NAME

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pc_alpha - Compute a persistence diagram from an alpha filtration of a point cloud

SYNOPSIS

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homcloud-pc-alpha
    [-h] [-V] [-t TYPE] [-n NOISE] [-d DIMENSION] [-w]
    [--square] [--no-square] [-P] [-A]
    [--save-suppl-info SAVE_SUPPL_INFO] [-M SAVE_BOUNDARY_MAP]
    [--save-phtrees SAVE_PHTREES] [--algorithm ALGORITHM]
    [--vertex-symbols VERTEX_SYMBOLS]
    [--periodicity xmin xmax ymin ymax zmin zmax] [--license]
    INPUT OUTPUT

This program can also be invoked as python3 -m homcloud.cli.pc_alpha.

ALIAS

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homcloud-pc-alpha

DESCRIPTION

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This program computes a persistence diagram from a (weighted or non-weighted) alpha filtration built from a 2D/3D point cloud, and writes the result as a .pdgm file.

OPTIONS

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-h, --help            show this help message and exit
-V, --version         show program's version number and exit
-t TYPE, --type TYPE  input file format type
-n NOISE, --noise NOISE
                      level of additive noise
-d DIMENSION, --dimension DIMENSION
                      dimension of the input data
-w, --weighted        use an weighted alpha filtration
--square              squared output (default)
--no-square           no squared output, if a birth radius is negative,
                      the output is -sqrt(abs(r))
-P, --partial-filtration
                      Compute partial filtration (relative homology)
-A, --check-acyclicity
                      Check acyclicity for paritial filtration
--save-suppl-info SAVE_SUPPL_INFO
                      save supplementary information of PD
                      (yes/no, default:yes)
-M SAVE_BOUNDARY_MAP, --save-boundary-map SAVE_BOUNDARY_MAP
                      save boundary map into the output pdgm file
                      (only available with phat-* algorithms, *on*/off)
--save-phtrees SAVE_PHTREES
                      save phtrees into output pdgm file
                      (only available with phat-* algorithms, on/*off*)
--algorithm ALGORITHM
                      algorithm (phat-twist(default), phat-chunk-parallel)
--vertex-symbols VERTEX_SYMBOLS
                      vertex symbols file
--periodicity xmin xmax ymin ymax zmin zmax
                      use a periodic alpha filtration
--license             show license and exit

INPUT FILE FORMAT

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You can use both weighted and non-weighted alpha filtration.

The input format of a non-weighted 3d point cloud is:

# A line starting with a sharp sign is ignored
x_1 y_1 z_1
x_2 y_2 z_2
:

You can use a 2d point cloud:

x_1 y_1
x_2 y_2
  :

In the weighted case, the input file for 3d is:

x_1 y_1 z_1 w_1
x_2 y_2 z_2 w_2
   :

The weights should be squared (for example, you should put the square of the van der Waals radius). The lines starting with a sharp sign are always ignored.

2D weighted alpha filtration is not supported because of the limitation of CGAL.

OUTPUT FILE

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This program always writes a .pdgm file into OUTPUT. Old output formats (.complex, .icomplex, .diagram, .idiagram) are no longer supported; giving OUTPUT one of these extensions raises an error.

If -M on (the default) is given, the boundary map is embedded into the pdgm file, which is required by homcloud-optvol and other volume-optimal-cycle tools.

NOTES

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This module was previously named pc2diphacomplex and renamed to pc_alpha. The old -I/--combine-index-map and -D/--convert-to-diagram options (used when the program produced dipha/idipha complex or diagram files) have been removed: the program always computes and writes a pdgm file directly now.

-P/--partial-filtration and -A/--check-acyclicity are still accepted by the argument parser but are currently unimplemented; the program raises an internal assertion error if either is given.