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Package ylmdec (in ylmdec.i) - compute Ylm coefficients using hex ray tracer
Index of documented functions or symbols:
DOCUMENT alm= accumulate(n, f, mesh, rcap, rtrack, pts, dylm, flux, nrpp)
Do N batches (approximately rays_per_batch each, default 13000) of
rays from file F, MESH = hydra_mesh(F), analyzing the symmetry of
a capsule of radius RCAP (all rays tangent to this sphere),
tracing the rays only down to radius RTRACK (>1.001*RCAP).
This routine is designed to be called several times successively
to get better statistics. PTS, DYLM, FLUX, and NRPP are all updated.
PTS = unit vectors in directions of points on capsule surface
defaults to bucky(3,1): 1280 points with an intrinsic
fidelity of about 1% out to l=12
use bucky(4,1,domega), dylm= get_ylm(pts,lmax,list)*domega(-,..)
to get 5120 points and intrinsic fidelity of about 0.2% at l=12
DYLM = ylm*domega for PTS
FLUX = accumulated flux at each of PTS; units are power/area
NRPP = accumulated number of rays per point of capsule surface
ALM = 91 coefficients of Ylm up to l=12 corresponding to FLUX
l= [0, 1,1, 2,2,2, 3,3,3,3, 4,4,4,4,4, ...]
m= [0, 0,1, 0,1,2, 0,1,2,3, 0,1,2,3,4, ...]
DOCUMENT get_ylm(pts, lmax, list)
returns values of Ylm at the 3-by-anything array of unit vectors
PTS, for all l and m up to LMAX. The return value is
(lmax+1)*(lmax+2)/2-by-anything. The LIST is also returned; its
value is [1, 2,2, 3,3,3, 4,4,4,4, ..., LMAX+1,LMAX+1,...,LMAX+1]
-- i copies of each integer i up to LMAX+1. This can be useful
in conjunction with the histogram function; its values are l+1
for each element of the returned array's first index. The m
values are [0, 0,1, 0,1,2, 0,1,2,3, 0,1,2,3,4, ...]. Negative m
values are omitted, since they would be the conjugates of m>0.
llist= list-1;
mlist= (!list(dif))(cum)-(list-2)*(list-1)/2;