How to interpolate a matrix

Essentially I didn't know how to ask this as it probably is simple but I don't quite know what to do.

Essentially I want to create a response function for an earthquake record, where ultimately I want to plot the peak displacement against a varying time period. I am using the Runge-Kutta Method to integrate to get displacement from the acceleration data.

I have got a range of values for the time period -T0 and have calculated the state-space matrix A from this.

essentially I am unsure if i need to interpolate my A matrix to be the same size as my Npts in order for the loop to work.

Hope it makes sense and hope you can help!

Thanks in advance!!

for i=0.1:0.1:4; % Range of Time Periods defined 
     T0=(i);% seconds
     w = (2*pi)/T0(1:end); %rad/s
     w2=w(1:end)*w(1:end);
     zita=0.05;
     m=773; % Mass in MG
     A1=[0        1
        -w2(1:end)   -(2*zita*w(1:end))]; %state-space matrix of coefficients 
    b=[0
       1/m];  %state-space load vector

    end 

ft = m*acc.'; %acceleration data- converting to force f=ma

    dt    = 0.02; %seconds 
    NPTS = size(ft); %no.of points 
    tf    = (NPTS-1)*dt;
    t = 0:dt:tf;
    A=A1(1:end);

    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,t_interp);

    for i=1:(NPTS_interp-1)% Runge-Kutta loop, i = incremental time step

        g1 = A(1:end)*yt(:,i)+b*ft_interp(i);
        g2 = A(1:end)*(yt(:,i)+ 0.5*g1*dt_interp)+0.5*b*(ft_interp(i)+ft_interp(i+1));
        g3 = A(1:end)*(yt(:,i)+ 0.5*g2*dt_interp)+0.5*b*(ft_interp(i)+ft_interp(i+1));
        g4 = A(1:end)*(yt(:,i)+g3*dt_interp)+b*ft_interp(i+1);

        ynew = yt(:,i)+(g1+2*g2+2*g3+g4)*dt_interp/6;
        yt(:,i+1)=ynew; %storage
        ut=yt(1,:); %displacement values
        vt=yt(2,:);%velocity values
       [pks,locs]=findpeaks(ut,t_interp);
       Max_displacement=max(pks);
    end

[Bob Thompson]

Have you tried running the code yet? If so, what errors do you get?

Typically you don't have to have A match the number of points, as you can interpolate the specific value within the loop, but yes, you will ultimately need one input for each output.

[Serena Solanki]

Hi Bob I have run the code and do not get an error but in the output pane in the workspace, I do not get any outputs for my displacement or peaks-so it isn't quite working.

I want to interpolate my A matrix so that the number of values match the no. of values for the NPTS_interpolate for the RK4 loop.

is there another method?

Thanks

[Bob Thompson]

Do you know about the interp1() and interp2() commands? They are built in Matlab commands that I have used for interpolation purposes. These are both linear interpolators, so if you need something more complex you're probably going to need to get help from somebody other than me.

[Stephen23]

"... interp1() and interp2() commands? .... These are both linear interpolators..."

Reading the interp1 and interp2 documentation shows that they support a lot more than just linear interpolation, including variations of splines and cubic interpolation. The documentation is available online for everyone to read.

"essentially I am unsure if i need to interpolate my A matrix to be the same size as my Npts in order for the loop to work."

Writing code by guessing is not very efficient. Even before you get to writing code down you should first understand the algorithm that you want to implement. Even write it out on paper, and work through a few iterations by hand: this will give you something to compare your code's output against (you do confirm that your code is giving reasonable output values, don't you?) and it allows you to understand the prerequisites and conditions for the algorithm to work.

https://www.mathworks.com/matlabcentral/answers/228557-experts-of-matlab-how-did-you-learn-any-advice-for-beginner-intermediate-users

"How to interpolate a matrix"

Read the iterp1 and interp2 documentation carefully. Try the examples. Try it with your data.

[Serena Solanki]

Hi Stephen

Thanks for the advice

I have tried doing this and have found a nested loop may be a better way forward rather than interpolating as it isn't what I actually needed.

Writing it out definitely helped!