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Spherical isometries, triangular block-banded eigensolvers, generalized Zernike and Dunkl-Xu OPs on the disk

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@MikaelSlevinsky MikaelSlevinsky released this 25 Nov 16:12
· 64 commits to master since this release
b60c2fb

This release:

  • adds support for spherical isometries (rotations and reflections and general orthogonal coordinate transformations of spherical harmonic expansions), thanks in part to @ikaroruan.
  • includes an implementation of the factored alternating direction implicit method for diagonal matrix equations with low-rank right-hand sides, thanks in part to @BrockKlippenstein.
  • adds methods for the complete elliptic integrals K(k) and E(k) and Jacobian elliptic functions sn(x,k), cn(x,k), and dn(x,k).
  • converts associated classical orthogonal polynomial connection problems from two parameter triangular banded eigenvalue problems to quadratic triangular banded generalized eigenvalue problems.
  • adds fast divide and conquer methods for block 2x2 triangular-banded generalized eigenvalue problems (for linearizations of the QEPs above).
  • generalizes Zernike polynomials to a real orthonormal basis for L2(D2, r2α+1(1-r^2)β dr dθ), a breaking change to the API.
  • adds Dunkl-Xu polynomials on the disk, a real orthonormal basis for L2(D2, (1-x^2-y^2)β dx dy), updating the holomorphic.c example to show the duality of the approaches.