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commit-2018/11/17@18:11CST
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ltcptgeneral
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282
analysis.py
282
analysis.py
@ -8,7 +8,7 @@
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#setup:
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__version__ = "1.0.3.001"
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__version__ = "1.0.3.005"
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__author__ = (
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"Arthur Lu <arthurlu@ttic.edu>, "
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@ -25,16 +25,17 @@ __all__ = [
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'basic_stats',
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'z_score',
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'stdev_z_split',
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'histo_analysis', #histo_analysis_old is intentionally left out as it has been depreciated
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'histo_analysis', #histo_analysis_old is intentionally left out as it has been depreciated since v 1.0.1.005
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'poly_regression',
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'r_squared',
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'rms',
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'basic_analysis',
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#all statistics functions left out due to integration in other functions
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]
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#now back to your regularly scheduled programming:
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import statistics
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#import statistics <-- statistics.py functions have been integrated into analysis.py as of v 1.0.3.002
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import math
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import csv
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import functools
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@ -44,10 +45,8 @@ import torch
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import scipy
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import matplotlib
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from sklearn import *
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import collections
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import numbers
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from fractions import Fraction
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from decimal import Decimal
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from itertools import groupby
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@ -56,7 +55,7 @@ from bisect import bisect_left, bisect_right
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def _init_device (setting, arg): #initiates computation device for ANNs
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if setting == "cuda":
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temp = setting + ":" + arg
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temp = setting + ":" + str(arg)
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the_device_woman = torch.device(temp if torch.cuda.is_available() else "cpu")
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return the_device_woman #name that reference
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elif setting == "cpu":
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@ -311,13 +310,13 @@ def load_csv(filepath):
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file_array = list(csv.reader(csvfile))
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return file_array
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def basic_stats(data, mode, arg): # data=array, mode = ['1d':1d_basic_stats, 'column':c_basic_stats, 'row':r_basic_stats], arg for mode 1 or mode 2 for column or row
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if mode == 'debug':
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def basic_stats(data, method, arg): # data=array, mode = ['1d':1d_basic_stats, 'column':c_basic_stats, 'row':r_basic_stats], arg for mode 1 or mode 2 for column or row
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if method == 'debug':
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out = "basic_stats requires 3 args: data, mode, arg; where data is data to be analyzed, mode is an int from 0 - 2 depending on type of analysis (by column or by row) and is only applicable to 2d arrays (for 1d arrays use mode 1), and arg is row/column number for mode 1 or mode 2; function returns: [mean, median, mode, stdev, variance]"
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return out
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if mode == "1d" or mode == 0:
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if method == "1d" or method == 0:
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data_t = []
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@ -325,29 +324,29 @@ def basic_stats(data, mode, arg): # data=array, mode = ['1d':1d_basic_stats, 'co
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data_t.append(float(data[i]))
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mean = statistics.mean(data_t)
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median = statistics.median(data_t)
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_mean = mean(data_t)
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_median = median(data_t)
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try:
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mode = statistics.mode(data_t)
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_mode = mode(data_t)
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except:
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mode = None
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_mode = None
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try:
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stdev = statistics.stdev(data)
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_stdev = stdev(data_t)
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except:
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stdev = None
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_stdev = None
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try:
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variance = statistics.variance(data_t)
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_variance = variance(data_t)
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except:
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variance = None
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_variance = None
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out = [mean, median, mode, stdev, variance]
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out = [_mean, _median, _mode, _stdev, _variance]
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return out
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elif mode == "column" or mode == 1:
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elif method == "column" or method == 1:
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c_data = []
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c_data_sorted = []
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@ -358,52 +357,52 @@ def basic_stats(data, mode, arg): # data=array, mode = ['1d':1d_basic_stats, 'co
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except:
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pass
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mean = statistics.mean(c_data)
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median = statistics.median(c_data)
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_mean = mean(c_data)
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_median = median(c_data)
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try:
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mode = statistics.mode(c_data)
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_mode = mode(c_data)
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except:
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mode = None
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_mode = None
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try:
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stdev = statistics.stdev(c_data)
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_stdev = stdev(c_data)
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except:
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stdev = None
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_stdev = None
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try:
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variance = statistics.variance(c_data)
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_variance = variance(c_data)
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except:
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variance = None
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_variance = None
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out = [mean, median, mode, stdev, variance]
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out = [_mean, _median, _mode, _stdev, _variance]
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return out
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elif mode == "row" or mode == 2:
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elif method == "row" or method == 2:
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r_data = []
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for i in range(len(data[arg])):
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r_data.append(float(data[arg][i]))
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mean = statistics.mean(r_data)
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median = statistics.median(r_data)
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_mean = mean(r_data)
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_median = median(r_data)
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try:
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mode = statistics.mode(r_data)
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_mode = mode(r_data)
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except:
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mode = None
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_mode = None
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try:
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stdev = statistics.stdev(r_data)
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_stdev = stdev(r_data)
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except:
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stdev = None
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_stdev = None
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try:
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variance = statistics.variance(r_data)
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_variance = variance(r_data)
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except:
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variance = None
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_variance = None
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out = [mean, median, mode, stdev, variance]
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out = [_mean, _median, _mode, _stdev, _variance]
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return out
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else:
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return ["mode_error", "mode_error"]
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return ["ERROR: method error"]
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def z_score(point, mean, stdev): #returns z score with inputs of point, mean and standard deviation of spread
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score = (point - mean)/stdev
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@ -427,7 +426,7 @@ def stdev_z_split(mean, stdev, delta, low_bound, high_bound): #returns n-th perc
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return z_split
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def histo_analysis_old(hist_data): #note: depreciated
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def histo_analysis_old(hist_data): #note: depreciated since v 1.0.1.005
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if hist_data == 'debug':
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return['lower estimate (5%)', 'lower middle estimate (25%)', 'middle estimate (50%)', 'higher middle estimate (75%)', 'high estimate (95%)', 'standard deviation', 'note: this has been depreciated']
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@ -495,13 +494,15 @@ def histo_analysis(hist_data, delta, low_bound, high_bound):
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def poly_regression(x, y, power):
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if x == "null":
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if x == "null": #if x is 'null', then x will be filled with integer points between 1 and the size of y
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x = []
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for i in range(len(y)):
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x.append(i)
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print(i)
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x.append(i+1)
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reg_eq = scipy.polyfit(x, y, deg = power)
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@ -581,3 +582,198 @@ def basic_analysis(filepath): #assumes that rows are the independent variable an
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column_b_stats.append(basic_stats(data, "column", i))
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return[row_b_stats, column_b_stats, row_histo]
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#statistics def below------------------------------------------------------------------------------------------------------------------------------------------------------
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class StatisticsError(ValueError):
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pass
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def _sum(data, start=0):
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count = 0
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n, d = _exact_ratio(start)
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partials = {d: n}
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partials_get = partials.get
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T = _coerce(int, type(start))
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for typ, values in groupby(data, type):
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T = _coerce(T, typ) # or raise TypeError
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for n,d in map(_exact_ratio, values):
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count += 1
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partials[d] = partials_get(d, 0) + n
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if None in partials:
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total = partials[None]
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assert not _isfinite(total)
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else:
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total = sum(Fraction(n, d) for d, n in sorted(partials.items()))
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return (T, total, count)
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def _isfinite(x):
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try:
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return x.is_finite() # Likely a Decimal.
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except AttributeError:
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return math.isfinite(x) # Coerces to float first.
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def _coerce(T, S):
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assert T is not bool, "initial type T is bool"
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if T is S: return T
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if S is int or S is bool: return T
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if T is int: return S
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if issubclass(S, T): return S
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if issubclass(T, S): return T
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if issubclass(T, int): return S
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if issubclass(S, int): return T
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if issubclass(T, Fraction) and issubclass(S, float):
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return S
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if issubclass(T, float) and issubclass(S, Fraction):
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return T
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msg = "don't know how to coerce %s and %s"
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raise TypeError(msg % (T.__name__, S.__name__))
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def _exact_ratio(x):
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try:
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if type(x) is float or type(x) is Decimal:
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return x.as_integer_ratio()
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try:
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return (x.numerator, x.denominator)
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except AttributeError:
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try:
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return x.as_integer_ratio()
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except AttributeError:
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pass
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except (OverflowError, ValueError):
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assert not _isfinite(x)
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return (x, None)
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msg = "can't convert type '{}' to numerator/denominator"
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raise TypeError(msg.format(type(x).__name__))
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def _convert(value, T):
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if type(value) is T:
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return value
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if issubclass(T, int) and value.denominator != 1:
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T = float
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try:
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return T(value)
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except TypeError:
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if issubclass(T, Decimal):
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return T(value.numerator)/T(value.denominator)
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else:
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raise
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def _counts(data):
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table = collections.Counter(iter(data)).most_common()
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if not table:
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return table
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maxfreq = table[0][1]
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for i in range(1, len(table)):
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if table[i][1] != maxfreq:
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table = table[:i]
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break
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return table
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def _find_lteq(a, x):
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i = bisect_left(a, x)
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if i != len(a) and a[i] == x:
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return i
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raise ValueError
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def _find_rteq(a, l, x):
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i = bisect_right(a, x, lo=l)
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if i != (len(a)+1) and a[i-1] == x:
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return i-1
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raise ValueError
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def _fail_neg(values, errmsg='negative value'):
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for x in values:
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if x < 0:
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raise StatisticsError(errmsg)
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yield x
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def mean(data):
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if iter(data) is data:
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data = list(data)
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n = len(data)
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if n < 1:
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raise StatisticsError('mean requires at least one data point')
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T, total, count = _sum(data)
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assert count == n
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return _convert(total/n, T)
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def median(data):
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data = sorted(data)
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n = len(data)
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if n == 0:
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raise StatisticsError("no median for empty data")
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if n%2 == 1:
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return data[n//2]
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else:
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i = n//2
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return (data[i - 1] + data[i])/2
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def mode(data):
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table = _counts(data)
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if len(table) == 1:
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return table[0][0]
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elif table:
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raise StatisticsError(
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'no unique mode; found %d equally common values' % len(table)
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)
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else:
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raise StatisticsError('no mode for empty data')
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def _ss(data, c=None):
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if c is None:
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c = mean(data)
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T, total, count = _sum((x-c)**2 for x in data)
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U, total2, count2 = _sum((x-c) for x in data)
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assert T == U and count == count2
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total -= total2**2/len(data)
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assert not total < 0, 'negative sum of square deviations: %f' % total
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return (T, total)
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def variance(data, xbar=None):
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if iter(data) is data:
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data = list(data)
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n = len(data)
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if n < 2:
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raise StatisticsError('variance requires at least two data points')
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T, ss = _ss(data, xbar)
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return _convert(ss/(n-1), T)
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def stdev(data, xbar=None):
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var = variance(data, xbar)
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try:
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return var.sqrt()
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except AttributeError:
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return math.sqrt(var)
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BIN
analysis.pyc
BIN
analysis.pyc
Binary file not shown.
@ -1,7 +1,9 @@
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import analysis
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data = analysis.load_csv('data.txt')
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print("--------------------------------")
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print(analysis.basic_stats(0, 'debug', 0))
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print(analysis.basic_stats(data, "column", 0))
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print(analysis.basic_stats(data, "row", 0))
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@ -9,6 +11,8 @@ print(analysis.z_score(10, analysis.basic_stats(data, "column", 0)[0],analysis.b
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print(analysis.histo_analysis(data[0], 0.01, -1, 1))
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print(analysis.stdev_z_split(3.3, 0.2, 0.1, -5, 5))
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print("--------------------------------")
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game_c_entities = analysis.c_entities(["bot", "bot", "bot"], [0, 1, 2], [[10, 10], [-10, -10], [10, -10]], ["shit", "bad", "worse"], ["triangle", "square", "circle"])
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game_c_entities.append("bot", 3, [-10, 10], "useless", "pentagram")
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game_c_entities.edit(0, "null", "null", "null", "null", "triagon")
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@ -16,6 +20,8 @@ print(game_c_entities.search(0))
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print(game_c_entities.debug())
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print(game_c_entities.regurgitate())
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print("--------------------------------")
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game_nc_entities = analysis.nc_entities(["cube", "cube", "ball"], [0, 1, 2], [[0, 0.5], [1, 1.5], [2, 2]], ["1;1;1;10', '2;1;1;20", "r=0.5, 5"], ["1", "1", "0"])
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game_nc_entities.append("cone", 3, [1, -1], "property", "effect")
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game_nc_entities.edit(2, "sphere", 10, [5, -5], "new prop", "new effect")
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@ -23,6 +29,8 @@ print(game_nc_entities.search(10))
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print(game_nc_entities.debug())
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print(game_nc_entities.regurgitate())
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print("--------------------------------")
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game_obstacles = analysis.obstacles(["wall", "fortress", "castle"], [0, 1, 2],[[[10, 10], [10, 9], [9, 10], [9, 9]], [[-10, 9], [-10, -9], [-9, -10]], [[5, 0], [4, -1], [-4, -1]]] , [0, 0.01, 10])
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game_obstacles.append("bastion", 3, [[50, 50], [49, 50], [50, 49], [49, 49]], 75)
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game_obstacles.edit(0, "motte and bailey", "null", [[10, 10], [9, 10], [10, 9], [9, 9]], 0.01)
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@ -30,9 +38,15 @@ print(game_obstacles.search(0))
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print(game_obstacles.debug())
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print(game_obstacles.regurgitate())
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print("--------------------------------")
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game_objectives = analysis.objectives(["switch", "scale", "climb"], [0,1,2], [[0,0],[1,1],[2,0]], ["0,1", "1,1", "0,5"])
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game_objectives.append("auto", 3, [0, 10], "1, 10")
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game_objectives.edit(3, "null", 4, "null", "null")
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print(game_objectives.search(4))
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print(game_objectives.debug())
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print(game_objectives.regurgitate())
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print("--------------------------------")
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print(analysis.poly_regression([1, 2, 3, 4, 5], [1, 2, 4, 8, 16], 2))
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669
statistics.py
669
statistics.py
@ -1,669 +0,0 @@
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"""
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Basic statistics module.
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This module provides functions for calculating statistics of data, including
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averages, variance, and standard deviation.
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Calculating averages
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--------------------
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================== =============================================
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Function Description
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================== =============================================
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mean Arithmetic mean (average) of data.
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harmonic_mean Harmonic mean of data.
|
||||
median Median (middle value) of data.
|
||||
median_low Low median of data.
|
||||
median_high High median of data.
|
||||
median_grouped Median, or 50th percentile, of grouped data.
|
||||
mode Mode (most common value) of data.
|
||||
================== =============================================
|
||||
|
||||
Calculate the arithmetic mean ("the average") of data:
|
||||
|
||||
>>> mean([-1.0, 2.5, 3.25, 5.75])
|
||||
2.625
|
||||
|
||||
|
||||
Calculate the standard median of discrete data:
|
||||
|
||||
>>> median([2, 3, 4, 5])
|
||||
3.5
|
||||
|
||||
|
||||
Calculate the median, or 50th percentile, of data grouped into class intervals
|
||||
centred on the data values provided. E.g. if your data points are rounded to
|
||||
the nearest whole number:
|
||||
|
||||
>>> median_grouped([2, 2, 3, 3, 3, 4]) #doctest: +ELLIPSIS
|
||||
2.8333333333...
|
||||
|
||||
This should be interpreted in this way: you have two data points in the class
|
||||
interval 1.5-2.5, three data points in the class interval 2.5-3.5, and one in
|
||||
the class interval 3.5-4.5. The median of these data points is 2.8333...
|
||||
|
||||
|
||||
Calculating variability or spread
|
||||
---------------------------------
|
||||
|
||||
================== =============================================
|
||||
Function Description
|
||||
================== =============================================
|
||||
pvariance Population variance of data.
|
||||
variance Sample variance of data.
|
||||
pstdev Population standard deviation of data.
|
||||
stdev Sample standard deviation of data.
|
||||
================== =============================================
|
||||
|
||||
Calculate the standard deviation of sample data:
|
||||
|
||||
>>> stdev([2.5, 3.25, 5.5, 11.25, 11.75]) #doctest: +ELLIPSIS
|
||||
4.38961843444...
|
||||
|
||||
If you have previously calculated the mean, you can pass it as the optional
|
||||
second argument to the four "spread" functions to avoid recalculating it:
|
||||
|
||||
>>> data = [1, 2, 2, 4, 4, 4, 5, 6]
|
||||
>>> mu = mean(data)
|
||||
>>> pvariance(data, mu)
|
||||
2.5
|
||||
|
||||
|
||||
Exceptions
|
||||
----------
|
||||
|
||||
A single exception is defined: StatisticsError is a subclass of ValueError.
|
||||
|
||||
"""
|
||||
|
||||
__all__ = [ 'StatisticsError',
|
||||
'pstdev', 'pvariance', 'stdev', 'variance',
|
||||
'median', 'median_low', 'median_high', 'median_grouped',
|
||||
'mean', 'mode', 'harmonic_mean',
|
||||
]
|
||||
|
||||
import collections
|
||||
import math
|
||||
import numbers
|
||||
|
||||
from fractions import Fraction
|
||||
from decimal import Decimal
|
||||
from itertools import groupby
|
||||
from bisect import bisect_left, bisect_right
|
||||
|
||||
|
||||
|
||||
# === Exceptions ===
|
||||
|
||||
class StatisticsError(ValueError):
|
||||
pass
|
||||
|
||||
|
||||
# === Private utilities ===
|
||||
|
||||
def _sum(data, start=0):
|
||||
"""_sum(data [, start]) -> (type, sum, count)
|
||||
|
||||
Return a high-precision sum of the given numeric data as a fraction,
|
||||
together with the type to be converted to and the count of items.
|
||||
|
||||
If optional argument ``start`` is given, it is added to the total.
|
||||
If ``data`` is empty, ``start`` (defaulting to 0) is returned.
|
||||
|
||||
|
||||
Examples
|
||||
--------
|
||||
|
||||
>>> _sum([3, 2.25, 4.5, -0.5, 1.0], 0.75)
|
||||
(<class 'float'>, Fraction(11, 1), 5)
|
||||
|
||||
Some sources of round-off error will be avoided:
|
||||
|
||||
# Built-in sum returns zero.
|
||||
>>> _sum([1e50, 1, -1e50] * 1000)
|
||||
(<class 'float'>, Fraction(1000, 1), 3000)
|
||||
|
||||
Fractions and Decimals are also supported:
|
||||
|
||||
>>> from fractions import Fraction as F
|
||||
>>> _sum([F(2, 3), F(7, 5), F(1, 4), F(5, 6)])
|
||||
(<class 'fractions.Fraction'>, Fraction(63, 20), 4)
|
||||
|
||||
>>> from decimal import Decimal as D
|
||||
>>> data = [D("0.1375"), D("0.2108"), D("0.3061"), D("0.0419")]
|
||||
>>> _sum(data)
|
||||
(<class 'decimal.Decimal'>, Fraction(6963, 10000), 4)
|
||||
|
||||
Mixed types are currently treated as an error, except that int is
|
||||
allowed.
|
||||
"""
|
||||
count = 0
|
||||
n, d = _exact_ratio(start)
|
||||
partials = {d: n}
|
||||
partials_get = partials.get
|
||||
T = _coerce(int, type(start))
|
||||
for typ, values in groupby(data, type):
|
||||
T = _coerce(T, typ) # or raise TypeError
|
||||
for n,d in map(_exact_ratio, values):
|
||||
count += 1
|
||||
partials[d] = partials_get(d, 0) + n
|
||||
if None in partials:
|
||||
# The sum will be a NAN or INF. We can ignore all the finite
|
||||
# partials, and just look at this special one.
|
||||
total = partials[None]
|
||||
assert not _isfinite(total)
|
||||
else:
|
||||
# Sum all the partial sums using builtin sum.
|
||||
# FIXME is this faster if we sum them in order of the denominator?
|
||||
total = sum(Fraction(n, d) for d, n in sorted(partials.items()))
|
||||
return (T, total, count)
|
||||
|
||||
|
||||
def _isfinite(x):
|
||||
try:
|
||||
return x.is_finite() # Likely a Decimal.
|
||||
except AttributeError:
|
||||
return math.isfinite(x) # Coerces to float first.
|
||||
|
||||
|
||||
def _coerce(T, S):
|
||||
"""Coerce types T and S to a common type, or raise TypeError.
|
||||
|
||||
Coercion rules are currently an implementation detail. See the CoerceTest
|
||||
test class in test_statistics for details.
|
||||
"""
|
||||
# See http://bugs.python.org/issue24068.
|
||||
assert T is not bool, "initial type T is bool"
|
||||
# If the types are the same, no need to coerce anything. Put this
|
||||
# first, so that the usual case (no coercion needed) happens as soon
|
||||
# as possible.
|
||||
if T is S: return T
|
||||
# Mixed int & other coerce to the other type.
|
||||
if S is int or S is bool: return T
|
||||
if T is int: return S
|
||||
# If one is a (strict) subclass of the other, coerce to the subclass.
|
||||
if issubclass(S, T): return S
|
||||
if issubclass(T, S): return T
|
||||
# Ints coerce to the other type.
|
||||
if issubclass(T, int): return S
|
||||
if issubclass(S, int): return T
|
||||
# Mixed fraction & float coerces to float (or float subclass).
|
||||
if issubclass(T, Fraction) and issubclass(S, float):
|
||||
return S
|
||||
if issubclass(T, float) and issubclass(S, Fraction):
|
||||
return T
|
||||
# Any other combination is disallowed.
|
||||
msg = "don't know how to coerce %s and %s"
|
||||
raise TypeError(msg % (T.__name__, S.__name__))
|
||||
|
||||
|
||||
def _exact_ratio(x):
|
||||
"""Return Real number x to exact (numerator, denominator) pair.
|
||||
|
||||
>>> _exact_ratio(0.25)
|
||||
(1, 4)
|
||||
|
||||
x is expected to be an int, Fraction, Decimal or float.
|
||||
"""
|
||||
try:
|
||||
# Optimise the common case of floats. We expect that the most often
|
||||
# used numeric type will be builtin floats, so try to make this as
|
||||
# fast as possible.
|
||||
if type(x) is float or type(x) is Decimal:
|
||||
return x.as_integer_ratio()
|
||||
try:
|
||||
# x may be an int, Fraction, or Integral ABC.
|
||||
return (x.numerator, x.denominator)
|
||||
except AttributeError:
|
||||
try:
|
||||
# x may be a float or Decimal subclass.
|
||||
return x.as_integer_ratio()
|
||||
except AttributeError:
|
||||
# Just give up?
|
||||
pass
|
||||
except (OverflowError, ValueError):
|
||||
# float NAN or INF.
|
||||
assert not _isfinite(x)
|
||||
return (x, None)
|
||||
msg = "can't convert type '{}' to numerator/denominator"
|
||||
raise TypeError(msg.format(type(x).__name__))
|
||||
|
||||
|
||||
def _convert(value, T):
|
||||
"""Convert value to given numeric type T."""
|
||||
if type(value) is T:
|
||||
# This covers the cases where T is Fraction, or where value is
|
||||
# a NAN or INF (Decimal or float).
|
||||
return value
|
||||
if issubclass(T, int) and value.denominator != 1:
|
||||
T = float
|
||||
try:
|
||||
# FIXME: what do we do if this overflows?
|
||||
return T(value)
|
||||
except TypeError:
|
||||
if issubclass(T, Decimal):
|
||||
return T(value.numerator)/T(value.denominator)
|
||||
else:
|
||||
raise
|
||||
|
||||
|
||||
def _counts(data):
|
||||
# Generate a table of sorted (value, frequency) pairs.
|
||||
table = collections.Counter(iter(data)).most_common()
|
||||
if not table:
|
||||
return table
|
||||
# Extract the values with the highest frequency.
|
||||
maxfreq = table[0][1]
|
||||
for i in range(1, len(table)):
|
||||
if table[i][1] != maxfreq:
|
||||
table = table[:i]
|
||||
break
|
||||
return table
|
||||
|
||||
|
||||
def _find_lteq(a, x):
|
||||
'Locate the leftmost value exactly equal to x'
|
||||
i = bisect_left(a, x)
|
||||
if i != len(a) and a[i] == x:
|
||||
return i
|
||||
raise ValueError
|
||||
|
||||
|
||||
def _find_rteq(a, l, x):
|
||||
'Locate the rightmost value exactly equal to x'
|
||||
i = bisect_right(a, x, lo=l)
|
||||
if i != (len(a)+1) and a[i-1] == x:
|
||||
return i-1
|
||||
raise ValueError
|
||||
|
||||
|
||||
def _fail_neg(values, errmsg='negative value'):
|
||||
"""Iterate over values, failing if any are less than zero."""
|
||||
for x in values:
|
||||
if x < 0:
|
||||
raise StatisticsError(errmsg)
|
||||
yield x
|
||||
|
||||
|
||||
# === Measures of central tendency (averages) ===
|
||||
|
||||
def mean(data):
|
||||
"""Return the sample arithmetic mean of data.
|
||||
|
||||
>>> mean([1, 2, 3, 4, 4])
|
||||
2.8
|
||||
|
||||
>>> from fractions import Fraction as F
|
||||
>>> mean([F(3, 7), F(1, 21), F(5, 3), F(1, 3)])
|
||||
Fraction(13, 21)
|
||||
|
||||
>>> from decimal import Decimal as D
|
||||
>>> mean([D("0.5"), D("0.75"), D("0.625"), D("0.375")])
|
||||
Decimal('0.5625')
|
||||
|
||||
If ``data`` is empty, StatisticsError will be raised.
|
||||
"""
|
||||
if iter(data) is data:
|
||||
data = list(data)
|
||||
n = len(data)
|
||||
if n < 1:
|
||||
raise StatisticsError('mean requires at least one data point')
|
||||
T, total, count = _sum(data)
|
||||
assert count == n
|
||||
return _convert(total/n, T)
|
||||
|
||||
|
||||
def harmonic_mean(data):
|
||||
"""Return the harmonic mean of data.
|
||||
|
||||
The harmonic mean, sometimes called the subcontrary mean, is the
|
||||
reciprocal of the arithmetic mean of the reciprocals of the data,
|
||||
and is often appropriate when averaging quantities which are rates
|
||||
or ratios, for example speeds. Example:
|
||||
|
||||
Suppose an investor purchases an equal value of shares in each of
|
||||
three companies, with P/E (price/earning) ratios of 2.5, 3 and 10.
|
||||
What is the average P/E ratio for the investor's portfolio?
|
||||
|
||||
>>> harmonic_mean([2.5, 3, 10]) # For an equal investment portfolio.
|
||||
3.6
|
||||
|
||||
Using the arithmetic mean would give an average of about 5.167, which
|
||||
is too high.
|
||||
|
||||
If ``data`` is empty, or any element is less than zero,
|
||||
``harmonic_mean`` will raise ``StatisticsError``.
|
||||
"""
|
||||
# For a justification for using harmonic mean for P/E ratios, see
|
||||
# http://fixthepitch.pellucid.com/comps-analysis-the-missing-harmony-of-summary-statistics/
|
||||
# http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2621087
|
||||
if iter(data) is data:
|
||||
data = list(data)
|
||||
errmsg = 'harmonic mean does not support negative values'
|
||||
n = len(data)
|
||||
if n < 1:
|
||||
raise StatisticsError('harmonic_mean requires at least one data point')
|
||||
elif n == 1:
|
||||
x = data[0]
|
||||
if isinstance(x, (numbers.Real, Decimal)):
|
||||
if x < 0:
|
||||
raise StatisticsError(errmsg)
|
||||
return x
|
||||
else:
|
||||
raise TypeError('unsupported type')
|
||||
try:
|
||||
T, total, count = _sum(1/x for x in _fail_neg(data, errmsg))
|
||||
except ZeroDivisionError:
|
||||
return 0
|
||||
assert count == n
|
||||
return _convert(n/total, T)
|
||||
|
||||
|
||||
# FIXME: investigate ways to calculate medians without sorting? Quickselect?
|
||||
def median(data):
|
||||
"""Return the median (middle value) of numeric data.
|
||||
|
||||
When the number of data points is odd, return the middle data point.
|
||||
When the number of data points is even, the median is interpolated by
|
||||
taking the average of the two middle values:
|
||||
|
||||
>>> median([1, 3, 5])
|
||||
3
|
||||
>>> median([1, 3, 5, 7])
|
||||
4.0
|
||||
|
||||
"""
|
||||
data = sorted(data)
|
||||
n = len(data)
|
||||
if n == 0:
|
||||
raise StatisticsError("no median for empty data")
|
||||
if n%2 == 1:
|
||||
return data[n//2]
|
||||
else:
|
||||
i = n//2
|
||||
return (data[i - 1] + data[i])/2
|
||||
|
||||
|
||||
def median_low(data):
|
||||
"""Return the low median of numeric data.
|
||||
|
||||
When the number of data points is odd, the middle value is returned.
|
||||
When it is even, the smaller of the two middle values is returned.
|
||||
|
||||
>>> median_low([1, 3, 5])
|
||||
3
|
||||
>>> median_low([1, 3, 5, 7])
|
||||
3
|
||||
|
||||
"""
|
||||
data = sorted(data)
|
||||
n = len(data)
|
||||
if n == 0:
|
||||
raise StatisticsError("no median for empty data")
|
||||
if n%2 == 1:
|
||||
return data[n//2]
|
||||
else:
|
||||
return data[n//2 - 1]
|
||||
|
||||
|
||||
def median_high(data):
|
||||
"""Return the high median of data.
|
||||
|
||||
When the number of data points is odd, the middle value is returned.
|
||||
When it is even, the larger of the two middle values is returned.
|
||||
|
||||
>>> median_high([1, 3, 5])
|
||||
3
|
||||
>>> median_high([1, 3, 5, 7])
|
||||
5
|
||||
|
||||
"""
|
||||
data = sorted(data)
|
||||
n = len(data)
|
||||
if n == 0:
|
||||
raise StatisticsError("no median for empty data")
|
||||
return data[n//2]
|
||||
|
||||
|
||||
def median_grouped(data, interval=1):
|
||||
"""Return the 50th percentile (median) of grouped continuous data.
|
||||
|
||||
>>> median_grouped([1, 2, 2, 3, 4, 4, 4, 4, 4, 5])
|
||||
3.7
|
||||
>>> median_grouped([52, 52, 53, 54])
|
||||
52.5
|
||||
|
||||
This calculates the median as the 50th percentile, and should be
|
||||
used when your data is continuous and grouped. In the above example,
|
||||
the values 1, 2, 3, etc. actually represent the midpoint of classes
|
||||
0.5-1.5, 1.5-2.5, 2.5-3.5, etc. The middle value falls somewhere in
|
||||
class 3.5-4.5, and interpolation is used to estimate it.
|
||||
|
||||
Optional argument ``interval`` represents the class interval, and
|
||||
defaults to 1. Changing the class interval naturally will change the
|
||||
interpolated 50th percentile value:
|
||||
|
||||
>>> median_grouped([1, 3, 3, 5, 7], interval=1)
|
||||
3.25
|
||||
>>> median_grouped([1, 3, 3, 5, 7], interval=2)
|
||||
3.5
|
||||
|
||||
This function does not check whether the data points are at least
|
||||
``interval`` apart.
|
||||
"""
|
||||
data = sorted(data)
|
||||
n = len(data)
|
||||
if n == 0:
|
||||
raise StatisticsError("no median for empty data")
|
||||
elif n == 1:
|
||||
return data[0]
|
||||
# Find the value at the midpoint. Remember this corresponds to the
|
||||
# centre of the class interval.
|
||||
x = data[n//2]
|
||||
for obj in (x, interval):
|
||||
if isinstance(obj, (str, bytes)):
|
||||
raise TypeError('expected number but got %r' % obj)
|
||||
try:
|
||||
L = x - interval/2 # The lower limit of the median interval.
|
||||
except TypeError:
|
||||
# Mixed type. For now we just coerce to float.
|
||||
L = float(x) - float(interval)/2
|
||||
|
||||
# Uses bisection search to search for x in data with log(n) time complexity
|
||||
# Find the position of leftmost occurrence of x in data
|
||||
l1 = _find_lteq(data, x)
|
||||
# Find the position of rightmost occurrence of x in data[l1...len(data)]
|
||||
# Assuming always l1 <= l2
|
||||
l2 = _find_rteq(data, l1, x)
|
||||
cf = l1
|
||||
f = l2 - l1 + 1
|
||||
return L + interval*(n/2 - cf)/f
|
||||
|
||||
|
||||
def mode(data):
|
||||
"""Return the most common data point from discrete or nominal data.
|
||||
|
||||
``mode`` assumes discrete data, and returns a single value. This is the
|
||||
standard treatment of the mode as commonly taught in schools:
|
||||
|
||||
>>> mode([1, 1, 2, 3, 3, 3, 3, 4])
|
||||
3
|
||||
|
||||
This also works with nominal (non-numeric) data:
|
||||
|
||||
>>> mode(["red", "blue", "blue", "red", "green", "red", "red"])
|
||||
'red'
|
||||
|
||||
If there is not exactly one most common value, ``mode`` will raise
|
||||
StatisticsError.
|
||||
"""
|
||||
# Generate a table of sorted (value, frequency) pairs.
|
||||
table = _counts(data)
|
||||
if len(table) == 1:
|
||||
return table[0][0]
|
||||
elif table:
|
||||
raise StatisticsError(
|
||||
'no unique mode; found %d equally common values' % len(table)
|
||||
)
|
||||
else:
|
||||
raise StatisticsError('no mode for empty data')
|
||||
|
||||
|
||||
# === Measures of spread ===
|
||||
|
||||
# See http://mathworld.wolfram.com/Variance.html
|
||||
# http://mathworld.wolfram.com/SampleVariance.html
|
||||
# http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance
|
||||
#
|
||||
# Under no circumstances use the so-called "computational formula for
|
||||
# variance", as that is only suitable for hand calculations with a small
|
||||
# amount of low-precision data. It has terrible numeric properties.
|
||||
#
|
||||
# See a comparison of three computational methods here:
|
||||
# http://www.johndcook.com/blog/2008/09/26/comparing-three-methods-of-computing-standard-deviation/
|
||||
|
||||
def _ss(data, c=None):
|
||||
"""Return sum of square deviations of sequence data.
|
||||
|
||||
If ``c`` is None, the mean is calculated in one pass, and the deviations
|
||||
from the mean are calculated in a second pass. Otherwise, deviations are
|
||||
calculated from ``c`` as given. Use the second case with care, as it can
|
||||
lead to garbage results.
|
||||
"""
|
||||
if c is None:
|
||||
c = mean(data)
|
||||
T, total, count = _sum((x-c)**2 for x in data)
|
||||
# The following sum should mathematically equal zero, but due to rounding
|
||||
# error may not.
|
||||
U, total2, count2 = _sum((x-c) for x in data)
|
||||
assert T == U and count == count2
|
||||
total -= total2**2/len(data)
|
||||
assert not total < 0, 'negative sum of square deviations: %f' % total
|
||||
return (T, total)
|
||||
|
||||
|
||||
def variance(data, xbar=None):
|
||||
"""Return the sample variance of data.
|
||||
|
||||
data should be an iterable of Real-valued numbers, with at least two
|
||||
values. The optional argument xbar, if given, should be the mean of
|
||||
the data. If it is missing or None, the mean is automatically calculated.
|
||||
|
||||
Use this function when your data is a sample from a population. To
|
||||
calculate the variance from the entire population, see ``pvariance``.
|
||||
|
||||
Examples:
|
||||
|
||||
>>> data = [2.75, 1.75, 1.25, 0.25, 0.5, 1.25, 3.5]
|
||||
>>> variance(data)
|
||||
1.3720238095238095
|
||||
|
||||
If you have already calculated the mean of your data, you can pass it as
|
||||
the optional second argument ``xbar`` to avoid recalculating it:
|
||||
|
||||
>>> m = mean(data)
|
||||
>>> variance(data, m)
|
||||
1.3720238095238095
|
||||
|
||||
This function does not check that ``xbar`` is actually the mean of
|
||||
``data``. Giving arbitrary values for ``xbar`` may lead to invalid or
|
||||
impossible results.
|
||||
|
||||
Decimals and Fractions are supported:
|
||||
|
||||
>>> from decimal import Decimal as D
|
||||
>>> variance([D("27.5"), D("30.25"), D("30.25"), D("34.5"), D("41.75")])
|
||||
Decimal('31.01875')
|
||||
|
||||
>>> from fractions import Fraction as F
|
||||
>>> variance([F(1, 6), F(1, 2), F(5, 3)])
|
||||
Fraction(67, 108)
|
||||
|
||||
"""
|
||||
if iter(data) is data:
|
||||
data = list(data)
|
||||
n = len(data)
|
||||
if n < 2:
|
||||
raise StatisticsError('variance requires at least two data points')
|
||||
T, ss = _ss(data, xbar)
|
||||
return _convert(ss/(n-1), T)
|
||||
|
||||
|
||||
def pvariance(data, mu=None):
|
||||
"""Return the population variance of ``data``.
|
||||
|
||||
data should be an iterable of Real-valued numbers, with at least one
|
||||
value. The optional argument mu, if given, should be the mean of
|
||||
the data. If it is missing or None, the mean is automatically calculated.
|
||||
|
||||
Use this function to calculate the variance from the entire population.
|
||||
To estimate the variance from a sample, the ``variance`` function is
|
||||
usually a better choice.
|
||||
|
||||
Examples:
|
||||
|
||||
>>> data = [0.0, 0.25, 0.25, 1.25, 1.5, 1.75, 2.75, 3.25]
|
||||
>>> pvariance(data)
|
||||
1.25
|
||||
|
||||
If you have already calculated the mean of the data, you can pass it as
|
||||
the optional second argument to avoid recalculating it:
|
||||
|
||||
>>> mu = mean(data)
|
||||
>>> pvariance(data, mu)
|
||||
1.25
|
||||
|
||||
This function does not check that ``mu`` is actually the mean of ``data``.
|
||||
Giving arbitrary values for ``mu`` may lead to invalid or impossible
|
||||
results.
|
||||
|
||||
Decimals and Fractions are supported:
|
||||
|
||||
>>> from decimal import Decimal as D
|
||||
>>> pvariance([D("27.5"), D("30.25"), D("30.25"), D("34.5"), D("41.75")])
|
||||
Decimal('24.815')
|
||||
|
||||
>>> from fractions import Fraction as F
|
||||
>>> pvariance([F(1, 4), F(5, 4), F(1, 2)])
|
||||
Fraction(13, 72)
|
||||
|
||||
"""
|
||||
if iter(data) is data:
|
||||
data = list(data)
|
||||
n = len(data)
|
||||
if n < 1:
|
||||
raise StatisticsError('pvariance requires at least one data point')
|
||||
T, ss = _ss(data, mu)
|
||||
return _convert(ss/n, T)
|
||||
|
||||
|
||||
def stdev(data, xbar=None):
|
||||
"""Return the square root of the sample variance.
|
||||
|
||||
See ``variance`` for arguments and other details.
|
||||
|
||||
>>> stdev([1.5, 2.5, 2.5, 2.75, 3.25, 4.75])
|
||||
1.0810874155219827
|
||||
|
||||
"""
|
||||
var = variance(data, xbar)
|
||||
try:
|
||||
return var.sqrt()
|
||||
except AttributeError:
|
||||
return math.sqrt(var)
|
||||
|
||||
|
||||
def pstdev(data, mu=None):
|
||||
"""Return the square root of the population variance.
|
||||
|
||||
See ``pvariance`` for arguments and other details.
|
||||
|
||||
>>> pstdev([1.5, 2.5, 2.5, 2.75, 3.25, 4.75])
|
||||
0.986893273527251
|
||||
|
||||
"""
|
||||
var = pvariance(data, mu)
|
||||
try:
|
||||
return var.sqrt()
|
||||
except AttributeError:
|
||||
return math.sqrt(var)
|
||||
Loading…
Reference in New Issue
Block a user