weightMatrixFromSigma2

Build the observation-weight matrix from per-observation variances.

Developer documentation: this item describes internal implementation details.

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Declaration

 W = weightMatrixFromSigma2(sigma2,rho_X)

Parameters

• sigma2 per-observation variances
• rho_X optional observation correlation matrix

Returns

• W weight representation for the fit

Discussion

For independent errors this returns the diagonal weights

\[W = \mathrm{diag}(\sigma_1^{-2},\ldots,\sigma_N^{-2}),\]

represented here by the vector 1./sigma2.

With correlated errors, it builds the observation covariance

\[\Sigma_{ij} = \sigma_i \rho_{ij} \sigma_j,\]

and returns a MATLAB decomposition object for \(\Sigma\), which is then used in left-division solves by weightedNormalEquations.