solve32.py

#Run in sageMath https://sagecell.sagemath.org/
import numpy as np
from math import sqrt

#Return the dot product of v & w
def dotProduct(v,w):
    return sum(map(lambda x, y: x*y, v, w))

#Return the norm of vector v
def norm(v):
    return sqrt(dotProduct(v,v))

#Returns a unit vector with the same direction as vector v
def getUnitVector(v):
    length = norm(v)
    return map(lambda x: x/length, v)

#Returns a list of n random unit vectors
def randomVector(n,vectors=[]):
    if n == 0:
        return vectors
    else:
        #generating normalized random unit vectors
        theta = 2 * np.pi * np.random.random()
        phi = np.pi * np.random.random()
        vectors.append(vector([np.cos(theta) * np.sin(phi), np.sin(theta) * np.sin(phi), np.cos(phi)]))
        return randomVector(n-1, vectors)


u = randomVector(1)[0]
U = randomVector(100)
   
products = list(map(lambda x: abs(dotProduct(x, u)), U))
plotList = zip(U, map(lambda x: x*255, products))
avgDotProduct = sum(products)/len(products)
plots = list(map(lambda x: plot(x[0], color=(x[1],x[1],x[1])), plotList))
plots.append(plot(u, color='red'))
show(sum(plots))
print('Average dot product: ' + str(avgDotProduct))