covmat1DMarkov

Workspace.covmat1DMarkov(self: pyarts.arts._Workspace, output: pyarts.arts.WorkspaceVariable | pyarts.arts.Matrix | pyarts.arts.Sparse, out_inverse: pyarts.arts.WorkspaceVariable | pyarts.arts.Matrix | pyarts.arts.Sparse, grid: pyarts.arts.WorkspaceVariable | pyarts.arts.Vector, sigma: pyarts.arts.WorkspaceVariable | pyarts.arts.Vector, lc: pyarts.arts.WorkspaceVariable | pyarts.arts.Numeric, co: pyarts.arts.WorkspaceVariable | pyarts.arts.Numeric | None = 0.0, verbosity: pyarts.arts.WorkspaceVariable | pyarts.arts.Verbosity | None = self.verbosity) → None

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.

Author(s): Simon Pfreundschuh

Parameters:

  • output (Matrix or Sparse) – The matrix in which to store the covariance matrix. [OUT]

  • out_inverse (Matrix or Sparse) – The matrix in which to store the inverse of the covariance matrix. [OUT]

  • grid (Vector) – The retrieval grid. [IN]

  • sigma (Vector) – The vairance for each grid point. [IN]

  • lc (Numeric) – The correlation length of the Markov process. [IN]

  • co (Numeric, optional) – The cutoff value below which elements will be set to 0.0. Defaults to 0.0 [IN]

  • verbosity (Verbosity) – ARTS verbosity. See verbosity, defaults to self.verbosity [IN]