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

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Sooraj Narayan on 19 Dec 2019
Edited: Andrei Bobrov on 24 Dec 2019
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).
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### Answers (2)

Kaashyap Pappu on 23 Dec 2019
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!
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Andrei Bobrov on 23 Dec 2019
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.
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Sooraj Narayan on 24 Dec 2019
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 on 24 Dec 2019
Edited: Andrei Bobrov on 24 Dec 2019
subplot(2,1,1)
plot(A,'g-')
subplot(2,1,2)
plot(N,'r-')

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