pyFTS/benchmarks/benchmarks.py

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

import numpy as np
import pandas as pd
import matplotlib as plt
import matplotlib.colors as pltcolors
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
# from sklearn.cross_validation import KFold
from pyFTS.benchmarks import Measures, naive, ResidualAnalysis
from pyFTS.partitioners import Grid
from pyFTS.common import Membership, FuzzySet, FLR, Transformations, Util
from pyFTS import fts, chen, yu, ismailefendi, sadaei, hofts, hwang, pfts, ifts


def allPointForecasters(data_train, data_test, partitions, max_order=3, statistics=True, residuals=True, series=True,
                        save=False, file=None, tam=[20, 5]):
    models = [naive.Naive, chen.ConventionalFTS, yu.WeightedFTS, ismailefendi.ImprovedWeightedFTS,
              sadaei.ExponentialyWeightedFTS, hofts.HighOrderFTS,  pfts.ProbabilisticFTS]

    objs = []

    all_colors = [clr for clr in pltcolors.cnames.keys()  ]

    data_train_fs = Grid.GridPartitionerTrimf(data_train,partitions)

    count = 1

    colors = []

    for model in models:
        #print(model)
        mfts = model("")
        if not mfts.isHighOrder:
            mfts.train(data_train, data_train_fs)
            objs.append(mfts)
            colors.append( all_colors[count] )
        else:
            for order in np.arange(1,max_order+1):
                if order >= mfts.minOrder:
                    mfts = model(" n = " + str(order))
                    mfts.train(data_train, data_train_fs, order=order)
                    objs.append(mfts)
                    colors.append(all_colors[count])
        count += 10

    if statistics:
        print(getPointStatistics(data_test, objs))

    if residuals:
        print(ResidualAnalysis.compareResiduals(data_test, objs))
        ResidualAnalysis.plotResiduals(data_test, objs, save=save, file=file, tam=[tam[0], 5 * tam[1]])

    if series:
        plotComparedSeries(data_test, objs, colors, typeonlegend=False, save=save, file=file, tam=tam,  intervals=False)


def getPointStatistics(data, models, externalmodels = None, externalforecasts = None):
    ret = "Model		& Order     & RMSE		& MAPE      & Theil's U		& Theil's I	\\\\ \n"
    for fts in models:
        forecasts = fts.forecast(data)
        ret += fts.shortname + "		& "
        ret += str(fts.order) + "		& "
        ret += str(round(Measures.rmse(np.array(data[fts.order:]), np.array(forecasts[:-1])), 2)) + "		& "
        ret += str(round(Measures.mape(np.array(data[fts.order:]), np.array(forecasts[:-1])), 2))+ "		& "
        ret += str(round(Measures.UStatistic(np.array(data[fts.order:]), np.array(forecasts[:-1])), 2))+ "		& "
        ret += str(round(Measures.TheilsInequality(np.array(data[fts.order:]), np.array(forecasts[:-1])), 4))
        ret += "	\\\\ \n"
    if externalmodels is not None:
        l = len(externalmodels)
        for k in np.arange(0,l):
            ret += externalmodels[k] + "		& "
            ret += " 1		& "
            ret += str(round(Measures.rmse(data[fts.order:], externalforecasts[k][:-1]), 2)) + "		& "
            ret += str(round(Measures.mape(data[fts.order:], externalforecasts[k][:-1]), 2))+ "		& "
            ret += str(round(Measures.UStatistic(np.array(data[fts.order:]), np.array(forecasts[:-1])), 2))
            ret += "	\\\\ \n"
    return ret


def allIntervalForecasters(data_train, data_test, partitions, max_order=3,save=False, file=None, tam=[20, 5]):
    models = [ifts.IntervalFTS, pfts.ProbabilisticFTS]

    objs = []

    all_colors = [clr for clr in pltcolors.cnames.keys()  ]

    data_train_fs = Grid.GridPartitionerTrimf(data_train,partitions)

    count = 1

    colors = []

    for model in models:
        #print(model)
        mfts = model("")
        if not mfts.isHighOrder:
            mfts.train(data_train, data_train_fs)
            objs.append(mfts)
            colors.append( all_colors[count] )
        else:
            for order in np.arange(1,max_order+1):
                if order >= mfts.minOrder:
                    mfts = model(" n = " + str(order))
                    mfts.train(data_train, data_train_fs, order=order)
                    objs.append(mfts)
                    colors.append(all_colors[count])
        count += 5

    print(getIntervalStatistics(data_test, objs))

    plotComparedSeries(data_test, objs, colors, typeonlegend=False, save=save, file=file, tam=tam,  intervals=True)


def getIntervalStatistics(original, models):
    ret = "Model	& Order     & Sharpness		& Resolution		& Coverage	\\ \n"
    for fts in models:
        forecasts = fts.forecastInterval(original)
        ret += fts.shortname + "		& "
        ret += str(fts.order) + "		& "
        ret += str(round(Measures.sharpness(forecasts), 2)) + "		& "
        ret += str(round(Measures.resolution(forecasts), 2)) + "		& "
        ret += str(round(Measures.coverage(original[fts.order:], forecasts[:-1]), 2)) + "	\\ \n"
    return ret


def plotDistribution(dist):
    for k in dist.index:
        alpha = np.array([dist[x][k] for x in dist]) * 100
        x = [k for x in np.arange(0, len(alpha))]
        y = dist.columns
        plt.scatter(x, y, c=alpha, marker='s', linewidths=0, cmap='Oranges', norm=pltcolors.Normalize(vmin=0, vmax=1),
                    vmin=0, vmax=1, edgecolors=None)


def plotComparedSeries(original, models, colors, typeonlegend=False, save=False, file=None, tam=[20, 5],
                       intervals=True):
    fig = plt.figure(figsize=tam)
    ax = fig.add_subplot(111)

    mi = []
    ma = []

    ax.plot(original, color='black', label="Original", linewidth=1.5)
    count = 0
    for fts in models:
        if fts.hasPointForecasting and not intervals:
            forecasted = fts.forecast(original)
            mi.append(min(forecasted) * 0.95)
            ma.append(max(forecasted) * 1.05)
            for k in np.arange(0, fts.order):
                forecasted.insert(0, None)
            lbl = fts.shortname
            if typeonlegend: lbl += " (Point)"
            ax.plot(forecasted, color=colors[count], label=lbl, ls="-")

        if fts.hasIntervalForecasting and intervals:
            forecasted = fts.forecastInterval(original)
            lower = [kk[0] for kk in forecasted]
            upper = [kk[1] for kk in forecasted]
            mi.append(min(lower) * 0.95)
            ma.append(max(upper) * 1.05)
            for k in np.arange(0, fts.order):
                lower.insert(0, None)
                upper.insert(0, None)
            lbl = fts.shortname
            if typeonlegend: lbl += " (Interval)"
            ax.plot(lower, color=colors[count], label=lbl, ls="-")
            ax.plot(upper, color=colors[count], ls="-")

        handles0, labels0 = ax.get_legend_handles_labels()
        ax.legend(handles0, labels0, loc=2)
        count = count + 1
    # ax.set_title(fts.name)
    ax.set_ylim([min(mi), max(ma)])
    ax.set_ylabel('F(T)')
    ax.set_xlabel('T')
    ax.set_xlim([0, len(original)])

    Util.showAndSaveImage(fig, file, save)


def plotComparedIntervalsAhead(original, models, colors, distributions, time_from, time_to,
                               interpol=False, save=False, file=None, tam=[20, 5], resolution=None):
    fig = plt.figure(figsize=tam)
    ax = fig.add_subplot(111)

    if resolution is None: resolution = (max(original) - min(original)) / 100

    mi = []
    ma = []

    count = 0
    for fts in models:
        if fts.hasDistributionForecasting and distributions[count]:
            density = fts.forecastAheadDistribution(original[time_from - fts.order:time_from], time_to, resolution,
                                                    parameters=None)

            y = density.columns
            t = len(y)

            for k in density.index:
                alpha = np.array([density[q][k] for q in density]) * 100

                x = [time_from + k for x in np.arange(0, t)]

                for cc in np.arange(0, resolution, 5):
                    ax.scatter(x, y + cc, c=alpha, marker='s', linewidths=0, cmap='Oranges', edgecolors=None)
                if interpol and k < max(density.index):
                    diffs = [(density[q][k + 1] - density[q][k]) / 50 for q in density]
                    for p in np.arange(0, 50):
                        xx = [time_from + k + 0.02 * p for q in np.arange(0, t)]
                        alpha2 = np.array(
                            [density[density.columns[q]][k] + diffs[q] * p for q in np.arange(0, t)]) * 100
                        ax.scatter(xx, y, c=alpha2, marker='s', linewidths=0, cmap='Oranges',
                                   norm=pltcolors.Normalize(vmin=0, vmax=1), vmin=0, vmax=1, edgecolors=None)

        if fts.hasIntervalForecasting:
            forecasts = fts.forecastAheadInterval(original[time_from - fts.order:time_from], time_to)
            lower = [kk[0] for kk in forecasts]
            upper = [kk[1] for kk in forecasts]
            mi.append(min(lower))
            ma.append(max(upper))
            for k in np.arange(0, time_from - fts.order):
                lower.insert(0, None)
                upper.insert(0, None)
            ax.plot(lower, color=colors[count], label=fts.shortname)
            ax.plot(upper, color=colors[count])

        else:
            forecasts = fts.forecast(original)
            mi.append(min(forecasts))
            ma.append(max(forecasts))
            for k in np.arange(0, time_from):
                forecasts.insert(0, None)
            ax.plot(forecasts, color=colors[count], label=fts.shortname)

        count = count + 1
    ax.plot(original, color='black', label="Original")
    handles0, labels0 = ax.get_legend_handles_labels()
    ax.legend(handles0, labels0, loc=2)
    # ax.set_title(fts.name)
    ax.set_ylim([min(mi), max(ma)])
    ax.set_ylabel('F(T)')
    ax.set_xlabel('T')
    ax.set_xlim([0, len(original)])

    Util.showAndSaveImage(fig, file, save)


def plotCompared(original, forecasts, labels, title):
    fig = plt.figure(figsize=[13, 6])
    ax = fig.add_subplot(111)
    ax.plot(original, color='k', label="Original")
    for c in range(0, len(forecasts)):
        ax.plot(forecasts[c], label=labels[c])
    handles0, labels0 = ax.get_legend_handles_labels()
    ax.legend(handles0, labels0)
    ax.set_title(title)
    ax.set_ylabel('F(T)')
    ax.set_xlabel('T')
    ax.set_xlim([0, len(original)])
    ax.set_ylim([min(original), max(original)])


def SelecaoKFold_MenorRMSE(original, parameters, modelo):
    nfolds = 5
    ret = []
    errors = np.array([[0 for k in parameters] for z in np.arange(0, nfolds)])
    forecasted_best = []
    print("Série Original")
    fig = plt.figure(figsize=[18, 10])
    fig.suptitle("Comparação de modelos ")
    ax0 = fig.add_axes([0, 0.5, 0.65, 0.45])  # left, bottom, width, height
    ax0.set_xlim([0, len(original)])
    ax0.set_ylim([min(original), max(original)])
    ax0.set_title('Série Temporal')
    ax0.set_ylabel('F(T)')
    ax0.set_xlabel('T')
    ax0.plot(original, label="Original")
    min_rmse_fold = 100000.0
    best = None
    fc = 0  # Fold count
    kf = KFold(len(original), n_folds=nfolds)
    for train_ix, test_ix in kf:
        train = original[train_ix]
        test = original[test_ix]
        min_rmse = 100000.0
        best_fold = None
        forecasted_best_fold = []
        errors_fold = []
        pc = 0  # Parameter count
        for p in parameters:
            sets = Grid.GridPartitionerTrimf(train, p)
            fts = modelo(str(p) + " particoes")
            fts.train(train, sets)
            forecasted = [fts.forecast(xx) for xx in test]
            error = Measures.rmse(np.array(forecasted), np.array(test))
            errors_fold.append(error)
            print(fc, p, error)
            errors[fc, pc] = error
            if error < min_rmse:
                min_rmse = error
                best_fold = fts
                forecasted_best_fold = forecasted
            pc = pc + 1
        forecasted_best_fold = [best_fold.forecast(xx) for xx in original]
        ax0.plot(forecasted_best_fold, label=best_fold.name)
        if np.mean(errors_fold) < min_rmse_fold:
            min_rmse_fold = np.mean(errors)
            best = best_fold
            forecasted_best = forecasted_best_fold
        fc = fc + 1
    handles0, labels0 = ax0.get_legend_handles_labels()
    ax0.legend(handles0, labels0)
    ax1 = Axes3D(fig, rect=[0.7, 0.5, 0.3, 0.45], elev=30, azim=144)
    # ax1 = fig.add_axes([0.6, 0.0, 0.45, 0.45], projection='3d')
    ax1.set_title('Comparação dos Erros Quadráticos Médios')
    ax1.set_zlabel('RMSE')
    ax1.set_xlabel('K-fold')
    ax1.set_ylabel('Partições')
    X, Y = np.meshgrid(np.arange(0, nfolds), parameters)
    surf = ax1.plot_surface(X, Y, errors.T, rstride=1, cstride=1, antialiased=True)
    ret.append(best)
    ret.append(forecasted_best)

    # Modelo diferencial
    print("\nSérie Diferencial")
    errors = np.array([[0 for k in parameters] for z in np.arange(0, nfolds)])
    forecastedd_best = []
    ax2 = fig.add_axes([0, 0, 0.65, 0.45])  # left, bottom, width, height
    ax2.set_xlim([0, len(original)])
    ax2.set_ylim([min(original), max(original)])
    ax2.set_title('Série Temporal')
    ax2.set_ylabel('F(T)')
    ax2.set_xlabel('T')
    ax2.plot(original, label="Original")
    min_rmse = 100000.0
    min_rmse_fold = 100000.0
    bestd = None
    fc = 0
    diff = Transformations.differential(original)
    kf = KFold(len(original), n_folds=nfolds)
    for train_ix, test_ix in kf:
        train = diff[train_ix]
        test = diff[test_ix]
        min_rmse = 100000.0
        best_fold = None
        forecasted_best_fold = []
        errors_fold = []
        pc = 0
        for p in parameters:
            sets = Grid.GridPartitionerTrimf(train, p)
            fts = modelo(str(p) + " particoes")
            fts.train(train, sets)
            forecasted = [fts.forecastDiff(test, xx) for xx in np.arange(len(test))]
            error = Measures.rmse(np.array(forecasted), np.array(test))
            print(fc, p, error)
            errors[fc, pc] = error
            errors_fold.append(error)
            if error < min_rmse:
                min_rmse = error
                best_fold = fts
            pc = pc + 1
        forecasted_best_fold = [best_fold.forecastDiff(original, xx) for xx in np.arange(len(original))]
        ax2.plot(forecasted_best_fold, label=best_fold.name)
        if np.mean(errors_fold) < min_rmse_fold:
            min_rmse_fold = np.mean(errors)
            best = best_fold
            forecasted_best = forecasted_best_fold
        fc = fc + 1
    handles0, labels0 = ax2.get_legend_handles_labels()
    ax2.legend(handles0, labels0)
    ax3 = Axes3D(fig, rect=[0.7, 0, 0.3, 0.45], elev=30, azim=144)
    # ax1 = fig.add_axes([0.6, 0.0, 0.45, 0.45], projection='3d')
    ax3.set_title('Comparação dos Erros Quadráticos Médios')
    ax3.set_zlabel('RMSE')
    ax3.set_xlabel('K-fold')
    ax3.set_ylabel('Partições')
    X, Y = np.meshgrid(np.arange(0, nfolds), parameters)
    surf = ax3.plot_surface(X, Y, errors.T, rstride=1, cstride=1, antialiased=True)
    ret.append(best)
    ret.append(forecasted_best)
    return ret


def SelecaoSimples_MenorRMSE(original, parameters, modelo):
    ret = []
    errors = []
    forecasted_best = []
    print("Série Original")
    fig = plt.figure(figsize=[20, 12])
    fig.suptitle("Comparação de modelos ")
    ax0 = fig.add_axes([0, 0.5, 0.65, 0.45])  # left, bottom, width, height
    ax0.set_xlim([0, len(original)])
    ax0.set_ylim([min(original), max(original)])
    ax0.set_title('Série Temporal')
    ax0.set_ylabel('F(T)')
    ax0.set_xlabel('T')
    ax0.plot(original, label="Original")
    min_rmse = 100000.0
    best = None
    for p in parameters:
        sets = Grid.GridPartitionerTrimf(original, p)
        fts = modelo(str(p) + " particoes")
        fts.train(original, sets)
        # print(original)
        forecasted = fts.forecast(original)
        forecasted.insert(0, original[0])
        # print(forecasted)
        ax0.plot(forecasted, label=fts.name)
        error = Measures.rmse(np.array(forecasted), np.array(original))
        print(p, error)
        errors.append(error)
        if error < min_rmse:
            min_rmse = error
            best = fts
            forecasted_best = forecasted
    handles0, labels0 = ax0.get_legend_handles_labels()
    ax0.legend(handles0, labels0)
    ax1 = fig.add_axes([0.7, 0.5, 0.3, 0.45])  # left, bottom, width, height
    ax1.set_title('Comparação dos Erros Quadráticos Médios')
    ax1.set_ylabel('RMSE')
    ax1.set_xlabel('Quantidade de Partições')
    ax1.set_xlim([min(parameters), max(parameters)])
    ax1.plot(parameters, errors)
    ret.append(best)
    ret.append(forecasted_best)
    # Modelo diferencial
    print("\nSérie Diferencial")
    difffts = Transformations.differential(original)
    errors = []
    forecastedd_best = []
    ax2 = fig.add_axes([0, 0, 0.65, 0.45])  # left, bottom, width, height
    ax2.set_xlim([0, len(difffts)])
    ax2.set_ylim([min(difffts), max(difffts)])
    ax2.set_title('Série Temporal')
    ax2.set_ylabel('F(T)')
    ax2.set_xlabel('T')
    ax2.plot(difffts, label="Original")
    min_rmse = 100000.0
    bestd = None
    for p in parameters:
        sets = Grid.GridPartitionerTrimf(difffts, p)
        fts = modelo(str(p) + " particoes")
        fts.train(difffts, sets)
        forecasted = fts.forecast(difffts)
        forecasted.insert(0, difffts[0])
        ax2.plot(forecasted, label=fts.name)
        error = Measures.rmse(np.array(forecasted), np.array(difffts))
        print(p, error)
        errors.append(error)
        if error < min_rmse:
            min_rmse = error
            bestd = fts
            forecastedd_best = forecasted
    handles0, labels0 = ax2.get_legend_handles_labels()
    ax2.legend(handles0, labels0)
    ax3 = fig.add_axes([0.7, 0, 0.3, 0.45])  # left, bottom, width, height
    ax3.set_title('Comparação dos Erros Quadráticos Médios')
    ax3.set_ylabel('RMSE')
    ax3.set_xlabel('Quantidade de Partições')
    ax3.set_xlim([min(parameters), max(parameters)])
    ax3.plot(parameters, errors)
    ret.append(bestd)
    ret.append(forecastedd_best)
    return ret


def compareModelsPlot(original, models_fo, models_ho):
    fig = plt.figure(figsize=[13, 6])
    fig.suptitle("Comparação de modelos ")
    ax0 = fig.add_axes([0, 0, 1, 1])  # left, bottom, width, height
    rows = []
    for model in models_fo:
        fts = model["model"]
        ax0.plot(model["forecasted"], label=model["name"])
    for model in models_ho:
        fts = model["model"]
        ax0.plot(model["forecasted"], label=model["name"])
    handles0, labels0 = ax0.get_legend_handles_labels()
    ax0.legend(handles0, labels0)


def compareModelsTable(original, models_fo, models_ho):
    fig = plt.figure(figsize=[12, 4])
    fig.suptitle("Comparação de modelos ")
    columns = ['Modelo', 'Ordem', 'Partições', 'RMSE', 'MAPE (%)']
    rows = []
    for model in models_fo:
        fts = model["model"]
        error_r = Measures.rmse(model["forecasted"], original)
        error_m = round(Measures.mape(model["forecasted"], original) * 100, 2)
        rows.append([model["name"], fts.order, len(fts.sets), error_r, error_m])
    for model in models_ho:
        fts = model["model"]
        error_r = Measures.rmse(model["forecasted"][fts.order:], original[fts.order:])
        error_m = round(Measures.mape(model["forecasted"][fts.order:], original[fts.order:]) * 100, 2)
        rows.append([model["name"], fts.order, len(fts.sets), error_r, error_m])
    ax1 = fig.add_axes([0, 0, 1, 1])  # left, bottom, width, height
    ax1.set_xticks([])
    ax1.set_yticks([])
    ax1.table(cellText=rows,
              colLabels=columns,
              cellLoc='center',
              bbox=[0, 0, 1, 1])
    sup = "\\begin{tabular}{"
    header = ""
    body = ""
    footer = ""

    for c in columns:
        sup = sup + "|c"
        if len(header) > 0:
            header = header + " & "
        header = header + "\\textbf{" + c + "} "
    sup = sup + "|} \\hline\n"
    header = header + "\\\\ \\hline \n"

    for r in rows:
        lin = ""
        for c in r:
            if len(lin) > 0:
                lin = lin + " & "
            lin = lin + str(c)

        body = body + lin + "\\\\ \\hline \n"

    return sup + header + body + "\\end{tabular}"


def simpleSearch_RMSE(original, model, partitions, orders, save=False, file=None, tam=[10, 15], plotforecasts=False,
                      elev=30, azim=144):
    ret = []
    errors = np.array([[0 for k in range(len(partitions))] for kk in range(len(orders))])
    forecasted_best = []
    fig = plt.figure(figsize=tam)
    # fig.suptitle("Comparação de modelos ")
    if plotforecasts:
        ax0 = fig.add_axes([0, 0.4, 0.9, 0.5])  # left, bottom, width, height
        ax0.set_xlim([0, len(original)])
        ax0.set_ylim([min(original) * 0.9, max(original) * 1.1])
        ax0.set_title('Forecasts')
        ax0.set_ylabel('F(T)')
        ax0.set_xlabel('T')
    min_rmse = 1000000.0
    best = None
    pc = 0
    for p in partitions:
        oc = 0
        for o in orders:
            sets = Grid.GridPartitionerTrimf(original, p)
            fts = model("q = " + str(p) + " n = " + str(o))
            fts.train(original, sets, o)
            forecasted = fts.forecast(original)
            error = Measures.rmse(np.array(original[o:]), np.array(forecasted[:-1]))
            mape = Measures.mape(np.array(original[o:]), np.array(forecasted[:-1]))
            # print(original[o:])
            # print(forecasted[-1])
            for kk in range(o):
                forecasted.insert(0, None)
                if plotforecasts: ax0.plot(forecasted, label=fts.name)
            # print(o, p, mape)
            errors[oc, pc] = error
            if error < min_rmse:
                min_rmse = error
                best = fts
                forecasted_best = forecasted
            oc += 1
        pc += 1
    # print(min_rmse)
    if plotforecasts:
        # handles0, labels0 = ax0.get_legend_handles_labels()
        # ax0.legend(handles0, labels0)
        ax0.plot(original, label="Original", linewidth=3.0, color="black")
        ax1 = Axes3D(fig, rect=[0, 1, 0.9, 0.9], elev=elev, azim=azim)
    if not plotforecasts: ax1 = Axes3D(fig, rect=[0, 1, 0.9, 0.9], elev=elev, azim=azim)
    # ax1 = fig.add_axes([0.6, 0.5, 0.45, 0.45], projection='3d')
    ax1.set_title('Error Surface')
    ax1.set_ylabel('Model order')
    ax1.set_xlabel('Number of partitions')
    ax1.set_zlabel('RMSE')
    X, Y = np.meshgrid(partitions, orders)
    surf = ax1.plot_surface(X, Y, errors, rstride=1, cstride=1, antialiased=True)
    ret.append(best)
    ret.append(forecasted_best)

    # plt.tight_layout()

    Util.showAndSaveImage(fig, file, save)

    return ret


def pftsExploreOrderAndPartitions(data,save=False, file=None):
    fig, axes = plt.subplots(nrows=4, ncols=1, figsize=[6, 8])
    data_fs1 = Grid.GridPartitionerTrimf(data, 10)
    mi = []
    ma = []

    axes[0].set_title('Point Forecasts by Order')
    axes[2].set_title('Interval Forecasts by Order')

    for order in np.arange(1, 6):
        fts = pfts.ProbabilisticFTS("")
        fts.shortname = "n = " + str(order)
        fts.train(data, data_fs1, order=order)
        point_forecasts = fts.forecast(data)
        interval_forecasts = fts.forecastInterval(data)
        lower = [kk[0] for kk in interval_forecasts]
        upper = [kk[1] for kk in interval_forecasts]
        mi.append(min(lower) * 0.95)
        ma.append(max(upper) * 1.05)
        for k in np.arange(0, order):
            point_forecasts.insert(0, None)
            lower.insert(0, None)
            upper.insert(0, None)
        axes[0].plot(point_forecasts, label=fts.shortname)
        axes[2].plot(lower, label=fts.shortname)
        axes[2].plot(upper)

    axes[1].set_title('Point Forecasts by Number of Partitions')
    axes[3].set_title('Interval Forecasts by Number of Partitions')

    for partitions in np.arange(5, 11):
        data_fs = Grid.GridPartitionerTrimf(data, partitions)
        fts = pfts.ProbabilisticFTS("")
        fts.shortname = "q = " + str(partitions)
        fts.train(data, data_fs, 1)
        point_forecasts = fts.forecast(data)
        interval_forecasts = fts.forecastInterval(data)
        lower = [kk[0] for kk in interval_forecasts]
        upper = [kk[1] for kk in interval_forecasts]
        mi.append(min(lower) * 0.95)
        ma.append(max(upper) * 1.05)
        point_forecasts.insert(0, None)
        lower.insert(0, None)
        upper.insert(0, None)
        axes[1].plot(point_forecasts, label=fts.shortname)
        axes[3].plot(lower, label=fts.shortname)
        axes[3].plot(upper)

    for ax in axes:
        ax.set_ylabel('F(T)')
        ax.set_xlabel('T')
        ax.plot(data, label="Original", color="black", linewidth=1.5)
        handles, labels = ax.get_legend_handles_labels()
        ax.legend(handles, labels, loc=2, bbox_to_anchor=(1, 1))
        ax.set_ylim([min(mi), max(ma)])
        ax.set_xlim([0, len(data)])

    plt.tight_layout()

    Util.showAndSaveImage(fig, file, save)