Grid test.m

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Plots grid integration quality as a function of spherical rank.




The quality of a grid is defined as the norm of the residual of spherical harmonics or Wigner functions integrated using the grid provided.


     alphas - alpha Euler angles of the grid, in radians,
              zeros for single-angle grids

      betas - beta Euler angles of the grid, in radians

     gammas - gamma Euler angles of the grid, in radians,
              zeros for two-angle grids

    weights - point weights of the grid

   max_rank - maximum spherical rank to consider

       sfun - spherical function type: for three-angle
              grids use 'D_lmn', for two-angle grids use
              'Y_lm', for single-angle grids use 'Y_l0'.


   grid_profile - a vector of residual norms in each spherical rank

The function also produces a figure showing the absolute value of the integration residual as a function of the spherical rank.


Perfomance of the 400-point 2-angle REPULSION grid on spherical harmonics of different ranks.


A good grid produces near-zero answers for as many spherical ranks as possible.

See also

grid_kron.m, repulsion.m, shrewd.m, wigner.m, spher_harmon.m

Version 1.10, authors: Ilya Kuprov