From dad195a00f95559f905165357f5c32063da1cccc Mon Sep 17 00:00:00 2001
From: Arthur Lu <learthurgo@gmail.com>
Date: Tue, 9 Nov 2021 22:52:04 +0000
Subject: [PATCH 1/4] fixed/optimized imports, fixed headers

Signed-off-by: Arthur Lu <learthurgo@gmail.com>
---
 analysis-master/tra_analysis/Analysis.py      | 24 ++++---------------
 .../tra_analysis/ClassificationMetric.py      |  5 ++--
 .../tra_analysis/CorrelationTest.py           |  5 ++--
 analysis-master/tra_analysis/KNN.py           |  5 ++--
 analysis-master/tra_analysis/NaiveBayes.py    |  7 +++---
 analysis-master/tra_analysis/RandomForest.py  |  7 +++---
 .../tra_analysis/RegressionMetric.py          |  5 ++--
 analysis-master/tra_analysis/SVM.py           |  5 ++--
 analysis-master/tra_analysis/Sort.py          |  2 +-
 .../tra_analysis/StatisticalTest.py           |  9 +++----
 analysis-master/tra_analysis/__init__.py      |  3 +++
 11 files changed, 37 insertions(+), 40 deletions(-)

diff --git a/analysis-master/tra_analysis/Analysis.py b/analysis-master/tra_analysis/Analysis.py
index df81951c..e736ec62 100644
--- a/analysis-master/tra_analysis/Analysis.py
+++ b/analysis-master/tra_analysis/Analysis.py
@@ -7,10 +7,13 @@
 #    current benchmark of optimization: 1.33 times faster
 # setup:
 
-__version__ = "3.0.4"
+__version__ = "3.0.5"
 
 # changelog should be viewed using print(analysis.__changelog__)
 __changelog__ = """changelog:
+	3.0.5:
+		- removed extra submodule imports
+		- fixed/optimized header
 	3.0.4:
 		- removed -_obj imports
 	3.0.3:
@@ -361,7 +364,6 @@ __all__ = [
 	'histo_analysis',
 	'regression',
 	'Metric',
-	'kmeans',
 	'pca',
 	'decisiontree',
 	# all statistics functions left out due to integration in other functions
@@ -374,21 +376,14 @@ __all__ = [
 import csv
 from tra_analysis.metrics import elo as Elo
 from tra_analysis.metrics import glicko2 as Glicko2
-import math
 import numpy as np
 import scipy
-from scipy import optimize, stats
-import sklearn
-from sklearn import preprocessing, pipeline, linear_model, metrics, cluster, decomposition, tree, neighbors, naive_bayes, svm, model_selection, ensemble
+import sklearn, sklearn.cluster
 from tra_analysis.metrics import trueskill as Trueskill
-import warnings
 
 # import submodules
 
-from .Array import Array
 from .ClassificationMetric import ClassificationMetric
-from .RegressionMetric import RegressionMetric
-from . import SVM
 
 class error(ValueError):
 	pass
@@ -599,16 +594,7 @@ def npmin(data):
 def npmax(data):
 
 	return np.amax(data)
-""" need to decide what to do with this function
-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)
diff --git a/analysis-master/tra_analysis/ClassificationMetric.py b/analysis-master/tra_analysis/ClassificationMetric.py
index a1afcf25..6dc2ff31 100644
--- a/analysis-master/tra_analysis/ClassificationMetric.py
+++ b/analysis-master/tra_analysis/ClassificationMetric.py
@@ -4,9 +4,11 @@
 #    this should be imported as a python module using 'from tra_analysis import ClassificationMetric'
 # setup:
 
-__version__ = "1.0.1"
+__version__ = "1.0.2"
 
 __changelog__ = """changelog:
+	1.0.2:
+		- optimized imports
 	1.0.1:
 		- fixed __all__
 	1.0.0:
@@ -22,7 +24,6 @@ __all__ = [
 ]
 
 import sklearn
-from sklearn import metrics
 
 class ClassificationMetric():
 
diff --git a/analysis-master/tra_analysis/CorrelationTest.py b/analysis-master/tra_analysis/CorrelationTest.py
index bc35ce92..ddb27939 100644
--- a/analysis-master/tra_analysis/CorrelationTest.py
+++ b/analysis-master/tra_analysis/CorrelationTest.py
@@ -4,9 +4,11 @@
 #    this should be imported as a python module using 'from tra_analysis import CorrelationTest'
 # setup:
 
-__version__ = "1.0.1"
+__version__ = "1.0.2"
 
 __changelog__ = """changelog:
+	1.0.2:
+		- optimized imports
 	1.0.1:
 		- fixed __all__
 	1.0.0:
@@ -29,7 +31,6 @@ __all__ = [
 ]
 
 import scipy
-from scipy import stats
 
 def anova_oneway(*args): #expects arrays of samples
 
diff --git a/analysis-master/tra_analysis/KNN.py b/analysis-master/tra_analysis/KNN.py
index d594c72f..09d663f3 100644
--- a/analysis-master/tra_analysis/KNN.py
+++ b/analysis-master/tra_analysis/KNN.py
@@ -4,9 +4,11 @@
 #    this should be imported as a python module using 'from tra_analysis import KNN'
 # setup:
 
-__version__ = "1.0.0"
+__version__ = "1.0.1"
 
 __changelog__ = """changelog:
+	1.0.1:
+		- optimized imports
 	1.0.0:
 		- ported analysis.KNN() here
 		- removed classness
@@ -23,7 +25,6 @@ __all__ = [
 ]
 
 import sklearn
-from sklearn import model_selection, neighbors
 from . import ClassificationMetric, RegressionMetric
 
 def knn_classifier(data, labels, n_neighbors = 5, test_size = 0.3, algorithm='auto', leaf_size=30, metric='minkowski', metric_params=None, n_jobs=None, p=2, weights='uniform'): #expects *2d data and 1d labels post-scaling
diff --git a/analysis-master/tra_analysis/NaiveBayes.py b/analysis-master/tra_analysis/NaiveBayes.py
index f6b68f1e..007d3e6e 100644
--- a/analysis-master/tra_analysis/NaiveBayes.py
+++ b/analysis-master/tra_analysis/NaiveBayes.py
@@ -4,9 +4,11 @@
 #    this should be imported as a python module using 'from tra_analysis import NaiveBayes'
 # setup:
 
-__version__ = "1.0.0"
+__version__ = "1.0.1"
 
 __changelog__ = """changelog:
+	1.0.1:
+		- optimized imports
 	1.0.0:
 		- ported analysis.NaiveBayes() here
 		- removed classness
@@ -24,8 +26,7 @@ __all__ = [
 ]
 
 import sklearn
-from sklearn import model_selection, naive_bayes
-from . import ClassificationMetric, RegressionMetric
+from . import ClassificationMetric
 
 def gaussian(data, labels, test_size = 0.3, priors = None, var_smoothing = 1e-09):
 
diff --git a/analysis-master/tra_analysis/RandomForest.py b/analysis-master/tra_analysis/RandomForest.py
index 44bee009..02afe73c 100644
--- a/analysis-master/tra_analysis/RandomForest.py
+++ b/analysis-master/tra_analysis/RandomForest.py
@@ -4,9 +4,11 @@
 #    this should be imported as a python module using 'from tra_analysis import RandomForest'
 # setup:
 
-__version__ = "1.0.1"
+__version__ = "1.0.2"
 
 __changelog__ = """changelog:
+	1.0.2:
+		- optimized imports
 	1.0.1:
 		- fixed __all__
 	1.0.0:
@@ -23,8 +25,7 @@ __all__ = [
 	"random_forest_regressor",
 ]
 
-import sklearn
-from sklearn import ensemble, model_selection
+import sklearn, sklearn.ensemble, sklearn.naive_bayes
 from . import ClassificationMetric, RegressionMetric
 
 def random_forest_classifier(data, labels, test_size, n_estimators, 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):
diff --git a/analysis-master/tra_analysis/RegressionMetric.py b/analysis-master/tra_analysis/RegressionMetric.py
index 0b985493..e71689d4 100644
--- a/analysis-master/tra_analysis/RegressionMetric.py
+++ b/analysis-master/tra_analysis/RegressionMetric.py
@@ -4,9 +4,11 @@
 #    this should be imported as a python module using 'from tra_analysis import RegressionMetric'
 # setup:
 
-__version__ = "1.0.0"
+__version__ = "1.0.1"
 
 __changelog__ = """changelog:
+	1.0.1:
+		- optimized imports
 	1.0.0:
 		- ported analysis.RegressionMetric() here
 """
@@ -21,7 +23,6 @@ __all__ = [
 
 import numpy as np
 import sklearn
-from sklearn import metrics
 
 class RegressionMetric():
 
diff --git a/analysis-master/tra_analysis/SVM.py b/analysis-master/tra_analysis/SVM.py
index acf189f3..02b86138 100644
--- a/analysis-master/tra_analysis/SVM.py
+++ b/analysis-master/tra_analysis/SVM.py
@@ -4,9 +4,11 @@
 #    this should be imported as a python module using 'from tra_analysis import SVM'
 # setup:
 
-__version__ = "1.0.2"
+__version__ = "1.0.3"
 
 __changelog__ = """changelog:
+	1.0.3:
+		- optimized imports
 	1.0.2: 
 		- fixed __all__
 	1.0.1:
@@ -30,7 +32,6 @@ __all__ = [
 ]
 
 import sklearn
-from sklearn import svm
 from . import ClassificationMetric, RegressionMetric
 
 class CustomKernel:
diff --git a/analysis-master/tra_analysis/Sort.py b/analysis-master/tra_analysis/Sort.py
index 63dc3677..90ba6409 100644
--- a/analysis-master/tra_analysis/Sort.py
+++ b/analysis-master/tra_analysis/Sort.py
@@ -16,7 +16,7 @@ __changelog__ = """changelog:
 
 __author__ = (
 	"Arthur Lu <learthurgo@gmail.com>",
-	"James Pan <zpan@imsa.edu>"
+	"James Pan <zpan@imsa.edu>",
 )
 
 __all__ = [
diff --git a/analysis-master/tra_analysis/StatisticalTest.py b/analysis-master/tra_analysis/StatisticalTest.py
index 44fa3a07..e07649e9 100644
--- a/analysis-master/tra_analysis/StatisticalTest.py
+++ b/analysis-master/tra_analysis/StatisticalTest.py
@@ -4,9 +4,11 @@
 #    this should be imported as a python module using 'from tra_analysis import StatisticalTest'
 # setup:
 
-__version__ = "1.0.2"
+__version__ = "1.0.3"
 
 __changelog__ = """changelog:
+	1.0.3:
+		- optimized imports
 	1.0.2:
 		- added tukey_multicomparison
 		- fixed styling
@@ -61,7 +63,6 @@ __all__ = [
 
 import numpy as np
 import scipy
-from scipy import stats, interpolate
 
 def ttest_onesample(a, popmean, axis = 0, nan_policy = 'propagate'):
 
@@ -279,9 +280,9 @@ def get_tukeyQcrit(k, df, alpha=0.05):
 	cv001 = c[:, 2::2]
 
 	if alpha == 0.05:
-		intp = interpolate.interp1d(crows, cv005[:,k-2])
+		intp = scipy.interpolate.interp1d(crows, cv005[:,k-2])
 	elif alpha == 0.01:
-		intp = interpolate.interp1d(crows, cv001[:,k-2])
+		intp = scipy.interpolate.interp1d(crows, cv001[:,k-2])
 	else:
 		raise ValueError('only implemented for alpha equal to 0.01 and 0.05')
 	return intp(df)
diff --git a/analysis-master/tra_analysis/__init__.py b/analysis-master/tra_analysis/__init__.py
index 0f170bdd..d74c1c9d 100644
--- a/analysis-master/tra_analysis/__init__.py
+++ b/analysis-master/tra_analysis/__init__.py
@@ -16,6 +16,8 @@ __changelog__ = """changelog:
 		- deprecated titanlearn.py
 		- deprecated visualization.py
 		- removed matplotlib from requirements
+		- removed extra submodule imports in Analysis
+		- added typehinting, docstrings for each function
 	3.0.0:
 		- incremented version to release 3.0.0
 	3.0.0-rc2:
@@ -45,6 +47,7 @@ __all__ = [
 	"Analysis",
 	"Array",
 	"ClassificationMetric",
+	"Clustering",
 	"CorrelationTest",
 	"Expression",
 	"Fit",

From 27a77c3edb3e6dabf7c40193b9c5cdadc9c78de3 Mon Sep 17 00:00:00 2001
From: Arthur Lu <learthurgo@gmail.com>
Date: Tue, 16 Nov 2021 20:17:46 +0000
Subject: [PATCH 2/4] added type hinting for a few functions, added typedef
 module to hold custom typings

Signed-off-by: Arthur Lu <learthurgo@gmail.com>
---
 analysis-master/tra_analysis/Analysis.py | 33 +++++++++++++++++++-----
 analysis-master/tra_analysis/__init__.py |  4 ++-
 analysis-master/tra_analysis/typedef.py  |  4 +++
 3 files changed, 34 insertions(+), 7 deletions(-)
 create mode 100644 analysis-master/tra_analysis/typedef.py

diff --git a/analysis-master/tra_analysis/Analysis.py b/analysis-master/tra_analysis/Analysis.py
index e736ec62..b9f4443b 100644
--- a/analysis-master/tra_analysis/Analysis.py
+++ b/analysis-master/tra_analysis/Analysis.py
@@ -380,6 +380,7 @@ import numpy as np
 import scipy
 import sklearn, sklearn.cluster
 from tra_analysis.metrics import trueskill as Trueskill
+from tra_analysis.typedef import R, List, Dict
 
 # import submodules
 
@@ -388,15 +389,27 @@ from .ClassificationMetric import ClassificationMetric
 class error(ValueError):
 	pass
 
-def load_csv(filepath):
+def load_csv(filepath: str) -> np.ndarray:
+	"""
+	Loads csv file into 2D numpy array. Does not check csv file validity.
+	parameters:
+		filepath: String path to the csv file
+	return:
+		2D numpy array of values stored in csv file
+	"""
 	with open(filepath, newline='') as csvfile:
 		file_array = np.array(list(csv.reader(csvfile)))
 		csvfile.close()
 	return file_array
 
-# expects 1d array
-def basic_stats(data):
-
+def basic_stats(data: List[R]) -> Dict[str, R]:
+	"""
+	Calculates mean, median, standard deviation, variance, minimum, maximum of a simple set of elements
+	parameters:
+		data: List representing set of unordered elements
+	return:
+		Dictionary with (mean, median, standard-deviation, variance, minimum, maximum) as keys and corresponding values
+	"""
 	data_t = np.array(data).astype(float)
 
 	_mean = mean(data_t)
@@ -408,8 +421,16 @@ def basic_stats(data):
 
 	return {"mean": _mean, "median": _median, "standard-deviation": _stdev, "variance": _variance, "minimum": _min, "maximum": _max}
 
-# returns z score with inputs of point, mean and standard deviation of spread
-def z_score(point, mean, stdev):
+def z_score(point: R, mean: R, stdev: R) -> R:
+	"""
+	Calculates z score of a specific point given mean and standard deviation of data
+	parameters:
+		point: Real value corresponding to a single point of data
+		mean: Real value corresponding to the mean of the dataset
+		stdev: Real value corresponding to the standard deviation of the dataset
+	return:
+		Real value that is the point's z score
+	"""
 	score = (point - mean) / stdev
 	
 	return score
diff --git a/analysis-master/tra_analysis/__init__.py b/analysis-master/tra_analysis/__init__.py
index d74c1c9d..2df41075 100644
--- a/analysis-master/tra_analysis/__init__.py
+++ b/analysis-master/tra_analysis/__init__.py
@@ -73,4 +73,6 @@ from . import RandomForest
 from .RegressionMetric import RegressionMetric
 from . import Sort
 from . import StatisticalTest
-from . import SVM
\ No newline at end of file
+from . import SVM
+
+from . import typedef
\ No newline at end of file
diff --git a/analysis-master/tra_analysis/typedef.py b/analysis-master/tra_analysis/typedef.py
new file mode 100644
index 00000000..875776a0
--- /dev/null
+++ b/analysis-master/tra_analysis/typedef.py
@@ -0,0 +1,4 @@
+from typing import TypeVar, List, Dict
+List = List
+Dict = Dict
+R = TypeVar('R', int, float)
\ No newline at end of file

From 3c868672c9c1196540201006a1b543d598464a19 Mon Sep 17 00:00:00 2001
From: Arthur Lu <learthurgo@gmail.com>
Date: Thu, 18 Nov 2021 09:23:19 +0000
Subject: [PATCH 3/4] finished Analysis docstrings, removed typehinting to
 rework

---
 analysis-master/tra_analysis/Analysis.py | 101 +++++++++++++++++++----
 analysis-master/tra_analysis/__init__.py |   4 +-
 analysis-master/tra_analysis/typedef.py  |   4 -
 3 files changed, 87 insertions(+), 22 deletions(-)
 delete mode 100644 analysis-master/tra_analysis/typedef.py

diff --git a/analysis-master/tra_analysis/Analysis.py b/analysis-master/tra_analysis/Analysis.py
index b9f4443b..204c58d2 100644
--- a/analysis-master/tra_analysis/Analysis.py
+++ b/analysis-master/tra_analysis/Analysis.py
@@ -380,7 +380,6 @@ import numpy as np
 import scipy
 import sklearn, sklearn.cluster
 from tra_analysis.metrics import trueskill as Trueskill
-from tra_analysis.typedef import R, List, Dict
 
 # import submodules
 
@@ -389,7 +388,7 @@ from .ClassificationMetric import ClassificationMetric
 class error(ValueError):
 	pass
 
-def load_csv(filepath: str) -> np.ndarray:
+def load_csv(filepath):
 	"""
 	Loads csv file into 2D numpy array. Does not check csv file validity.
 	parameters:
@@ -402,9 +401,9 @@ def load_csv(filepath: str) -> np.ndarray:
 		csvfile.close()
 	return file_array
 
-def basic_stats(data: List[R]) -> Dict[str, R]:
+def basic_stats(data):
 	"""
-	Calculates mean, median, standard deviation, variance, minimum, maximum of a simple set of elements
+	Calculates mean, median, standard deviation, variance, minimum, maximum of a simple set of elements.
 	parameters:
 		data: List representing set of unordered elements
 	return:
@@ -421,9 +420,9 @@ def basic_stats(data: List[R]) -> Dict[str, R]:
 
 	return {"mean": _mean, "median": _median, "standard-deviation": _stdev, "variance": _variance, "minimum": _min, "maximum": _max}
 
-def z_score(point: R, mean: R, stdev: R) -> R:
+def z_score(point, mean, stdev):
 	"""
-	Calculates z score of a specific point given mean and standard deviation of data
+	Calculates z score of a specific point given mean and standard deviation of data.
 	parameters:
 		point: Real value corresponding to a single point of data
 		mean: Real value corresponding to the mean of the dataset
@@ -437,7 +436,14 @@ def z_score(point: R, mean: R, stdev: R) -> R:
 
 # expects 2d array, normalizes across all axes
 def z_normalize(array, *args):
-
+	"""
+	Applies sklearn.normalize(array, axis = args) on any arraylike parseable by numpy.
+	parameters:
+		array: array like structure of reals aka nested indexables
+		*args: arguments relating to axis normalized against
+	return:
+		numpy array of normalized values from ArrayLike input
+	"""
 	array = np.array(array)
 	for arg in args:
 		array = sklearn.preprocessing.normalize(array, axis = arg)
@@ -446,7 +452,13 @@ def z_normalize(array, *args):
 
 # expects 2d array of [x,y]
 def histo_analysis(hist_data):
-
+	"""
+	Calculates the mean and standard deviation of derivatives of (x,y) points. Requires at least 2 points to compute.
+	parameters:
+		hist_data: list of real coordinate point data (x, y)
+	return:
+		Dictionary with (mean, deviation) as keys to corresponding values
+	"""
 	if len(hist_data[0]) > 2:
 
 		hist_data = np.array(hist_data)
@@ -462,7 +474,15 @@ def histo_analysis(hist_data):
 		return None
 
 def regression(inputs, outputs, args): # inputs, outputs expects N-D array 
-
+	"""
+	Applies specified regression kernels onto input, output data pairs.
+	parameters:
+		inputs: List of Reals representing independent variable values of each point
+		outputs: List of Reals representing dependent variable values of each point
+		args: List of Strings from values (lin, log, exp, ply, sig)
+	return:
+		Dictionary with keys (lin, log, exp, ply, sig) as keys to correspondiong regression models
+	"""
 	X = np.array(inputs)
 	y = np.array(outputs)
 
@@ -566,13 +586,39 @@ def regression(inputs, outputs, args): # inputs, outputs expects N-D array
 	return regressions
 
 class Metric:
-
+	"""
+	The metric class wraps the metrics models. Call without instantiation as Metric.<method>(...)
+	"""
 	def elo(self, starting_score, opposing_score, observed, N, K):
-
+		"""
+		Calculates an elo adjusted ELO score given a player's current score, opponent's score, and outcome of match.
+		reference: https://en.wikipedia.org/wiki/Elo_rating_system
+		parameters:
+			starting_score: Real value representing player's ELO score before a match
+			opposing_score: Real value representing opponent's score before the match
+			observed: Array of Real values representing multiple sequential match outcomes against the same opponent. 1 for match win, 0.5 for tie, 0 for loss.
+			N: Real value representing the normal or mean score expected (usually 1200)
+			K: R eal value representing a system constant, determines how quickly players will change scores (usually 24)
+		return:
+			Real value representing the player's new ELO score
+		"""
 		return Elo.calculate(starting_score, opposing_score, observed, N, K)
 
 	def glicko2(self, starting_score, starting_rd, starting_vol, opposing_score, opposing_rd, observations):
-
+		"""
+		Calculates an adjusted Glicko-2 score given a player's current score, multiple opponent's score, and outcome of several matches.
+		reference: http://www.glicko.net/glicko/glicko2.pdf
+		parameters:
+			starting_score: Real value representing the player's Glicko-2 score
+			starting_rd: Real value representing the player's RD
+			starting_vol: Real value representing the player's volatility
+			opposing_score: List of Real values representing multiple opponent's Glicko-2 scores
+			opposing_rd: List of Real values representing multiple opponent's RD
+			opposing_vol: List of Real values representing multiple opponent's volatility
+			observations: List of Real values representing the outcome of several matches, where each match's opponent corresponds with the opposing_score, opposing_rd, opposing_vol values of the same indesx. Outcomes can be a score, presuming greater score is better. 
+		return:
+			Tuple of 3 Real values representing the player's new score, rd, and vol
+		"""
 		player = Glicko2.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)
@@ -580,7 +626,15 @@ class Metric:
 		return (player.rating, player.rd, player.vol)
 
 	def trueskill(self, teams_data, observations): # teams_data is array of array of tuples ie. [[(mu, sigma), (mu, sigma), (mu, sigma)], [(mu, sigma), (mu, sigma), (mu, sigma)]]
-
+		"""
+		Calculates the score changes for multiple teams playing in a single match accoding to the trueskill algorithm.
+		reference: https://trueskill.org/
+		parameters:
+			teams_data: List of List of Tuples of 2 Real values representing multiple player ratings. List of teams, which is a List of players. Each player rating is a Tuple of 2 Real values (mu, sigma).
+			observations: List of Real values representing the match outcome. Each value in the List is the score corresponding to the team at the same index in teams_data.
+		return:
+			List of List of Tuples of 2 Real values representing new player ratings. Same structure as teams_data. 
+		"""
 		team_ratings = []
 
 		for team in teams_data:
@@ -617,13 +671,30 @@ def npmax(data):
 	return np.amax(data)
 
 def pca(data, n_components = None, copy = True, whiten = False, svd_solver = "auto", tol = 0.0, iterated_power = "auto", random_state = None):
-
+	"""
+	Performs a principle component analysis on the input data.
+	reference: https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html
+	parameters:
+		data: Arraylike of Reals representing the set of data to perform PCA on
+		* : refer to reference for usage, parameters follow same usage
+	return:
+		Arraylike of Reals representing the set of data that has had PCA performed. The dimensionality of the Arraylike may be smaller or equal. 
+	"""
 	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
-
+	"""
+	Generates a decision tree classifier fitted to the given data. 
+	reference: https://scikit-learn.org/stable/modules/generated/sklearn.tree.DecisionTreeClassifier.html
+	parameters:
+		data: List of values representing each data point of multiple axes
+		labels: List of values represeing the labels corresponding to the same index at data
+		* : refer to reference for usage, parameters follow same usage
+	return:
+		DecisionTreeClassifier model and corresponding classification accuracy metrics
+	"""
 	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)
diff --git a/analysis-master/tra_analysis/__init__.py b/analysis-master/tra_analysis/__init__.py
index 2df41075..d74c1c9d 100644
--- a/analysis-master/tra_analysis/__init__.py
+++ b/analysis-master/tra_analysis/__init__.py
@@ -73,6 +73,4 @@ from . import RandomForest
 from .RegressionMetric import RegressionMetric
 from . import Sort
 from . import StatisticalTest
-from . import SVM
-
-from . import typedef
\ No newline at end of file
+from . import SVM
\ No newline at end of file
diff --git a/analysis-master/tra_analysis/typedef.py b/analysis-master/tra_analysis/typedef.py
deleted file mode 100644
index 875776a0..00000000
--- a/analysis-master/tra_analysis/typedef.py
+++ /dev/null
@@ -1,4 +0,0 @@
-from typing import TypeVar, List, Dict
-List = List
-Dict = Dict
-R = TypeVar('R', int, float)
\ No newline at end of file

From 3dabe87ead0f9b1ab9fee12263b16efe7a56a55c Mon Sep 17 00:00:00 2001
From: Arthur Lu <learthurgo@gmail.com>
Date: Thu, 18 Nov 2021 09:24:52 +0000
Subject: [PATCH 4/4] removed unessasary comments, updated version and
 changelog

---
 analysis-master/tra_analysis/Analysis.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/analysis-master/tra_analysis/Analysis.py b/analysis-master/tra_analysis/Analysis.py
index 204c58d2..2316a026 100644
--- a/analysis-master/tra_analysis/Analysis.py
+++ b/analysis-master/tra_analysis/Analysis.py
@@ -7,10 +7,12 @@
 #    current benchmark of optimization: 1.33 times faster
 # setup:
 
-__version__ = "3.0.5"
+__version__ = "3.0.6"
 
 # changelog should be viewed using print(analysis.__changelog__)
 __changelog__ = """changelog:
+	3.0.6:
+		- added docstrings
 	3.0.5:
 		- removed extra submodule imports
 		- fixed/optimized header
@@ -434,7 +436,6 @@ def z_score(point, mean, stdev):
 	
 	return score
 
-# expects 2d array, normalizes across all axes
 def z_normalize(array, *args):
 	"""
 	Applies sklearn.normalize(array, axis = args) on any arraylike parseable by numpy.
@@ -450,7 +451,6 @@ def z_normalize(array, *args):
 
 	return array
 
-# expects 2d array of [x,y]
 def histo_analysis(hist_data):
 	"""
 	Calculates the mean and standard deviation of derivatives of (x,y) points. Requires at least 2 points to compute.