PivotNR

A lightweight C++ Newton-Raphson solver for nonlinear systems of equations.

Instead of explicitly computing the Jacobian inverse,

$$ \Delta x = -J^{-1}F(x) $$

the solver directly solves

$$ J(x)\Delta x = -F(x) $$

using Gaussian elimination, which is typically faster and numerically more stable.

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Example

Solve the nonlinear system:

$$ \begin{cases} x_1^2 + x_2^2 - 4 = 0 \\ x_1 x_2 - 1 = 0 \end{cases} $$

#include "../include/newton.hpp"
#include <iostream>

int main() {

    using pivot_nr::Vec;
    using pivot_nr::Mat;

    pivot_nr::SystemFn systemFn = [](const Vec& x, Vec& f) {
        f[0] = x[0]*x[0] + x[1]*x[1] - 4.0;
        f[1] = x[0]*x[1] - 1.0;
    };
    pivot_nr::JacobianFn jacobianFn = [](const Vec& x, Mat& J) {
        J[0][0] = 2.0*x[0]; J[0][1] = 2.0*x[1];
        J[1][0] = x[1];     J[1][1] = x[0];
    };
    pivot_nr::RootFinderResult res = pivot_nr::newton_solve(systemFn, jacobianFn, Vec{2.0, 1.0});
    std::cout << "2D nonlinear system\n";
    std::cout << " (x1, x2) = (" << res.x[0] << ", " << res.x[1] << ")\n";
    std::cout << " Residual = " << res.residual << "\n";
    std::cout << " Iterations = " << res.iterations << "\n";

    return 0;
}

Build and execution

    make clean
    make
    cd bin
    ./newton

- make                  Default: debug build
- make debug            Same as above
- make release          Optimised build
- make profile          Optimised + debug symbols (for perf)
- make clean            Clean all artefacts

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