Question

(code examples are python)
Lets assume we have a list of percentages that add up to 100:

mylist = [2.0, 7.0, 12.0, 35.0, 21.0, 23.0]   

Some values of mylist may be changed, others must stay fixed.
Lets assume the first 3 (2.0, 7.0, 12.0) must stay fixed and the last three (35.0, 21.0, 23.0) may be changed.

fix = mylist[:3] vari = mylist[3:] 

The goal is to add a new item to mylist, while sum(mylist) stays 100.0 and vari
items keep their relations to each other. For that we need to substract a CERTAIN
PERCENTAGE from each vari item. Example: lets assume we want to add 4.0 to mylist.
Using an ugly aproximation loop I found out that i need to substract ca. 5.0634%
of each vari item (CERTAIN PERCENTAGE = 5.0634):

adjusted =[] for number in vari:     adjusted.append(number-(number*(5.0634/100.0))) adjusted.extend(fix) adjusted.append(4.0) 

adjusted now contains my desired result.

My question is how to calculate CERTAIN PERCENTAGE ;.)

Answer 1

How’s this?

def adjustAppend( v, n ):     weight= -n/sum(v)     return [ i+i*weight for i in v ] + [n] 

Given a list of numbers v, append a new number, n. Weight the existing number to keep the sum the same.

 sum(v) == sum( v + [n] ) 

Each element of v, i, must be reduced by some function of i, r(i) such that

sum(r(i)) == -n 

or

sum( map( r, v ) ) == -n 

Therefore, the weighting function is -(n*i)/sum(v)