""" Non-linear solver that implements a Newton's method."""

from math import isnan

from openmdao.solvers.backtracking import BackTracking
from openmdao.solvers.solver_base import NonLinearSolver
from openmdao.util.record_util import update_local_meta, create_local_meta


class Newton(NonLinearSolver):
    """A python Newton solver that solves a linear system to determine the
    next direction to step. Also uses `Backtracking` as the default line
    search algorithm, but you can choose a different one by specifying
    `self.line_search`. A linear solver can also be specified by assigning it
    to `self.ln_solver` to use a different solver than the one in the
    parent system.

    Options
    -------
    options['alpha'] :  float(1.0)
        Initial over-relaxation factor.
    options['atol'] :  float(1e-12)
        Absolute convergence tolerance.
    options['iprint'] :  int(0)
        Set to 0 to disable printing, set to 1 to print the residual to stdout
        each iteration, set to 2 to print subiteration residuals as well.
    options['maxiter'] :  int(20)
        Maximum number of iterations.
    options['rtol'] :  float(1e-10)
        Relative convergence tolerance.
    options['solve_subsystems'] :  bool(True)
        Set to True to solve subsystems. You may need this for solvers nested under Newton.
    """

    def __init__(self):
        super(Newton, self).__init__()

        opt = self.options
        opt.add_option('atol', 1e-12, lower=0.0,
                       desc='Absolute convergence tolerance.')
        opt.add_option('rtol', 1e-10, lower=0.0,
                       desc='Relative convergence tolerance.')
        opt.add_option('maxiter', 20, lower=0,
                       desc='Maximum number of iterations.')
        opt.add_option('alpha', 1.0,
                       desc='Initial over-relaxation factor.')
        opt.add_option('solve_subsystems', True,
                       desc='Set to True to solve subsystems. You may need this for solvers nested under Newton.')

        self.print_name = 'NEWTON'

        # Only one choice, but the user could write their own.
        self.line_search = BackTracking()

        # User can specify a different linear solver for Newton. Default is
        # to use the parent's solver.
        self.ln_solver = None

    def setup(self, sub):
        """ Initialize sub solvers.

        Args
        ----
        sub: `System`
            System that owns this solver.
        """
        if self.line_search:
            self.line_search.setup(sub)
        if self.ln_solver:
            self.ln_solver.setup(sub)

    def solve(self, params, unknowns, resids, system, metadata=None):
        """ Solves the system using a Netwon's Method.

        Args
        ----
        params : `VecWrapper`
            `VecWrapper` containing parameters. (p)

        unknowns : `VecWrapper`
            `VecWrapper` containing outputs and states. (u)

        resids : `VecWrapper`
            `VecWrapper` containing residuals. (r)

        system : `System`
            Parent `System` object.

        metadata : dict, optional
            Dictionary containing execution metadata (e.g. iteration coordinate).
        """

        atol = self.options['atol']
        rtol = self.options['rtol']
        maxiter = self.options['maxiter']
        alpha = self.options['alpha']

        # Metadata setup
        self.iter_count = 0
        local_meta = create_local_meta(metadata, system.pathname)
        system.ln_solver.local_meta = local_meta
        update_local_meta(local_meta, (self.iter_count, 0))

        # Perform an initial run to propagate srcs to targets.
        system.children_solve_nonlinear(local_meta)
        system.apply_nonlinear(params, unknowns, resids)

        f_norm = resids.norm()
        f_norm0 = f_norm

        if self.options['iprint'] > 0:
            self.print_norm(self.print_name, system.pathname, 0, f_norm,
                            f_norm0)

        arg = system.drmat[None]
        result = system.dumat[None]

        while self.iter_count < maxiter and f_norm > atol and \
                f_norm/f_norm0 > rtol:

            # Linearize Model with partial derivatives
            system._sys_linearize(params, unknowns, resids, total_derivs=False)

            # Calculate direction to take step
            arg.vec[:] = resids.vec
            with system._dircontext:
                system.solve_linear(system.dumat, system.drmat,
                                    [None], mode='fwd', solver=self.ln_solver)

            # Step in that direction,
            self.iter_count += 1
            f_norm = self.line_search.solve(params, unknowns, resids, system,
                                            self, alpha, f_norm0, metadata)

        # Need to make sure the whole workflow is executed at the final
        # point, not just evaluated.
        #self.iter_count += 1
        #update_local_meta(local_meta, (self.iter_count, 0))
        #system.children_solve_nonlinear(local_meta)

        if self.options['iprint'] > 0:

            if self.iter_count == maxiter or isnan(f_norm):
                msg = 'FAILED to converge after max iterations'
            else:
                msg = 'converged'

            self.print_norm(self.print_name, system.pathname, self.iter_count,
                            f_norm, f_norm0, msg=msg)

    def print_all_convergence(self):
        """ Turns on iprint for this solver and all subsolvers. Override if
        your solver has subsolvers."""
        self.options['iprint'] = 1
        self.line_search.options['iprint'] = 1
