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Spherical 3D Isotropic Wavelet Transform on the Ball
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===================================================================================== MRS3D - MultiResolution in Spherical 3D Library and tools v1.0b 09/2013 ===================================================================================== MRS3D is a C++ package providing a library and a set of tools allowing the manipulation of Spherical Fourier-Bessel Coefficients and the implementation of MultiResolution algorithms adapted to 3D data in spherical coordinates. In particular, MRS3D implements a Spherical 3D Isotropic Wavelet Decomposition. As a part of MRS3D, this package also contains the FastDSBT C++ library wich implements a Discrete Spherical Bessel Transform based on a matrix formalism. MRS3D is distributed under the CeCILL License (see LICENSE.CeCILL) in the hope that it will be usefull but without any warranty. The following softwares are used in MRS3D: - HEALPix (http://healpix.jpl.nasa.gov/) distributed under the GNU GPL - 3DEX (https://github.com/ixkael/3DEX) developed by Boris Leistedt and released under the CeCiLL License. See the ArXiV paper http://arxiv.org/abs/1111.3591. Author: François Lanusse (firstname.lastname@example.org) Copyright CEA 2013 =================== Requirements =================== In order to be able to compile the MRS3D package, the following softwares are required: - cmake (http://cmake.org/cmake/resources/software.html) - HEALPix (http://sourceforge.net/projects/healpix/files/) - cfitsio (http://heasarc.gsfc.nasa.gov/fitsio/) - OpenMPI or other MPI implementation - gfortran and gcc The following softwares are optional: - Doxygen - IDL =================== Building =================== Before building the MRS3D package, it is necessary to build and install the HEALPix package (Fortran AND CXX versions). First, unpack the tar.gz archive: $ tar -xvzf MRS3D.tar.gz $ cd MRS3D Set the CFITSIO_DIR environment variable to the directory containing libcfitsio.a: $ export CFITSIO_DIR=/usr/lib If IDL is installed on your system, you can build the MRS3D IDL interface by setting the environment variable IDL_DIR to the IDL root directory: $ export IDL_DIR=/Applications/itt/idl By default, the binary tools, headers and libraries will be installed in the MRS3D directory. To install them elsewhere on your sytem (e.g. /usr/local), you can set the INSTALL_DIR environment variable: $ export INSTALL_DIR=/usr/local [ Optional ] Compile the package: $ mkdir build $ cd build $ cmake .. $ make all $ make install To build the documentation: $ make doc The html documentation will be available at doc/html/index.html. If LaTeX is installed on your system, you can also build the pdf documentation by going to the doc/latex subdirectory and typing make. =================== Running the code =================== The transformations implemented in MRS3D require the values of zeros of Bessel functions. Instead of behing calculated each time, these values are tabulated inside a binary FITS file. This file, referred to as qlnTable, must be provided as first argument of all MRS3D commands. A precomputed qlnTable is provided with MRS3D and contains the first 3000 zeros of Bessel functions up to the order 2000. This file should be sufficient for most applications. To compute a larger qlnTable, the gen_qln tool is provided. The following command will generate a table containing the first 2000 zeros of Bessel functions up to order 4000. $ gen_qln qlnTable.fits 4000 2000 MRS3D provides two main binary tools almn2wavelet and waveletThresholding: > almn2wavelet : Computes an Isotropic Undecimated Spherical 3D Wavelet decomposition from an almn .fits file. > waveletThresholding : Applies wavelet hard thresholding to the input almn .fits file. These tools work on Spherical Fourier-Bessel coefficients stored in "almn" FITS files. In order to compute almn coefficients to test these functions, two additional tools are provided field2almn and almn2field: > field2almn : Computes the Discrete Spherical Fourier-Bessel Transform from a 3D cartesian field .fits file. > almn2field : Reconstructs a cartesian 3D field from an almn .fits file. As an example, to decompose a field into wavelet scales from the MRS3D root directory run: $ bin/field2almn test/qlnTable.fits test/VirgoField256.fits test/VirgoAlmn.fits 512 250.0 256 256 256 Will store in "VirgoAlmn.fits" coefficients computed from the field "VirgoField256.fits" using a HEALPix resolution of nside=512, a boundary condition rmax=250.0 Mpc/h, up to the orders lmax=256, mmax=256 and nmax=256. $ bin/almn2wavelet test/qlnTable.fits test/VirgoAlmn.fits wavelet 512 4 3.5 This command will produce 5 FITS files (wavelet_0.fits wavelet_1.fits...), one for each wavelet scale, plus one for the smoothed density. The cutoff frequency of the low pass filter is set to 3.5 $ bin/almn2field test/qlnTable.fits test/wavelet_0.fits test/waveletField_0.fits 256 479.0 512 Reconstructs the density field of the first wavelet scale inside a cube of size 256x256x256 and physical size 479.0 Mpc/h using a Healpix resolution of nside=512. Now, to visualize the density fields, the IDL interface can be used, see the next section. =================== IDL Interface =================== To work on spherical Fourier-Bessel coefficients and 3D fields from IDL, MRS3D comes with an IDL interface. The IDL procedures are in src/IDL. In order to work these procedures load libMRS3DIDL and by default expect the library to be in the same directory. To setup the IDL procedures, go to src/IDL and create a symlink to the libMRS3DIDL library: $ ln -s ../../lib/libmrs3d_IDL.dylib ./libmrs3d_IDL.dylib To setup the FastDSBT IDL interface use as well: $ ln -s ../../lib/libfastDSBT_IDL.dylib ./libfastDSBT_IDL.dylib (under linux, the libraries in /lib will be .so and not .dylib but keep the name in .dylib for the symlinks) In the /src/IDL directory, launch IDL. Available features: - Compute power spectrum from almn - Save/Load power spectrum to/from FITS files - Save/Load almn to/from FITS files - Save/Load cartesian density fiels to/from FITS files - Convert almn to field and field to almn (The use of the binary tools is prefered) Example of how to visualize the wavelet scale computed at the previous section: IDL> fieldWavelet = mrs3d_load_field('/path-to-MRS3D/test/waveletField_0.fits') IDL> ivolume, fieldWavelet To get help on the mrs3d_* commands, set the help keyword (e.g. mrs3d_save_field,/help) =================== Parallel execution =================== MRS3D is designed to take full advantage of OpenMP and MPI. All the tools provided with MRS3D are parallelized using OpenMP and will by default run using a thread by processor core. To manually set the number of threads used by the command set the environment variable OMP_NUM_THREADS: export OMP_NUM_THREADS=4 (bash) or setenv OMP_NUM_THREADS 4 (tcsh) To launch a command using several MPI processes: mpirun -np 4 [command followed by arguments] !!!!!!!!!!!!!!!!!!!!!!!!! WARNING !!!!!!!!!!!!!!!!!!!!! When using MPI, be sure to use powers of 2 for the number of l,m and n coefficients. Since l goes from 0 to lmax, you must set l=2^i -1 !!!! The same goes for m. Since n varies from 1 to nmax you can directly set nmax= 2^l A valid set of (lmax,mmax,nmax) is : 1023 1023 512 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! An example of a PBS script to run a command on a computer cluster is provided below: -----------------------------------waveletThresholding.job---------------------------------- #!/bin/sh #PBS -l pmem=15G #PBS -l pvmem=16G #PBS -l mem=120G #PBS -l vmem=128G #PBS -l nodes=8:ppn=1 #PBS -W x=NACCESSPOLICY:SINGLEJOB #PBS -l walltime=100:00:00 #PBS -M [your email address] #PBS -m abe export OMP_NUM_THREADS=8 cd [path to working directory] cat $PBS_NODEFILE | sort | uniq > machinefile.txt echo "----Begining job----" > log date >> log echo "--------------------" >> log mpiexec -machinefile machinefile.txt -np 8 ./waveletThresholding qlnTable_2000_3000.fits Almn.fits ThresholdedAlmn.fits 2048 250.0 5 5 9.0 0.75 >> log echo "----Job done--------" >> log date >> log ---------------------------------------------------------------------------------------------- To launch the job : qsub waveletThresholding.job