python 自定义 计算向量投影 正交 函数

# coding=utf-8
from math import sqrt, acos, pi

class Vector(object):
"""docstring for Vector"""
"""根据坐标轴列表输入 创建向量, 并创建该向量所处的空间维度"""
CANNOT_NORMALIZE_ZERO_VECTOR_MSG = 'Cannot normalize the zero vector'
def __init__(self, coordinates):
super(Vector, self).__init__()
try:
if not coordinates:
raise ValueError
self.coordinates = tuple(coordinates)
self.dimension = len(coordinates)
except ValueError:
raise ValueError('The coordinates must be nonempty')
except TypeError:
raise TypeError('The coordinates must be an iterable')

# '''能够使python的内置print函数 输出向量坐标轴'''

def __str__(self):
return 'Vector: {}'.format(self.coordinates)

def scalarMultiply(self,num):
new_corrdinate =[num * x for x in self.coordinates]
return Vector(new_corrdinate)

def minus(self,v):
new_corrdinate = [x-y for x,y in zip(self.coordinates, v.coordinates)]
return Vector(new_corrdinate)

# 将向量归一化
def normalized(self):
try:
magnitude = self.magnitude()
return  Vector([x *1.0/ magnitude for x in self.coordinates])
except ZeroDivisionError:
raise Exception('Cannot normalized the zero myVector2')

# 点积
def dot(self, v):
# print([x*y for x,y in zip(self.coordinates, v.coordinates)])
return sum([round(x*y,3) for x,y in zip(self.coordinates, v.coordinates)])

# 投影
def projection(self, b):
ub = b.normalized()
dot_num = self.dot(ub)
new_cordinates = ub.scalarMultiply(dot_num)
return new_cordinates
# 垂直
def vertical(self,b):
projection_v = self.projection(b)
new_cordinates = self.minus(projection_v)
return new_cordinates

v1 = Vector([3.039, 1.879])
v2 = Vector([0.825, 2.036])
print v1.projection(v2)

v3 = Vector([-9.88, -3.264, -8.159])
v4 = Vector([-2.155, -9.353, -9.473])
print v3.vertical(v4)

v5 = Vector([3.009,-6.172,3.692,-2.51])
v6 = Vector([6.404,-9.144,2.759,8.718])
print v5.projection(v6)
print v5.vertical(v6)

# 输出
# Vector: (1.0823253260174353, 2.671047713662422)
# Vector: (-8.350069611957737, 3.3761108674521076, -1.4336957930745413)
# Vector: (1.968617063395022, -2.810904813817002, 0.8481284319030084, 2.679950586926578)
# Vector: (1.040382936604978, -3.3610951861829976, 2.8438715680969917, -5.189950586926578)
# [Finished in 0.2s]

优化后 def component_parallel_to(self, basis):
try:
u = basis.normalized()
weight = self.dot(u)
return u.scalarMultiply(weight)
except Exception as e:
if str(e) == self.CANNOT_NORMALIZE_ZERO_VECTOR_MSG:
raise Exception(self.CANNOT_NORMALIZE_ZERO_VECTOR_MSG)
else:
raise e

def component_orthogonal_to(self, basis):
try:
projection = self.component_parallel_to(basis)
return self.minus(projection)
except Exception, e:
if str(e) == self.NO_UNIQUE_ORTHOGONAL_COMPONENT_MSG:
raise Exception(self.NO_UNIQUE_ORTHOGONAL_COMPONENT_MSG)
else:
raise e