为什么我的代码不这样处理并行向量？

Question

我编写了以下代码，旨在通知其用户两个给定向量是否 parallel/orthogonal 以及两个向量之间的角度是多少：

import math
from numpy import arccos, array, dot

def oracle(a, b):
    n= 0
    scalar = a[n]/b[n]
    while n < len(a):
        s = a[n]/b[n]
        if s != scalar or (not s < (scalar + 0.001) and not s > (scalar -0.001)): #in order to avoid false negatives related to the limited precision
            break
        else: 
            if n == (len(a) - 1):
                print("The two vectors are parallel.")
        n = n + 1
                
def normalize2(a):
    if dot(a, a) == 0:
        print("The magnitude of this vector is 0 - it is a zero vector and so it has no direction.") 
        return
    return (dot(a, a))**0.5
    

def find_angle(a, b): 
    c = dot(a, b)
    if c == 0 or c < 0.001 and c > -0.001:#otherwise with just if c == 0 you get a lot of false negatives
        print("The two vectors are orthogonal.")
    theta = arccos(c/(normalize2(a) * normalize2(b)) )
    print(f"The angle, the shorter one, between the two vectors is {theta} radians or {math.degrees(theta)} degrees.")


a = array([-7.5, -7.8])
print(a)
b = array([22.5, 23.4])
print(b)

find_angle(a, b)
oracle(a, b)


a = array([-1.0, -2.0])
print(a)
b = array([2.0, 4.0])
print(b)

find_angle(a, b)
oracle(a, b)

当我运行代码时，我得到以下输出：

[-7.5 -7.8]
[22.5 23.4]
-351.27
The angle, the shorter one, between the two vectors is 3.141592638688632 radians or 179.99999914622634 degrees.
[-1. -2.]
[2. 4.]
-10.0
The angle, the shorter one, between the two vectors is 3.1415926325163688 radians or 179.99999879258172 degrees.
The two vectors are parallel.

我不知道为什么 oracle 函数会运行因为 array([-7.5, -7.8]) 和 array([22.5, 23.4]) 不是并行的。然而，这两个向量显然是平行的。为什么会这样？

Answer 1

您的有限精度逻辑似乎不正确。当出现精度问题时，s != scalar 将为 return True，因为您使用了 or，所以整个检查都为 True。（也是一种非常复杂的方式）

if s != scalar or (not s < (scalar + 0.001) and not s > (scalar -0.001)):

应该是

if abs(scalar-s) > 0.001

为什么我的代码不这样处理并行向量？

Why does my code doesn't treat parallel vectors as such?

python

precision

numpy

linear-algebra