# -*- coding: utf-8 -*- # This file is part of pygal # # A python svg graph plotting library # Copyright © 2012-2016 Kozea # # This library is free software: you can redistribute it and/or modify it under # the terms of the GNU Lesser General Public License as published by the Free # Software Foundation, either version 3 of the License, or (at your option) any # later version. # # This library is distributed in the hope that it will be useful, but WITHOUT # ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS # FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more # details. # # You should have received a copy of the GNU Lesser General Public License # along with pygal. If not, see . """ Box plot: a convenient way to display series as box with whiskers and outliers Different types are available throught the box_mode option """ from bisect import bisect_left, bisect_right from pygal.graph.graph import Graph from pygal.util import alter, decorate class Box(Graph): """ Box plot For each series, shows the median value, the 25th and 75th percentiles, and the values within 1.5 times the interquartile range of the 25th and 75th percentiles. See http://en.wikipedia.org/wiki/Box_plot """ _series_margin = .06 def _value_format(self, value, serie): """ Format value for dual value display. """ if self.box_mode == "extremes": return ( 'Min: %s\nQ1 : %s\nQ2 : %s\nQ3 : %s\nMax: %s' % tuple(map(self._y_format, serie.points[1:6])) ) elif self.box_mode in ["tukey", "stdev", "pstdev"]: return ( 'Min: %s\nLower Whisker: %s\nQ1: %s\nQ2: %s\nQ3: %s\n' 'Upper Whisker: %s\nMax: %s' % tuple(map(self._y_format, serie.points)) ) elif self.box_mode == '1.5IQR': # 1.5IQR mode return 'Q1: %s\nQ2: %s\nQ3: %s' % tuple( map(self._y_format, serie.points[2:5]) ) else: return self._y_format(serie.points) def _compute(self): """ Compute parameters necessary for later steps within the rendering process """ for serie in self.series: serie.points, serie.outliers = \ self._box_points(serie.values, self.box_mode) self._x_pos = [(i + .5) / self._order for i in range(self._order)] if self._min: self._box.ymin = min(self._min, self.zero) if self._max: self._box.ymax = max(self._max, self.zero) def _plot(self): """Plot the series data""" for serie in self.series: self._boxf(serie) @property def _len(self): """Len is always 7 here""" return 7 def _boxf(self, serie): """For a specific series, draw the box plot.""" serie_node = self.svg.serie(serie) # Note: q0 and q4 do not literally mean the zero-th quartile # and the fourth quartile, but rather the distance from 1.5 times # the inter-quartile range to Q1 and Q3, respectively. boxes = self.svg.node(serie_node['plot'], class_="boxes") metadata = serie.metadata.get(0) box = decorate(self.svg, self.svg.node(boxes, class_='box'), metadata) val = self._format(serie, 0) x_center, y_center = self._draw_box( box, serie.points[1:6], serie.outliers, serie.index, metadata ) self._tooltip_data( box, val, x_center, y_center, "centered", self._get_x_label(serie.index) ) self._static_value(serie_node, val, x_center, y_center, metadata) def _draw_box(self, parent_node, quartiles, outliers, box_index, metadata): """ Return the center of a bounding box defined by a box plot. Draws a box plot on self.svg. """ width = (self.view.x(1) - self.view.x(0)) / self._order series_margin = width * self._series_margin left_edge = self.view.x(0) + width * box_index + series_margin width -= 2 * series_margin # draw lines for whiskers - bottom, median, and top for i, whisker in enumerate((quartiles[0], quartiles[2], quartiles[4])): whisker_width = width if i == 1 else width / 2 shift = (width - whisker_width) / 2 xs = left_edge + shift xe = left_edge + width - shift alter( self.svg.line( parent_node, coords=[(xs, self.view.y(whisker)), (xe, self.view.y(whisker))], class_='reactive tooltip-trigger', attrib={'stroke-width': 3} ), metadata ) # draw lines connecting whiskers to box (Q1 and Q3) alter( self.svg.line( parent_node, coords=[(left_edge + width / 2, self.view.y(quartiles[0])), (left_edge + width / 2, self.view.y(quartiles[1]))], class_='reactive tooltip-trigger', attrib={'stroke-width': 2} ), metadata ) alter( self.svg.line( parent_node, coords=[(left_edge + width / 2, self.view.y(quartiles[4])), (left_edge + width / 2, self.view.y(quartiles[3]))], class_='reactive tooltip-trigger', attrib={'stroke-width': 2} ), metadata ) # box, bounded by Q1 and Q3 alter( self.svg.node( parent_node, tag='rect', x=left_edge, y=self.view.y(quartiles[1]), height=self.view.y(quartiles[3]) - self.view.y(quartiles[1]), width=width, class_='subtle-fill reactive tooltip-trigger' ), metadata ) # draw outliers for o in outliers: alter( self.svg.node( parent_node, tag='circle', cx=left_edge + width / 2, cy=self.view.y(o), r=3, class_='subtle-fill reactive tooltip-trigger' ), metadata ) return ( left_edge + width / 2, self.view.y(sum(quartiles) / len(quartiles)) ) @staticmethod def _box_points(values, mode='extremes'): """ Default mode: (mode='extremes' or unset) Return a 7-tuple of 2x minimum, Q1, Median, Q3, and 2x maximum for a list of numeric values. 1.5IQR mode: (mode='1.5IQR') Return a 7-tuple of min, Q1 - 1.5 * IQR, Q1, Median, Q3, Q3 + 1.5 * IQR and max for a list of numeric values. Tukey mode: (mode='tukey') Return a 7-tuple of min, q[0..4], max and a list of outliers Outliers are considered values x: x < q1 - IQR or x > q3 + IQR SD mode: (mode='stdev') Return a 7-tuple of min, q[0..4], max and a list of outliers Outliers are considered values x: x < q2 - SD or x > q2 + SD SDp mode: (mode='pstdev') Return a 7-tuple of min, q[0..4], max and a list of outliers Outliers are considered values x: x < q2 - SDp or x > q2 + SDp The iterator values may include None values. Uses quartile definition from Mendenhall, W. and Sincich, T. L. Statistics for Engineering and the Sciences, 4th ed. Prentice-Hall, 1995. """ def median(seq): n = len(seq) if n % 2 == 0: # seq has an even length return (seq[n // 2] + seq[n // 2 - 1]) / 2 else: # seq has an odd length return seq[n // 2] def mean(seq): return sum(seq) / len(seq) def stdev(seq): m = mean(seq) l = len(seq) v = sum((n - m)**2 for n in seq) / (l - 1) # variance return v**0.5 # sqrt def pstdev(seq): m = mean(seq) l = len(seq) v = sum((n - m)**2 for n in seq) / l # variance return v**0.5 # sqrt outliers = [] # sort the copy in case the originals must stay in original order s = sorted([x for x in values if x is not None]) n = len(s) if not n: return (0, 0, 0, 0, 0, 0, 0), [] elif n == 1: return (s[0], s[0], s[0], s[0], s[0], s[0], s[0]), [] else: q2 = median(s) # See 'Method 3' in http://en.wikipedia.org/wiki/Quartile if n % 2 == 0: # even q1 = median(s[:n // 2]) q3 = median(s[n // 2:]) else: # odd if n == 1: # special case q1 = s[0] q3 = s[0] elif n % 4 == 1: # n is of form 4n + 1 where n >= 1 m = (n - 1) // 4 q1 = 0.25 * s[m - 1] + 0.75 * s[m] q3 = 0.75 * s[3 * m] + 0.25 * s[3 * m + 1] else: # n is of form 4n + 3 where n >= 1 m = (n - 3) // 4 q1 = 0.75 * s[m] + 0.25 * s[m + 1] q3 = 0.25 * s[3 * m + 1] + 0.75 * s[3 * m + 2] iqr = q3 - q1 min_s = s[0] max_s = s[-1] if mode == 'extremes': q0 = min_s q4 = max_s elif mode == 'tukey': # the lowest datum still within 1.5 IQR of the lower quartile, # and the highest datum still within 1.5 IQR of the upper # quartile [Tukey box plot, Wikipedia ] b0 = bisect_left(s, q1 - 1.5 * iqr) b4 = bisect_right(s, q3 + 1.5 * iqr) q0 = s[b0] q4 = s[b4 - 1] outliers = s[:b0] + s[b4:] elif mode == 'stdev': # one standard deviation above and below the mean of the data sd = stdev(s) b0 = bisect_left(s, q2 - sd) b4 = bisect_right(s, q2 + sd) q0 = s[b0] q4 = s[b4 - 1] outliers = s[:b0] + s[b4:] elif mode == 'pstdev': # one population standard deviation above and below # the mean of the data sdp = pstdev(s) b0 = bisect_left(s, q2 - sdp) b4 = bisect_right(s, q2 + sdp) q0 = s[b0] q4 = s[b4 - 1] outliers = s[:b0] + s[b4:] elif mode == '1.5IQR': # 1.5IQR mode q0 = q1 - 1.5 * iqr q4 = q3 + 1.5 * iqr return (min_s, q0, q1, q2, q3, q4, max_s), outliers