Implementing a sum of series with a sum of series

I am having trouble implementing a formula shown below:

Specifically, the sum of series with a sum of series. I am currently using nested for loops to execute this but I don't think my execution is correct.

a,b,C are constants

D(t0) = 0 in this case so it is omitted

trajectoryArraywithShear is a cell array with matrices sized (nx5) with the tau (shear) values

dose1 in this case is the to calculate the first sum of series

totDose1 is the cumulative dose (BDI(t))

a1 = 0.77;
b1 = 3.075;
C1 = 3.31 * 10^-6;
BDI1 = 0;
for z = 1:length(trajectoryArraywithShear) %for each trajectory, where tau is located
    totDose1 = 0; %set initial total dose to 0;
    for w = 1:size(trajectoryArraywithShear{z},1) %for the size of the trajectory
        dose1 = 0;
        for r = 1:w %dose1 at r = 1 is 0
            dose1 = dose1 + trajectoryArraywithShear{z}(r,5)^(b1/a1) * timeStep;
        end
        dose1 = dose1^(a1-1);
        totDose1 = totDose1 + (C1 * a1 * dose1 * timeStep * trajectoryArraywithShear{z}(w,5)^(b1/a1));
    end
    BDI1 = totDose1;
    trajectoryArraywithShear{z}(1,6) = BDI1;

[Rik]

Why do you think this is incorrect? (note that I did not look in detail at the implementation)

Answer 1

[Nipun]

Hi Curtis,

I understand that you want to implement the given formula in MATLAB without using nested loops. Here is how you can do it using matrix operations:

a1 = 0.77;
b1 = 3.075;
C1 = 3.31 * 10^-6;
timeStep = ...; % Define your time step
trajectoryArraywithShear = ...; % Your input cell array

BDI1 = 0;
for z = 1:length(trajectoryArraywithShear)
    tau = trajectoryArraywithShear{z}(:, 5);
    n = length(tau);
    T = tril(repmat(tau.^(b1/a1) * timeStep, 1, n));
    dose1 = sum(T, 2).^(a1 - 1);
    totDose1 = C1 * a1 * sum(dose1 .* tau.^(b1/a1) * timeStep);
    BDI1 = totDose1;
    trajectoryArraywithShear{z}(1, 6) = BDI1;
end

Refer to the following MathWorks documentation for matrix indexing and operations in MATLAB: https://www.mathworks.com/company/technical-articles/matrix-indexing-in-matlab.html

Hope this helps.

Regards,

Nipun