\right| = \max(\max(m) - \mathrm{Median}(m), \mathrm{Median}(m) - \min(m)). \]

• Depends on: magnitude
• Minimum number of observations: 1
• 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, 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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.PercentDifferenceMagnitudePercentile

Bases: _FeatureEvaluator

Ratio of \(p\)th inter-percentile range to the median

\[ p\mathrm{~percent~difference~magnitude~percentile} \equiv \frac{Q(1-p) - Q(p)}{\mathrm{Median}(m)}. \]

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

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

Parameters:

Name	Type	Description	Default
quantile	positive float	Relative range size	0.05
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, 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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.ReducedChi2

Bases: _FeatureEvaluator

Reduced \(\chi^2\) of magnitude measurements

\[ \mathrm{reduced~}\chi^2 \equiv \frac1{N-1} \sum_i\left(\frac{m_i - \bar{m}}{\delta\_i}\right)^2, \]

where \(N\) is the number of observations, and \(\bar{m}\) is the weighted mean magnitude.

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

This is a good measure of variability which takes into account observations uncertainties.

Wikipedia

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, same as giving True. The default for this feature is 'ln1p' '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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.Roms

Bases: _FeatureEvaluator

Robust median statistic

\[ \frac1{N-1} \sum_{i=0}^{N-1} \frac{|m_i - \mathrm{median}(m_i)|}{\sigma_i} \]

For non-variable data, it should be less than one.

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

Enoch, Brown, Burgasser 2003. DOI:10.1086/376598

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, 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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.Skew

Bases: _FeatureEvaluator

Skewness of magnitude \(G_1\)

\[ G_1 \equiv \frac{N}{(N - 1)(N - 2)} \frac{\sum_i(m_i - \langle m \rangle)^3}{\sigma_m^3}, \]

where \(N\) is the number of observations, \(\langle m \rangle\) is the mean magnitude, \(\sigma_m = \sqrt{\sum_i (m_i - \langle m \rangle)^2 / (N-1)}\) is the magnitude standard deviation.

• Depends on: magnitude
• Minimum number of observations: 3
• Number of features: 1

Wikipedia

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, same as giving True. The default for this feature is 'arcsinh' '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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.StandardDeviation

Bases: _FeatureEvaluator

Standard deviation of magnitude \(\sigma_m\)

\[ \sigma_m \equiv \sqrt{\sum_i (m_i - \langle m \rangle)^2 / (N-1)}, \]

\(N\) is the number of observations and \(\langle m \rangle\) is the mean magnitude.

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

Wikipedia

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, 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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.StetsonK

Bases: _FeatureEvaluator

Stetson \(K\) coefficient described light curve shape

\[ \mathrm{Stetson}~K \equiv \frac{\sum_i\left|\frac{m_i - \bar{m}}{\delta_i}\right|}{\sqrt{N\\,\chi^2}}, \]

where N is the number of observations, \(\bar{m}\) is the weighted mean magnitude and \(\chi^2 = \sum_i\left(\frac{m_i - \langle m \rangle}{\delta\_i}\right)^2\).

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

P. B. Stetson, 1996. DOI:10.1086/133808

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, 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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel

---

light_curve.WeightedMean

Bases: _FeatureEvaluator

Weighted mean magnitude

\[ \bar{m} \equiv \frac{\sum_i m_i / \delta_i^2}{\sum_i 1 / \delta_i^2}. \]

See Mean for non-weighted mean.

• Depends on: magnitude, magnitude error
• Minimum number of observations: 1
• Number of features: 1

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, 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, True uses the default transformer, False disables it. If None, no transformation is applied (default)	None
bands	list of str or None	Passband names for multiband mode. If provided, the feature is evaluated independently per passband and the outputs are concatenated in passband order. If None (default), single-band mode is used.	required

Attributes:

Name	Type	Description
names	list of str	Feature names
descriptions	list of str	Feature descriptions
bands	numpy.ndarray of str or None	Passband names for multiband mode, or None for single-band mode

Methods:

Name	Description
__call__	Extract features and return them as a numpy array
many	Extract features from multiple light curves in parallel