```
This is the first public release of the spherical harmonics rotation library
Date: April 13, 2012

Version 0.3 - First external release.

%% Copyright (C) 2009-2012: Leslie Greengard and Zydrunas Gimbutas
%% Contact: greengard@cims.nyu.edu
%% 
%% This program is free software; you can redistribute it and/or modify 
%% it under the terms of the GNU General Public License as published by 
%% the Free Software Foundation; either version 2 of the License, or 
%% (at your option) any later version.  This program is distributed in 
%% the hope that it will be useful, but WITHOUT ANY WARRANTY; without 
%% even the implied warranty of MERCHANTABILITY or FITNESS FOR A 
%% PARTICULAR PURPOSE.  See the GNU General Public License for more 
%% details. You should have received a copy of the GNU General Public 
%% License along with this program; 
%% if not, see <http://www.gnu.org/licenses/>.

./ - Fortran source code and drivers
matlab/ - matlab scripts and mex files 
contrib/mwrap-0.33.3/ - mwrap source code


To test the library, please type 'make all'. 


Fortran
=======

rotproj_cmpl.f    Rotate the complex spherical harmonic expansion 
                  about the Y-axis (pseudo-spectral projection scheme)

rotproj_cmpl2.f    Rotate the complex spherical harmonic expansion 
                   about the X-axis then about the Y-axis
		   (pseudo-spectral projection scheme)

rotviarecur3.f    Rotate the complex spherical harmonic expansion 
                  about the Y-axis (recurrence scheme)

Matlab
======

rotviaproj.m -  Rotate the complex spherical harmonic expansion 
                about the Y-axis (pseudo-spectral projection scheme)

rotviarecur.m  -  Rotate the complex spherical harmonic expansion 
                  about the Y-axis (recurrence scheme)


The main routines are in rotproj_cmpl.f and rotviarecur3.f, with the
drivers in rotproj_dr.f and rotviarecur3_dr.f.  The supplied makefile
assumes that you have gfortran installed and will run timing and
precision tests for both recursion and projection based (the
projection algorithm from the paper) schemes.

Note that we define Ynm(theta,phi) = sqrt( 2n+1) sqrt((n-m)!/(n+m)!)
Pnm(cos theta) e^(im phi) Yn,-m(theta,phi) = sqrt( 2n+1)
sqrt((n-m)!/(n+m)!) Pnm(cos theta) e^(-im phi) for m >= 0, without
Condon-Shortley phase convention, and we are also omitting the
normalization factor 1/(4pi) - different communities have
disagreements on these conventions.



$ make all
gfortran -O2 rotviarecur3_dr.f rotviarecur3.f 
./a.out
 recur_test
 nterms=
     100
 angle=
  0.10472E+01
 time/call=
  0.44002E-02
 speed=
  0.22726E+03
 errors=
  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00  0.11102E-15  0.55511E-16
  0.00000E+00  0.00000E+00  0.27756E-16  -.27756E-16  0.83267E-16  0.55511E-16
  0.19429E-15  0.19429E-15  0.11102E-15  0.55511E-16  0.11102E-15  0.22204E-15
  0.11102E-15  0.30531E-15  0.27756E-15  0.33307E-15  0.33307E-15  0.41633E-15
  0.44409E-15  0.58287E-15  0.55511E-15  0.61062E-15  0.80491E-15  0.74940E-15
  0.10825E-14  0.11935E-14  0.16237E-14  0.19429E-14  0.21788E-14  0.28033E-14
  0.35666E-14  0.41495E-14  0.51348E-14  0.60368E-14  0.74385E-14  0.87430E-14
  0.10186E-13  0.12018E-13  0.14280E-13  0.16515E-13  0.19429E-13  0.22829E-13
  0.26396E-13  0.30545E-13  0.35291E-13  0.40024E-13  0.44936E-13  0.49780E-13
  0.53818E-13  0.57288E-13  0.59064E-13  0.58509E-13  0.55400E-13  0.48378E-13
  0.36443E-13  0.18222E-13  -.86875E-14  -.46685E-13  -.99198E-13  -.17135E-12
  -.26892E-12  -.39985E-12  -.57297E-12  -.79887E-12  -.10894E-11  -.14583E-11
  -.19196E-11  -.24899E-11  -.31879E-11  -.40364E-11  -.50666E-11  -.63199E-11
  -.78566E-11  -.97605E-11  -.12148E-10  -.15177E-10  -.19051E-10  -.24030E-10
  -.30430E-10  -.38624E-10  -.49035E-10  -.62138E-10  -.78445E-10  -.98507E-10
  -.12292E-09  -.15232E-09  -.18748E-09  -.22928E-09  -.27889E-09  -.33783E-09
  -.40813E-09  -.49252E-09  -.59463E-09  -.71913E-09  -.87195E-09
gfortran -O2 rotproj_cmpl_dr.f rotproj_cmpl.f dfft.f yrecursion.f 
./a.out
 proj_test
 nterms=
     100
 angle=
  0.10472E+01
 time/call=
  0.72004E-02
 speed=
  0.13888E+03
 errors=
  0.00000E+00  0.11102E-15  0.55511E-16  0.11102E-15  0.55511E-16  -.11102E-15
  0.00000E+00  -.55511E-16  0.27756E-16  -.13878E-15  0.00000E+00  -.27756E-16
  0.27756E-16  0.55511E-16  -.55511E-16  -.27756E-16  -.55511E-16  0.55511E-16
  -.13878E-15  0.55511E-16  -.55511E-16  0.83267E-16  -.27756E-16  0.55511E-16
  -.27756E-16  0.11102E-15  -.27756E-16  0.00000E+00  0.55511E-16  -.83267E-16
  0.00000E+00  -.27756E-16  0.41633E-16  0.97145E-16  -.97145E-16  -.69389E-16
  0.97145E-16  -.97145E-16  0.41633E-16  -.83267E-16  0.12490E-15  0.83267E-16
  -.41633E-16  -.12490E-15  0.26368E-15  -.18041E-15  0.12490E-15  -.27756E-16
  0.27756E-16  -.18041E-15  0.16653E-15  -.69389E-16  0.41633E-16  -.41633E-16
  -.41633E-16  0.27756E-16  0.13878E-15  -.13878E-15  -.13878E-16  -.41633E-16
  -.11102E-15  0.16653E-15  0.13878E-16  0.55511E-16  -.13878E-16  0.24980E-15
  -.27756E-16  0.34694E-15  -.29143E-15  0.16653E-15  -.12490E-15  0.16653E-15
  -.55511E-16  0.22204E-15  -.12490E-15  0.26368E-15  -.18041E-15  0.23592E-15
  -.55511E-16  0.69389E-16  0.69389E-16  0.13878E-16  0.11102E-15  0.27756E-15
  0.55511E-16  -.69389E-16  0.19429E-15  -.55511E-16  -.27756E-16  0.41633E-16
  0.19429E-15  -.15266E-15  0.18041E-15  -.12490E-15  0.54123E-15  -.37470E-15
  0.45797E-15  -.36082E-15  0.48572E-15  -.12490E-15  0.20817E-15
```