# -*- coding: utf8 -*-

"""Provide an implementation of geometric FBA."""

from __future__ import absolute_import, division

import logging

from optlang.symbolics import Zero

from cobra.flux_analysis.parsimonious import add_pfba
from cobra.flux_analysis.variability import flux_variability_analysis

LOGGER = logging.getLogger(__name__)


def geometric_fba(model, epsilon=1E-06, max_tries=200):
    """
    Perform geometric FBA to obtain a unique, centered flux distribution.

    Geometric FBA [1]_ formulates the problem as a polyhedron and
    then solves it by bounding the convex hull of the polyhedron.
    The bounding forms a box around the convex hull which reduces
    with every iteration and extracts a unique solution in this way.

    Parameters
    ----------
    model: cobra.Model
        The model to perform geometric FBA on.
    epsilon: float, optional
        The convergence tolerance of the model (default 1E-06).
    max_tries: int, optional
        Maximum number of iterations (default 200).

    Returns
    -------
    cobra.Solution
        The solution object containing all the constraints required
        for geometric FBA.

    References
    ----------
    .. [1] Smallbone, Kieran & Simeonidis, Vangelis. (2009).
           Flux balance analysis: A geometric perspective.
           Journal of theoretical biology.258. 311-5.
           10.1016/j.jtbi.2009.01.027.

    """

    with model:
        # Variables' and constraints' storage variables.
        consts = []
        obj_vars = []
        updating_vars_cons = []

        # The first iteration.
        prob = model.problem
        add_pfba(model)  # Minimize the solution space to a convex hull.
        model.optimize()
        fva_sol = flux_variability_analysis(model)
        mean_flux = (fva_sol["maximum"] + fva_sol["minimum"]).abs() / 2

        # Set the gFBA constraints.
        for rxn in model.reactions:
            var = prob.Variable("geometric_fba_" + rxn.id,
                                lb=0,
                                ub=mean_flux[rxn.id])
            upper_const = prob.Constraint(rxn.flux_expression - var,
                                          ub=mean_flux[rxn.id],
                                          name="geometric_fba_upper_const_" +
                                          rxn.id)
            lower_const = prob.Constraint(rxn.flux_expression + var,
                                          lb=fva_sol.at[rxn.id, "minimum"],
                                          name="geometric_fba_lower_const_" +
                                          rxn.id)
            updating_vars_cons.append((rxn.id, var, upper_const, lower_const))
            consts.extend([var, upper_const, lower_const])
            obj_vars.append(var)
        model.add_cons_vars(consts)

        # Minimize the distance between the flux distribution and center.
        model.objective = prob.Objective(Zero, sloppy=True, direction="min")
        model.objective.set_linear_coefficients({v: 1.0 for v in obj_vars})
        # Update loop variables.
        sol = model.optimize()
        fva_sol = flux_variability_analysis(model)
        mean_flux = (fva_sol["maximum"] + fva_sol["minimum"]).abs() / 2
        delta = (fva_sol["maximum"] - fva_sol["minimum"]).max()
        count = 1
        LOGGER.debug("Iteration: %d; delta: %.3g; status: %s.",
                     count, delta, sol.status)

        # Following iterations that minimize the distance below threshold.
        while delta > epsilon and count <= max_tries:
            for rxn_id, var, u_c, l_c in updating_vars_cons:
                var.ub = mean_flux[rxn_id]
                u_c.ub = mean_flux[rxn_id]
                l_c.lb = fva_sol.at[rxn_id, "minimum"]
            # Update loop variables.
            sol = model.optimize()
            fva_sol = flux_variability_analysis(model)
            mean_flux = (fva_sol["maximum"] + fva_sol["minimum"]).abs() / 2
            delta = (fva_sol["maximum"] - fva_sol["minimum"]).max()
            count += 1
            LOGGER.debug("Iteration: %d; delta: %.3g; status: %s.",
                         count, delta, sol.status)

        if count == max_tries:
            raise RuntimeError(
                "The iterations have exceeded the maximum value of {}. "
                "This is probably due to the increased complexity of the "
                "model and can lead to inaccurate results. Please set a "
                "different convergence tolerance and/or increase the "
                "maximum iterations".format(max_tries)
            )

    return sol
