# https://en.wikipedia.org/wiki/Cosine_similarity
# Cosine similarity measures how alike or different two vectors are 
# It divides the (dot) product between two vectors by the magnitude of each vector

# make up vectors of the same length
A = c(2, -4, 5, -3, 1)
#B = c(1, 2, 3, -2, 2)
#B = c(4, -8, 10, -6, 2)  # B=2*A
#B = c(-2, 4, -5, 3, -1)  # B= -A
#B = c(-2, -1, -3, -5, 0) # B is orthogonal to A

# a product of two vectors  
prod = A*B

# the dot-product is the sum of the elements above
dot_prod= sum(prod)

# a vector's magnitude is the square root of its dot product with itself
mag_A = sqrt(sum(A*A))
mag_B = sqrt(sum(B*B))

# cos similarity should be between -1 and 1 
cos_simil = dot_prod/(mag_A*mag_B)