Given an additive matrix $$D$$ and a leaf $$j$$, LimbLength($$j$$) is equal to the minimum value of \[ \frac{D_{i, j} + D_{j, k} - D_{i, k}}{2} \] over all leaves $$i$$ and $$k$$.

Assignment

Add a method limb_length to the class DistanceMatrix that takes the index $$i$$ of a row/column in the distance matrix and returns LimbLength($$i$$).

Example

In the following example we assume the text file distances.txt¹ to be located in the current directory.

>>> D = DistanceMatrix.loadtxt('distances.txt')
>>> float(D.limb_length(0))
11.0
>>> float(D.limb_length(1))
2.0
>>> float(D.limb_length(2))
6.0
>>> float(D.limb_length(3))
7.0