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Ripser / ripser

Ripser: efficient computation of Vietoris–Rips persistence barcodes
http://ripser.org
MIT License
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Homology of a cube #16

Closed alexdkeros closed 6 years ago

alexdkeros commented 6 years ago

Dear Ripser developers,

While trying to compute the persistent homology of a cube, expecting results similar to a 2-sphere, I get the following results:

point cloud
--------------
0.25 0.25 0.25
0.75 0.25 0.25
0.25 0.75 0.25
0.75 0.75 0.25
0.25 0.25 0.75
0.75 0.25 0.75
0.25 0.75 0.75
0.75 0.75 0.75

Results: sneky_riipser_bug

The issues are the following:

1.There are only 5 generators of dimension 1. 2.There are no generators in dimension 2. 3.There is a generator in dimension 3 that should ideally be in dimension 2.

Could you please shed some light to this issue?

Thank you in advance, Alexandros

ubauer commented 6 years ago

Dear Alex,

this result is (surprisingly) correct. It is not too difficult to see that there should only be 5 generators in dimension 1. It is a very interesting and non-obvious exercise to show that there are no generators in dimension 2, but a generator in dimension 3.

Best, Uli