josmangarsal / copositivity-detection-bundfuss-faces

Copositivity matrix detection using simplices, faces refinement vs Bundfuss bisection

CoPositivity detection

Prerequisites:

- C++17

- Python3

With numpy and scipy for matrix null space and LP.

- Install Intel MKL library as a standalone package

1. Go to https://software.seek.intel.com/performance-libraries
2. Register
3. Download Intel MKL
4. tar zxvf l_mkl_2019.0.117.tgz
5. cd folder
6. ./install_GUI.sh
7. Customize installation to install just Intel Math Kernel Library for C/C++ with GNU C/C++ compiler support
8. cd ~/intel/mkl/bin$ && sh ./mklvars.sh intel64

How to compile:

• make clean: Clean build and exec.
• make: Compile
• make total: Clean, compile and run
• IMPORTANT:
  • Check your Intel MKL and Python 3 path in the makefile.
  • .../intel/mkl/lib/intel64 must be in LD_LIBRARY_PATH (make total performs that).

How to run:

Run run -? to see help.

usage:
  run  options

where options are:
  -n, --dimension <dimension>         Problem dimension (integer) [Required]
  -M, --matrix <matrix_path>          Matrix file (string) [n!=3,5]
  -t <dimacs_t>                       Dimacs t value (integer) [n!=3,5]
  -D, --division <division_method>    Division method (string) ['facet',
                                      'bundfuss', 'zbund'] [Required]
  -?, -h, --help                      display usage information

Remainder: Matrix dim 3 and dim 5 (Horn) is harcoded, run them using:

• run -n 3 -D <division_method>
• run -n 5 -D <division_method>

Division methods:

• facet: Facets and monotonicity (SARTECO18)
• bundfuss: Bundfuss
• zbund: Bundfuss and monotonicity