det_update_UD

pyoptex.doe.fixed_structure.splitk_plot.formulas.det_update_UD(U, D, Minv)

Compute the determinant adjustment as a factor. In other words: \(|M^*|=\alpha*|M|\). The new information matrix originates from the following update formula: \(M^* = M + U^T D U\).

The actual update is described as

\[\alpha = |D| |P| = |D| |D^{-1} + U M^{-1} U.T|\]

Parameters

Unp.array(2d)

The U matrix in the update.

Dnp.array(2d)

The diagonal D matrix in the update. It is inserted as a 1d array representing the diagonal for each set of a-priori variance ratios.

Minv: np.array(3d)

The current inverses of the information matrices for each set of a-priori variance ratios.

Returns

alphafloat

The update factor.

Pnp.array(3d)

The P matrix of the update.