klips/python/linear-regression/linear-regression.py

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