plotting.py

# -*- coding: utf-8 -*-
import numpy as np
import pandas as pd
from lifetimes.utils import calculate_alive_path, expected_cumulative_transactions
from scipy import stats

__all__ = [
    "plot_period_transactions",
    "plot_calibration_purchases_vs_holdout_purchases",
    "plot_frequency_recency_matrix",
    "plot_probability_alive_matrix",
    "plot_expected_repeat_purchases",
    "plot_history_alive",
    "plot_cumulative_transactions",
    "plot_incremental_transactions",
    "plot_transaction_rate_heterogeneity",
    "plot_dropout_rate_heterogeneity",
]


def coalesce(*args):
    return next(s for s in args if s is not None)


def plot_period_transactions(
    model,
    max_frequency=7,
    title="Frequency of Repeat Transactions",
    xlabel="Number of Calibration Period Transactions",
    ylabel="Customers",
    **kwargs
):
    """
    Plot a figure with period actual and predicted transactions.

    Parameters
    ----------
    model: lifetimes model
        A fitted lifetimes model.
    max_frequency: int, optional
        The maximum frequency to plot.
    title: str, optional
        Figure title
    xlabel: str, optional
        Figure xlabel
    ylabel: str, optional
        Figure ylabel
    kwargs
        Passed into the matplotlib.pyplot.plot command.

    Returns
    -------
    axes: matplotlib.AxesSubplot

    """
    from matplotlib import pyplot as plt

    labels = kwargs.pop("label", ["Actual", "Model"])

    n = model.data.shape[0]
    simulated_data = model.generate_new_data(size=n)

    model_counts = pd.DataFrame(model.data["frequency"].value_counts().sort_index().iloc[:max_frequency])
    simulated_counts = pd.DataFrame(simulated_data["frequency"].value_counts().sort_index().iloc[:max_frequency])
    combined_counts = model_counts.merge(simulated_counts, how="outer", left_index=True, right_index=True).fillna(0)
    combined_counts.columns = labels

    ax = combined_counts.plot(kind="bar", **kwargs)

    plt.legend()
    plt.title(title)
    plt.ylabel(ylabel)
    plt.xlabel(xlabel)
    return ax


def plot_calibration_purchases_vs_holdout_purchases(
    model, calibration_holdout_matrix, kind="frequency_cal", n=7, **kwargs
):
    """
    Plot calibration purchases vs holdout.

    This currently relies too much on the lifetimes.util calibration_and_holdout_data function.

    Parameters
    ----------
    model: lifetimes model
        A fitted lifetimes model.
    calibration_holdout_matrix: pandas DataFrame
        DataFrame from calibration_and_holdout_data function.
    kind: str, optional
        x-axis :"frequency_cal". Purchases in calibration period,
                 "recency_cal". Age of customer at last purchase,
                 "T_cal". Age of customer at the end of calibration period,
                 "time_since_last_purchase". Time since user made last purchase
    n: int, optional
        Number of ticks on the x axis
    Returns
    -------
    axes: matplotlib.AxesSubplot

    """
    from matplotlib import pyplot as plt

    x_labels = {
        "frequency_cal": "Purchases in calibration period",
        "recency_cal": "Age of customer at last purchase",
        "T_cal": "Age of customer at the end of calibration period",
        "time_since_last_purchase": "Time since user made last purchase",
    }
    summary = calibration_holdout_matrix.copy()
    duration_holdout = summary.iloc[0]["duration_holdout"]

    summary["model_predictions"] = model.conditional_expected_number_of_purchases_up_to_time(
            duration_holdout, summary["frequency_cal"], summary["recency_cal"], summary["T_cal"])

    if kind == "time_since_last_purchase":
        summary["time_since_last_purchase"] = summary["T_cal"] - summary["recency_cal"]
        ax = (
            summary.groupby(["time_since_last_purchase"])[["frequency_holdout", "model_predictions"]]
            .mean()
            .iloc[:n]
            .plot(**kwargs)
        )
    else:
        ax = summary.groupby(kind)[["frequency_holdout", "model_predictions"]].mean().iloc[:n].plot(**kwargs)

    plt.title("Actual Purchases in Holdout Period vs Predicted Purchases")
    plt.xlabel(x_labels[kind])
    plt.ylabel("Average of Purchases in Holdout Period")
    plt.legend()

    return ax


def plot_frequency_recency_matrix(
    model,
    T=1,
    max_frequency=None,
    max_recency=None,
    title=None,
    xlabel="Customer's Historical Frequency",
    ylabel="Customer's Recency",
    **kwargs
):
    """
    Plot recency frequecy matrix as heatmap.

    Plot a figure of expected transactions in T next units of time by a customer's frequency and recency.

    Parameters
    ----------
    model: lifetimes model
        A fitted lifetimes model.
    T: fload, optional
        Next units of time to make predictions for
    max_frequency: int, optional
        The maximum frequency to plot. Default is max observed frequency.
    max_recency: int, optional
        The maximum recency to plot. This also determines the age of the customer.
        Default to max observed age.
    title: str, optional
        Figure title
    xlabel: str, optional
        Figure xlabel
    ylabel: str, optional
        Figure ylabel
    kwargs
        Passed into the matplotlib.imshow command.

    Returns
    -------
    axes: matplotlib.AxesSubplot

    """
    from matplotlib import pyplot as plt

    if max_frequency is None:
        max_frequency = int(model.data["frequency"].max())

    if max_recency is None:
        max_recency = int(model.data["T"].max())

    Z = np.zeros((max_recency + 1, max_frequency + 1))
    for i, recency in enumerate(np.arange(max_recency + 1)):
        for j, frequency in enumerate(np.arange(max_frequency + 1)):
            Z[i, j] = model.conditional_expected_number_of_purchases_up_to_time(T, frequency, recency, max_recency)

    interpolation = kwargs.pop("interpolation", "none")

    ax = plt.subplot(111)
    pcm = ax.imshow(Z, interpolation=interpolation, **kwargs)
    plt.xlabel(xlabel)
    plt.ylabel(ylabel)
    if title is None:
        title = (
            "Expected Number of Future Purchases for {} Unit{} of Time,".format(T, "s"[T == 1 :])
            + "\nby Frequency and Recency of a Customer"
        )
    plt.title(title)

    # turn matrix into square
    forceAspect(ax)

    # plot colorbar beside matrix
    plt.colorbar(pcm, ax=ax)

    return ax


def plot_probability_alive_matrix(
    model,
    max_frequency=None,
    max_recency=None,
    title="Probability Customer is Alive,\nby Frequency and Recency of a Customer",
    xlabel="Customer's Historical Frequency",
    ylabel="Customer's Recency",
    **kwargs
):
    """
    Plot probability alive matrix as heatmap.

    Plot a figure of the probability a customer is alive based on their
    frequency and recency.

    Parameters
    ----------
    model: lifetimes model
        A fitted lifetimes model.
    max_frequency: int, optional
        The maximum frequency to plot. Default is max observed frequency.
    max_recency: int, optional
        The maximum recency to plot. This also determines the age of the customer.
        Default to max observed age.
    title: str, optional
        Figure title
    xlabel: str, optional
        Figure xlabel
    ylabel: str, optional
        Figure ylabel
    kwargs
        Passed into the matplotlib.imshow command.

    Returns
    -------
    axes: matplotlib.AxesSubplot

    """
    from matplotlib import pyplot as plt

    z = model.conditional_probability_alive_matrix(max_frequency, max_recency)

    interpolation = kwargs.pop("interpolation", "none")

    ax = plt.subplot(111)
    pcm = ax.imshow(z, interpolation=interpolation, **kwargs)
    plt.xlabel(xlabel)
    plt.ylabel(ylabel)
    plt.title(title)

    # turn matrix into square
    forceAspect(ax)

    # plot colorbar beside matrix
    plt.colorbar(pcm, ax=ax)

    return ax


def plot_expected_repeat_purchases(
    model,
    title="Expected Number of Repeat Purchases per Customer",
    xlabel="Time Since First Purchase",
    ax=None,
    label=None,
    **kwargs
):
    """
    Plot expected repeat purchases on calibration period .

    Parameters
    ----------
    model: lifetimes model
        A fitted lifetimes model.
    max_frequency: int, optional
        The maximum frequency to plot.
    title: str, optional
        Figure title
    xlabel: str, optional
        Figure xlabel
    ax: matplotlib.AxesSubplot, optional
        Using user axes
    label: str, optional
        Label for plot.
    kwargs
        Passed into the matplotlib.pyplot.plot command.

    Returns
    -------
    axes: matplotlib.AxesSubplot

    """
    from matplotlib import pyplot as plt

    if ax is None:
        ax = plt.subplot(111)

    if plt.matplotlib.__version__ >= "1.5":
        color_cycle = ax._get_lines.prop_cycler
        color = coalesce(kwargs.pop("c", None), kwargs.pop("color", None), next(color_cycle)["color"])
    else:
        color_cycle = ax._get_lines.color_cycle
        color = coalesce(kwargs.pop("c", None), kwargs.pop("color", None), next(color_cycle))

    max_T = model.data["T"].max()

    times = np.linspace(0, max_T, 100)
    ax.plot(times, model.expected_number_of_purchases_up_to_time(times), color=color, label=label, **kwargs)

    times = np.linspace(max_T, 1.5 * max_T, 100)
    ax.plot(times, model.expected_number_of_purchases_up_to_time(times), color=color, ls="--", **kwargs)

    plt.title(title)
    plt.xlabel(xlabel)
    plt.legend(loc="lower right")
    return ax


def plot_history_alive(model, t, transactions, datetime_col, freq="D", start_date=None, ax=None, **kwargs):
    """
    Draw a graph showing the probability of being alive for a customer in time.

    Parameters
    ----------
    model: lifetimes model
        A fitted lifetimes model.
    t: int
        the number of time units since the birth we want to draw the p_alive
    transactions: pandas DataFrame
        DataFrame containing the transactions history of the customer_id
    datetime_col: str
        The column in the transactions that denotes the datetime the purchase was made
    freq: str, optional
        Default 'D' for days. Other examples= 'W' for weekly
    start_date: datetime, optional
        Limit xaxis to start date
    ax: matplotlib.AxesSubplot, optional
        Using user axes
    kwargs
        Passed into the matplotlib.pyplot.plot command.

    Returns
    -------
    axes: matplotlib.AxesSubplot

    """
    from matplotlib import pyplot as plt

    if start_date is None:
        start_date = min(transactions[datetime_col])

    if ax is None:
        ax = plt.subplot(111)

    # Get purchasing history of user
    customer_history = transactions[[datetime_col]].copy()
    customer_history.index = pd.DatetimeIndex(customer_history[datetime_col])

    # Add transactions column
    customer_history["transactions"] = 1
    customer_history = customer_history.resample(freq).sum()

    # plot alive_path
    path = calculate_alive_path(model, transactions, datetime_col, t, freq)
    path_dates = pd.date_range(start=min(transactions[datetime_col]), periods=len(path), freq=freq)
    plt.plot(path_dates, path, "-", label="P_alive")

    # plot buying dates
    payment_dates = customer_history[customer_history["transactions"] >= 1].index
    plt.vlines(payment_dates.values, ymin=0, ymax=1, colors="r", linestyles="dashed", label="purchases")

    plt.ylim(0, 1.0)
    plt.yticks(np.arange(0, 1.1, 0.1))
    plt.xlim(start_date, path_dates[-1])
    plt.legend(loc=3)
    plt.ylabel("P_alive")
    plt.title("History of P_alive")

    return ax


def plot_cumulative_transactions(
    model,
    transactions,
    datetime_col,
    customer_id_col,
    t,
    t_cal,
    datetime_format=None,
    freq="D",
    set_index_date=False,
    title="Tracking Cumulative Transactions",
    xlabel="day",
    ylabel="Cumulative Transactions",
    ax=None,
    **kwargs
):
    """
    Plot a figure of the predicted and actual cumulative transactions of users.

    Parameters
    ----------
    model: lifetimes model
        A fitted lifetimes model
    transactions: pandas DataFrame
        DataFrame containing the transactions history of the customer_id
    datetime_col: str
        The column in transactions that denotes the datetime the purchase was made.
    customer_id_col: str
        The column in transactions that denotes the customer_id
    t: float
        The number of time units since the begining of
        data for which we want to calculate cumulative transactions
    t_cal: float
        A marker used to indicate where the vertical line for plotting should be.
    datetime_format: str, optional
        A string that represents the timestamp format. Useful if Pandas
        can't understand the provided format.
    freq: str, optional
        Default 'D' for days, 'W' for weeks, 'M' for months... etc.
        Full list here:
        http://pandas.pydata.org/pandas-docs/stable/timeseries.html#dateoffset-objects
    set_index_date: bool, optional
        When True set date as Pandas DataFrame index, default False - number of time units
    title: str, optional
        Figure title
    xlabel: str, optional
        Figure xlabel
    ylabel: str, optional
        Figure ylabel
    ax: matplotlib.AxesSubplot, optional
        Using user axes
    kwargs
        Passed into the pandas.DataFrame.plot command.

    Returns
    -------
    axes: matplotlib.AxesSubplot

    """
    from matplotlib import pyplot as plt

    if ax is None:
        ax = plt.subplot(111)

    df_cum_transactions = expected_cumulative_transactions(
        model,
        transactions,
        datetime_col,
        customer_id_col,
        t,
        datetime_format=datetime_format,
        freq=freq,
        set_index_date=set_index_date,
    )

    ax = df_cum_transactions.plot(ax=ax, title=title, **kwargs)

    if set_index_date:
        x_vline = df_cum_transactions.index[int(t_cal)]
        xlabel = "date"
    else:
        x_vline = t_cal
    ax.axvline(x=x_vline, color="r", linestyle="--")
    ax.set_xlabel(xlabel)
    ax.set_ylabel(ylabel)
    return ax


def plot_incremental_transactions(
    model,
    transactions,
    datetime_col,
    customer_id_col,
    t,
    t_cal,
    datetime_format=None,
    freq="D",
    set_index_date=False,
    title="Tracking Daily Transactions",
    xlabel="day",
    ylabel="Transactions",
    ax=None,
    **kwargs
):
    """
    Plot a figure of the predicted and actual incremental transactions of users.

    Parameters
    ----------
    model: lifetimes model
        A fitted lifetimes model
    transactions: pandas DataFrame
        DataFrame containing the transactions history of the customer_id
    datetime_col: str
        The column in transactions that denotes the datetime the purchase was made.
    customer_id_col: str
        The column in transactions that denotes the customer_id
    t: float
        The number of time units since the begining of
        data for which we want to calculate cumulative transactions
    t_cal: float
        A marker used to indicate where the vertical line for plotting should be.
    datetime_format: str, optional
        A string that represents the timestamp format. Useful if Pandas
        can't understand the provided format.
    freq: str, optional
        Default 'D' for days, 'W' for weeks, 'M' for months... etc.
        Full list here:
        http://pandas.pydata.org/pandas-docs/stable/timeseries.html#dateoffset-objects
    set_index_date: bool, optional
        When True set date as Pandas DataFrame index, default False - number of time units
    title: str, optional
        Figure title
    xlabel: str, optional
        Figure xlabel
    ylabel: str, optional
        Figure ylabel
    ax: matplotlib.AxesSubplot, optional
        Using user axes
    kwargs
        Passed into the pandas.DataFrame.plot command.

    Returns
    -------
    axes: matplotlib.AxesSubplot

    """
    from matplotlib import pyplot as plt

    if ax is None:
        ax = plt.subplot(111)

    df_cum_transactions = expected_cumulative_transactions(
        model,
        transactions,
        datetime_col,
        customer_id_col,
        t,
        datetime_format=datetime_format,
        freq=freq,
        set_index_date=set_index_date,
    )

    # get incremental from cumulative transactions
    df_cum_transactions = df_cum_transactions.apply(lambda x: x - x.shift(1))
    ax = df_cum_transactions.plot(ax=ax, title=title, **kwargs)

    if set_index_date:
        x_vline = df_cum_transactions.index[int(t_cal)]
        xlabel = "date"
    else:
        x_vline = t_cal
    ax.axvline(x=x_vline, color="r", linestyle="--")
    ax.set_xlabel(xlabel)
    ax.set_ylabel(ylabel)
    return ax


def plot_transaction_rate_heterogeneity(
    model,
    suptitle="Heterogeneity in Transaction Rate",
    xlabel="Transaction Rate",
    ylabel="Density",
    suptitle_fontsize=14,
    **kwargs
):
    """
    Plot the estimated gamma distribution of lambda (customers' propensities to purchase).

    Parameters
    ----------
    model: lifetimes model
        A fitted lifetimes model, for now only for BG/NBD
    suptitle: str, optional
        Figure suptitle
    xlabel: str, optional
        Figure xlabel
    ylabel: str, optional
        Figure ylabel
    kwargs
        Passed into the matplotlib.pyplot.plot command.

    Returns
    -------
    axes: matplotlib.AxesSubplot

    """
    from matplotlib import pyplot as plt

    r, alpha = model._unload_params("r", "alpha")
    rate_mean = r / alpha
    rate_var = r / alpha ** 2

    rv = stats.gamma(r, scale=1 / alpha)
    lim = rv.ppf(0.99)
    x = np.linspace(0, lim, 100)

    fig, ax = plt.subplots(1)
    fig.suptitle("Heterogeneity in Transaction Rate", fontsize=suptitle_fontsize, fontweight="bold")

    ax.set_title("mean: {:.3f}, var: {:.3f}".format(rate_mean, rate_var))
    ax.set_xlabel(xlabel)
    ax.set_ylabel(ylabel)

    fig.tight_layout(rect=[0, 0.03, 1, 0.95])
    plt.plot(x, rv.pdf(x), **kwargs)
    return ax


def plot_dropout_rate_heterogeneity(
    model,
    suptitle="Heterogeneity in Dropout Probability",
    xlabel="Dropout Probability p",
    ylabel="Density",
    suptitle_fontsize=14,
    **kwargs
):
    """
    Plot the estimated beta distribution of p.

    p - (customers' probability of dropping out immediately after a transaction).

    Parameters
    ----------
    model: lifetimes model
        A fitted lifetimes model, for now only for BG/NBD
    suptitle: str, optional
        Figure suptitle
    xlabel: str, optional
        Figure xlabel
    ylabel: str, optional
        Figure ylabel
    kwargs
        Passed into the matplotlib.pyplot.plot command.

    Returns
    -------
    axes: matplotlib.AxesSubplot

    """
    from matplotlib import pyplot as plt

    a, b = model._unload_params("a", "b")
    beta_mean = a / (a + b)
    beta_var = a * b / ((a + b) ** 2) / (a + b + 1)

    rv = stats.beta(a, b)
    lim = rv.ppf(0.99)
    x = np.linspace(0, lim, 100)

    fig, ax = plt.subplots(1)
    fig.suptitle(suptitle, fontsize=suptitle_fontsize, fontweight="bold")

    ax.set_title("mean: {:.3f}, var: {:.3f}".format(beta_mean, beta_var))
    ax.set_xlabel(xlabel)
    ax.set_ylabel(ylabel)

    fig.tight_layout(rect=[0, 0.03, 1, 0.95])
    plt.plot(x, rv.pdf(x), **kwargs)
    return ax


def forceAspect(ax, aspect=1):
    im = ax.get_images()
    extent = im[0].get_extent()
    ax.set_aspect(abs((extent[1] - extent[0]) / (extent[3] - extent[2])) / aspect)