|
1 ******************************************************************************** |
|
2 * Rips-ZZ: Rips Zigzags for Homology Inference * |
|
3 ******************************************************************************** |
|
4 |
|
5 This is an extension to the Rips package of the Dionysus library. It |
|
6 adapts the code of the Morozov zigzag (M-ZZ) and image Rips zigzag |
|
7 (iR-ZZ) to the context of the following paper: |
|
8 |
|
9 Title: Zigzag Zoology: Rips Zigzags for Homology Inference |
|
10 Authors: Steve Y. Oudot and Donald R. Sheehy |
|
11 |
|
12 It also provides two variants of the M-ZZ: the discretized Morozov |
|
13 zigzag (dM-ZZ) and the oscillating Rips zigzag (oR-ZZ). |
|
14 |
|
15 |
|
16 Source files: |
|
17 |
|
18 - M-ZZ.cpp: implementation of the Morozov zigzag |
|
19 - dM-ZZ.cpp: implementation of the discretized Morozov zigzag |
|
20 - oR-ZZ.cpp: implementation of the oscillating Rips zigzag |
|
21 - iR-ZZ.cpp: implementation of the image Rips zigzag |
|
22 - rips-pairwise.cpp: computation of the standard Rips filtration |
|
23 and its persistent homology. |
|
24 |
|
25 Execution: |
|
26 |
|
27 - the list of arguments required by a program can be obtained by |
|
28 running that program without arguments. |
|
29 |
|
30 - every program takes in a point cloud file, in xyz... format (no |
|
31 need to indicate the ambient dimension at the beginning of the |
|
32 file. A sample point cloud is provided in the file |
|
33 input/spiral_3d_10k.xyz |
|
34 |
|
35 - every program also asks for the name of the output file in which |
|
36 the barcode will be written. The output format is such that the |
|
37 file can be executed in Matlab. This creates a cells structures |
|
38 that can be read by the px_homologyplot function from the PLEX 2.5 |
|
39 library (a copy of which is provided). This function will plot the |
|
40 barcode dimension per dimension. |
|
41 |
|
42 |
|
43 |