TpTnOsc 1.1

Tools for analyzing TP, TN and OSC matrices

TpTnOsc

A Python package for analyzing totally positive (TP), totally non-negative (TN), and oscillatory (OSC) matrices.

The tool contains many functions and classes that can perform the following:

• compute matrix minors and multiplicative compound matrices
• compute and display the SEB factorization of an Invertible TN (I-TN) matrix
• test if a matrix is TP, TN, I-TN, or OSC
• compute the number of (cyclic and non-cyclic) sign variations in a vector
• compute the exponent of an oscillatory matrix
• compute and display families of vertex-disjoint paths corresponding to lower-left and upper-right corner minors of oscillatory matrices

See notebook for details and examples.

Modules

• utils.py contains several functions related to the number of sign variations in a vector, multiplicative compound matrices, SEB factorization, planar networks and other TP/TN/OSC matrices related functions.
• osc_exp.py contains the functions and classes to compute the exponent of an oscillatory matrix and the corresponding families of vertex-disjoint paths.

Examples

• osc_exp_examples.ipynb contains examples of using the triangle graph (derived from the planar networks of an SEB factorization) to deduce the exponent of an oscillatory matrix , and to compute the families of vertex-disjoint paths of each corner minor of , where is the exponent of

• basic_examples.py contains few basic examples

• mat_call_py_example.m is a Matlab example of using Python functions from utils.py

Install

Install using pip: pip install TpTnOsc.