minkowski3 - README

A program for calculating Minkowski functionals of density fields with periodic boundary conditions

written by Jens Schmalzing. January 1997; updated by Thomas Buchert.
email: buchert@obs.univ-lyon1.fr

The program calculates densities of Minkowski functionals in the V normalization. Minkowski functionals are discussed in all the references below. The derivation of the formulae and the analytical values used in the program are given in [8]. References [2,7,9,10] provide background reading on Minkowski functionals, while [1,3,4,5,6] present some applications on points processes.

Unpacking:

The program is distributed as an uuencoded compressed tar file `beyond.uu' (Type: uudecode beyond.uu; gunzip beyond.tar.gz; tar -xvf beyond.tar) Now the directory `beyond' should look like this: Makefile fourier.c image.h minkowski.c org.h Readme fourier.h main.c minkowski.h beyond.sm image.c main.h org.c

Installation:

Go into the directory `beyond' and type: make Perhaps you have to choose a different c-compiler and different flags in the first few lines of Makefile. You may also alter the program name there. If `make' gives no error you probably generated the program `beyond' successfully. To check the installation type: make test Then the examples explained in the next section are calculated. You can plot the results using the SuperMongo macro `beyond' provided in the file `beyond.sm' To restore the original files type: make realclean This will remove all files generated by previous calls of make.

Examples:

beyond -\?
get a list of options and the actual (default) values of the parameters.
beyond -l-4 -h4 -b10 -s4 -L10 -x32 -y32 -z32 -otest.res -0test.xpm
calculate the Minkowski functionals at 10 threshold values between -4 and 4, for 10 realizations of a Gaussian random field with scale-free power spectrum, normalized to mean 0 and variance 1. Density values are obtained on 32^3 lattice points in a unit box, with Gaussian smoothing of 4/32=0.125. The mean and variance of the Minkowski functionals over all realizations are output to the file test.res. Also, the final realization is given as a XPM bitmap in test.xpm.

CPU load:

On a hp 715/80 the test calculation took a little more than 1 minute, using less than 1 MByte of memory. An IBM RS/6000 can do a single realization for a 256^3 lattice at 100 threshold values in about one hour, using roughly 192 MByte of memory.

References:

[1] Thomas Buchert (1996): `Robust morphological measures for large-scale structure', in: 11. Potsdam Cosmology Workshop on Large-scale Structure in the Universe, Geltow 1995, F.R.G., J. Mücket, S. Gottlöber, V. Müller (eds.), World Scientific, 156-161.

[2] Martin Kerscher, Jens Schmalzing and Thomas Buchert (1996): `Analyzing Galaxy Catalogues with Minkowski Functionals', in: Mapping, Measuring and Modelling the Universe, Valencia 1995, P. Coles, V.J. Martinez, M.J. Pons (eds.), ASP Conference Series, 247-252.

[3] Martin Kerscher, Jens Schmalzing, Thomas Buchert and Herbert Wagner (1998): `Fluctuations in the IRAS 1.2 Jy catalogue', Astron. Astrophys., 333, 1-12.

[4] Martin Kerscher, Jens Schmalzing, J&oumrg Retzlaff, Stefano Borgani, Thomas Buchert, Stephan Gottlöber, Volker Müller, Manolis Plionis and Herbert Wagner (1997): `Minkowski Functionals of Abell/ACO clusters', M.N.R.A.S., 284, 73-84.

[5] Martin Kerscher, Klaus R. Mecke, Jens Schmalzing, Claus Beisbart, Thomas Buchert and Herbert Wagner (2001): `Morphological fluctuations of large-scale structure: The PSCz survey', Astron. Astrophys., 373, 1-11.

[6] C. Hikage, J. Schmalzing, T. Buchert, Y. Suto, I. Kayo, A. Taruya, Michael S. Vogeley, F. Hoyle, J.R. Gott III and J. Brinkmann (2003): `Minkowski Functionals of SDSS Galaxies I : Analysis of Excursion Sets', P.A.S.J., 55, 911-931.

[7] Klaus R. Mecke, Thomas Buchert and Herbert Wagner (1994): `Robust morphological measures for large-scale structure in the Universe', Astron. Astrophys. 288, 697-704.

[8] Jens Schmalzing and Thomas Buchert (1997): `Beyond genus statistics: a unifying approach to the morphology of cosmic structure', Ap.J. Lett. 482, L1-L4.

[9] Jens Schmalzing, Martin Kerscher and Thomas Buchert (1996): `Minkowski functionals in Cosmology', in: Proc. International School Enrico Fermi, Course CXXXII (Dark Matter in the Universe), Varenna 1995, S. Bonometto, J. Primack, A. Provenzale (eds.), IOS Press Amsterdam, 281-291.

[10] Jens Schmalzing, Diplomarbeit, Ludwig--Maximilians--Universit&aumt M&uumnchen, 1996, in German, English excerpts available.