Shrewd.m

Computes SHREWD weights for a given two- or three-angle spherical grid.

Syntax

    weights=shrewd(alphas,betas,gammas,max_rank,max_error)

Description

See the paper by Eden and Levitt for details on now the algorithm works: http://dx.doi.org/10.1006/jmre.1998.1427 - it is not entirely clear, in the magnetic resonance context, whether this procedure is even necessary.

Arguments

     alphas - alpha Euler angles of the grid, in radians

      betas - beta Euler angles of the grid, in radians

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

   max_rank - maximum spherical rank to take into consi-
              deration when minimizing residuals

  max_error - maximum residual absolute error per spheri-
              cal function

Returns

The output is a vector of grid weights for each [alpha beta gamma] point supplied.

Examples

See kernel/grids directory for a long list of one-, two- and three angle grids.

Notes

for a given arrangement of angles, this is the most consistent weight selection procedure in the literature. Lebedev grids satisfy SHREWD condition by definition, all other grids may be rebalanced towards better description of low spherical ranks by the use of this procedure.

See also

get_hull.m, grid_kron.m, grid_test.m, repulsion.m

Version 1.10, authors: Ilya Kuprov