Polar shapelet coefficients are complex. They store twice as much information as there is in an wholly real image. This routine compresses the redundant information, creating a floating point array with as many entries as there were in the original complex array. It is of relatively little use in most situations, but helps to simplify the shapelet parameter space when looking at the distribution of galaxy morphologies (e.g. for creating simulated images).
Use shapelets_polar_expand.pro to restore the full set of complex polar shapelet coefficients.
See also the header below, which has been extracted from the source code for this routine.
; Apr 02 - RM removed a degeneracy in phase coefficients ; Feb 02 - Written by Richard Massey ; ; Removes the duplicated/degenerate coefficients when cartesian shapelets have ; been converted into polar form and leaves only the minimum number of ; independent parameters. This will speed up (and make possible) parametisation ; of all HDF galaxies in shapelet (probability) space. Put them back with ; shapelets_polar_expand.pro. ; ; This is achieved because, while polar shapelet coefficients are in general ; complex, diagonal (n=0) elements are wholly real and entries mirrored in the ; n=0 diagonal (ie m=-m) are complex conjugates of each other. Both of these ; constraints are necessary and sufficient requirements for the resulting object ; to be real itself. ; ; The first version of this code seperated them into Real & Imaginary parts - it ; now splits into r & theta, which I think is more physically meaningful.
View the full source code for this routine, return to the shapelets web page, or return to the code help menu.
|Last modified on 2nd Mar 2009 by Richard Massey.|