1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
|
# Matching distance between bifiltrations and 2-persistence modules.
## Accompanying paper
M. Kerber, A. Nigmetov,
Efficient Approximation of the Matching Distance for 2-parameter persistence.
SoCG 2020.
Bug reports can be sent to "anigmetov EMAIL SIGN lbl DOT gov".
## Dependencies
* Your compiler must support C++11.
* Boost.
## Usage:
1. To use a standalone command-line utility matching_dist:
`./matching_dist -d dimension -e relative_error file1 file2`
If `relative_error` is not specified, the default 0.1 is used.
If `dimension` is not specified, the default value is 0.
Run `./matching_dist` without parameters to see other options.
The output is an approximation of the exact distance (which is assumed to be non-zero).
Precisely: if *d_exact* is the true distance and *d_approx* is the output, then
> | d_exact - d_approx | / d_exact < relative_error.
Files file1 and file2 must contain 1-critical bi-filtrations in a plain text format which is similar to PHAT. The first line of a file must say *bifiltration_phat_like*. The second line contains the total number of simplices *N*. The next *N* lines contain simplices in the format *dim x y boundary*.
* *dim*: the dimension of the simplex
* *x, y*: coordinates of the critical value
* *boundary*: indices of simplices forming the boundary of the current simplex. Indices are separated by space.
* Simplices are indexed starting from 0.
For example, the bi-filtration of a segment with vertices appearing at (0,0) and the 1-segment appearing at (3,4) shall be written as:
> bifiltration_phat_like
> 3
> \# lines starting with \# are ignored
> \# vertex A has dimension 0, hence no boundary, its index is 0
> 0 0 0
> \# vertex B has index 1
> 0 0 0
> \# 1-dimensional simplex {A, B}
> 1 3 4 0 1
2. To use from your code.
Here you can compute the matching distance either between bi-filtrations or between persistence modules.
First, you need to include `#include "matching_distance.h"` Practically every class you need is parameterized by Real type, which should be either float or double. The header provides two functions called `matching_distance.`
See `example/module_example.cpp` for additional details.
## License
See `licence.txt` in the repository root folder.
## Building
CMakeLists.txt can be used to build the command-line utility in the standard
way. On Linux/Mac/Windows with Cygwin:
> `mkdir build`
> `cd build`
> `cmake ..`
> `make`
On Windows with Visual Studio: use `cmake-gui` to create the solution in build directory and build it with VS.
The library itself is header-only and does not require separate compilation.
|
