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Homotopy Continuation Solver

A homotopy method solver that finds fixed points of C2 functions. The solver is an implementation of the predictor-corrector scheme.

Prerequisites

  • scipy
  • numpy
  • pickle

Getting Started

  • "caseTest.py" contains 3 test examples.

  • test 1: finds a root of multi-polynomial equation

  • test 2: finds the equilibrium of an LSTM neural network map

  • test 3: finds the equilibria of LSTM NN during the training

To Run:

  • Step 1: choose test ={1,2,3}.
  • Step 2: run python main.py

Orginization of the code

  • HomPCSolver/*Impl_.py: abstract classes that contain the main implementation of the homotopy solver. Any personal use should inherent from the class "HomotopyPCSolver"

  • demo/LSTMS.py: an implementation of a simple n dimensional LSTM map.

Reference:

  • Garcia, C. B., & Zangwill, W. I. Pathways to solutions, fixed points, and equilibria. 1981.

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Homotopy based fixed point solver with application to RNNs

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