Indicator#

class IndicatorVariogramData(input_array, number_of_thresholds)[source]

Class describes indicator variogram data.

Parameters:

input_arraynumpy array, list, tuple: Coordinates and their values: (pt x, pt y, value)
number_of_thresholds: int: The number of thresholds to model data.

See also

ExperimentalIndicatorVariogram: Class that calculates experimental variograms for each indicator.

Attributes:

input_arraynumpy array, list, tuple: Coordinates and their values: (pt x, pt y, value)
n_thresholds: int: The number of thresholds to model data.
thresholdsnumpy array: The 1D numpy array with thresholds.
idsnumpy array: The numpy array with [coordinate_x, coordinate_y, threshold_0, ..., threshold_n].

class ExperimentalIndicatorVariogram(input_array, number_of_thresholds, step_size, max_range, weights=None, direction=None, tolerance=1.0, method='t', fit=True)[source]

Class describes Experimental Indicator Variogram models.

Parameters:

input_arraynumpy array, list, tuple

Coordinates and their values: (pt x, pt y, value)

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.

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.

methodstr, default = triangular

The method used for neighbors selection. Available methods:

“triangle” or “t”, default method where a point neighbors are selected from a triangular area,
“ellipse” or “e”, the most accurate method but also the slowest one.

fitbool, default = True

Should models be fitted in the class initialization?

References

Goovaerts P. AUTO-IK: a 2D indicator kriging program for automated non-parametric modeling of local uncertainty in earth sciences. DOI: TODO

Attributes:

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

Methods

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

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

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

class IndicatorVariograms(experimental_indicator_variogram)[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.

fit(model_name='linear', nugget=0, rang=None, min_range=0.1, max_range=0.5, number_of_ranges=64, sill=None, min_sill=0.5, max_sill=1.5, number_of_sills=64, direction=None, error_estimator='rmse', deviation_weighting='equal', auto_update_attributes=True, warn_about_set_params=True, verbose=False)[source]

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

Parameters:

model_namestr, default = “linear”

The name of a modeling function. Available models:

‘all’,
‘safe’ : linear, power and spherical models,
‘exponential’,
‘gaussian’,
‘linear’,
‘power’,
‘spherical’.

nuggetfloat, default = 0

Nugget (bias) of a variogram. Default value is 0.

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 = 64

How many equally spaced ranges are tested between min_range and max_range.

sillfloat, default = None

If given, then sill is fixed to this value.

min_sillfloat, default = 0

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

max_sillfloat, default = 1

The maximum fraction of the variogram variance at lag 0 to find a sill. It should be lower or equal to 1. It is possible to set it above 1, but then warning is printed.

number_of_sillsint, default = 64

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 a 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 a lag.

auto_update_attributesbool, default = True

Update sill, range, model type and nugget based on the best model.

warn_about_set_params: bool, default=True

Should class invoke warning if model parameters has been set during initialization?

verbosebool, default = False

Show iteration results.

Raises:

ValueError: Raised when sill < 0 or range < 0 or range > 1.
KeyError: Raised when wrong model name(s) are provided by the users.
KeyError: Raised when wrong error type is provided by the users.

Warns:

SillOutsideSafeRangeWarning: Warning printed when max_sill > 1.
RangeOutsideSafeDistanceWarning: Warning printed when max_range > 0.5.
Warning: Model parameters were given during initilization but program is forced to fit the new set of parameters.
Warning: Passed experimental_variogram is a numpy array and direction parameter is None.

show(subplots=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 scatter single plot.