How to normalize a vector considering both maximum and the sum of values?

For instance; I have a vector

A=[

7782

7761

7707

7832

8154

8442

8690

9151

9318

9300 ];

The maximum is 9300 and the sum is 84137. Now I need to normalize this vector so that I get the same shape pattern for a new maximum (say 9900) and new sum (say 8700).

Answer 1

[Kaashyap Pappu]

You can use the normalize function with the ‘range’ method to preserve the shape of your normalized plot. This will consider values in the range [a,b] where a is the minimum value and b is the maximum value. The other methods could also be used as needed.

Hope this helps!

Answer 2

[Andrei Bobrov]

Please run follow m - file:

SN = 8700;
Nmx = 9900;

nmn = fzero(@(x)func1(x,Nmx,SN,A),-10000);
[~,N] = func1(nmn,Nmx,SN,A);

function [dt,N] = func1(Nmn,Nmx,SN,A)
    mn = min(A);
    N = (Nmx - Nmn)/(max(A) - mn)*(A - mn) + Nmn;
    dt = sum(N) - SN;
end

Here N - your output vector.

[Sooraj Narayan]

Thanks a lot for the reply. But would you kindly mind elaborating on the mathematics behind the code? I am having doubts whether it is actually possible to retain the shape of a vector while normalizing it using the maximum and the sum?

[Andrei Bobrov]

subplot(2,1,1)
plot(A,'g-')
subplot(2,1,2)
plot(N,'r-')