NewtonsMethod.py

import math
import numpy as np

def T1(x):
    return x
def T1P(x):
    return 1
def T2(x):
	return 2*(x**2) - 1
def T2P(x):
	return (4*x)
def T3(x):
	return 4 * (x**3) - 3*x
def T3P(x):
	return (12*(x**2)) - 3
def T4(x):
	return 8*(x**4) - 8*(x**2) + 1
def T4P(x):
	return (32*(x**3))-(16*x)

def Newtons(x, y):
	if (((x > 1) and (y > 1)) or ((x < -1) and (y < -1))):
		result = math.sqrt(((x - 1)**2) + ((y - 1)**2))
		result2 = math.sqrt(((x + 1) ** 2) + ((y + 1)**2))
		print("Distance: " + str(min(result,result2)) + " Point: (1,1)")
		#this obviously only work for this assignment bc im lazy
		return 0
	# HERE WE CHOOSE N
	n = 10
	# Pick n points by dividing the interval by 1/n
#	nlist = [-1 + (1/3), -1 + (2/3), -1 + (3/3), -1 + (4/3), -1 + (5/3), -1 + (6/3)]
	#k = 10
	currbestpt = [0,0]
	currbestdist = 1809418903
	for i in range(-50,50,5):
		i = i/50 #Can't use floats in range so n = 10
		pt1 = [i, T2(i)]
		pt2 = [x,y]
		v1 = [pt2[0] - pt1[0], pt2[1] - pt1[1]]
	    # Tangent Vector
		v2 = [i,T2P(i)]
		dist = math.sqrt(((pt2[0]-pt1[0])**2)+((pt2[1]-pt1[1])**2))
		if (dist < currbestdist) and (dist != 0):
			currbestpt = pt1
			currbestdist = dist
	print("Distance: " + str(currbestdist) + " Point: " + str(currbestpt))
	return 0
			

    
#Newtons(2,2)
Newtons(3,0)
# dot product - np.dot([v1],[v2])
        #Test the endpoints, print closest one, return)
    # If condition: IF it's a point outside of the interval but still on the function
    # Return whichever one of the endpoints has a closer distance
    # All the intervals are from [-1,1]
    # Divide curve into 1/n segments and from there get n points on the curve
    # loop:
        # Test each distance
        # v1 - vector from the point to pk
        # v2 - tangent line at that point
        # v1 * v2 = 0 - test how close it is to epsilon (+- 10^-6)
        # Break if it's within epsilon and save that point
        # Keep a list of 'close points'
        # Apply eqn to find next points
        # pk = p(k-1) - f(pk-1)/f*(pk-1)
    # Test endpoints
    # Print the closest