File formats

Table of Contents

• OFF file format
• Persistence Diagram
• Iso-cuboid
• Perseus

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

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.
  # Some comments
  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::persistent_cohomology::Persistent_cohomology::output_diagram() and read with Gudhi::read_persistence_intervals_and_dimension(), Gudhi::read_persistence_intervals_grouped_by_dimension() or Gudhi::read_persistence_intervals_in_dimension().

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 (http://www.sas.upenn.edu/~vnanda/perseus/) 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

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

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).