# computeAuxVariables

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##### Auxiliary variables for kriging

Computes or updates some auxiliary variables used for kriging (see below). This is useful in several situations : when all parameters are known (as for one basic step in Bayesian analysis), or when some new data is added but one does not want to re-estimate the model coefficients. On the other hand, computeAuxVariables is not used during the estimation of covariance parameters, since this function requires to compute the trend coefficients at each optimization step; the alternative given by (Park, Baek, 2001) is preferred.

Keywords
models
##### Usage
computeAuxVariables(model)
##### Arguments
model

an object of class km with missing (or non updated) items.

##### Value

An updated km objet, where the changes concern the following items:

T

a matrix equal to the upper triangular factor of the Choleski decomposition of C, such that t(T)*T = C (where C is the covariance matrix).

z

a vector equal to inv(t(T))*(y - F*beta), with y, F, beta are respectively the response, the experimental matrix and the trend coefficients specified in model@trend.coef. If model@trend.coef is empty, z is not computed.

M

a matrix equal to inv(t(T))*F.

##### Note

T is computed with the base function chol. z and M are computed by solving triangular linear systems with backsolve. z is not computed if model@trend.coef is empty.

##### References

J.-S. Park and J. Baek (2001), Efficient computation of maximum likelihood estimators in a spatial linear model with power exponential covariogram, Computer Geosciences, 27 no. 1, 1-7.

covMatrix, chol, backsolve.