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diff --git a/example/Persistent_cohomology/README b/example/Persistent_cohomology/README new file mode 100644 index 00000000..7803e5ab --- /dev/null +++ b/example/Persistent_cohomology/README @@ -0,0 +1,152 @@ +To build the example, run in a Terminal: + +cd /path-to-example/ +cmake . +make + +*********************************************************************************************************************** +Example of use of RIPS: + +Computation of the persistent homology with Z/2Z coefficients of the Rips complex on points +sampling a Klein bottle: + +./rips_persistence ../../data/points/Kl.txt -r 0.25 -d 3 -p 2 -m 100 + +output: +210 0 0 inf +210 1 0.0702103 inf +2 1 0.0702103 inf +2 2 0.159992 inf + + +Every line is of this format: p1*...*pr dim b d +where + p1*...*pr is the product of prime numbers pi such that the homology feature exists in homology with Z/piZ coefficients. + dim is the dimension of the homological feature, + b and d are respectively the birth and death of the feature and + + + +with Z/3Z coefficients: + +./rips_persistence ../../data/points/Kl.txt -r 0.25 -d 3 -p 3 -m 100 + +output: +3 0 0 inf +3 1 0.0702103 inf + +and the computation with Z/2Z and Z/3Z coefficients simultaneously: + +./rips_multifield_persistence ../../data/points/Kl.txt -r 0.25 -d 3 -p 2 -q 3 -m 100 + +output: +6 0 0 inf +6 1 0.0702103 inf +2 1 0.0702103 inf +2 2 0.159992 inf + +and finally the computation with all Z/pZ for 2 <= p <= 71 (20 first prime numbers): + + ./rips_multifield_persistence ../../data/points/Kl.txt -r 0.25 -d 3 -p 2 -q 71 -m 100 + +output: +557940830126698960967415390 0 0 inf +557940830126698960967415390 1 0.0702103 inf +2 1 0.0702103 inf +2 2 0.159992 inf + +*********************************************************************************************************************** +Example of use of ALPHA: + +For a more verbose mode, please run cmake with option "DEBUG_TRACES=TRUE" and recompile the programs. + +1) 3D special case +------------------ +Computation of the persistent homology with Z/2Z coefficients of the alpha complex on points +sampling a torus 3D: + +./alpha_complex_3d_persistence ../../data/points/tore3D_300.off 2 0.45 + +output: +Simplex_tree dim: 3 +2 0 0 inf +2 1 0.0682162 1.0001 +2 1 0.0934117 1.00003 +2 2 0.56444 1.03938 + +Here we retrieve expected Betti numbers on a tore 3D: +Betti numbers[0] = 1 +Betti numbers[1] = 2 +Betti numbers[2] = 1 + +N.B.: - alpha_complex_3d_persistence accepts only OFF files in 3D dimension. + - filtration values are alpha square values + +2) d-Dimension case +------------------- +Computation of the persistent homology with Z/2Z coefficients of the alpha complex on points +sampling a torus 3D: + +./alpha_complex_persistence -r 32 -p 2 -m 0.45 ../../data/points/tore3D_300.off + +output: +Alpha complex is of dimension 3 - 9273 simplices - 300 vertices. +Simplex_tree dim: 3 +2 0 0 inf +2 1 0.0682162 1.0001 +2 1 0.0934117 1.00003 +2 2 0.56444 1.03938 + +Here we retrieve expected Betti numbers on a tore 3D: +Betti numbers[0] = 1 +Betti numbers[1] = 2 +Betti numbers[2] = 1 + +N.B.: - alpha_complex_persistence accepts OFF files in d-Dimension. + - filtration values are alpha square values + +3) 3D periodic special case +--------------------------- +./periodic_alpha_complex_3d_persistence ../../data/points/grid_10_10_10_in_0_1.off 3 1.0 + +output: +Periodic Delaunay computed. +Simplex_tree dim: 3 +3 0 0 inf +3 1 0.0025 inf +3 1 0.0025 inf +3 1 0.0025 inf +3 2 0.005 inf +3 2 0.005 inf +3 2 0.005 inf +3 3 0.0075 inf + +Here we retrieve expected Betti numbers on a tore 3D: +Betti numbers[0] = 1 +Betti numbers[1] = 3 +Betti numbers[2] = 3 +Betti numbers[3] = 1 + +N.B.: - periodic_alpha_complex_3d_persistence accepts only OFF files in 3D dimension. In this example, the periodic cube +is hard coded to { x = [0,1]; y = [0,1]; z = [0,1] } + - filtration values are alpha square values + +*********************************************************************************************************************** +Example of use of PLAIN HOMOLOGY: + +This example computes the plain homology of the following simplicial complex without filtration values: + /* Complex to build. */ + /* 1 3 */ + /* o---o */ + /* /X\ / */ + /* o---o o */ + /* 2 0 4 */ + +./plain_homology + +output: +2 0 0 inf +2 0 0 inf +2 1 0 inf + +Here we retrieve the 2 entities {0,1,2,3} and {4} (Betti numbers[0] = 2) and the hole in {0,1,3} (Betti numbers[1] = 1) |