Condensed distance matrix and Pairwise index #python #numpy

condensed_distance_matrix_and_pairwise_index.py

# sometimes you want to get the distance matrix
# and once you have that distance matrix
# you want to be able to know what pairs contributed to that distance
# instead of converting it to the squareform
# which has redundant data
# we can do a little calculation

# note that there's a parallel version of pdist https://stackoverflow.com/a/29639465/582917
# however it doesn't return the condensed matrix

from scipy.spatial.distance import pdist, squareform

arr = np.array([1,2,3])
dist = pdist(arr)
square = squareform(dist)

def pair_ind_to_dist_ind(d, i, j):
  index = d*(d-1)/2 - (d-i)*(d-i-1)/2 + j - i - 1
  return index

def dist_ind_to_pair_ind(d, i):
    b = 1 - 2 * d
    x = np.floor((-b - np.sqrt(b**2 - 8*i))/2).astype(int)
    y = (i + x * (b + x + 2) / 2 + 1).astype(int)
    return (x,y)

What are d, i and j?