Indicator Semivariogram#

class pyinterpolate.ExperimentalIndicatorVariogram(number_of_thresholds: int, step_size: float, max_range: float, ds: ArrayLike | VariogramPoints = None, values: ArrayLike = None, geometries: ArrayLike = None, custom_weights=None, custom_bins=None, direction: float = None, tolerance: float = None, fit=True)[source]

Class describes Experimental Indicator Variogram models.

Parameters:

number_of_thresholds: int

The number of thresholds to model data.

step_sizefloat

The distance between lags within each points are included in the calculations.

max_rangefloat

The maximum range of analysis.

dsArrayLike, optional

[x, y, value]

valuesArrayLike, optional

Observation in the i-th geometry (from geometries). Optional parameter, if not given then ds must be provided.

geometriesArrayLike, optional

Array or similar structure with geometries. It must have the same length as values. Optional parameter, if not given then ds must be provided. Point type geometry.

custom_weightsnumpy array, default=None

Weights assigned to points, index of weight must be the same as index of point.

directionfloat (in range [0, 360]), default=None

Direction of semivariogram, values from 0 to 360 degrees:

0 or 180: is E-W,
90 or 270 is N-S,
45 or 225 is NE-SW,
135 or 315 is NW-SE.

tolerancefloat (in range [0, 1]), default=1

If tolerance is 0 then points must be placed at a single line with the beginning in the origin of the coordinate system and the direction given by y axis and direction parameter. If tolerance is > 0 then the bin is selected as an elliptical area with major axis pointed in the same direction as the line for 0 tolerance.

The major axis size == step_size.
The minor axis size is tolerance * step_size
The baseline point is at a center of the ellipse.
The tolerance == 1 creates an omnidirectional semivariogram.

fitbool, default = True

Should models be fitted in the class initialization?

Attributes:

dsIndicatorVariogramData: Prepared indicator data.
step_sizefloat: Derived from the step_size parameter.
max_rangefloat: Derived from the max_range parameter.
custom_weightsnumpy array: Derived from the weights parameter.
directionfloat: Derived from the direction parameter.
tolerancefloat: Derived from the tolerance parameter.
experimental_modelsList: The [threshold, experimental_variogram] pairs.

Methods

fit()	Fits indicators to experimental variograms.
show()	Show experimental variograms for each indicator.

References

Goovaerts P. AUTO-IK: a 2D indicator kriging program for automated non-parametric modeling of local uncertainty in earth sciences. DOI: https://doi.org/10.1016/j.cageo.2008.08.014

Examples

>>> import numpy as np
>>> from pyinterpolate import ExperimentalIndicatorVariogram
>>>
>>>
>>> dem = np.random.random(size=(1000, 3))
>>> step_size = 0.1
>>> max_range = 0.6
>>> exp_indicator = ExperimentalIndicatorVariogram(
...     values=dem[:, -1],
...     geometries=dem[:, :-1],
...     number_of_thresholds=5,
...     step_size=step_size,
...     max_range=max_range
... )
>>> print(len(exp_indicator.experimental_models))
5
>>> exp_indicator.show()  # plots variogram for each threshold

fit()[source]: Function fits indicators to models and updates class models.

show()[source]: Function shows generated experimental variograms for each indicator.

class pyinterpolate.TheoreticalIndicatorVariogram(experimental_indicator_variogram: ExperimentalIndicatorVariogram)[source]

Class models indicator variograms for all indices.

Parameters:

experimental_indicator_variogramExperimentalIndicatorVariogram: Fitted experimanetal variograms with indicators for each threshold.

Attributes:

experimental_indicator_variogramExperimentalIndicatorVariogram: See experimental_indicator_variogram parameter.
theoretical_indicator_variogramsDict: Dictionary with fitted theoretical models for each threshold.

Methods

fit()	Fits theoretical models to experimental variograms.
show()	Shows experimental and theoretical variograms for each threshold.

Examples

>>> import numpy as np
>>> from pyinterpolate import (
...     ExperimentalIndicatorVariogram,
...     TheoreticalIndicatorVariogram
... )
>>>
>>>
>>> dem = np.random.random(size=(1000, 3))
>>> step_size = 0.1
>>> max_range = 0.6
>>> exp_indicator = ExperimentalIndicatorVariogram(
...     values=dem[:, -1],
...     geometries=dem[:, :-1],
...     number_of_thresholds=5,
...     step_size=step_size,
...     max_range=max_range
... )
>>> theo_indicator = TheoreticalIndicatorVariogram(
...     experimental_indicator_variogram=exp_indicator
... )
>>> theo_indicator.fit()
>>> print(len(theo_indicator.theoretical_indicator_variograms))
5
>>> theo_indicator.show()  # plots theoretical models' curves

fit(models_group: str | list = 'safe', nugget=None, min_nugget=0, max_nugget=0.5, number_of_nuggets=16, rang=None, min_range=0.1, max_range=0.5, number_of_ranges=16, sill=None, n_sill_values=5, sill_from_variance=False, min_sill=0.5, max_sill=2, number_of_sills=16, direction=None, error_estimator='rmse', deviation_weighting='equal')[source]

Method tries to find the optimal range, sill and model (function) of the theoretical semivariogram.

Parameters:

models_groupstr or list, default=’safe’

Models group to test:

‘all’ - the same as list with all models,
‘safe’ - [‘linear’, ‘power’, ‘spherical’]
as a list: multiple model types to test
as a single model type from:
- ‘circular’,
- ‘cubic’,
- ‘exponential’,
- ‘gaussian’,
- ‘linear’,
- ‘power’,
- ‘spherical’.

nuggetfloat, optional

Nugget (bias) of a variogram. If given then it is fixed to this value.

min_nuggetfloat, default = 0

The minimum nugget as the ratio of the parameter to the first lag variance.

max_nuggetfloat, default = 0.5

The maximum nugget as the ratio of the parameter to the first lag variance.

number_of_nuggetsint, default = 16

How many equally spaced nuggets tested between min_nugget and max_nugget.

rangfloat, optional

If given, then range is fixed to this value.

min_rangefloat, default = 0.1

The minimal fraction of a variogram range, 0 < min_range <= max_range.

max_rangefloat, default = 0.5

The maximum fraction of a variogram range, min_range <= max_range <= 1. Parameter max_range greater than 0.5 raises warning.

number_of_rangesint, default = 16

How many bins are tested between min_range and max_range.

sillfloat, default = None

Partial sill, or sill when nugget is set to zero. Total sill is a sum of partial sill and nugget. If given, then partial sill is fixed to this value.

n_sill_valuesint, default = 5

The last n experimental semivariance records for sill estimation. (Used only when sill_from_variance is set to False).

sill_from_variancebool, default = False

Estimate sill from the variance (semivariance at distance 0).

min_sillfloat, default = 0.5

The minimal fraction of the variogram variance at lag 0 to find partial sill, 0 <= min_sill <= max_sill.

max_sillfloat, default = 2

The maximum fraction of the variogram variance at lag 0 to find partial sill.

number_of_sillsint, default = 16

How many equally spaced sill values are tested between min_sill and max_sill.

directionfloat, in range [0, 360], default=None

The direction of a semivariogram. If None given then semivariogram is isotropic. This parameter is required if passed experimental variogram is stored in a numpy array.

error_estimatorstr, default = ‘rmse’

A model error estimation method. Available options are:

‘rmse’: Root Mean Squared Error,
‘mae’: Mean Absolute Error,
‘bias’: Forecast Bias,
‘smape’: Symmetric Mean Absolute Percentage Error.

deviation_weightingstr, default = “equal”

The name of the method used to weight error at a given lags. Works only with RMSE. Available methods:

equal: no weighting,
closest: lags at a close range have bigger weights,
distant: lags that are further away have bigger weights,
dense: error is weighted by the number of point pairs within lag.

show(subplots: bool = False)[source]

Method plots experimental and theoretical variograms.

Parameters:

subplotsbool, default = False: If True then each indicator variogram is plotted on a separate plot. Otherwise, all variograms are plotted on a single plot.

Indicator Semivariogram#

This Page