Solvers: reusable nonlinear solvers

newton description

srlife.solvers.newton is a reusable Newton-Raphson solver with backtracking line search that can be used wherever we need to solve a nonlinear system of equations.

srlife.solvers.newton(RJ, x0, rel_tol=-5.0, abs_tol=1e-08, miters=20, linear_solver=<function solve>, verbose=True, return_extra=False, linesearch=True, max_search=10)

Simple newton-raphson solver

Parameters:

  • RJ – function that gives the residual and jacobian values

  • x0 – initial guess

  • rel_tol (Optional[1.0e-6]) – relative convergence tolerance

  • abs_tol (Optional[1.0e-8]) – absolute convergence tolerance

  • miters (Optional[20]) – maximum number of iterations

  • linear_solver (Optional[numpy.linalg.solve]) – function that solves the linear system A x = b

  • verbose (Optional[True]) – if true, print debug info,

  • return_extra (Optional[False]) – if true also return the final residual vector and Jacobian

  • linesearch (Optional[True]) – if true do backtracking linesearch

  • max_search (Optional[10]) – max number of backtracking steps