[FIXED] Adding 2 vectors and comparing the angle of the result to both vectors does not give same result. Why?

Issue

I want to calculate the angle between vectors. I thought the sum of 2 vectors should be in the middle of the 2. But calculating the angle with my method gives different results. I guess it has to be with rounding but the result is too different. I tried 2 different approaches. Can you explain me, why? Or am I wrong with my math understanding?

from numpy import (array, dot, arccos, clip, sum)
from numpy.linalg import norm
import spectral
import numpy as np


def calculateAngle(u, v):
    c = dot(u, v) / norm(u) / norm(v)  # -> cosine of the angle
    angle = arccos(clip(c, -1, 1))  # if you really want the angle
    return c, angle


def calc_with_numpy():
    print("Method 2:")

    v = (u1_norm + u2_norm)
    c1, angle1 = calculateAngle(u1, v)
    c2, angle2 = calculateAngle(u2, v)

    print("angle1:", angle1)
    print("angle2:", angle2)

def calc_with_spectral():
    print("Method 1:")
    v = (u1_norm + u2_norm)
    img=np.array([v]).reshape((1,1,v.size))
    means = np.array([u1, u2])
    angles = spectral.spectral_angles(img, means)
    print("angle1:", angles[0,0,0])
    print("angle2:", angles[0, 0, 1])

u1 = array([1.0,2.0], dtype="float64")
u1_norm = u1 / sum(u1)
u2 = array([3.0,2.0], dtype="float64")
u2_norm = u2 / sum(u2)

calc_with_spectral()
calc_with_numpy()

My results:

Method 1:

angle1: 0.25518239062081866

angle2: 0.2639637236257044

Method 2:

angle1: 0.2551823906208191

angle2: 0.2639637236257044

Solution

You are wrong here

u1_norm = u1 / sum(u1)
u2_norm = u2 / sum(u2)

To get normalized (unit length) vector, you need to divide it's components by vector length, not by component sum (like you perform right job inside calculateAngle)

u1_norm = u1 / np.linalg.norm(u1)

Answered By - MBo