ReduceMonomsRBC 0.1

Reduce monomial basis for SDP computations for ROM of Rayleigh–Bénard convection.

ReduceMonomsRBC

ReduceMonomsRBC is a Python package that reduces the list of monomials for sum-of-squares (SOS) optimization of reduced-order models (ROMS). The monomials are reduced by applying highest-degree cancellation and symmetry conditions derived from the structure of the ROM. This package is built for ROMs of 2D Rayleigh–Bénard convection, but can be adapted to any ROM whose general structure is known.

Features:

• Reduce list of monomials and save list for use in SOS optimization
• Generate ouptut file with number of monomials at each reduction step.

Package Requirements

• numpy (Version 1.5 or later)
• sympy (Version 1.6 or later)
• csv (any version)
• scipy (Version 0.10 or later)

Installation

To install the package, either:

• download or clone this repository and use from ReduceMonomsRBC import monom_reduction from the directory containing the package, OR
• install package directly using pip install ReduceMonomsRBC then from ReduceMonomsRBC import monom_reduction

Instructions

To construct a system of ROMs, use the command monom_reduction(*args). Options can be passed as function arguments as detailed below.

Options:

• ode_name : Name of ODE
• num_vars : Number of variables in ODE
• monom_deg : Maximum degree of auxilary functions. Typically an even number
• hk_hier : If True, uses HK hierarchy for Rayleigh–Bénard
• hier_num : Model number in the HK hierarchy. Only matters if hk_hier=True
• monom_stats : If True, outputs stats on number of monomials after each step
• out_file : Name of output file
• out_dir : Specify output directory

Examples:

monom_reduction('HK4', 4, 6, hk_hier=True, hier_num=1)
Generates and reduces list of monomials of degree 6 for the HK4 model (in the HK hierarchy of ROMs)