OKlibrary  0.2.1.6
general.hpp File Reference

Plans on linear algebra in Maxima. More...

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Detailed Description

Plans on linear algebra in Maxima.

Todo:
Create milestones
Todo:
Write tests
Todo:
Write docus
Todo:
Indices
  • Also hermitian_rank_eig and hermitian_rank_charpoly should be changed to compute the indices as pnn_indices.
  • So that we get pnn_indices_eig and pnn_indices_charpoly.
  • Perhaps then we create a generic function for computing the hermitian rank from a version of pnn_indices.
  • We should write a general function for counting the number of sign changes in a polynomial; function hermitian_rank_charpoly then should use this function.
  • The sign-test in hermitian_rank_eig w.r.t. bfloat-values should be extracted, and moved to module Numerical.
Todo:
Algorithms for the hermitian rank
  • Currently hermitian_rank_charpoly seems fastest.
  • I (OK) would guess that the algorithm for hermitian_rank (the variation of Gaussian elimination) should be nevertheless the fastest:
    1. Since at this level we don't want to go into implementation details, I (OK) don't see how to improve the implementation of "pnn_indices".
    2. Study the literature on computing the pnn-indices.
    3. And then there are the sparsity-considerations.

Definition in file general.hpp.