Issue with my nested loop- taking forever to run

Hi All

Unfortunately I am having a few issues with my nested loop. Fundamentally the outputs in the workspace show that I am getting the ouputs of the right dimension. However my loop is taking forever to run and often I have had to cancel it- with it taking over 40mins !! It shouldn't be taking this long and I am wondering if my loop logic is not quite correct.

I have tried multiple things- such as changing index and order of some calculations.

Overall I am calculating my A matrix which is a 2*2 matrix and contains variables. I have calculated 40 sets of these 2*2 matrices and wish to save them into an array.

Then I am using the RK4 loop to calculate displacement for the acceleration and finding the peak displacement. So I want to get 40 different peak displacements with my associated state-space 2*2 A matrix.

Is there something wrong with my logic? as it is not outputting this and is taking forever to run.

Thanks in advance!!

dt_interp=0.0001;
t_interp=dt_interp:dt_interp:tf;
ft_interp=F_interp(t,ft,t_interp);
NPTS_interp=size(t_interp,2);

yt=zeros(2,NPTS_interp);

for T0=0.1:0.1:4;
for i=1:(NPTS_interp-1);
        w=(2*pi)/T0;
        w2=w*w;
        zita=0.05;
        m=773;
        A1=[0   1  ; -w2     -(2*zita*w)];
       A=A1(:,:);
        b=[0
           1/m];
       g1=A(:,:)*yt(:,i)+b*ft_interp(i);
       g2=A(:,:)*(yt(:,i)+0.5*g1*dt_interp)+0.5*b*(ft_interp(i)+ft_interp(i+1));
       g3=A(:,:)*(yt(:,i)+0.5*g2*dt_interp)+0.5*b*(ft_interp(i)+ft_interp(i+1));
       g4=A(:,:)*(yt(:,i)+g3*dt_interp)+b*ft_interp(i+1);

         ynew=yt(:,i)+(g1+g2+g3+g4)*dt_interp/6;
         yt(:,i+1)=ynew;

         ut=yt(1,:);
         vt=yt(2,:);

         Sd_max(T0)=max(ut);
  end 
   end  

   Maximum_displacement=Sd_max(1,:);

   figure(1)

   plot(T0,Maximum_displacement);
   grid on
   grid minor
   xlabel('Time Period (s)');
   ylabel('Peak Displacement (m)');
   title('Response Spectrum for Earthquake 1');

function a=F_interp(time, F, t)
a = interp1(time, F, t);
end

[Stephen23]

Badly aligned code is one way that beginners hide mistakes in their code. You should use the default alignment of the MATLAB editor, then it is a lot clearer how the code is structured:

dt_interp = 0.0001;
t_interp = dt_interp:dt_interp:tf;
ft_interp = F_interp(t, ft, t_interp);
NPTS_interp = size(t_interp, 2);
yt = zeros(2, NPTS_interp);
for T0 = 0.1:0.1:4;
    for i = 1:(NPTS_interp - 1);
        w = (2 * pi) / T0;
        w2 = w * w;
        zita = 0.05;
        m = 773;
        A1 = [0 1; - w2 - (2 * zita * w)];
        A = A1(:, :);
        b = [0
        1 / m];
        g1 = A(:, :) * yt(:, i) + b * ft_interp(i);
        g2 = A(:, :) * (yt(:, i) + 0.5 * g1 * dt_interp) + 0.5 * b * (ft_interp(i) + ft_interp(i + 1));
        g3 = A(:, :) * (yt(:, i) + 0.5 * g2 * dt_interp) + 0.5 * b * (ft_interp(i) + ft_interp(i + 1));
        g4 = A(:, :) * (yt(:, i) + g3 * dt_interp) + b * ft_interp(i + 1);
        ynew = yt(:, i) + (g1 + g2 + g3 + g4) * dt_interp / 6;
        yt(:, i + 1) = ynew;
        ut = yt(1, :);
        vt = yt(2, :);
        Sd_max(T0) = max(ut);
    end
end
Maximum_displacement = Sd_max(1, :);
figure(1)
plot(T0, Maximum_displacement);
grid on
grid minor
xlabel('Time Period (s)');
ylabel('Peak Displacement (m)');
title('Response Spectrum for Earthquake 1');
function a = F_interp(time, F, t)
a = interp1(time, F, t);
end

[Serena Solanki]

Hi Stephen

Thank you for pointing this out- this has pointed out some errors. essentially I am struggling to save my A-matrix into an array and be able to call data from A into my RK4 loop.

Is there any way i can save my A- matrix data into an array? I have tried indexing however it seems to be overwriting my values rather than saving all of the outputs.

Again thank you for your help

[Stephen23]

@Serena Solanki: is that really the code that you are running? Apparently you are using fractional values as indices, and I have never seen that work before:

for T0 = 0.1:0.1:4;
    for i = ...
        ...
        Sd_max(T0) = max(ut);
    end
end

"Is there any way i can save my A- matrix data into an array?"

Of course: preallocate an array of the correct size, and then use indexing. As you do not really explain the algorithm and the code above has mistakes in it I am not sure what changes you need to make.