logo  GpRegressNd ND Gaussian Process Regression

=GpRegressNd(Variogram, Scaling, xValues, fValues, errValues, xStar,
RangeOrBeta, SillOrAlpha, Nugget, CalcError)


Variogram: (see Variograms section for details)

Scaling: Scaling of parameters

xValues: Function parameters values

fValues: Function values

xStar: Parameters value(s) to interpolate

errValues: Function estimated error(s). A unique value or one value per function value

RangeOrBeta: [Optional if Variogram=10] Distance in which the difference of the variogram from the sill becomes negligible (Range) or exponent of the power variogram (β)

SillOrAlpha: [Optional if Variogram=10] Limit of the variogram tending to infinity lag distances (Sill) or power variogram constant (α)

Nugget: [Optional] Height of the jump of the variogram at the discontinuity at the origin (default = 0)

CalcError: [Optional]

If CalcError = 1, GpRegressNd must be entered as an array formula. Select a range of one line by two columns starting with the GpRegressNd cell if the results are arranged in columns or select a range of two lines by one column starting with the GpRegressNd cell if the results are arranged in rows. Press F2 to start edit mode and press CTRL+SHIFT+ENTER to insert the function. If the formula is not entered as an array formula, the single result is the regression result.


The variogram represent function dependence on parameters. Four variograms are available. The α parameter of the power variogram can be fitted on data if requested.

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Available Variograms

Exponential (Variogram = 3)

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Exponential variogram

Spherical (Variogram = 5)

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Spherical variogram

Gaussian (Variogram = 9)

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Gaussian variogram

Power (Variogram = 10)

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Power variogram

With 1 ≤ β ≤ 1.99

If the parameter β (RangeOrBeta) is missing, β is calculated to fit the data.

If the parameter α (SillOrAlpha) is missing, α is calculated to fit the data.

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