Why one function are giving diffrent errors in Python - python-3.x

Question

This is an assignment in Udacity linear algebra refresher course and I have solved it in my way although there is a solution available for this assignment I am trying to solve it in my way. But I am getting error while finding angle between 2 vector that is vectore v1 and v2 .
There is 2 problems asked 2 solve to this program. But even if there is same. but to programs is giving to diffrent out put even if there "angle" function is same.
import math
from decimal import Decimal,getcontext
getcontext().prec = 30
class Vector(object):
def __init__(self,coordinates):
try:
if not coordinates:
raise ValueError
#if coordinates is not passed then it will rise Value Error
self.coordinates = tuple([Decimal(x)for x in coordinates])
#Outside Class :-Vector.coordinates will give print vectors in tuple form
#Inside Class :- self.coordinates will print vectors in tuple form
self.dimension = len(coordinates)
#Outside Class :-Vector.dimension will print vectors dimension/size
#Inside Class :- self.dimension will print vectors dimension/size
except ValueError:
raise ValueError('The coordinates must be non empty')
except TypeError:
raise TypeError('The coordinates must be itterable')
def __str__(self):
return 'Vector:{}'.format(self,coordinates)
def __eq__(self,v):
return self.coordinates == v.coordinates
def add (self,v):
coordinates=[]
for i in range(0,self.dimension):
i=self.coordinates[i]+v.coordinates[i]
coordinates.append(i)
return coordinates
def mul(self,v):
coordinates=[]
for i in range(0,self.dimension):
i=self.coordinates[i]*v.coordinates[i]
coordinates.append(i)
return coordinates
def sub (self,v):
coordinates=[]
for i in range(0,self.dimension):
i=self.coordinates[i]-v.coordinates[i]
coordinates.append(i)
return coordinates
def scal_mul(self,s):
coordinates=[]
for i in self.coordinates:
i=i*Decimal(s)
coordinates.append(i)
return coordinates
def magnitude(self):
mag = 0
for i in self.coordinates:
i=i*i
mag =mag+i
return math.sqrt(mag)
def magnitude1(self):
mag = 0
coordinate_squre=[i*i for i in self.coordinates]
return math.sqrt(sum(coordinate_squre))
# def normalize(self):
# try:
# recip = Decimal(1)/self.magnitude()
# return Vector(self.scal_mul(recip))
# except ZeroDivisionError:
# raise Exception("Can not Normalize Zero Vector")
def normalize(self):
try:
recip = 1/self.magnitude()
return self.scal_mul(recip)
except ZeroDivisionError:
raise Exception("Can not Normalize Zero Vector")
def dot_product(self,v):
mul = self.mul(v)
return sum(mul)
def dot_product2(self,v):
self.mul = [x*y for x,y in zip(self.coordinates,v.coordinates)]
return sum(self.mul)
#-----------------angle functionn is giving wrong answer-------------
def angle_rad(self,v):
norm = self.normalize()
angle = 1/ math.cos(norm.dot_product2(v))
return angle
def angle(self,v,in_degree=False):
nrm_self = self.normalize()
nrm_v = v.normalize()
angle_rad = math.acos(nrm_self.dot_product2(nrm_v))
if in_degree:
angle_in_degree = angle_rad * 180./math.pi
return angle_in_degree
else:
return angle_rad
v1 = Vector([7.887,4.138])
v2 = Vector([-8.802,6.776])
print(v1.angle(v2))
v1 = Vector([-7.579,-7.88])
v2 = Vector([22.737,23.64])
v2.angle(v1)
This Code is giving Error as following
AttributeError Traceback (most recent call last)
<ipython-input-44-2087e4f0ca26> in <module>()
101 v1 = Vector([7.887,4.138])
102 v2 = Vector([-8.802,6.776])
--> 103 print(v1.angle(v2))
104 v1 = Vector([-7.579,-7.88])
105 v2 = Vector([22.737,23.64])
<ipython-input-44-2087e4f0ca26> in angle(self, v, in_degree)
92 nrm_self = self.normalize()
93 nrm_v = v.normalize()
---> 94 angle_rad = math.acos(nrm_self.dot_product2(nrm_v))
95 if in_degree:
96 angle_in_degree = angle_rad * 180./math.pi
AttributeError: 'list' object has no attribute 'dot_product2'
And another program with exactly same angle function is
import math
class Vector(object):
def __init__(self,coordinates):
try:
if not coordinates:
raise ValueError
#if coordinates is not passed then it will rise Value Error
self.coordinates = tuple(coordinates)
#Outside Class :-Vector.coordinates will give print vectors in tuple form
#Inside Class :- self.coordinates will print vectors in tuple form
self.dimension = len(coordinates)
#Outside Class :-Vector.dimension will print vectors dimension/size
#Inside Class :- self.dimension will print vectors dimension/size
except ValueError:
raise ValueError('The coordinates must be non empty')
except TypeError:
raise TypeError('The coordinates must be itterable')
def __str__(self):
return 'Vector:{}'.format(self,coordinates)
def __eq__(self,v):
return self.coordinates == v.coordinates
def add (self,v):
coordinates=[]
for i in range(0,self.dimension):
i=self.coordinates[i]+v.coordinates[i]
coordinates.append(i)
return coordinates
def mul(self,v):
coordinates=[]
for i in range(0,self.dimension):
i=self.coordinates[i]*v.coordinates[i]
coordinates.append(i)
return coordinates
def sub (self,v):
coordinates=[]
for i in range(0,self.dimension):
i=self.coordinates[i]-v.coordinates[i]
coordinates.append(i)
return coordinates
def scal_mul(self,s):
coordinates=[]
for i in self.coordinates:
i=i*s
coordinates.append(i)
return coordinates
def magnitude(self):
mag = 0
for i in self.coordinates:
i=i*i
mag =mag+i
return math.sqrt(mag)
def magnitude1(self):
mag = 0
coordinate_squre=[i*i for i in self.coordinates]
return math.sqrt(sum(coordinate_squre))
def normalize(self):
try:
recip = 1/self.magnitude()
return Vector(self.scal_mul(recip))
except ZeroDivisionError:
raise Exception("Can not Normalize Zero Vector")
def dot_product(self,v):
mul = self.mul(v)
return sum(mul)
def dot_product2(self,v):
self.mul = [x*y for x,y in zip(self.coordinates,v.coordinates)]
return sum(self.mul)
#-----------------angle functionn is giving wrong answer-------------
def angle_rad(self,v):
norm = self.normalize()
angle = 1/ math.cos(norm.dot_product2(v))
return angle
def angle(self,v,in_degree=False):
nrm_self = self.normalize()
nrm_v = v.normalize()
angle_rad = math.acos(nrm_self.dot_product2(nrm_v))
if in_degree:
angle_in_degree = angle_rad * 180./math.pi
return angle_in_degree
else:
return angle_rad
v1 = Vector([7.887,4.138])
v2 = Vector([-8.802,6.776])
print(v1.angle(v2))
v1 = Vector([-7.579,-7.88])
v2 = Vector([22.737,23.64])
v2.angle(v1)
it is giving Error as following
2.0023426999774925
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-214-2e3bee12967a> in <module>()
95 v1 = Vector([-7.579,-7.88])
96 v2 = Vector([22.737,23.64])
---> 97 v2.angle(v1)
98
<ipython-input-214-2e3bee12967a> in angle(self, v, in_degree)
82 nrm_self = self.normalize()
83 nrm_v = v.normalize()
---> 84 angle_rad = math.acos(nrm_self.dot_product2(nrm_v))
85 if in_degree:
86 angle_in_degree = angle_rad * 180./math.pi
ValueError: math domain error
We can see they are having same angle function

Answer 1

The problem with your first program is that the normalize method returns a list of coordinates, return self.scal_mul(recip) but doesn't convert that list into a Vector object like the second program, which instead return Vector(self.scal_mul(recip)). When you call nrm_self.dot_product2(nrm_v), the object nrm_self is a list, not a Vector, and it doesn't have a dot_product2 method. You need to add an explicit call to the constructor Vector(), like in the second program, to be able to invoke methods from the norm_self object.
The math domain error is being thrown because dot_product2 is returning a value larger than 1 (unfortunately, 1.0000000000000002), and the inverse cosine acos(x) is only defined for values between -1 and 1. This is due to numerical error in the normalization, and can be corrected by always rounding the reciprocal slightly up.