fix version numbers

Analysis v4

.devcontainer/Dockerfile

@@ -0,0 +1,6 @@
+FROM python:slim
+WORKDIR /
+RUN apt-get -y update; apt-get -y upgrade
+RUN apt-get -y install git
+COPY requirements.txt .
+RUN pip install -r requirements.txt

.devcontainer/devcontainer.json

@@ -0,0 +1,22 @@
+{
+    "name": "TRA Analysis Development Environment",
+    "build": {
+		"dockerfile": "Dockerfile",
+    },
+    "settings": { 
+		"terminal.integrated.shell.linux": "/bin/bash",
+		"python.pythonPath": "",
+		"python.linting.enabled": true,
+		"python.linting.pylintEnabled": true,
+		"python.linting.pylintPath": "",
+		"python.testing.pytestPath": "",
+    "editor.tabSize": 4,
+    "editor.insertSpaces": false
+	},
+	"extensions": [
+		"mhutchie.git-graph",
+		"ms-python.python",
+		"waderyan.gitblame"
+	],
+		"postCreateCommand": ""
+	}

.devcontainer/requirements.txt

@@ -0,0 +1,8 @@
+numpy
+scipy
+scikit-learn
+six
+pyparsing
+
+pylint
+pytest

.gitattributes

@@ -1,2 +1,4 @@
 # Auto detect text files and perform LF normalization
-* text=auto
+* text=auto eol=lf
+*.{cmd,[cC][mM][dD]} text eol=crlf
+*.{bat,[bB][aA][tT]} text eol=crlf

.github/ISSUE_TEMPLATE/bug_report.md

@@ -0,0 +1,38 @@
+---
+name: Bug report
+about: Create a report to help us improve
+title: ''
+labels: ''
+assignees: ''
+
+---
+
+**Describe the bug**
+A clear and concise description of what the bug is.
+
+**To Reproduce**
+Steps to reproduce the behavior:
+1. Go to '...'
+2. Click on '....'
+3. Scroll down to '....'
+4. See error
+
+**Expected behavior**
+A clear and concise description of what you expected to happen.
+
+**Screenshots**
+If applicable, add screenshots to help explain your problem.
+
+**Desktop (please complete the following information):**
+ - OS: [e.g. iOS]
+ - Browser [e.g. chrome, safari]
+ - Version [e.g. 22]
+
+**Smartphone (please complete the following information):**
+ - Device: [e.g. iPhone6]
+ - OS: [e.g. iOS8.1]
+ - Browser [e.g. stock browser, safari]
+ - Version [e.g. 22]
+
+**Additional context**
+Add any other context about the problem here.

.github/ISSUE_TEMPLATE/feature_request.md

@@ -0,0 +1,20 @@
+---
+name: Feature request
+about: Suggest an idea for this project
+title: ''
+labels: ''
+assignees: ''
+
+---
+
+**Is your feature request related to a problem? Please describe.**
+A clear and concise description of what the problem is. Ex. I'm always frustrated when [...]
+
+**Describe the solution you'd like**
+A clear and concise description of what you want to happen.
+
+**Describe alternatives you've considered**
+A clear and concise description of any alternative solutions or features you've considered.
+
+**Additional context**
+Add any other context or screenshots about the feature request here.

.github/PULL_REQUEST_TEMPLATE.md

@@ -0,0 +1,7 @@
+Fixes #
+
+## Proposed Changes
+
+  -
+  -
+  -

.github/workflows/publish-analysis.yml

@@ -0,0 +1,40 @@
+# This workflows will upload a Python Package using Twine when a release is created
+# For more information see: https://help.github.com/en/actions/language-and-framework-guides/using-python-with-github-actions#publishing-to-package-registries
+
+name: Upload Analysis Package
+
+on:
+  release:
+    types: [published, edited]
+jobs:
+  deploy:
+
+    runs-on: ubuntu-latest
+
+    env:
+      working-directory: ./analysis-master/
+    steps:
+    - uses: actions/checkout@v2
+    - name: Set up Python
+      uses: actions/setup-python@v2
+      with:
+        python-version: '3.x'
+    - name: Install dependencies
+      working-directory: ${{env.working-directory}}
+      run: |
+        python -m pip install --upgrade pip
+        pip install setuptools wheel twine
+    - name: Install package deps
+      working-directory: ${{env.working-directory}}
+      run: |
+        pip install -r requirements.txt
+    - name: Build package
+      working-directory: ${{env.working-directory}}
+      run: |
+        python setup.py sdist bdist_wheel
+    - name: Publish package to PyPI
+      uses: pypa/gh-action-pypi-publish@master
+      with:
+        user: __token__
+        password: ${{ secrets.PYPI_TOKEN }}
+        packages_dir: analysis-master/dist/

.github/workflows/ut-analysis.yml

@@ -0,0 +1,38 @@
+# This workflow will install Python dependencies, run tests and lint with a variety of Python versions
+# For more information see: https://help.github.com/actions/language-and-framework-guides/using-python-with-github-actions
+
+name: Analysis Unit Tests
+
+on:
+  push:
+    branches: [ master ]
+  pull_request:
+    branches: [ master ]
+
+jobs:
+  unittest:
+
+    runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        python-version: ["3.7", "3.8", "3.9", "3.10"]
+
+    env:
+      working-directory: ./analysis-master/
+
+    steps:
+    - uses: actions/checkout@v2
+    - name: Set up Python ${{ matrix.python-version }}
+      uses: actions/setup-python@v2
+      with:
+        python-version: ${{ matrix.python-version }}
+    - name: Install dependencies
+      run: |
+        python -m pip install --upgrade pip
+        pip install pytest
+        if [ -f requirements.txt ]; then pip install -r requirements.txt; fi
+      working-directory: ${{ env.working-directory }}
+    - name: Test with pytest
+      run: |
+        pytest
+      working-directory: ${{ env.working-directory }}

.gitignore

@@ -1,2 +1,9 @@
+/.vscode/
 
-benchmark_data.csv
+**/__pycache__/
+**/.pytest_cache/
+**/*.pyc
+
+**/build/
+**/*.egg-info/
+**/dist/

CONTRIBUTING.md

@@ -0,0 +1,66 @@
+# Contributing Guidelines
+
+This project accept contributions via GitHub pull requests.
+This document outlines some of the
+conventions on development workflow, commit message formatting, contact points,
+and other resources to make it easier to get your contribution accepted.
+
+## Certificate of Origin
+
+By contributing to this project, you agree to the [Developer Certificate of
+Origin (DCO)](https://developercertificate.org/). This document was created by the Linux Kernel community and is a
+simple statement that you, as a contributor, have the legal right to make the
+contribution.
+
+In order to show your agreement with the DCO you should include at the end of the commit message,
+the following line: `Signed-off-by: John Doe <john.doe@example.com>`, using your real name.
+
+This can be done easily using the [`-s`](https://github.com/git/git/blob/b2c150d3aa82f6583b9aadfecc5f8fa1c74aca09/Documentation/git-commit.txt#L154-L161) flag on the `git commit`.
+
+Visual Studio code also has a flag to enable signoff on commits 
+
+If you find yourself pushed a few commits without `Signed-off-by`, you can still add it afterwards. Read this for help: [fix-DCO.md](https://github.com/src-d/guide/blob/master/developer-community/fix-DCO.md).
+
+## Support Channels
+
+The official support channel, for both users and contributors, is:
+
+- GitHub issues: each repository has its own list of issues.
+
+*Before opening a new issue or submitting a new pull request, it's helpful to
+search the project - it's likely that another user has already reported the
+issue you're facing, or it's a known issue that we're already aware of.
+
+
+## How to Contribute
+In general, please use conventional approaches to development and contribution such as:
+* Create branches for additions or deletions, and or side projects
+* Do not commit to master!
+* Use Pull Requests (PRs) to indicate that an addition is ready to merge. 
+PRs are the main and exclusive way to contribute code to source{d} projects.
+In order for a PR to be accepted it needs to pass this list of requirements:
+
+- The contribution must be correctly explained with natural language and providing a minimum working example that reproduces it.
+- All PRs must be written idiomaticly:
+    - for Node: formatted according to [AirBnB standards](https://github.com/airbnb/javascript), and no warnings from `eslint` using the AirBnB style guide
+    - for other languages, similar constraints apply.
+- They should in general include tests, and those shall pass.
+    - In any case, all the PRs have to pass the personal evaluation of at least one of the [maintainers](MAINTAINERS) of the project.
+
+
+### Format of the commit message
+
+Every commit message should describe what was changed, under which context and, if applicable, the issue it relates to (mentioning a GitHub issue number when applicable):
+
+For small changes, or changes to a testing or personal branch, the commit message should be a short changelog entry
+
+For larger changes or for changes on branches that are more widely used, the commit message should simply reference an entry to some other changelog system. It is encouraged to use some sort of versioning system to log changes. Example commit messages:
+```
+superscript.py v 2.0.5.006
+```
+
+The format can be described more formally as follows:
+
+```
+<package> v <version number>
+```

LICENSE

@@ -0,0 +1,29 @@
+BSD 3-Clause License
+
+Copyright (c) 2020, Titan Scouting
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+1. Redistributions of source code must retain the above copyright notice, this
+   list of conditions and the following disclaimer.
+
+2. Redistributions in binary form must reproduce the above copyright notice,
+   this list of conditions and the following disclaimer in the documentation
+   and/or other materials provided with the distribution.
+
+3. Neither the name of the copyright holder nor the names of its
+   contributors may be used to endorse or promote products derived from
+   this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
+FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

MAINTAINERS

@@ -0,0 +1,3 @@
+Arthur Lu <learthurgo@gmail.com>
+Jacob Levine <jacoblevine18@gmail.com>
+Dev Singh <dev@devksingh.com>

README.md

@@ -0,0 +1,70 @@
+# Red Alliance Analysis · ![GitHub release (latest by date)](https://img.shields.io/github/v/release/titanscout2022/red-alliance-analysis)
+
+Titan Robotics 2022 Strategy Team Repository for Data Analysis Tools. Included with these tools are the backend data analysis engine formatted as a python package, associated binaries for the analysis package, and premade scripts that can be pulled directly from this repository and will integrate with other Red Alliance applications to quickly deploy FRC scouting tools.
+
+---
+
+# `tra-analysis`
+
+`tra-analysis` is a higher level package for data processing and analysis. It is a python library that combines popular data science tools like numpy, scipy, and sklearn along with other tools to create an easy-to-use data analysis engine. tra-analysis includes analysis in all ranges of complexity from basic statistics like mean, median, mode to complex kernel based classifiers and allows user to more quickly deploy these algorithms. The package also includes performance metrics for score based applications including elo, glicko2, and trueskill ranking systems.
+
+At the core of the tra-analysis package is the modularity of each analytical tool. The package encapsulates the setup code for the included data science tools. For example, there are many packages that allow users to generate many different types of regressions. With the tra-analysis package, one function can be called to generate many regressions and sort them by accuracy.
+
+## Prerequisites
+---
+
+* Python >= 3.6
+* Pip which can be installed by running\
+`curl https://bootstrap.pypa.io/get-pip.py -o get-pip.py`\
+`python get-pip.py`\
+after installing python, or with a package manager on linux. Refer to the [pip installation instructions](https://pip.pypa.io/en/stable/installing/) for more information.
+
+## Installing
+---
+
+#### Standard Platforms
+
+For the latest version of tra-analysis, run `pip install tra-analysis` or `pip install tra_analysis`. The requirements for tra-analysis should be automatically installed.
+
+#### Exotic Platforms (Android)
+
+[Termux](https://termux.com/) is recommended for a linux environemnt on Android. Consult the [documentation](https://titanscouting.github.io/analysis/general/installation#exotic-platforms-android) for advice on installing the prerequisites. After installing the prerequisites, the package should be installed normally with `pip install tra-analysis` or `pip install tra_analysis`. 
+
+## Use
+
+---
+
+tra-analysis operates like any other python package. Consult the [documentation](https://titanscouting.github.io/analysis/tra_analysis/) for more information.
+
+## Supported Platforms
+
+---
+
+Although any modern 64 bit platform should be supported, the following platforms have been tested to be working:
+* AMD64 (Tested on Zen, Zen+, and Zen 2)
+* Intel 64/x86_64/x64 (Tested on Kaby Lake, Ice Lake)
+* ARM64 (Tested on Broadcom BCM2836 SoC, Broadcom BCM2711 SoC)
+
+The following OSes have been tested to be working:
+* Linux Kernel 3.16, 4.4, 4.15, 4.19, 5.4
+	* Ubuntu 16.04, 18.04, 20.04
+	* Debian (and Debian derivaives) Jessie, Buster
+* Windows 7, 10
+
+The following python versions are supported:
+* python 3.6 (not tested)
+* python 3.7
+* python 3.8
+
+---
+
+# `data-analysis`
+
+Data analysis has been separated into its own [repository](https://github.com/titanscouting/tra-data-analysis).
+
+# Contributing
+
+Read our included contributing guidelines (`CONTRIBUTING.md`) for more information and feel free to reach out to any current maintainer for more information. 
+
+# Build Statuses
+![Analysis Unit Tests](https://github.com/titanscout2022/red-alliance-analysis/workflows/Analysis%20Unit%20Tests/badge.svg)

SECURITY.md

@@ -0,0 +1,6 @@
+# Security Policy
+
+
+## Reporting a Vulnerability
+
+Please email `titanscout2022@gmail.com` to report a vulnerability.

analysis-master/build.sh

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

analysis-master/requirements.txt

@@ -0,0 +1,8 @@
+numpy
+scipy
+scikit-learn
+six
+pyparsing
+
+pylint
+pytest

analysis-master/setup.py

@@ -0,0 +1,28 @@
+import setuptools
+import tra_analysis
+
+requirements = []
+
+with open("requirements.txt", 'r') as file:
+	for line in file:
+		requirements.append(line)
+
+setuptools.setup(
+	name="tra_analysis",
+	version=tra_analysis.__version__,
+	author="The Titan Scouting Team",
+	author_email="titanscout2022@gmail.com",
+	description="Analysis package developed by Titan Scouting for The Red Alliance",
+	long_description="../README.md",
+	long_description_content_type="text/markdown",
+	url="https://github.com/titanscout2022/tr2022-strategy",
+	packages=setuptools.find_packages(),
+	install_requires=requirements,
+	license = "BSD 3-Clause License",
+	classifiers=[
+		"Programming Language :: Python :: 3",
+		"Operating System :: OS Independent",
+	],
+	python_requires='>=3.6',
+	keywords="data analysis tools"
+)

analysis-master/test_analysis.py

@@ -0,0 +1,253 @@
+import numpy as np
+import sklearn
+from sklearn import metrics
+
+from tra_analysis import Analysis as an
+from tra_analysis import Array
+from tra_analysis import ClassificationMetric
+from tra_analysis import Clustering
+from tra_analysis import CorrelationTest
+from tra_analysis import Fit
+from tra_analysis import KNN
+from tra_analysis import metrics as m
+from tra_analysis import NaiveBayes
+from tra_analysis import RandomForest
+from tra_analysis import RegressionMetric
+from tra_analysis import Sort
+from tra_analysis import StatisticalTest
+from tra_analysis import SVM
+
+from tra_analysis.equation.parser import BNF
+
+test_data_linear = [1, 3, 6, 7, 9]
+test_data_linear2 = [2, 2, 5, 7, 13]
+test_data_linear3 = [2, 5, 8, 6, 14]
+test_data_array = Array(test_data_linear)
+
+x_data_circular = []
+y_data_circular = []
+
+y_data_ccu = [1, 3, 7, 14, 21]
+y_data_ccd = [8.66, 8.5, 7, 5, 1]
+
+test_data_scrambled = [-32, 34, 19, 72, -65, -11, -43, 6, 85, -17, -98, -26, 12, 20, 9, -92, -40, 98, -78, 17, -20, 49, 93, -27, -24, -66, 40, 84, 1, -64, -68, -25, -42, -46, -76, 43, -3, 30, -14, -34, -55, -13, 41, -30, 0, -61, 48, 23, 60, 87, 80, 77, 53, 73, 79, 24, -52, 82, 8, -44, 65, 47, -77, 94, 7, 37, -79, 36, -94, 91, 59, 10, 97, -38, -67, 83, 54, 31, -95, -63, 16, -45, 21, -12, 66, -48, -18, -96, -90, -21, -83, -74, 39, 64, 69, -97, 13, 55, 27, -39]
+test_data_sorted = [-98, -97, -96, -95, -94, -92, -90, -83, -79, -78, -77, -76, -74, -68, -67, -66, -65, -64, -63, -61, -55, -52, -48, -46, -45, -44, -43, -42, -40, -39, -38, -34, -32, -30, -27, -26, -25, -24, -21, -20, -18, -17, -14, -13, -12, -11, -3, 0, 1, 6, 7, 8, 9, 10, 12, 13, 16, 17, 19, 20, 21, 23, 24, 27, 30, 31, 34, 36, 37, 39, 40, 41, 43, 47, 48, 49, 53, 54, 55, 59, 60, 64, 65, 66, 69, 72, 73, 77, 79, 80, 82, 83, 84, 85, 87, 91, 93, 94, 97, 98]
+
+test_data_2D_pairs = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]])
+test_data_2D_positive = np.array([[23, 51], [21, 32], [15, 25], [17, 31]])
+test_output = np.array([1, 3, 4, 5])
+test_labels_2D_pairs = np.array([1, 1, 2, 2])
+validation_data_2D_pairs = np.array([[-0.8, -1], [0.8, 1.2]])
+validation_labels_2D_pairs = np.array([1, 2])
+
+def test_basicstats():
+
+	assert an.basic_stats(test_data_linear) == {"mean": 5.2, "median": 6.0, "standard-deviation": 2.85657137141714, "variance": 8.16, "minimum": 1.0, "maximum": 9.0}
+	assert an.z_score(3.2, 6, 1.5) == -1.8666666666666665
+	assert an.z_normalize([test_data_linear], 1).tolist() == [[0.07537783614444091, 0.22613350843332272, 0.45226701686664544, 0.5276448530110863, 0.6784005252999682]]
+
+def test_regression():
+
+	assert all(isinstance(item, str) for item in an.regression(test_data_linear, y_data_ccu, ["lin"])) == True
+	assert all(isinstance(item, str) for item in an.regression(test_data_linear, y_data_ccd, ["log"])) == True
+	assert all(isinstance(item, str) for item in an.regression(test_data_linear, y_data_ccu, ["exp"])) == True
+	assert all(isinstance(item, str) for item in an.regression(test_data_linear, y_data_ccu, ["ply"])) == True
+	assert all(isinstance(item, str) for item in an.regression(test_data_linear, y_data_ccd, ["sig"])) == True
+
+def test_metrics():
+
+	assert an.Metric().elo(1500, 1500, [1, 0], 400, 24) == 1512.0
+	assert an.Metric().glicko2(1500, 250, 0.06, [1500, 1400], [250, 240], [1, 0]) == (1478.864307445517, 195.99122679202452, 0.05999602937563585)
+	e = [[(21.346, 7.875), (20.415, 7.808), (29.037, 7.170)], [(28.654, 7.875), (28.654, 7.875), (23.225, 6.287)]]
+	r = an.Metric().trueskill([[(25, 8.33), (24, 8.25), (32, 7.5)], [(25, 8.33), (25, 8.33), (21, 6.5)]], [1, 0])
+	i = 0
+	for group in r:
+		j = 0
+		for team in group:
+			assert abs(team.mu - e[i][j][0]) < 0.001
+			assert abs(team.sigma - e[i][j][1]) < 0.001
+			j+=1
+		i+=1
+
+def test_array():
+
+	assert test_data_array.elementwise_mean() == 5.2
+	assert test_data_array.elementwise_median() == 6.0
+	assert test_data_array.elementwise_stdev() == 2.85657137141714
+	assert test_data_array.elementwise_variance() == 8.16
+	assert test_data_array.elementwise_npmin() == 1
+	assert test_data_array.elementwise_npmax() == 9
+	assert test_data_array.elementwise_stats() == (5.2, 6.0, 2.85657137141714, 8.16, 1, 9)
+
+	for i in range(len(test_data_array)):
+		assert test_data_array[i] == test_data_linear[i]
+	
+	test_data_array[0] = 100
+	expected = [100, 3, 6, 7, 9]
+	for i in range(len(test_data_array)):
+		assert test_data_array[i] == expected[i]
+
+def test_classifmetric():
+
+	classif_metric = ClassificationMetric(test_data_linear2, test_data_linear)
+	assert classif_metric[0].all() == metrics.confusion_matrix(test_data_linear, test_data_linear2).all()
+	assert classif_metric[1] == metrics.classification_report(test_data_linear, test_data_linear2)
+
+def test_correlationtest():
+
+	assert all(np.isclose(list(CorrelationTest.anova_oneway(test_data_linear, test_data_linear2).values()), [0.05825242718446602, 0.8153507906592907], rtol=1e-10))
+	assert all(np.isclose(list(CorrelationTest.pearson(test_data_linear, test_data_linear2).values()),  [0.9153061540753287, 0.02920895440940868], rtol=1e-10))
+	assert all(np.isclose(list(CorrelationTest.spearman(test_data_linear, test_data_linear2).values()), [0.9746794344808964, 0.004818230468198537], rtol=1e-10))
+	assert all(np.isclose(list(CorrelationTest.point_biserial(test_data_linear, test_data_linear2).values()), [0.9153061540753287, 0.02920895440940868], rtol=1e-10))
+	assert all(np.isclose(list(CorrelationTest.kendall(test_data_linear, test_data_linear2).values()), [0.9486832980505137, 0.022977401503206086], rtol=1e-10))
+	assert all(np.isclose(list(CorrelationTest.kendall_weighted(test_data_linear, test_data_linear2).values()), [0.9750538072369643, np.nan], rtol=1e-10, equal_nan=True))
+
+def test_fit():
+
+	assert Fit.CircleFit(x=[0,0,-1,1], y=[1, -1, 0, 0]).LSC() == (0.0, 0.0, 1.0, 0.0)
+
+def test_knn():
+
+	model, metric = KNN.knn_classifier(test_data_2D_pairs, test_labels_2D_pairs, 2)
+	assert isinstance(model, sklearn.neighbors.KNeighborsClassifier)
+	assert np.array([[0,0], [2,0]]).all() == metric[0].all()
+	assert '              precision    recall  f1-score   support\n\n           1       0.00      0.00      0.00       0.0\n           2       0.00      0.00      0.00       2.0\n\n    accuracy                           0.00       2.0\n   macro avg       0.00      0.00      0.00       2.0\nweighted avg       0.00      0.00      0.00       2.0\n' == metric[1]
+	model, metric = KNN.knn_regressor(test_data_2D_pairs, test_output, 2)
+	assert isinstance(model, sklearn.neighbors.KNeighborsRegressor)
+	assert (-25.0, 6.5, 2.5495097567963922) == metric
+
+def test_naivebayes():
+
+	model, metric = NaiveBayes.gaussian(test_data_2D_pairs, test_labels_2D_pairs)
+	assert isinstance(model, sklearn.naive_bayes.GaussianNB)
+	assert metric[0].all() == np.array([[0, 0], [2, 0]]).all()
+
+	model, metric = NaiveBayes.multinomial(test_data_2D_positive, test_labels_2D_pairs)
+	assert isinstance(model, sklearn.naive_bayes.MultinomialNB)
+	assert metric[0].all() == np.array([[0, 0], [2, 0]]).all()
+
+	model, metric = NaiveBayes.bernoulli(test_data_2D_pairs, test_labels_2D_pairs)
+	assert isinstance(model, sklearn.naive_bayes.BernoulliNB)
+	assert metric[0].all() == np.array([[0, 0], [2, 0]]).all()
+
+	model, metric = NaiveBayes.complement(test_data_2D_positive, test_labels_2D_pairs)
+	assert isinstance(model, sklearn.naive_bayes.ComplementNB)
+	assert metric[0].all() == np.array([[0, 0], [2, 0]]).all()
+
+def test_randomforest():
+
+	model, metric = RandomForest.random_forest_classifier(test_data_2D_pairs, test_labels_2D_pairs, 0.3, 2)
+	assert isinstance(model, sklearn.ensemble.RandomForestClassifier)
+	assert metric[0].all() == np.array([[0, 0], [2, 0]]).all()
+	model, metric = RandomForest.random_forest_regressor(test_data_2D_pairs, test_labels_2D_pairs, 0.3, 2)
+	assert isinstance(model, sklearn.ensemble.RandomForestRegressor)
+	assert metric == (0.0, 1.0, 1.0)
+
+def test_regressionmetric():
+
+	assert RegressionMetric(test_data_linear, test_data_linear2)== (0.7705314009661837, 3.8, 1.9493588689617927)
+
+def test_sort():
+	sorts = [Sort.quicksort, Sort.mergesort, Sort.heapsort, Sort.introsort, Sort.insertionsort, Sort.timsort, Sort.selectionsort, Sort.shellsort, Sort.bubblesort, Sort.cyclesort, Sort.cocktailsort]
+	for sort in sorts:
+		assert all(a == b for a, b in zip(sort(test_data_scrambled), test_data_sorted))
+
+def test_statisticaltest():
+
+	assert StatisticalTest.tukey_multicomparison([test_data_linear, test_data_linear2, test_data_linear3]) == \
+		{'group 1 and group 2': [0.32571517201527916, False], 'group 1 and group 3': [0.977145516045838, False], 'group 2 and group 3': [0.6514303440305589, False]}
+
+def test_svm():
+
+	data = test_data_2D_pairs
+	labels = test_labels_2D_pairs
+	test_data = validation_data_2D_pairs
+	test_labels = validation_labels_2D_pairs
+
+	lin_kernel = SVM.PrebuiltKernel.Linear()
+	#ply_kernel = SVM.PrebuiltKernel.Polynomial(3, 0)
+	rbf_kernel = SVM.PrebuiltKernel.RBF('scale')
+	sig_kernel = SVM.PrebuiltKernel.Sigmoid(0)
+
+	lin_kernel = SVM.fit(lin_kernel, data, labels)
+	#ply_kernel = SVM.fit(ply_kernel, data, labels)
+	rbf_kernel = SVM.fit(rbf_kernel, data, labels)
+	sig_kernel = SVM.fit(sig_kernel, data, labels)
+
+	for i in range(len(test_data)):
+
+		assert lin_kernel.predict([test_data[i]]).tolist() == [test_labels[i]]
+
+	#for i in range(len(test_data)):
+
+	#	assert ply_kernel.predict([test_data[i]]).tolist() == [test_labels[i]]
+
+	for i in range(len(test_data)):
+
+		assert rbf_kernel.predict([test_data[i]]).tolist() == [test_labels[i]]
+
+	for i in range(len(test_data)):
+
+		assert sig_kernel.predict([test_data[i]]).tolist() == [test_labels[i]]
+
+def test_equation():
+
+	parser = BNF()
+	correctParse = {
+		"9": 9.0,
+		"-9": -9.0,
+		"--9": 9.0,
+		"-E": -2.718281828459045,
+		"9 + 3 + 6": 18.0,
+		"9 + 3 / 11": 9.272727272727273,
+		"(9 + 3)": 12.0,
+		"(9+3) / 11": 1.0909090909090908,
+		"9 - 12 - 6": -9.0,
+		"9 - (12 - 6)": 3.0,
+		"2*3.14159": 6.28318,
+		"3.1415926535*3.1415926535 / 10": 0.9869604400525172,
+		"PI * PI / 10": 0.9869604401089358,
+		"PI*PI/10": 0.9869604401089358,
+		"PI^2": 9.869604401089358,
+		"round(PI^2)": 10,
+		"6.02E23 * 8.048": 4.844896e+24,
+		"e / 3": 0.9060939428196817,
+		"sin(PI/2)": 1.0,
+		"10+sin(PI/4)^2": 10.5,
+		"trunc(E)": 2,
+		"trunc(-E)": -2,
+		"round(E)": 3,
+		"round(-E)": -3,
+		"E^PI": 23.140692632779263,
+		"exp(0)": 1.0,
+		"exp(1)": 2.718281828459045,
+		"2^3^2": 512.0,
+		"(2^3)^2": 64.0,
+		"2^3+2": 10.0,
+		"2^3+5": 13.0,
+		"2^9": 512.0,
+		"sgn(-2)": -1,
+		"sgn(0)": 0,
+		"sgn(0.1)": 1,
+		"sgn(cos(PI/4))": 1,
+		"sgn(cos(PI/2))": 0,
+		"sgn(cos(PI*3/4))": -1,
+		"+(sgn(cos(PI/4)))": 1,
+		"-(sgn(cos(PI/4)))": -1,
+	}
+	for key in list(correctParse.keys()):
+		assert parser.eval(key) == correctParse[key]
+
+def test_clustering():
+
+	normalizer = sklearn.preprocessing.Normalizer()
+
+	data = X = np.array([[1, 2], [2, 2], [2, 3], [8, 7], [8, 8], [25, 80]])
+
+	assert Clustering.dbscan(data, eps=3, min_samples=2).tolist() == [0, 0, 0, 1, 1, -1]
+	assert Clustering.dbscan(data, normalizer=normalizer, eps=3, min_samples=2).tolist() == [0, 0, 0, 0, 0, 0]
+
+	data = np.array([[1, 1], [2, 1], [1, 0], [4, 7], [3, 5], [3, 6]])
+
+	assert Clustering.spectral(data, n_clusters=2, assign_labels='discretize', random_state=0).tolist() == [1, 1, 1, 0, 0, 0]
+	assert Clustering.spectral(data, normalizer=normalizer, n_clusters=2, assign_labels='discretize', random_state=0).tolist() == [0, 1, 1, 0, 0, 0]

analysis-master/tra_analysis/Analysis.py

@@ -0,0 +1,704 @@
+# Titan Robotics Team 2022: Analysis Module
+# Written by Arthur Lu
+# Notes:
+#    this should be imported as a python module using 'from tra_analysis 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__ = "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
+	3.0.4:
+		- removed -_obj imports
+	3.0.3:
+		- fixed spelling of deprecate
+	3.0.2:
+		- fixed __all__
+	3.0.1:
+		- removed numba dependency and calls
+	3.0.0:
+		- exported several submodules to their own files while preserving backwards compatibility:
+			- Array
+			- ClassificationMetric
+			- CorrelationTest
+			- KNN
+			- NaiveBayes
+			- RandomForest
+			- RegressionMetric
+			- Sort
+			- StatisticalTest
+			- SVM
+		- note: above listed submodules will not be supported in the future
+		- future changes to all submodules will be held in their respective changelogs
+		- future changes altering the parent package will be held in the __changelog__ of the parent package (in __init__.py)
+		- changed reference to module name to Analysis
+	2.3.1:
+		- fixed bugs in Array class
+	2.3.0:
+		- overhauled Array class
+	2.2.3:
+		- fixed spelling of RandomForest
+		- made n_neighbors required for KNN
+		- made n_classifiers required for SVM
+	2.2.2:
+		- fixed 2.2.1 changelog entry
+		- changed regression to return dictionary
+	2.2.1:
+		- changed all references to parent package analysis to tra_analysis
+	2.2.0:
+		- added Sort class
+		- added several array sorting functions to Sort class including:
+			- quick sort
+			- merge sort
+			- intro(spective) sort
+			- heap sort
+			- insertion sort
+			- tim sort
+			- selection sort
+			- bubble sort
+			- cycle sort
+			- cocktail sort
+		- tested all sorting algorithms with both lists and numpy arrays
+		- deprecated sort function from Array class
+		- added warnings as an import
+	2.1.4:
+		- added sort and search functions to Array class
+	2.1.3:
+		- changed output of basic_stats and histo_analysis to libraries
+		- fixed __all__
+	2.1.2:
+		- renamed ArrayTest class to Array
+	2.1.1:
+		- added add, mul, neg, and inv functions to ArrayTest class
+		- added normalize function to ArrayTest class
+		- added dot and cross functions to ArrayTest class
+	2.1.0:
+		- added ArrayTest class
+		- added elementwise mean, median, standard deviation, variance, min, max functions to ArrayTest class
+		- added elementwise_stats to ArrayTest which encapsulates elementwise statistics
+		- appended to __all__ to reflect changes
+	2.0.6:
+		- renamed func functions in regression to lin, log, exp, and sig 
+	2.0.5:
+		- moved random_forrest_regressor and random_forrest_classifier to RandomForrest class
+		- renamed Metrics to Metric
+		- renamed RegressionMetrics to RegressionMetric
+		- renamed ClassificationMetrics to ClassificationMetric
+		- renamed CorrelationTests to CorrelationTest
+		- renamed StatisticalTests to StatisticalTest
+		- reflected rafactoring to all mentions of above classes/functions
+	2.0.4:
+		- fixed __all__ to reflected the correct functions and classes
+		- fixed CorrelationTests and StatisticalTests class functions to require self invocation
+		- added missing math import
+		- fixed KNN class functions to require self invocation
+		- fixed Metrics class functions to require self invocation
+		- various spelling fixes in CorrelationTests and StatisticalTests
+	2.0.3:
+		- bug fixes with CorrelationTests and StatisticalTests
+		- moved glicko2 and trueskill to the metrics subpackage
+		- moved elo to a new metrics subpackage
+	2.0.2:
+		- fixed docs
+	2.0.1:
+		- fixed docs
+	2.0.0:
+		- cleaned up wild card imports with scipy and sklearn
+		- added CorrelationTests class
+		- added StatisticalTests class
+		- added several correlation tests to CorrelationTests
+		- added several statistical tests to StatisticalTests
+	1.13.9:
+		- moved elo, glicko2, trueskill functions under class Metrics
+	1.13.8:
+		- moved Glicko2 to a seperate package
+	1.13.7:
+		- fixed bug with trueskill
+	1.13.6:
+		- cleaned up imports
+	1.13.5:
+		- cleaned up package
+	1.13.4:
+		- small fixes to regression to improve performance
+	1.13.3:
+		- filtered nans from regression
+	1.13.2:
+		- removed torch requirement, and moved Regression back to regression.py
+	1.13.1:
+		- bug fix with linear regression not returning a proper value
+		- cleaned up regression
+		- fixed bug with polynomial regressions
+	1.13.0:
+		- fixed all regressions to now properly work
+	1.12.6:
+		- fixed bg with a division by zero in histo_analysis
+	1.12.5:
+		- fixed numba issues by removing numba  from elo, glicko2 and trueskill
+	1.12.4:
+		- renamed gliko to glicko
+	1.12.3:
+		- removed deprecated code
+	1.12.2:
+		- removed team first time trueskill instantiation in favor of integration in superscript.py
+	1.12.1:
+		- 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
+	1.12.0:
+		- temporarily fixed polynomial regressions by using sklearn's PolynomialFeatures
+	1.11.010:
+		- alphabeticaly ordered import lists
+	1.11.9:
+		- bug fixes
+	1.11.8:
+		- bug fixes
+	1.11.7:
+		- bug fixes
+	1.11.6:
+		- tested min and max
+		- bug fixes 
+	1.11.5:
+		- added min and max in basic_stats
+	1.11.4:
+		- bug fixes
+	1.11.3:
+		- bug fixes
+	1.11.2:
+		- consolidated metrics
+		- fixed __all__
+	1.11.1:
+		- added test/train split to RandomForestClassifier and RandomForestRegressor
+	1.11.0:
+		- added RandomForestClassifier and RandomForestRegressor
+		- note: untested
+	1.10.0:
+		- added numba.jit to remaining functions
+	1.9.2:
+		- kernelized PCA and KNN
+	1.9.1:
+		- fixed bugs with SVM and NaiveBayes
+	1.9.0:
+		- added SVM class, subclasses, and functions
+		- note: untested
+	1.8.0:
+		- added NaiveBayes classification engine
+		- note: untested
+	1.7.0:
+		- added knn()
+		- added confusion matrix to decisiontree()
+	1.6.2:
+		- changed layout of __changelog to be vscode friendly
+	1.6.1:
+		- added additional hyperparameters to decisiontree()
+	1.6.0:
+		- fixed __version__
+		- fixed __all__ order
+		- added decisiontree()
+	1.5.3:
+		- added pca
+	1.5.2:
+		- reduced import list
+		- added kmeans clustering engine
+	1.5.1:
+		- simplified regression by using .to(device)
+	1.5.0:
+		- added polynomial regression to regression(); untested
+	1.4.0:
+		- added trueskill()
+	1.3.2:
+		- renamed regression class to Regression, regression_engine() to regression gliko2_engine class to Gliko2
+	1.3.1:
+		- changed glicko2() to return tuple instead of array
+	1.3.0:
+		- added glicko2_engine class and glicko()
+		- verified glicko2() accuracy
+	1.2.3:
+		- fixed elo()
+	1.2.2:
+		- added elo()
+		- elo() has bugs to be fixed
+	1.2.1:
+		- readded regrression import
+	1.2.0:
+		- integrated regression.py as regression class
+		- removed regression import
+		- fixed metadata for regression class
+		- fixed metadata for analysis class
+	1.1.1:
+		- regression_engine() bug fixes, now actaully regresses
+	1.1.0:
+		- added regression_engine()
+		- added all regressions except polynomial
+	1.0.7:
+		- updated _init_device()
+	1.0.6:
+		- removed useless try statements
+	1.0.5:
+		- removed impossible outcomes
+	1.0.4:
+		- added performance metrics (r^2, mse, rms)
+	1.0.3:
+		- resolved nopython mode for mean, median, stdev, variance
+	1.0.2:
+		- 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
+	1.0.1:
+		- removed from sklearn import * to resolve uneeded wildcard imports
+	1.0.0:
+		- removed c_entities,nc_entities,obstacles,objectives from __all__
+		- applied numba.jit to all functions
+		- deprecated and removed stdev_z_split
+		- cleaned up histo_analysis to include numpy and numba.jit optimizations
+		- deprecated and removed all regression functions in favor of future pytorch optimizer
+		- deprecated 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
+	0.9.0:
+		- refactored
+		- numpyed everything
+		- removed stats in favor of numpy functions
+	0.8.5:
+		- minor fixes
+	0.8.4:
+		- removed a few unused dependencies
+	0.8.3:
+		- added p_value function
+	0.8.2:
+		- updated __all__ correctly to contain changes made in v 0.8.0 and v 0.8.1
+	0.8.1:
+		- refactors
+		- bugfixes
+	0.8.0:
+		- deprecated histo_analysis_old
+		- deprecated debug
+		- altered basic_analysis to take array data instead of filepath
+		- refactor
+		- optimization
+	0.7.2:
+		- bug fixes
+	0.7.1:
+		- bug fixes
+	0.7.0:
+		- added tanh_regression (logistical regression)
+		- bug fixes
+	0.6.5:
+		- added z_normalize function to normalize dataset
+		- bug fixes
+	0.6.4:
+		- bug fixes
+	0.6.3:
+		- bug fixes
+	0.6.2:
+		- bug fixes
+	0.6.1:
+		- corrected __all__ to contain all of the functions
+	0.6.0:
+		- added calc_overfit, which calculates two measures of overfit, error and performance
+		- added calculating overfit to optimize_regression
+	0.5.0:
+		- 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
+	0.4.2:
+		- added __changelog__
+		- updated debug function with log and exponential regressions
+	0.4.1:
+		- added log regressions
+		- added exponential regressions
+		- added log_regression and exp_regression to __all__
+	0.3.8:
+		- added debug function to further consolidate functions
+	0.3.7:
+		- added builtin benchmark function
+		- added builtin random (linear) data generation function
+		- added device initialization (_init_device)
+	0.3.6:
+		- reorganized the imports list to be in alphabetical order
+		- added search and regurgitate functions to c_entities, nc_entities, obstacles, objectives
+	0.3.5:
+		- major bug fixes
+		- updated historical analysis
+		- deprecated old historical analysis
+	0.3.4:
+		- added __version__, __author__, __all__
+		- added polynomial regression
+		- added root mean squared function
+		- added r squared function
+	0.3.3:
+		- bug fixes
+		- added c_entities
+	0.3.2:
+		- bug fixes
+		- added nc_entities, obstacles, objectives
+		- consolidated statistics.py to analysis.py
+	0.3.1:
+		- compiled 1d, column, and row basic stats into basic stats function
+	0.3.0:
+		- added historical analysis function
+	0.2.x:
+		- added z score test
+	0.1.x:
+		- major bug fixes
+	0.0.x:
+		- added loading csv
+		- added 1d, column, row basic stats
+"""
+
+__author__ = (
+	"Arthur Lu <learthurgo@gmail.com>",
+)
+
+__all__ = [
+	'load_csv',
+	'basic_stats',
+	'z_score',
+	'z_normalize',
+	'histo_analysis',
+	'regression',
+	'Metric',
+	'pca',
+	'decisiontree',
+	# all statistics functions left out due to integration in other functions
+]
+
+# now back to your regularly scheduled programming:
+
+# imports (now in alphabetical order! v 0.3.006):
+
+import csv
+from tra_analysis.metrics import elo as Elo
+from tra_analysis.metrics import glicko2 as Glicko2
+import numpy as np
+import scipy
+import sklearn, sklearn.cluster, sklearn.pipeline
+from tra_analysis.metrics import trueskill as Trueskill
+
+# import submodules
+
+from .ClassificationMetric import ClassificationMetric
+
+class error(ValueError):
+	pass
+
+def load_csv(filepath):
+	"""
+	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
+
+def basic_stats(data):
+	"""
+	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)
+	_median = median(data_t)
+	_stdev = stdev(data_t)
+	_variance = variance(data_t)
+	_min = npmin(data_t)
+	_max = npmax(data_t)
+
+	return {"mean": _mean, "median": _median, "standard-deviation": _stdev, "variance": _variance, "minimum": _min, "maximum": _max}
+
+def z_score(point, mean, stdev):
+	"""
+	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
+
+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)
+
+	return array
+
+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)
+		derivative = np.array(len(hist_data) - 1, dtype = float)
+		t = np.diff(hist_data)
+		derivative = t[1] / t[0]
+		np.sort(derivative)
+
+		return {"mean": basic_stats(derivative)["mean"], "deviation": basic_stats(derivative)["standard-deviation"]}
+
+	else:
+
+		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)
+
+	regressions = {}
+
+	if 'lin' in args: # formula: ax + b
+
+		try:
+
+			def lin(x, a, b):
+
+				return a * x + b
+
+			popt, pcov = scipy.optimize.curve_fit(lin, X, y)
+
+			coeffs = popt.flatten().tolist()
+			regressions["lin"] = (str(coeffs[0]) + "*x+" + str(coeffs[1]))
+
+		except Exception as e:
+
+			pass
+
+	if 'log' in args: # formula: a log (b(x + c)) + d
+
+		try:
+
+			def log(x, a, b, c, d):
+
+				return a * np.log(b*(x + c)) + d
+
+			popt, pcov = scipy.optimize.curve_fit(log, X, y)
+
+			coeffs = popt.flatten().tolist()
+			regressions["log"] = (str(coeffs[0]) + "*log(" + str(coeffs[1]) + "*(x+" + str(coeffs[2]) + "))+" + str(coeffs[3]))
+
+		except Exception as e:
+			
+			pass
+
+	if 'exp' in args: # formula: a e ^ (b(x + c)) + d
+
+		try:        
+
+			def exp(x, a, b, c, d):
+
+				return a * np.exp(b*(x + c)) + d
+
+			popt, pcov = scipy.optimize.curve_fit(exp, X, y)
+
+			coeffs = popt.flatten().tolist()
+			regressions["exp"] = (str(coeffs[0]) + "*e^(" + str(coeffs[1]) + "*(x+" + str(coeffs[2]) + "))+" + str(coeffs[3]))
+
+		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 = params.flatten().tolist()
+
+			temp = ""
+			counter = 0
+			for param in params:
+				temp += "(" + str(param) + "*x^" + str(counter) + ")"
+				counter += 1
+			plys["x^" + str(i)] = (temp)
+
+		regressions["ply"] = (plys)
+
+	if 'sig' in args: # formula: a tanh (b(x + c)) + d
+
+		try:        
+
+			def sig(x, a, b, c, d):
+
+				return a * np.tanh(b*(x + c)) + d
+
+			popt, pcov = scipy.optimize.curve_fit(sig, X, y)
+
+			coeffs = popt.flatten().tolist()
+			regressions["sig"] = (str(coeffs[0]) + "*tanh(" + str(coeffs[1]) + "*(x+" + str(coeffs[2]) + "))+" + str(coeffs[3]))
+
+		except Exception as e:
+		   
+			pass
+
+	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)
+
+		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:
+			team_temp = ()
+			for player in team:
+				player = Trueskill.Rating(player[0], player[1])
+				team_temp = team_temp + (player,)
+			team_ratings.append(team_temp)
+
+		return Trueskill.rate(team_ratings, ranks=observations)
+
+def mean(data):
+
+	return np.mean(data)
+
+def median(data):
+
+	return np.median(data)
+
+def stdev(data):
+
+	return np.std(data)
+
+def variance(data):
+
+	return np.var(data)
+
+def npmin(data):
+
+	return np.amin(data)
+
+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)
+	predictions = model.predict(data_test)
+	metrics = ClassificationMetric(predictions, labels_test)
+
+	return model, metrics

analysis-master/tra_analysis/Array.py

@@ -0,0 +1,166 @@
+# Titan Robotics Team 2022: Array submodule
+# Written by Arthur Lu
+# Notes:
+#    this should be imported as a python module using 'from tra_analysis import Array'
+# setup:
+
+__version__ = "1.0.4"
+
+__changelog__ = """changelog:
+	1.0.4:
+		- fixed spelling of deprecate
+	1.0.3:
+		- fixed __all__
+	1.0.2:
+		- fixed several implementation bugs with magic methods
+	1.0.1:
+		- removed search and __search functions
+	1.0.0:
+		- ported analysis.Array() here
+"""
+
+__author__ = (
+	"Arthur Lu <learthurgo@gmail.com>",
+)
+
+__all__ = [
+	"Array",
+]
+
+import numpy as np
+import warnings
+
+class Array(): # tests on nd arrays independent of basic_stats
+
+	def __init__(self, narray):
+
+		self.array = np.array(narray)
+
+	def __str__(self):
+
+		return str(self.array)
+
+	def __repr__(self):
+
+		return str(self.array)
+	
+	def elementwise_mean(self, axis = 0): # expects arrays that are size normalized
+
+		return np.mean(self.array, axis = axis)
+
+	def elementwise_median(self, axis = 0):
+
+		return np.median(self.array, axis = axis)
+
+	def elementwise_stdev(self, axis = 0):
+
+		return np.std(self.array, axis = axis)
+
+	def elementwise_variance(self, axis = 0):
+
+		return np.var(self.array, axis = axis)
+
+	def elementwise_npmin(self, axis = 0):
+		return np.amin(self.array, axis = axis)
+
+
+	def elementwise_npmax(self, axis = 0):
+		return np.amax(self.array, axis = axis)
+
+	def elementwise_stats(self, axis = 0):
+
+		_mean = self.elementwise_mean(axis = axis)
+		_median = self.elementwise_median(axis = axis)
+		_stdev = self.elementwise_stdev(axis = axis)
+		_variance = self.elementwise_variance(axis = axis)
+		_min = self.elementwise_npmin(axis = axis)
+		_max = self.elementwise_npmax(axis = axis)
+
+		return _mean, _median, _stdev, _variance, _min, _max
+
+	def __getitem__(self, key):
+
+		return self.array[key]
+
+	def __setitem__(self, key, value):
+
+		self.array[key] = value
+
+	def __len__(self):
+
+		return len(self.array)
+
+	def normalize(self):
+
+		a = np.atleast_1d(np.linalg.norm(self.array))
+		a[a==0] = 1
+		return Array(self.array / np.expand_dims(a, -1))
+
+	def __add__(self, other):
+
+		return Array(self.array + other.array)
+
+	def __sub__(self, other):
+
+		return Array(self.array - other.array)
+
+	def __neg__(self):
+		
+		return Array(-self.array)
+
+	def __abs__(self):
+
+		return Array(abs(self.array))
+
+	def __invert__(self):
+
+		return Array(1/self.array)
+
+	def __mul__(self, other):
+
+		if(isinstance(other, Array)):
+			return Array(self.array.dot(other.array))
+		elif(isinstance(other, int)):
+			return Array(other * self.array)
+		else:
+			raise Exception("unsupported multiplication between Array and " + str(type(other)))
+
+	def __rmul__(self, other):
+
+		return self.__mul__(other)
+
+	def cross(self, other):
+
+		return np.cross(self.array, other.array)
+
+	def transpose(self):
+
+		return Array(np.transpose(self.array))
+
+	def sort(self, array): # deprecated
+		warnings.warn("Array.sort has been deprecated in favor of Sort")
+		array_length = len(array)
+		if array_length <= 1:
+			return array
+		middle_index = int(array_length / 2)
+		left = array[0:middle_index]
+		right = array[middle_index:]
+		left = self.sort(left)
+		right = self.sort(right)
+		return self.__merge(left, right)
+
+	def __merge(self, left, right):
+		sorted_list = []
+		left = left[:]
+		right = right[:]
+		while len(left) > 0 or len(right) > 0:
+			if len(left) > 0 and len(right) > 0:
+				if left[0] <= right[0]:
+					sorted_list.append(left.pop(0))
+				else:
+					sorted_list.append(right.pop(0))
+			elif len(left) > 0:
+				sorted_list.append(left.pop(0))
+			elif len(right) > 0:
+				sorted_list.append(right.pop(0))
+		return sorted_list

analysis-master/tra_analysis/ClassificationMetric.py

@@ -0,0 +1,40 @@
+# Titan Robotics Team 2022: ClassificationMetric submodule
+# Written by Arthur Lu
+# Notes:
+#    this should be imported as a python module using 'from tra_analysis import ClassificationMetric'
+# setup:
+
+__version__ = "1.0.2"
+
+__changelog__ = """changelog:
+	1.0.2:
+		- optimized imports
+	1.0.1:
+		- fixed __all__
+	1.0.0:
+		- ported analysis.ClassificationMetric() here
+"""
+
+__author__ = (
+	"Arthur Lu <learthurgo@gmail.com>",
+)
+
+__all__ = [
+	"ClassificationMetric",
+]
+
+import sklearn
+
+class ClassificationMetric():
+
+	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)

analysis-master/tra_analysis/Clustering.py

@@ -0,0 +1,63 @@
+# Titan Robotics Team 2022: Clustering submodule
+# Written by Arthur Lu
+# Notes:
+#    this should be imported as a python module using 'from tra_analysis import Clustering'
+# setup:
+
+__version__ = "2.0.2"
+
+# changelog should be viewed using print(analysis.__changelog__)
+__changelog__ = """changelog:
+	2.0.2:
+		- generalized optional args to **kwargs
+	2.0.1:
+		- added normalization preprocessing to clustering, expects instance of sklearn.preprocessing.Normalizer()
+	2.0.0:
+		- added dbscan clustering algo
+		- added spectral clustering algo
+    1.0.0:
+        - created this submodule
+        - copied kmeans clustering from Analysis
+"""
+
+__author__ = (
+	"Arthur Lu <learthurgo@gmail.com>",
+)
+
+__all__ = [
+	"kmeans",
+	"dbscan",
+	"spectral",
+]
+
+import sklearn
+
+def kmeans(data, normalizer = None, **kwargs):
+
+	if  normalizer != None:
+		data = normalizer.transform(data)
+
+	kernel = sklearn.cluster.KMeans(**kwargs)
+	kernel.fit(data)
+	predictions = kernel.predict(data)
+	centers = kernel.cluster_centers_
+
+	return centers, predictions
+
+def dbscan(data, normalizer=None, **kwargs):
+
+	if  normalizer != None:
+		data = normalizer.transform(data)
+
+	model = sklearn.cluster.DBSCAN(**kwargs).fit(data)
+
+	return model.labels_
+
+def spectral(data, normalizer=None, **kwargs):
+
+	if  normalizer != None:
+		data = normalizer.transform(data)
+
+	model = sklearn.cluster.SpectralClustering(**kwargs).fit(data)
+
+	return model.labels_

analysis-master/tra_analysis/CorrelationTest.py

@@ -0,0 +1,70 @@
+# Titan Robotics Team 2022: CorrelationTest submodule
+# Written by Arthur Lu
+# Notes:
+#    this should be imported as a python module using 'from tra_analysis import CorrelationTest'
+# setup:
+
+__version__ = "1.0.3"
+
+__changelog__ = """changelog:
+	1.0.3:
+		- generalized optional args to **kwargs
+	1.0.2:
+		- optimized imports
+	1.0.1:
+		- fixed __all__
+	1.0.0:
+		- ported analysis.CorrelationTest() here
+		- removed classness
+"""
+
+__author__ = (
+	"Arthur Lu <learthurgo@gmail.com>",
+)
+
+__all__ = [
+	"anova_oneway",
+	"pearson",
+	"spearman",
+	"point_biserial",
+	"kendall",
+	"kendall_weighted",
+	"mgc",
+]
+
+import scipy
+
+def anova_oneway(*args): #expects arrays of samples
+
+	results = scipy.stats.f_oneway(*args)
+	return {"f-value": results[0], "p-value": results[1]}
+
+def pearson(x, y):
+
+	results = scipy.stats.pearsonr(x, y)
+	return {"r-value": results[0], "p-value": results[1]}
+
+def spearman(a, b = None, **kwargs):
+
+	results = scipy.stats.spearmanr(a, b = b, **kwargs)
+	return {"r-value": results[0], "p-value": results[1]}
+
+def point_biserial(x, y):
+
+	results = scipy.stats.pointbiserialr(x, y)
+	return {"r-value": results[0], "p-value": results[1]}
+
+def kendall(x, y, **kwargs):
+
+	results = scipy.stats.kendalltau(x, y, **kwargs)
+	return {"tau": results[0], "p-value": results[1]}
+
+def kendall_weighted(x, y, **kwargs):
+
+	results = scipy.stats.weightedtau(x, y, **kwargs)
+	return {"tau": results[0], "p-value": results[1]}
+
+def mgc(x, y, **kwargs):
+
+	results = scipy.stats.multiscale_graphcorr(x, y, **kwargs)
+	return {"k-value": results[0], "p-value": results[1], "data": results[2]} # unsure if MGC test returns a k value

analysis-master/tra_analysis/Fit.py

@@ -0,0 +1,87 @@
+# Titan Robotics Team 2022: CPU fitting models
+# Written by Dev Singh
+# Notes:
+#   this module is cuda-optimized (as appropriate) and vectorized (except for one small part)
+# setup:
+
+__version__ = "0.0.2"
+
+# changelog should be viewed using print(analysis.fits.__changelog__)
+__changelog__ = """changelog:
+	0.0.2:
+		- renamed module to Fit
+	0.0.1:
+		- initial release, add circle fitting with LSC
+"""
+
+__author__ = (
+	"Dev Singh <dev@devksingh.com>"
+)
+
+__all__ = [
+	'CircleFit'
+]
+
+import numpy as np
+
+class CircleFit:
+	"""Class to fit data to a circle using the Least Square Circle (LSC) method"""
+	# For more information on the LSC method, see: 
+	# http://www.dtcenter.org/sites/default/files/community-code/met/docs/write-ups/circle_fit.pdf
+	def __init__(self, x, y, xy=None):
+		self.ournp = np #todo: implement cupy correctly
+		if type(x) == list:
+			x = np.array(x)
+		if type(y) == list:
+			y = np.array(y)
+		if type(xy) == list:
+			xy = np.array(xy)
+		if xy != None: 
+			self.coords = xy
+		else: 
+			# following block combines x and y into one array if not already done
+			self.coords = self.ournp.vstack(([x.T], [y.T])).T
+	def calc_R(x, y, xc, yc):
+		"""Returns distance between center and point"""
+		return self.ournp.sqrt((x-xc)**2 + (y-yc)**2)
+	def f(c, x, y):
+		"""Returns distance between point and circle at c"""
+		Ri = calc_R(x, y, *c)
+		return Ri - Ri.mean()
+	def LSC(self):
+		"""Fits given data to a circle and returns the center, radius, and variance"""
+		x = self.coords[:, 0]
+		y = self.coords[:, 1]
+		# guessing at a center
+		x_m = self.ournp.mean(x)
+		y_m = self.ournp.mean(y)
+
+		# calculation of the reduced coordinates
+		u = x - x_m
+		v = y - y_m
+
+		# linear system defining the center (uc, vc) in reduced coordinates:
+		#    Suu * uc +  Suv * vc = (Suuu + Suvv)/2
+		#    Suv * uc +  Svv * vc = (Suuv + Svvv)/2
+		Suv  = self.ournp.sum(u*v)
+		Suu  = self.ournp.sum(u**2)
+		Svv  = self.ournp.sum(v**2)
+		Suuv = self.ournp.sum(u**2 * v)
+		Suvv = self.ournp.sum(u * v**2)
+		Suuu = self.ournp.sum(u**3)
+		Svvv = self.ournp.sum(v**3)
+
+		# Solving the linear system
+		A = self.ournp.array([ [ Suu, Suv ], [Suv, Svv]])
+		B = self.ournp.array([ Suuu + Suvv, Svvv + Suuv ])/2.0
+		uc, vc = self.ournp.linalg.solve(A, B)
+
+		xc_1 = x_m + uc
+		yc_1 = y_m + vc
+
+		# Calculate the distances from center (xc_1, yc_1)
+		Ri_1     = self.ournp.sqrt((x-xc_1)**2 + (y-yc_1)**2)
+		R_1      = self.ournp.mean(Ri_1)
+		# calculate residual error
+		residu_1 = self.ournp.sum((Ri_1-R_1)**2)
+		return (xc_1, yc_1, R_1, residu_1)

analysis-master/tra_analysis/KNN.py

@@ -0,0 +1,48 @@
+# Titan Robotics Team 2022: KNN submodule
+# Written by Arthur Lu
+# Notes:
+#    this should be imported as a python module using 'from tra_analysis import KNN'
+# setup:
+
+__version__ = "1.0.2"
+
+__changelog__ = """changelog:
+	1.0.2:
+		- generalized optional args to **kwargs
+	1.0.1:
+		- optimized imports
+	1.0.0:
+		- ported analysis.KNN() here
+		- removed classness
+"""
+
+__author__ = (
+	"Arthur Lu <learthurgo@gmail.com>",
+	"James Pan <zpan@imsa.edu>"
+)
+
+__all__ = [
+	'knn_classifier',
+	'knn_regressor'
+]
+
+import sklearn
+from . import ClassificationMetric, RegressionMetric
+
+def knn_classifier(data, labels, n_neighbors = 5, test_size = 0.3, **kwargs): #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(n_neighbors = n_neighbors, **kwargs)
+	model.fit(data_train, labels_train)
+	predictions = model.predict(data_test)
+
+	return model, ClassificationMetric(predictions, labels_test)
+
+def knn_regressor(data, outputs, n_neighbors = 5, test_size = 0.3, **kwargs):
+
+	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, **kwargs)
+	model.fit(data_train, outputs_train)
+	predictions = model.predict(data_test)
+
+	return model, RegressionMetric.RegressionMetric(predictions, outputs_test)

analysis-master/tra_analysis/NaiveBayes.py

@@ -0,0 +1,67 @@
+# Titan Robotics Team 2022: NaiveBayes submodule
+# Written by Arthur Lu
+# Notes:
+#    this should be imported as a python module using 'from tra_analysis import NaiveBayes'
+# setup:
+
+__version__ = "1.0.2"
+
+__changelog__ = """changelog:
+	1.0.2:
+		- generalized optional args to **kwargs
+	1.0.1:
+		- optimized imports
+	1.0.0:
+		- ported analysis.NaiveBayes() here
+		- removed classness
+"""
+
+__author__ = (
+	"Arthur Lu <learthurgo@gmail.com>",
+)
+
+__all__ = [
+	'gaussian',
+	'multinomial',
+	'bernoulli',
+	'complement',
+]
+
+import sklearn
+from . import ClassificationMetric
+
+def gaussian(data, labels, test_size = 0.3, **kwargs):
+
+	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(**kwargs)
+	model.fit(data_train, labels_train)
+	predictions = model.predict(data_test)
+
+	return model, ClassificationMetric(predictions, labels_test)
+
+def multinomial(data, labels, test_size = 0.3, **kwargs):
+
+	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(**kwargs)
+	model.fit(data_train, labels_train)
+	predictions = model.predict(data_test)
+
+	return model, ClassificationMetric(predictions, labels_test)
+
+def bernoulli(data, labels, test_size = 0.3, **kwargs):
+
+	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(**kwargs)
+	model.fit(data_train, labels_train)
+	predictions = model.predict(data_test)
+
+	return model, ClassificationMetric(predictions, labels_test)
+
+def complement(data, labels, test_size = 0.3, **kwargs):
+
+	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(**kwargs)
+	model.fit(data_train, labels_train)
+	predictions = model.predict(data_test)
+
+	return model, ClassificationMetric(predictions, labels_test)

analysis-master/tra_analysis/RandomForest.py

@@ -0,0 +1,50 @@
+# Titan Robotics Team 2022: RandomForest submodule
+# Written by Arthur Lu
+# Notes:
+#    this should be imported as a python module using 'from tra_analysis import RandomForest'
+# setup:
+
+__version__ = "1.0.3"
+
+__changelog__ = """changelog:
+	1.0.3:
+		- updated RandomForestClassifier and RandomForestRegressor parameters to match sklearn v 1.0.2
+		- changed default values for kwargs to rely on sklearn
+	1.0.2:
+		- optimized imports
+	1.0.1:
+		- fixed __all__
+	1.0.0:
+		- ported analysis.RandomFores() here
+		- removed classness
+"""
+
+__author__ = (
+	"Arthur Lu <learthurgo@gmail.com>",
+)
+
+__all__ = [
+	"random_forest_classifier",
+	"random_forest_regressor",
+]
+
+import sklearn, sklearn.ensemble, sklearn.naive_bayes
+from . import ClassificationMetric, RegressionMetric
+
+def random_forest_classifier(data, labels, test_size, n_estimators, **kwargs):
+
+	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, **kwargs)
+	kernel.fit(data_train, labels_train)
+	predictions = kernel.predict(data_test)
+
+	return kernel, ClassificationMetric(predictions, labels_test)
+
+def random_forest_regressor(data, outputs, test_size, n_estimators, **kwargs):
+
+	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, **kwargs)
+	kernel.fit(data_train, outputs_train)
+	predictions = kernel.predict(data_test)
+
+	return kernel, RegressionMetric.RegressionMetric(predictions, outputs_test)

analysis-master/tra_analysis/RegressionMetric.py

@@ -0,0 +1,43 @@
+# Titan Robotics Team 2022: RegressionMetric submodule
+# Written by Arthur Lu
+# Notes:
+#    this should be imported as a python module using 'from tra_analysis import RegressionMetric'
+# setup:
+
+__version__ = "1.0.1"
+
+__changelog__ = """changelog:
+	1.0.1:
+		- optimized imports
+	1.0.0:
+		- ported analysis.RegressionMetric() here
+"""
+
+__author__ = (
+	"Arthur Lu <learthurgo@gmail.com>",
+)
+
+__all__ = [
+	'RegressionMetric'
+]
+
+import numpy as np
+import sklearn
+
+class RegressionMetric():
+
+	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 np.sqrt(sklearn.metrics.mean_squared_error(targets, predictions))

analysis-master/tra_analysis/SVM.py

@@ -0,0 +1,89 @@
+# Titan Robotics Team 2022: SVM submodule
+# Written by Arthur Lu
+# Notes:
+#    this should be imported as a python module using 'from tra_analysis import SVM'
+# setup:
+
+__version__ = "1.0.3"
+
+__changelog__ = """changelog:
+	1.0.3:
+		- optimized imports
+	1.0.2: 
+		- fixed __all__
+	1.0.1:
+		- removed unessasary self calls
+		- removed classness
+	1.0.0:
+		- ported analysis.SVM() here
+"""
+
+__author__ = (
+	"Arthur Lu <learthurgo@gmail.com>",
+)
+
+__all__ = [
+	"CustomKernel",
+	"StandardKernel",
+	"PrebuiltKernel",
+	"fit",
+	"eval_classification",
+	"eval_regression",
+]
+
+import sklearn
+from . import ClassificationMetric, RegressionMetric
+
+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(kernel, train_data, train_outputs): # expects *2d data, 1d labels or outputs
+
+	return kernel.fit(train_data, train_outputs)
+
+def eval_classification(kernel, test_data, test_outputs):
+
+	predictions = kernel.predict(test_data)
+
+	return ClassificationMetric(predictions, test_outputs)
+
+def eval_regression(kernel, test_data, test_outputs):
+
+	predictions = kernel.predict(test_data)
+
+	return RegressionMetric(predictions, test_outputs)

analysis-master/tra_analysis/Sort.py

@@ -0,0 +1,424 @@
+# Titan Robotics Team 2022: Sort submodule
+# Written by Arthur Lu and James Pan
+# Notes:
+#    this should be imported as a python module using 'from tra_analysis import Sort'
+# setup:
+
+__version__ = "1.0.1"
+
+__changelog__ = """changelog:
+	1.0.1:
+		- fixed __all__
+	1.0.0:
+		- ported analysis.Sort() here
+		- removed classness
+"""
+
+__author__ = (
+	"Arthur Lu <learthurgo@gmail.com>",
+	"James Pan <zpan@imsa.edu>",
+)
+
+__all__ = [
+	"quicksort",
+	"mergesort",
+	"introsort",
+	"heapsort",
+	"insertionsort",
+	"timsort",
+	"selectionsort",
+	"shellsort",
+	"bubblesort",
+	"cyclesort",
+	"cocktailsort",
+]
+
+import numpy as np
+
+def quicksort(a):
+
+	def sort(array):
+
+		less = []
+		equal = []
+		greater = []
+
+		if len(array) > 1:
+			pivot = array[0]
+			for x in array:
+				if x < pivot:
+					less.append(x)
+				elif x == pivot:
+					equal.append(x)
+				elif x > pivot:
+					greater.append(x)
+			return sort(less)+equal+sort(greater) 
+		else:
+			return array
+
+	return np.array(sort(a))
+
+def mergesort(a):
+
+	def sort(array):
+
+		array = array
+
+		if len(array) >1: 
+			middle = len(array) // 2
+			L = array[:middle]
+			R = array[middle:]
+	
+			sort(L)
+			sort(R)
+	
+			i = j = k = 0
+
+			while i < len(L) and j < len(R): 
+				if L[i] < R[j]: 
+					array[k] = L[i] 
+					i+= 1
+				else: 
+					array[k] = R[j] 
+					j+= 1
+				k+= 1
+
+			while i < len(L): 
+				array[k] = L[i] 
+				i+= 1
+				k+= 1
+			
+			while j < len(R): 
+				array[k] = R[j] 
+				j+= 1
+				k+= 1
+
+			return array
+
+	return sort(a)
+
+def introsort(a):
+
+	def sort(array, start, end, maxdepth):
+
+		array = array
+
+		if end - start <= 1:
+			return
+		elif maxdepth == 0:
+			heapsort(array, start, end)
+		else:
+			p = partition(array, start, end)
+			sort(array, start, p + 1, maxdepth - 1)
+			sort(array, p + 1, end, maxdepth - 1)
+
+		return array
+
+	def partition(array, start, end):
+		pivot = array[start]
+		i = start - 1
+		j = end
+	
+		while True:
+			i = i + 1
+			while array[i] < pivot:
+				i = i + 1
+			j = j - 1
+			while array[j] > pivot:
+				j = j - 1
+	
+			if i >= j:
+				return j
+	
+			swap(array, i, j)
+
+	def swap(array, i, j):
+		array[i], array[j] = array[j], array[i]
+
+	def heapsort(array, start, end):
+		build_max_heap(array, start, end)
+		for i in range(end - 1, start, -1):
+			swap(array, start, i)
+			max_heapify(array, index=0, start=start, end=i)
+
+	def build_max_heap(array, start, end):
+		def parent(i):
+			return (i - 1)//2
+		length = end - start
+		index = parent(length - 1)
+		while index >= 0:
+			max_heapify(array, index, start, end)
+			index = index - 1
+
+	def max_heapify(array, index, start, end):
+		def left(i):
+			return 2*i + 1
+		def right(i):
+			return 2*i + 2
+	
+		size = end - start
+		l = left(index)
+		r = right(index)
+		if (l < size and array[start + l] > array[start + index]):
+			largest = l
+		else:
+			largest = index
+		if (r < size and array[start + r] > array[start + largest]):
+			largest = r
+		if largest != index:
+			swap(array, start + largest, start + index)
+			max_heapify(array, largest, start, end)
+
+	maxdepth = (len(a).bit_length() - 1)*2
+
+	return sort(a, 0, len(a), maxdepth)
+
+def heapsort(a):
+
+	def sort(array):
+		
+		array = array
+
+		n = len(array) 
+
+		for i in range(n//2 - 1, -1, -1): 
+			heapify(array, n, i) 
+
+		for i in range(n-1, 0, -1): 
+			array[i], array[0] = array[0], array[i]
+			heapify(array, i, 0) 
+
+		return array
+
+	def heapify(array, n, i):
+
+		array = array
+
+		largest = i
+		l = 2 * i + 1
+		r = 2 * i + 2
+
+		if l < n and array[i] < array[l]: 
+			largest = l 
+
+		if r < n and array[largest] < array[r]: 
+			largest = r 
+
+		if largest != i: 
+			array[i],array[largest] = array[largest],array[i]
+			heapify(array, n, largest)
+		
+		return array
+
+	return sort(a)
+
+def insertionsort(a):
+
+	def sort(array):
+
+		array = array
+
+		for i in range(1, len(array)): 
+	
+			key = array[i] 
+
+			j = i-1
+			while j >=0 and key < array[j] : 
+					array[j+1] = array[j] 
+					j -= 1
+			array[j+1] = key 
+
+		return array
+
+	return sort(a)
+
+def timsort(a, block = 32):
+
+	BLOCK = block
+
+	def sort(array, n):
+
+		array = array
+
+		for i in range(0, n, BLOCK):  
+			insertionsort(array, i, min((i+31), (n-1)))
+
+		size = BLOCK 
+		while size < n:
+
+			for left in range(0, n, 2*size):  
+	
+				mid = left + size - 1 
+				right = min((left + 2*size - 1), (n-1))  
+				merge(array, left, mid, right)  
+		
+			size = 2*size
+
+		return array
+
+	def insertionsort(array, left, right):
+
+		array = array 
+
+		for i in range(left + 1, right+1):  
+		
+			temp = array[i]  
+			j = i - 1 
+			while j >= left and array[j] > temp :  
+			
+				array[j+1] = array[j]  
+				j -= 1
+			
+			array[j+1] = temp
+
+		return array
+		
+
+	def merge(array, l, m, r): 
+	
+		len1, len2 =  m - l + 1, r - m  
+		left, right = [], []  
+		for i in range(0, len1):  
+			left.append(array[l + i])  
+		for i in range(0, len2):  
+			right.append(array[m + 1 + i])  
+		
+		i, j, k = 0, 0, l 
+
+		while i < len1 and j < len2:  
+		
+			if left[i] <= right[j]:  
+				array[k] = left[i]  
+				i += 1 
+			
+			else: 
+				array[k] = right[j]  
+				j += 1 
+			
+			k += 1
+
+		while i < len1:  
+		
+			array[k] = left[i]  
+			k += 1 
+			i += 1
+
+		while j < len2:  
+			array[k] = right[j]  
+			k += 1
+			j += 1
+
+	return sort(a, len(a))
+
+def selectionsort(a):
+	array = a
+	for i in range(len(array)): 
+		min_idx = i
+		for j in range(i+1, len(array)): 
+			if array[min_idx] > array[j]: 
+				min_idx = j         
+		array[i], array[min_idx] = array[min_idx], array[i]
+	return array
+
+def shellsort(a):
+	array = a
+	n = len(array)
+	gap = n//2
+
+	while gap > 0: 
+
+		for i in range(gap,n): 
+
+			temp = array[i] 
+			j = i 
+			while  j >= gap and array[j-gap] >temp: 
+				array[j] = array[j-gap] 
+				j -= gap 
+			array[j] = temp 
+		gap //= 2
+
+	return array
+
+def bubblesort(a):
+
+	def sort(array):
+		for i, num in enumerate(array):
+			try:
+				if array[i+1] < num:
+					array[i] = array[i+1]
+					array[i+1] = num
+					sort(array)
+			except IndexError:
+				pass
+		return array
+
+	return sort(a)
+
+def cyclesort(a):
+
+	def sort(array):
+
+		array = array
+		writes = 0
+
+		for cycleStart in range(0, len(array) - 1): 
+			item = array[cycleStart] 
+
+			pos = cycleStart 
+			for i in range(cycleStart + 1, len(array)): 
+				if array[i] < item: 
+					pos += 1
+
+			if pos == cycleStart: 
+				continue
+
+			while item == array[pos]: 
+				pos += 1
+				array[pos], item = item, array[pos] 
+				writes += 1
+
+			while pos != cycleStart: 
+
+				pos = cycleStart 
+				for i in range(cycleStart + 1, len(array)): 
+					if array[i] < item: 
+						pos += 1
+
+				while item == array[pos]: 
+					pos += 1
+				array[pos], item = item, array[pos] 
+				writes += 1
+			
+		return array
+	
+	return sort(a)
+
+def cocktailsort(a):
+
+	def sort(array):
+
+		array = array
+
+		n = len(array) 
+		swapped = True
+		start = 0
+		end = n-1
+		while (swapped == True): 
+			swapped = False
+			for i in range (start, end): 
+				if (array[i] > array[i + 1]) : 
+					array[i], array[i + 1]= array[i + 1], array[i] 
+					swapped = True
+			if (swapped == False): 
+				break
+			swapped = False
+			end = end-1
+			for i in range(end-1, start-1, -1): 
+				if (array[i] > array[i + 1]): 
+					array[i], array[i + 1] = array[i + 1], array[i] 
+					swapped = True
+			start = start + 1
+
+		return array
+
+	return sort(a)

analysis-master/tra_analysis/StatisticalTest.py

@@ -0,0 +1,315 @@
+# Titan Robotics Team 2022: StatisticalTest submodule
+# Written by Arthur Lu
+# Notes:
+#    this should be imported as a python module using 'from tra_analysis import StatisticalTest'
+# setup:
+
+__version__ = "1.0.3"
+
+__changelog__ = """changelog:
+	1.0.3:
+		- optimized imports
+	1.0.2:
+		- added tukey_multicomparison
+		- fixed styling
+	1.0.1:
+		- fixed typo in __all__
+	1.0.0:
+		- ported analysis.StatisticalTest() here
+		- removed classness
+"""
+
+__author__ = (
+	"Arthur Lu <learthurgo@gmail.com>",
+	"James Pan <zpan@imsa.edu>",
+)
+
+__all__ = [
+	'ttest_onesample',
+	'ttest_independent',
+	'ttest_statistic',
+	'ttest_related',
+	'ks_fitness',
+	'chisquare',
+	'powerdivergence'
+	'ks_twosample',
+	'es_twosample',
+	'mw_rank',
+	'mw_tiecorrection',
+	'rankdata',
+	'wilcoxon_ranksum',
+	'wilcoxon_signedrank',
+	'kw_htest',
+	'friedman_chisquare',
+	'bm_wtest',
+	'combine_pvalues',
+	'jb_fitness',
+	'ab_equality',
+	'bartlett_variance',
+	'levene_variance',
+	'sw_normality',
+	'shapiro',
+	'ad_onesample',
+	'ad_ksample',
+	'binomial',
+	'fk_variance',
+	'mood_mediantest',
+	'mood_equalscale',
+	'skewtest',
+	'kurtosistest',
+	'normaltest',
+	'tukey_multicomparison'
+]
+
+import numpy as np
+import scipy
+
+def ttest_onesample(a, popmean, axis = 0, nan_policy = 'propagate'):
+
+	results = scipy.stats.ttest_1samp(a, popmean, axis = axis, nan_policy = nan_policy)
+	return {"t-value": results[0], "p-value": results[1]}
+
+def ttest_independent(a, b, equal = True, nan_policy = 'propagate'):
+
+	results = scipy.stats.ttest_ind(a, b, equal_var = equal, nan_policy = nan_policy)
+	return {"t-value": results[0], "p-value": results[1]}
+
+def ttest_statistic(o1, o2, equal = True):
+
+	results = scipy.stats.ttest_ind_from_stats(o1["mean"], o1["std"], o1["nobs"], o2["mean"], o2["std"], o2["nobs"], equal_var = equal)
+	return {"t-value": results[0], "p-value": results[1]}
+
+def ttest_related(a, b, axis = 0, nan_policy='propagate'):
+
+	results = scipy.stats.ttest_rel(a, b, axis = axis, nan_policy = nan_policy)
+	return {"t-value": results[0], "p-value": results[1]}
+
+def ks_fitness(rvs, cdf, args = (), N = 20, alternative = 'two-sided', mode = 'approx'):
+
+	results = scipy.stats.kstest(rvs, cdf, args = args, N = N, alternative = alternative, mode = mode)
+	return {"ks-value": results[0], "p-value": results[1]}
+
+def chisquare(f_obs, f_exp = None, ddof = None, axis = 0):
+
+	results = scipy.stats.chisquare(f_obs, f_exp = f_exp, ddof = ddof, axis = axis)
+	return {"chisquared-value": results[0], "p-value": results[1]}
+
+def powerdivergence(f_obs, f_exp = None, ddof = None, axis = 0, lambda_ = None):
+
+	results = scipy.stats.power_divergence(f_obs, f_exp = f_exp, ddof = ddof, axis = axis, lambda_ = lambda_)
+	return {"powerdivergence-value": results[0], "p-value": results[1]}
+
+def ks_twosample(x, y, alternative = 'two_sided', mode = 'auto'):
+	
+	results = scipy.stats.ks_2samp(x, y, alternative = alternative, mode = mode)
+	return {"ks-value": results[0], "p-value": results[1]}
+
+def es_twosample(x, y, t = (0.4, 0.8)):
+
+	results = scipy.stats.epps_singleton_2samp(x, y, t = t)
+	return {"es-value": results[0], "p-value": results[1]}
+
+def mw_rank(x, y, use_continuity = True, alternative = None):
+
+	results = scipy.stats.mannwhitneyu(x, y, use_continuity = use_continuity, alternative = alternative)
+	return {"u-value": results[0], "p-value": results[1]}
+
+def mw_tiecorrection(rank_values):
+
+	results = scipy.stats.tiecorrect(rank_values)
+	return {"correction-factor": results}
+
+def rankdata(a, method = 'average'):
+
+	results = scipy.stats.rankdata(a, method = method)
+	return results
+
+def wilcoxon_ranksum(a, b): # this seems to be superceded by Mann Whitney Wilcoxon U Test
+
+	results = scipy.stats.ranksums(a, b)
+	return {"u-value": results[0], "p-value": results[1]}
+
+def wilcoxon_signedrank(x, y = None, zero_method = 'wilcox', correction = False, alternative = 'two-sided'):
+
+	results = scipy.stats.wilcoxon(x, y = y, zero_method = zero_method, correction = correction, alternative = alternative)
+	return {"t-value": results[0], "p-value": results[1]}
+
+def kw_htest(*args, nan_policy = 'propagate'):
+
+	results = scipy.stats.kruskal(*args, nan_policy = nan_policy)
+	return {"h-value": results[0], "p-value": results[1]}
+
+def friedman_chisquare(*args):
+
+	results = scipy.stats.friedmanchisquare(*args)
+	return {"chisquared-value": results[0], "p-value": results[1]}
+
+def bm_wtest(x, y, alternative = 'two-sided', distribution = 't', nan_policy = 'propagate'):
+
+	results = scipy.stats.brunnermunzel(x, y, alternative = alternative, distribution = distribution, nan_policy = nan_policy)
+	return {"w-value": results[0], "p-value": results[1]}
+
+def combine_pvalues(pvalues, method = 'fisher', weights = None):
+
+	results = scipy.stats.combine_pvalues(pvalues, method = method, weights = weights)
+	return {"combined-statistic": results[0], "p-value": results[1]}
+
+def jb_fitness(x):
+
+	results = scipy.stats.jarque_bera(x)
+	return {"jb-value": results[0], "p-value": results[1]}
+
+def ab_equality(x, y):
+
+	results = scipy.stats.ansari(x, y)
+	return {"ab-value": results[0], "p-value": results[1]}
+
+def bartlett_variance(*args):
+
+	results = scipy.stats.bartlett(*args)
+	return {"t-value": results[0], "p-value": results[1]}
+
+def levene_variance(*args, center = 'median', proportiontocut = 0.05):
+
+	results = scipy.stats.levene(*args, center = center, proportiontocut = proportiontocut)
+	return {"w-value": results[0], "p-value": results[1]}
+
+def sw_normality(x):
+
+	results = scipy.stats.shapiro(x)
+	return {"w-value": results[0], "p-value": results[1]}
+
+def shapiro(x):
+
+	return "destroyed by facts and logic"
+
+def ad_onesample(x, dist = 'norm'):
+
+	results = scipy.stats.anderson(x, dist = dist)
+	return {"d-value": results[0], "critical-values": results[1], "significance-value": results[2]}
+
+def ad_ksample(samples, midrank = True):
+
+	results = scipy.stats.anderson_ksamp(samples, midrank = midrank)
+	return {"d-value": results[0], "critical-values": results[1], "significance-value": results[2]}
+
+def binomial(x, n = None, p = 0.5, alternative = 'two-sided'):
+
+	results = scipy.stats.binom_test(x, n = n, p = p, alternative = alternative)
+	return {"p-value": results}
+
+def fk_variance(*args, center = 'median', proportiontocut = 0.05):
+
+	results = scipy.stats.fligner(*args, center = center, proportiontocut = proportiontocut)
+	return {"h-value": results[0], "p-value": results[1]} # unknown if the statistic is an h value
+
+def mood_mediantest(*args, ties = 'below', correction = True, lambda_ = 1, nan_policy = 'propagate'):
+
+	results = scipy.stats.median_test(*args, ties = ties, correction = correction, lambda_ = lambda_, nan_policy = nan_policy)
+	return {"chisquared-value": results[0], "p-value": results[1], "m-value": results[2], "table": results[3]}
+
+def mood_equalscale(x, y, axis = 0):
+
+	results = scipy.stats.mood(x, y, axis = axis)
+	return {"z-score": results[0], "p-value": results[1]}
+
+def skewtest(a, axis = 0, nan_policy = 'propogate'):
+
+	results = scipy.stats.skewtest(a, axis = axis, nan_policy = nan_policy)
+	return {"z-score": results[0], "p-value": results[1]}
+
+def kurtosistest(a, axis = 0, nan_policy = 'propogate'):
+
+	results = scipy.stats.kurtosistest(a, axis = axis, nan_policy = nan_policy)
+	return {"z-score": results[0], "p-value": results[1]}
+
+def normaltest(a, axis = 0, nan_policy = 'propogate'):
+
+	results = scipy.stats.normaltest(a, axis = axis, nan_policy = nan_policy)
+	return {"z-score": results[0], "p-value": results[1]}
+
+def get_tukeyQcrit(k, df, alpha=0.05):
+	'''
+	From statsmodels.sandbox.stats.multicomp
+	
+	return critical values for Tukey's HSD (Q)
+
+	Parameters
+	----------
+	k : int in {2, ..., 10}
+		number of tests
+	df : int
+		degrees of freedom of error term
+	alpha : {0.05, 0.01}
+		type 1 error, 1-confidence level
+
+	not enough error checking for limitations
+	'''
+	# qtable from statsmodels.sandbox.stats.multicomp
+	qcrit = '''
+	2     3     4     5     6     7     8     9     10
+	5   3.64 5.70   4.60 6.98   5.22 7.80   5.67 8.42   6.03 8.91   6.33 9.32   6.58 9.67   6.80 9.97   6.99 10.24
+	6   3.46 5.24   4.34 6.33   4.90 7.03   5.30 7.56   5.63 7.97   5.90 8.32   6.12 8.61   6.32 8.87   6.49 9.10
+	7   3.34 4.95   4.16 5.92   4.68 6.54   5.06 7.01   5.36 7.37   5.61 7.68   5.82 7.94   6.00 8.17   6.16 8.37
+	8   3.26 4.75   4.04 5.64   4.53 6.20   4.89 6.62   5.17 6.96   5.40 7.24       5.60 7.47   5.77 7.68   5.92 7.86
+	9   3.20 4.60   3.95 5.43   4.41 5.96   4.76 6.35   5.02 6.66   5.24 6.91       5.43 7.13   5.59 7.33   5.74 7.49
+	10  3.15 4.48   3.88 5.27   4.33 5.77   4.65 6.14   4.91 6.43   5.12 6.67       5.30 6.87   5.46 7.05   5.60 7.21
+	11  3.11 4.39   3.82 5.15   4.26 5.62   4.57 5.97   4.82 6.25   5.03 6.48 5.20 6.67   5.35 6.84   5.49 6.99
+	12  3.08 4.32   3.77 5.05   4.20 5.50   4.51 5.84   4.75 6.10   4.95 6.32 5.12 6.51   5.27 6.67   5.39 6.81
+	13  3.06 4.26   3.73 4.96   4.15 5.40   4.45 5.73   4.69 5.98   4.88 6.19 5.05 6.37   5.19 6.53   5.32 6.67
+	14  3.03 4.21   3.70 4.89   4.11 5.32   4.41 5.63   4.64 5.88   4.83 6.08 4.99 6.26   5.13 6.41   5.25 6.54
+	15  3.01 4.17   3.67 4.84   4.08 5.25   4.37 5.56   4.59 5.80   4.78 5.99 4.94 6.16   5.08 6.31   5.20 6.44
+	16  3.00 4.13   3.65 4.79   4.05 5.19   4.33 5.49   4.56 5.72   4.74 5.92 4.90 6.08   5.03 6.22   5.15 6.35
+	17  2.98 4.10   3.63 4.74   4.02 5.14   4.30 5.43   4.52 5.66   4.70 5.85 4.86 6.01   4.99 6.15   5.11 6.27
+	18  2.97 4.07   3.61 4.70   4.00 5.09   4.28 5.38   4.49 5.60   4.67 5.79 4.82 5.94   4.96 6.08   5.07 6.20
+	19  2.96 4.05   3.59 4.67   3.98 5.05   4.25 5.33   4.47 5.55   4.65 5.73 4.79 5.89   4.92 6.02   5.04 6.14
+	20  2.95 4.02   3.58 4.64   3.96 5.02   4.23 5.29   4.45 5.51   4.62 5.69 4.77 5.84   4.90 5.97   5.01 6.09
+	24  2.92 3.96   3.53 4.55   3.90 4.91   4.17 5.17   4.37 5.37   4.54 5.54 4.68 5.69   4.81 5.81   4.92 5.92
+	30  2.89 3.89   3.49 4.45   3.85 4.80   4.10 5.05   4.30 5.24   4.46 5.40 4.60 5.54   4.72 5.65   4.82 5.76
+	40  2.86 3.82   3.44 4.37   3.79 4.70   4.04 4.93   4.23 5.11   4.39 5.26 4.52 5.39   4.63 5.50   4.73 5.60
+	60  2.83 3.76   3.40 4.28   3.74 4.59   3.98 4.82   4.16 4.99   4.31 5.13 4.44 5.25   4.55 5.36   4.65 5.45
+	120   2.80 3.70   3.36 4.20   3.68 4.50   3.92 4.71   4.10 4.87   4.24 5.01 4.36 5.12   4.47 5.21   4.56 5.30
+	infinity  2.77 3.64   3.31 4.12   3.63 4.40   3.86 4.60   4.03 4.76   4.17 4.88   4.29 4.99   4.39 5.08   4.47 5.16
+	'''
+	res = [line.split() for line in qcrit.replace('infinity','9999').split('\n')]
+	c=np.array(res[2:-1]).astype(float)
+	#c[c==9999] = np.inf
+	ccols = np.arange(2,11)
+	crows = c[:,0]
+	cv005 = c[:, 1::2]
+	cv001 = c[:, 2::2]
+
+	if alpha == 0.05:
+		intp = scipy.interpolate.interp1d(crows, cv005[:,k-2])
+	elif alpha == 0.01:
+		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)
+
+def tukey_multicomparison(groups, alpha=0.05):
+	#formulas according to https://astatsa.com/OneWay_Anova_with_TukeyHSD/
+
+	k = len(groups)
+	df = 0
+	means = []
+	MSE = 0
+	for group in groups:
+		df+= len(group)
+		mean = sum(group)/len(group)
+		means.append(mean)
+		MSE += sum([(i-mean)**2 for i in group])
+	df -= k
+	MSE /= df
+
+	q_dict = {}
+	crit_q = get_tukeyQcrit(k, df, alpha)
+
+	for i in range(k-1):
+		for j in range(i+1, k):
+			numerator = abs(means[i] - means[j])
+			denominator = np.sqrt( MSE / ( 2/(1/len(groups[i]) + 1/len(groups[j])) ))
+			q = numerator/denominator
+			q_dict["group "+ str(i+1) + " and group " + str(j+1)] = [q, q>crit_q]
+	
+	return q_dict

analysis-master/tra_analysis/__init__.py

@@ -0,0 +1,76 @@
+# Titan Robotics Team 2022: tra_analysis package
+# Written by Arthur Lu, Jacob Levine, Dev Singh, and James Pan
+# Notes:
+#    this should be imported as a python package using 'import tra_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__ = "4.0.0"
+
+# changelog should be viewed using print(analysis.__changelog__)
+__changelog__ = """changelog:
+	4.0.0:
+		- deprecated all *_obj.py compatibility modules
+		- 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:
+		- fixed __changelog__
+		- fixed __all__ of Analysis, Array, ClassificationMetric, CorrelationTest, RandomForest, Sort, SVM
+		- populated __all__
+	3.0.0-alpha.4:
+		- changed version to 3 because of significant changes
+		- added backwards compatibility import of analysis
+	2.1.0-alpha.3:
+		- fixed indentation in meta data
+	2.1.0-alpha.2:
+		- updated SVM import
+	2.1.0-alpha.1:
+		- moved multiple submodules under analysis to their own modules/files
+		- added header, __version__, __changelog__, __author__, __all__ (unpopulated)
+"""
+
+__author__ = (
+	"Arthur Lu <learthurgo@gmail.com>",
+	"Jacob Levine <jlevine@imsa.edu>",
+	"Dev Singh <dev@devksingh.com>",
+	"James Pan <zpan@imsa.edu>"
+)
+
+__all__ = [
+	"Analysis",
+	"Array",
+	"ClassificationMetric",
+	"Clustering",
+	"CorrelationTest",
+	"Expression",
+	"Fit",
+	"KNN",
+	"NaiveBayes",
+	"RandomForest",
+	"RegressionMetric",
+	"Sort",
+	"StatisticalTest",
+	"SVM"
+]
+
+from . import Analysis as Analysis
+from .Array import Array
+from .ClassificationMetric import ClassificationMetric
+from . import Clustering
+from . import CorrelationTest
+from .equation import Expression
+from . import Fit
+from . import KNN
+from . import NaiveBayes
+from . import RandomForest
+from .RegressionMetric import RegressionMetric
+from . import Sort
+from . import StatisticalTest
+from . import SVM

analysis-master/tra_analysis/equation/Expression.py

@@ -0,0 +1,37 @@
+# Titan Robotics Team 2022: Expression submodule
+# Written by Arthur Lu
+# Notes:
+#    this should be imported as a python module using 'from tra_analysis.Equation import Expression'
+# 	 TODO:
+#	 	 - add option to pick parser backend
+#		 - fix unit tests
+# setup:
+
+__version__ = "0.0.1-alpha"
+
+__changelog__ = """changelog:
+	0.0.1-alpha:
+		- used the HybridExpressionParser as backend for Expression
+"""
+
+__author__ = (
+	"Arthur Lu <learthurgo@gmail.com>",
+)
+
+__all__ = {
+	"Expression"
+}
+
+import re
+from .parser import BNF, RegexInplaceParser, HybridExpressionParser, Core, equation_base
+
+class Expression(HybridExpressionParser):
+
+	expression = None
+	core = None
+
+	def __init__(self,expression,argorder=[],*args,**kwargs):
+		self.core = Core()
+		equation_base.equation_extend(self.core)
+		self.core.recalculateFMatch()
+		super().__init__(self.core, expression, argorder=[],*args,**kwargs)

analysis-master/tra_analysis/equation/__init__.py

@@ -0,0 +1,22 @@
+# Titan Robotics Team 2022: Expression submodule
+# Written by Arthur Lu
+# Notes:
+#    this should be imported as a python module using 'from tra_analysis import Equation'
+# setup:
+
+__version__ = "0.0.1-alpha"
+
+__changelog__ = """changelog:
+	0.0.1-alpha:
+		- made first prototype of Expression
+"""
+
+__author__ = (
+	"Arthur Lu <learthurgo@gmail.com>",
+)
+
+__all__ = {
+    "Expression"
+}
+
+from .Expression import Expression

analysis-master/tra_analysis/equation/parser/BNF.py

@@ -0,0 +1,97 @@
+from __future__ import division
+from pyparsing import (Literal, CaselessLiteral, Word, Combine, Group, Optional, ZeroOrMore, Forward, nums, alphas, oneOf)
+from . import py2
+import math
+import operator
+
+class BNF(object):
+
+	def pushFirst(self, strg, loc, toks):
+		self.exprStack.append(toks[0])
+
+	def pushUMinus(self, strg, loc, toks):
+		if toks and toks[0] == '-':
+			self.exprStack.append('unary -')
+
+	def __init__(self):
+		"""
+		expop   :: '^'
+		multop  :: '*' | '/'
+		addop   :: '+' | '-'
+		integer :: ['+' | '-'] '0'..'9'+
+		atom    :: PI | E | real | fn '(' expr ')' | '(' expr ')'
+		factor  :: atom [ expop factor ]*
+		term    :: factor [ multop factor ]*
+		expr    :: term [ addop term ]*
+		"""
+		point = Literal(".")
+		e = CaselessLiteral("E")
+		fnumber = Combine(Word("+-" + nums, nums) +
+						  Optional(point + Optional(Word(nums))) +
+						  Optional(e + Word("+-" + nums, nums)))
+		ident = Word(alphas, alphas + nums + "_$")
+		plus = Literal("+")
+		minus = Literal("-")
+		mult = Literal("*")
+		div = Literal("/")
+		lpar = Literal("(").suppress()
+		rpar = Literal(")").suppress()
+		addop = plus | minus
+		multop = mult | div
+		expop = Literal("^")
+		pi = CaselessLiteral("PI")
+		expr = Forward()
+		atom = ((Optional(oneOf("- +")) +
+				 (ident + lpar + expr + rpar | pi | e | fnumber).setParseAction(self.pushFirst))
+				| Optional(oneOf("- +")) + Group(lpar + expr + rpar)
+				).setParseAction(self.pushUMinus)
+		factor = Forward()
+		factor << atom + \
+			ZeroOrMore((expop + factor).setParseAction(self.pushFirst))
+		term = factor + \
+			ZeroOrMore((multop + factor).setParseAction(self.pushFirst))
+		expr << term + \
+			ZeroOrMore((addop + term).setParseAction(self.pushFirst))
+
+		self.bnf = expr
+
+		epsilon = 1e-12
+		
+		self.opn = {"+": operator.add,
+					"-": operator.sub,
+					"*": operator.mul,
+					"/": operator.truediv,
+					"^": operator.pow}
+		self.fn = {"sin": math.sin,
+				   "cos": math.cos,
+				   "tan": math.tan,
+				   "exp": math.exp,
+				   "abs": abs,
+				   "trunc": lambda a: int(a),
+				   "round": round,
+				   "sgn": lambda a: abs(a) > epsilon and py2.cmp(a, 0) or 0}
+
+	def evaluateStack(self, s):
+		op = s.pop()
+		if op == 'unary -':
+			return -self.evaluateStack(s)
+		if op in "+-*/^":
+			op2 = self.evaluateStack(s)
+			op1 = self.evaluateStack(s)
+			return self.opn[op](op1, op2)
+		elif op == "PI":
+			return math.pi
+		elif op == "E":
+			return math.e
+		elif op in self.fn:
+			return self.fn[op](self.evaluateStack(s))
+		elif op[0].isalpha():
+			return 0
+		else:
+			return float(op)
+
+	def eval(self, num_string, parseAll=True):
+		self.exprStack = []
+		results = self.bnf.parseString(num_string, parseAll)
+		val = self.evaluateStack(self.exprStack[:])
+		return val

analysis-master/tra_analysis/equation/parser/Hybrid.py

@@ -0,0 +1,521 @@
+from .Hybrid_Utils import Core, ExpressionFunction, ExpressionVariable, ExpressionValue
+import sys
+
+if sys.version_info >= (3,):
+	xrange = range
+	basestring = str
+
+class HybridExpressionParser(object):
+
+	def __init__(self,core,expression,argorder=[],*args,**kwargs):
+		super(HybridExpressionParser,self).__init__(*args,**kwargs)
+		if isinstance(expression,type(self)): # clone the object
+			self.core = core
+			self.__args = list(expression.__args)
+			self.__vars = dict(expression.__vars) # intenral array of preset variables
+			self.__argsused = set(expression.__argsused)
+			self.__expr = list(expression.__expr)
+			self.variables = {} # call variables
+		else:
+			self.__expression = expression
+			self.__args = argorder;
+			self.__vars = {} # intenral array of preset variables
+			self.__argsused = set()
+			self.__expr = [] # compiled equation tokens
+			self.variables = {} # call variables
+			self.__compile()
+			del self.__expression
+
+	def __getitem__(self, name):
+		if name in self.__argsused:
+			if name in self.__vars:
+				return self.__vars[name]
+			else:
+				return None
+		else:
+			raise KeyError(name)
+
+	def __setitem__(self,name,value):
+
+		if name in self.__argsused:
+			self.__vars[name] = value
+		else:
+			raise KeyError(name)
+
+	def __delitem__(self,name):
+
+		if name in self.__argsused:
+			if name in self.__vars:
+				del self.__vars[name]
+		else:
+			raise KeyError(name)
+
+	def __contains__(self, name):
+
+		return name in self.__argsused
+
+	def __call__(self,*args,**kwargs):
+
+		if len(self.__expr) == 0:
+			return None
+		self.variables = {}
+		self.variables.update(self.core.constants)
+		self.variables.update(self.__vars)
+		if len(args) > len(self.__args):
+			raise TypeError("<{0:s}.{1:s}({2:s}) object at {3:0=#10x}>() takes at most {4:d} arguments ({5:d} given)".format(
+					type(self).__module__,type(self).__name__,repr(self),id(self),len(self.__args),len(args)))
+		for i in xrange(len(args)):
+			if i < len(self.__args):
+				if self.__args[i] in kwargs:
+					raise TypeError("<{0:s}.{1:s}({2:s}) object at {3:0=#10x}>() got multiple values for keyword argument '{4:s}'".format(
+						type(self).__module__,type(self).__name__,repr(self),id(self),self.__args[i]))
+				self.variables[self.__args[i]] = args[i]
+		self.variables.update(kwargs)
+		for arg in self.__argsused:
+			if arg not in self.variables:
+				min_args = len(self.__argsused - (set(self.__vars.keys()) | set(self.core.constants.keys())))
+				raise TypeError("<{0:s}.{1:s}({2:s}) object at {3:0=#10x}>() takes at least {4:d} arguments ({5:d} given) '{6:s}' not defined".format(
+					type(self).__module__,type(self).__name__,repr(self),id(self),min_args,len(args)+len(kwargs),arg))
+		expr = self.__expr[::-1]
+		args = []
+		while len(expr) > 0:
+			t = expr.pop()
+			r = t(args,self)
+			args.append(r)
+		if len(args) > 1:
+			return args
+		else:
+			return args[0]
+
+	def __next(self,__expect_op):
+		if __expect_op:
+			m = self.core.gematch.match(self.__expression)
+			if m != None:
+				self.__expression = self.__expression[m.end():]
+				g = m.groups()
+				return g[0],'CLOSE'
+			m = self.core.smatch.match(self.__expression)
+			if m != None:
+				self.__expression = self.__expression[m.end():]
+				return ",",'SEP'
+			m = self.core.omatch.match(self.__expression)
+			if m != None:
+				self.__expression = self.__expression[m.end():]
+				g = m.groups()
+				return g[0],'OP'
+		else:
+			m = self.core.gsmatch.match(self.__expression)
+			if m != None:
+				self.__expression = self.__expression[m.end():]
+				g = m.groups()
+				return g[0],'OPEN'
+			m = self.core.vmatch.match(self.__expression)
+			if m != None:
+				self.__expression = self.__expression[m.end():]
+				g = m.groupdict(0)
+				if g['dec']:
+					if g["ivalue"]:
+						return complex(int(g["rsign"]+"1")*float(g["rvalue"])*10**int(g["rexpoent"]),int(g["isign"]+"1")*float(g["ivalue"])*10**int(g["iexpoent"])),'VALUE'
+					elif g["rexpoent"] or g["rvalue"].find('.')>=0:
+						return int(g["rsign"]+"1")*float(g["rvalue"])*10**int(g["rexpoent"]),'VALUE'
+					else:
+						return int(g["rsign"]+"1")*int(g["rvalue"]),'VALUE'
+				elif g["hex"]:
+					return int(g["hexsign"]+"1")*int(g["hexvalue"],16),'VALUE'
+				elif g["oct"]:
+					return int(g["octsign"]+"1")*int(g["octvalue"],8),'VALUE'
+				elif g["bin"]:
+					return int(g["binsign"]+"1")*int(g["binvalue"],2),'VALUE'
+				else:
+					raise NotImplemented("'{0:s}' Values Not Implemented Yet".format(m.string))
+			m = self.core.nmatch.match(self.__expression)
+			if m != None:
+				self.__expression = self.__expression[m.end():]
+				g = m.groups()
+				return g[0],'NAME'
+			m = self.core.fmatch.match(self.__expression)
+			if m != None:
+				self.__expression = self.__expression[m.end():]
+				g = m.groups()
+				return g[0],'FUNC'
+			m = self.core.umatch.match(self.__expression)
+			if m != None:
+				self.__expression = self.__expression[m.end():]
+				g = m.groups()
+				return g[0],'UNARY'
+			return None
+
+	def show(self):
+		"""Show RPN tokens
+
+		This will print out the internal token list (RPN) of the expression
+		one token perline.
+		"""
+		for expr in self.__expr:
+			print(expr)
+
+	def __str__(self):
+		"""str(fn)
+
+		Generates a Printable version of the Expression
+
+		Returns
+		-------
+		str
+			Latex String respresation of the Expression, suitable for rendering the equation
+		"""
+		expr = self.__expr[::-1]
+		if len(expr) == 0:
+			return ""
+		args = [];
+		while len(expr) > 0:
+			t = expr.pop()
+			r = t.toStr(args,self)
+			args.append(r)
+		if len(args) > 1:
+			return args
+		else:
+			return args[0]
+
+	def __repr__(self):
+		"""repr(fn)
+
+		Generates a String that correctrly respresents the equation
+
+		Returns
+		-------
+		str
+			Convert the Expression to a String that passed to the constructor, will constuct
+			an identical equation object (in terms of sequence of tokens, and token type/value)
+		"""
+		expr = self.__expr[::-1]
+		if len(expr) == 0:
+			return ""
+		args = [];
+		while len(expr) > 0:
+			t = expr.pop()
+			r = t.toRepr(args,self)
+			args.append(r)
+		if len(args) > 1:
+			return args
+		else:
+			return args[0]
+
+	def __iter__(self):
+		return iter(self.__argsused)
+
+	def __lt__(self, other):
+		if isinstance(other, Expression):
+			return repr(self) < repr(other)
+		else:
+			raise TypeError("{0:s} is not an {1:s} Object, and can't be compared to an Expression Object".format(repr(other), type(other)))
+
+	def __eq__(self, other):
+		if isinstance(other, Expression):
+			return repr(self) == repr(other)
+		else:
+			raise TypeError("{0:s} is not an {1:s} Object, and can't be compared to an Expression Object".format(repr(other), type(other)))
+
+	def __combine(self,other,op):
+		if op not in self.core.ops or not isinstance(other,(int,float,complex,type(self),basestring)):
+			return NotImplemented
+		else:
+			obj = type(self)(self)
+			if isinstance(other,(int,float,complex)):
+				obj.__expr.append(ExpressionValue(other))
+			else:
+				if isinstance(other,basestring):
+					try:
+						other = type(self)(other)
+					except:
+						raise SyntaxError("Can't Convert string, \"{0:s}\" to an Expression Object".format(other))
+				obj.__expr += other.__expr
+				obj.__argsused |= other.__argsused
+				for v in other.__args:
+					if v not in obj.__args:
+						obj.__args.append(v)
+				for k,v in other.__vars.items():
+					if k not in obj.__vars:
+						obj.__vars[k] = v
+					elif v != obj.__vars[k]:
+						raise RuntimeError("Predifined Variable Conflict in '{0:s}' two differing values defined".format(k))
+			fn = self.core.ops[op]
+			obj.__expr.append(ExpressionFunction(fn['func'],fn['args'],fn['str'],fn['latex'],op,False))
+		return obj
+
+	def __rcombine(self,other,op):
+		if op not in self.core.ops or not isinstance(other,(int,float,complex,type(self),basestring)):
+			return NotImplemented
+		else:
+			obj = type(self)(self)
+			if isinstance(other,(int,float,complex)):
+				obj.__expr.insert(0,ExpressionValue(other))
+			else:
+				if isinstance(other,basestring):
+					try:
+						other = type(self)(other)
+					except:
+						raise SyntaxError("Can't Convert string, \"{0:s}\" to an Expression Object".format(other))
+				obj.__expr = other.__expr + self.__expr
+				obj.__argsused = other.__argsused | self.__expr
+				__args = other.__args
+				for v in obj.__args:
+					if v not in __args:
+						__args.append(v)
+				obj.__args = __args
+				for k,v in other.__vars.items():
+					if k not in obj.__vars:
+						obj.__vars[k] = v
+					elif v != obj.__vars[k]:
+						raise RuntimeError("Predifined Variable Conflict in '{0:s}' two differing values defined".format(k))
+			fn = self.core.ops[op]
+			obj.__expr.append(ExpressionFunction(fn['func'],fn['args'],fn['str'],fn['latex'],op,False))
+		return obj
+
+	def __icombine(self,other,op):
+		if op not in self.core.ops or not isinstance(other,(int,float,complex,type(self),basestring)):
+			return NotImplemented
+		else:
+			obj = self
+			if isinstance(other,(int,float,complex)):
+				obj.__expr.append(ExpressionValue(other))
+			else:
+				if isinstance(other,basestring):
+					try:
+						other = type(self)(other)
+					except:
+						raise SyntaxError("Can't Convert string, \"{0:s}\" to an Expression Object".format(other))
+				obj.__expr += other.__expr
+				obj.__argsused |= other.__argsused
+				for v in other.__args:
+					if v not in obj.__args:
+						obj.__args.append(v)
+				for k,v in other.__vars.items():
+					if k not in obj.__vars:
+						obj.__vars[k] = v
+					elif v != obj.__vars[k]:
+						raise RuntimeError("Predifined Variable Conflict in '{0:s}' two differing values defined".format(k))
+			fn = self.core.ops[op]
+			obj.__expr.append(ExpressionFunction(fn['func'],fn['args'],fn['str'],fn['latex'],op,False))
+		return obj
+
+	def __apply(self,op):
+		fn = self.core.unary_ops[op]
+		obj = type(self)(self)
+		obj.__expr.append(ExpressionFunction(fn['func'],1,fn['str'],fn['latex'],op,False))
+		return obj
+
+	def __applycall(self,op):
+		fn = self.core.functions[op]
+		if 1 not in fn['args'] or '*' not in fn['args']:
+			raise RuntimeError("Can't Apply {0:s} function, dosen't accept only 1 argument".format(op))
+		obj = type(self)(self)
+		obj.__expr.append(ExpressionFunction(fn['func'],1,fn['str'],fn['latex'],op,False))
+		return obj
+
+	def __add__(self,other):
+		return self.__combine(other,'+')
+
+	def __sub__(self,other):
+		return self.__combine(other,'-')
+
+	def __mul__(self,other):
+		return self.__combine(other,'*')
+
+	def __div__(self,other):
+		return self.__combine(other,'/')
+
+	def __truediv__(self,other):
+		return self.__combine(other,'/')
+
+	def __pow__(self,other):
+		return self.__combine(other,'^')
+
+	def __mod__(self,other):
+		return self.__combine(other,'%')
+
+	def __and__(self,other):
+		return self.__combine(other,'&')
+
+	def __or__(self,other):
+		return self.__combine(other,'|')
+
+	def __xor__(self,other):
+		return self.__combine(other,'</>')
+
+	def __radd__(self,other):
+		return self.__rcombine(other,'+')
+
+	def __rsub__(self,other):
+		return self.__rcombine(other,'-')
+
+	def __rmul__(self,other):
+		return self.__rcombine(other,'*')
+
+	def __rdiv__(self,other):
+		return self.__rcombine(other,'/')
+
+	def __rtruediv__(self,other):
+		return self.__rcombine(other,'/')
+
+	def __rpow__(self,other):
+		return self.__rcombine(other,'^')
+
+	def __rmod__(self,other):
+		return self.__rcombine(other,'%')
+
+	def __rand__(self,other):
+		return self.__rcombine(other,'&')
+
+	def __ror__(self,other):
+		return self.__rcombine(other,'|')
+
+	def __rxor__(self,other):
+		return self.__rcombine(other,'</>')
+
+	def __iadd__(self,other):
+		return self.__icombine(other,'+')
+
+	def __isub__(self,other):
+		return self.__icombine(other,'-')
+
+	def __imul__(self,other):
+		return self.__icombine(other,'*')
+
+	def __idiv__(self,other):
+		return self.__icombine(other,'/')
+
+	def __itruediv__(self,other):
+		return self.__icombine(other,'/')
+
+	def __ipow__(self,other):
+		return self.__icombine(other,'^')
+
+	def __imod__(self,other):
+		return self.__icombine(other,'%')
+
+	def __iand__(self,other):
+		return self.__icombine(other,'&')
+
+	def __ior__(self,other):
+		return self.__icombine(other,'|')
+
+	def __ixor__(self,other):
+		return self.__icombine(other,'</>')
+
+	def __neg__(self):
+		return self.__apply('-')
+
+	def __invert__(self):
+		return self.__apply('!')
+
+	def __abs__(self):
+		return self.__applycall('abs')
+
+	def __getfunction(self,op):
+		if op[1] == 'FUNC':
+			fn = self.core.functions[op[0]]
+			fn['type'] = 'FUNC'
+		elif op[1] == 'UNARY':
+			fn = self.core.unary_ops[op[0]]
+			fn['type'] = 'UNARY'
+			fn['args'] = 1
+		elif op[1] == 'OP':
+			fn = self.core.ops[op[0]]
+			fn['type'] = 'OP'
+		return fn
+
+	def __compile(self):
+		self.__expr = []
+		stack = []
+		argc = []
+		__expect_op = False
+		v = self.__next(__expect_op)
+		while v != None:
+			if not __expect_op and v[1] == "OPEN":
+				stack.append(v)
+				__expect_op = False
+			elif __expect_op and v[1] == "CLOSE":
+				op = stack.pop()
+				while op[1] != "OPEN":
+					fs = self.__getfunction(op)
+					self.__expr.append(ExpressionFunction(fs['func'],fs['args'],fs['str'],fs['latex'],op[0],False))
+					op = stack.pop()
+				if len(stack) > 0 and stack[-1][0] in self.core.functions:
+					op = stack.pop()
+					fs = self.core.functions[op[0]]
+					args = argc.pop()
+					if fs['args'] != '+' and (args != fs['args'] and args not in fs['args']):
+						raise SyntaxError("Invalid number of arguments for {0:s} function".format(op[0]))
+					self.__expr.append(ExpressionFunction(fs['func'],args,fs['str'],fs['latex'],op[0],True))
+				__expect_op = True
+			elif __expect_op and v[0] == ",":
+				argc[-1] += 1
+				op = stack.pop()
+				while op[1] != "OPEN":
+					fs = self.__getfunction(op)
+					self.__expr.append(ExpressionFunction(fs['func'],fs['args'],fs['str'],fs['latex'],op[0],False))
+					op = stack.pop()
+				stack.append(op)
+				__expect_op = False
+			elif __expect_op and v[0] in self.core.ops:
+				fn = self.core.ops[v[0]]
+				if len(stack) == 0:
+					stack.append(v)
+					__expect_op = False
+					v = self.__next(__expect_op)
+					continue
+				op = stack.pop()
+				if op[0] == "(":
+					stack.append(op)
+					stack.append(v)
+					__expect_op = False
+					v = self.__next(__expect_op)
+					continue
+				fs = self.__getfunction(op)
+				while True:
+					if (fn['prec'] >= fs['prec']):
+						self.__expr.append(ExpressionFunction(fs['func'],fs['args'],fs['str'],fs['latex'],op[0],False))
+						if len(stack) == 0:
+							stack.append(v)
+							break
+						op = stack.pop()
+						if op[0] == "(":
+							stack.append(op)
+							stack.append(v)
+							break
+						fs = self.__getfunction(op)
+					else:
+						stack.append(op)
+						stack.append(v)
+						break
+				__expect_op = False
+			elif not __expect_op and v[0] in self.core.unary_ops:
+				fn = self.core.unary_ops[v[0]]
+				stack.append(v)
+				__expect_op = False
+			elif not __expect_op and v[0] in self.core.functions:
+				stack.append(v)
+				argc.append(1)
+				__expect_op = False
+			elif not __expect_op and v[1] == 'NAME':
+				self.__argsused.add(v[0])
+				if v[0] not in self.__args:
+					self.__args.append(v[0])
+				self.__expr.append(ExpressionVariable(v[0]))
+				__expect_op = True
+			elif not __expect_op and v[1] == 'VALUE':
+				self.__expr.append(ExpressionValue(v[0]))
+				__expect_op = True
+			else:
+				raise SyntaxError("Invalid Token \"{0:s}\" in Expression, Expected {1:s}".format(v,"Op" if __expect_op else "Value"))
+			v = self.__next(__expect_op)
+		if len(stack) > 0:
+			op = stack.pop()
+			while op != "(":
+				fs = self.__getfunction(op)
+				self.__expr.append(ExpressionFunction(fs['func'],fs['args'],fs['str'],fs['latex'],op[0],False))
+				if len(stack) > 0:
+					op = stack.pop()
+				else:
+					break

analysis-master/tra_analysis/equation/parser/Hybrid_Utils/ExpressionCore.py

@@ -0,0 +1,237 @@
+import math
+import sys
+import re
+
+if sys.version_info >= (3,):
+	xrange = range
+	basestring = str
+
+class ExpressionObject(object):
+	def __init__(self,*args,**kwargs):
+		super(ExpressionObject,self).__init__(*args,**kwargs)
+
+	def toStr(self,args,expression):
+		return ""
+
+	def toRepr(self,args,expression):
+		return ""
+
+	def __call__(self,args,expression):
+		pass
+
+class ExpressionValue(ExpressionObject):
+	def __init__(self,value,*args,**kwargs):
+		super(ExpressionValue,self).__init__(*args,**kwargs)
+		self.value = value
+
+	def toStr(self,args,expression):
+		if (isinstance(self.value,complex)):
+			V = [self.value.real,self.value.imag]
+			E = [0,0]
+			B = [0,0]
+			out = ["",""]
+			for i in xrange(2):
+				if V[i] == 0:
+					E[i] = 0
+					B[i] = 0
+				else:
+					E[i] = int(math.floor(math.log10(abs(V[i]))))
+					B[i] = V[i]*10**-E[i]
+					if E[i] in [0,1,2,3] and str(V[i])[-2:] == ".0":
+						B[i] = int(V[i])
+						E[i] = 0
+					if E[i] in [-1,-2] and len(str(V[i])) <= 7:
+						B[i] = V[i]
+						E[i] = 0
+				if i == 1:
+					fmt = "{{0:+{0:s}}}"
+				else:
+					fmt = "{{0:-{0:s}}}"
+				if type(B[i]) == int:
+					out[i] += fmt.format('d').format(B[i])
+				else:
+					out[i] += fmt.format('.5f').format(B[i]).rstrip("0.")
+				if i == 1:
+					out[i] += "\\imath"
+				if E[i] != 0:
+					out[i] += "\\times10^{{{0:d}}}".format(E[i])
+			return "\\left(" + ''.join(out) + "\\right)"
+		elif (isinstance(self.value,float)):
+			V = self.value
+			E = 0
+			B = 0
+			out = ""
+			if V == 0:
+				E = 0
+				B = 0
+			else:
+				E = int(math.floor(math.log10(abs(V))))
+				B = V*10**-E
+				if E in [0,1,2,3] and str(V)[-2:] == ".0":
+					B = int(V)
+					E = 0
+				if E in [-1,-2] and len(str(V)) <= 7:
+					B = V
+					E = 0
+			if type(B) == int:
+				out += "{0:-d}".format(B)
+			else:
+				out += "{0:-.5f}".format(B).rstrip("0.")
+			if E != 0:
+				out += "\\times10^{{{0:d}}}".format(E)
+				return "\\left(" + out + "\\right)"
+			else:
+				return out
+		else:
+			return str(self.value)
+
+	def toRepr(self,args,expression):
+		return str(self.value)
+
+	def __call__(self,args,expression):
+		return self.value
+
+	def __repr__(self):
+			return "<{0:s}.{1:s}({2:s}) object at {3:0=#10x}>".format(type(self).__module__,type(self).__name__,str(self.value),id(self))
+
+class ExpressionFunction(ExpressionObject):
+	def __init__(self,function,nargs,form,display,id,isfunc,*args,**kwargs):
+		super(ExpressionFunction,self).__init__(*args,**kwargs)
+		self.function = function
+		self.nargs = nargs
+		self.form = form
+		self.display = display
+		self.id = id
+		self.isfunc = isfunc
+
+	def toStr(self,args,expression):
+		params = []
+		for i in xrange(self.nargs):
+			params.append(args.pop())
+		if self.isfunc:
+			return str(self.display.format(','.join(params[::-1])))
+		else:
+			return str(self.display.format(*params[::-1]))
+
+	def toRepr(self,args,expression):
+		params = []
+		for i in xrange(self.nargs):
+			params.append(args.pop())
+		if self.isfunc:
+			return str(self.form.format(','.join(params[::-1])))
+		else:
+			return str(self.form.format(*params[::-1]))
+
+	def __call__(self,args,expression):
+		params = []
+		for i in xrange(self.nargs):
+			params.append(args.pop())
+		return self.function(*params[::-1])
+
+	def __repr__(self):
+		return "<{0:s}.{1:s}({2:s},{3:d}) object at {4:0=#10x}>".format(type(self).__module__,type(self).__name__,str(self.id),self.nargs,id(self))
+
+class ExpressionVariable(ExpressionObject):
+	def __init__(self,name,*args,**kwargs):
+		super(ExpressionVariable,self).__init__(*args,**kwargs)
+		self.name = name
+
+	def toStr(self,args,expression):
+		return str(self.name)
+
+	def toRepr(self,args,expression):
+		return str(self.name)
+
+	def __call__(self,args,expression):
+		if self.name in expression.variables:
+			return expression.variables[self.name]
+		else:
+			return 0 # Default variables to return 0
+
+	def __repr__(self):
+		return "<{0:s}.{1:s}({2:s}) object at {3:0=#10x}>".format(type(self).__module__,type(self).__name__,str(self.name),id(self))
+
+class Core():
+
+	constants = {}
+	unary_ops = {}
+	ops = {}
+	functions = {}
+	smatch = re.compile(r"\s*,")
+	vmatch = re.compile(r"\s*"
+						"(?:"
+							"(?P<oct>"
+								"(?P<octsign>[+-]?)"
+								r"\s*0o"
+								"(?P<octvalue>[0-7]+)"
+							")|(?P<hex>"
+								"(?P<hexsign>[+-]?)"
+								r"\s*0x"
+								"(?P<hexvalue>[0-9a-fA-F]+)"
+							")|(?P<bin>"
+								"(?P<binsign>[+-]?)"
+								r"\s*0b"
+								"(?P<binvalue>[01]+)"
+							")|(?P<dec>"
+								"(?P<rsign>[+-]?)"
+								r"\s*"
+								r"(?P<rvalue>(?:\d+\.\d+|\d+\.|\.\d+|\d+))"
+								"(?:"
+									"[Ee]"
+									r"(?P<rexpoent>[+-]?\d+)"
+								")?"
+								"(?:"
+									r"\s*"
+									r"(?P<sep>(?(rvalue)\+|))?"
+									r"\s*"
+									"(?P<isign>(?(rvalue)(?(sep)[+-]?|[+-])|[+-]?)?)"
+									r"\s*"
+									r"(?P<ivalue>(?:\d+\.\d+|\d+\.|\.\d+|\d+))"
+									"(?:"
+										"[Ee]"
+										r"(?P<iexpoent>[+-]?\d+)"
+									")?"
+									"[ij]"
+								")?"
+							")"
+						")")
+	nmatch = re.compile(r"\s*([a-zA-Z_][a-zA-Z0-9_]*)")
+	gsmatch = re.compile(r'\s*(\()')
+	gematch = re.compile(r'\s*(\))')
+
+	def recalculateFMatch(self):
+		
+		fks = sorted(self.functions.keys(), key=len, reverse=True)
+		oks = sorted(self.ops.keys(), key=len, reverse=True)
+		uks = sorted(self.unary_ops.keys(), key=len, reverse=True)
+		self.fmatch = re.compile(r'\s*(' + '|'.join(map(re.escape,fks)) + ')')
+		self.omatch = re.compile(r'\s*(' + '|'.join(map(re.escape,oks)) + ')')
+		self.umatch = re.compile(r'\s*(' + '|'.join(map(re.escape,uks)) + ')')
+
+	def addFn(self,id,str,latex,args,func):
+		self.functions[id] = {
+			'str': str,
+			'latex': latex,
+			'args': args,
+			'func': func}
+
+	def addOp(self,id,str,latex,single,prec,func):
+		if single:
+			raise RuntimeError("Single Ops Not Yet Supported")
+		self.ops[id] = {
+			'str': str,
+			'latex': latex,
+			'args': 2,
+			'prec': prec,
+			'func': func}
+
+	def addUnaryOp(self,id,str,latex,func):
+		self.unary_ops[id] = {
+			'str': str,
+			'latex': latex,
+			'args': 1,
+			'prec': 0,
+			'func': func}
+	
+	def addConst(self,name,value):
+		self.constants[name] = value

analysis-master/tra_analysis/equation/parser/Hybrid_Utils/__init__.py

@@ -0,0 +1,2 @@
+from . import equation_base as equation_base
+from .ExpressionCore import ExpressionValue, ExpressionFunction, ExpressionVariable, Core

analysis-master/tra_analysis/equation/parser/Hybrid_Utils/equation_base.py

@@ -0,0 +1,106 @@
+try:
+	import numpy as np
+	has_numpy = True
+except ImportError:
+	import math
+	has_numpy = False
+try:
+	import scipy.constants
+	has_scipy = True
+except ImportError:
+	has_scipy = False
+import operator as op
+from .similar import sim, nsim, gsim, lsim
+
+def equation_extend(core):
+	def product(*args):
+		if len(args) == 1 and has_numpy:
+			return np.prod(args[0])
+		else:
+			return reduce(op.mul,args,1)
+
+	def sumargs(*args):
+		if len(args) == 1:
+			return sum(args[0])
+		else:
+			return sum(args)
+
+	core.addOp('+',"({0:s} + {1:s})","\\left({0:s} + {1:s}\\right)",False,3,op.add)
+	core.addOp('-',"({0:s} - {1:s})","\\left({0:s} - {1:s}\\right)",False,3,op.sub)
+	core.addOp('*',"({0:s} * {1:s})","\\left({0:s} \\times {1:s}\\right)",False,2,op.mul)
+	core.addOp('/',"({0:s} / {1:s})","\\frac{{{0:s}}}{{{1:s}}}",False,2,op.truediv)
+	core.addOp('%',"({0:s} % {1:s})","\\left({0:s} \\bmod {1:s}\\right)",False,2,op.mod)
+	core.addOp('^',"({0:s} ^ {1:s})","{0:s}^{{{1:s}}}",False,1,op.pow)
+	core.addOp('**',"({0:s} ^ {1:s})","{0:s}^{{{1:s}}}",False,1,op.pow)
+	core.addOp('&',"({0:s} & {1:s})","\\left({0:s} \\land {1:s}\\right)",False,4,op.and_)
+	core.addOp('|',"({0:s} | {1:s})","\\left({0:s} \\lor {1:s}\\right)",False,4,op.or_)
+	core.addOp('</>',"({0:s} </> {1:s})","\\left({0:s} \\oplus {1:s}\\right)",False,4,op.xor)
+	core.addOp('&|',"({0:s} </> {1:s})","\\left({0:s} \\oplus {1:s}\\right)",False,4,op.xor)
+	core.addOp('|&',"({0:s} </> {1:s})","\\left({0:s} \\oplus {1:s}\\right)",False,4,op.xor)
+	core.addOp('==',"({0:s} == {1:s})","\\left({0:s} = {1:s}\\right)",False,5,op.eq)
+	core.addOp('=',"({0:s} == {1:s})","\\left({0:s} = {1:s}\\right)",False,5,op.eq)
+	core.addOp('~',"({0:s} ~ {1:s})","\\left({0:s} \\approx {1:s}\\right)",False,5,sim)
+	core.addOp('!~',"({0:s} !~ {1:s})","\\left({0:s} \\not\\approx {1:s}\\right)",False,5,nsim)
+	core.addOp('!=',"({0:s} != {1:s})","\\left({0:s} \\neg {1:s}\\right)",False,5,op.ne)
+	core.addOp('<>',"({0:s} != {1:s})","\\left({0:s} \\neg {1:s}\\right)",False,5,op.ne)
+	core.addOp('><',"({0:s} != {1:s})","\\left({0:s} \\neg {1:s}\\right)",False,5,op.ne)
+	core.addOp('<',"({0:s} < {1:s})","\\left({0:s} < {1:s}\\right)",False,5,op.lt)
+	core.addOp('>',"({0:s} > {1:s})","\\left({0:s} > {1:s}\\right)",False,5,op.gt)
+	core.addOp('<=',"({0:s} <= {1:s})","\\left({0:s} \\leq {1:s}\\right)",False,5,op.le)
+	core.addOp('>=',"({0:s} >= {1:s})","\\left({0:s} \\geq {1:s}\\right)",False,5,op.ge)
+	core.addOp('=<',"({0:s} <= {1:s})","\\left({0:s} \\leq {1:s}\\right)",False,5,op.le)
+	core.addOp('=>',"({0:s} >= {1:s})","\\left({0:s} \\geq {1:s}\\right)",False,5,op.ge)
+	core.addOp('<~',"({0:s} <~ {1:s})","\\left({0:s} \lessapprox {1:s}\\right)",False,5,lsim)
+	core.addOp('>~',"({0:s} >~ {1:s})","\\left({0:s} \\gtrapprox {1:s}\\right)",False,5,gsim)
+	core.addOp('~<',"({0:s} <~ {1:s})","\\left({0:s} \lessapprox {1:s}\\right)",False,5,lsim)
+	core.addOp('~>',"({0:s} >~ {1:s})","\\left({0:s} \\gtrapprox {1:s}\\right)",False,5,gsim)
+	core.addUnaryOp('!',"(!{0:s})","\\neg{0:s}",op.not_)
+	core.addUnaryOp('-',"-{0:s}","-{0:s}",op.neg)
+	core.addFn('abs',"abs({0:s})","\\left|{0:s}\\right|",1,op.abs)
+	core.addFn('sum',"sum({0:s})","\\sum\\left({0:s}\\right)",'+',sumargs)
+	core.addFn('prod',"prod({0:s})","\\prod\\left({0:s}\\right)",'+',product)
+	if has_numpy:
+		core.addFn('floor',"floor({0:s})","\\lfloor {0:s} \\rfloor",1,np.floor)
+		core.addFn('ceil',"ceil({0:s})","\\lceil {0:s} \\rceil",1,np.ceil)
+		core.addFn('round',"round({0:s})","\\lfloor {0:s} \\rceil",1,np.round)
+		core.addFn('sin',"sin({0:s})","\\sin\\left({0:s}\\right)",1,np.sin)
+		core.addFn('cos',"cos({0:s})","\\cos\\left({0:s}\\right)",1,np.cos)
+		core.addFn('tan',"tan({0:s})","\\tan\\left({0:s}\\right)",1,np.tan)
+		core.addFn('re',"re({0:s})","\\Re\\left({0:s}\\right)",1,np.real)
+		core.addFn('im',"re({0:s})","\\Im\\left({0:s}\\right)",1,np.imag)
+		core.addFn('sqrt',"sqrt({0:s})","\\sqrt{{{0:s}}}",1,np.sqrt)
+		core.addConst("pi",np.pi)
+		core.addConst("e",np.e)
+		core.addConst("Inf",np.Inf)
+		core.addConst("NaN",np.NaN)
+	else:
+		core.addFn('floor',"floor({0:s})","\\lfloor {0:s} \\rfloor",1,math.floor)
+		core.addFn('ceil',"ceil({0:s})","\\lceil {0:s} \\rceil",1,math.ceil)
+		core.addFn('round',"round({0:s})","\\lfloor {0:s} \\rceil",1,round)
+		core.addFn('sin',"sin({0:s})","\\sin\\left({0:s}\\right)",1,math.sin)
+		core.addFn('cos',"cos({0:s})","\\cos\\left({0:s}\\right)",1,math.cos)
+		core.addFn('tan',"tan({0:s})","\\tan\\left({0:s}\\right)",1,math.tan)
+		core.addFn('re',"re({0:s})","\\Re\\left({0:s}\\right)",1,complex.real)
+		core.addFn('im',"re({0:s})","\\Im\\left({0:s}\\right)",1,complex.imag)
+		core.addFn('sqrt',"sqrt({0:s})","\\sqrt{{{0:s}}}",1,math.sqrt)
+		core.addConst("pi",math.pi)
+		core.addConst("e",math.e)
+		core.addConst("Inf",float("Inf"))
+		core.addConst("NaN",float("NaN"))
+	if has_scipy:
+		core.addConst("h",scipy.constants.h)
+		core.addConst("hbar",scipy.constants.hbar)
+		core.addConst("m_e",scipy.constants.m_e)
+		core.addConst("m_p",scipy.constants.m_p)
+		core.addConst("m_n",scipy.constants.m_n)
+		core.addConst("c",scipy.constants.c)
+		core.addConst("N_A",scipy.constants.N_A)
+		core.addConst("mu_0",scipy.constants.mu_0)
+		core.addConst("eps_0",scipy.constants.epsilon_0)
+		core.addConst("k",scipy.constants.k)
+		core.addConst("G",scipy.constants.G)
+		core.addConst("g",scipy.constants.g)
+		core.addConst("q",scipy.constants.e)
+		core.addConst("R",scipy.constants.R)
+		core.addConst("sigma",scipy.constants.e)
+		core.addConst("Rb",scipy.constants.Rydberg)

analysis-master/tra_analysis/equation/parser/Hybrid_Utils/similar.py

@@ -0,0 +1,49 @@
+_tol = 1e-5
+
+def sim(a,b):
+	if (a==b):
+		return True
+	elif a == 0 or b == 0:
+		return False
+	if (a<b):
+		return (1-a/b)<=_tol
+	else:
+		return (1-b/a)<=_tol
+
+def nsim(a,b):
+	if (a==b):
+		return False
+	elif a == 0 or b == 0:
+		return True
+	if (a<b):
+		return (1-a/b)>_tol
+	else:
+		return (1-b/a)>_tol
+	
+def gsim(a,b):
+	if a >= b:
+		return True
+	return (1-a/b)<=_tol
+
+def lsim(a,b):
+	if a <= b:
+		return True
+	return (1-b/a)<=_tol
+	
+def set_tol(value=1e-5):
+	r"""Set Error Tolerance
+	
+	Set the tolerance for detriming if two numbers are simliar, i.e
+	:math:`\left|\frac{a}{b}\right| = 1 \pm tolerance`
+	
+	Parameters
+	----------
+	value: float
+		The Value to set the tolerance to show be very small as it respresents the
+		percentage of acceptable error in detriming if two values are the same.
+	"""
+	global _tol
+	if isinstance(value,float):
+		_tol = value
+	else:
+		raise TypeError(type(value))

analysis-master/tra_analysis/equation/parser/RegexInplaceParser.py

@@ -0,0 +1,51 @@
+import re
+from decimal import Decimal
+from functools import reduce
+
+class RegexInplaceParser(object):
+
+	def __init__(self, string):
+
+		self.string = string
+
+	def add(self, string):
+		while(len(re.findall("[+]{1}[-]?", string)) != 0):
+			string = re.sub("[-]?\d+[.]?\d*[+]{1}[-]?\d+[.]?\d*", str("%f" % reduce((lambda x, y: x + y), [Decimal(i) for i in re.split("[+]{1}", re.search("[-]?\d+[.]?\d*[+]{1}[-]?\d+[.]?\d*", string).group())])), string, 1)
+		return string
+
+	def sub(self, string):
+		while(len(re.findall("\d+[.]?\d*[-]{1,2}\d+[.]?\d*", string)) != 0):
+			g = re.search("\d+[.]?\d*[-]{1,2}\d+[.]?\d*", string).group()
+			if(re.search("[-]{1,2}", g).group() == "-"):
+				r = re.sub("[-]{1}", "+-", g, 1)
+				string = re.sub(g, r, string, 1)
+			elif(re.search("[-]{1,2}", g).group() == "--"):
+				r = re.sub("[-]{2}", "+", g, 1)
+				string = re.sub(g, r, string, 1)
+			else:
+				pass
+		return string
+
+	def mul(self, string):
+		while(len(re.findall("[*]{1}[-]?", string)) != 0):
+			string = re.sub("[-]?\d+[.]?\d*[*]{1}[-]?\d+[.]?\d*", str("%f" % reduce((lambda x, y: x * y), [Decimal(i) for i in re.split("[*]{1}", re.search("[-]?\d+[.]?\d*[*]{1}[-]?\d+[.]?\d*", string).group())])), string, 1)
+		return string
+
+	def div(self, string):
+		while(len(re.findall("[/]{1}[-]?", string)) != 0):
+			string = re.sub("[-]?\d+[.]?\d*[/]{1}[-]?\d+[.]?\d*", str("%f" % reduce((lambda x, y: x / y), [Decimal(i) for i in re.split("[/]{1}", re.search("[-]?\d+[.]?\d*[/]{1}[-]?\d+[.]?\d*", string).group())])), string, 1)
+		return string
+
+	def exp(self, string):
+		while(len(re.findall("[\^]{1}[-]?", string)) != 0):
+			string = re.sub("[-]?\d+[.]?\d*[\^]{1}[-]?\d+[.]?\d*", str("%f" % reduce((lambda x, y: x ** y), [Decimal(i) for i in re.split("[\^]{1}", re.search("[-]?\d+[.]?\d*[\^]{1}[-]?\d+[.]?\d*", string).group())])), string, 1)
+		return string
+
+	def evaluate(self):
+		string = self.string
+		string = self.exp(string)
+		string = self.div(string)
+		string = self.mul(string)
+		string = self.sub(string)
+		string = self.add(string)
+		return string

analysis-master/tra_analysis/equation/parser/__init__.py

@@ -0,0 +1,34 @@
+# Titan Robotics Team 2022: Expression submodule
+# Written by Arthur Lu
+# Notes:
+#    this should be imported as a python module using 'from tra_analysis.Equation import parser'
+# setup:
+
+__version__ = "0.0.4-alpha"
+
+__changelog__ = """changelog:
+	0.0.4-alpha:
+		- moved individual parsers to their own files
+	0.0.3-alpha:
+		- readded old regex based parser as RegexInplaceParser
+	0.0.2-alpha:
+		- wrote BNF using pyparsing and uses a BNF metasyntax
+		- renamed this submodule parser
+	0.0.1-alpha:
+		- took items from equation.ipynb and ported here
+"""
+
+__author__ = (
+	"Arthur Lu <learthurgo@gmail.com>",
+)
+
+__all__ = {
+	"BNF",
+	"RegexInplaceParser",
+	"HybridExpressionParser"
+}
+
+from .BNF import BNF as BNF
+from .RegexInplaceParser import RegexInplaceParser as RegexInplaceParser
+from .Hybrid import HybridExpressionParser
+from .Hybrid_Utils import equation_base, Core

analysis-master/tra_analysis/equation/parser/py2.py

@@ -0,0 +1,21 @@
+# Titan Robotics Team 2022: py2 module
+# Written by Arthur Lu
+# Notes:
+#    this module should only be used internally, contains old python 2.X functions that have been removed.
+# setup:
+
+from __future__ import division
+
+__version__ = "1.0.0"
+
+__changelog__ = """changelog:
+	1.0.0:
+	- added cmp function
+"""
+
+__author__ = (
+	"Arthur Lu <learthurgo@gmail.com>",
+)
+
+def cmp(a, b):
+    return (a > b) - (a < b) 

analysis-master/tra_analysis/metrics/__init__.py

@@ -0,0 +1,24 @@
+# Titan Robotics Team 2022: Metrics submodule
+# Written by Arthur Lu
+# Notes:
+#    this should be imported as a python module using 'from tra_analysis import metrics'
+# setup:
+
+__version__ = "1.0.0"
+
+__changelog__ = """changelog:
+	1.0.0:
+		- implemented elo, glicko2, trueskill
+"""
+
+__author__ = (
+	"Arthur Lu <learthurgo@gmail.com>",
+)
+
+__all__ = {
+	"Expression"
+}
+
+from . import elo
+from . import glicko2
+from . import trueskill

analysis-master/tra_analysis/metrics/elo.py

@@ -0,0 +1,7 @@
+import numpy as np
+
+def calculate(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))

analysis-master/tra_analysis/metrics/glicko2.py

@@ -0,0 +1,99 @@
+import math
+
+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/tra_analysis/metrics/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)

data analysis/generate_data.py

@@ -1,16 +0,0 @@
-import random
-
-def generate(filename, x, y, low, high):
-
-    file = open(filename, "w")
-
-    for i in range (0, y, 1):
-
-        temp = ""
-        
-        for j in range (0, x - 1, 1):
-
-            temp = str(random.uniform(low, high)) +  ","  + temp
-
-        temp = temp + str(random.uniform(low, high))
-        file.write(temp + "\n")

data analysis/repack_json.py

@@ -1,28 +0,0 @@
-import os
-import json
-import ordereddict
-import collections
-import unicodecsv
-
-content = open("realtimeDatabaseExport2018.json").read()
-
-dict_content = json.loads(content)
-list_of_new_data = []
-
-for datak, datav in dict_content.iteritems():
-    for teamk, teamv in datav["teams"].iteritems():
-        for matchk, matchv in teamv.iteritems():
-            for detailk, detailv in matchv.iteritems():
-                new_data = collections.OrderedDict(detailv)
-                new_data["uuid"] = detailk
-                new_data["match"] = matchk
-                new_data["team"] = teamk
-                
-                list_of_new_data.append(new_data)
-
-allkey = reduce(lambda x, y: x.union(y.keys()), list_of_new_data, set())
-output_file = open('realtimeDatabaseExport2018.csv', 'wb')
-dict_writer = unicodecsv.DictWriter(csvfile=output_file, fieldnames=allkey)
-dict_writer.writerow(dict((fn,fn) for fn in dict_writer.fieldnames))
-dict_writer.writerows(list_of_new_data)
-output_file.close()