from math import sqrt,acos,pi
from decimal import Decimal,getcontext
getcontext().prec =30 #保留30小数
class Vector(object):
def __init__(self, coordinates):
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')
CANNOT_NORMALIZE_ZERO_VECTOR_MSG = 'Cannot normalize the zero vector'
#向量相加
def plus(self,v):
new_coordinates = [x+y for x,y in zip(self.coordinates,v.coordinates)]
return Vector(new_coordinates)
#向量相减
def minus(self,v):
new_coordinates = [x-y for x,y in zip(self.coordinates,v.coordinates)]
return Vector(new_coordinates)
#数乘
def times_scalar(self,c):
new_coordinates = [Decimal(c)*x for x in self.coordinates]
return Vector(new_coordinates)
#向量的模
def magnitude(self):
coordinates_squared = [x*x for x in self.coordinates]
return sqrt(sum(coordinates_squared))
#方向函数（化为单位向量）
def normalized(self):
try:
magnitude = self.magnitude()
return self.times_scalar(Decimal(1.0)/Decimal(magnitude))
except ZeroDivisionError:
raise Exception(self.CANNOT_NORMALIZE_ZERO_VECTOR_MSG)
#向量点乘（内积）
def dot(self,v):
return sum([x*y for x,y in zip(self.coordinates,v.coordinates)])
#向量叉乘（外积、向量积）
def cross(self,v):
try:
x_1,y_1,z_1=self.coordinates
x_2,y_2,z_2=v.coordinates
new_coordinates=[y_1*z_2-y_2*z_1,
-(x_1*z_2-x_2*z_1),
x_1*y_2-x_2*y_1]
return Vector(new_coordinates)
except ValueError as e:
msg = str(e)
if msg == 'need more than 2 values to unpack':
self_embedded_in_R3 = Vector(self.coordinates+('0',))
v_embedded_in_R3 = Vector(v.coordinates+('0',))
return self_embedded_in_R3*v_embedded_in_R3
elif (msg == 'too many values to unpack' or
msg == 'need more than 1 values to unpack'):
raise Exception(self.ONLY_DEFINED_IN_TWO_THREE_DIMS_MSG)
else:
raise e
#用于计算两个向量形成的平行四边形的面积
def area_of_parallelogram_with(self,v):
cross_product = self.cross(v)
return cross_product.magnitude()
#用于计算两个向量形成的三角形的面积
def area_of_triangle_with(self,v):
return self.area_of_parallelogram_with(v)/2.0
#计算向量夹角
def angle_with(self,v,in_degrees=False):
try:
u1=self.normalized()
u2=v.normalized()
dots=u1.dot(u2)
if abs(abs(dots) - 1) < 1e-10:
if dots < 0:
dots = -1
else:
dots = 1
angle_in_radians =acos(dots)
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
#判断两向量之间平行
def is_parallel_to(self,v):
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):#1乘以10的-10次方
return self.magnitude()<tolerance
#判断两向量正交
def is_orthogonal_to(self,v,tolerance=1e-10):
return abs(self.dot(v))<tolerance
#利用向量投影分解的水平向量
def component_parallel_to(self,basis):
try:
u=basis.normalized()
weight=self.dot(u)
return u.times_scalar(weight)
except Exception as e:
if str(e)==self.CANNOT_NORMALIZE_ZERO_VECTOR_MSG:
raise Exception(self.NO_UNIQUE_PARALLEL_COMPONENT_MSG)
else:
raise e
#利用向量投影分解出的垂直向量
def component_orthogonal_to(self,basis):
try:
projection=self.component_parallel_to(basis)
return self.minus(projection)
except Exception as e:
if str(e)==self.NO_UNIQUE_PARALLEL_COMPONENT_MSG:
raise Exception(self.NO_UNIQUE_ORTHOGNOAL_COMPONENT_MSG)
else:
raise e
#
def __str__(self):
return 'Vector: {}'.format(self.coordinates)
def __eq__(self, v):
return self.coordinates == v.coordinates
#向量相加
vector1 = Vector(['8.218','-9.341'])
vector2 = Vector(['-1.129','2.111'])
print (vector1.plus(vector2))#Vector.plus(vector1,vector2)
#向量相减
vector3 = Vector(['7.119','8.215'])
vector4 = Vector(['-8.223','0.878'])
print (vector3.minus(vector4))#Vector.minus(vector3,vector4)
#数乘
vector5 = Vector(['1.671','-1.012','-0.318'])
c=7.41
print (vector5.times_scalar(c))#Vector.times_scalar(vector5,c)
#向量的模和方向函数（化为单位向量）
vector6 = Vector(['3','4'])
print(Vector.magnitude(vector6))
print(Vector.normalized(vector6))
#向量点乘（内积）
v = Vector(['7.887','4.138'])
w = Vector(['-8.802','6.776'])
print(v.dot(w))
v = Vector(['-5.955','-4.904','-1.874'])
w = Vector(['-4.496','-8.755','7.103'])
print(v.dot(w))
#计算向量夹角
v = Vector(['3.183','-7.627'])
w =Vector(['-2.668','5.319'])
print(v.angle_with(w))
v = Vector(['7.6','1','5.188'])
w = Vector(['2.751','8.259','3.985'])
print(v.angle_with(w,in_degrees=True))
#判断两向量之间平行或正交
print('first pair')
v = Vector(['-7.579','-7.88'])
w = Vector(['22.737','23.64'])
print ('is parallel:',v.is_parallel_to(w))
print ('is orthogonal:',v.is_orthogonal_to(w))
print('second pair')
v = Vector(['-2.029','9.97','4.172'])
w = Vector(['-9.231','-6.639','-7.245'])
print ('is parallel:',v.is_parallel_to(w))
print ('is orthogonal:',v.is_orthogonal_to(w))
print('third pair')
v = Vector(['-2.328','-7.284','-1.214'])
w = Vector(['-1.1821','1.072','-2.94'])
print ('is parallel:',v.is_parallel_to(w))
print ('is orthogonal:',v.is_orthogonal_to(w))
print('four pair')
v = Vector(['2.118','4.827'])
w = Vector(['0','0'])
print ('is parallel:',v.is_parallel_to(w))
print ('is orthogonal:',v.is_orthogonal_to(w))
#利用向量投影分解出一个水平向量、一个垂直向量
print('\n#1')
v = Vector(['3.039','1.879'])
w = Vector(['0.825','2.036'])
print(v.component_parallel_to(w))
print('\n#2')
v = Vector(['-9.88','-3.264','-8.159'])
w = Vector(['-2.155','-9.353','-9.473'])
print(v.component_orthogonal_to(w))
print('\n#3')
v = Vector(['3.009','-6.172','3.692','-2.51'])
w = Vector(['6.404','-9.144','2.759','8.718'])
vpar = v.component_parallel_to(w)
vort = v.component_orthogonal_to(w)
print('parallel component:',vpar)
print('orthogonal component:',vort)
未完待续
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