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tutorial:persistent_homology [2017/09/18 23:38] – [Vietoris-Rips filtration] oroehrig | user_guide:tutorials:persistent_homology [2019/01/25 09:38] – ↷ Page moved from user_guide:persistent_homology to user_guide:tutorials:persistent_homology oroehrig | ||
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A filtration can be initialized by passing the Hasse diagram of the last frame of the filtration and an array containing the degree of each cell, indexed in the same order as the node indexing in the Hasse diagram (without the empty set and the dummy node with index 0, thus shifted by one). Consider this small three-frame example filtration: | A filtration can be initialized by passing the Hasse diagram of the last frame of the filtration and an array containing the degree of each cell, indexed in the same order as the node indexing in the Hasse diagram (without the empty set and the dummy node with index 0, thus shifted by one). Consider this small three-frame example filtration: | ||
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You can construct it in '' | You can construct it in '' | ||
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===== Computing Persistence ===== | ===== Computing Persistence ===== | ||
There are two different functions, one to compute persistent homology for coefficients from arbitrary euclidean domains, and another for computing persistence barcodes for field coefficients. Both are templated by the boundary matrix type. The following examples compute both for this filtration of the 5-simplex, whose 3rd frame is the real projective plane: | There are two different functions, one to compute persistent homology for coefficients from arbitrary euclidean domains, and another for computing persistence barcodes for field coefficients. Both are templated by the boundary matrix type. The following examples compute both for this filtration of the 5-simplex, whose 3rd frame is the real projective plane: | ||
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The function for coefficients from arbitrary euclidean domains takes as parameters a filtration object matching the matrix type and indices '' | The function for coefficients from arbitrary euclidean domains takes as parameters a filtration object matching the matrix type and indices '' | ||
- | The following code loads a filtration object with Integer coefficients containing the example that was previously saved to disk, which you can download {{ :tutorial: | + | The following code loads a filtration object with Integer coefficients containing the example that was previously saved to disk, which you can download {{ user_guide: |
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==== Field coefficients and barcodes ==== | ==== Field coefficients and barcodes ==== | ||
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< | < |