oemMeasurementBasisCalc

Workspace.oemMeasurementBasisCalc(self, oem: OptimalEstimationData = self.oem) → None

Construct a measurement-only projection by grouping proportional Jacobian rows.

Compares every state derivative in each row of oem.measurement_jac. Rows are divided by their signed largest-magnitude entry and grouped when all resulting entries match exactly. Opposite signs and different amplitudes can belong to the same group. No approximate similarity threshold is used. All-zero rows form one group. With no matching rows, the result is a sparse identity.

For diagonal oem.measurement_vec_error_covmat, with variances \(\sigma_i^2\) and row amplitudes \(a_i\), each group produces one noise-normalized measurement:

\[C_{g i}=\frac{a_i/\sigma_i^2} {\sqrt{\sum_{k\in g}a_k^2/\sigma_k^2}},\quad i\in g.\]

Other entries are zero. The Sparse result stores one entry per channel. The state basis and covariances are unchanged. For measurement-only retrieval, use an identity oem.model_state_basis_mat with oemCalcReduced().

For correlated noise, define \(T_{ig}=a_i\) for channels in group g and zero otherwise. The result is \(\mathbf C=\mathbf T^\top\mathbf S_\epsilon^{-1}\), computed by a covariance solve, not by constructing an inverse. This result can be dense and its projected noise covariance need not be identity. Keeping correlations is necessary even when Jacobian rows match exactly.

These combinations preserve the state-dependent likelihood of the supplied linear Gaussian model. For nonlinear models, this is a local statement at the supplied Jacobian. Floating-point row normalization can fail to recognize mathematically proportional rows. General linear dependencies between distinct row directions are left to oemBasisCalc() and oemBasisReduce(). This method does not set their singular spectrum or loss outputs; its groups are not singular modes and must not be passed to oemBasisReduce(). No agenda runs and no Jacobian is recomputed.

Author: Richard Larsson

Parameters:

oem (~pyarts3.arts.OptimalEstimationData, optional) – Numerical problem and results for oemCalc() and oemCalcReduced(). Defaults to self.oem. [INOUT]