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Diffstat (limited to 'src')
-rw-r--r-- | src/Persistent_cohomology/example/README | 121 | ||||
-rw-r--r-- | src/Persistent_cohomology/utilities/README | 114 |
2 files changed, 125 insertions, 110 deletions
diff --git a/src/Persistent_cohomology/example/README b/src/Persistent_cohomology/example/README index 794b94ae..f39d9584 100644 --- a/src/Persistent_cohomology/example/README +++ b/src/Persistent_cohomology/example/README @@ -1,43 +1,14 @@ -To build the example, run in a Terminal: +To build the examples, run in a Terminal: -cd /path-to-example/ +cd /path-to-examples/ 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/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 2 - -output: -2 0 0 inf -2 1 0.0983494 inf -2 1 0.104347 inf -2 2 0.138335 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/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 3 - -output: -3 0 0 inf -3 1 0.0983494 inf -3 1 0.104347 inf -3 2 0.138335 inf - -and the computation with Z/2Z and Z/3Z coefficients simultaneously: +Computation of the persistent homology with Z/2Z and Z/3Z coefficients simultaneously of the Rips complex +on points sampling a 3D torus: ./rips_multifield_persistence ../../data/points/tore3D_1307.off -r 0.25 -m 0.12 -d 3 -p 2 -q 3 @@ -53,7 +24,13 @@ output: 6 0 0 0.12047 6 0 0 0.120414 -and finally the computation with all Z/pZ for 2 <= p <= 71 (20 first prime numbers): +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 + +and the computation with all Z/pZ for 2 <= p <= 71 (20 first prime numbers): ./rips_multifield_persistence ../../data/points/Kl.off -r 0.25 -m 0.5 -d 3 -p 2 -q 71 @@ -70,82 +47,6 @@ output: 557940830126698960967415390 0 0 0.120414 *********************************************************************************************************************** -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 ../../data/points/iso_cuboid_3_in_0_1.txt 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: diff --git a/src/Persistent_cohomology/utilities/README b/src/Persistent_cohomology/utilities/README new file mode 100644 index 00000000..76e960da --- /dev/null +++ b/src/Persistent_cohomology/utilities/README @@ -0,0 +1,114 @@ +To build the utilities, run in a Terminal: + +cd /path-to-utilities/ +cmake . +make + +*********************************************************************************************************************** +Example of use of RIPS: + +Computation of the persistent homology with Z/2Z coefficients of the Rips complex on points +sampling a 3D torus: + +./rips_persistence ../../data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 2 + +output: +2 0 0 inf +2 1 0.0983494 inf +2 1 0.104347 inf +2 2 0.138335 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/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 3 + +output: +3 0 0 inf +3 1 0.0983494 inf +3 1 0.104347 inf +3 2 0.138335 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 ../../data/points/iso_cuboid_3_in_0_1.txt 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 |