# File formats¶

## OFF file format¶

OFF files must be conform to format described here: http://www.geomview.org/docs/html/OFF.html

OFF files are mainly used as point cloud inputs. Here is an example of 7 points in a 3-dimensional space. As edges and faces are not used for point set, there is no need to specify them (just set their numbers to 0):

# Default is 3 dimension
OFF
# 7 vertices - 0 face - 0 edge
7 0 0
# Point set:
1.0 1.0  0.0
7.0 0.0  0.0
4.0 6.0  0.0
9.0 6.0  0.0
0.0 14.0 0.0
2.0 19.0 0.0
9.0 17.0 0.0


../../points/alphacomplexdoc.off

For dimensions bigger than 3, the dimension can be set like here:

# Dimension is no more 3
nOFF
# dimension 4 - 7 vertices - 0 face - 0 edge
4 7 0 0
# Point set:
1.0 1.0  0.0 0.0
7.0 0.0  0.0 0.0
4.0 6.0  0.0 0.0
9.0 6.0  0.0 0.0
0.0 14.0 0.0 0.0
2.0 19.0 0.0 0.0
9.0 17.0 0.0 0.0


## Persistence Diagram¶

Such a file, whose extension is usually .pers, contains a list of persistence intervals.

Lines starting with # are ignored (comments).

Other lines might contain 2, 3 or 4 values (the number of values on each line must be the same for all lines):

[[field] dimension] birth death


Here is a simple sample file:

# Persistence diagram example
2 2.7 3.7
2 9.6 14.
3 34.2 34.974
4 3. inf


Other sample files can be found in the data/persistence_diagram folder.

Such files can be generated with gudhi.SimplexTree.write_persistence_diagram(), read with gudhi.read_persistence_intervals_grouped_by_dimension(), or gudhi.read_persistence_intervals_in_dimension() and displayed with gudhi.plot_persistence_barcode() or gudhi.plot_persistence_diagram().

## Iso-cuboid¶

Such a file describes an iso-oriented cuboid with diagonal opposite vertices (min_x, min_y, min_z,…) and (max_x, max_y, max_z, …). The format is:

min_x min_y [min_z ...]
max_x max_y [max_z ...]


Here is a simple sample file in the 3D case:

-1. -1. -1.
1. 1. 1.


## Perseus¶

This file format is a format inspired from the Perseus software by Vidit Nanda. The first line contains a number d begin the dimension of the bitmap (2 in the example below). Next d lines are the numbers of top dimensional cubes in each dimensions (3 and 3 in the example below). Next, in lexicographical order, the filtration of top dimensional cubes is given (1 4 6 8 20 4 7 6 5 in the example below).

Example of a input data.

The input file for the following complex is:

2
3
3
1
4
6
8
20
4
7
6
5


../../data/bitmap/cubicalcomplexdoc.txt

To indicate periodic boundary conditions in a given direction, then number of top dimensional cells in this direction have to be multiplied by -1. For instance:

2
-3
3
1
4
6
8
20
4
7
6
5


../../data/bitmap/periodiccubicalcomplexdoc.txt

Indicate that we have imposed periodic boundary conditions in the direction x, but not in the direction y.

Other sample files can be found in the data/bitmap folder.

Note

Unlike in Perseus format the filtration on the maximal cubes can be any double precision number. Consequently one cannot mark the cubes that are not present with -1’s. To do that please set their filtration value to $$+\infty$$ (aka. inf in the file).