cc Contact: shravan@umich.edu; zydrunas.gimbutas@gmail.com Release 3.0, Apr 29, 2014 This directory contains Matlab codes for fast grid rotation method on a sphere. The algorithm contructs a set of grids, obtained by rotating the original grid by nphi uniformly spaced angles phi. This release contains optional calls to the nonuniform FFT in two dimensions for testing/timing purposes, and should handle odd number of nphi in the initial grid correctly. The naming of routines has been slightly changed, the main routines now have the 'rotgrid' prefix. References: Z. Gimbutas and S. Veerapaneni, "A Fast Algorithm for Spherical Grid Rotations and its Application to Singular Quadrature", SIAM Journal on Scientific Computing, Vol. 35(6), 2013, pp. A2738-A2751. ==== The package requires nuFFT 1D and 2D packages http://www.cims.nyu.edu/cmcl/nufft/nufft.html cc Copyright (C) 2004-2009: Leslie Greengard and June-Yub Lee cc Contact: greengard@cims.nyu.edu cc cc This program is free software; you can redistribute it and/or modify cc it under the terms of the GNU General Public License as published by cc the Free Software Foundation; either version 2 of the License, or cc (at your option) any later version. This program is distributed in cc the hope that it will be useful, but WITHOUT ANY WARRANTY; without cc even the implied warranty of MERCHANTABILITY or FITNESS FOR A cc PARTICULAR PURPOSE. See the GNU General Public License for more cc details. You should have received a copy of the GNU General Public cc License along with this program; cc if not, see <http://www.gnu.org/licenses/>. cc ==== rotgrid_ref_cmpl.m requires optimized shiftphase.m routines, but it is easy to switch to regular Matlab by uncommenting several lines above the shiftphase call. ==== To run a simple test, from the "tests" directory, please type 'octave test_rotgrid.m' from the command line or 'test_rotgrid' in Matlab The output should look as: nphi = 30 ntheta = 30 nphi1 = 30 ntheta1 = 15 nrot = 450 Elapsed time is 0.01083 seconds. errors = Columns 1 through 6: 9.1138e-14 9.5956e-14 9.7719e-14 9.9192e-14 9.7382e-14 9.8978e-14 Columns 7 through 12: 9.6945e-14 9.2933e-14 9.6933e-14 9.0302e-14 8.6574e-14 8.6283e-14 Columns 13 through 18: 8.1918e-14 8.0267e-14 8.1629e-14 8.0789e-14 7.8961e-14 7.8707e-14 Columns 19 through 24: 8.0565e-14 7.8953e-14 8.0139e-14 7.8398e-14 8.1377e-14 8.0041e-14 Columns 25 through 30: 7.8107e-14 7.8561e-14 8.2652e-14 8.1167e-14 8.5414e-14 9.1389e-14