#Titan Robotics Team 2022: Data Analysis Module #Written by Arthur Lu & Jacob Levine #Notes: # this should be imported as a python module using 'import analysis' # this should be included in the local directory or environment variable # this module has not been optimized for multhreaded computing #number of easter eggs: 2 #setup: __version__ = "1.0.7.000" #changelog should be viewed using print(analysis.__changelog__) __changelog__ = """changelog: 1.0.7.000: - added tanh_regression (logistical regression) - bug fixes 1.0.6.005: - added z_normalize function to normalize dataset - bug fixes 1.0.6.004: - bug fixes 1.0.6.003: - bug fixes 1.0.6.002: - bug fixes 1.0.6.001: - corrected __all__ to contain all of the functions 1.0.6.000: - added calc_overfit, which calculates two measures of overfit, error and performance - added calculating overfit to optimize_regression 1.0.5.000: - added optimize_regression function, which is a sample function to find the optimal regressions - optimize_regression function filters out some overfit funtions (functions with r^2 = 1) - planned addition: overfit detection in the optimize_regression function 1.0.4.002: - added __changelog__ - updated debug function with log and exponential regressions 1.0.4.001: - added log regressions - added exponential regressions - added log_regression and exp_regression to __all__ 1.0.3.008: - added debug function to further consolidate functions 1.0.3.007: - added builtin benchmark function - added builtin random (linear) data generation function - added device initialization (_init_device) 1.0.3.006: - reorganized the imports list to be in alphabetical order - added search and regurgitate functions to c_entities, nc_entities, obstacles, objectives 1.0.3.005: - major bug fixes - updated historical analysis - depreciated old historical analysis 1.0.3.004: - added __version__, __author__, __all__ - added polynomial regression - added root mean squared function - added r squared function 1.0.3.003: - bug fixes - added c_entities 1.0.3.002: - bug fixes - added nc_entities, obstacles, objectives - consolidated statistics.py to analysis.py 1.0.3.001: - compiled 1d, column, and row basic stats into basic stats function 1.0.3.000: - added historical analysis function 1.0.2.xxx: - added z score test 1.0.1.xxx: - major bug fixes 1.0.0.xxx: - added loading csv - added 1d, column, row basic stats """ __author__ = ( "Arthur Lu , " "Jacob Levine ," ) __all__ = [ '_init_device', 'c_entities', 'nc_entities', 'obstacles', 'objectives', 'load_csv', 'basic_stats', 'z_score', 'stdev_z_split', 'histo_analysis', #histo_analysis_old is intentionally left out as it has been depreciated since v 1.0.1.005 'poly_regression', 'log_regression', 'exp_regression', 'r_squared', 'rms', 'calc_overfit', 'strip_data', 'optimize_regression', 'basic_analysis', #all statistics functions left out due to integration in other functions ] #now back to your regularly scheduled programming: #imports (now in alphabetical order! v 1.0.3.006): from bisect import bisect_left, bisect_right import collections import csv from decimal import Decimal import functools from fractions import Fraction from itertools import groupby import math import matplotlib import numbers import numpy as np import pandas import random import scipy from scipy.optimize import curve_fit from sklearn import * #import statistics <-- statistics.py functions have been integrated into analysis.py as of v 1.0.3.002 import time import torch class error(ValueError): pass def _init_device (setting, arg): #initiates computation device for ANNs if setting == "cuda": temp = setting + ":" + str(arg) try: the_device_woman = torch.device(temp if torch.cuda.is_available() else "cpu") return the_device_woman #name that reference except: raise error("could not assign cuda or cpu") elif setting == "cpu": try: the_device_woman = torch.device("cpu") return the_device_woman #name that reference except: raise error("could not assign cpu") else: raise error("specified device does not exist") class c_entities: c_names = [] c_ids = [] c_pos = [] c_properties = [] c_logic = [] def debug(self): print("c_entities has attributes names, ids, positions, properties, and logic. __init__ takes self, 1d array of names, 1d array of ids, 2d array of positions, nd array of properties, and nd array of logic") return[self.c_names, self.c_ids, self.c_pos, self.c_properties, self.c_logic] def __init__(self, names, ids, pos, properties, logic): self.c_names = names self.c_ids = ids self.c_pos = pos self.c_properties = properties self.c_logic = logic return None def append(self, n_name, n_id, n_pos, n_property, n_logic): self.c_names.append(n_name) self.c_ids.append(n_id) self.c_pos.append(n_pos) self.c_properties.append(n_property) self.c_logic.append(n_logic) return None def edit(self, search, n_name, n_id, n_pos, n_property, n_logic): position = 0 for i in range(0, len(self.c_ids), 1): if self.c_ids[i] == search: position = i if n_name != "null": self.c_names[position] = n_name if n_id != "null": self.c_ids[position] = n_id if n_pos != "null": self.c_pos[position] = n_pos if n_property != "null": self.c_properties[position] = n_property if n_logic != "null": self.c_logic[position] = n_logic return None def search(self, search): position = 0 for i in range(0, len(self.c_ids), 1): if self.c_ids[i] == search: position = i return [self.c_names[position], self.c_ids[position], self.c_pos[position], self.c_properties[position], self.c_logic[position]] def regurgitate(self): return[self.c_names, self.c_ids, self.c_pos, self.c_properties, self.c_logic] class nc_entities: c_names = [] c_ids = [] c_pos = [] c_properties = [] c_effects = [] def debug(self): print ("nc_entities (non-controlable entities) has attributes names, ids, positions, properties, and effects. __init__ takes self, 1d array of names, 1d array of ids, 2d array of positions, 2d array of properties, and 2d array of effects.") return[self.c_names, self.c_ids, self.c_pos, self.c_properties, self.c_effects] def __init__(self, names, ids, pos, properties, effects): self.c_names = names self.c_ids = ids self.c_pos = pos self.c_properties = properties self.c_effects = effects return None def append(self, n_name, n_id, n_pos, n_property, n_effect): self.c_names.append(n_name) self.c_ids.append(n_id) self.c_pos.append(n_pos) self.c_properties.append(n_property) self.c_effects.append(n_effect) return None def edit(self, search, n_name, n_id, n_pos, n_property, n_effect): position = 0 for i in range(0, len(self.c_ids), 1): if self.c_ids[i] == search: position = i if n_name != "null": self.c_names[position] = n_name if n_id != "null": self.c_ids[position] = n_id if n_pos != "null": self.c_pos[position] = n_pos if n_property != "null": self.c_properties[position] = n_property if n_effect != "null": self.c_effects[position] = n_effect return None def search(self, search): position = 0 for i in range(0, len(self.c_ids), 1): if self.c_ids[i] == search: position = i return [self.c_names[position], self.c_ids[position], self.c_pos[position], self.c_properties[position], self.c_effects[position]] def regurgitate(self): return[self.c_names, self.c_ids, self.c_pos, self.c_properties, self.c_effects] class obstacles: c_names = [] c_ids = [] c_perim = [] c_effects = [] def debug(self): print("obstacles has atributes names, ids, positions, perimeters, and effects. __init__ takes self, 1d array of names, 1d array of ids, 2d array of position, 3d array of perimeters, 2d array of effects.") return [self.c_names, self.c_ids, self.c_perim, self.c_effects] def __init__(self, names, ids, perims, effects): self.c_names = names self.c_ids = ids self.c_perim = perims self.c_effects = effects return None def append(self, n_name, n_id, n_perim, n_effect): self.c_names.append(n_name) self.c_ids.append(n_id) self.c_perim.append(n_perim) self.c_effects.append(n_effect) return None def edit(self, search, n_name, n_id, n_perim, n_effect): position = 0 for i in range(0, len(self.c_ids), 1): if self.c_ids[i] == search: position = i if n_name != "null": self.c_names[position] = n_name if n_id != "null": self.c_ids[position] = n_id if n_perim != "null": self.c_perim[position] = n_perim if n_effect != "null": self.c_effects[position] = n_effect return None def search(self, search): position = 0 for i in range(0, len(self.c_ids), 1): if self.c_ids[i] == search: position = i return [self.c_names[position], self.c_ids[position], self.c_perim[position], self.c_effects[position]] def regurgitate(self): return[self.c_names, self.c_ids, self.c_perim, self.c_effects] class objectives: c_names = [] c_ids = [] c_pos = [] c_effects = [] def debug(self): print("objectives has atributes names, ids, positions, and effects. __init__ takes self, 1d array of names, 1d array of ids, 2d array of position, 1d array of effects.") return [self.c_names, self.c_ids, self.c_pos, self.c_effects] def __init__(self, names, ids, pos, effects): self.c_names = names self.c_ids = ids self.c_pos = pos self.c_effects = effects return None def append(self, n_name, n_id, n_pos, n_effect): self.c_names.append(n_name) self.c_ids.append(n_id) self.c_pos.append(n_pos) self.c_effects.append(n_effect) return None def edit(self, search, n_name, n_id, n_pos, n_effect): position = 0 print(self.c_ids) for i in range(0, len(self.c_ids), 1): if self.c_ids[i] == search: position = i if n_name != "null": self.c_names[position] = n_name if n_id != "null": self.c_ids[position] = n_id if n_pos != "null": self.c_pos[position] = n_pos if n_effect != "null": self.c_effects[position] = n_effect return None def search(self, search): position = 0 for i in range(0, len(self.c_ids), 1): if self.c_ids[i] == search: position = i return [self.c_names[position], self.c_ids[position], self.c_pos[position], self.c_effects[position]] def regurgitate(self): return[self.c_names, self.c_ids, self.c_pos, self.c_effects] def load_csv(filepath): with open(filepath, newline = '') as csvfile: file_array = list(csv.reader(csvfile)) return file_array 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 if method == 'debug': 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]" return out if method == "1d" or method == 0: data_t = [] for i in range (0, len(data) - 1, 1): data_t.append(float(data[i])) _mean = mean(data_t) _median = median(data_t) try: _mode = mode(data_t) except: _mode = None try: _stdev = stdev(data_t) except: _stdev = None try: _variance = variance(data_t) except: _variance = None return _mean, _median, _mode, _stdev, _variance elif method == "column" or method == 1: c_data = [] c_data_sorted = [] for i in data: try: c_data.append(float(i[arg])) except: pass _mean = mean(c_data) _median = median(c_data) try: _mode = mode(c_data) except: _mode = None try: _stdev = stdev(c_data) except: _stdev = None try: _variance = variance(c_data) except: _variance = None return _mean, _median, _mode, _stdev, _variance elif method == "row" or method == 2: r_data = [] for i in range(len(data[arg])): r_data.append(float(data[arg][i])) _mean = mean(r_data) _median = median(r_data) try: _mode = mode(r_data) except: _mode = None try: _stdev = stdev(r_data) except: _stdev = None try: _variance = variance(r_data) except: _variance = None return _mean, _median, _mode, _stdev, _variance else: raise error("method error") def z_score(point, mean, stdev): #returns z score with inputs of point, mean and standard deviation of spread score = (point - mean)/stdev return score def z_normalize(x, y, mode): #mode is either 'x' or 'y' or 'both' depending on the variable(s) to be normalized x_norm = [] y_norm = [] mean = 0 stdev = 0 if mode == 'x': _mean, _median, _mode, _stdev, _variance = basic_stats(x, "1d", 0) for i in range (0, len(x), 1): x_norm.append(z_score(x[i], _mean, _stdev)) return x_norm, y if mode == 'y': _mean, _median, _mode, _stdev, _variance = basic_stats(y, "1d", 0) for i in range (0, len(y), 1): y_norm.append(z_score(y[i], _mean, _stdev)) return x, y_norm if mode == 'both': _mean, _median, _mode, _stdev, _variance = basic_stats(x, "1d", 0) for i in range (0, len(x), 1): x_norm.append(z_score(x[i], _mean, _stdev)) _mean, _median, _mode, _stdev, _variance = basic_stats(y, "1d", 0) for i in range (0, len(y), 1): y_norm.append(z_score(y[i], _mean, _stdev)) return x_norm, y_norm else: return error('method error') def stdev_z_split(mean, stdev, delta, low_bound, high_bound): #returns n-th percentile of spread given mean, standard deviation, lower z-score, and upper z-score z_split = [] i = low_bound while True: z_split.append(float((1 / (stdev * math.sqrt(2 * math.pi))) * math.e ** (-0.5 * (((i - mean) / stdev) ** 2)))) i = i + delta if i > high_bound: break return z_split def histo_analysis_old(hist_data): #note: depreciated since v 1.0.1.005 if hist_data == 'debug': 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'] derivative = [] for i in range(0, len(hist_data) - 1, 1): derivative.append(float(hist_data[i+1]) - float(hist_data[i])) derivative_sorted = sorted(derivative, key=int) mean_derivative = basic_stats(derivative_sorted, "1d", 0)[0] print(mean_derivative) stdev_derivative = basic_stats(derivative_sorted, "1d", 0)[3] low_bound = mean_derivative + -1.645 * stdev_derivative lm_bound = mean_derivative + -0.674 * stdev_derivative mid_bound = mean_derivative * 0 * stdev_derivative hm_bound = mean_derivative + 0.674 * stdev_derivative high_bound = mean_derivative + 1.645 * stdev_derivative low_est = float(hist_data[-1:][0]) + low_bound lm_est = float(hist_data[-1:][0]) + lm_bound mid_est = float(hist_data[-1:][0]) + mid_bound hm_est = float(hist_data[-1:][0]) + hm_bound high_est = float(hist_data[-1:][0]) + high_bound return [low_est, lm_est, mid_est, hm_est, high_est, stdev_derivative] def histo_analysis(hist_data, delta, low_bound, high_bound): if hist_data == 'debug': return ('returns list of predicted values based on historical data; input delta for delta step in z-score and lower and higher bounds in number for standard deviations') derivative = [] for i in range(0, len(hist_data) - 1, 1): derivative.append(float(hist_data[i + 1]) - float(hist_data [i])) derivative_sorted = sorted(derivative, key=int) mean_derivative = basic_stats(derivative_sorted,"1d", 0)[0] stdev_derivative = basic_stats(derivative_sorted, "1d", 0)[3] predictions = [] pred_change = 0 i = low_bound while True: if i > high_bound: break try: pred_change = mean_derivative + i * stdev_derivative except: pred_change = mean_derivative predictions.append(float(hist_data[-1:][0]) + pred_change) i = i + delta return predictions def poly_regression(x, y, power): if x == "null": #if x is 'null', then x will be filled with integer points between 1 and the size of y x = [] for i in range(len(y)): print(i) x.append(i+1) reg_eq = scipy.polyfit(x, y, deg = power) eq_str = "" for i in range(0, len(reg_eq), 1): if i < len(reg_eq)- 1: eq_str = eq_str + str(reg_eq[i]) + "*(z**" + str(len(reg_eq) - i - 1) + ")+" else: eq_str = eq_str + str(reg_eq[i]) + "*(z**" + str(len(reg_eq) - i - 1) + ")" vals = [] for i in range(0, len(x), 1): z = x[i] exec("vals.append(" + eq_str + ")") _rms = rms(vals, y) r2_d2 = r_squared(vals, y) return [eq_str, _rms, r2_d2] def log_regression(x, y, base): x_fit = [] for i in range(len(x)): x_fit.append(np.log(x[i]) / np.log(base)) #change of base for logs reg_eq = np.polyfit(x_fit, y, 1) # y = reg_eq[0] * log(x, base) + reg_eq[1] eq_str = str(reg_eq[0]) + "* (np.log(z) / np.log(" + str(base) +"))+" + str(reg_eq[1]) vals = [] for i in range(len(x)): z = x[i] exec("vals.append(" + eq_str + ")") _rms = rms(vals, y) r2_d2 = r_squared(vals, y) return eq_str, _rms, r2_d2 def exp_regression(x, y, base): y_fit = [] for i in range(len(y)): y_fit.append(np.log(y[i]) / np.log(base)) #change of base for logs reg_eq = np.polyfit(x, y_fit, 1, w=np.sqrt(y_fit)) # y = base ^ (reg_eq[0] * x) * base ^ (reg_eq[1]) eq_str = "(" + str(base) + "**(" + str(reg_eq[0]) + "*z))*(" + str(base) + "**(" + str(reg_eq[1]) + "))" vals = [] for i in range(len(x)): z = x[i] exec("vals.append(" + eq_str + ")") _rms = rms(vals, y) r2_d2 = r_squared(vals, y) return eq_str, _rms, r2_d2 def tanh_regression(x, y): def tanh (x, a, b, c, d): return a * np.tanh(b * (x - c)) + d reg_eq = np.float64(curve_fit(tanh, np.array(x), np.array(y))[0]).tolist() eq_str = str(reg_eq[0]) + " * np.tanh(" + str(reg_eq[1]) + "*(z - " + str(reg_eq[2]) + ")) + " + str(reg_eq[3]) vals = [] for i in range(len(x)): z = x[i] exec("vals.append(" + eq_str + ")") in globals(), locals() _rms = rms(vals, y) r2_d2 = r_squared(vals, y) return eq_str, _rms, r2_d2 def r_squared(predictions, targets): # assumes equal size inputs out = metrics.r2_score(targets, predictions) return out def rms(predictions, targets): # assumes equal size inputs out = 0 _sum = 0 for i in range(0, len(targets), 1): _sum = (targets[i] - predictions[i]) ** 2 return float(math.sqrt(_sum/len(targets))) def calc_overfit(equation, rms_train, r2_train, x_test, y_test): #performance overfit = performance(train) - performance(test) where performance is r^2 #error overfit = error(train) - error(test) where error is rms; biased towards smaller values vals = [] for i in range(0, len(x_test), 1): z = x_test[i] exec("vals.append(" + equation + ")") r2_test = r_squared(vals, y_test) rms_test = rms(vals, y_test) return rms_train - rms_test, r2_train - r2_test def strip_data(data, mode): if mode == "adam": #x is the row number, y are the data pass if mode == "eve": #x are the data, y is the column number pass else: raise error("mode error") def optimize_regression(x, y, _range, resolution):#_range in poly regression is the range of powers tried, and in log/exp it is the inverse of the stepsize taken from -1000 to 1000 #usage not: for demonstration purpose only, performance is shit if type(resolution) != int: raise error("resolution must be int") x_train = x y_train = y x_test = [] y_test = [] for i in range (0, math.floor(len(x) * 0.4), 1): index = random.randint(0, len(x) - 1) x_test.append(x[index]) y_test.append(y[index]) x_train.pop(index) y_train.pop(index) #print(x_train, x_test) #print(y_train, y_test) eqs = [] rmss = [] r2s = [] for i in range (0, _range + 1, 1): x, y, z = poly_regression(x_train, y_train, i) eqs.append(x) rmss.append(y) r2s.append(z) for i in range (1, 100 * resolution + 1): try: x, y, z = exp_regression(x_train, y_train, float(i / resolution)) eqs.append(x) rmss.append(y) r2s.append(z) except: pass for i in range (1, 100 * resolution + 1): try: x, y, z = log_regression(x_train, y_train, float(i / resolution)) eqs.append(x) rmss.append(y) r2s.append(z) except: pass x, y, z = tanh_regression(x_train, y_train) eqs.append(x) rmss.append(y) r2s.append(z) print (eqs[::-1]) for i in range (0, len(eqs), 1): #marks all equations where r2 = 1 as they 95% of the time overfit the data if r2s[i] == 1: eqs[i] = "" rmss[i] = "" r2s[i] = "" while True: #removes all equations marked for removal try: eqs.remove('') rmss.remove('') r2s.remove('') except: break overfit = [] for i in range (0, len(eqs), 1): overfit.append(calc_overfit(eqs[i], rmss[i], r2s[i], x_test, y_test)) return eqs, rmss, r2s, overfit def basic_analysis(filepath): #assumes that rows are the independent variable and columns are the dependant. also assumes that time flows from lowest column to highest column. data = load_csv(filepath) row = len(data) column = [] for i in range(0, row, 1): column.append(len(data[i])) column_max = max(column) row_b_stats = [] row_histo = [] for i in range(0, row, 1): row_b_stats.append(basic_stats(data, "row", i)) row_histo.append(histo_analysis(data[i], 0.67449, -0.67449, 0.67449)) column_b_stats = [] for i in range(0, column_max, 1): column_b_stats.append(basic_stats(data, "column", i)) return[row_b_stats, column_b_stats, row_histo] def benchmark(x, y): start_g = time.time() generate_data("data.csv", x, y, -10, 10) end_g = time.time() start_a = time.time() basic_analysis("data.csv") end_a = time.time() return [(end_g - start_g), (end_a - start_a)] def generate_data(filename, x, y, low, high): file = open(filename, "w") for i in range (0, y, 1): temp = "" for j in range (0, x - 1, 1): temp = str(random.uniform(low, high)) + "," + temp temp = temp + str(random.uniform(low, high)) file.write(temp + "\n") def debug(): data = load_csv('data.csv') print("--------------------------------") print(basic_stats(0, 'debug', 0)) print(basic_stats(data, "column", 0)) print(basic_stats(data, "row", 0)) print(z_score(10, basic_stats(data, "column", 0)[0], basic_stats(data, "column", 0)[3])) print(histo_analysis(data[0], 0.01, -1, 1)) print(stdev_z_split(3.3, 0.2, 0.1, -5, 5)) print("--------------------------------") game_c_entities = c_entities(["bot", "bot", "bot"], [0, 1, 2], [[10, 10], [-10, -10], [10, -10]], ["shit", "bad", "worse"], ["triangle", "square", "circle"]) game_c_entities.append("bot", 3, [-10, 10], "useless", "pentagram") game_c_entities.edit(0, "null", "null", "null", "null", "triagon") print(game_c_entities.search(0)) print(game_c_entities.debug()) print(game_c_entities.regurgitate()) print("--------------------------------") game_nc_entities = 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"]) game_nc_entities.append("cone", 3, [1, -1], "property", "effect") game_nc_entities.edit(2, "sphere", 10, [5, -5], "new prop", "new effect") print(game_nc_entities.search(10)) print(game_nc_entities.debug()) print(game_nc_entities.regurgitate()) print("--------------------------------") game_obstacles = 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]) game_obstacles.append("bastion", 3, [[50, 50], [49, 50], [50, 49], [49, 49]], 75) game_obstacles.edit(0, "motte and bailey", "null", [[10, 10], [9, 10], [10, 9], [9, 9]], 0.01) print(game_obstacles.search(0)) print(game_obstacles.debug()) print(game_obstacles.regurgitate()) print("--------------------------------") game_objectives = objectives(["switch", "scale", "climb"], [0,1,2], [[0,0],[1,1],[2,0]], ["0,1", "1,1", "0,5"]) game_objectives.append("auto", 3, [0, 10], "1, 10") game_objectives.edit(3, "null", 4, "null", "null") print(game_objectives.search(4)) print(game_objectives.debug()) print(game_objectives.regurgitate()) print("--------------------------------") print(poly_regression([1, 2, 3, 4, 5], [1, 2, 4, 8, 16], 2)) print(log_regression([1, 2, 3, 4], [2, 4, 8, 16], 2.717)) print(exp_regression([1, 2, 3, 4], [2, 4, 8, 16], 2.717)) x, y, z, o = optimize_regression([0, 1, 2, 3, 4], [1, 2, 4, 7, 19], 10, 100) for i in range(0, len(x), 1): print(str(x[i]) + " | " + str(y[i]) + " | " + str(z[i]) + " | " + str(o[i][0]) + " | " + str(o[i][1])) #statistics def below class StatisticsError(ValueError): pass def _sum(data, start=0): 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: total = partials[None] assert not _isfinite(total) else: 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): assert T is not bool, "initial type T is bool" if T is S: return T if S is int or S is bool: return T if T is int: return S if issubclass(S, T): return S if issubclass(T, S): return T if issubclass(T, int): return S if issubclass(S, int): return T if issubclass(T, Fraction) and issubclass(S, float): return S if issubclass(T, float) and issubclass(S, Fraction): return T msg = "don't know how to coerce %s and %s" raise TypeError(msg % (T.__name__, S.__name__)) def _exact_ratio(x): try: if type(x) is float or type(x) is Decimal: return x.as_integer_ratio() try: return (x.numerator, x.denominator) except AttributeError: try: return x.as_integer_ratio() except AttributeError: pass except (OverflowError, ValueError): 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): if type(value) is T: return value if issubclass(T, int) and value.denominator != 1: T = float try: return T(value) except TypeError: if issubclass(T, Decimal): return T(value.numerator)/T(value.denominator) else: raise def _counts(data): table = collections.Counter(iter(data)).most_common() if not table: return table 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): i = bisect_left(a, x) if i != len(a) and a[i] == x: return i raise ValueError def _find_rteq(a, l, 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'): for x in values: if x < 0: raise StatisticsError(errmsg) yield x def mean(data): 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 median(data): 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 mode(data): 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') def _ss(data, c=None): if c is None: c = mean(data) T, total, count = _sum((x-c)**2 for x in data) 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): 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 stdev(data, xbar=None): var = variance(data, xbar) try: return var.sqrt() except AttributeError: return math.sqrt(var)