`pc_alpha`

- Compute a persistence diagram from alpha filtration

```
python3 -m homcloud.pc2diphacomplex
[-h] [-t TYPE] [-n NOISE]
[-d DIMENSION] [-w] [--no-square] [-I] [-P] [-A]
INPUT OUTPUT
```

```
homcloud-pc-alpha
```

This program computes (weighted and non-weighted) alpha filtration for dipha from (weighted or non-weighted) point clouds.

```
-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 weighed alpha filtraion
--no-square no squared output, if a birth radius is negative, the
output is -sqrt(abs(r))
-I, --combine-index-map
combine the index map with the output filtration
-D, --convert-to-diagram
call dipha and directly convert to a diagram
-P, --partial-filtration
Compute partial filtration (relative homology)
-A, --check-acyclicity
Check acyclicity for paritial filtration
-M SAVE_BOUNDARY_MAP, --save-boundary-map SAVE_BOUNDARY_MAP
save boundary map into idiagram file(only available
with phat-* algorithms, *on*/off)
--algorithm ALGORITHM
algorithm (dipha, phat-twist(default), phat-chunk-
parallel)
--vertex-symbols VERTEX_SYMBOLS
vertex symbols file
--license show license and exit
```

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

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

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

You can use 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 vanderwaals radius. The lines starting with sharp sign are always ignored.

Now 2d weighted alpha filtration is not supported because of the limitation of cgal.

If `-D`

option is given, the output file is a diagram data.
In this case, a persistence diagram is computed
from the boundary matrix.
dipha's diagram file is written if `-I`

option is not given, and
indexed-diagram file (idiagarm) file is written if `-I`

option is given.

This module was previously named `pc2diphacomplex`

and renamed to
`pc_alpha`

. Now the name `pc2diphacomplex`

is obsolete.

Now the usage of `-D`

option is always reocommend. This option is planned
to be mandatory and removed in a future version.