199 lines
6.7 KiB
Python
199 lines
6.7 KiB
Python
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################################################################################
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# Author: Shaun Reed #
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# About: Linear regression CLI #
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# Contact: shaunrd0@gmail.com | URL: www.shaunreed.com | GitHub: shaunrd0 #
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################################################################################
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from ast import literal_eval
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from matplotlib import pyplot as plt
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from typing import List
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import argparse
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import math
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import numpy as np
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import sys
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################################################################################
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# Commandline Argument Parser
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################################################################################
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# ==============================================================================
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def init_parser():
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parser = argparse.ArgumentParser(
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description='Find most fitting line plot for given data points and predict value given some X',
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formatter_class=argparse.RawTextHelpFormatter
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)
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parser.add_argument(
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'given', metavar='GIVEN_X', type=float, nargs='?',
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help=
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'''Value for X for prediction using linear regression
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(default: '%(default)s')
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''',
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default=4.5
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)
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parser.add_argument(
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'data', metavar='X,Y', type=point, nargs='*',
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help=
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'''A list of data points separated by spaces as: x,y x,y x,y ...
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(default: '%(default)s')
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''',
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default=[(1, 3), (2, 7), (3, 5), (4, 9), (5, 11), (6, 12), (7, 15)]
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)
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parser.add_argument(
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'--silent', action='store_true',
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help=
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'''When this flag is set, line plot visualization will not be shown
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(default: '%(default)s')
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''',
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default=False
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)
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parser.add_argument(
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'--file', '-f', metavar='FILE_PATH', nargs='?', type=open,
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help=
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'''Optionally provide file for data to be read from. Each point must be on it\'s own line with format x,y
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''',
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)
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return parser
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def point(arg):
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"""
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Helper function for parsing x,y points provided through argparse CLI
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:param arg: A single argument passed to an option or positional argument
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:return: A tuple (x, y) representing a data point
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"""
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try:
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x, y = literal_eval(arg)
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return x, y
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except:
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raise argparse.ArgumentTypeError("Please provide data points in x,y format")
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################################################################################
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# Linear Regression Calculation
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################################################################################
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# ==============================================================================
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def points_average(data):
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"""
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Finds average (x, y) for points in data list [(x, y), (x, y), ...]
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Used for updating cluster centroid positions
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:param data: List [(x, y), (x, y), ...]
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:return: An average (x, y) position for the list of points
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"""
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x, y = 0, 0
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for pair in data:
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x += pair[0]
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y += pair[1]
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x = float(x / len(data))
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y = float(y / len(data))
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return x, y
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def points_variance(data, points_avg):
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"""
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Find variance for a series of data points
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:param data: List of data points [(x, y), (x, y), ...]
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:param points_avg: Average (x, y) position for the list of points in data
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:return: Variance of X and Y for the data set as a tuple (x, y)
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"""
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x, y = 0, 0
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for point in data:
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x += math.pow((point[0] - points_avg[0]), 2)
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y += math.pow((point[1] - points_avg[1]), 2)
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return x, y
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def points_covariance(data, points_avg):
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"""
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Find covariance between X, Y within the data set
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:param data: List of data points [(x, y), (x, y), ...]
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:param points_avg: Tuple of average X, Y for data set list
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:return: Single float value representing covariance
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"""
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cov = 0
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for point in data:
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cov += (point[0] - points_avg[0]) * (point[1] - points_avg[1])
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return float(cov / (len(data) - 1))
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def show_regression(data, beta, alpha):
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"""
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Shows the linear regression in the matplotlib subplot
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Line drawn with Y = BX + A
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:param data: Data to show on the scatter plot
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:param beta: Value for B in the line equation
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:param alpha: Value for A in the line equation
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"""
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dataX, dataY = zip(*data)
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scaleX = np.linspace(min(dataX) - 1, max(dataX) + 1, 100)
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scaleY = beta * scaleX + alpha
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plt.plot(scaleX, scaleY, c='g')
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plt.scatter(dataX, dataY, c='k')
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print(f'For X = {context.given}, Y is predicted to be {beta * context.given + alpha} ')
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plt.scatter(context.given, beta * context.given + alpha, c='#e6e600')
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plt.show()
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################################################################################
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# Main
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################################################################################
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# ==============================================================================
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def main(args: List[str]):
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parser = init_parser()
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global context
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context = parser.parse_args(args[1:])
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print(f'Finding fitting line plot for given data {context.data}')
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if context.file: # If a file was provided, use that data instead
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context.data = [literal_eval(line.rstrip()) for line in context.file]
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context.data = [(float(x), float(y)) for x, y in context.data]
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# Find the average for the data X and Y points
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data_avg = points_average(context.data)
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print(f'points_avg: {data_avg}')
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# Find the variance for the data X and Y points
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data_variance = points_variance(context.data, data_avg)
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print(f'variance: {data_variance}')
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# Find the standard deviations for X and Y values
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data_sigma = (math.sqrt(float(data_variance[0] / (len(context.data) - 1))),
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math.sqrt(float(data_variance[1] / (len(context.data) - 1))))
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print(f'sigma: {data_sigma}')
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# Find the covariance between X, Y within data set
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data_covariance = points_covariance(context.data, data_avg)
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print(f'covariance: {data_covariance}')
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# Find correlation between X, Y within data set
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data_correlation = (1.0/math.prod(data_sigma)) * data_covariance
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print(f'correlation: {data_correlation}')
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# Find equation for linear regression for the given data set
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print(f'Our line Y = BX + A must pass through the point {data_avg}')
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data_beta = data_correlation * float(data_sigma[1] / data_sigma[0])
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data_alpha = data_avg[1] - data_beta * data_avg[0]
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print(f'Y = ({data_beta})X + {data_alpha}')
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# Show the final graph produced by linear regression calculations
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# + Predicts the Y value, given the X value provided through the CLI
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if not context.silent:
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show_regression(context.data, data_beta, data_alpha)
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if __name__ == "__main__":
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sys.exit(main(sys.argv))
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