Package for solving non-linear systems of equations. The package implements Jacobian-Free Newton Krylov method, where the Jacobian is approximated via finite differences. However, since the Krylov space methods only require the action of the Jacboian on a search direction v, the full Jacobian matrix is never explicitly stored, which makes the technique very memory efficient.
import (
"fmt"
"math"
"github.com/davidkleiven/gononlin/nonlin"
)
func ExampleNewtonKrylov() {
// This example shows how one can use NewtonKrylov to solve the
// system of equations
// (x-1)^2*(x - y) = 0
// (x-2)^3*cos(2*x/y) = 0
problem := nonlin.Problem{
F: func(out, x []float64) {
out[0] = math.Pow(x[0]-1.0, 2.0) * (x[0] - x[1])
out[1] = math.Pow(x[1]-2.0, 3.0) * math.Cos(2.0*x[0]/x[1])
},
}
solver := nonlin.NewtonKrylov{
// Maximum number of Newton iterations
Maxiter: 1000,
// Stepsize used to appriximate jacobian with finite differences
StepSize: 1e-2,
// Tolerance for the solution
Tol: 1e-7,
}
x0 := []float64{0.0, 3.0}
res := solver.Solve(problem, x0)
fmt.Printf("Root: (x, y) = (%.2f, %.2f)\n", res.X[0], res.X[1])
fmt.Printf("Function value: (%.2f, %.2f)\n", res.F[0], res.F[1])
// Output:
//
// Root: (x, y) = (1.00, 2.00)
// Function value: (-0.00, 0.00)
}
- Gonum is used to solve the linear system of equations arising in the NewtonKrylov method