********************** minkowski 2.1 ********************** A program for calculating Minkowski functionals of a Boolean grain model with boundary correction. Written by Jens Schmalzing and Martin Kerscher. Minkowski functionals are discussed in all the references below. The computational method for a Boolean grain model without boundary conditions is discussed in [1]. The computational method for boundaries is a generalization of this method [2]. The deconvolution of the boundaries is discussed in [2], [3]. Download: --------- The program is distributed as a compressed tar file. You may download the actual version from http://homepages.physik.uni-muenchen.de/~Martin.Kerscher/software/ Installation: ------------- Go into the directory you unpacked the code and type: make Perhaps you have to choose a different c-compiler and different flags in the makefile. If `make' gives no error you probably generated the program `main' successfully. Examples: --------- ./main -h get a list of options and the actual (default) values of the parameters. ./main -n100 -l10 -R0.3 -obox.res calculate the mean Minkowski functionals of 10 realization of a binomial process with 100 points within a cube of sidelength 1. The results go to box.res. ./main -n1000 -s0.1 -r0 -R0.17 -d0.01 -iparticle.dat -oparticle_sub.res Subsample 10%, i.e. 1000 points from the 10k points in particle.dat Then calculate the Minkowski functionals for radii from 0 to 0.17 with steps 0.01. The points in particle.dat were extracted from a sample used in [4]. With ./main -n1000 -l10 -S128 -r0 -R0.17 -d0.01 -orandom_sub.res we simulate 10 realizations of randomly distributed points (binomial process) with the same scaling as in the preceding calculations. From the 10 realizations we can estimate the fluctuations around the randomly distributed points and hence compare with particle_sub.res (see plotparticle.gpl). ./main -n10000 -r0 -R0.1 -d0.005 -iparticle.dat -oparticle.res Finally, calculate the Minkowski functionals of all 10k points in particle.dat. This may take some time. Results of these calculations are saved in corresponding files *.ores for your reference. Simple gnuplot macros for plotting the Minkowski functionals can be found in box.plot, particle_sub.plot and particle.plot . Hints and known limitations: ---------------------------- - The definition of the geometry of the sample window is in the file objects.c . - The input procedure for the cluster data used in reference [3] is in the file cluster.c, the input procedure used for analyzing tubulent multiphase flow [4] is in bubble.c (definitions of the sample window are in objects.c). - Up to now the code was used only for convex boundaries. - There is some documentation in the source code. - The Program calculates the volume densities v of the V-measures (compare the definitions in [2]). - If several realizations are drawn, the program computes the mean and the standard error of the v-measures. - The time needed for a calculation strongly depends on the type of clustering. With 100k points this ranges from several hours (Poisson) to several weeks (strong filamentary clustering). Samples with less than 1k points are typically no problem (several minutes) on present day (2007) hardware. - No precautions are taken to check for degenerate positions. E.g. four points lying in a plane, especially if they (almost) form a rectangle will lead to numerical problems. Probably this is the reason that for some large strongly clustering samples, the calculation delivers a "nan" (not a number). - Another source of numerical problems are degenerate spherical triangles, i.e. triangles with comparatively large sidelengths, but vanishing areas. Such problems mostly occur while analyzing large (>10k) and very strongly clustered data sets. Compared to minkowski 2.0, some crude workarounds are built in (see minkowski.c and recipes.c). - Sometimes it helps to randomize the positions slightly to get rid of these numerical problems. Applications: ------------- The code minkowski 2.0 has been used in several situations, namely to calculate the Minkowski functionals of Abell/ACO clusters as shown in [3]. The typical sample size was <1000 points with moderately complex boundaries. Recently the updated code minkowski 2.1 has been used to calculate the Minkowski functionals of particles in turbulent flow [4]. The sample sizes was 100K points with simple boundaries. Versions History: ----------------- 2.0 The code was developed in 1996 by Jens Schmalzing and Martin Kerscher based on a Fortran program by Klaus Mecke. 2.1 Some corrections and simplifications have been made in 2007 by Martin Kerscher. You can obtain the old code minkowski2 from Thomas Buchert (buchert@cosmunix.de) . As you may have guessed from the version history, donīt expect frequent updates. Legal stuff, acknowledgements, contact -------------------------------------- The code in recipes.c is adopted from Numerical Recipes (see copyright information in this file). The rest of the code is covered by the GPL (for details see main.c and gpl-3.0.txt). Just to make sure, this program is provided "as is" without warranty of any kind. If you use the code for your publications, it would be nice if you could cite [1] for the method and [3] for the code. If you have comments, suggestions, improvements, feel free to contact me. Martin Kerscher Fakultaet fuer Physik Schellingstr. 4 D-80799 Muenchen martin.kerscher@lmu.de References: ----------- [1] K.R. Mecke, T. Buchert, H. Wagner (1994): ``Robust Morphological Measures for Large-scale Structure in the Universe'', Astron. Astrophys. 288, 697-704. astro-ph/9312028 [2] J. Schmalzing, M. Kerscher, T. Buchert (1996): ``Minkowski functionals in Cosmology'', in: Proc. of the International School Enrico Fermi Course CXXXII: Dark Matter in the Universe, eds.: Bonometto, Primack, Provenzale. pp. 281--291, astro-ph/9508154 [3] M. Kerscher, J. Schmalzing, J. Retzlaff, S. Borgani, T. Buchert, S. Gottl"ober, V. M"uller, M. Plionis, H. Wagner : ``Minkowski functionals of Abell/ACO Clusters'', Mon. Not. R. Astr. Soc., 284 (1997) pp. 73-84, astro-ph/9606133 [4] E. Calzavarini, M. Kerscher, D. Lohse, F. Toschi: Dimensionality and Morphology of Particle and Bubble Clusters in Turbulent Flow (in preparation 2007)