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Copy path1-1-4 vectors - dot product angle.py
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1-1-4 vectors - dot product angle.py
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"""Use a set of functions for vectors."""
from math import sqrt, acos, pi
from decimal import Decimal, getcontext
getcontext().prec = 30
class Vector(object):
"""Use that class for playing with vectors."""
CANNOT_NORMALIZE_ZERO_VECTOR_MSG = 'Cannot normalize the zero vector'
def __init__(self, coordinates):
"""Use it to initiate vectors."""
try:
if not coordinates:
raise ValueError
self.coordinates = tuple([Decimal(x) for x in coordinates])
self.dimension = len(self.coordinates)
except ValueError:
raise ValueError('The coordinates must be nonempty')
except TypeError:
raise TypeError('The coordinates must be an iterable')
def __str__(self):
"""Use that function for printing vector."""
return 'Vector: {}'.format(self.coordinates)
def __eq__(self, v):
"""Use this function to compare two vectors."""
return self.coordinates == v.coordinates
def plus(self, v):
"""Use if for adding two vectors."""
new_coordinates = \
[x + y for x, y in zip(self.coordinates, v.coordinates)]
return Vector(new_coordinates)
def minus(self, v):
"""Use if for distracting two vectors."""
new_coordinates = [x-y for x, y in zip(self.coordinates, v.coordinates)]
return Vector(new_coordinates)
def multiply(self, a):
"""Use if for multiplying two vectors.
Scalar Multiple."""
new_coordinates = [Decimal(a) * x for x in self.coordinates]
return Vector(new_coordinates)
def magnitude(self):
"""Use if for magnitude calculation."""
coordinates_squared = [x**2 for x in self.coordinates]
return sqrt(sum(coordinates_squared))
'''
calculated_mag = 0
for x in range(len(self.coordinates)):
calculated_mag += self.coordinates[x] * self.coordinates[x]
calculated_mag = sqrt(calculated_mag)
return calculated_mag
'''
def normalized(self):
"""Use it to calculate a normalization of a vector."""
try:
calculated_mag = self.magnitude()
return self.multiply(Decimal('1.0')/Decimal(calculated_mag))
except ZeroDivisionError:
raise Exception(self.CANNOT_NORMALIZE_ZERO_VECTOR_MSG)
'''
calculated_dir = 1/self.magnitude()
calculated_dir = self.multiply(calculated_dir)
'''
def dot(self, v):
"""Use if for calculation a dot product of two vectors."""
"""Dot product."""
return sum([x * y for x, y in zip(self.coordinates, v.coordinates)])
'''
calculated_product = 0
for x, y in zip(self.coordinates, v.coordinates):
calculated_product += x * y
return calculated_product
'''
def angle_with(self, v, in_degrees=False):
"""Use if to calculate angle between two vectors."""
try:
v_1 = self.normalized()
v_2 = v.normalized()
angle_in_radians = acos(v_1.dot(v_2))
if in_degrees:
degrees_per_radian = 180. / pi
return angle_in_radians / degrees_per_radian
else:
return angle_in_radians
except Exception as e:
if str(e) == self.CANNOT_NORMALIZE_ZERO_VECTOR_MSG:
raise Exception('Cannot compute \
an angle with the zero vector ')
else:
raise e
pass
def is_orthogonal_to(self, v, tolerance=1e-10):
"""Check if two vectors are orthogonal to each other."""
# 1e-10 dopuszcza tolerancje wyniku od minus 10 do plus 10.
return abs(self.dot(v)) < tolerance
def is_parrallel_to(self, v):
"""Check if two vectors are parralel."""
return (self.is_zero() or
v.is_zero() or
self.angle_with(v) == 0 or
self.angle_with(v) == pi)
def is_zero(self, tolerance=1e-10):
"""Check if vector is zero vector."""
return self.magnitude() < tolerance
# plus------------------------------
# vector_1 = Vector([8.218, -9.341])
# vector_2 = Vector([-1.129, 2.111])
# print (vector_1.plus(vector_2))
# print (Vector([8.218, -9.341]))
# minus-----------------------------
# vector_3 = Vector([7.119, 8.215])
# vector_4 = Vector([-8.223, 0.878])
# print (vector_3.minus(vector_4))
# scalar multiply-------------------
# vector_5 = Vector([1.671, -1.012, -0.318])
# print (vector_5.multiply(3))
# magnitude-------------------------
# vector_6 = Vector([-0.221, 7.437])
# vector_7 = Vector([8.813, -1.331, -6.247])
#
# print (vector_6.magnitude())
# print (vector_7.magnitude())
# direction / normalization---------
# vector_8 = Vector([5.581, -2.136])
# vector_9 = Vector([1.996, 3.108, -4.554])
# vector_10 = Vector([0, 0, 0])
#
# print (vector_8.normalized())
# print (vector_9.normalized())
# print (vector_10.normalized())
# product & angle---------------
# vector_11 = Vector([7.887, 4.138])
# vector_12 = Vector([-8.802, 6.776])
# vector_13 = Vector([-5.955, -4.904, -1.874])
# vector_14 = Vector([-4.496, -8.755, 7.103])
# vector_15 = Vector([3.183, -7.627])
# vector_16 = Vector([-2.668, 5.319])
# vector_17 = Vector([7.35, 0.221, 5.188])
# vector_18 = Vector([2.751, 8.259, 3.985])
# print (vector_11.product(vector_12))
# print (vector_13.product(vector_14))
# print (vector_15.angle(vector_16))
# print (vector_17.angle(vector_18, in_degrees=True))
# orthogonal or parallel ---------------------------
# vector_19 = Vector([1, 3, 5])
# vector_20 = Vector([2, 6, 10])
# vector_21 = Vector([-7.579, -7.88])
# vector_22 = Vector([22.737, 23.64])
# vector_23 = Vector([-2.029, 9.97, 4.172])
# vector_24 = Vector([-9.231, -6.639, -7.245])
# vector_25 = Vector([-2.328, -7.284, -1.214])
# vector_26 = Vector([-1.821, 1.072, -2.94])
# vector_25 = Vector([-2, -7, -1])
# vector_26 = Vector([-1, 1, -2])
# vector_27 = Vector([2.118, 4.827])
# vector_28 = Vector([0, 0])
# print (vector_21.is_orthogonal_to(vector_22))
# print (vector_27.is_parrallel_to(vector_28))