#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Thu Apr 24 09:46:46 2025

@author: amriksen
"""

import numpy as np
import matplotlib.pyplot as plt
np.random.seed(42)
# x1: Study hours for Subject 1
x1_values = np.arange(1, 25, 1) # from 1 to 24, step 1
print("Study hours (x1):", x1_values)
# # x2: Study hours for Subject 2 (linearly dependent)
# x2_values = 1.2 * x1_values
# print("Lab study minutes (x2):", x2_values)
# Scale the quadratic and linear terms to keep the marks in a realistic range
# Adjust coefficients so that output is naturally between 10 and 100
a, c = 3.5, 20 # Chosen to keep marks in desired range
noise = np.random.randint(-25, 5, size=x1_values.shape) # Small integer noise
marks = (a * x1_values + c + noise).astype(int)
print("Generated marks:", marks)
# Ensure all marks are strictly within [10, 100] using coefficient tuning only
print(f"\nMin mark: {marks.min()}, Max mark: {marks.max()}")
# Construct matrix A with linearly dependent columns
A = np.vstack([x1_values, np.ones_like(x1_values)]).T
b_vec = marks
# QR factorization for least squares solution
Q, R = np.linalg.qr(A)
x = np.linalg.inv(R) @ Q.T @ b_vec
# Extract coefficients
a_fit, b2_fit = x
print(f"\nFitted curve: y = {a_fit:.6f} * x + {b2_fit:.6f}")
# Plot
plt.figure(figsize=(8, 6))
plt.scatter(x1_values, marks, color='green', label='Data points', alpha=0.8)
# Best fit curve using x1 and dependent x2
x1_fit = np.linspace(min(x1_values), max(x1_values), 300)
y_fit = a_fit * x1_fit + b2_fit
plt.plot(x1_fit, y_fit, color='blue', label='Best fit curve')
plt.xlabel('Study Hours for Subject 1')
plt.ylabel('Marks')
plt.title('Marks vs Study Hours (Subjects 1) – Natural Range Fit')
plt.legend()
plt.grid(True)
plt.ylim(0, 110)
plt.show()