90 | | ! The routine is called during the analysis step. |

91 | | ! It has to compute the product of the inverse of |

92 | | ! the observation error covariance matrix with |

93 | | ! the matrix of observed EOF modes (SEEK) or |

94 | | ! observed ensemble perturbations (SEIK/ETKF). |

| 92 | The routine is called during the analysis step. In the algorithms the product of the inverse of the observation error covariance matrix with some matrix has to be computed. For the SEIK filter this matrix holds the observed part of the ensemble perturbations ('''HL'''). The matrix is provided as `A_p`. The product has to be given as `C_p`. |

| 93 | |

| 94 | |

| 95 | Hints: |

| 96 | * the routine does not require that the product is implemented as a real matrix-matrix product. Rather, the product can be implemented in its most efficient form. For example, if the observation error covariance matrix is diagonal, only the multiplication of the diagonal with matrix `A_p` has to be implemented. |

| 97 | * The observation vector `obs_p` is provided through the interface for cases where the observation error variance is relative to the actual value of the observations. |