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To build the examples, run in a Terminal:
cd /path-to-examples/
cmake .
make
***********************************************************************************************************************
Example of use of RIPS:
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
output:
6 0 0 inf
6 1 0.0983494 inf
6 1 0.104347 inf
6 2 0.138335 inf
6 0 0 0.122545
6 0 0 0.121171
6 0 0 0.120964
6 0 0 0.12057
6 0 0 0.12047
6 0 0 0.120414
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
output:
557940830126698960967415390 0 0 inf
557940830126698960967415390 1 0.0983494 inf
557940830126698960967415390 1 0.104347 inf
557940830126698960967415390 2 0.138335 inf
557940830126698960967415390 0 0 0.122545
557940830126698960967415390 0 0 0.121171
557940830126698960967415390 0 0 0.120964
557940830126698960967415390 0 0 0.12057
557940830126698960967415390 0 0 0.12047
557940830126698960967415390 0 0 0.120414
***********************************************************************************************************************
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)
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