test case: galaxy density field reconstruction

At astro tea today, I described the following test case for BASIN, which
yields a "reconstruction" of a smoothed density field from the point
distribution of galaxies such as from the SDSS:

Step one: setup galaxy data
---------------------------
read galaxy positions (RA, DEC, redshift) from disk
define user function to map redshift to radial distance
   (with user input to specify cosmological parameters)
convert galaxy (RA, DEC, redshift) to (x, y, z)
    (uses user-defined function or combination of mathematical functions)

Step two: setup data mask using random points
---------------------------------------------
read catalog of random angular positions (RA, DEC) from disk
bin (RA, DEC) onto 2D grid (this forms the "angular mask")
read radial selection function table from disk
   (create user-defined function)
compute radial coordinate for randoms using selection function
    (generate random number, distribute using sel fun as prob distribution)
convert random (RA, DEC, distance) to (x, y, z)
   (again, user defined or comb of math functions)

Step three: make normalized density field
-----------------------------------------------
Cloud-in-Cell bin galaxies onto 3D cartesian grid
   with user input for grid size
CIC bin randoms onto 3D cartesian grid
divide 3D grids to obtain normalized 3D density grid
use angular mask to flag pixels outside of survey region
   (create binary mask 3D grid)

Step four: analysis and visualization
--------------------------------------
compute moments (mean, sigma, etc) of density grid
   (use mask to include only pixels inside survey)
compute and plot density histogram
smooth with specified kernel (not necessarily Gaussian!)
   (need convolution routine)
compute moments of smoothed density
threshold to flag pixels above/below threshold
compute volume fraction above/below threshold
visualize isodensity contours

Given Step three above (or, in some cases, even just the CIC binned
galaxies) it also becomes possible to
estimate the power spectrum using FFTW of the galaxies and randoms
estimate the two-point correlation function

Given Step three we have serial code that will
estimate the topological genus of isodensity contours
It may be of interest to parallelize that code

Another application is void finding, for which we already have a
(serial) algorithm.

I'll let Dave follow up this email with his thoughts about requirements
for user-defined functions.

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Michael S. Vogeley
Department of Physics, Drexel University, Philadelphia, PA 19104
Phone: (215)895-2710 FAX: (215)895-5934
Web: www.physics.drexel.edu Email: vogeley@drexel.edu
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Received on Thu Aug 18 20:57:20 2005