inv_update_UD

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

Compute the update of the inverse of the information matrix. In other words: \(M^{-1}^* = M^{-1} - M_{up}\). The new information matrix originates from the following update formula: \(M^* = M + U^T D U\).

The actual update is described as

\[M_{up} = M^{-1} U^T P^{-1} U M^{-1}\]

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

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.

Pnp.array(3d)

The P matrix if already pre-computed.

Returns

Mupnp.array(3d)

The updates to the inverses of the information matrices.