Complex math formula Python

Question

I have been trying to program a math formula in python. The code is running but I have strong belief that the code is not reflecting the actual math formulas,but I am so lost I don't know where I could have gone wrong. Below is my code and I have attached the actual maths formula. Please check if the python code matches the math formula -if not, assist on where I am going wrong. I am honestly so lost.

## Inter cluster distance
inter = 0 
for i in range(centr.shape[1]-1):
  for j in range(i+1,centr.shape[1]):
    for l in range(centr.shape[0]):
      inter = inter + (centr[l][i]-centr[l][j])**2    
print('Intercluster distance: '+ str(inter))
## Intra cluster cluster
intra = 0
for i in range(data.shape[0]):
  for j in range(centr.shape[0]):[enter image description here][2]
    intra = intra + (data[i][j] - centr[j][Cc[i]-1])**2
print('Intracluster distance: '+ str(intra))

Math equation intra-cluster distance Mth equation inter-cluster distance

My code in python

Answer 1

Observe how the range constructor works:

>>> list(range(3))
[0, 1, 2]

>>> list(range(1, 3))
[1, 2]

So the default start value is 0, and the stop value is never included. You thus need slightly different start and stop values.

Also, the indices for the matrix elements z in your code are probably all off by 1 unit compared to the formula you give, because Python indexing works similarly to range, starting at 0, whereas in the formula they apparently start at 1.

So e.g. for the inter-cluster distance, we should have this code:

## Inter cluster distance
inter = 0 
for i in range(1, centr.shape[1]):
    for j in range(i+1, centr.shape[1] + 1):
        for l in range(1, 3 + 1):
            inter = inter + (centr[l - 1][i - 1] - centr[l - 1][j - 1])**2    
print('Intercluster distance: '+ str(inter))

Or you could make the indices i, j, l all one unit smaller and index the z values accordingly, which should yield the same result:

## Inter cluster distance
inter = 0 
for i in range(centr.shape[1] - 1):
    for j in range(i, centr.shape[1]):
        for l in range(3):
            inter = inter + (centr[l][i] - centr[l][j])**2    
print('Intercluster distance: '+ str(inter))