NLABench

This MATLAB app allows to test solvers for Algebraic Nonlinear Equations.

# NLABench - GUI to test Nonlinear Algebraic Solvers

% Copyright 2026 Jorge Paloschi

This MATLAB app is meant to help testing solvers for Nonlinear Algebraic Equations. In particular, it is meant to be used together with the hsolve solver available in the MathWorks File Exchange ( it assumes this is installed and available in the path). It also needs the NLAlgEx AppDesigner app (set of nonlinear examples coded in MATLAB), also available from MathWorks File Exchange.

It uses as a bench 80 examples available in the NLAlgEx app implementation, and allows to test a particular solver on all the examples, on one example, compare several solvers from those available. The GUI also has functionality to allow adding your own solvers, which must satisfy the following footprint:

function [sols,fval,exitflag] = testSolver( fun , jac, x0, lb, ub, options)

% Output parameters

% sols: cell array with obtained solutions

% fval: function values at solutions

% exitflag: should be = 1 if success

% Input parameters

% fun: function handle to evaluate

% jac: function handle to jacobian evaluation (could be empty if not available)

% x0: initial point

% lb: lower bounds

% ub: upper bounds

% options: solver options

If the hsolve solver is selected, the GUI allows to plot the homotopy path followed by the solver (results in the tabs "Path plots" and "Path table". The animate speed slider allows to customize the plot speed and the Var range input field in the app allows to select particular variables to plot (by default all are selected). You can enter, for instance 1:3, and then variables 1 to 3 will be plotted. You can also enter 1,3 and then only variables 1 and 3 will be plotted.

There is a dropdown menu to select a particular problem or all of them, and the Results tab will show details about the solutions found, if any.

The app assumes the availability of the MATLAB Optimization Toolbox

References:

Jorge Paloschi (2026). hsolve - Homotopy solver for algebraic nonlinear equations (https://es.mathworks.com/matlabcentral/fileexchange/166286-hsolve-homotopy-solver-for-algebraic-nonlinear-equations), MATLAB Central File Exchange. Recuperado 2 septiembre, 2026.

Jorge Paloschi (2026). Set of systems of algebraic nonlinear equations .mat coded (https://es.mathworks.com/matlabcentral/fileexchange/184637-set-of-systems-of-algebraic-nonlinear-equations-mat-coded), MATLAB Central File Exchange. Recuperado 2 septiembre, 2026.

## License

See the license.txt file provided