worked

analysis-master/analysis.egg-info/PKG-INFO

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+Metadata-Version: 2.1
+Name: analysis
+Version: 1.0.0.8
+Summary: analysis package developed by Titan Scouting for The Red Alliance
+Home-page: https://github.com/titanscout2022/tr2022-strategy
+Author: The Titan Scouting Team
+Author-email: titanscout2022@gmail.com
+License: GNU General Public License v3.0
+Description: UNKNOWN
+Platform: UNKNOWN
+Classifier: Programming Language :: Python :: 3
+Classifier: Operating System :: OS Independent
+Requires-Python: >=3.6
+Description-Content-Type: text/markdown

analysis-master/analysis.egg-info/SOURCES.txt

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+setup.py
+analysis/__init__.py
+analysis/analysis.py
+analysis/regression.py
+analysis/titanlearn.py
+analysis/trueskill.py
+analysis/visualization.py
+analysis.egg-info/PKG-INFO
+analysis.egg-info/SOURCES.txt
+analysis.egg-info/dependency_links.txt
+analysis.egg-info/requires.txt
+analysis.egg-info/top_level.txt

analysis-master/analysis.egg-info/dependency_links.txt

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+

analysis-master/analysis.egg-info/requires.txt

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+numba
+numpy
+scipy
+scikit-learn
+six
+matplotlib

analysis-master/analysis.egg-info/top_level.txt

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+analysis

analysis-master/analysis/analysis.py

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+# 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()

analysis-master/analysis/regression.py

@@ -0,0 +1,220 @@
+# Titan Robotics Team 2022: CUDA-based Regressions Module
+# Written by Arthur Lu & Jacob Levine
+# Notes:
+#   this module has been automatically inegrated into analysis.py, and should be callable as a class from the package
+#   this module is cuda-optimized and vectorized (except for one small part)
+# setup:
+
+__version__ = "1.0.0.004"
+
+# changelog should be viewed using print(analysis.regression.__changelog__)
+__changelog__ = """
+    1.0.0.004:
+        - bug fixes
+        - fixed changelog
+    1.0.0.003:
+        - bug fixes
+    1.0.0.002:
+        -Added more parameters to log, exponential, polynomial
+        -Added SigmoidalRegKernelArthur, because Arthur apparently needs
+        to train the scaling and shifting of sigmoids
+    1.0.0.001:
+        -initial release, with linear, log, exponential, polynomial, and sigmoid kernels
+        -already vectorized (except for polynomial generation) and CUDA-optimized
+"""
+
+__author__ = (
+    "Jacob Levine <jlevine@imsa.edu>",
+    "Arthur Lu <learthurgo@gmail.com>"
+)
+
+__all__ = [
+    'factorial',
+    'take_all_pwrs',
+    'num_poly_terms',
+    'set_device',
+    'LinearRegKernel',
+    'SigmoidalRegKernel',
+    'LogRegKernel',
+    'PolyRegKernel',
+    'ExpRegKernel',
+    'SigmoidalRegKernelArthur',
+    'SGDTrain',
+    'CustomTrain'
+]
+
+import torch
+
+global device
+
+device = "cuda:0" if torch.torch.cuda.is_available() else "cpu"
+
+#todo: document completely
+
+def set_device(self, new_device):
+    device=new_device
+
+class LinearRegKernel():
+    parameters= []
+    weights=None
+    bias=None
+    def __init__(self, num_vars):
+        self.weights=torch.rand(num_vars, requires_grad=True, device=device)
+        self.bias=torch.rand(1, requires_grad=True, device=device)
+        self.parameters=[self.weights,self.bias]
+    def forward(self,mtx):
+        long_bias=self.bias.repeat([1,mtx.size()[1]])
+        return torch.matmul(self.weights,mtx)+long_bias
+
+class SigmoidalRegKernel():
+    parameters= []
+    weights=None
+    bias=None
+    sigmoid=torch.nn.Sigmoid()
+    def __init__(self, num_vars):
+        self.weights=torch.rand(num_vars, requires_grad=True, device=device)
+        self.bias=torch.rand(1, requires_grad=True, device=device)
+        self.parameters=[self.weights,self.bias]
+    def forward(self,mtx):
+        long_bias=self.bias.repeat([1,mtx.size()[1]])
+        return self.sigmoid(torch.matmul(self.weights,mtx)+long_bias)
+
+class SigmoidalRegKernelArthur():
+    parameters= []
+    weights=None
+    in_bias=None
+    scal_mult=None
+    out_bias=None
+    sigmoid=torch.nn.Sigmoid()
+    def __init__(self, num_vars):
+        self.weights=torch.rand(num_vars, requires_grad=True, device=device)
+        self.in_bias=torch.rand(1, requires_grad=True, device=device)
+        self.scal_mult=torch.rand(1, requires_grad=True, device=device)
+        self.out_bias=torch.rand(1, requires_grad=True, device=device)
+        self.parameters=[self.weights,self.in_bias, self.scal_mult, self.out_bias]
+    def forward(self,mtx):
+        long_in_bias=self.in_bias.repeat([1,mtx.size()[1]])
+        long_out_bias=self.out_bias.repeat([1,mtx.size()[1]])
+        return (self.scal_mult*self.sigmoid(torch.matmul(self.weights,mtx)+long_in_bias))+long_out_bias
+
+class LogRegKernel():
+    parameters= []
+    weights=None
+    in_bias=None
+    scal_mult=None
+    out_bias=None
+    def __init__(self, num_vars):
+        self.weights=torch.rand(num_vars, requires_grad=True, device=device)
+        self.in_bias=torch.rand(1, requires_grad=True, device=device)
+        self.scal_mult=torch.rand(1, requires_grad=True, device=device)
+        self.out_bias=torch.rand(1, requires_grad=True, device=device)
+        self.parameters=[self.weights,self.in_bias, self.scal_mult, self.out_bias]
+    def forward(self,mtx):
+        long_in_bias=self.in_bias.repeat([1,mtx.size()[1]])
+        long_out_bias=self.out_bias.repeat([1,mtx.size()[1]])
+        return (self.scal_mult*torch.log(torch.matmul(self.weights,mtx)+long_in_bias))+long_out_bias
+
+class ExpRegKernel():
+    parameters= []
+    weights=None
+    in_bias=None
+    scal_mult=None
+    out_bias=None
+    def __init__(self, num_vars):
+        self.weights=torch.rand(num_vars, requires_grad=True, device=device)
+        self.in_bias=torch.rand(1, requires_grad=True, device=device)
+        self.scal_mult=torch.rand(1, requires_grad=True, device=device)
+        self.out_bias=torch.rand(1, requires_grad=True, device=device)
+        self.parameters=[self.weights,self.in_bias, self.scal_mult, self.out_bias]
+    def forward(self,mtx):
+        long_in_bias=self.in_bias.repeat([1,mtx.size()[1]])
+        long_out_bias=self.out_bias.repeat([1,mtx.size()[1]])
+        return (self.scal_mult*torch.exp(torch.matmul(self.weights,mtx)+long_in_bias))+long_out_bias
+
+class PolyRegKernel():
+    parameters= []
+    weights=None
+    bias=None
+    power=None
+    def __init__(self, num_vars, power):
+        self.power=power
+        num_terms=self.num_poly_terms(num_vars, power)
+        self.weights=torch.rand(num_terms, requires_grad=True, device=device)
+        self.bias=torch.rand(1, requires_grad=True, device=device)
+        self.parameters=[self.weights,self.bias]
+    def num_poly_terms(self,num_vars, power):
+        if power == 0:
+            return 0
+        return int(self.factorial(num_vars+power-1) / self.factorial(power) / self.factorial(num_vars-1)) + self.num_poly_terms(num_vars, power-1)
+    def factorial(self,n):
+        if n==0:
+            return 1
+        else:
+            return n*self.factorial(n-1)
+    def take_all_pwrs(self, vec, pwr):
+        #todo: vectorize (kinda)
+        combins=torch.combinations(vec, r=pwr, with_replacement=True)
+        out=torch.ones(combins.size()[0]).to(device).to(torch.float)
+        for i in torch.t(combins).to(device).to(torch.float):
+            out *= i
+        if pwr == 1:
+            return out
+        else:
+            return torch.cat((out,self.take_all_pwrs(vec, pwr-1)))
+    def forward(self,mtx):
+        #TODO: Vectorize the last part
+        cols=[]
+        for i in torch.t(mtx):
+            cols.append(self.take_all_pwrs(i,self.power))
+        new_mtx=torch.t(torch.stack(cols))
+        long_bias=self.bias.repeat([1,mtx.size()[1]])
+        return torch.matmul(self.weights,new_mtx)+long_bias
+
+def SGDTrain(self, kernel, data, ground, loss=torch.nn.MSELoss(), iterations=1000, learning_rate=.1, return_losses=False):
+    optim=torch.optim.SGD(kernel.parameters, lr=learning_rate)
+    data_cuda=data.to(device)
+    ground_cuda=ground.to(device)
+    if (return_losses):
+        losses=[]
+        for i in range(iterations):
+            with torch.set_grad_enabled(True):
+                optim.zero_grad()
+                pred=kernel.forward(data_cuda)
+                ls=loss(pred,ground_cuda)
+                losses.append(ls.item())
+                ls.backward()
+                optim.step()
+        return [kernel,losses]
+    else:
+        for i in range(iterations):
+            with torch.set_grad_enabled(True):
+                optim.zero_grad()
+                pred=kernel.forward(data_cuda)
+                ls=loss(pred,ground_cuda)
+                ls.backward()
+                optim.step()
+        return kernel
+
+def CustomTrain(self, kernel, optim, data, ground, loss=torch.nn.MSELoss(), iterations=1000, return_losses=False):
+    data_cuda=data.to(device)
+    ground_cuda=ground.to(device)
+    if (return_losses):
+        losses=[]
+        for i in range(iterations):
+            with torch.set_grad_enabled(True):
+                optim.zero_grad()
+                pred=kernel.forward(data)
+                ls=loss(pred,ground)
+                losses.append(ls.item())
+                ls.backward()
+                optim.step()
+        return [kernel,losses]
+    else:
+        for i in range(iterations):
+            with torch.set_grad_enabled(True):
+                optim.zero_grad()
+                pred=kernel.forward(data_cuda)
+                ls=loss(pred,ground_cuda)
+                ls.backward()
+                optim.step()
+        return kernel

analysis-master/analysis/titanlearn.py

@@ -0,0 +1,122 @@
+# Titan Robotics Team 2022: ML Module
+# Written by Arthur Lu & Jacob Levine
+# Notes:
+#    this should be imported as a python module using 'import titanlearn'
+#    this should be included in the local directory or environment variable
+#    this module is optimized for multhreaded computing
+#    this module learns from its mistakes far faster than 2022's captains
+# setup:
+
+__version__ = "2.0.1.001"
+
+#changelog should be viewed using print(analysis.__changelog__)
+__changelog__ = """changelog:
+    2.0.1.001:
+        - removed matplotlib import
+        - removed graphloss()
+    2.0.1.000:
+        - added net, dataset, dataloader, and stdtrain template definitions
+        - added graphloss function
+    2.0.0.001:
+        - added clear functions
+    2.0.0.000:
+        - complete rewrite planned
+        - depreciated 1.0.0.xxx versions
+        - added simple training loop
+    1.0.0.xxx:
+        -added generation of ANNS, basic SGD training
+"""
+
+__author__ = (
+    "Arthur Lu <arthurlu@ttic.edu>,"
+    "Jacob Levine <jlevine@ttic.edu>,"
+    )
+
+__all__ = [
+    'clear',
+    'net',
+    'dataset',
+    'dataloader',
+    'train',
+    'stdtrainer',
+    ]
+
+import torch
+from os import system, name
+import numpy as np
+
+def clear(): 
+    if name == 'nt': 
+        _ = system('cls') 
+    else: 
+        _ = system('clear') 
+
+class net(torch.nn.Module): #template for standard neural net
+    def __init__(self):
+        super(Net, self).__init__()
+        
+    def forward(self, input):
+        pass
+
+class dataset(torch.utils.data.Dataset): #template for standard dataset
+    
+    def __init__(self):
+        super(torch.utils.data.Dataset).__init__()
+        
+    def __getitem__(self, index):
+        pass
+    
+    def __len__(self):
+        pass
+
+def dataloader(dataset, batch_size, num_workers, shuffle = True):
+
+    return torch.utils.data.DataLoader(dataset, batch_size=batch_size, shuffle=shuffle, num_workers=num_workers)
+
+def train(device, net, epochs, trainloader, optimizer, criterion): #expects standard dataloader, whch returns (inputs, labels)
+
+    dataset_len = trainloader.dataset.__len__()
+    iter_count = 0
+    running_loss = 0
+    running_loss_list = []
+
+    for epoch in range(epochs):  # loop over the dataset multiple times
+
+        for i, data in enumerate(trainloader, 0):
+
+            inputs = data[0].to(device)
+            labels = data[1].to(device)
+
+            optimizer.zero_grad()
+
+            outputs = net(inputs)
+            loss = criterion(outputs, labels.to(torch.float))
+            
+            loss.backward()
+            optimizer.step()
+
+            # monitoring steps below
+
+            iter_count += 1
+            running_loss += loss.item()
+            running_loss_list.append(running_loss)
+            clear()
+
+            print("training on: " + device)
+            print("iteration: " + str(i) + "/" + str(int(dataset_len / trainloader.batch_size)) + " | " + "epoch: " + str(epoch) + "/" + str(epochs))
+            print("current batch loss: " + str(loss.item))
+            print("running loss: " + str(running_loss / iter_count))
+        
+    return net, running_loss_list
+    print("finished training")
+
+def stdtrainer(net, criterion, optimizer, dataloader, epochs, batch_size):
+
+    device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")
+
+    net = net.to(device)
+    criterion = criterion.to(device)
+    optimizer = optimizer.to(device)
+    trainloader = dataloader
+    
+    return train(device, net, epochs, trainloader, optimizer, criterion)

analysis-master/analysis/trueskill.py

@@ -0,0 +1,907 @@
+from __future__ import absolute_import
+
+from itertools import chain
+import math
+
+from six import iteritems
+from six.moves import map, range, zip
+from six import iterkeys
+
+import copy
+try:
+    from numbers import Number
+except ImportError:
+    Number = (int, long, float, complex)
+
+inf = float('inf')
+
+class Gaussian(object):
+    #: Precision, the inverse of the variance.
+    pi = 0
+    #: Precision adjusted mean, the precision multiplied by the mean.
+    tau = 0
+
+    def __init__(self, mu=None, sigma=None, pi=0, tau=0):
+        if mu is not None:
+            if sigma is None:
+                raise TypeError('sigma argument is needed')
+            elif sigma == 0:
+                raise ValueError('sigma**2 should be greater than 0')
+            pi = sigma ** -2
+            tau = pi * mu
+        self.pi = pi
+        self.tau = tau
+
+    @property
+    def mu(self):
+        return self.pi and self.tau / self.pi
+
+    @property
+    def sigma(self):
+        return math.sqrt(1 / self.pi) if self.pi else inf
+
+    def __mul__(self, other):
+        pi, tau = self.pi + other.pi, self.tau + other.tau
+        return Gaussian(pi=pi, tau=tau)
+
+    def __truediv__(self, other):
+        pi, tau = self.pi - other.pi, self.tau - other.tau
+        return Gaussian(pi=pi, tau=tau)
+
+    __div__ = __truediv__  # for Python 2
+
+    def __eq__(self, other):
+        return self.pi == other.pi and self.tau == other.tau
+
+    def __lt__(self, other):
+        return self.mu < other.mu
+
+    def __le__(self, other):
+        return self.mu <= other.mu
+
+    def __gt__(self, other):
+        return self.mu > other.mu
+
+    def __ge__(self, other):
+        return self.mu >= other.mu
+
+    def __repr__(self):
+        return 'N(mu={:.3f}, sigma={:.3f})'.format(self.mu, self.sigma)
+
+    def _repr_latex_(self):
+        latex = r'\mathcal{{ N }}( {:.3f}, {:.3f}^2 )'.format(self.mu, self.sigma)
+        return '$%s$' % latex
+
+class Matrix(list):
+    def __init__(self, src, height=None, width=None):
+        if callable(src):
+            f, src = src, {}
+            size = [height, width]
+            if not height:
+                def set_height(height):
+                    size[0] = height
+                size[0] = set_height
+            if not width:
+                def set_width(width):
+                    size[1] = width
+                size[1] = set_width
+            try:
+                for (r, c), val in f(*size):
+                    src[r, c] = val
+            except TypeError:
+                raise TypeError('A callable src must return an interable '
+                                'which generates a tuple containing '
+                                'coordinate and value')
+            height, width = tuple(size)
+            if height is None or width is None:
+                raise TypeError('A callable src must call set_height and '
+                                'set_width if the size is non-deterministic')
+        if isinstance(src, list):
+            is_number = lambda x: isinstance(x, Number)
+            unique_col_sizes = set(map(len, src))
+            everything_are_number = filter(is_number, sum(src, []))
+            if len(unique_col_sizes) != 1 or not everything_are_number:
+                raise ValueError('src must be a rectangular array of numbers')
+            two_dimensional_array = src
+        elif isinstance(src, dict):
+            if not height or not width:
+                w = h = 0
+                for r, c in iterkeys(src):
+                    if not height:
+                        h = max(h, r + 1)
+                    if not width:
+                        w = max(w, c + 1)
+                if not height:
+                    height = h
+                if not width:
+                    width = w
+            two_dimensional_array = []
+            for r in range(height):
+                row = []
+                two_dimensional_array.append(row)
+                for c in range(width):
+                    row.append(src.get((r, c), 0))
+        else:
+            raise TypeError('src must be a list or dict or callable')
+        super(Matrix, self).__init__(two_dimensional_array)
+
+    @property
+    def height(self):
+        return len(self)
+
+    @property
+    def width(self):
+        return len(self[0])
+
+    def transpose(self):
+        height, width = self.height, self.width
+        src = {}
+        for c in range(width):
+            for r in range(height):
+                src[c, r] = self[r][c]
+        return type(self)(src, height=width, width=height)
+
+    def minor(self, row_n, col_n):
+        height, width = self.height, self.width
+        if not (0 <= row_n < height):
+            raise ValueError('row_n should be between 0 and %d' % height)
+        elif not (0 <= col_n < width):
+            raise ValueError('col_n should be between 0 and %d' % width)
+        two_dimensional_array = []
+        for r in range(height):
+            if r == row_n:
+                continue
+            row = []
+            two_dimensional_array.append(row)
+            for c in range(width):
+                if c == col_n:
+                    continue
+                row.append(self[r][c])
+        return type(self)(two_dimensional_array)
+
+    def determinant(self):
+        height, width = self.height, self.width
+        if height != width:
+            raise ValueError('Only square matrix can calculate a determinant')
+        tmp, rv = copy.deepcopy(self), 1.
+        for c in range(width - 1, 0, -1):
+            pivot, r = max((abs(tmp[r][c]), r) for r in range(c + 1))
+            pivot = tmp[r][c]
+            if not pivot:
+                return 0.
+            tmp[r], tmp[c] = tmp[c], tmp[r]
+            if r != c:
+                rv = -rv
+            rv *= pivot
+            fact = -1. / pivot
+            for r in range(c):
+                f = fact * tmp[r][c]
+                for x in range(c):
+                    tmp[r][x] += f * tmp[c][x]
+        return rv * tmp[0][0]
+
+    def adjugate(self):
+        height, width = self.height, self.width
+        if height != width:
+            raise ValueError('Only square matrix can be adjugated')
+        if height == 2:
+            a, b = self[0][0], self[0][1]
+            c, d = self[1][0], self[1][1]
+            return type(self)([[d, -b], [-c, a]])
+        src = {}
+        for r in range(height):
+            for c in range(width):
+                sign = -1 if (r + c) % 2 else 1
+                src[r, c] = self.minor(r, c).determinant() * sign
+        return type(self)(src, height, width)
+
+    def inverse(self):
+        if self.height == self.width == 1:
+            return type(self)([[1. / self[0][0]]])
+        return (1. / self.determinant()) * self.adjugate()
+
+    def __add__(self, other):
+        height, width = self.height, self.width
+        if (height, width) != (other.height, other.width):
+            raise ValueError('Must be same size')
+        src = {}
+        for r in range(height):
+            for c in range(width):
+                src[r, c] = self[r][c] + other[r][c]
+        return type(self)(src, height, width)
+
+    def __mul__(self, other):
+        if self.width != other.height:
+            raise ValueError('Bad size')
+        height, width = self.height, other.width
+        src = {}
+        for r in range(height):
+            for c in range(width):
+                src[r, c] = sum(self[r][x] * other[x][c]
+                                for x in range(self.width))
+        return type(self)(src, height, width)
+
+    def __rmul__(self, other):
+        if not isinstance(other, Number):
+            raise TypeError('The operand should be a number')
+        height, width = self.height, self.width
+        src = {}
+        for r in range(height):
+            for c in range(width):
+                src[r, c] = other * self[r][c]
+        return type(self)(src, height, width)
+
+    def __repr__(self):
+        return '{}({})'.format(type(self).__name__, super(Matrix, self).__repr__())
+
+    def _repr_latex_(self):
+        rows = [' && '.join(['%.3f' % cell for cell in row]) for row in self]
+        latex = r'\begin{matrix} %s \end{matrix}' % r'\\'.join(rows)
+        return '$%s$' % latex
+
+def _gen_erfcinv(erfc, math=math):
+    def erfcinv(y):
+        """The inverse function of erfc."""
+        if y >= 2:
+            return -100.
+        elif y <= 0:
+            return 100.
+        zero_point = y < 1
+        if not zero_point:
+            y = 2 - y
+        t = math.sqrt(-2 * math.log(y / 2.))
+        x = -0.70711 * \
+            ((2.30753 + t * 0.27061) / (1. + t * (0.99229 + t * 0.04481)) - t)
+        for i in range(2):
+            err = erfc(x) - y
+            x += err / (1.12837916709551257 * math.exp(-(x ** 2)) - x * err)
+        return x if zero_point else -x
+    return erfcinv
+
+def _gen_ppf(erfc, math=math):
+    erfcinv = _gen_erfcinv(erfc, math)
+    def ppf(x, mu=0, sigma=1):
+        return mu - sigma * math.sqrt(2) * erfcinv(2 * x)
+    return ppf
+
+def erfc(x):
+    z = abs(x)
+    t = 1. / (1. + z / 2.)
+    r = t * math.exp(-z * z - 1.26551223 + t * (1.00002368 + t * (
+        0.37409196 + t * (0.09678418 + t * (-0.18628806 + t * (
+            0.27886807 + t * (-1.13520398 + t * (1.48851587 + t * (
+                -0.82215223 + t * 0.17087277
+            )))
+        )))
+    )))
+    return 2. - r if x < 0 else r
+
+def cdf(x, mu=0, sigma=1):
+    return 0.5 * erfc(-(x - mu) / (sigma * math.sqrt(2)))
+
+
+def pdf(x, mu=0, sigma=1):
+    return (1 / math.sqrt(2 * math.pi) * abs(sigma) *
+            math.exp(-(((x - mu) / abs(sigma)) ** 2 / 2)))
+
+ppf = _gen_ppf(erfc)
+
+def choose_backend(backend):
+    if backend is None:  # fallback
+        return cdf, pdf, ppf
+    elif backend == 'mpmath':
+        try:
+            import mpmath
+        except ImportError:
+            raise ImportError('Install "mpmath" to use this backend')
+        return mpmath.ncdf, mpmath.npdf, _gen_ppf(mpmath.erfc, math=mpmath)
+    elif backend == 'scipy':
+        try:
+            from scipy.stats import norm
+        except ImportError:
+            raise ImportError('Install "scipy" to use this backend')
+        return norm.cdf, norm.pdf, norm.ppf
+    raise ValueError('%r backend is not defined' % backend)
+
+def available_backends():
+    backends = [None]
+    for backend in ['mpmath', 'scipy']:
+        try:
+            __import__(backend)
+        except ImportError:
+            continue
+        backends.append(backend)
+    return backends
+
+class Node(object):
+
+    pass
+
+class Variable(Node, Gaussian):
+
+    def __init__(self):
+        self.messages = {}
+        super(Variable, self).__init__()
+
+    def set(self, val):
+        delta = self.delta(val)
+        self.pi, self.tau = val.pi, val.tau
+        return delta
+
+    def delta(self, other):
+        pi_delta = abs(self.pi - other.pi)
+        if pi_delta == inf:
+            return 0.
+        return max(abs(self.tau - other.tau), math.sqrt(pi_delta))
+
+    def update_message(self, factor, pi=0, tau=0, message=None):
+        message = message or Gaussian(pi=pi, tau=tau)
+        old_message, self[factor] = self[factor], message
+        return self.set(self / old_message * message)
+
+    def update_value(self, factor, pi=0, tau=0, value=None):
+        value = value or Gaussian(pi=pi, tau=tau)
+        old_message = self[factor]
+        self[factor] = value * old_message / self
+        return self.set(value)
+
+    def __getitem__(self, factor):
+        return self.messages[factor]
+
+    def __setitem__(self, factor, message):
+        self.messages[factor] = message
+
+    def __repr__(self):
+        args = (type(self).__name__, super(Variable, self).__repr__(),
+                len(self.messages), '' if len(self.messages) == 1 else 's')
+        return '<%s %s with %d connection%s>' % args
+
+
+class Factor(Node):
+
+    def __init__(self, variables):
+        self.vars = variables
+        for var in variables:
+            var[self] = Gaussian()
+
+    def down(self):
+        return 0
+
+    def up(self):
+        return 0
+
+    @property
+    def var(self):
+        assert len(self.vars) == 1
+        return self.vars[0]
+
+    def __repr__(self):
+        args = (type(self).__name__, len(self.vars),
+                '' if len(self.vars) == 1 else 's')
+        return '<%s with %d connection%s>' % args
+
+
+class PriorFactor(Factor):
+
+    def __init__(self, var, val, dynamic=0):
+        super(PriorFactor, self).__init__([var])
+        self.val = val
+        self.dynamic = dynamic
+
+    def down(self):
+        sigma = math.sqrt(self.val.sigma ** 2 + self.dynamic ** 2)
+        value = Gaussian(self.val.mu, sigma)
+        return self.var.update_value(self, value=value)
+
+
+class LikelihoodFactor(Factor):
+
+    def __init__(self, mean_var, value_var, variance):
+        super(LikelihoodFactor, self).__init__([mean_var, value_var])
+        self.mean = mean_var
+        self.value = value_var
+        self.variance = variance
+
+    def calc_a(self, var):
+        return 1. / (1. + self.variance * var.pi)
+
+    def down(self):
+        # update value.
+        msg = self.mean / self.mean[self]
+        a = self.calc_a(msg)
+        return self.value.update_message(self, a * msg.pi, a * msg.tau)
+
+    def up(self):
+        # update mean.
+        msg = self.value / self.value[self]
+        a = self.calc_a(msg)
+        return self.mean.update_message(self, a * msg.pi, a * msg.tau)
+
+
+class SumFactor(Factor):
+
+    def __init__(self, sum_var, term_vars, coeffs):
+        super(SumFactor, self).__init__([sum_var] + term_vars)
+        self.sum = sum_var
+        self.terms = term_vars
+        self.coeffs = coeffs
+
+    def down(self):
+        vals = self.terms
+        msgs = [var[self] for var in vals]
+        return self.update(self.sum, vals, msgs, self.coeffs)
+
+    def up(self, index=0):
+        coeff = self.coeffs[index]
+        coeffs = []
+        for x, c in enumerate(self.coeffs):
+            try:
+                if x == index:
+                    coeffs.append(1. / coeff)
+                else:
+                    coeffs.append(-c / coeff)
+            except ZeroDivisionError:
+                coeffs.append(0.)
+        vals = self.terms[:]
+        vals[index] = self.sum
+        msgs = [var[self] for var in vals]
+        return self.update(self.terms[index], vals, msgs, coeffs)
+
+    def update(self, var, vals, msgs, coeffs):
+        pi_inv = 0
+        mu = 0
+        for val, msg, coeff in zip(vals, msgs, coeffs):
+            div = val / msg
+            mu += coeff * div.mu
+            if pi_inv == inf:
+                continue
+            try:
+                # numpy.float64 handles floating-point error by different way.
+                # For example, it can just warn RuntimeWarning on n/0 problem
+                # instead of throwing ZeroDivisionError.  So div.pi, the
+                # denominator has to be a built-in float.
+                pi_inv += coeff ** 2 / float(div.pi)
+            except ZeroDivisionError:
+                pi_inv = inf
+        pi = 1. / pi_inv
+        tau = pi * mu
+        return var.update_message(self, pi, tau)
+
+
+class TruncateFactor(Factor):
+
+    def __init__(self, var, v_func, w_func, draw_margin):
+        super(TruncateFactor, self).__init__([var])
+        self.v_func = v_func
+        self.w_func = w_func
+        self.draw_margin = draw_margin
+
+    def up(self):
+        val = self.var
+        msg = self.var[self]
+        div = val / msg
+        sqrt_pi = math.sqrt(div.pi)
+        args = (div.tau / sqrt_pi, self.draw_margin * sqrt_pi)
+        v = self.v_func(*args)
+        w = self.w_func(*args)
+        denom = (1. - w)
+        pi, tau = div.pi / denom, (div.tau + sqrt_pi * v) / denom
+        return val.update_value(self, pi, tau)
+
+#: Default initial mean of ratings.
+MU = 25.
+#: Default initial standard deviation of ratings.
+SIGMA = MU / 3
+#: Default distance that guarantees about 76% chance of winning.
+BETA = SIGMA / 2
+#: Default dynamic factor.
+TAU = SIGMA / 100
+#: Default draw probability of the game.
+DRAW_PROBABILITY = .10
+#: A basis to check reliability of the result.
+DELTA = 0.0001
+
+
+def calc_draw_probability(draw_margin, size, env=None):
+    if env is None:
+        env = global_env()
+    return 2 * env.cdf(draw_margin / (math.sqrt(size) * env.beta)) - 1
+
+
+def calc_draw_margin(draw_probability, size, env=None):
+    if env is None:
+        env = global_env()
+    return env.ppf((draw_probability + 1) / 2.) * math.sqrt(size) * env.beta
+
+
+def _team_sizes(rating_groups):
+    team_sizes = [0]
+    for group in rating_groups:
+        team_sizes.append(len(group) + team_sizes[-1])
+    del team_sizes[0]
+    return team_sizes
+
+
+def _floating_point_error(env):
+    if env.backend == 'mpmath':
+        msg = 'Set "mpmath.mp.dps" to higher'
+    else:
+        msg = 'Cannot calculate correctly, set backend to "mpmath"'
+    return FloatingPointError(msg)
+
+
+class Rating(Gaussian):
+    def __init__(self, mu=None, sigma=None):
+        if isinstance(mu, tuple):
+            mu, sigma = mu
+        elif isinstance(mu, Gaussian):
+            mu, sigma = mu.mu, mu.sigma
+        if mu is None:
+            mu = global_env().mu
+        if sigma is None:
+            sigma = global_env().sigma
+        super(Rating, self).__init__(mu, sigma)
+
+    def __int__(self):
+        return int(self.mu)
+
+    def __long__(self):
+        return long(self.mu)
+
+    def __float__(self):
+        return float(self.mu)
+
+    def __iter__(self):
+        return iter((self.mu, self.sigma))
+
+    def __repr__(self):
+        c = type(self)
+        args = ('.'.join([c.__module__, c.__name__]), self.mu, self.sigma)
+        return '%s(mu=%.3f, sigma=%.3f)' % args
+
+
+class TrueSkill(object):
+    def __init__(self, mu=MU, sigma=SIGMA, beta=BETA, tau=TAU,
+                 draw_probability=DRAW_PROBABILITY, backend=None):
+        self.mu = mu
+        self.sigma = sigma
+        self.beta = beta
+        self.tau = tau
+        self.draw_probability = draw_probability
+        self.backend = backend
+        if isinstance(backend, tuple):
+            self.cdf, self.pdf, self.ppf = backend
+        else:
+            self.cdf, self.pdf, self.ppf = choose_backend(backend)
+
+    def create_rating(self, mu=None, sigma=None):
+        if mu is None:
+            mu = self.mu
+        if sigma is None:
+            sigma = self.sigma
+        return Rating(mu, sigma)
+
+    def v_win(self, diff, draw_margin):
+        x = diff - draw_margin
+        denom = self.cdf(x)
+        return (self.pdf(x) / denom) if denom else -x
+
+    def v_draw(self, diff, draw_margin):
+        abs_diff = abs(diff)
+        a, b = draw_margin - abs_diff, -draw_margin - abs_diff
+        denom = self.cdf(a) - self.cdf(b)
+        numer = self.pdf(b) - self.pdf(a)
+        return ((numer / denom) if denom else a) * (-1 if diff < 0 else +1)
+
+    def w_win(self, diff, draw_margin):
+        x = diff - draw_margin
+        v = self.v_win(diff, draw_margin)
+        w = v * (v + x)
+        if 0 < w < 1:
+            return w
+        raise _floating_point_error(self)
+
+    def w_draw(self, diff, draw_margin):
+        abs_diff = abs(diff)
+        a, b = draw_margin - abs_diff, -draw_margin - abs_diff
+        denom = self.cdf(a) - self.cdf(b)
+        if not denom:
+            raise _floating_point_error(self)
+        v = self.v_draw(abs_diff, draw_margin)
+        return (v ** 2) + (a * self.pdf(a) - b * self.pdf(b)) / denom
+
+    def validate_rating_groups(self, rating_groups):
+        # check group sizes
+        if len(rating_groups) < 2:
+            raise ValueError('Need multiple rating groups')
+        elif not all(rating_groups):
+            raise ValueError('Each group must contain multiple ratings')
+        # check group types
+        group_types = set(map(type, rating_groups))
+        if len(group_types) != 1:
+            raise TypeError('All groups should be same type')
+        elif group_types.pop() is Rating:
+            raise TypeError('Rating cannot be a rating group')
+        # normalize rating_groups
+        if isinstance(rating_groups[0], dict):
+            dict_rating_groups = rating_groups
+            rating_groups = []
+            keys = []
+            for dict_rating_group in dict_rating_groups:
+                rating_group, key_group = [], []
+                for key, rating in iteritems(dict_rating_group):
+                    rating_group.append(rating)
+                    key_group.append(key)
+                rating_groups.append(tuple(rating_group))
+                keys.append(tuple(key_group))
+        else:
+            rating_groups = list(rating_groups)
+            keys = None
+        return rating_groups, keys
+
+    def validate_weights(self, weights, rating_groups, keys=None):
+        if weights is None:
+            weights = [(1,) * len(g) for g in rating_groups]
+        elif isinstance(weights, dict):
+            weights_dict, weights = weights, []
+            for x, group in enumerate(rating_groups):
+                w = []
+                weights.append(w)
+                for y, rating in enumerate(group):
+                    if keys is not None:
+                        y = keys[x][y]
+                    w.append(weights_dict.get((x, y), 1))
+        return weights
+
+    def factor_graph_builders(self, rating_groups, ranks, weights):
+        flatten_ratings = sum(map(tuple, rating_groups), ())
+        flatten_weights = sum(map(tuple, weights), ())
+        size = len(flatten_ratings)
+        group_size = len(rating_groups)
+        # create variables
+        rating_vars = [Variable() for x in range(size)]
+        perf_vars = [Variable() for x in range(size)]
+        team_perf_vars = [Variable() for x in range(group_size)]
+        team_diff_vars = [Variable() for x in range(group_size - 1)]
+        team_sizes = _team_sizes(rating_groups)
+        # layer builders
+        def build_rating_layer():
+            for rating_var, rating in zip(rating_vars, flatten_ratings):
+                yield PriorFactor(rating_var, rating, self.tau)
+        def build_perf_layer():
+            for rating_var, perf_var in zip(rating_vars, perf_vars):
+                yield LikelihoodFactor(rating_var, perf_var, self.beta ** 2)
+        def build_team_perf_layer():
+            for team, team_perf_var in enumerate(team_perf_vars):
+                if team > 0:
+                    start = team_sizes[team - 1]
+                else:
+                    start = 0
+                end = team_sizes[team]
+                child_perf_vars = perf_vars[start:end]
+                coeffs = flatten_weights[start:end]
+                yield SumFactor(team_perf_var, child_perf_vars, coeffs)
+        def build_team_diff_layer():
+            for team, team_diff_var in enumerate(team_diff_vars):
+                yield SumFactor(team_diff_var,
+                                team_perf_vars[team:team + 2], [+1, -1])
+        def build_trunc_layer():
+            for x, team_diff_var in enumerate(team_diff_vars):
+                if callable(self.draw_probability):
+                    # dynamic draw probability
+                    team_perf1, team_perf2 = team_perf_vars[x:x + 2]
+                    args = (Rating(team_perf1), Rating(team_perf2), self)
+                    draw_probability = self.draw_probability(*args)
+                else:
+                    # static draw probability
+                    draw_probability = self.draw_probability
+                size = sum(map(len, rating_groups[x:x + 2]))
+                draw_margin = calc_draw_margin(draw_probability, size, self)
+                if ranks[x] == ranks[x + 1]:  # is a tie?
+                    v_func, w_func = self.v_draw, self.w_draw
+                else:
+                    v_func, w_func = self.v_win, self.w_win
+                yield TruncateFactor(team_diff_var,
+                                     v_func, w_func, draw_margin)
+        # build layers
+        return (build_rating_layer, build_perf_layer, build_team_perf_layer,
+                build_team_diff_layer, build_trunc_layer)
+
+    def run_schedule(self, build_rating_layer, build_perf_layer,
+                     build_team_perf_layer, build_team_diff_layer,
+                     build_trunc_layer, min_delta=DELTA):
+        if min_delta <= 0:
+            raise ValueError('min_delta must be greater than 0')
+        layers = []
+        def build(builders):
+            layers_built = [list(build()) for build in builders]
+            layers.extend(layers_built)
+            return layers_built
+        # gray arrows
+        layers_built = build([build_rating_layer,
+                              build_perf_layer,
+                              build_team_perf_layer])
+        rating_layer, perf_layer, team_perf_layer = layers_built
+        for f in chain(*layers_built):
+            f.down()
+        # arrow #1, #2, #3
+        team_diff_layer, trunc_layer = build([build_team_diff_layer,
+                                              build_trunc_layer])
+        team_diff_len = len(team_diff_layer)
+        for x in range(10):
+            if team_diff_len == 1:
+                # only two teams
+                team_diff_layer[0].down()
+                delta = trunc_layer[0].up()
+            else:
+                # multiple teams
+                delta = 0
+                for x in range(team_diff_len - 1):
+                    team_diff_layer[x].down()
+                    delta = max(delta, trunc_layer[x].up())
+                    team_diff_layer[x].up(1)  # up to right variable
+                for x in range(team_diff_len - 1, 0, -1):
+                    team_diff_layer[x].down()
+                    delta = max(delta, trunc_layer[x].up())
+                    team_diff_layer[x].up(0)  # up to left variable
+            # repeat until to small update
+            if delta <= min_delta:
+                break
+        # up both ends
+        team_diff_layer[0].up(0)
+        team_diff_layer[team_diff_len - 1].up(1)
+        # up the remainder of the black arrows
+        for f in team_perf_layer:
+            for x in range(len(f.vars) - 1):
+                f.up(x)
+        for f in perf_layer:
+            f.up()
+        return layers
+
+    def rate(self, rating_groups, ranks=None, weights=None, min_delta=DELTA):
+        rating_groups, keys = self.validate_rating_groups(rating_groups)
+        weights = self.validate_weights(weights, rating_groups, keys)
+        group_size = len(rating_groups)
+        if ranks is None:
+            ranks = range(group_size)
+        elif len(ranks) != group_size:
+            raise ValueError('Wrong ranks')
+        # sort rating groups by rank
+        by_rank = lambda x: x[1][1]
+        sorting = sorted(enumerate(zip(rating_groups, ranks, weights)),
+                         key=by_rank)
+        sorted_rating_groups, sorted_ranks, sorted_weights = [], [], []
+        for x, (g, r, w) in sorting:
+            sorted_rating_groups.append(g)
+            sorted_ranks.append(r)
+            # make weights to be greater than 0
+            sorted_weights.append(max(min_delta, w_) for w_ in w)
+        # build factor graph
+        args = (sorted_rating_groups, sorted_ranks, sorted_weights)
+        builders = self.factor_graph_builders(*args)
+        args = builders + (min_delta,)
+        layers = self.run_schedule(*args)
+        # make result
+        rating_layer, team_sizes = layers[0], _team_sizes(sorted_rating_groups)
+        transformed_groups = []
+        for start, end in zip([0] + team_sizes[:-1], team_sizes):
+            group = []
+            for f in rating_layer[start:end]:
+                group.append(Rating(float(f.var.mu), float(f.var.sigma)))
+            transformed_groups.append(tuple(group))
+        by_hint = lambda x: x[0]
+        unsorting = sorted(zip((x for x, __ in sorting), transformed_groups),
+                           key=by_hint)
+        if keys is None:
+            return [g for x, g in unsorting]
+        # restore the structure with input dictionary keys
+        return [dict(zip(keys[x], g)) for x, g in unsorting]
+
+    def quality(self, rating_groups, weights=None):
+        rating_groups, keys = self.validate_rating_groups(rating_groups)
+        weights = self.validate_weights(weights, rating_groups, keys)
+        flatten_ratings = sum(map(tuple, rating_groups), ())
+        flatten_weights = sum(map(tuple, weights), ())
+        length = len(flatten_ratings)
+        # a vector of all of the skill means
+        mean_matrix = Matrix([[r.mu] for r in flatten_ratings])
+        # a matrix whose diagonal values are the variances (sigma ** 2) of each
+        # of the players.
+        def variance_matrix(height, width):
+            variances = (r.sigma ** 2 for r in flatten_ratings)
+            for x, variance in enumerate(variances):
+                yield (x, x), variance
+        variance_matrix = Matrix(variance_matrix, length, length)
+        # the player-team assignment and comparison matrix
+        def rotated_a_matrix(set_height, set_width):
+            t = 0
+            for r, (cur, _next) in enumerate(zip(rating_groups[:-1],
+                                                rating_groups[1:])):
+                for x in range(t, t + len(cur)):
+                    yield (r, x), flatten_weights[x]
+                    t += 1
+                x += 1
+                for x in range(x, x + len(_next)):
+                    yield (r, x), -flatten_weights[x]
+            set_height(r + 1)
+            set_width(x + 1)
+        rotated_a_matrix = Matrix(rotated_a_matrix)
+        a_matrix = rotated_a_matrix.transpose()
+        # match quality further derivation
+        _ata = (self.beta ** 2) * rotated_a_matrix * a_matrix
+        _atsa = rotated_a_matrix * variance_matrix * a_matrix
+        start = mean_matrix.transpose() * a_matrix
+        middle = _ata + _atsa
+        end = rotated_a_matrix * mean_matrix
+        # make result
+        e_arg = (-0.5 * start * middle.inverse() * end).determinant()
+        s_arg = _ata.determinant() / middle.determinant()
+        return math.exp(e_arg) * math.sqrt(s_arg)
+
+    def expose(self, rating):
+        k = self.mu / self.sigma
+        return rating.mu - k * rating.sigma
+
+    def make_as_global(self):
+        return setup(env=self)
+
+    def __repr__(self):
+        c = type(self)
+        if callable(self.draw_probability):
+            f = self.draw_probability
+            draw_probability = '.'.join([f.__module__, f.__name__])
+        else:
+            draw_probability = '%.1f%%' % (self.draw_probability * 100)
+        if self.backend is None:
+            backend = ''
+        elif isinstance(self.backend, tuple):
+            backend = ', backend=...'
+        else:
+            backend = ', backend=%r' % self.backend
+        args = ('.'.join([c.__module__, c.__name__]), self.mu, self.sigma,
+                self.beta, self.tau, draw_probability, backend)
+        return ('%s(mu=%.3f, sigma=%.3f, beta=%.3f, tau=%.3f, '
+                'draw_probability=%s%s)' % args)
+
+
+def rate_1vs1(rating1, rating2, drawn=False, min_delta=DELTA, env=None):
+    if env is None:
+        env = global_env()
+    ranks = [0, 0 if drawn else 1]
+    teams = env.rate([(rating1,), (rating2,)], ranks, min_delta=min_delta)
+    return teams[0][0], teams[1][0]
+
+
+def quality_1vs1(rating1, rating2, env=None):
+    if env is None:
+        env = global_env()
+    return env.quality([(rating1,), (rating2,)])
+
+
+def global_env():
+    try:
+        global_env.__trueskill__
+    except AttributeError:
+        # setup the default environment
+        setup()
+    return global_env.__trueskill__
+
+
+def setup(mu=MU, sigma=SIGMA, beta=BETA, tau=TAU,
+          draw_probability=DRAW_PROBABILITY, backend=None, env=None):
+    if env is None:
+        env = TrueSkill(mu, sigma, beta, tau, draw_probability, backend)
+    global_env.__trueskill__ = env
+    return env
+
+
+def rate(rating_groups, ranks=None, weights=None, min_delta=DELTA):
+    return global_env().rate(rating_groups, ranks, weights, min_delta)
+
+
+def quality(rating_groups, weights=None):
+    return global_env().quality(rating_groups, weights)
+
+
+def expose(rating):
+    return global_env().expose(rating)

analysis-master/analysis/visualization.py

@@ -0,0 +1,34 @@
+# Titan Robotics Team 2022: Visualization Module
+# Written by Arthur Lu & Jacob Levine
+# Notes:
+#    this should be imported as a python module using 'import visualization'
+#    this should be included in the local directory or environment variable
+#    fancy
+# setup:
+
+__version__ = "1.0.0.000"
+
+#changelog should be viewed using print(analysis.__changelog__)
+__changelog__ = """changelog:
+    1.0.0.000:
+        - created visualization.py
+        - added graphloss()
+        - added imports
+"""
+
+__author__ = (
+    "Arthur Lu <arthurlu@ttic.edu>,"
+    "Jacob Levine <jlevine@ttic.edu>,"
+    )
+
+__all__ = [
+    'graphloss',
+    ]
+
+import matplotlib.pyplot as plt
+
+def graphloss(losses):
+
+    x = range(0, len(losses))
+    plt.plot(x, losses)
+    plt.show()

analysis-master/build.sh

@@ -0,0 +1 @@
+python3 setup.py sdist bdist_wheel

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

@@ -0,0 +1,790 @@
+# 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()

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

@@ -0,0 +1,220 @@
+# Titan Robotics Team 2022: CUDA-based Regressions Module
+# Written by Arthur Lu & Jacob Levine
+# Notes:
+#   this module has been automatically inegrated into analysis.py, and should be callable as a class from the package
+#   this module is cuda-optimized and vectorized (except for one small part)
+# setup:
+
+__version__ = "1.0.0.004"
+
+# changelog should be viewed using print(analysis.regression.__changelog__)
+__changelog__ = """
+    1.0.0.004:
+        - bug fixes
+        - fixed changelog
+    1.0.0.003:
+        - bug fixes
+    1.0.0.002:
+        -Added more parameters to log, exponential, polynomial
+        -Added SigmoidalRegKernelArthur, because Arthur apparently needs
+        to train the scaling and shifting of sigmoids
+    1.0.0.001:
+        -initial release, with linear, log, exponential, polynomial, and sigmoid kernels
+        -already vectorized (except for polynomial generation) and CUDA-optimized
+"""
+
+__author__ = (
+    "Jacob Levine <jlevine@imsa.edu>",
+    "Arthur Lu <learthurgo@gmail.com>"
+)
+
+__all__ = [
+    'factorial',
+    'take_all_pwrs',
+    'num_poly_terms',
+    'set_device',
+    'LinearRegKernel',
+    'SigmoidalRegKernel',
+    'LogRegKernel',
+    'PolyRegKernel',
+    'ExpRegKernel',
+    'SigmoidalRegKernelArthur',
+    'SGDTrain',
+    'CustomTrain'
+]
+
+import torch
+
+global device
+
+device = "cuda:0" if torch.torch.cuda.is_available() else "cpu"
+
+#todo: document completely
+
+def set_device(self, new_device):
+    device=new_device
+
+class LinearRegKernel():
+    parameters= []
+    weights=None
+    bias=None
+    def __init__(self, num_vars):
+        self.weights=torch.rand(num_vars, requires_grad=True, device=device)
+        self.bias=torch.rand(1, requires_grad=True, device=device)
+        self.parameters=[self.weights,self.bias]
+    def forward(self,mtx):
+        long_bias=self.bias.repeat([1,mtx.size()[1]])
+        return torch.matmul(self.weights,mtx)+long_bias
+
+class SigmoidalRegKernel():
+    parameters= []
+    weights=None
+    bias=None
+    sigmoid=torch.nn.Sigmoid()
+    def __init__(self, num_vars):
+        self.weights=torch.rand(num_vars, requires_grad=True, device=device)
+        self.bias=torch.rand(1, requires_grad=True, device=device)
+        self.parameters=[self.weights,self.bias]
+    def forward(self,mtx):
+        long_bias=self.bias.repeat([1,mtx.size()[1]])
+        return self.sigmoid(torch.matmul(self.weights,mtx)+long_bias)
+
+class SigmoidalRegKernelArthur():
+    parameters= []
+    weights=None
+    in_bias=None
+    scal_mult=None
+    out_bias=None
+    sigmoid=torch.nn.Sigmoid()
+    def __init__(self, num_vars):
+        self.weights=torch.rand(num_vars, requires_grad=True, device=device)
+        self.in_bias=torch.rand(1, requires_grad=True, device=device)
+        self.scal_mult=torch.rand(1, requires_grad=True, device=device)
+        self.out_bias=torch.rand(1, requires_grad=True, device=device)
+        self.parameters=[self.weights,self.in_bias, self.scal_mult, self.out_bias]
+    def forward(self,mtx):
+        long_in_bias=self.in_bias.repeat([1,mtx.size()[1]])
+        long_out_bias=self.out_bias.repeat([1,mtx.size()[1]])
+        return (self.scal_mult*self.sigmoid(torch.matmul(self.weights,mtx)+long_in_bias))+long_out_bias
+
+class LogRegKernel():
+    parameters= []
+    weights=None
+    in_bias=None
+    scal_mult=None
+    out_bias=None
+    def __init__(self, num_vars):
+        self.weights=torch.rand(num_vars, requires_grad=True, device=device)
+        self.in_bias=torch.rand(1, requires_grad=True, device=device)
+        self.scal_mult=torch.rand(1, requires_grad=True, device=device)
+        self.out_bias=torch.rand(1, requires_grad=True, device=device)
+        self.parameters=[self.weights,self.in_bias, self.scal_mult, self.out_bias]
+    def forward(self,mtx):
+        long_in_bias=self.in_bias.repeat([1,mtx.size()[1]])
+        long_out_bias=self.out_bias.repeat([1,mtx.size()[1]])
+        return (self.scal_mult*torch.log(torch.matmul(self.weights,mtx)+long_in_bias))+long_out_bias
+
+class ExpRegKernel():
+    parameters= []
+    weights=None
+    in_bias=None
+    scal_mult=None
+    out_bias=None
+    def __init__(self, num_vars):
+        self.weights=torch.rand(num_vars, requires_grad=True, device=device)
+        self.in_bias=torch.rand(1, requires_grad=True, device=device)
+        self.scal_mult=torch.rand(1, requires_grad=True, device=device)
+        self.out_bias=torch.rand(1, requires_grad=True, device=device)
+        self.parameters=[self.weights,self.in_bias, self.scal_mult, self.out_bias]
+    def forward(self,mtx):
+        long_in_bias=self.in_bias.repeat([1,mtx.size()[1]])
+        long_out_bias=self.out_bias.repeat([1,mtx.size()[1]])
+        return (self.scal_mult*torch.exp(torch.matmul(self.weights,mtx)+long_in_bias))+long_out_bias
+
+class PolyRegKernel():
+    parameters= []
+    weights=None
+    bias=None
+    power=None
+    def __init__(self, num_vars, power):
+        self.power=power
+        num_terms=self.num_poly_terms(num_vars, power)
+        self.weights=torch.rand(num_terms, requires_grad=True, device=device)
+        self.bias=torch.rand(1, requires_grad=True, device=device)
+        self.parameters=[self.weights,self.bias]
+    def num_poly_terms(self,num_vars, power):
+        if power == 0:
+            return 0
+        return int(self.factorial(num_vars+power-1) / self.factorial(power) / self.factorial(num_vars-1)) + self.num_poly_terms(num_vars, power-1)
+    def factorial(self,n):
+        if n==0:
+            return 1
+        else:
+            return n*self.factorial(n-1)
+    def take_all_pwrs(self, vec, pwr):
+        #todo: vectorize (kinda)
+        combins=torch.combinations(vec, r=pwr, with_replacement=True)
+        out=torch.ones(combins.size()[0]).to(device).to(torch.float)
+        for i in torch.t(combins).to(device).to(torch.float):
+            out *= i
+        if pwr == 1:
+            return out
+        else:
+            return torch.cat((out,self.take_all_pwrs(vec, pwr-1)))
+    def forward(self,mtx):
+        #TODO: Vectorize the last part
+        cols=[]
+        for i in torch.t(mtx):
+            cols.append(self.take_all_pwrs(i,self.power))
+        new_mtx=torch.t(torch.stack(cols))
+        long_bias=self.bias.repeat([1,mtx.size()[1]])
+        return torch.matmul(self.weights,new_mtx)+long_bias
+
+def SGDTrain(self, kernel, data, ground, loss=torch.nn.MSELoss(), iterations=1000, learning_rate=.1, return_losses=False):
+    optim=torch.optim.SGD(kernel.parameters, lr=learning_rate)
+    data_cuda=data.to(device)
+    ground_cuda=ground.to(device)
+    if (return_losses):
+        losses=[]
+        for i in range(iterations):
+            with torch.set_grad_enabled(True):
+                optim.zero_grad()
+                pred=kernel.forward(data_cuda)
+                ls=loss(pred,ground_cuda)
+                losses.append(ls.item())
+                ls.backward()
+                optim.step()
+        return [kernel,losses]
+    else:
+        for i in range(iterations):
+            with torch.set_grad_enabled(True):
+                optim.zero_grad()
+                pred=kernel.forward(data_cuda)
+                ls=loss(pred,ground_cuda)
+                ls.backward()
+                optim.step()
+        return kernel
+
+def CustomTrain(self, kernel, optim, data, ground, loss=torch.nn.MSELoss(), iterations=1000, return_losses=False):
+    data_cuda=data.to(device)
+    ground_cuda=ground.to(device)
+    if (return_losses):
+        losses=[]
+        for i in range(iterations):
+            with torch.set_grad_enabled(True):
+                optim.zero_grad()
+                pred=kernel.forward(data)
+                ls=loss(pred,ground)
+                losses.append(ls.item())
+                ls.backward()
+                optim.step()
+        return [kernel,losses]
+    else:
+        for i in range(iterations):
+            with torch.set_grad_enabled(True):
+                optim.zero_grad()
+                pred=kernel.forward(data_cuda)
+                ls=loss(pred,ground_cuda)
+                ls.backward()
+                optim.step()
+        return kernel

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

@@ -0,0 +1,122 @@
+# Titan Robotics Team 2022: ML Module
+# Written by Arthur Lu & Jacob Levine
+# Notes:
+#    this should be imported as a python module using 'import titanlearn'
+#    this should be included in the local directory or environment variable
+#    this module is optimized for multhreaded computing
+#    this module learns from its mistakes far faster than 2022's captains
+# setup:
+
+__version__ = "2.0.1.001"
+
+#changelog should be viewed using print(analysis.__changelog__)
+__changelog__ = """changelog:
+    2.0.1.001:
+        - removed matplotlib import
+        - removed graphloss()
+    2.0.1.000:
+        - added net, dataset, dataloader, and stdtrain template definitions
+        - added graphloss function
+    2.0.0.001:
+        - added clear functions
+    2.0.0.000:
+        - complete rewrite planned
+        - depreciated 1.0.0.xxx versions
+        - added simple training loop
+    1.0.0.xxx:
+        -added generation of ANNS, basic SGD training
+"""
+
+__author__ = (
+    "Arthur Lu <arthurlu@ttic.edu>,"
+    "Jacob Levine <jlevine@ttic.edu>,"
+    )
+
+__all__ = [
+    'clear',
+    'net',
+    'dataset',
+    'dataloader',
+    'train',
+    'stdtrainer',
+    ]
+
+import torch
+from os import system, name
+import numpy as np
+
+def clear(): 
+    if name == 'nt': 
+        _ = system('cls') 
+    else: 
+        _ = system('clear') 
+
+class net(torch.nn.Module): #template for standard neural net
+    def __init__(self):
+        super(Net, self).__init__()
+        
+    def forward(self, input):
+        pass
+
+class dataset(torch.utils.data.Dataset): #template for standard dataset
+    
+    def __init__(self):
+        super(torch.utils.data.Dataset).__init__()
+        
+    def __getitem__(self, index):
+        pass
+    
+    def __len__(self):
+        pass
+
+def dataloader(dataset, batch_size, num_workers, shuffle = True):
+
+    return torch.utils.data.DataLoader(dataset, batch_size=batch_size, shuffle=shuffle, num_workers=num_workers)
+
+def train(device, net, epochs, trainloader, optimizer, criterion): #expects standard dataloader, whch returns (inputs, labels)
+
+    dataset_len = trainloader.dataset.__len__()
+    iter_count = 0
+    running_loss = 0
+    running_loss_list = []
+
+    for epoch in range(epochs):  # loop over the dataset multiple times
+
+        for i, data in enumerate(trainloader, 0):
+
+            inputs = data[0].to(device)
+            labels = data[1].to(device)
+
+            optimizer.zero_grad()
+
+            outputs = net(inputs)
+            loss = criterion(outputs, labels.to(torch.float))
+            
+            loss.backward()
+            optimizer.step()
+
+            # monitoring steps below
+
+            iter_count += 1
+            running_loss += loss.item()
+            running_loss_list.append(running_loss)
+            clear()
+
+            print("training on: " + device)
+            print("iteration: " + str(i) + "/" + str(int(dataset_len / trainloader.batch_size)) + " | " + "epoch: " + str(epoch) + "/" + str(epochs))
+            print("current batch loss: " + str(loss.item))
+            print("running loss: " + str(running_loss / iter_count))
+        
+    return net, running_loss_list
+    print("finished training")
+
+def stdtrainer(net, criterion, optimizer, dataloader, epochs, batch_size):
+
+    device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")
+
+    net = net.to(device)
+    criterion = criterion.to(device)
+    optimizer = optimizer.to(device)
+    trainloader = dataloader
+    
+    return train(device, net, epochs, trainloader, optimizer, criterion)

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

@@ -0,0 +1,907 @@
+from __future__ import absolute_import
+
+from itertools import chain
+import math
+
+from six import iteritems
+from six.moves import map, range, zip
+from six import iterkeys
+
+import copy
+try:
+    from numbers import Number
+except ImportError:
+    Number = (int, long, float, complex)
+
+inf = float('inf')
+
+class Gaussian(object):
+    #: Precision, the inverse of the variance.
+    pi = 0
+    #: Precision adjusted mean, the precision multiplied by the mean.
+    tau = 0
+
+    def __init__(self, mu=None, sigma=None, pi=0, tau=0):
+        if mu is not None:
+            if sigma is None:
+                raise TypeError('sigma argument is needed')
+            elif sigma == 0:
+                raise ValueError('sigma**2 should be greater than 0')
+            pi = sigma ** -2
+            tau = pi * mu
+        self.pi = pi
+        self.tau = tau
+
+    @property
+    def mu(self):
+        return self.pi and self.tau / self.pi
+
+    @property
+    def sigma(self):
+        return math.sqrt(1 / self.pi) if self.pi else inf
+
+    def __mul__(self, other):
+        pi, tau = self.pi + other.pi, self.tau + other.tau
+        return Gaussian(pi=pi, tau=tau)
+
+    def __truediv__(self, other):
+        pi, tau = self.pi - other.pi, self.tau - other.tau
+        return Gaussian(pi=pi, tau=tau)
+
+    __div__ = __truediv__  # for Python 2
+
+    def __eq__(self, other):
+        return self.pi == other.pi and self.tau == other.tau
+
+    def __lt__(self, other):
+        return self.mu < other.mu
+
+    def __le__(self, other):
+        return self.mu <= other.mu
+
+    def __gt__(self, other):
+        return self.mu > other.mu
+
+    def __ge__(self, other):
+        return self.mu >= other.mu
+
+    def __repr__(self):
+        return 'N(mu={:.3f}, sigma={:.3f})'.format(self.mu, self.sigma)
+
+    def _repr_latex_(self):
+        latex = r'\mathcal{{ N }}( {:.3f}, {:.3f}^2 )'.format(self.mu, self.sigma)
+        return '$%s$' % latex
+
+class Matrix(list):
+    def __init__(self, src, height=None, width=None):
+        if callable(src):
+            f, src = src, {}
+            size = [height, width]
+            if not height:
+                def set_height(height):
+                    size[0] = height
+                size[0] = set_height
+            if not width:
+                def set_width(width):
+                    size[1] = width
+                size[1] = set_width
+            try:
+                for (r, c), val in f(*size):
+                    src[r, c] = val
+            except TypeError:
+                raise TypeError('A callable src must return an interable '
+                                'which generates a tuple containing '
+                                'coordinate and value')
+            height, width = tuple(size)
+            if height is None or width is None:
+                raise TypeError('A callable src must call set_height and '
+                                'set_width if the size is non-deterministic')
+        if isinstance(src, list):
+            is_number = lambda x: isinstance(x, Number)
+            unique_col_sizes = set(map(len, src))
+            everything_are_number = filter(is_number, sum(src, []))
+            if len(unique_col_sizes) != 1 or not everything_are_number:
+                raise ValueError('src must be a rectangular array of numbers')
+            two_dimensional_array = src
+        elif isinstance(src, dict):
+            if not height or not width:
+                w = h = 0
+                for r, c in iterkeys(src):
+                    if not height:
+                        h = max(h, r + 1)
+                    if not width:
+                        w = max(w, c + 1)
+                if not height:
+                    height = h
+                if not width:
+                    width = w
+            two_dimensional_array = []
+            for r in range(height):
+                row = []
+                two_dimensional_array.append(row)
+                for c in range(width):
+                    row.append(src.get((r, c), 0))
+        else:
+            raise TypeError('src must be a list or dict or callable')
+        super(Matrix, self).__init__(two_dimensional_array)
+
+    @property
+    def height(self):
+        return len(self)
+
+    @property
+    def width(self):
+        return len(self[0])
+
+    def transpose(self):
+        height, width = self.height, self.width
+        src = {}
+        for c in range(width):
+            for r in range(height):
+                src[c, r] = self[r][c]
+        return type(self)(src, height=width, width=height)
+
+    def minor(self, row_n, col_n):
+        height, width = self.height, self.width
+        if not (0 <= row_n < height):
+            raise ValueError('row_n should be between 0 and %d' % height)
+        elif not (0 <= col_n < width):
+            raise ValueError('col_n should be between 0 and %d' % width)
+        two_dimensional_array = []
+        for r in range(height):
+            if r == row_n:
+                continue
+            row = []
+            two_dimensional_array.append(row)
+            for c in range(width):
+                if c == col_n:
+                    continue
+                row.append(self[r][c])
+        return type(self)(two_dimensional_array)
+
+    def determinant(self):
+        height, width = self.height, self.width
+        if height != width:
+            raise ValueError('Only square matrix can calculate a determinant')
+        tmp, rv = copy.deepcopy(self), 1.
+        for c in range(width - 1, 0, -1):
+            pivot, r = max((abs(tmp[r][c]), r) for r in range(c + 1))
+            pivot = tmp[r][c]
+            if not pivot:
+                return 0.
+            tmp[r], tmp[c] = tmp[c], tmp[r]
+            if r != c:
+                rv = -rv
+            rv *= pivot
+            fact = -1. / pivot
+            for r in range(c):
+                f = fact * tmp[r][c]
+                for x in range(c):
+                    tmp[r][x] += f * tmp[c][x]
+        return rv * tmp[0][0]
+
+    def adjugate(self):
+        height, width = self.height, self.width
+        if height != width:
+            raise ValueError('Only square matrix can be adjugated')
+        if height == 2:
+            a, b = self[0][0], self[0][1]
+            c, d = self[1][0], self[1][1]
+            return type(self)([[d, -b], [-c, a]])
+        src = {}
+        for r in range(height):
+            for c in range(width):
+                sign = -1 if (r + c) % 2 else 1
+                src[r, c] = self.minor(r, c).determinant() * sign
+        return type(self)(src, height, width)
+
+    def inverse(self):
+        if self.height == self.width == 1:
+            return type(self)([[1. / self[0][0]]])
+        return (1. / self.determinant()) * self.adjugate()
+
+    def __add__(self, other):
+        height, width = self.height, self.width
+        if (height, width) != (other.height, other.width):
+            raise ValueError('Must be same size')
+        src = {}
+        for r in range(height):
+            for c in range(width):
+                src[r, c] = self[r][c] + other[r][c]
+        return type(self)(src, height, width)
+
+    def __mul__(self, other):
+        if self.width != other.height:
+            raise ValueError('Bad size')
+        height, width = self.height, other.width
+        src = {}
+        for r in range(height):
+            for c in range(width):
+                src[r, c] = sum(self[r][x] * other[x][c]
+                                for x in range(self.width))
+        return type(self)(src, height, width)
+
+    def __rmul__(self, other):
+        if not isinstance(other, Number):
+            raise TypeError('The operand should be a number')
+        height, width = self.height, self.width
+        src = {}
+        for r in range(height):
+            for c in range(width):
+                src[r, c] = other * self[r][c]
+        return type(self)(src, height, width)
+
+    def __repr__(self):
+        return '{}({})'.format(type(self).__name__, super(Matrix, self).__repr__())
+
+    def _repr_latex_(self):
+        rows = [' && '.join(['%.3f' % cell for cell in row]) for row in self]
+        latex = r'\begin{matrix} %s \end{matrix}' % r'\\'.join(rows)
+        return '$%s$' % latex
+
+def _gen_erfcinv(erfc, math=math):
+    def erfcinv(y):
+        """The inverse function of erfc."""
+        if y >= 2:
+            return -100.
+        elif y <= 0:
+            return 100.
+        zero_point = y < 1
+        if not zero_point:
+            y = 2 - y
+        t = math.sqrt(-2 * math.log(y / 2.))
+        x = -0.70711 * \
+            ((2.30753 + t * 0.27061) / (1. + t * (0.99229 + t * 0.04481)) - t)
+        for i in range(2):
+            err = erfc(x) - y
+            x += err / (1.12837916709551257 * math.exp(-(x ** 2)) - x * err)
+        return x if zero_point else -x
+    return erfcinv
+
+def _gen_ppf(erfc, math=math):
+    erfcinv = _gen_erfcinv(erfc, math)
+    def ppf(x, mu=0, sigma=1):
+        return mu - sigma * math.sqrt(2) * erfcinv(2 * x)
+    return ppf
+
+def erfc(x):
+    z = abs(x)
+    t = 1. / (1. + z / 2.)
+    r = t * math.exp(-z * z - 1.26551223 + t * (1.00002368 + t * (
+        0.37409196 + t * (0.09678418 + t * (-0.18628806 + t * (
+            0.27886807 + t * (-1.13520398 + t * (1.48851587 + t * (
+                -0.82215223 + t * 0.17087277
+            )))
+        )))
+    )))
+    return 2. - r if x < 0 else r
+
+def cdf(x, mu=0, sigma=1):
+    return 0.5 * erfc(-(x - mu) / (sigma * math.sqrt(2)))
+
+
+def pdf(x, mu=0, sigma=1):
+    return (1 / math.sqrt(2 * math.pi) * abs(sigma) *
+            math.exp(-(((x - mu) / abs(sigma)) ** 2 / 2)))
+
+ppf = _gen_ppf(erfc)
+
+def choose_backend(backend):
+    if backend is None:  # fallback
+        return cdf, pdf, ppf
+    elif backend == 'mpmath':
+        try:
+            import mpmath
+        except ImportError:
+            raise ImportError('Install "mpmath" to use this backend')
+        return mpmath.ncdf, mpmath.npdf, _gen_ppf(mpmath.erfc, math=mpmath)
+    elif backend == 'scipy':
+        try:
+            from scipy.stats import norm
+        except ImportError:
+            raise ImportError('Install "scipy" to use this backend')
+        return norm.cdf, norm.pdf, norm.ppf
+    raise ValueError('%r backend is not defined' % backend)
+
+def available_backends():
+    backends = [None]
+    for backend in ['mpmath', 'scipy']:
+        try:
+            __import__(backend)
+        except ImportError:
+            continue
+        backends.append(backend)
+    return backends
+
+class Node(object):
+
+    pass
+
+class Variable(Node, Gaussian):
+
+    def __init__(self):
+        self.messages = {}
+        super(Variable, self).__init__()
+
+    def set(self, val):
+        delta = self.delta(val)
+        self.pi, self.tau = val.pi, val.tau
+        return delta
+
+    def delta(self, other):
+        pi_delta = abs(self.pi - other.pi)
+        if pi_delta == inf:
+            return 0.
+        return max(abs(self.tau - other.tau), math.sqrt(pi_delta))
+
+    def update_message(self, factor, pi=0, tau=0, message=None):
+        message = message or Gaussian(pi=pi, tau=tau)
+        old_message, self[factor] = self[factor], message
+        return self.set(self / old_message * message)
+
+    def update_value(self, factor, pi=0, tau=0, value=None):
+        value = value or Gaussian(pi=pi, tau=tau)
+        old_message = self[factor]
+        self[factor] = value * old_message / self
+        return self.set(value)
+
+    def __getitem__(self, factor):
+        return self.messages[factor]
+
+    def __setitem__(self, factor, message):
+        self.messages[factor] = message
+
+    def __repr__(self):
+        args = (type(self).__name__, super(Variable, self).__repr__(),
+                len(self.messages), '' if len(self.messages) == 1 else 's')
+        return '<%s %s with %d connection%s>' % args
+
+
+class Factor(Node):
+
+    def __init__(self, variables):
+        self.vars = variables
+        for var in variables:
+            var[self] = Gaussian()
+
+    def down(self):
+        return 0
+
+    def up(self):
+        return 0
+
+    @property
+    def var(self):
+        assert len(self.vars) == 1
+        return self.vars[0]
+
+    def __repr__(self):
+        args = (type(self).__name__, len(self.vars),
+                '' if len(self.vars) == 1 else 's')
+        return '<%s with %d connection%s>' % args
+
+
+class PriorFactor(Factor):
+
+    def __init__(self, var, val, dynamic=0):
+        super(PriorFactor, self).__init__([var])
+        self.val = val
+        self.dynamic = dynamic
+
+    def down(self):
+        sigma = math.sqrt(self.val.sigma ** 2 + self.dynamic ** 2)
+        value = Gaussian(self.val.mu, sigma)
+        return self.var.update_value(self, value=value)
+
+
+class LikelihoodFactor(Factor):
+
+    def __init__(self, mean_var, value_var, variance):
+        super(LikelihoodFactor, self).__init__([mean_var, value_var])
+        self.mean = mean_var
+        self.value = value_var
+        self.variance = variance
+
+    def calc_a(self, var):
+        return 1. / (1. + self.variance * var.pi)
+
+    def down(self):
+        # update value.
+        msg = self.mean / self.mean[self]
+        a = self.calc_a(msg)
+        return self.value.update_message(self, a * msg.pi, a * msg.tau)
+
+    def up(self):
+        # update mean.
+        msg = self.value / self.value[self]
+        a = self.calc_a(msg)
+        return self.mean.update_message(self, a * msg.pi, a * msg.tau)
+
+
+class SumFactor(Factor):
+
+    def __init__(self, sum_var, term_vars, coeffs):
+        super(SumFactor, self).__init__([sum_var] + term_vars)
+        self.sum = sum_var
+        self.terms = term_vars
+        self.coeffs = coeffs
+
+    def down(self):
+        vals = self.terms
+        msgs = [var[self] for var in vals]
+        return self.update(self.sum, vals, msgs, self.coeffs)
+
+    def up(self, index=0):
+        coeff = self.coeffs[index]
+        coeffs = []
+        for x, c in enumerate(self.coeffs):
+            try:
+                if x == index:
+                    coeffs.append(1. / coeff)
+                else:
+                    coeffs.append(-c / coeff)
+            except ZeroDivisionError:
+                coeffs.append(0.)
+        vals = self.terms[:]
+        vals[index] = self.sum
+        msgs = [var[self] for var in vals]
+        return self.update(self.terms[index], vals, msgs, coeffs)
+
+    def update(self, var, vals, msgs, coeffs):
+        pi_inv = 0
+        mu = 0
+        for val, msg, coeff in zip(vals, msgs, coeffs):
+            div = val / msg
+            mu += coeff * div.mu
+            if pi_inv == inf:
+                continue
+            try:
+                # numpy.float64 handles floating-point error by different way.
+                # For example, it can just warn RuntimeWarning on n/0 problem
+                # instead of throwing ZeroDivisionError.  So div.pi, the
+                # denominator has to be a built-in float.
+                pi_inv += coeff ** 2 / float(div.pi)
+            except ZeroDivisionError:
+                pi_inv = inf
+        pi = 1. / pi_inv
+        tau = pi * mu
+        return var.update_message(self, pi, tau)
+
+
+class TruncateFactor(Factor):
+
+    def __init__(self, var, v_func, w_func, draw_margin):
+        super(TruncateFactor, self).__init__([var])
+        self.v_func = v_func
+        self.w_func = w_func
+        self.draw_margin = draw_margin
+
+    def up(self):
+        val = self.var
+        msg = self.var[self]
+        div = val / msg
+        sqrt_pi = math.sqrt(div.pi)
+        args = (div.tau / sqrt_pi, self.draw_margin * sqrt_pi)
+        v = self.v_func(*args)
+        w = self.w_func(*args)
+        denom = (1. - w)
+        pi, tau = div.pi / denom, (div.tau + sqrt_pi * v) / denom
+        return val.update_value(self, pi, tau)
+
+#: Default initial mean of ratings.
+MU = 25.
+#: Default initial standard deviation of ratings.
+SIGMA = MU / 3
+#: Default distance that guarantees about 76% chance of winning.
+BETA = SIGMA / 2
+#: Default dynamic factor.
+TAU = SIGMA / 100
+#: Default draw probability of the game.
+DRAW_PROBABILITY = .10
+#: A basis to check reliability of the result.
+DELTA = 0.0001
+
+
+def calc_draw_probability(draw_margin, size, env=None):
+    if env is None:
+        env = global_env()
+    return 2 * env.cdf(draw_margin / (math.sqrt(size) * env.beta)) - 1
+
+
+def calc_draw_margin(draw_probability, size, env=None):
+    if env is None:
+        env = global_env()
+    return env.ppf((draw_probability + 1) / 2.) * math.sqrt(size) * env.beta
+
+
+def _team_sizes(rating_groups):
+    team_sizes = [0]
+    for group in rating_groups:
+        team_sizes.append(len(group) + team_sizes[-1])
+    del team_sizes[0]
+    return team_sizes
+
+
+def _floating_point_error(env):
+    if env.backend == 'mpmath':
+        msg = 'Set "mpmath.mp.dps" to higher'
+    else:
+        msg = 'Cannot calculate correctly, set backend to "mpmath"'
+    return FloatingPointError(msg)
+
+
+class Rating(Gaussian):
+    def __init__(self, mu=None, sigma=None):
+        if isinstance(mu, tuple):
+            mu, sigma = mu
+        elif isinstance(mu, Gaussian):
+            mu, sigma = mu.mu, mu.sigma
+        if mu is None:
+            mu = global_env().mu
+        if sigma is None:
+            sigma = global_env().sigma
+        super(Rating, self).__init__(mu, sigma)
+
+    def __int__(self):
+        return int(self.mu)
+
+    def __long__(self):
+        return long(self.mu)
+
+    def __float__(self):
+        return float(self.mu)
+
+    def __iter__(self):
+        return iter((self.mu, self.sigma))
+
+    def __repr__(self):
+        c = type(self)
+        args = ('.'.join([c.__module__, c.__name__]), self.mu, self.sigma)
+        return '%s(mu=%.3f, sigma=%.3f)' % args
+
+
+class TrueSkill(object):
+    def __init__(self, mu=MU, sigma=SIGMA, beta=BETA, tau=TAU,
+                 draw_probability=DRAW_PROBABILITY, backend=None):
+        self.mu = mu
+        self.sigma = sigma
+        self.beta = beta
+        self.tau = tau
+        self.draw_probability = draw_probability
+        self.backend = backend
+        if isinstance(backend, tuple):
+            self.cdf, self.pdf, self.ppf = backend
+        else:
+            self.cdf, self.pdf, self.ppf = choose_backend(backend)
+
+    def create_rating(self, mu=None, sigma=None):
+        if mu is None:
+            mu = self.mu
+        if sigma is None:
+            sigma = self.sigma
+        return Rating(mu, sigma)
+
+    def v_win(self, diff, draw_margin):
+        x = diff - draw_margin
+        denom = self.cdf(x)
+        return (self.pdf(x) / denom) if denom else -x
+
+    def v_draw(self, diff, draw_margin):
+        abs_diff = abs(diff)
+        a, b = draw_margin - abs_diff, -draw_margin - abs_diff
+        denom = self.cdf(a) - self.cdf(b)
+        numer = self.pdf(b) - self.pdf(a)
+        return ((numer / denom) if denom else a) * (-1 if diff < 0 else +1)
+
+    def w_win(self, diff, draw_margin):
+        x = diff - draw_margin
+        v = self.v_win(diff, draw_margin)
+        w = v * (v + x)
+        if 0 < w < 1:
+            return w
+        raise _floating_point_error(self)
+
+    def w_draw(self, diff, draw_margin):
+        abs_diff = abs(diff)
+        a, b = draw_margin - abs_diff, -draw_margin - abs_diff
+        denom = self.cdf(a) - self.cdf(b)
+        if not denom:
+            raise _floating_point_error(self)
+        v = self.v_draw(abs_diff, draw_margin)
+        return (v ** 2) + (a * self.pdf(a) - b * self.pdf(b)) / denom
+
+    def validate_rating_groups(self, rating_groups):
+        # check group sizes
+        if len(rating_groups) < 2:
+            raise ValueError('Need multiple rating groups')
+        elif not all(rating_groups):
+            raise ValueError('Each group must contain multiple ratings')
+        # check group types
+        group_types = set(map(type, rating_groups))
+        if len(group_types) != 1:
+            raise TypeError('All groups should be same type')
+        elif group_types.pop() is Rating:
+            raise TypeError('Rating cannot be a rating group')
+        # normalize rating_groups
+        if isinstance(rating_groups[0], dict):
+            dict_rating_groups = rating_groups
+            rating_groups = []
+            keys = []
+            for dict_rating_group in dict_rating_groups:
+                rating_group, key_group = [], []
+                for key, rating in iteritems(dict_rating_group):
+                    rating_group.append(rating)
+                    key_group.append(key)
+                rating_groups.append(tuple(rating_group))
+                keys.append(tuple(key_group))
+        else:
+            rating_groups = list(rating_groups)
+            keys = None
+        return rating_groups, keys
+
+    def validate_weights(self, weights, rating_groups, keys=None):
+        if weights is None:
+            weights = [(1,) * len(g) for g in rating_groups]
+        elif isinstance(weights, dict):
+            weights_dict, weights = weights, []
+            for x, group in enumerate(rating_groups):
+                w = []
+                weights.append(w)
+                for y, rating in enumerate(group):
+                    if keys is not None:
+                        y = keys[x][y]
+                    w.append(weights_dict.get((x, y), 1))
+        return weights
+
+    def factor_graph_builders(self, rating_groups, ranks, weights):
+        flatten_ratings = sum(map(tuple, rating_groups), ())
+        flatten_weights = sum(map(tuple, weights), ())
+        size = len(flatten_ratings)
+        group_size = len(rating_groups)
+        # create variables
+        rating_vars = [Variable() for x in range(size)]
+        perf_vars = [Variable() for x in range(size)]
+        team_perf_vars = [Variable() for x in range(group_size)]
+        team_diff_vars = [Variable() for x in range(group_size - 1)]
+        team_sizes = _team_sizes(rating_groups)
+        # layer builders
+        def build_rating_layer():
+            for rating_var, rating in zip(rating_vars, flatten_ratings):
+                yield PriorFactor(rating_var, rating, self.tau)
+        def build_perf_layer():
+            for rating_var, perf_var in zip(rating_vars, perf_vars):
+                yield LikelihoodFactor(rating_var, perf_var, self.beta ** 2)
+        def build_team_perf_layer():
+            for team, team_perf_var in enumerate(team_perf_vars):
+                if team > 0:
+                    start = team_sizes[team - 1]
+                else:
+                    start = 0
+                end = team_sizes[team]
+                child_perf_vars = perf_vars[start:end]
+                coeffs = flatten_weights[start:end]
+                yield SumFactor(team_perf_var, child_perf_vars, coeffs)
+        def build_team_diff_layer():
+            for team, team_diff_var in enumerate(team_diff_vars):
+                yield SumFactor(team_diff_var,
+                                team_perf_vars[team:team + 2], [+1, -1])
+        def build_trunc_layer():
+            for x, team_diff_var in enumerate(team_diff_vars):
+                if callable(self.draw_probability):
+                    # dynamic draw probability
+                    team_perf1, team_perf2 = team_perf_vars[x:x + 2]
+                    args = (Rating(team_perf1), Rating(team_perf2), self)
+                    draw_probability = self.draw_probability(*args)
+                else:
+                    # static draw probability
+                    draw_probability = self.draw_probability
+                size = sum(map(len, rating_groups[x:x + 2]))
+                draw_margin = calc_draw_margin(draw_probability, size, self)
+                if ranks[x] == ranks[x + 1]:  # is a tie?
+                    v_func, w_func = self.v_draw, self.w_draw
+                else:
+                    v_func, w_func = self.v_win, self.w_win
+                yield TruncateFactor(team_diff_var,
+                                     v_func, w_func, draw_margin)
+        # build layers
+        return (build_rating_layer, build_perf_layer, build_team_perf_layer,
+                build_team_diff_layer, build_trunc_layer)
+
+    def run_schedule(self, build_rating_layer, build_perf_layer,
+                     build_team_perf_layer, build_team_diff_layer,
+                     build_trunc_layer, min_delta=DELTA):
+        if min_delta <= 0:
+            raise ValueError('min_delta must be greater than 0')
+        layers = []
+        def build(builders):
+            layers_built = [list(build()) for build in builders]
+            layers.extend(layers_built)
+            return layers_built
+        # gray arrows
+        layers_built = build([build_rating_layer,
+                              build_perf_layer,
+                              build_team_perf_layer])
+        rating_layer, perf_layer, team_perf_layer = layers_built
+        for f in chain(*layers_built):
+            f.down()
+        # arrow #1, #2, #3
+        team_diff_layer, trunc_layer = build([build_team_diff_layer,
+                                              build_trunc_layer])
+        team_diff_len = len(team_diff_layer)
+        for x in range(10):
+            if team_diff_len == 1:
+                # only two teams
+                team_diff_layer[0].down()
+                delta = trunc_layer[0].up()
+            else:
+                # multiple teams
+                delta = 0
+                for x in range(team_diff_len - 1):
+                    team_diff_layer[x].down()
+                    delta = max(delta, trunc_layer[x].up())
+                    team_diff_layer[x].up(1)  # up to right variable
+                for x in range(team_diff_len - 1, 0, -1):
+                    team_diff_layer[x].down()
+                    delta = max(delta, trunc_layer[x].up())
+                    team_diff_layer[x].up(0)  # up to left variable
+            # repeat until to small update
+            if delta <= min_delta:
+                break
+        # up both ends
+        team_diff_layer[0].up(0)
+        team_diff_layer[team_diff_len - 1].up(1)
+        # up the remainder of the black arrows
+        for f in team_perf_layer:
+            for x in range(len(f.vars) - 1):
+                f.up(x)
+        for f in perf_layer:
+            f.up()
+        return layers
+
+    def rate(self, rating_groups, ranks=None, weights=None, min_delta=DELTA):
+        rating_groups, keys = self.validate_rating_groups(rating_groups)
+        weights = self.validate_weights(weights, rating_groups, keys)
+        group_size = len(rating_groups)
+        if ranks is None:
+            ranks = range(group_size)
+        elif len(ranks) != group_size:
+            raise ValueError('Wrong ranks')
+        # sort rating groups by rank
+        by_rank = lambda x: x[1][1]
+        sorting = sorted(enumerate(zip(rating_groups, ranks, weights)),
+                         key=by_rank)
+        sorted_rating_groups, sorted_ranks, sorted_weights = [], [], []
+        for x, (g, r, w) in sorting:
+            sorted_rating_groups.append(g)
+            sorted_ranks.append(r)
+            # make weights to be greater than 0
+            sorted_weights.append(max(min_delta, w_) for w_ in w)
+        # build factor graph
+        args = (sorted_rating_groups, sorted_ranks, sorted_weights)
+        builders = self.factor_graph_builders(*args)
+        args = builders + (min_delta,)
+        layers = self.run_schedule(*args)
+        # make result
+        rating_layer, team_sizes = layers[0], _team_sizes(sorted_rating_groups)
+        transformed_groups = []
+        for start, end in zip([0] + team_sizes[:-1], team_sizes):
+            group = []
+            for f in rating_layer[start:end]:
+                group.append(Rating(float(f.var.mu), float(f.var.sigma)))
+            transformed_groups.append(tuple(group))
+        by_hint = lambda x: x[0]
+        unsorting = sorted(zip((x for x, __ in sorting), transformed_groups),
+                           key=by_hint)
+        if keys is None:
+            return [g for x, g in unsorting]
+        # restore the structure with input dictionary keys
+        return [dict(zip(keys[x], g)) for x, g in unsorting]
+
+    def quality(self, rating_groups, weights=None):
+        rating_groups, keys = self.validate_rating_groups(rating_groups)
+        weights = self.validate_weights(weights, rating_groups, keys)
+        flatten_ratings = sum(map(tuple, rating_groups), ())
+        flatten_weights = sum(map(tuple, weights), ())
+        length = len(flatten_ratings)
+        # a vector of all of the skill means
+        mean_matrix = Matrix([[r.mu] for r in flatten_ratings])
+        # a matrix whose diagonal values are the variances (sigma ** 2) of each
+        # of the players.
+        def variance_matrix(height, width):
+            variances = (r.sigma ** 2 for r in flatten_ratings)
+            for x, variance in enumerate(variances):
+                yield (x, x), variance
+        variance_matrix = Matrix(variance_matrix, length, length)
+        # the player-team assignment and comparison matrix
+        def rotated_a_matrix(set_height, set_width):
+            t = 0
+            for r, (cur, _next) in enumerate(zip(rating_groups[:-1],
+                                                rating_groups[1:])):
+                for x in range(t, t + len(cur)):
+                    yield (r, x), flatten_weights[x]
+                    t += 1
+                x += 1
+                for x in range(x, x + len(_next)):
+                    yield (r, x), -flatten_weights[x]
+            set_height(r + 1)
+            set_width(x + 1)
+        rotated_a_matrix = Matrix(rotated_a_matrix)
+        a_matrix = rotated_a_matrix.transpose()
+        # match quality further derivation
+        _ata = (self.beta ** 2) * rotated_a_matrix * a_matrix
+        _atsa = rotated_a_matrix * variance_matrix * a_matrix
+        start = mean_matrix.transpose() * a_matrix
+        middle = _ata + _atsa
+        end = rotated_a_matrix * mean_matrix
+        # make result
+        e_arg = (-0.5 * start * middle.inverse() * end).determinant()
+        s_arg = _ata.determinant() / middle.determinant()
+        return math.exp(e_arg) * math.sqrt(s_arg)
+
+    def expose(self, rating):
+        k = self.mu / self.sigma
+        return rating.mu - k * rating.sigma
+
+    def make_as_global(self):
+        return setup(env=self)
+
+    def __repr__(self):
+        c = type(self)
+        if callable(self.draw_probability):
+            f = self.draw_probability
+            draw_probability = '.'.join([f.__module__, f.__name__])
+        else:
+            draw_probability = '%.1f%%' % (self.draw_probability * 100)
+        if self.backend is None:
+            backend = ''
+        elif isinstance(self.backend, tuple):
+            backend = ', backend=...'
+        else:
+            backend = ', backend=%r' % self.backend
+        args = ('.'.join([c.__module__, c.__name__]), self.mu, self.sigma,
+                self.beta, self.tau, draw_probability, backend)
+        return ('%s(mu=%.3f, sigma=%.3f, beta=%.3f, tau=%.3f, '
+                'draw_probability=%s%s)' % args)
+
+
+def rate_1vs1(rating1, rating2, drawn=False, min_delta=DELTA, env=None):
+    if env is None:
+        env = global_env()
+    ranks = [0, 0 if drawn else 1]
+    teams = env.rate([(rating1,), (rating2,)], ranks, min_delta=min_delta)
+    return teams[0][0], teams[1][0]
+
+
+def quality_1vs1(rating1, rating2, env=None):
+    if env is None:
+        env = global_env()
+    return env.quality([(rating1,), (rating2,)])
+
+
+def global_env():
+    try:
+        global_env.__trueskill__
+    except AttributeError:
+        # setup the default environment
+        setup()
+    return global_env.__trueskill__
+
+
+def setup(mu=MU, sigma=SIGMA, beta=BETA, tau=TAU,
+          draw_probability=DRAW_PROBABILITY, backend=None, env=None):
+    if env is None:
+        env = TrueSkill(mu, sigma, beta, tau, draw_probability, backend)
+    global_env.__trueskill__ = env
+    return env
+
+
+def rate(rating_groups, ranks=None, weights=None, min_delta=DELTA):
+    return global_env().rate(rating_groups, ranks, weights, min_delta)
+
+
+def quality(rating_groups, weights=None):
+    return global_env().quality(rating_groups, weights)
+
+
+def expose(rating):
+    return global_env().expose(rating)

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

@@ -0,0 +1,34 @@
+# Titan Robotics Team 2022: Visualization Module
+# Written by Arthur Lu & Jacob Levine
+# Notes:
+#    this should be imported as a python module using 'import visualization'
+#    this should be included in the local directory or environment variable
+#    fancy
+# setup:
+
+__version__ = "1.0.0.000"
+
+#changelog should be viewed using print(analysis.__changelog__)
+__changelog__ = """changelog:
+    1.0.0.000:
+        - created visualization.py
+        - added graphloss()
+        - added imports
+"""
+
+__author__ = (
+    "Arthur Lu <arthurlu@ttic.edu>,"
+    "Jacob Levine <jlevine@ttic.edu>,"
+    )
+
+__all__ = [
+    'graphloss',
+    ]
+
+import matplotlib.pyplot as plt
+
+def graphloss(losses):
+
+    x = range(0, len(losses))
+    plt.plot(x, losses)
+    plt.show()

analysis-master/setup.py

@@ -0,0 +1,27 @@
+import setuptools
+
+setuptools.setup(
+    name="analysis", # Replace with your own username
+    version="1.0.0.008",
+    author="The Titan Scouting Team",
+    author_email="titanscout2022@gmail.com",
+    description="analysis package developed by Titan Scouting for The Red Alliance",
+    long_description="",
+    long_description_content_type="text/markdown",
+    url="https://github.com/titanscout2022/tr2022-strategy",
+    packages=setuptools.find_packages(),
+    install_requires=[
+        "numba",
+        "numpy",
+        "scipy",
+        "scikit-learn",
+        "six",
+        "matplotlib"
+    ],
+    license = "GNU General Public License v3.0",
+    classifiers=[
+        "Programming Language :: Python :: 3",
+        "Operating System :: OS Independent",
+    ],
+    python_requires='>=3.6',
+)

data analysis/config/competition.config

@@ -0,0 +1 @@
+2020ilch

data analysis/config/stats.config

@@ -0,0 +1,14 @@
+balls-blocked,basic_stats,historical_analysis,regression_linear,regression_logarithmic,regression_exponential,regression_polynomial,regression_sigmoidal
+balls-collected,basic_stats,historical_analysis,regression_linear,regression_logarithmic,regression_exponential,regression_polynomial,regression_sigmoidal
+balls-lower-teleop,basic_stats,historical_analysis,regression_linear,regression_logarithmic,regression_exponential,regression_polynomial,regression_sigmoidal
+balls-lower-auto,basic_stats,historical_analysis,regression_linear,regression_logarithmic,regression_exponential,regression_polynomial,regression_sigmoidal
+balls-started,basic_stats,historical_analyss,regression_linear,regression_logarithmic,regression_exponential,regression_polynomial,regression_sigmoidal
+balls-upper-teleop,basic_stats,historical_analysis,regression_linear,regression_logarithmic,regression_exponential,regression_polynomial,regression_sigmoidal
+balls-upper-auto,basic_stats,historical_analysis,regression_linear,regression_logarithmic,regression_exponential,regression_polynomial,regression_sigmoidal
+wheel-mechanism
+low-balls
+high-balls
+wheel-success
+strategic-focus
+climb-mechanism
+attitude

data analysis/data.py

@@ -0,0 +1,102 @@
+import requests
+import pymongo
+import pandas as pd
+import time
+
+def pull_new_tba_matches(apikey, competition, cutoff):
+    api_key= apikey 
+    x=requests.get("https://www.thebluealliance.com/api/v3/event/"+competition+"/matches/simple", headers={"X-TBA-Auth_Key":api_key})
+    out = []
+    for i in x.json():
+        if (i["actual_time"] != None and i["actual_time"]-cutoff >= 0 and i["comp_level"] == "qm"):
+            out.append({"match" : i['match_number'], "blue" : list(map(lambda x: int(x[3:]), i['alliances']['blue']['team_keys'])), "red" : list(map(lambda x: int(x[3:]), i['alliances']['red']['team_keys'])), "winner": i["winning_alliance"]})
+    return out
+
+def get_team_match_data(apikey, competition, team_num):
+    client = pymongo.MongoClient(apikey)
+    db = client.data_scouting
+    mdata = db.matchdata
+    out = {}
+    for i in mdata.find({"competition" : competition, "team_scouted": team_num}):
+        out[i['match']] = i['data']
+    return pd.DataFrame(out)
+
+def get_team_pit_data(apikey, competition, team_num):
+    client = pymongo.MongoClient(apikey)
+    db = client.data_scouting
+    mdata = db.pitdata
+    out = {}
+    return mdata.find_one({"competition" : competition, "team_scouted": team_num})["data"]
+
+def get_team_metrics_data(apikey, competition, team_num):
+    client = pymongo.MongoClient(apikey)
+    db = client.data_processing
+    mdata = db.team_metrics
+    return mdata.find_one({"competition" : competition, "team": team_num})
+
+def unkeyify_2l(layered_dict):
+    out = {}
+    for i in layered_dict.keys():
+        add = []
+        sortkey = []
+        for j in layered_dict[i].keys():
+            add.append([j,layered_dict[i][j]])
+        add.sort(key = lambda x: x[0])
+        out[i] = list(map(lambda x: x[1], add))
+    return out
+
+def get_match_data_formatted(apikey, competition):
+    client = pymongo.MongoClient(apikey)
+    db = client.data_scouting
+    mdata = db.teamlist
+    x=mdata.find_one({"competition":competition})
+    out = {}
+    for i in x:
+        try:
+            out[int(i)] = unkeyify_2l(get_team_match_data(apikey, competition, int(i)).transpose().to_dict())
+        except:
+            pass
+    return out
+
+def get_pit_data_formatted(apikey, competition):
+    client = pymongo.MongoClient(apikey)
+    db = client.data_scouting
+    mdata = db.teamlist
+    x=mdata.find_one({"competition":competition})
+    out = {}
+    for i in x:
+        try:
+            out[int(i)] = get_team_pit_data(apikey, competition, int(i))
+        except:
+            pass
+    return out
+
+def push_team_tests_data(apikey, competition, team_num, data, dbname = "data_processing", colname = "team_tests"):
+    client = pymongo.MongoClient(apikey)
+    db = client[dbname]
+    mdata = db[colname]
+    mdata.replace_one({"competition" : competition, "team": team_num}, {"_id": competition+str(team_num)+"am", "competition" : competition, "team" : team_num, "data" : data}, True)
+
+def push_team_metrics_data(apikey, competition, team_num, data, dbname = "data_processing", colname = "team_metrics"):
+    client = pymongo.MongoClient(apikey)
+    db = client[dbname]
+    mdata = db[colname]
+    mdata.replace_one({"competition" : competition, "team": team_num}, {"_id": competition+str(team_num)+"am", "competition" : competition, "team" : team_num, "metrics" : data}, True)
+
+def push_team_pit_data(apikey, competition, variable, data, dbname = "data_processing", colname = "team_pit"):
+    client = pymongo.MongoClient(apikey)
+    db = client[dbname]
+    mdata = db[colname]
+    mdata.replace_one({"competition" : competition, "variable": variable}, {"competition" : competition, "variable" : variable, "data" : data}, True)
+
+def get_analysis_flags(apikey, flag):
+    client = pymongo.MongoClient(apikey)
+    db = client.data_processing
+    mdata = db.flags
+    return mdata.find_one({flag:{"$exists":True}})
+
+def set_analysis_flags(apikey, flag, data):
+    client = pymongo.MongoClient(apikey)
+    db = client.data_processing
+    mdata = db.flags
+    return mdata.replace_one({flag:{"$exists":True}}, data, True)

data analysis/get_team_rankings.py

@@ -0,0 +1,59 @@
+import data as d
+from analysis import analysis as an
+import pymongo
+import operator
+
+def load_config(file):
+    config_vector = {}
+    file = an.load_csv(file)
+    for line in file[1:]:
+        config_vector[line[0]] = line[1:]
+
+    return (file[0][0], config_vector)
+
+def get_metrics_processed_formatted(apikey, competition):
+    client = pymongo.MongoClient(apikey)
+    db = client.data_scouting
+    mdata = db.teamlist
+    x=mdata.find_one({"competition":competition})
+    out = {}
+    for i in x:
+        try:
+            out[int(i)] = d.get_team_metrics_data(apikey, competition, int(i))
+        except:
+            pass
+    return out
+
+def main():
+
+    apikey = an.load_csv("keys.txt")[0][0]
+    tbakey = an.load_csv("keys.txt")[1][0]
+
+    competition, config = load_config("config.csv")
+
+    metrics = get_metrics_processed_formatted(apikey, competition)
+
+    elo = {}
+    gl2 = {}
+
+    for team in metrics:
+
+        elo[team] = metrics[team]["metrics"]["elo"]["score"]
+        gl2[team] = metrics[team]["metrics"]["gl2"]["score"]
+
+    elo = {k: v for k, v in sorted(elo.items(), key=lambda item: item[1])}
+    gl2 = {k: v for k, v in sorted(gl2.items(), key=lambda item: item[1])}
+
+    for team in elo:
+
+        print("teams sorted by elo:")
+        print("" + str(team) + " | " + str(elo[team]))
+
+    print("*"*25)
+
+    for team in gl2:
+
+        print("teams sorted by glicko2:")
+        print("" + str(team) + " | " + str(gl2[team]))
+
+main()

data analysis/superscript.py

@@ -0,0 +1,374 @@
+# Titan Robotics Team 2022: Superscript Script
+# Written by Arthur Lu & Jacob Levine
+# Notes:
+# setup:
+
+__version__ = "0.0.5.000"
+
+# changelog should be viewed using print(analysis.__changelog__)
+__changelog__ = """changelog:
+    0.0.5.000:
+        improved user interface
+    0.0.4.002:
+        - removed unessasary code
+    0.0.4.001:
+        - fixed bug where X range for regression was determined before sanitization
+        - better sanitized data
+    0.0.4.000:
+        - fixed spelling issue in __changelog__
+        - addressed nan bug in regression
+        - fixed errors on line 335 with metrics calling incorrect key "glicko2"
+        - fixed errors in metrics computing 
+    0.0.3.000:
+        - added analysis to pit data
+    0.0.2.001:
+        - minor stability patches
+        - implemented db syncing for timestamps
+        - fixed bugs
+    0.0.2.000:
+        - finalized testing and small fixes
+    0.0.1.004:
+        - finished metrics implement, trueskill is bugged
+    0.0.1.003:
+        - working
+    0.0.1.002:
+        - started implement of metrics
+    0.0.1.001:
+        - cleaned up imports
+    0.0.1.000:
+        - tested working, can push to database
+    0.0.0.009:
+        - tested working
+        - prints out stats for the time being, will push to database later
+    0.0.0.008:
+        - added data import
+        - removed tba import
+        - finished main method
+    0.0.0.007:
+        - added load_config
+        - optimized simpleloop for readibility
+        - added __all__ entries
+        - added simplestats engine
+        - pending testing
+    0.0.0.006:
+        - fixes
+    0.0.0.005:
+        - imported pickle
+        - created custom database object
+    0.0.0.004:
+        - fixed simpleloop to actually return a vector
+    0.0.0.003:
+        - added metricsloop which is unfinished
+    0.0.0.002:
+        - added simpleloop which is untested until data is provided
+    0.0.0.001:
+        - created script
+        - added analysis, numba, numpy imports
+"""
+
+__author__ = (
+    "Arthur Lu <learthurgo@gmail.com>",
+    "Jacob Levine <jlevine@imsa.edu>",
+)
+
+__all__ = [
+    "main", 
+    "load_config",
+    "simpleloop",
+    "simplestats",
+    "metricsloop"
+]
+
+# imports:
+
+from analysis import analysis as an
+import data as d
+import numpy as np
+import matplotlib.pyplot as plt
+from os import system, name
+from pathlib import Path
+import time
+import warnings
+
+def main():
+    warnings.filterwarnings("ignore")
+    while(True):
+
+        current_time = time.time()
+        print("[OK] time: " + str(current_time))
+
+        start = time.time()
+        config = load_config(Path("config/stats.config"))
+        competition = an.load_csv(Path("config/competition.config"))[0][0]
+        print("[OK] configs loaded")
+
+        apikey = an.load_csv(Path("config/keys.config"))[0][0]
+        tbakey = an.load_csv(Path("config/keys.config"))[1][0]
+        print("[OK] loaded keys")
+
+        previous_time = d.get_analysis_flags(apikey, "latest_update")
+
+        if(previous_time == None):
+
+            d.set_analysis_flags(apikey, "latest_update", 0)
+            previous_time = 0
+
+        else:
+
+            previous_time = previous_time["latest_update"]
+
+        print("[OK] analysis backtimed to: " + str(previous_time))
+
+        print("[OK] loading data")
+        start = time.time()
+        data = d.get_match_data_formatted(apikey, competition)
+        pit_data = d.pit = d.get_pit_data_formatted(apikey, competition)
+        print("[OK] loaded data in " + str(time.time() - start) + " seconds")
+
+        print("[OK] running tests")
+        start = time.time()
+        results = simpleloop(data, config)
+        print("[OK] finished tests in " + str(time.time() - start) + " seconds")
+
+        print("[OK] running metrics")
+        start = time.time()
+        metricsloop(tbakey, apikey, competition, previous_time)
+        print("[OK] finished metrics in " + str(time.time() - start) + " seconds")
+
+        print("[OK] running pit analysis")
+        start = time.time()
+        pit = pitloop(pit_data, config)
+        print("[OK] finished pit analysis in " + str(time.time() - start) + " seconds")
+
+        d.set_analysis_flags(apikey, "latest_update", {"latest_update":current_time})
+        
+        print("[OK] pushing to database")
+        start = time.time()
+        push_to_database(apikey, competition, results, pit)
+        print("[OK] pushed to database in " + str(time.time() - start) + " seconds")
+
+        clear()
+
+def clear(): 
+    
+    # for windows 
+    if name == 'nt': 
+        _ = system('cls') 
+  
+    # for mac and linux(here, os.name is 'posix') 
+    else: 
+        _ = system('clear')
+
+def load_config(file):
+    config_vector = {}
+    file = an.load_csv(file)
+    for line in file:
+        config_vector[line[0]] = line[1:]
+
+    return config_vector
+
+def simpleloop(data, tests): # expects 3D array with [Team][Variable][Match]
+
+    return_vector = {}
+    for team in data:
+        variable_vector = {}
+        for variable in data[team]:
+            test_vector = {}
+            variable_data = data[team][variable]
+            if(variable in tests):
+                for test in tests[variable]:
+                    test_vector[test] = simplestats(variable_data, test)
+            else:
+                pass      
+            variable_vector[variable] = test_vector
+        return_vector[team] = variable_vector
+
+    return return_vector
+
+def simplestats(data, test):
+
+    data = np.array(data)
+    data = data[np.isfinite(data)]
+    ranges = list(range(len(data)))
+
+    if(test == "basic_stats"):
+        return an.basic_stats(data)
+
+    if(test == "historical_analysis"):
+        return an.histo_analysis([ranges, data])
+
+    if(test == "regression_linear"):
+        return an.regression(ranges, data, ['lin'])
+
+    if(test == "regression_logarithmic"):
+        return an.regression(ranges, data, ['log'])
+
+    if(test == "regression_exponential"):
+        return an.regression(ranges, data, ['exp'])
+
+    if(test == "regression_polynomial"):
+        return an.regression(ranges, data, ['ply'])
+
+    if(test == "regression_sigmoidal"):
+        return an.regression(ranges, data, ['sig'])
+
+def push_to_database(apikey, competition, results, pit):
+
+    for team in results:
+
+        d.push_team_tests_data(apikey, competition, team, results[team])
+
+    for variable in pit:
+
+        d.push_team_pit_data(apikey, competition, variable, pit[variable])
+
+def metricsloop(tbakey, apikey, competition, timestamp): # listener based metrics update
+
+    elo_N = 400
+    elo_K = 24
+
+    matches = d.pull_new_tba_matches(tbakey, competition, timestamp)
+
+    red = {}
+    blu = {}
+
+    for match in matches:
+
+        red = load_metrics(apikey, competition, match, "red")
+        blu = load_metrics(apikey, competition, match, "blue")
+ 
+        elo_red_total = 0
+        elo_blu_total = 0
+
+        gl2_red_score_total = 0
+        gl2_blu_score_total = 0
+
+        gl2_red_rd_total = 0
+        gl2_blu_rd_total = 0
+
+        gl2_red_vol_total = 0
+        gl2_blu_vol_total = 0
+
+        for team in red:
+
+            elo_red_total += red[team]["elo"]["score"]
+
+            gl2_red_score_total += red[team]["gl2"]["score"]
+            gl2_red_rd_total += red[team]["gl2"]["rd"]
+            gl2_red_vol_total += red[team]["gl2"]["vol"]
+
+        for team in blu:
+
+            elo_blu_total += blu[team]["elo"]["score"]
+
+            gl2_blu_score_total += blu[team]["gl2"]["score"]
+            gl2_blu_rd_total += blu[team]["gl2"]["rd"]
+            gl2_blu_vol_total += blu[team]["gl2"]["vol"]
+
+        red_elo = {"score": elo_red_total / len(red)}
+        blu_elo = {"score": elo_blu_total / len(blu)}
+
+        red_gl2 = {"score": gl2_red_score_total / len(red), "rd": gl2_red_rd_total / len(red), "vol": gl2_red_vol_total / len(red)}
+        blu_gl2 = {"score": gl2_blu_score_total / len(blu), "rd": gl2_blu_rd_total / len(blu), "vol": gl2_blu_vol_total / len(blu)}
+
+
+        if(match["winner"] == "red"):
+
+            observations = {"red": 1, "blu": 0}
+
+        elif(match["winner"] == "blue"):
+
+            observations = {"red": 0, "blu": 1}
+
+        else:
+
+            observations = {"red": 0.5, "blu": 0.5}
+
+        red_elo_delta = an.elo(red_elo["score"], blu_elo["score"], observations["red"], elo_N, elo_K) - red_elo["score"]
+        blu_elo_delta = an.elo(blu_elo["score"], red_elo["score"], observations["blu"], elo_N, elo_K) - blu_elo["score"]
+
+        new_red_gl2_score, new_red_gl2_rd, new_red_gl2_vol = an.glicko2(red_gl2["score"], red_gl2["rd"], red_gl2["vol"], [blu_gl2["score"]], [blu_gl2["rd"]], [observations["red"], observations["blu"]])
+        new_blu_gl2_score, new_blu_gl2_rd, new_blu_gl2_vol = an.glicko2(blu_gl2["score"], blu_gl2["rd"], blu_gl2["vol"], [red_gl2["score"]], [red_gl2["rd"]], [observations["blu"], observations["red"]])
+
+        red_gl2_delta = {"score": new_red_gl2_score - red_gl2["score"], "rd": new_red_gl2_rd - red_gl2["rd"], "vol": new_red_gl2_vol - red_gl2["vol"]}
+        blu_gl2_delta = {"score": new_blu_gl2_score - blu_gl2["score"], "rd": new_blu_gl2_rd - blu_gl2["rd"], "vol": new_blu_gl2_vol - blu_gl2["vol"]}
+
+        for team in red:
+
+            red[team]["elo"]["score"] = red[team]["elo"]["score"] + red_elo_delta
+
+            red[team]["gl2"]["score"] = red[team]["gl2"]["score"] + red_gl2_delta["score"]
+            red[team]["gl2"]["rd"] = red[team]["gl2"]["rd"] + red_gl2_delta["rd"]
+            red[team]["gl2"]["vol"] = red[team]["gl2"]["vol"] + red_gl2_delta["vol"]
+
+        for team in blu:
+
+            blu[team]["elo"]["score"] = blu[team]["elo"]["score"] + blu_elo_delta
+
+            blu[team]["gl2"]["score"] = blu[team]["gl2"]["score"] + blu_gl2_delta["score"]
+            blu[team]["gl2"]["rd"] = blu[team]["gl2"]["rd"] + blu_gl2_delta["rd"]
+            blu[team]["gl2"]["vol"] = blu[team]["gl2"]["vol"] + blu_gl2_delta["vol"]
+
+        temp_vector = {}
+        temp_vector.update(red)
+        temp_vector.update(blu)
+
+        for team in temp_vector:
+
+            d.push_team_metrics_data(apikey, competition, team, temp_vector[team])
+
+def load_metrics(apikey, competition, match, group_name):
+
+    group = {}
+
+    for team in match[group_name]:
+
+        db_data = d.get_team_metrics_data(apikey, competition, team)
+
+        if d.get_team_metrics_data(apikey, competition, team) == None:
+
+            elo = {"score": 1500}
+            gl2 = {"score": 1500, "rd": 250, "vol": 0.06}
+            ts = {"mu": 25, "sigma": 25/3}
+
+            #d.push_team_metrics_data(apikey, competition, team, {"elo":elo, "gl2":gl2,"trueskill":ts})
+
+            group[team] = {"elo": elo, "gl2": gl2, "ts": ts}
+
+        else:
+
+            metrics = db_data["metrics"]
+
+            elo = metrics["elo"]
+            gl2 = metrics["gl2"]
+            ts = metrics["ts"]
+
+            group[team] = {"elo": elo, "gl2": gl2, "ts": ts}
+
+    return group
+
+def pitloop(pit, tests):
+
+    return_vector = {}
+    for team in pit:
+        for variable in pit[team]:
+            if(variable in tests):
+                if(not variable in return_vector):
+                    return_vector[variable] = []
+                return_vector[variable].append(pit[team][variable])
+
+    return return_vector
+
+main()
+
+"""
+Metrics Defaults:
+
+elo starting score = 1500
+elo N = 400
+elo K = 24
+
+gl2 starting score = 1500
+gl2 starting rd = 350
+gl2 starting vol = 0.06
+"""

data analysis/visualize_pit.py

@@ -0,0 +1,59 @@
+# To add a new cell, type '# %%'
+# To add a new markdown cell, type '# %% [markdown]'
+# %%
+import matplotlib.pyplot as plt
+import data as d
+import pymongo
+
+
+# %%
+def get_pit_variable_data(apikey, competition):
+    client = pymongo.MongoClient(apikey)
+    db = client.data_processing
+    mdata = db.team_pit
+    out = {}
+    return mdata.find()
+
+
+# %%
+def get_pit_variable_formatted(apikey, competition):
+    temp = get_pit_variable_data(apikey, competition)
+    out = {}
+    for i in temp:
+        out[i["variable"]] = i["data"]
+    return out
+
+
+# %%
+pit = get_pit_variable_formatted("mongodb+srv://api-user-new:titanscout2022@2022-scouting-4vfuu.mongodb.net/test?authSource=admin&replicaSet=2022-scouting-shard-0&readPreference=primary&appname=MongoDB%20Compass&ssl=true", "2020ilch")
+
+
+# %%
+import matplotlib.pyplot as plt
+import numpy as np
+
+
+# %%
+fig, ax = plt.subplots(1, len(pit), sharey=True, figsize=(80,15))
+
+i = 0
+
+for variable in pit:
+
+    ax[i].hist(pit[variable])
+    ax[i].invert_xaxis()
+
+    ax[i].set_xlabel('')
+    ax[i].set_ylabel('Frequency')
+    ax[i].set_title(variable)
+
+    plt.yticks(np.arange(len(pit[variable])))
+
+    i+=1
+
+plt.show()
+
+
+# %%
+
+