File formats

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

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()`

.

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.

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).

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).

GUDHI Version 3.0.0 - C++ library for Topological Data Analysis (TDA) and Higher Dimensional Geometry Understanding. - Copyright : MIT | Generated on Tue Sep 24 2019 09:57:51 for GUDHI by Doxygen 1.8.13 |