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