completed assignment of backslash (shree)

assMath/ass2B/shree/.ipynb_checkpoints/Q1C-checkpoint.ipynb

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+{
+ "cells": [],
+ "metadata": {},
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

assMath/ass2B/shree/1B.py

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+# -*- coding: utf-8 -*-
+"""
+Created on Sun Jun 25 01:44:31 2023
+
+@author: Shree
+"""
+
+import numpy as np
+from matplotlib import pyplot as plt
+from scipy.optimize import fsolve
+
+np.random.seed(22)
+
+def generate_data(n_dims, n_points, std):
+    global coefs
+    # equation will be of the form a1x1 + a2x2 + a3x3 ... = 0 forming a hyperplane
+    features = np.random.normal(0, std, (n_points, n_dims))
+    coefs = np.random.normal(0, std, (1, n_dims))
+    print(coefs.flatten())
+    # class will be decided based upon the distance and direction from the hyperplane 
+    ys = (coefs @ features.T).flatten() + np.random.normal(0, 1, n_points)
+
+    return features, ys
+
+n_dims = 10
+n_points = 100
+std = 5
+features, ys = generate_data(n_dims, n_points, std)
+
+plt.scatter(features[:, 0], ys)
+
+# use scipy to solve system of equations
+def equation_gen(coefficients):    
+    #MLE estimate
+    return [np.sum((ys-coefficients[None, :]@features.T)*features[:, j]) for j in range(n_dims)]
+
+def solve(equations):
+    solved_coefs = fsolve(equations, np.zeros(n_dims), )
+    return solved_coefs.flatten()
+
+solved_coefs = solve(equation_gen)
+print(solved_coefs)
+plt.plot(features[:, 0], solved_coefs[0]*features[:, 0], c='red')
+plt.plot(features[:, 0], coefs[0, 0]*features[:, 0], c='green')