Nonlinear Solvers: Levenberg-Marquardt

API, Parameters and Requirements

solver = solvers.create_levenberg_marquardt(problem, state, linear_solver)         (1)

solver = solvers.create_weighted_levenberg_marquardt(problem, state, \             (2)
                                                     linear_solver, weigh_functor)

• problem:
  • instance of your problem meeting the residual/jacobian API
• state:
  • rank-1 numpy.array storing initial condition
• linear_solver:
  • an object that is used to solve the linear problem stemming from the normal equations

  • must meet the following API:

    class LinearSolver:
      def solve(self, A, b, x):
        '''
        Here you need to solve Ax = b.
        Remember that you need to properly overwrite x
        '''

• weigh_functor:
  • applicable only to overload 2
  • callable that is called to apply weighting to operators at each nonlinear iteration

  • must meet the following API:

    class WeighingFunctor
      def __call__(self, operand, result):
        # apply your weighting to operand and store into result
        # remember to properly overwrite result