tra-analysis/data analysis/analysis/analysis.py

# Titan Robotics Team 2022: Data Analysis Module
# Written by Arthur Lu & Jacob Levine
# Notes:
#    this should be imported as a python module using 'import analysis'
#    this should be included in the local directory or environment variable
#    this module has been optimized for multhreaded computing
#    current benchmark of optimization: 1.33 times faster
# setup:

__version__ = "1.1.9.002"

# changelog should be viewed using print(analysis.__changelog__)
__changelog__ = """changelog:
    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__ = [
    '_init_device',
    'load_csv',
    'basic_stats',
    'z_score',
    'z_normalize',
    'histo_analysis',
    'regression',
    'elo',
    'gliko2',
    'trueskill',
    'r_squared',
    'mse',
    'rms',
    'kmeans',
    'pca',
    'decisiontree',
    'knn',
    'NaiveBayes',
    'SVM',
    'Regression',
    'Gliko2',
    # 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 math
try:
    from analysis import trueskill as Trueskill
except:
    import trueskill as Trueskill
import sklearn
from sklearn import *
import torch

class error(ValueError):
    pass

def _init_device():  # initiates computation device for ANNs
    device = 'cuda:0' if torch.cuda.is_available() else 'cpu'
    return device

@jit(forceobj=True)
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)

    return _mean, _median, _stdev, _variance

# 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):

    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]

@jit(forceobj=True)
def regression(device, inputs, outputs, args, loss = torch.nn.MSELoss(), _iterations = 10000, lr = 0.01, _iterations_ply = 10000, lr_ply = 0.01, power_limit = None): # inputs, outputs expects N-D array 

    if power_limit == None:
        power_limit = len(outputs)
    else:
        power_limit += 1

    regressions = []
    Regression.set_device(device)

    if 'lin' in args:

        model = Regression.SGDTrain(Regression.LinearRegKernel(len(inputs)), torch.tensor(inputs).to(torch.float).to(device), torch.tensor([outputs]).to(torch.float).to(device), iterations=_iterations, learning_rate=lr, return_losses=True)
        regressions.append((model[0].parameters, model[1][::-1][0]))

    if 'log' in args:

        model = Regression.SGDTrain(Regression.LogRegKernel(len(inputs)), torch.tensor(inputs).to(torch.float).to(device), torch.tensor(outputs).to(torch.float).to(device), iterations=_iterations, learning_rate=lr, return_losses=True)
        regressions.append((model[0].parameters, model[1][::-1][0]))

    if 'exp' in args:

        model = Regression.SGDTrain(Regression.ExpRegKernel(len(inputs)), torch.tensor(inputs).to(torch.float).to(device), torch.tensor(outputs).to(torch.float).to(device), iterations=_iterations, learning_rate=lr, return_losses=True)
        regressions.append((model[0].parameters, model[1][::-1][0]))

    if 'ply' in args:

        plys = []

        for i in range(2, power_limit):

            model = Regression.SGDTrain(Regression.PolyRegKernel(len(inputs),i), torch.tensor(inputs).to(torch.float).to(device), torch.tensor(outputs).to(torch.float).to(device), iterations=_iterations_ply * 10 ** i, learning_rate=lr_ply * 10 ** -i, return_losses=True)
            plys.append((model[0].parameters, model[1][::-1][0]))
        
        regressions.append(plys)

    if 'sig' in args:

        model = Regression.SGDTrain(Regression.SigmoidalRegKernelArthur(len(inputs)), torch.tensor(inputs).to(torch.float).to(device), torch.tensor(outputs).to(torch.float).to(device), iterations=_iterations, learning_rate=lr, return_losses=True)
        regressions.append((model[0].parameters, model[1][::-1][0]))

    return regressions

@jit(nopython=True)
def elo(starting_score, opposing_scores, observed, N, K):

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

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

@jit(forceobj=True)
def gliko2(starting_score, starting_rd, starting_vol, opposing_scores, opposing_rd, observations):

    player = Gliko2(rating = starting_score, rd = starting_rd, vol = starting_vol)

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

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

@jit(forceobj=True)
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:
            if player != None:
                player = Trueskill.Rating(player[0], player[1])
                team_temp.append(player)
            else:
                player = Trueskill.Rating()
                team_temp.append(player)
        team_ratings.append(team_temp)

    return Trueskill.rate(teams_data, observations)

@jit(forceobj=True)
def r_squared(predictions, targets):  # assumes equal size inputs

    return sklearn.metrics.r2_score(np.array(targets), np.array(predictions))

@jit(forceobj=True)
def mse(predictions, targets):

    return sklearn.metrics.mean_squared_error(np.array(targets), np.array(predictions))

@jit(forceobj=True)
def rms(predictions, targets):

    return math.sqrt(sklearn.metrics.mean_squared_error(np.array(targets), np.array(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)

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

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)

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)
    cm = sklearn.metrics.confusion_matrix(labels_test, predictions)
    cr = sklearn.metrics.classification_report(labels_test, predictions)

    return model, cm, cr

def knn(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)
    cm = sklearn.metrics.confusion_matrix(labels_test, predictions)
    cr = sklearn.metrics.classification_report(labels_test, predictions)

    return model, cm, cr

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)
        cm = sklearn.metrics.confusion_matrix(labels_test, predictions)
        cr = sklearn.metrics.classification_report(labels_test, predictions)

        return model, cm, cr

    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)
        cm = sklearn.metrics.confusion_matrix(labels_test, predictions)
        cr = sklearn.metrics.classification_report(labels_test, predictions)

        return model, cm, cr

    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)
        cm = sklearn.metrics.confusion_matrix(labels_test, predictions)
        cr = sklearn.metrics.classification_report(labels_test, predictions)

        return model, cm, cr

    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)
        cm = sklearn.metrics.confusion_matrix(labels_test, predictions)
        cr = sklearn.metrics.classification_report(labels_test, predictions)

        return model, cm, cr

class SVM:

    class CustomKernel:

        def __new__(self, 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__(self, 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__(self):

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

        class Polynomial:

            def __new__(self, power, r_bias):

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

        class RBF:

            def __new__(self, gamma):

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

        class Sigmoid:

            def __new__(self, 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)
        cm = sklearn.metrics.confusion_matrix(predictions, predictions)
        cr = sklearn.metrics.classification_report(predictions, predictions)

        return cm, cr

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

        predictions = kernel.predict(test_data)
        r_2 = r_squared(predictions, test_outputs)
        _mse = mse(predictions, test_outputs)
        _rms = rms(predictions, test_outputs)

        return r_2, _mse, _rms

class Regression:

    # 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__ = "1.0.0.002"

    # changelog should be viewed using print(analysis.regression.__changelog__)
    __changelog__ = """
    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'
    ]

    device = "cuda:0" if torch.torch.cuda.is_available() else "cpu"

    #todo: document completely

    def set_device(new_device):
        global 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(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(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

class Gliko2:

    _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()