value range: [1,2]
distance matrix with 13 points
persistence intervals in dim 0:
 [0,1)
 [0,1)
 [0,1)
 [0,1)
 [0,1)
 [0,1)
 [0,1)
 [0,1)
 [0,1)
 [0,1)
 [0,1)
 [0,1)
 [0, )
persistence intervals in dim 1:
 [1,2)
persistence intervals in dim 2:
 [1,2)