#  ___________________________________________________________________________
#
#  Pyomo: Python Optimization Modeling Objects
#  Copyright 2017 National Technology and Engineering Solutions of Sandia, LLC
#  Under the terms of Contract DE-NA0003525 with National Technology and 
#  Engineering Solutions of Sandia, LLC, the U.S. Government retains certain 
#  rights in this software.
#  This software is distributed under the 3-clause BSD License.
#  ___________________________________________________________________________

"""Transformation to propagate state through an equality set."""

from pyomo.common.collections import ComponentSet, ComponentMap
from pyomo.core.base.constraint import Constraint
from pyomo.core.base.transformation import TransformationFactory
from pyomo.core.base.suffix import Suffix
from pyomo.core.expr.numvalue import value
from pyomo.core.plugins.transform.hierarchy import IsomorphicTransformation
from pyomo.repn.standard_repn import generate_standard_repn
from pyomo.common.config import ConfigBlock, ConfigValue, add_docstring_list


def _build_equality_set(m):
    """Construct an equality set map.

    Maps all variables to the set of variables that are linked to them by
    equality. Mapping takes place using id(). That is, if you have x = y, then
    you would have id(x) -> ComponentSet([x, y]) and id(y) -> ComponentSet([x,
    y]) in the mapping.

    """
    #: dict: map of var UID to the set of all equality-linked var UIDs
    eq_var_map = ComponentMap()
    relevant_vars = ComponentSet()
    for constr in m.component_data_objects(ctype=Constraint,
                                           active=True,
                                           descend_into=True):
        # Check to make sure the constraint is of form v1 - v2 == 0
        if (value(constr.lower) == 0 and value(constr.upper) == 0 and
                constr.body.polynomial_degree() == 1):
            repn = generate_standard_repn(constr.body)
            # only take the variables with nonzero coefficients
            vars_ = [v for i, v in enumerate(repn.linear_vars)
                     if repn.linear_coefs[i]]
            if (len(vars_) == 2 and
                    sorted(l for l in repn.linear_coefs if l) == [-1, 1]):
                # this is an a == b constraint.
                v1 = vars_[0]
                v2 = vars_[1]
                set1 = eq_var_map.get(v1, ComponentSet([v1]))
                set2 = eq_var_map.get(v2, ComponentSet([v2]))
                relevant_vars.update([v1, v2])
                set1.update(set2)  # set1 is now the union
                for v in set1:
                    eq_var_map[v] = set1

    return eq_var_map, relevant_vars


def _detect_fixed_variables(m):
    """Detect fixed variables due to constraints of form var = const."""
    new_fixed_vars = ComponentSet()
    for constr in m.component_data_objects(ctype=Constraint,
                                           active=True,
                                           descend_into=True):
        if constr.equality and constr.body.polynomial_degree() == 1:
            repn = generate_standard_repn(constr.body)
            if len(repn.linear_vars) == 1 and repn.linear_coefs[0]:
                var = repn.linear_vars[0]
                coef = float(repn.linear_coefs[0])
                const = repn.constant
                var_val = (value(constr.lower) - value(const)) / coef
                var.fix(var_val)
                new_fixed_vars.add(var)
    return new_fixed_vars



@TransformationFactory.register('contrib.propagate_fixed_vars',
          doc="Propagate variable fixing for equalities of type x = y.")
class FixedVarPropagator(IsomorphicTransformation):
    """Propagate variable fixing for equalities of type :math:`x = y`.

    If :math:`x` is fixed and :math:`y` is not fixed, then this transformation
    will fix :math:`y` to the value of :math:`x`.

    This transformation can also be performed as a temporary transformation,
    whereby the transformed variables are saved and can be later unfixed.

    Keyword arguments below are specified for the ``apply_to`` and
    ``create_using`` functions.

    """

    CONFIG = ConfigBlock()
    CONFIG.declare("tmp", ConfigValue(
        default=False, domain=bool,
        description="True to store the set of transformed variables and "
        "their old states so that they can be later restored."
    ))

    __doc__ = add_docstring_list(__doc__, CONFIG)

    def _apply_to(self, instance, **kwds):
        config = self.CONFIG(kwds)
        if config.tmp and not hasattr(instance, '_tmp_propagate_fixed'):
            instance._tmp_propagate_fixed = ComponentSet()
        eq_var_map, relevant_vars = _build_equality_set(instance)
        #: ComponentSet: The set of all fixed variables
        fixed_vars = ComponentSet((v for v in relevant_vars if v.fixed))
        newly_fixed = _detect_fixed_variables(instance)
        if config.tmp:
            instance._tmp_propagate_fixed.update(newly_fixed)
        fixed_vars.update(newly_fixed)
        processed = ComponentSet()
        # Go through each fixed variable to propagate the 'fixed' status to all
        # equality-linked variabes.
        for v1 in fixed_vars:
            # If we have already processed the variable, skip it.
            if v1 in processed:
                continue

            eq_set = eq_var_map.get(v1, ComponentSet([v1]))
            for v2 in eq_set:
                if (v2.fixed and value(v1) != value(v2)):
                    raise ValueError(
                        'Variables {} and {} have conflicting fixed '
                        'values of {} and {}, but are linked by '
                        'equality constraints.'
                        .format(v1.name,
                                v2.name,
                                value(v1),
                                value(v2)))
                elif not v2.fixed:
                    v2.fix(value(v1))
                    if config.tmp:
                        instance._tmp_propagate_fixed.add(v2)
            # Add all variables in the equality set to the set of processed
            # variables.
            processed.update(eq_set)

    def revert(self, instance):
        """Revert variables fixed by the transformation."""
        for var in instance._tmp_propagate_fixed:
            var.unfix()
        del instance._tmp_propagate_fixed


@TransformationFactory.register('contrib.propagate_eq_var_bounds',
          doc="Propagate variable bounds for equalities of type x = y.")
class VarBoundPropagator(IsomorphicTransformation):
    """Propagate variable bounds for equalities of type :math:`x = y`.

    If :math:`x` has a tighter bound then :math:`y`, then this transformation
    will adjust the bounds on :math:`y` to match those of :math:`x`.

    Keyword arguments below are specified for the ``apply_to`` and
    ``create_using`` functions.

    """

    CONFIG = ConfigBlock()
    CONFIG.declare("tmp", ConfigValue(
        default=False, domain=bool,
        description="True to store the set of transformed variables and "
        "their old states so that they can be later restored."
    ))

    __doc__ = add_docstring_list(__doc__, CONFIG)

    def _apply_to(self, instance, **kwds):
        config = self.CONFIG(kwds)
        if config.tmp and not hasattr(instance, '_tmp_propagate_original_bounds'):
            instance._tmp_propagate_original_bounds = Suffix(
                direction=Suffix.LOCAL)
        eq_var_map, relevant_vars = _build_equality_set(instance)
        processed = ComponentSet()
        # Go through each variable in an equality set to propagate the variable
        # bounds to all equality-linked variables.
        for var in relevant_vars:
            # If we have already processed the variable, skip it.
            if var in processed:
                continue

            var_equality_set = eq_var_map.get(var, ComponentSet([var]))

            #: variable lower bounds in the equality set
            lbs = [v.lb for v in var_equality_set if v.has_lb()]
            max_lb = max(lbs) if len(lbs) > 0 else None
            #: variable upper bounds in the equality set
            ubs = [v.ub for v in var_equality_set if v.has_ub()]
            min_ub = min(ubs) if len(ubs) > 0 else None

            # Check  for error due to bound cross-over
            if max_lb is not None and min_ub is not None and max_lb > min_ub:
                # the lower bound is above the upper bound. Raise a ValueError.
                # get variable with the highest lower bound
                v1 = next(v for v in var_equality_set if v.lb == max_lb)
                # get variable with the lowest upper bound
                v2 = next(v for v in var_equality_set if v.ub == min_ub)
                raise ValueError(
                    'Variable {} has a lower bound {} '
                    ' > the upper bound {} of variable {}, '
                    'but they are linked by equality constraints.'
                    .format(v1.name, value(v1.lb), value(v2.ub), v2.name))

            for v in var_equality_set:
                if config.tmp:
                    # TODO warn if overwriting
                    instance._tmp_propagate_original_bounds[v] = (
                        v.lb, v.ub)
                v.setlb(max_lb)
                v.setub(min_ub)

            processed.update(var_equality_set)

    def revert(self, instance):
        """Revert variable bounds."""
        for v in instance._tmp_propagate_original_bounds:
            old_LB, old_UB = instance._tmp_propagate_original_bounds[v]
            v.setlb(old_LB)
            v.setub(old_UB)
        del instance._tmp_propagate_original_bounds
