# pyFTS.models.pwfts — pyFTS 1.4 documentation

# Source code for pyFTS.models.pwfts

    #!/usr/bin/python
    # -*- coding: utf8 -*-

    import numpy as np
    import pandas as pd
    import math
    from operator import itemgetter
    from pyFTS.common import FLR, FuzzySet
    from pyFTS.models import hofts, ifts
    from pyFTS.probabilistic import ProbabilityDistribution
    from itertools import product

    class ProbabilisticWeightedFLRG(hofts.HighOrderFLRG):
        """High Order Probabilistic Weighted Fuzzy Logical Relationship Group"""
        def __init__(self, order):
            super(ProbabilisticWeightedFLRG, self).__init__(order)
            self.RHS = {}
            self.frequency_count = 0.0
            self.Z = None

        def get_membership(self, data, sets):
            if isinstance(data, (np.ndarray, list, tuple, set)):
                return np.nanprod([sets[key].membership(data[count])
                                   for count, key in enumerate(self.LHS, start=0)])
            else:
                return sets[self.LHS[0]].membership(data)

        def append_rhs(self, c, **kwargs):
            count = kwargs.get('count', 1.0)
            self.frequency_count += count
            if c in self.RHS:
                self.RHS[c] += count
            else:
                self.RHS[c] = count

        def lhs_conditional_probability(self, x, sets, norm, uod, nbins):
            pk = self.frequency_count / norm

            tmp = pk * (self.get_membership(x, sets) / self.partition_function(sets, uod, nbins=nbins))

            return tmp

        def rhs_unconditional_probability(self, c):
            return self.RHS[c] / self.frequency_count

        def rhs_conditional_probability(self, x, sets, uod, nbins):
            total = 0.0
            for rhs in self.RHS.keys():
                set = sets[rhs]
                wi = self.rhs_unconditional_probability(rhs)
                mv = set.membership(x) / set.partition_function(uod, nbins=nbins)
                total += wi * mv

            return total

        def partition_function(self, sets, uod, nbins=100):
            if self.Z is None:
                self.Z = 0.0
                for k in np.linspace(uod[0], uod[1], nbins):
                    for key in self.LHS:
                        self.Z += sets[key].membership(k)

            return self.Z

        def get_midpoint(self, sets):
            '''Return the expectation of the PWFLRG, the weighted sum'''
            if self.midpoint is None:
                self.midpoint = np.sum(np.array([self.rhs_unconditional_probability(s) * sets[s].centroid
                                                 for s in self.RHS.keys()]))

            return self.midpoint

        def get_upper(self, sets):
            if self.upper is None:
                self.upper = np.sum(np.array([self.rhs_unconditional_probability(s) * sets[s].upper
                                              for s in self.RHS.keys()]))

            return self.upper

        def get_lower(self, sets):
            if self.lower is None:
                self.lower = np.sum(np.array([self.rhs_unconditional_probability(s) * sets[s].lower
                                              for s in self.RHS.keys()]))

            return self.lower

        def __str__(self):
            tmp2 = ""
            for c in sorted(self.RHS.keys()):
                if len(tmp2) > 0:
                    tmp2 = tmp2 + ", "
                tmp2 = tmp2 + "(" + str(round(self.RHS[c] / self.frequency_count, 3)) + ")" + c
            return self.get_key() + " -> " + tmp2

    class ProbabilisticWeightedFTS(ifts.IntervalFTS):
        """High Order Probabilistic Weighted Fuzzy Time Series"""
        def __init__(self, **kwargs):
            super(ProbabilisticWeightedFTS, self).__init__(**kwargs)
            self.shortname = "PWFTS"
            self.name = "Probabilistic FTS"
            self.detail = "Silva, P.; Guimarães, F.; Sadaei, H."
            self.flrgs = {}
            self.global_frequency_count = 0
            self.has_point_forecasting = True
            self.has_interval_forecasting = True
            self.has_probability_forecasting = True
            self.is_high_order = True
            self.min_order = 1
            self.auto_update = kwargs.get('update',False)
            self.configure_lags(**kwargs)

        def train(self, data, **kwargs):

            self.configure_lags(**kwargs)
            parameters = kwargs.get('parameters','fuzzy')

            if parameters == 'monotonic':
                tmpdata = self.partitioner.fuzzyfy(data, mode='sets', method='maximum')
                flrs = FLR.generate_recurrent_flrs(tmpdata)
                self.generate_flrg(flrs)
            else:
                self.generate_flrg(data)

        def generate_lhs_flrg(self, sample, explain=False):
            nsample = [self.partitioner.fuzzyfy(k, mode="sets", alpha_cut=self.alpha_cut)
                       for k in sample]

            return self.generate_lhs_flrg_fuzzyfied(nsample, explain)

        def generate_lhs_flrg_fuzzyfied(self, sample, explain=False):
            lags = []

            flrgs = []

            for ct, o in enumerate(self.lags):
                lhs = sample[o - 1]
                lags.append( lhs )

                if explain:
                    print("\t (Lag {}) {} -> {} \n".format(o, sample[o-1], lhs))

            # Trace the possible paths
            for path in product(*lags):
                flrg = ProbabilisticWeightedFLRG(self.order)

                for lhs in path:
                    flrg.append_lhs(lhs)

                flrgs.append(flrg)

            return flrgs

        def generate_flrg(self, data):
            l = len(data)
            for k in np.arange(self.max_lag, l):
                if self.dump: print("FLR: " + str(k))

                sample = data[k - self.max_lag: k]

                flrgs = self.generate_lhs_flrg(sample)

                for flrg in flrgs:

                    lhs_mv = flrg.get_membership(sample, self.partitioner.sets)

                    if flrg.get_key() not in self.flrgs:
                        self.flrgs[flrg.get_key()] = flrg;

                    fuzzyfied = self.partitioner.fuzzyfy(data[k], mode='both', method='fuzzy',
                                                         alpha_cut=self.alpha_cut)

                    mvs = []
                    for set, mv in fuzzyfied:
                        self.flrgs[flrg.get_key()].append_rhs(set, count=lhs_mv * mv)
                        mvs.append(mv)

                    tmp_fq = sum([lhs_mv*kk for kk in mvs if kk > 0])

                    self.global_frequency_count += tmp_fq

        def update_model(self,data):
            pass

        def add_new_PWFLGR(self, flrg):
            if flrg.get_key() not in self.flrgs:
                tmp = ProbabilisticWeightedFLRG(self.order)
                for fs in flrg.LHS: tmp.append_lhs(fs)
                tmp.append_rhs(flrg.LHS[-1])
                self.flrgs[tmp.get_key()] = tmp;
                self.global_frequency_count += 1

        def flrg_lhs_unconditional_probability(self, flrg):
            if flrg.get_key() in self.flrgs:
                return self.flrgs[flrg.get_key()].frequency_count / self.global_frequency_count
            else:
                return 0.0
                #self.add_new_PWFLGR(flrg)
                #return self.flrg_lhs_unconditional_probability(flrg)

        def flrg_lhs_conditional_probability(self, x, flrg):
            mv = flrg.get_membership(x, self.partitioner.sets)
            pb = self.flrg_lhs_unconditional_probability(flrg)
            return mv * pb

        def get_midpoint(self, flrg):
            if flrg.get_key() in self.flrgs:
                tmp = self.flrgs[flrg.get_key()]
                ret = tmp.get_midpoint(self.partitioner.sets) #sum(np.array([tmp.rhs_unconditional_probability(s) * self.setsDict[s].centroid for s in tmp.RHS]))
            else:
                if len(flrg.LHS) > 0:
                    pi = 1 / len(flrg.LHS)
                    ret = sum(np.array([pi * self.partitioner.sets[s].centroid for s in flrg.LHS]))
                else:
                    ret = np.nan
            return ret

        def flrg_rhs_conditional_probability(self, x, flrg):

            if flrg.get_key() in self.flrgs:
                _flrg = self.flrgs[flrg.get_key()]
                cond = []
                for s in _flrg.RHS.keys():
                    _set = self.partitioner.sets[s]
                    tmp = _flrg.rhs_unconditional_probability(s) * (_set.membership(x) / _set.partition_function(uod=self.get_UoD()))
                    cond.append(tmp)
                ret = sum(np.array(cond))
            else:
                pi = 1 / len(flrg.LHS)
                ret = sum(np.array([pi * self.partitioner.sets[s].membership(x) for s in flrg.LHS]))
            return ret

        def get_upper(self, flrg):
            if flrg.get_key() in self.flrgs:
                tmp = self.flrgs[flrg.get_key()]
                ret = tmp.get_upper(self.partitioner.sets)
            else:
                ret = 0
            return ret

        def get_lower(self, flrg):
            if flrg.get_key() in self.flrgs:
                tmp = self.flrgs[flrg.get_key()]
                ret = tmp.get_lower(self.partitioner.sets)
            else:
                ret = 0
            return ret

        def forecast(self, data, **kwargs):
            method = kwargs.get('method','heuristic')

            l = len(data)

            ret = []

            for k in np.arange(self.max_lag - 1, l):
                sample = data[k - (self.max_lag - 1): k + 1]

                if method == 'heuristic':
                    ret.append(self.point_heuristic(sample, **kwargs))
                elif method == 'expected_value':
                    ret.append(self.point_expected_value(sample, **kwargs))
                else:
                    raise ValueError("Unknown point forecasting method!")

                if self.auto_update and k > self.order+1: self.update_model(data[k - self.order - 1 : k])

            return ret

        def point_heuristic(self, sample, **kwargs):

            explain = kwargs.get('explain', False)

            if explain:
                print("Fuzzyfication \n")

            flrgs = self.generate_lhs_flrg(sample, explain)

            mp = []
            norms = []

            if explain:
                print("Rules:\n")

            for flrg in flrgs:
                norm = self.flrg_lhs_conditional_probability(sample, flrg)

                if norm == 0:
                    norm = self.flrg_lhs_unconditional_probability(flrg)

                if explain:
                    print("\t {} \t Midpoint: {}\t Norm: {}\n".format(str(self.flrgs[flrg.get_key()]),
                                                                      self.get_midpoint(flrg), norm))

                mp.append(norm * self.get_midpoint(flrg))
                norms.append(norm)

            norm = sum(norms)

            final = sum(mp) / norm if norm != 0 else 0

            if explain:
                print("Deffuzyfied value: {} \n".format(final))
            return final

        def point_expected_value(self, sample, **kwargs):
            explain = kwargs.get('explain', False)

            dist = self.forecast_distribution(sample)[0]

            final = dist.expected_value()
            return final

        def forecast_interval(self, ndata, **kwargs):

            method = kwargs.get('method','heuristic')
            alpha = kwargs.get('alpha', 0.05)

            l = len(ndata)

            ret = []

            for k in np.arange(self.max_lag - 1, l):

                sample = ndata[k - (self.max_lag - 1): k + 1]

                if method == 'heuristic':
                    ret.append(self.interval_heuristic(sample))
                elif method == 'quantile':
                    ret.append(self.interval_quantile(sample, alpha))
                else:
                    raise ValueError("Unknown interval forecasting method!")

            return ret

        def interval_quantile(self, ndata, alpha):
            dist = self.forecast_distribution(ndata)
            itvl = dist[0].quantile([alpha, 1.0 - alpha])
            return itvl

        def interval_heuristic(self, sample):

            flrgs = self.generate_lhs_flrg(sample)

            up = []
            lo = []
            norms = []
            for flrg in flrgs:
                norm = self.flrg_lhs_conditional_probability(sample, flrg)
                if norm == 0:
                    norm = self.flrg_lhs_unconditional_probability(flrg)
                up.append(norm * self.get_upper(flrg))
                lo.append(norm * self.get_lower(flrg))
                norms.append(norm)

                # gerar o intervalo
            norm = sum(norms)
            if norm == 0:
                return [0, 0]
            else:
                lo_ = sum(lo) / norm
                up_ = sum(up) / norm
                return [lo_, up_]

        def forecast_distribution(self, ndata, **kwargs):

            smooth = kwargs.get("smooth", "none")

            l = len(ndata)
            uod = self.get_UoD()

            if 'bins' in kwargs:
                _bins = kwargs.pop('bins')
                nbins = len(_bins)
            else:
                nbins = kwargs.get("num_bins", 100)
                _bins = np.linspace(uod[0], uod[1], nbins)

            ret = []

            for k in np.arange(self.max_lag - 1, l):
                sample = ndata[k - (self.max_lag - 1): k + 1]

                flrgs = self.generate_lhs_flrg(sample)

                if 'type' in kwargs:
                    kwargs.pop('type')

                dist = ProbabilityDistribution.ProbabilityDistribution(smooth, uod=uod, bins=_bins, **kwargs)

                for bin in _bins:
                    num = []
                    den = []
                    for s in flrgs:
                        if s.get_key() in self.flrgs:
                            flrg = self.flrgs[s.get_key()]
                            pk = flrg.lhs_conditional_probability(sample, self.partitioner.sets, self.global_frequency_count, uod, nbins)
                            wi = flrg.rhs_conditional_probability(bin, self.partitioner.sets, uod, nbins)
                            num.append(wi * pk)
                            den.append(pk)
                        else:
                            num.append(0.0)
                            den.append(0.000000001)
                    pf = sum(num) / sum(den)

                    dist.set(bin, pf)

                ret.append(dist)

            return ret

        def __check_point_bounds(self, point):
            lower_set = self.partitioner.lower_set()
            upper_set = self.partitioner.upper_set()
            return point <= lower_set.lower or point >= upper_set.upper

        def forecast_ahead(self, data, steps, **kwargs):

            l = len(data)

            start = kwargs.get('start', self.max_lag)

            ret = data[start - self.max_lag: start].tolist()

            for k in np.arange(self.max_lag, steps+self.max_lag):

                if self.__check_point_bounds(ret[-1]) :
                    ret.append(ret[-1])
                else:
                    mp = self.forecast(ret[k - self.max_lag: k], **kwargs)
                    ret.append(mp[0])

            return ret[self.max_lag:]

        def __check_interval_bounds(self, interval):
            if len(self.transformations) > 0:
                lower_set = self.partitioner.lower_set()
                upper_set = self.partitioner.upper_set()
                return interval[0] <= lower_set.lower and interval[1] >= upper_set.upper
            elif len(self.transformations) == 0:
                return interval[0] <= self.original_min and interval[1] >= self.original_max

        def forecast_ahead_interval(self, data, steps, **kwargs):

            l = len(data)

            start = kwargs.get('start', self.max_lag)

            sample = data[start - self.max_lag: start]

            ret = [[k, k] for k in sample]

            ret.append(self.forecast_interval(sample)[0])

            for k in np.arange(self.max_lag+1, steps+self.max_lag):

                if len(ret) > 0 and self.__check_interval_bounds(ret[-1]):
                    ret.append(ret[-1])
                else:
                    lower = self.forecast_interval([ret[x][0] for x in np.arange(k - self.max_lag, k)], **kwargs)
                    upper = self.forecast_interval([ret[x][1] for x in np.arange(k - self.max_lag, k)], **kwargs)

                    ret.append([np.min(lower), np.max(upper)])

            return ret[self.order:]

        def forecast_ahead_distribution(self, ndata, steps, **kwargs):

            ret = []

            smooth = kwargs.get("smooth", "none")

            uod = self.get_UoD()

            if 'bins' in kwargs:
                _bins = kwargs.pop('bins')
                nbins = len(_bins)
            else:
                nbins = kwargs.get("num_bins", 100)
                _bins = np.linspace(uod[0], uod[1], nbins)

            start = kwargs.get('start', self.max_lag)

            sample = ndata[start - self.max_lag: start]

            for dat in sample:
                if 'type' in kwargs:
                    kwargs.pop('type')
                tmp = ProbabilityDistribution.ProbabilityDistribution(smooth, uod=uod, bins=_bins, **kwargs)
                tmp.set(dat, 1.0)
                ret.append(tmp)

            dist = self.forecast_distribution(sample, bins=_bins)[0]

            ret.append(dist)

            for k in np.arange(self.max_lag+1, steps+self.max_lag+1):
                dist = ProbabilityDistribution.ProbabilityDistribution(smooth, uod=uod, bins=_bins, **kwargs)

                lags = []

                # Find all bins of past distributions with probability greater than zero

                for ct, lag in enumerate(self.lags):
                    dd = ret[k - lag]
                    vals = [float(v) for v in dd.bins if np.round(dd.density(v), 4) > 0.0]
                    lags.append( sorted(vals) )

                # Trace all possible combinations between the bins of past distributions

                for path in product(*lags):

                    # get the combined probabilities for this path
                    pk = np.prod([ret[k - (self.max_lag + lag)].density(path[ct])
                                  for ct, lag in enumerate(self.lags)])

                    d = self.forecast_distribution(path)[0]

                    for bin in _bins:
                        dist.set(bin, dist.density(bin) + pk * d.density(bin))

                ret.append(dist)

            return ret[self.order:]

        def __str__(self):
            tmp = self.name + ":\n"
            for r in sorted(self.flrgs.keys()):
                p = round(self.flrgs[r].frequency_count / self.global_frequency_count, 3)
                tmp = tmp + "(" + str(p) + ") " + str(self.flrgs[r]) + "\n"
            return tmp

    def visualize_distributions(model, **kwargs):
        import matplotlib.pyplot as plt
        from matplotlib import gridspec
        import seaborn as sns

        ordered_sets = model.partitioner.ordered_sets
        ftpg_keys = sorted(model.flrgs.keys(), key=lambda x: model.flrgs[x].get_midpoint(model.sets))

        lhs_probs = [model.flrg_lhs_unconditional_probability(model.flrgs[k])
                     for k in ftpg_keys]

        mat = np.zeros((len(ftpg_keys), len(ordered_sets)))
        for row, w in enumerate(ftpg_keys):
            for col, k in enumerate(ordered_sets):
                if k in model.flrgs[w].RHS:
                    mat[row, col] = model.flrgs[w].rhs_unconditional_probability(k)

        size = kwargs.get('size', (5,10))

        fig = plt.figure(figsize=size)

        gs = gridspec.GridSpec(1, 2, width_ratios=[1, 4])
        ax1 = plt.subplot(gs[0])
        sns.barplot(x='y', y='x', color='darkblue', data={'x': ftpg_keys, 'y': lhs_probs}, ax=ax1)
        ax1.set_ylabel("LHS Probabilities")

        ind_sets = range(len(ordered_sets))
        ax = plt.subplot(gs[1])
        sns.heatmap(mat, cmap='Blues', ax=ax, yticklabels=False)
        ax.set_title("RHS probabilities")
        ax.set_xticks(ind_sets)
        ax.set_xticklabels(ordered_sets)
        ax.grid(True)
        ax.xaxis.set_tick_params(rotation=90)