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Multiple summations in one formula

Asked by Inti Vanmechelen on 10 Sep 2019
Latest activity Commented on by darova
on 10 Sep 2019
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Hi all,
I'm not very good at matlab and trying incorporate the above formula. I'm trying to do part (2) and (3) first, to get them more easily in the complete formula.
I am struggling with (3): Y is in my case a 101x14 matrix and I think the mean should then be one number. I can obviously take the mean of the columns and rows seperately, yielding a 101x1 and a 14x1 vector, but these are obvousily not compatible for matrix multiplication.
Any advice on how to make this work better?
Additionally, am I correct doing the following instead of symsum?
M = 1; % Test day
N = 14; % Number of runs (or repetitions)
T = 101; % Number of time points
for n = 1:N
for t = 1:T
R2 = ....
end
end
Many thanks in advance!

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2 Answers

Answer by Thales
on 10 Sep 2019
 Accepted Answer

You can use for loops to do the sum or use the sum function:
clc; clear; close all force;
M = 1; % Test day
N = 14; % Number of runs (or repetitions)
T = 101; % Number of time points
Y = rand(M,N,T); % random data to illustrate
% using for loops
Yi_for = zeros(M,1);
for i=1:M
for j=1:N
for t=1:T
Yi_for(i) = Yi_for(i) + Y(i,j,t);
end
end
Yi_for(i) = Yi_for(i)/N/T;
end
% using sums
Yi_sum = zeros(M,1);
for i=1:M
Yi_sum(i) = sum(sum(Y,2),3)/N/T;
end
You can expand this to calculate the average at time point t on the ith test day:
% Yit should be a matrix
Yit = zeros(M,T);
for i=1:M
for t=1:T
for j=1:N
Yit(i,t) = Yit(i,t)+Y(i,j,t);
end
Yit(i,t) = Yit(i,t)/N;
end
end
With Yi and Yit previously calculated, you can define Ra (I splitted the calculations of the numerator and denominator of the fraction to make it clearer):
% Ra
Yi = Yi_sum;
Ra = 1;
% partial sums
num = 0; % numerator
for i=1:M
for j=1:N
for t=1:T
num = num + (Y(i,j,t)-Yit(i,t))^2/M/T/(N-1);
end
end
end
den = 0; % denominator
for i=1:M
for j=1:N
for t=1:T
den = den + (Y(i,j,t)-Yi(i))^2/M/(N*T-1);
end
end
end
Ra2 = 1-num/den

  2 Comments

Thank you for the stepswise explanation!
This was really helpful!
This well definetely get me where I need to be, many thanks :)
darova
on 10 Sep 2019
By my answer is better :(

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Answer by darova
on 10 Sep 2019

Shorter version
clc,clear
Yit = repmat( mean(Yijt,2), [1 N 1] ); % get mean and make 3D matrix
Yi = mean(mean(Yijt,2),3); % get mean 2d and 3d dimensions
Yi = repmat( Yi, [1 N T] ); % make 3D matrix
upsum = (Yijt-Yit).^2;
botsum = (Yijt-Yi).^2;
R2a = 1 - sum(upsum(:))/sum(botsum(:)) * T*(N-1)/(N*T-1);

  1 Comment

Hi Darova,
Since I am still trying get my head around implementing stuff from other in matlab, the long answer helped me a bit better to understand all the steps :) But thank you for the reply!

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