Coregionalization ¶

Linear model of coregionalization: nugget and each structure's sills are symmetric positive semi-definite nvar × nvar matrices, else InvalidInput is raised. rotation and ratios are as in Variogram.

nugget `property` ¶

nugget

nvar x nvar nugget matrix.

structures `property` ¶

structures

(model, range, sills) per structure, sills its nvar x nvar matrix.

cross_covariance `method descriptor` ¶

cross_covariance(i, j, a, b)

Cross-covariance C_ij between paired rows of a and b.

fit `staticmethod` ¶

fit(
    experimentals,
    model=Ellipsis,
    *,
    weighting="count",
    nugget=True,
    ranges=None,
    directions=None,
    rotation=None,
    ratios=None,
    intrinsic=False,
)

Linear model of coregionalization fitted to the direct and cross experimental variograms of several variables together.

The structures, their shapes and ranges, are shared by all variables; the nugget and each structure's sill matrix are kept positive semi-definite. Each pair's residuals are divided by the square root of the product of the two variables' largest direct γ, so variables in different units count alike. For given ranges the matrices are updated in turn by weighted least squares, negative eigenvalues clipped; the ranges start from Variogram.fit on the pooled scaled direct variograms and are refined, deterministically. With directions, the shared anisotropy is fitted too, starting from Variogram.fit_directional on the scaled direct variograms.

Parameters:

Name	Type	Description	Default
`experimentals`	`VariogramSet or sequence of sequence of ExperimentalVariogram or None`	A `VariogramSet`, whose directions are used, or an `nvar x nvar` matrix: entry `[i][j]` for `i <= j` is the direct (`i == j`, required) or cross variogram of variables `i` and `j`; the lower triangle is ignored, and a missing cross pair (None) is left to the positive semi-definite constraint. With `directions`, each entry is a sequence of one per direction.	required
`model`		As in `Variogram.fit`; `count/gamma` weighs a cross pair by the model's `sqrt(γii γjj)`.	`Ellipsis`
`weighting`		As in `Variogram.fit`; `count/gamma` weighs a cross pair by the model's `sqrt(γii γjj)`.	`Ellipsis`
`ranges`		As in `Variogram.fit`; `count/gamma` weighs a cross pair by the model's `sqrt(γii γjj)`.	`Ellipsis`
`nugget`	`bool`	False fixes the nugget matrix at zero.	`True`
`directions`	`sequence of (float, float)`	Azimuth and dip in degrees of each experimental variogram.	`None`
`rotation`	`sequence of (None, float or (float, float))`	Azimuth, dip and rake, and the range ratios, free, fixed or bounded as in `Variogram.fit_directional`; need `directions`. Ranges are then major-axis ranges.	`None`
`ratios`	`sequence of (None, float or (float, float))`	Azimuth, dip and rake, and the range ratios, free, fixed or bounded as in `Variogram.fit_directional`; need `directions`. Ranges are then major-axis ranges.	`None`
`intrinsic`	`bool`	Fit an intrinsic model instead (see `Coregionalization.intrinsic`): one shape, fitted to the direct variograms each divided by its largest γ and pooled, scaled to a unit sill; then each pair's entry of the covariance matrix by weighted least squares on its variograms, the matrix projected on the positive semi-definite cone. A missing cross pair is taken as uncorrelated. With one variable this is `Variogram.fit`.	`False`

Returns:

Type	Description
`Coregionalization`

from_json `staticmethod` ¶

from_json(text)

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

intrinsic `staticmethod` ¶

intrinsic(variogram, covariance)

Intrinsic coregionalization: every direct and cross variogram is one shape scaled by an entry of covariance.

γ_ij(h) = covariance[i][j] · γ(h) / sill: all variables share the structures, ranges, nugget proportion and anisotropy of variogram, and the correlation between two variables is the same at every lag. The result is an ordinary Coregionalization for cokriging and cosimulation.

Parameters:

Name	Type	Description	Default
`variogram`	`Variogram`	The shape; only its proportions matter. Needs a finite positive sill.	required
`covariance`	`(array_like, shape(nvar, nvar))`	Symmetric positive semi-definite sill matrix, else InvalidInput.	required

Returns:

Type	Description
`Coregionalization`

to_json `method descriptor` ¶

to_json()

JSON of the parameters and, once fitted, the fitted state.

used in

Coregionalization ¶

nugget property ¶

structures property ¶

cross_covariance method descriptor ¶

fit staticmethod ¶

from_json staticmethod ¶

intrinsic staticmethod ¶

to_json method descriptor ¶