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Variogram

Nugget plus nested structures sharing one anisotropy. rotation is one azimuth, dip, rake triple in degrees for the whole model, where angles (as in LocalAnisotropy) holds one per location; ratios are semi-major/major and minor/major range ratios.

length_unit property 

length_unit

Length unit of the lags and ranges; None when not declared.

unit property 

unit

Unit of the values; semivariances and sills are in its square.

covariance method descriptor 

covariance(h)

Covariance C(h) = sill - γ(h) at scalar lags.

fit staticmethod 

fit(
    experimental,
    model=Ellipsis,
    *,
    weighting="count",
    nugget=None,
    sills=None,
    ranges=None,
)

Weighted least-squares fit of a nugget plus one to three nested structures.

Every parameter is free (None), fixed (a float) or bounded (a (low, high) pair). For given ranges the nugget and sills are solved exactly; the ranges are searched on a grid and refined, deterministically.

Parameters:

Name Type Description Default
experimental ExperimentalVariogram
required
model str or sequence of str

One shape per structure, shortest range first: fitted ranges increase in this order.

 Ellipsis
weighting (count, uniform, count / gamma, count / distance)

Least-squares weight per lag: N(h), 1, N(h)/γ(h)² or N(h)/h².

 "count"
nugget float or (float, float)
None
sills sequence of (None, float or (float, float))

Partial sill and range of each structure, one entry per model.

 None
ranges sequence of (None, float or (float, float))

Partial sill and range of each structure, one entry per model.

 None

Returns:

Type Description
Variogram

Isotropic; one free structure with a free nugget reproduces the single-structure fit.

fit_directional staticmethod 

fit_directional(
    experimentals,
    directions,
    model=Ellipsis,
    *,
    weighting="count",
    nugget=None,
    sills=None,
    ranges=None,
    rotation=None,
    ratios=None,
)

One anisotropic model fitted jointly to experimental variograms in several directions.

The structures share the anisotropy; their ranges are major-axis ranges. Nugget, sills and ranges are free, fixed or bounded as in Variogram.fit, and so is each angle and range ratio. Free ranges stay within the largest lag; bound them, e.g. ranges=[None, (50, 300)], to go further. The search is deterministic.

Parameters:

Name Type Description Default
experimentals sequence of ExperimentalVariogram
required
directions sequence of (float, float)

Azimuth and dip in degrees of each experimental variogram.

 required
model

As in Variogram.fit.

 Ellipsis
weighting

As in Variogram.fit.

 Ellipsis
nugget

As in Variogram.fit.

 Ellipsis
sills

As in Variogram.fit.

 Ellipsis
ranges

As in Variogram.fit.

 Ellipsis
rotation sequence of (None, float or (float, float))

Azimuth, dip and rake in degrees; free angles are returned with azimuth and rake in [0, 180).

 None
ratios sequence of (None, float or (float, float))

Semi-major/major and minor/major range ratios, in (0, 1] when free. When every direction is horizontal, dip and rake default to 0 and the minor ratio to 1: the fit is two-dimensional.

 None

Returns:

Type Description
Variogram

from_json staticmethod 

from_json(text)

Reads to_json output; raises InvalidInput on another class's JSON or a newer format.

gamma method descriptor 

gamma(h)

γ at scalar lags (along the major axis when anisotropic).

gamma_between method descriptor 

gamma_between(a, b)

γ between paired rows of a and b, honoring anisotropy.

standardized method descriptor 

standardized(*, sill=1.0)

The same shape with total sill sill, e.g. a fitted variogram scaled for normal scores; models, ranges and anisotropy are kept, the unit of the values is dropped.

to_json method descriptor 

to_json()

JSON of the model.

with_anisotropy method descriptor 

with_anisotropy(rotation, ratios)

Same structures with a new anisotropy.

used in