# ARTS built-in documentation server

## Workspace Method covmat1DMarkov

### Description

Create Markov Process Covariance Matrix.
Create a markov process covariance matrix for a retrieval quantity on
evenly spaced 1D grid. The correlation between two grid points i,j is
is computed as
cov(i,j) = sigma[i] * sigma[j] * exp(- d(i,j) / lc)
where d(i,j) = abs(grid[i] - grid[j]).
This function also sets covmat_inv_block to the analytically computed inverse
of the covariance matrix of the markov provess, which is tri-diagonal. Note
that this requires the retrieval grid to be evenly spaced.

**Authors: **Simon Pfreundschuh

### Synopsis

covmat1DMarkov( | out, out_inverse, grid, sigma, lc, co ) |

### Variables

GOUT | out | (Matrix, Sparse) | The matrix in which to store the covariance matrix. |

GOUT | out_inverse | (Matrix, Sparse) | The matrix in which to store the inverse of the covariance matrix. |

GIN | grid | (Vector) | The retrieval grid. |

GIN | sigma | (Vector) | The vairance for each grid point. |

GIN | lc | (Numeric) | The correlation length of the Markov process. |

GIN | co | (Numeric, Default: 0.0) | The cutoff value below which elements will be set to 0.0 |