# ARTS built-in documentation server

## Workspace Method covmat_sxAddInverseBlock

### Description

Add the inverse of a block in covariance matrix covmat_sx
This functions adds a given matrix as the inverse of a block in the covariance
matrix covmat_sx. The purpose of this function is to allow the user to
to use a precomputed inverse for this block in the covariance matrix, the may
for example by obtained analytically.
This function requires the non-inverse block to already be present in covmat_sx
If the 'i' and 'j' input arguments are not given, the inverse block
will be added at the position of the most recently added non-inverse diagonal
block.
Note that for this to work this retrieval quantity must be independent from
other retrieval quantities that do not have an inverse. Otherwise the inverse
will be ignored and recomputed numerically.
For the rest, the same requirements as for covmat_sxAddBlock apply.

**Authors: **Simon Pfreundschuh

### Synopsis

### Variables

OUT+IN | covmat_sx | (CovarianceMatrix) | Covariance matrix of a priori distribution This covariance matrix describes the Gaussian a priori distribution for an OEM retrieval. |

IN | jacobian_quantities | (ArrayOfRetrievalQuantity) | The retrieval quantities in the Jacobian matrix. |

GIN | block | (Matrix, Sparse) | The inverse block to add to the covariance matrix |

GIN | i | (Index, Default: -1) | Index of a retrieval quantity. Must satisfy ``i`` <= ``j``. |

GIN | j | (Index, Default: -1) | Index of a retrieval quantity. Must satisfy ``i`` <= ``j``. |