tra-analysis/analysis-master/build/lib/analysis/analysis.py

# 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 been optimized for multhreaded computing
#    current benchmark of optimization: 1.33 times faster
# setup:

__version__ = "1.1.13.006"

# changelog should be viewed using print(analysis.__changelog__)
__changelog__ = """changelog:
    1.1.13.006:
        - cleaned up imports
    1.1.13.005:
        - cleaned up package
    1.1.13.004:
        - small fixes to regression to improve performance
    1.1.13.003:
        - filtered nans from regression
    1.1.13.002:
        - removed torch requirement, and moved Regression back to regression.py
    1.1.13.001:
        - bug fix with linear regression not returning a proper value
        - cleaned up regression
        - fixed bug with polynomial regressions
    1.1.13.000:
        - fixed all regressions to now properly work
    1.1.12.006:
        - fixed bg with a division by zero in histo_analysis
    1.1.12.005:
        - fixed numba issues by removing numba  from elo, glicko2 and trueskill
    1.1.12.004:
        - renamed gliko to glicko
    1.1.12.003:
        - removed depreciated code
    1.1.12.002:
        - removed team first time trueskill instantiation in favor of integration in superscript.py
    1.1.12.001:
        - improved readibility of regression outputs by stripping tensor data
        - used map with lambda to acheive the improved readibility
        - lost numba jit support with regression, and generated_jit hangs at execution
        - TODO: reimplement correct numba integration in regression
    1.1.12.000:
        - temporarily fixed polynomial regressions by using sklearn's PolynomialFeatures
    1.1.11.010:
        - alphabeticaly ordered import lists
    1.1.11.009:
        - bug fixes
    1.1.11.008:
        - bug fixes
    1.1.11.007:
        - bug fixes
    1.1.11.006:
        - tested min and max
        - bug fixes 
    1.1.11.005:
        - added min and max in basic_stats
    1.1.11.004:
        - bug fixes
    1.1.11.003:
        - bug fixes
    1.1.11.002:
        - consolidated metrics
        - fixed __all__
    1.1.11.001:
        - added test/train split to RandomForestClassifier and RandomForestRegressor
    1.1.11.000:
        - added RandomForestClassifier and RandomForestRegressor
        - note: untested
    1.1.10.000:
        - added numba.jit to remaining functions
    1.1.9.002:
        - kernelized PCA and KNN
    1.1.9.001:
        - fixed bugs with SVM and NaiveBayes
    1.1.9.000:
        - added SVM class, subclasses, and functions
        - note: untested
    1.1.8.000:
        - added NaiveBayes classification engine
        - note: untested
    1.1.7.000:
        - added knn()
        - added confusion matrix to decisiontree()
    1.1.6.002:
        - changed layout of __changelog to be vscode friendly
    1.1.6.001:
        - added additional hyperparameters to decisiontree()
    1.1.6.000:
        - fixed __version__
        - fixed __all__ order
        - added decisiontree()
    1.1.5.003:
        - added pca
    1.1.5.002:
        - reduced import list
        - added kmeans clustering engine
    1.1.5.001:
        - simplified regression by using .to(device)
    1.1.5.000:
        - added polynomial regression to regression(); untested
    1.1.4.000:
        - added trueskill()
    1.1.3.002:
        - renamed regression class to Regression, regression_engine() to regression gliko2_engine class to Gliko2
    1.1.3.001:
        - changed glicko2() to return tuple instead of array
    1.1.3.000:
        - added glicko2_engine class and glicko()
        - verified glicko2() accuracy
    1.1.2.003:
        - fixed elo()
    1.1.2.002:
        - added elo()
        - elo() has bugs to be fixed
    1.1.2.001:
        - readded regrression import
    1.1.2.000:
        - integrated regression.py as regression class
        - removed regression import
        - fixed metadata for regression class
        - fixed metadata for analysis class
    1.1.1.001:
        - regression_engine() bug fixes, now actaully regresses
    1.1.1.000:
        - added regression_engine()
        - added all regressions except polynomial
    1.1.0.007:
        - updated _init_device()
    1.1.0.006:
        - removed useless try statements
    1.1.0.005:
        - removed impossible outcomes
    1.1.0.004:
        - added performance metrics (r^2, mse, rms)
    1.1.0.003:
        - resolved nopython mode for mean, median, stdev, variance
    1.1.0.002:
        - snapped (removed) majority of uneeded imports
        - forced object mode (bad) on all jit
        - TODO: stop numba complaining about not being able to compile in nopython mode
    1.1.0.001:
        - removed from sklearn import * to resolve uneeded wildcard imports
    1.1.0.000:
        - removed c_entities,nc_entities,obstacles,objectives from __all__
        - applied numba.jit to all functions
        - depreciated and removed stdev_z_split
        - cleaned up histo_analysis to include numpy and numba.jit optimizations
        - depreciated and removed all regression functions in favor of future pytorch optimizer
        - depreciated and removed all nonessential functions (basic_analysis, benchmark, strip_data)
        - optimized z_normalize using sklearn.preprocessing.normalize
        - TODO: implement kernel/function based pytorch regression optimizer
    1.0.9.000:
        - refactored
        - numpyed everything
        - removed stats in favor of numpy functions
    1.0.8.005:
        - minor fixes
    1.0.8.004:
        - removed a few unused dependencies
    1.0.8.003:
        - added p_value function
    1.0.8.002:
        - updated __all__ correctly to contain changes made in v 1.0.8.000 and v 1.0.8.001
    1.0.8.001:
        - refactors
        - bugfixes
    1.0.8.000:
        - depreciated histo_analysis_old
        - depreciated debug
        - altered basic_analysis to take array data instead of filepath
        - refactor
        - optimization
    1.0.7.002:
        - bug fixes
    1.0.7.001:
        - bug fixes
    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 <learthurgo@gmail.com>",
    "Jacob Levine <jlevine@imsa.edu>",
)

__all__ = [
    'load_csv',
    'basic_stats',
    'z_score',
    'z_normalize',
    'histo_analysis',
    'regression',
    'elo',
    'glicko2',
    'trueskill',
    'RegressionMetrics',
    'ClassificationMetrics',
    'kmeans',
    'pca',
    'decisiontree',
    'knn_classifier',
    'knn_regressor',
    'NaiveBayes',
    'SVM',
    'random_forest_classifier',
    'random_forest_regressor',
    'Glicko2',
    # 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):

import csv
import numba
from numba import jit
import numpy as np
import scipy
from scipy import *
import sklearn
from sklearn import *
from analysis import trueskill as Trueskill

class error(ValueError):
    pass

def load_csv(filepath):
    with open(filepath, newline='') as csvfile:
        file_array = np.array(list(csv.reader(csvfile)))
        csvfile.close()
    return file_array

# expects 1d array
@jit(forceobj=True)
def basic_stats(data):

    data_t = np.array(data).astype(float)

    _mean = mean(data_t)
    _median = median(data_t)
    _stdev = stdev(data_t)
    _variance = variance(data_t)
    _min = npmin(data_t)
    _max = npmax(data_t)

    return _mean, _median, _stdev, _variance, _min, _max

# returns z score with inputs of point, mean and standard deviation of spread
@jit(forceobj=True)
def z_score(point, mean, stdev):
    score = (point - mean) / stdev
    
    return score

# expects 2d array, normalizes across all axes
@jit(forceobj=True)
def z_normalize(array, *args):

   array = np.array(array)
   for arg in args:
       array = sklearn.preprocessing.normalize(array, axis = arg)

   return array

@jit(forceobj=True)
# expects 2d array of [x,y]
def histo_analysis(hist_data):

    if(len(hist_data[0]) > 2):

        hist_data = np.array(hist_data)
        derivative = np.array(len(hist_data) - 1, dtype = float)
        t = np.diff(hist_data)
        derivative = t[1] / t[0]
        np.sort(derivative)

        return basic_stats(derivative)[0], basic_stats(derivative)[3]

    else:

        return None

def regression(inputs, outputs, args): # inputs, outputs expects N-D array 

    X = np.array(inputs)
    y = np.array(outputs)

    regressions = []

    if 'lin' in args: # formula: ax + b

        try:

            def func(x, a, b):

                return a * x + b

            popt, pcov = scipy.optimize.curve_fit(func, X, y)

            regressions.append((popt.flatten().tolist(), None))

        except Exception as e:

            pass

    if 'log' in args: # formula: a log (b(x + c)) + d

        try:

            def func(x, a, b, c, d):

                return a * np.log(b*(x + c)) + d

            popt, pcov = scipy.optimize.curve_fit(func, X, y)

            regressions.append((popt.flatten().tolist(), None))

        except Exception as e:
            
            pass

    if 'exp' in args: # formula: a e ^ (b(x + c)) + d

        try:        

            def func(x, a, b, c, d):

                return a * np.exp(b*(x + c)) + d

            popt, pcov = scipy.optimize.curve_fit(func, X, y)

            regressions.append((popt.flatten().tolist(), None))

        except Exception as e:

            pass

    if 'ply' in args: # formula: a + bx^1 + cx^2 + dx^3 + ...
        
        inputs = np.array([inputs])
        outputs = np.array([outputs])

        plys = []
        limit = len(outputs[0])

        for i in range(2, limit):

            model = sklearn.preprocessing.PolynomialFeatures(degree = i)
            model = sklearn.pipeline.make_pipeline(model, sklearn.linear_model.LinearRegression())
            model = model.fit(np.rot90(inputs), np.rot90(outputs))

            params = model.steps[1][1].intercept_.tolist()
            params = np.append(params, model.steps[1][1].coef_[0].tolist()[1::])
            params.flatten()
            params = params.tolist()
            
            plys.append(params)

        regressions.append(plys)

    if 'sig' in args: # formula: a tanh (b(x + c)) + d

        try:        

            def func(x, a, b, c, d):

                return a * np.tanh(b*(x + c)) + d

            popt, pcov = scipy.optimize.curve_fit(func, X, y)

            regressions.append((popt.flatten().tolist(), None))

        except Exception as e:
           
            pass

    return regressions

def elo(starting_score, opposing_score, observed, N, K):

    expected = 1/(1+10**((np.array(opposing_score) - starting_score)/N))

    return starting_score + K*(np.sum(observed) - np.sum(expected))

def glicko2(starting_score, starting_rd, starting_vol, opposing_score, opposing_rd, observations):

    player = Glicko2(rating = starting_score, rd = starting_rd, vol = starting_vol)

    player.update_player([x for x in opposing_score], [x for x in opposing_rd], observations)

    return (player.rating, player.rd, player.vol)

def trueskill(teams_data, observations): # teams_data is array of array of tuples ie. [[(mu, sigma), (mu, sigma), (mu, sigma)], [(mu, sigma), (mu, sigma), (mu, sigma)]]

    team_ratings = []

    for team in teams_data:
        team_temp = []
        for player in team:
            player = Trueskill.Rating(player[0], player[1])
            team_temp.append(player)
        team_ratings.append(team_temp)

    return Trueskill.rate(teams_data, observations)

class RegressionMetrics():

    def __new__(cls, predictions, targets):

        return cls.r_squared(cls, predictions, targets), cls.mse(cls, predictions, targets), cls.rms(cls, predictions, targets)

    def r_squared(self, predictions, targets):  # assumes equal size inputs

        return sklearn.metrics.r2_score(targets, predictions)

    def mse(self, predictions, targets):

        return sklearn.metrics.mean_squared_error(targets, predictions)

    def rms(self, predictions, targets):

        return math.sqrt(sklearn.metrics.mean_squared_error(targets, predictions))

class ClassificationMetrics():

    def __new__(cls, predictions, targets):

        return cls.cm(cls, predictions, targets), cls.cr(cls, predictions, targets)

    def cm(self, predictions, targets):

        return sklearn.metrics.confusion_matrix(targets, predictions)

    def cr(self, predictions, targets):

        return sklearn.metrics.classification_report(targets, predictions)

@jit(nopython=True)
def mean(data):

    return np.mean(data)

@jit(nopython=True)
def median(data):

    return np.median(data)

@jit(nopython=True)
def stdev(data):

    return np.std(data)

@jit(nopython=True)
def variance(data):

    return np.var(data)

@jit(nopython=True)
def npmin(data):

    return np.amin(data)

@jit(nopython=True)
def npmax(data):

    return np.amax(data)

@jit(forceobj=True)
def kmeans(data, n_clusters=8, init="k-means++", n_init=10, max_iter=300, tol=0.0001, precompute_distances="auto", verbose=0, random_state=None, copy_x=True, n_jobs=None, algorithm="auto"):

    kernel = sklearn.cluster.KMeans(n_clusters = n_clusters, init = init, n_init = n_init, max_iter = max_iter, tol = tol, precompute_distances = precompute_distances, verbose = verbose, random_state = random_state, copy_x = copy_x, n_jobs = n_jobs, algorithm = algorithm)
    kernel.fit(data)
    predictions = kernel.predict(data)
    centers = kernel.cluster_centers_

    return centers, predictions

@jit(forceobj=True)
def pca(data, n_components = None, copy = True, whiten = False, svd_solver = "auto", tol = 0.0, iterated_power = "auto", random_state = None):

    kernel = sklearn.decomposition.PCA(n_components = n_components, copy = copy, whiten = whiten, svd_solver = svd_solver, tol = tol, iterated_power = iterated_power, random_state = random_state)

    return kernel.fit_transform(data)

@jit(forceobj=True)
def decisiontree(data, labels, test_size = 0.3, criterion = "gini", splitter = "default", max_depth = None): #expects *2d data and 1d labels

    data_train, data_test, labels_train, labels_test = sklearn.model_selection.train_test_split(data, labels, test_size=test_size, random_state=1)
    model = sklearn.tree.DecisionTreeClassifier(criterion = criterion, splitter = splitter, max_depth = max_depth)
    model = model.fit(data_train,labels_train)
    predictions = model.predict(data_test)
    metrics = ClassificationMetrics(predictions, labels_test)

    return model, metrics

@jit(forceobj=True)
def knn_classifier(data, labels, test_size = 0.3, algorithm='auto', leaf_size=30, metric='minkowski', metric_params=None, n_jobs=None, n_neighbors=5, p=2, weights='uniform'): #expects *2d data and 1d labels post-scaling

    data_train, data_test, labels_train, labels_test = sklearn.model_selection.train_test_split(data, labels, test_size=test_size, random_state=1)
    model = sklearn.neighbors.KNeighborsClassifier()
    model.fit(data_train, labels_train)
    predictions = model.predict(data_test)

    return model, ClassificationMetrics(predictions, labels_test)

def knn_regressor(data, outputs, test_size, n_neighbors = 5, weights = "uniform", algorithm = "auto", leaf_size = 30, p = 2, metric = "minkowski", metric_params = None, n_jobs = None):

    data_train, data_test, outputs_train, outputs_test = sklearn.model_selection.train_test_split(data, outputs, test_size=test_size, random_state=1)
    model = sklearn.neighbors.KNeighborsRegressor(n_neighbors = n_neighbors, weights = weights, algorithm = algorithm, leaf_size = leaf_size, p = p, metric = metric, metric_params = metric_params, n_jobs = n_jobs)
    model.fit(data_train, outputs_train)
    predictions = model.predict(data_test)

    return model, RegressionMetrics(predictions, outputs_test)

class NaiveBayes:

    def guassian(self, data, labels, test_size = 0.3, priors = None, var_smoothing = 1e-09):

        data_train, data_test, labels_train, labels_test = sklearn.model_selection.train_test_split(data, labels, test_size=test_size, random_state=1)
        model = sklearn.naive_bayes.GaussianNB(priors = priors, var_smoothing = var_smoothing)
        model.fit(data_train, labels_train)
        predictions = model.predict(data_test)

        return model, ClassificationMetrics(predictions, labels_test)

    def multinomial(self, data, labels, test_size = 0.3, alpha=1.0, fit_prior=True, class_prior=None):

        data_train, data_test, labels_train, labels_test = sklearn.model_selection.train_test_split(data, labels, test_size=test_size, random_state=1)
        model = sklearn.naive_bayes.MultinomialNB(alpha = alpha, fit_prior = fit_prior, class_prior = class_prior)
        model.fit(data_train, labels_train)
        predictions = model.predict(data_test)

        return model, ClassificationMetrics(predictions, labels_test)

    def bernoulli(self, data, labels, test_size = 0.3, alpha=1.0, binarize=0.0, fit_prior=True, class_prior=None):

        data_train, data_test, labels_train, labels_test = sklearn.model_selection.train_test_split(data, labels, test_size=test_size, random_state=1)
        model = sklearn.naive_bayes.BernoulliNB(alpha = alpha, binarize = binarize, fit_prior = fit_prior, class_prior = class_prior)
        model.fit(data_train, labels_train)
        predictions = model.predict(data_test)

        return model, ClassificationMetrics(predictions, labels_test)

    def complement(self, data, labels, test_size = 0.3, alpha=1.0, fit_prior=True, class_prior=None, norm=False):

        data_train, data_test, labels_train, labels_test = sklearn.model_selection.train_test_split(data, labels, test_size=test_size, random_state=1)
        model = sklearn.naive_bayes.ComplementNB(alpha = alpha, fit_prior = fit_prior, class_prior = class_prior, norm = norm)
        model.fit(data_train, labels_train)
        predictions = model.predict(data_test)

        return model, ClassificationMetrics(predictions, labels_test)

class SVM:

    class CustomKernel:

        def __new__(cls, C, kernel, degre, gamma, coef0, shrinking, probability, tol, cache_size, class_weight, verbose, max_iter, decision_function_shape, random_state):

            return sklearn.svm.SVC(C = C, kernel = kernel, gamma = gamma, coef0 = coef0, shrinking = shrinking, probability = probability, tol = tol, cache_size = cache_size, class_weight = class_weight, verbose = verbose, max_iter = max_iter, decision_function_shape = decision_function_shape, random_state = random_state)

    class StandardKernel:

        def __new__(cls, kernel, C=1.0, degree=3, gamma='auto_deprecated', coef0=0.0, shrinking=True, probability=False, tol=0.001, cache_size=200, class_weight=None, verbose=False, max_iter=-1, decision_function_shape='ovr', random_state=None):

            return sklearn.svm.SVC(C = C, kernel = kernel, gamma = gamma, coef0 = coef0, shrinking = shrinking, probability = probability, tol = tol, cache_size = cache_size, class_weight = class_weight, verbose = verbose, max_iter = max_iter, decision_function_shape = decision_function_shape, random_state = random_state)

    class PrebuiltKernel:

        class Linear:

            def __new__(cls):

                return sklearn.svm.SVC(kernel = 'linear')

        class Polynomial:

            def __new__(cls, power, r_bias):

                return sklearn.svm.SVC(kernel = 'polynomial', degree = power, coef0 = r_bias)

        class RBF:

            def __new__(cls, gamma):

                return sklearn.svm.SVC(kernel = 'rbf', gamma = gamma)

        class Sigmoid:

            def __new__(cls, r_bias):

                return sklearn.svm.SVC(kernel = 'sigmoid', coef0 = r_bias)

    def fit(self, kernel, train_data, train_outputs): # expects *2d data, 1d labels or outputs

        return kernel.fit(train_data, train_outputs)

    def eval_classification(self, kernel, test_data, test_outputs):

        predictions = kernel.predict(test_data)

        return ClassificationMetrics(predictions, test_outputs)

    def eval_regression(self, kernel, test_data, test_outputs):

        predictions = kernel.predict(test_data)

        return RegressionMetrics(predictions, test_outputs)

def random_forest_classifier(data, labels, test_size, n_estimators="warn", criterion="gini", max_depth=None, min_samples_split=2, min_samples_leaf=1, min_weight_fraction_leaf=0.0, max_features="auto", max_leaf_nodes=None, min_impurity_decrease=0.0, min_impurity_split=None, bootstrap=True, oob_score=False, n_jobs=None, random_state=None, verbose=0, warm_start=False, class_weight=None):

    data_train, data_test, labels_train, labels_test = sklearn.model_selection.train_test_split(data, labels, test_size=test_size, random_state=1)
    kernel = sklearn.ensemble.RandomForestClassifier(n_estimators = n_estimators, criterion = criterion, max_depth = max_depth, min_samples_split = min_samples_split, min_samples_leaf = min_samples_leaf, min_weight_fraction_leaf = min_weight_fraction_leaf, max_leaf_nodes = max_leaf_nodes, min_impurity_decrease = min_impurity_decrease, bootstrap = bootstrap, oob_score = oob_score, n_jobs = n_jobs, random_state = random_state, verbose = verbose, warm_start = warm_start, class_weight = class_weight)
    kernel.fit(data_train, labels_train)
    predictions = kernel.predict(data_test)

    return kernel, ClassificationMetrics(predictions, labels_test)

def random_forest_regressor(data, outputs, test_size, n_estimators="warn", criterion="mse", max_depth=None, min_samples_split=2, min_samples_leaf=1, min_weight_fraction_leaf=0.0, max_features="auto", max_leaf_nodes=None, min_impurity_decrease=0.0, min_impurity_split=None, bootstrap=True, oob_score=False, n_jobs=None, random_state=None, verbose=0, warm_start=False):

    data_train, data_test, outputs_train, outputs_test = sklearn.model_selection.train_test_split(data, outputs, test_size=test_size, random_state=1)
    kernel = sklearn.ensemble.RandomForestRegressor(n_estimators = n_estimators, criterion = criterion, max_depth = max_depth, min_samples_split = min_samples_split, min_weight_fraction_leaf = min_weight_fraction_leaf, max_features = max_features, max_leaf_nodes = max_leaf_nodes, min_impurity_decrease = min_impurity_decrease, min_impurity_split = min_impurity_split, bootstrap = bootstrap, oob_score = oob_score, n_jobs = n_jobs, random_state = random_state, verbose = verbose, warm_start = warm_start)
    kernel.fit(data_train, outputs_train)
    predictions = kernel.predict(data_test)

    return kernel, RegressionMetrics(predictions, outputs_test)

class Glicko2:

    _tau = 0.5

    def getRating(self):
        return (self.__rating * 173.7178) + 1500 

    def setRating(self, rating):
        self.__rating = (rating - 1500) / 173.7178

    rating = property(getRating, setRating)

    def getRd(self):
        return self.__rd * 173.7178

    def setRd(self, rd):
        self.__rd = rd / 173.7178

    rd = property(getRd, setRd)
     
    def __init__(self, rating = 1500, rd = 350, vol = 0.06):

        self.setRating(rating)
        self.setRd(rd)
        self.vol = vol
            
    def _preRatingRD(self):

        self.__rd = math.sqrt(math.pow(self.__rd, 2) + math.pow(self.vol, 2))
        
    def update_player(self, rating_list, RD_list, outcome_list):

        rating_list = [(x - 1500) / 173.7178 for x in rating_list]
        RD_list = [x / 173.7178 for x in RD_list]

        v = self._v(rating_list, RD_list)
        self.vol = self._newVol(rating_list, RD_list, outcome_list, v)
        self._preRatingRD()
        
        self.__rd = 1 / math.sqrt((1 / math.pow(self.__rd, 2)) + (1 / v))
        
        tempSum = 0
        for i in range(len(rating_list)):
            tempSum += self._g(RD_list[i]) * \
                       (outcome_list[i] - self._E(rating_list[i], RD_list[i]))
        self.__rating += math.pow(self.__rd, 2) * tempSum
        
        
    def _newVol(self, rating_list, RD_list, outcome_list, v):

        i = 0
        delta = self._delta(rating_list, RD_list, outcome_list, v)
        a = math.log(math.pow(self.vol, 2))
        tau = self._tau
        x0 = a
        x1 = 0
        
        while x0 != x1:
            # New iteration, so x(i) becomes x(i-1)
            x0 = x1
            d = math.pow(self.__rating, 2) + v + math.exp(x0)
            h1 = -(x0 - a) / math.pow(tau, 2) - 0.5 * math.exp(x0) \
            / d + 0.5 * math.exp(x0) * math.pow(delta / d, 2)
            h2 = -1 / math.pow(tau, 2) - 0.5 * math.exp(x0) * \
            (math.pow(self.__rating, 2) + v) \
            / math.pow(d, 2) + 0.5 * math.pow(delta, 2) * math.exp(x0) \
            * (math.pow(self.__rating, 2) + v - math.exp(x0)) / math.pow(d, 3)
            x1 = x0 - (h1 / h2)

        return math.exp(x1 / 2)
        
    def _delta(self, rating_list, RD_list, outcome_list, v):

        tempSum = 0
        for i in range(len(rating_list)):
            tempSum += self._g(RD_list[i]) * (outcome_list[i] - self._E(rating_list[i], RD_list[i]))
        return v * tempSum
        
    def _v(self, rating_list, RD_list):

        tempSum = 0
        for i in range(len(rating_list)):
            tempE = self._E(rating_list[i], RD_list[i])
            tempSum += math.pow(self._g(RD_list[i]), 2) * tempE * (1 - tempE)
        return 1 / tempSum
        
    def _E(self, p2rating, p2RD):

        return 1 / (1 + math.exp(-1 * self._g(p2RD) * \
                                 (self.__rating - p2rating)))
        
    def _g(self, RD):

        return 1 / math.sqrt(1 + 3 * math.pow(RD, 2) / math.pow(math.pi, 2))
        
    def did_not_compete(self):

        self._preRatingRD()