********************************************************************************

*		 Rips-ZZ: Rips Zigzags for Homology Inference                  *

********************************************************************************

This is an extension to the Rips package of the Dionysus library. It

adapts the code of the Morozov zigzag (M-ZZ) and image Rips zigzag

(iR-ZZ) to the context of the following paper:

Title: Zigzag Zoology: Rips Zigzags for Homology Inference

Authors: Steve Y. Oudot and Donald R. Sheehy

It also provides two variants of the M-ZZ: the discretized Morozov

zigzag (dM-ZZ) and the oscillating Rips zigzag (oR-ZZ).

Source files:

 - M-ZZ.cpp: implementation of the Morozov zigzag

 - dM-ZZ.cpp: implementation of the discretized Morozov zigzag

 - oR-ZZ.cpp: implementation of the oscillating Rips zigzag

 - iR-ZZ.cpp: implementation of the image Rips zigzag

 - rips-pairwise.cpp: computation of the standard Rips filtration 

                      and its persistent homology.

Execution:

 - the list of arguments required by a program can be obtained by

   running that program without arguments.

 - every program takes in a point cloud file, in xyz... format (no

   need to indicate the ambient dimension at the beginning of the

   file. A sample point cloud is provided in the file

   input/spiral_3d_10k.xyz

 - every program also asks for the name of the output file in which

   the barcode will be written. The output format is such that the

   file can be executed in Matlab. This creates a cells structures

   that can be read by the px_homologyplot function from the PLEX 2.5

   library (a copy of which is provided). This function will plot the

   barcode dimension per dimension.