Wheel of time

#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Calcualte stats for Wheel of Time series
Each row is the number of 5,4,3,2,1 rations for a book in the series
Collected from goodreads.com, amazon.com and amazon.co.uk
"""

goodreads = [
    [45132, 32768, 15394, 4462, 2287],  # 1
    [-1,    -1,    -1,    -1,   -1],   # 2
    [31992, 26753, 11780, 2265,  795],  # 3
    [24523, 21922, 10282, 1747,  430],  # 4
    [16119, 16903,  9131, 1749,  371],  # 5
    [12290, 12332,  7866, 1750,  399],  # 6
    [9925, 11312,  8258, 2068,  451],  # 7
    [8841,  9805,  8043, 2511,  542],  # 8
    [8891,  9205,  7464, 2438,  622],  # 9
    [7411,  7549,  6040, 2272,  864],  # 10
    [8959,  8456,  4699, 1202,  321],  # 11
    [14569,  9046,  3169,  676,  363],  # 12
    [14147,  7671,  2337,  451,  292]]  # 13

amazoncom = [
    [1279, 404, 188, 138, 157],  # 1
    [393, 139, 37, 13, 15],     # 2
    [292, 122, 35, 23, 17],     # 3
    [275,  93, 39, 17, 19],     # 4
    [204,  97, 54, 27, 24],     # 5
    [227, 83, 55, 35, 35],      # 6
    [335, 187, 116, 73, 54],    # 7
    [361, 330, 379, 352, 466],   # 8
    [331, 302, 191, 184, 185],  # 9
    [199, 146, 253, 396, 1581],  # 10
    [184, 155, 108, 81, 111],   # 11
    [540, 149, 31, 22, 14],     # 12
    [1628, 346, 150, 62, 358]]  # 13

amazoncouk = [
    [144, 47, 20, 19, 20],  # 1
    [33, 25, 4, 0, 1],     # 2
    [46, 25, 8, 0, 5],     # 3
    [32, 12, 7, 0, 1],     # 4
    [21, 17, 5, 5, 4],     # 5
    [25, 10, 10, 1, 2],    # 6
    [19, 12, 2, 0, 0],     # 7
    [20, 21, 22, 16, 19],  # 8
    [44, 33, 26, 9, 10],   # 9
    [20, 18, 32, 60, 76],  # 10
    [38, 42, 17, 6, 5],    # 11
    [125, 22, 6, 3, 1],    # 12
    [96, 31, 8, 8, 5]]     # 13

import math
import numpy as np
from matplotlib import pyplot as plot


def histo_stat(haxis, histo):
    """
    Parameters: haxis - x axis, histo - weight for each entry in axis
    Return: mean, standard devation and bin fractions
    """
    sumw = sum(h for h in histo)
    if sumw < 0:
        return 0, 0, [0] * len(haxis)
    ihisto = zip(histo, haxis)
    mean = 1. / sumw * sum(w * x for w, x in ihisto)
    std = math.sqrt(1. / sumw * sum(i[0] * (i[1] - mean) ** 2 for i in ihisto))
    frac = [float(h) / sumw for h in histo]
    return mean, std, frac


def run(name, data):
    """
    Paramters: name - datasetname, data - table with histgrams
    """
    fig = plot.figure(1)
    print("----{}----".format(name))
    haxis = range(5, 0, -1)
    stats = []
    percs = []
    for i, histo in enumerate(data):
        mean, std, frac = histo_stat(haxis, histo)
        if mean == 0:  # Special case with no data
            mean = 4.15
        stats += [(mean, std)]
        perc = ",".join("{:>6.1%}".format(fi) for fi in frac)
        percs += [[100 * fi for fi in frac]]
        print "{:>2}: {:.2f} +- {:.2f} [{}]".format(i + 1, mean, std, perc)
    return np.array(stats), np.array(percs)


def plot_stats(stats, color):
    """
    Plot statistics, can superimpose
    """
    nx = stats.shape[0]
    ax = plot.subplot(1, 1, 1, xlim=(1, 13))
    xaxis = range(1, nx + 1)
    plot.errorbar(
        xaxis, stats[:, 0], xerr=0.5, yerr=stats[:, 1], color=color, fmt='-o')
    plot.fill_between(xaxis, stats[:, 0] - stats[:, 1],  stats[
                      :, 0] + stats[:, 1], facecolor=color, alpha=0.3)
    plot.ylabel("score")
    plot.xlabel("book")


def plot_percs(isub, percs, name):
    """
    Plot percentages as image to a give subfig
    """
    plot.subplot(3, 1, isub)
    im = plot.imshow(
        percs.T, extent=(1, percs.T.shape[1], 1, percs.T.shape[0]),
        interpolation="nearest", clim=(0, 100))
    plot.title(name)
    plot.ylabel("score")
    plot.xlabel("book")
    return im

stats1, percs1 = run("Amazon.com", amazoncom)
stats2, percs2 = run("Amazon.co.uk", amazoncouk)
stats3, percs3 = run("Goodreads.com", goodreads)

fig1 = plot.figure(1)
plot_stats(stats1, "red")
plot_stats(stats2, "blue")
plot_stats(stats3, "green")

fig2 = plot.figure(2)
plot_percs(1, percs1, "Amazon.com")
plot_percs(2, percs2, "Amazon.co.uk")
im = plot_percs(3, percs3, "Goodreads.com")
cax = fig2.add_axes([0.8, 0.1, 0.03, 0.85])
fig2.colorbar(im, cax=cax, label="Percentage")
fig2.tight_layout()
plot.show()