# Source code for pymatgen.analysis.reaction_calculator

    # coding: utf-8
    # Copyright (c) Pymatgen Development Team.
    # Distributed under the terms of the MIT License.

    """
    This module provides classes that define a chemical reaction.
    """

    import logging
    import numpy as np
    import re

    from monty.json import MSONable
    from pymatgen.core.composition import Composition
    from pymatgen.entries.computed_entries import ComputedEntry
    from monty.json import MontyDecoder
    from monty.fractions import gcd_float

    from itertools import combinations, chain

    __author__ = "Shyue Ping Ong, Anubhav Jain"
    __copyright__ = "Copyright 2011, The Materials Project"
    __version__ = "2.0"
    __maintainer__ = "Shyue Ping Ong"
    __email__ = "shyuep@gmail.com"
    __status__ = "Production"
    __date__ = "Jul 11 2012"

    logger = logging.getLogger(__name__)

    class BalancedReaction(MSONable):
        """
        An object representing a complete chemical reaction.
        """

        # Tolerance for determining if a particular component fraction is > 0.
        TOLERANCE = 1e-6

        def __init__(self, reactants_coeffs, products_coeffs):
            """
            Reactants and products to be specified as dict of {Composition: coeff}.

            Args:
                reactants_coeffs ({Composition: float}): Reactants as dict of
                    {Composition: amt}.
                products_coeffs ({Composition: float}): Products as dict of
                    {Composition: amt}.
            """
            # sum reactants and products
            all_reactants = sum(
                [k * v for k, v in reactants_coeffs.items()], Composition({})
            )
            all_products = sum([k * v for k, v in products_coeffs.items()], Composition({}))

            if not all_reactants.almost_equals(all_products, rtol=0, atol=self.TOLERANCE):
                raise ReactionError("Reaction is unbalanced!")

            self._els = all_reactants.elements

            self.reactants_coeffs = reactants_coeffs
            self.products_coeffs = products_coeffs

            # calculate net reaction coefficients
            self._coeffs = []
            self._els = []
            self._all_comp = []
            for c in set(list(reactants_coeffs.keys()) + list(products_coeffs.keys())):
                coeff = products_coeffs.get(c, 0) - reactants_coeffs.get(c, 0)

                if abs(coeff) > self.TOLERANCE:
                    self._all_comp.append(c)
                    self._coeffs.append(coeff)

        def calculate_energy(self, energies):
            """
            Calculates the energy of the reaction.

            Args:
                energies ({Composition: float}): Energy for each composition.
                    E.g ., {comp1: energy1, comp2: energy2}.

            Returns:
                reaction energy as a float.
            """
            return sum([amt * energies[c] for amt, c in zip(self._coeffs, self._all_comp)])

        def normalize_to(self, comp, factor=1):
            """
            Normalizes the reaction to one of the compositions.
            By default, normalizes such that the composition given has a
            coefficient of 1. Another factor can be specified.

            Args:
                comp (Composition): Composition to normalize to
                factor (float): Factor to normalize to. Defaults to 1.
            """
            scale_factor = abs(1 / self._coeffs[self._all_comp.index(comp)] * factor)
            self._coeffs = [c * scale_factor for c in self._coeffs]

        def normalize_to_element(self, element, factor=1):
            """
            Normalizes the reaction to one of the elements.
            By default, normalizes such that the amount of the element is 1.
            Another factor can be specified.

            Args:
                element (Element/Specie): Element to normalize to.
                factor (float): Factor to normalize to. Defaults to 1.
            """
            all_comp = self._all_comp
            coeffs = self._coeffs
            current_el_amount = (sum([all_comp[i][element] * abs(coeffs[i])
                                      for i in range(len(all_comp))]) / 2)
            scale_factor = factor / current_el_amount
            self._coeffs = [c * scale_factor for c in coeffs]

        def get_el_amount(self, element):
            """
            Returns the amount of the element in the reaction.

            Args:
                element (Element/Specie): Element in the reaction

            Returns:
                Amount of that element in the reaction.
            """
            return (sum([self._all_comp[i][element] * abs(self._coeffs[i])
                        for i in range(len(self._all_comp))]) / 2)

        @property
        def elements(self):
            """
            List of elements in the reaction
            """
            return self._els[:]

        @property
        def coeffs(self):
            """
            Final coefficients of the calculated reaction
            """
            return self._coeffs[:]

        @property
        def all_comp(self):
            """
            List of all compositions in the reaction.
            """
            return self._all_comp

        @property
        def reactants(self):
            """
            List of reactants
            """
            return [self._all_comp[i] for i in range(len(self._all_comp))
                    if self._coeffs[i] < 0]

        @property
        def products(self):
            """
            List of products
            """
            return [self._all_comp[i] for i in range(len(self._all_comp))
                    if self._coeffs[i] > 0]

        def get_coeff(self, comp):
            """
            Returns coefficient for a particular composition
            """
            return self._coeffs[self._all_comp.index(comp)]

        def normalized_repr_and_factor(self):
            """
            Normalized representation for a reaction
            For example, ``4 Li + 2 O -> 2Li2O`` becomes ``2 Li + O -> Li2O``
            """
            return self._str_from_comp(self._coeffs, self._all_comp, True)

        @property
        def normalized_repr(self):
            """
            A normalized representation of the reaction. All factors are converted
            to lowest common factors.
            """
            return self.normalized_repr_and_factor()[0]

        def __eq__(self, other):
            if other is None:
                return False
            for comp in self._all_comp:
                coeff2 = other.get_coeff(comp) if comp in other._all_comp else 0
                if abs(self.get_coeff(comp) - coeff2) > self.TOLERANCE:
                    return False
            return True

        def __hash__(self):
            return 7

        @classmethod
        def _str_from_formulas(cls, coeffs, formulas):
            reactant_str = []
            product_str = []
            for amt, formula in zip(coeffs, formulas):
                if abs(amt + 1) < cls.TOLERANCE:
                    reactant_str.append(formula)
                elif abs(amt - 1) < cls.TOLERANCE:
                    product_str.append(formula)
                elif amt < -cls.TOLERANCE:
                    reactant_str.append("{:.4g} {}".format(-amt, formula))
                elif amt > cls.TOLERANCE:
                    product_str.append("{:.4g} {}".format(amt, formula))

            return " + ".join(reactant_str) + " -> " + " + ".join(product_str)

        @classmethod
        def _str_from_comp(cls, coeffs, compositions, reduce=False):
            r_coeffs = np.zeros(len(coeffs))
            r_formulas = []
            for i, (amt, comp) in enumerate(zip(coeffs, compositions)):
                formula, factor = comp.get_reduced_formula_and_factor()
                r_coeffs[i] = amt * factor
                r_formulas.append(formula)
            if reduce:
                factor = 1 / gcd_float(np.abs(r_coeffs))
                r_coeffs *= factor
            else:
                factor = 1
            return cls._str_from_formulas(r_coeffs, r_formulas), factor

        def __str__(self):
            return self._str_from_comp(self._coeffs, self._all_comp)[0]

        __repr__ = __str__

        def as_entry(self, energies):
            """
            Returns a ComputedEntry representation of the reaction.
            :return:
            """
            relevant_comp = [comp * abs(coeff) for coeff, comp
                             in zip(self._coeffs, self._all_comp)]
            comp = sum(relevant_comp, Composition())
            entry = ComputedEntry(0.5 * comp, self.calculate_energy(energies))
            entry.name = self.__str__()
            return entry

        def as_dict(self):
            """
            Returns:
                A dictionary representation of BalancedReaction.
            """
            return {
                "@module": self.__class__.__module__,
                "@class": self.__class__.__name__,
                "reactants": {
                    str(comp): coeff for comp, coeff in self.reactants_coeffs.items()
                },
                "products": {
                    str(comp): coeff for comp, coeff in self.products_coeffs.items()
                },
            }

        @classmethod
        def from_dict(cls, d):
            """
            Args:
                d (dict): from as_dict()

            Returns:
                A BalancedReaction object.
            """
            reactants = {Composition(comp): coeff for comp, coeff in d["reactants"].items()}
            products = {Composition(comp): coeff for comp, coeff in d["products"].items()}
            return cls(reactants, products)

        @staticmethod
        def from_string(rxn_string):
            """
            Generates a balanced reaction from a string. The reaction must
            already be balanced.

            Args:
                rxn_string:
                    The reaction string. For example, "4 Li + O2-> 2Li2O"

            Returns:
                BalancedReaction
            """
            rct_str, prod_str = rxn_string.split("->")

            def get_comp_amt(comp_str):
                return {
                    Composition(m.group(2)): float(m.group(1) or 1)
                    for m in re.finditer(
                        r"([\d\.]*(?:[eE]-?[\d\.]+)?)\s*([A-Z][\w\.\(\)]*)", comp_str
                    )
                }

            return BalancedReaction(get_comp_amt(rct_str), get_comp_amt(prod_str))

    class Reaction(BalancedReaction):
        """
        A more flexible class representing a Reaction. The reaction amounts will
        be automatically balanced. Reactants and products can swap sides so that
        all coefficients are positive, however this class will find the solution
        with the minimum number of swaps and coefficients of 0. Normalizes so that
        the *FIRST* product (or products, if underdetermined) has a coefficient of one.
        """

        def __init__(self, reactants, products):
            """
            Reactants and products to be specified as list of
            pymatgen.core.structure.Composition.  e.g., [comp1, comp2]

            Args:
                reactants ([Composition]): List of reactants.
                products ([Composition]): List of products.
            """
            self._input_reactants = reactants
            self._input_products = products
            self._all_comp = reactants + products
            self._num_comp = len(self.all_comp)

            all_elems = sorted({elem for c in self._all_comp for elem in c.elements})
            self._num_elems = len(all_elems)

            comp_matrix = np.array([[c[el] for el in all_elems] for c in self._all_comp]).T

            rank = np.linalg.matrix_rank(comp_matrix)
            diff = self._num_comp - rank
            num_constraints = diff if diff >= 2 else 1

            self._lowest_num_errors = np.inf  # an error = a component changing sides or disappearing

            self._coeffs = self._balance_coeffs(comp_matrix, num_constraints)
            self._els = all_elems

        def _balance_coeffs(self, comp_matrix, max_num_constraints):
            first_product_idx = len(self._input_reactants)

            # start with simplest product constraints, work towards most complex reactant constraints
            product_constraints = chain.from_iterable(
                [
                    combinations(range(first_product_idx, self._num_comp), n_constr)
                    for n_constr in range(max_num_constraints, 0, -1)
                ]
            )
            reactant_constraints = chain.from_iterable(
                [
                    combinations(range(0, first_product_idx), n_constr)
                    for n_constr in range(max_num_constraints, 0, -1)
                ]
            )
            best_soln = None
            balanced = False

            for constraints in chain(product_constraints, reactant_constraints):
                n_constr = len(constraints)

                comp_and_constraints = np.append(
                    comp_matrix, np.zeros((n_constr, self._num_comp)), axis=0
                )
                b = np.zeros((self._num_elems + n_constr, 1))
                b[-n_constr:] = 1 if min(constraints) >= first_product_idx else -1

                for num, idx in enumerate(constraints):
                    comp_and_constraints[self._num_elems + num, idx] = 1
                    # arbitrarily fix coeff to 1

                coeffs = np.matmul(np.linalg.pinv(comp_and_constraints), b)

                if np.allclose(np.matmul(comp_matrix, coeffs), np.zeros((self._num_elems, 1))):
                    balanced = True
                    expected_signs = np.array([-1] * len(self._input_reactants) +
                                              [+1] * len(self._input_products))
                    num_errors = np.sum(np.multiply(expected_signs, coeffs.T) < self.TOLERANCE)

                    if num_errors == 0:
                        self._lowest_num_errors = 0
                        return np.squeeze(coeffs)
                    elif num_errors < self._lowest_num_errors:
                        self._lowest_num_errors = num_errors
                        best_soln = coeffs

            if not balanced:
                raise ReactionError("Reaction cannot be balanced.")

            return np.squeeze(best_soln)

        def copy(self):
            """
            Returns a copy of the Reaction object.
            """
            return Reaction(self.reactants, self.products)

        def as_dict(self):
            """
            Returns:
                A dictionary representation of Reaction.
            """
            return {
                "@module": self.__class__.__module__,
                "@class": self.__class__.__name__,
                "reactants": [comp.as_dict() for comp in self._input_reactants],
                "products": [comp.as_dict() for comp in self._input_products],
            }

        @classmethod
        def from_dict(cls, d):
            """
            Args:
                d (dict): from as_dict()

            Returns:
                A Reaction object.
            """
            reactants = [Composition(sym_amt) for sym_amt in d["reactants"]]
            products = [Composition(sym_amt) for sym_amt in d["products"]]
            return cls(reactants, products)

    class ReactionError(Exception):
        """
        Exception class for Reactions. Allows more information in exception
        messages to cover situations not covered by standard exception classes.
        """

        def __init__(self, msg):
            """
            Create a ReactionError.

            Args:
                msg (str): More information about the ReactionError.
            """
            self.msg = msg

        def __str__(self):
            return self.msg

    class ComputedReaction(Reaction):
        """
        Convenience class to generate a reaction from ComputedEntry objects, with
        some additional attributes, such as a reaction energy based on computed
        energies.
        """

        def __init__(self, reactant_entries, product_entries):
            """
            Args:
                reactant_entries ([ComputedEntry]): List of reactant_entries.
                product_entries ([ComputedEntry]): List of product_entries.
            """
            self._reactant_entries = reactant_entries
            self._product_entries = product_entries
            self._all_entries = reactant_entries + product_entries
            reactant_comp = set(
                [e.composition.get_reduced_composition_and_factor()[0]
                    for e in reactant_entries])
            product_comp = set(
                [e.composition.get_reduced_composition_and_factor()[0]
                    for e in product_entries])
            super().__init__(list(reactant_comp), list(product_comp))

        @property
        def all_entries(self):
            """
            Equivalent of all_comp but returns entries, in the same order as the
            coefficients.
            """
            entries = []
            for c in self._all_comp:
                for e in self._all_entries:
                    if e.composition.reduced_formula == c.reduced_formula:
                        entries.append(e)
                        break
            return entries

        @property
        def calculated_reaction_energy(self):
            """
            Returns (float):
                The calculated reaction energy.
            """
            calc_energies = {}

            for entry in self._reactant_entries + self._product_entries:
                (comp, factor) = entry.composition.get_reduced_composition_and_factor()
                calc_energies[comp] = min(
                    calc_energies.get(comp, float("inf")), entry.energy / factor)

            return self.calculate_energy(calc_energies)

        def as_dict(self):
            """
            Returns:
                A dictionary representation of ComputedReaction.
            """
            return {
                "@module": self.__class__.__module__,
                "@class": self.__class__.__name__,
                "reactants": [e.as_dict() for e in self._reactant_entries],
                "products": [e.as_dict() for e in self._product_entries],
            }

        @classmethod
        def from_dict(cls, d):
            """
            Args:
                d (dict): from as_dict()

            Returns:
                A ComputedReaction object.
            """
            dec = MontyDecoder()
            reactants = [dec.process_decoded(e) for e in d["reactants"]]
            products = [dec.process_decoded(e) for e in d["products"]]
            return cls(reactants, products)