substitution_probability.py

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

"""
This module provides classes for representing species substitution
probabilities.
"""

import functools
import itertools
import json
import logging
import math
import os
from collections import defaultdict
from operator import mul

from monty.design_patterns import cached_class

from pymatgen.core.periodic_table import Species, get_el_sp

__author__ = "Will Richards, Geoffroy Hautier"
__copyright__ = "Copyright 2012, The Materials Project"
__version__ = "1.2"
__maintainer__ = "Will Richards"
__email__ = "wrichard@mit.edu"
__date__ = "Aug 31, 2012"


@cached_class
class SubstitutionProbability:
    """
    This class finds substitution probabilities given lists of atoms
    to substitute. The inputs make more sense if you look through the
    from_defaults static method.

    The substitution prediction algorithm is presented in:
    Hautier, G., Fischer, C., Ehrlacher, V., Jain, A., and Ceder, G. (2011)
    Data Mined Ionic Substitutions for the Discovery of New Compounds.
    Inorganic Chemistry, 50(2), 656-663. doi:10.1021/ic102031h
    """

    def __init__(self, lambda_table=None, alpha=-5):
        """
        Args:
            lambda_table:
                json table of the weight functions lambda if None,
                will use the default lambda.json table
            alpha:
                weight function for never observed substitutions
        """
        if lambda_table is not None:
            self._lambda_table = lambda_table
        else:
            module_dir = os.path.dirname(__file__)
            json_file = os.path.join(module_dir, "data", "lambda.json")
            with open(json_file) as f:
                self._lambda_table = json.load(f)

        # build map of specie pairs to lambdas
        self.alpha = alpha
        self._l = {}
        self.species = set()
        for row in self._lambda_table:
            if "D1+" not in row:
                s1 = Species.from_string(row[0])
                s2 = Species.from_string(row[1])
                self.species.add(s1)
                self.species.add(s2)
                self._l[frozenset([s1, s2])] = float(row[2])

        # create Z and px
        self.Z = 0
        self._px = defaultdict(float)
        for s1, s2 in itertools.product(self.species, repeat=2):
            value = math.exp(self.get_lambda(s1, s2))
            self._px[s1] += value / 2
            self._px[s2] += value / 2
            self.Z += value

    def get_lambda(self, s1, s2):
        """
        Args:
            s1 (Structure): 1st Structure
            s2 (Structure): 2nd Structure

        Returns:
            Lambda values
        """
        k = frozenset([get_el_sp(s1), get_el_sp(s2)])
        return self._l.get(k, self.alpha)

    def get_px(self, sp):
        """
        Args:
            sp (Species/Element): Species

        Returns:
            Probability
        """
        return self._px[get_el_sp(sp)]

    def prob(self, s1, s2):
        """
        Gets the probability of 2 species substitution. Not used by the
        structure predictor.

        Returns:
            Probability of s1 and s2 substitution.
        """
        return math.exp(self.get_lambda(s1, s2)) / self.Z

    def cond_prob(self, s1, s2):
        """
        Conditional probability of substituting s1 for s2.

        Args:
            s1:
                The *variable* specie
            s2:
                The *fixed* specie

        Returns:
            Conditional probability used by structure predictor.
        """
        return math.exp(self.get_lambda(s1, s2)) / self.get_px(s2)

    def pair_corr(self, s1, s2):
        """
        Pair correlation of two species.

        Returns:
            The pair correlation of 2 species
        """
        return math.exp(self.get_lambda(s1, s2)) * self.Z / (self.get_px(s1) * self.get_px(s2))

    def cond_prob_list(self, l1, l2):
        """
        Find the probabilities of 2 lists. These should include ALL species.
        This is the probability conditional on l2

        Args:
            l1, l2:
                lists of species

        Returns:
            The conditional probability (assuming these species are in
            l2)
        """
        assert len(l1) == len(l2)
        p = 1
        for s1, s2 in zip(l1, l2):
            p *= self.cond_prob(s1, s2)
        return p

    def as_dict(self):
        """
        Returns: MSONAble dict
        """
        return {
            "name": self.__class__.__name__,
            "version": __version__,
            "init_args": {"lambda_table": self._l, "alpha": self.alpha},
            "@module": self.__class__.__module__,
            "@class": self.__class__.__name__,
        }

    @classmethod
    def from_dict(cls, d):
        """
        Args:
            d(dict): Dict representation

        Returns:
            Class
        """
        return cls(**d["init_args"])


class SubstitutionPredictor:
    """
    Predicts likely substitutions either to or from a given composition
    or species list using the SubstitutionProbability
    """

    def __init__(self, lambda_table=None, alpha=-5, threshold=1e-3):
        """
        Args:
            lambda_table (): Input lambda table.
            alpha (float): weight function for never observed substitutions
            threshold (float): Threshold to use to identify high probability structures.
        """
        self.p = SubstitutionProbability(lambda_table, alpha)
        self.threshold = threshold

    def list_prediction(self, species, to_this_composition=True):
        """
        Args:
            species:
                list of species
            to_this_composition:
                If true, substitutions with this as a final composition
                will be found. If false, substitutions with this as a
                starting composition will be found (these are slightly
                different)
        Returns:
            List of predictions in the form of dictionaries.
            If to_this_composition is true, the values of the dictionary
            will be from the list species. If false, the keys will be
            from that list.
        """
        for sp in species:
            if get_el_sp(sp) not in self.p.species:
                raise ValueError("the species {} is not allowed for the" "probability model you are using".format(sp))
        max_probabilities = []
        for s1 in species:
            if to_this_composition:
                max_p = max([self.p.cond_prob(s2, s1) for s2 in self.p.species])
            else:
                max_p = max([self.p.cond_prob(s1, s2) for s2 in self.p.species])
            max_probabilities.append(max_p)

        output = []

        def _recurse(output_prob, output_species):
            best_case_prob = list(max_probabilities)
            best_case_prob[: len(output_prob)] = output_prob
            if functools.reduce(mul, best_case_prob) > self.threshold:
                if len(output_species) == len(species):
                    odict = {"probability": functools.reduce(mul, best_case_prob)}
                    if to_this_composition:
                        odict["substitutions"] = dict(zip(output_species, species))
                    else:
                        odict["substitutions"] = dict(zip(species, output_species))
                    if len(output_species) == len(set(output_species)):
                        output.append(odict)
                    return
                for sp in self.p.species:
                    i = len(output_prob)
                    if to_this_composition:
                        prob = self.p.cond_prob(sp, species[i])
                    else:
                        prob = self.p.cond_prob(species[i], sp)
                    _recurse(output_prob + [prob], output_species + [sp])

        _recurse([], [])
        logging.info("{} substitutions found".format(len(output)))
        return output

    def composition_prediction(self, composition, to_this_composition=True):
        """
        Returns charged balanced substitutions from a starting or ending
        composition.

        Args:
            composition:
                starting or ending composition
            to_this_composition:
                If true, substitutions with this as a final composition
                will be found. If false, substitutions with this as a
                starting composition will be found (these are slightly
                different)

        Returns:
            List of predictions in the form of dictionaries.
            If to_this_composition is true, the values of the dictionary
            will be from the list species. If false, the keys will be
            from that list.
        """
        preds = self.list_prediction(list(composition.keys()), to_this_composition)
        output = []
        for p in preds:
            if to_this_composition:
                subs = {v: k for k, v in p["substitutions"].items()}
            else:
                subs = p["substitutions"]
            charge = 0
            for k, v in composition.items():
                charge += subs[k].oxi_state * v
            if abs(charge) < 1e-8:
                output.append(p)
        logging.info("{} charge balanced substitutions found".format(len(output)))
        return output