# ARTS built-in documentation server

## Workspace Method covmat1D

### Description

```Create 1D covariance matrix.

Creates a 1D covariance matrix for two retrieval quantities on given
grids from a given functional form. Elements  of the covariance matrix
are computed as
S_{i,j} = sigma_i * sigma_j * f(d_{i,j} / l_{i,j})
where d_{i,j} is the distance between the two grid points and l_{i,j}
the mean of the correlation lengths of the grid points.

If a cutoff value co is given elements with absolute value less than this
are set to zero.

The following functional forms are available:
"exp": f(x) = exp(-x)
"lin": f(x) = 1.0 - x, for x > 1.0, 0.0 otherwise
"gauss": f(x) = exp(-x^2)

```

Authors: Simon Pfreundschuh

### Synopsis

 covmat1D( out, grid_1, grid_2, sigma_1, sigma_2, cls_1, cls_2, co, fname )

### Variables

 GOUT out (Matrix, Sparse) The matrix in which to store the covariance matrix. GIN grid_1 (Vector) The retrieval grid for the first retrieval quantity. GIN grid_2 (Vector, Default: []) The retrieval grid for the second retrieval quantity. (If empty taken as grid_1) GIN sigma_1 (Vector) The variances of the first retrieval quantity. GIN sigma_2 (Vector, Default: []) The variances of the second retrieval quantity.(If empty taken as sigma_1) GIN cls_1 (Vector) The correlations lengths of the first retrieval quantity. GIN cls_2 (Vector, Default: []) The correlations lengths of the second retrieval quantity.(If empty taken as cls_1) GIN co (Numeric, Default: 0.0) The cutoff value for covariance matrix elements. GIN fname (String) The name of the functional form to use.