Hi,
> F = exp(A), and A = > > a b c d > b a u v > c -u a w > d -v -w a > > This seems to be the case for all matrices that we are concerned about in > the propagation parts of ARTS, even in the scattering cases. Is this true? > After a bit of reading (e.g. del Toro Iniesta's "Spectropolarimetry"), I come to the conclusion that all RT propagation matrices (i.e. the K) exhibit this structure. It's an effect of the geometry relations between electric/magnetic field and polarization frame. And it's valid for individual (wave) K as well as the "bulk" K (over different medium constituents and wave interaction processes). Got me thinking, though, that we are wasting a lot of memory and a lot of > computing time keeping the entire 4X4 propagation-matrix [...] rather use > Vectors of these parameters to represent the matrix. However, that would > be overly simplistic and might not be beneficiary enough to justify the > extra work. > Seems a clean solution to redefine ext_mat (and similar containers) to only hold the (max) 7-element vector. As Patrick mentioned, for scattering data we do something similar already. at least for the input data (when needed in the RT solution, the data are currently also converted to the up to 4x4 matrix). The general particle class is not implemented, i.e. the 7-element format is not fixed. for the azimuthally random case we use order Kjj, K12, K34 (or, for the A definition above: a, b, (-)w). This, however, is not directly applicable for the all-sky RT ext_mat format since that is rather governed by the stokes dimensionality instead of symmetry relations (e.g., for stokes_dim=2 we don't need the K34 while for stokes_dim>2 we need additional elements that are 0 in the azimuthally random scattering particles case). >From the view point of elements we need for the different stokes_dim levels, format should be like [ a, | b, | c,u, | d,v,w ], i think (the vertical dashes indicate the limits for the different stokes_dim, i.e. the reduced ext_mat would have length 1,2,4, or 7 for stokes_dim=1,2,3,4 respectively). > > Instead, I would like to propose a similar class, PropagationMatrix, that > can store the entire propagation matrix in parameterized form that is > reduced to the seven variables above by simple mechanisms. > I can not judge, whether it's advantageous to further parametrize the K contributions from different physical processes. In any case, I don't see that this would be mutually exclusive with a matrix-to-vector format change of ext_mat (since, as written above, ANY K has to exhibit the structure of A, i.e. all parametrizations anyway happen only on the 7 elements individually, not on the 4x4 elements (or, differently expressed K34 will always be equal -K43, independent of any parametrization of the different processes and in different conditions, i.e. can always be expressed by just one value together). So, if that is advantageous, there could rather be different propmat classes, depending on the process. that in the RT solution (by the abs_xsec_agenda or so, i guess) than would need to be combined into one common ext_mat vector. Regarding the scattering matrix issues, Robin & Patrick brought up, I think we should discuss this independent of the propagation matrix issues here. hence, i'm taking this in a separate mail... wishes, Jana -- ===================================================================== Jana Mendrok, Ph.D. (Researcher) Chalmers University of Technology Department of Space, Earth and Environment SE-412 96 Gothenburg, Sweden Email: [email protected] Phone : +46 (0)31 772 1883 =====================================================================
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