FPSDP

Description

FPSDP is a Matlab toolbox for computation of lower bounds for roundoff error using semidefinite relaxations.

We consider the roundoff error r of a program implementing a polynomial function f(x):

		r(x,e) = l(x, e) + h(x, e)

with l(x, e) the part of r(x, e) linear w.r.t. e and h(x, e) the part of r(x, e) non-linear w.r.t. e.

FPSDP computes an upper bound of |l(x, e)| with x lying in a box, and e being bounded by a given machine epsilon.

For instance, one can consider f(x) = x1^3 + (3/4) x1 x2^2, with x1 in [-1, 1] and x2 in [-2, 2].

Installation instructions

Prerequisites

FPSDP has been tested with Matlab2015a and relies on two external libraries for Matlab:

• Yalmip to handle the poynomial representations (Free)
• Mosek SDP solver (Free Academic license)

Download

FPSDP is maintained as a GitHub repository at the address https://github.com/magronv/FPSDP.git

It can be obtained with the command:

$ git clone https://github.com/magronv/FPSDP.git

Benchmarks

In the Matlab command window, add to the path the Yalmip and Mosek directories.

	addpath(genpath('path to Yalmip')); addpath(genpath('path to Mosek'));

Go to code/ in order to execute the following scripts:

• do_all_benchs: executes all scripts id_Optimizer2.m, for each id in {'rigidbody1', 'rigidbody2', 'kepler0', 'kepler1', 'kepler2', 'sineTaylor', 'sineOrder3', 'sqroot', 'himmilbeau'}
• do_all_benchs_realvars: executes all scripts id_Optimizer3.m

After executing one of the above scripts, several files containing results are generated.

In your favorite shell terminal, go to code/ and execute ./bring_together. This generates one result file for each benchmark. A file named all_results containing all results is also generated.