Create NewtonsMethod.py

Some of my notes are a bit of a mess. Let me know if you need help with what I did.

NewtonsMethod.py

@@ -0,0 +1,69 @@
+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