# MATLAB CODE FOR ROOT MEAN SQUARED

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Grace on 13 Sep 2022
Edited: Torsten on 13 Sep 2022
Hello,please I have a matrix M, containng three distinct sets of data, and I intend to calculate the root mean squared. Coiuld some kinndly assist me; here is my trial code
clear all;close all;clc
A=[2 4 7 10 28]; %first
B=[1 3.6 8 11 27];%seccond
C=[0.5 5 9.5 13 32];%third
M=[A' B' C'];
[rows, columns] = size(M);
MEAN=zeros(rows, columns);
for row = 1 : rows
MEAN(row) = mean(M(row, :));
cal_rms=sqrt((MEAN-M(row, :)).^2./columns);
end
plot(cal_rms);

Torsten on 13 Sep 2022
This is not the standard definition for the root-mean-square value of a matrix.
Are you sure about the formula ? Then use
cal_rms(row) = sqrt((MEAN-M(row, :)).^2./columns);
cal_rms=sqrt((MEAN-M(row, :)).^2./columns);
##### 2 CommentsShowHide 1 older comment
Torsten on 13 Sep 2022
Edited: Torsten on 13 Sep 2022
MATLAB has a function "rms" for the rooot-mean-square value - you might want to use it, but it doesn't work with the matrix elements shifted by the mean value.
What you calculate is some kind of standard deviation of the rows of M, but in this case, you had to divide by (columns-1), not by (columns).
A=[2 4 7 10 28]; %first
B=[1 3.6 8 11 27];%seccond
C=[0.5 5 9.5 13 32];%third
M=[A.', B.', C.'];
[rows, columns] = size(M);
MEAN=zeros(rows,1);
for row = 1 : rows
MEAN(row) = mean(M(row, :));
cal_rms(row) = sqrt(sum((MEAN(row)-M(row,:)).^2)/columns);
end
plot(cal_rms)

Bruno Luong on 13 Sep 2022
Edited: Bruno Luong on 13 Sep 2022
To my book the mean should not be removed in calculation of RMS
M = rand(3,100);
[rows, columns] = size(M);
cal_rms = zeros(rows,1);
for row=1:size(M,1)
cal_rms(row) = sqrt( sum(M(row, :).^2) / columns );
end
cal_rms % theoretical value is sqrt(1/3) for rand()
cal_rms = 3×1
0.5737 0.5854 0.5894