add / interpolate arrays of different length

Hello community,

i have two array's tsol and ysol. Each array has the length of 9;

I have also an error estimate array errorEst. The error estimate has only 4 elements.

The four elements have a "time" length of 0.25.

The errorEst

tsol = linspace(0,1,9);
ysol = sin(tsol*pi);

errorEst = rand(1,4); %each bar has a length of 0.25;
bar(errorEst); 

plot([0 0.25 0.5 0.75; 0.25 0.5 0.75 1],[errorEst; errorEst]/0.25,'k')
title('gradient of errorEst ')
xlabel('t')
ylabel('d errorEst / dt')

% who could i integrate this gradient of errorEst w.r.t the time tSol and
% add to ysol?
% the first part should be a continous (function/plot)
% is there an elegant solution, which is parallelizable?

the solution should be plottet:

%yp = ysol + errorEstLin;
%ym= ysol -errorEstLin;

Answer 1

[Tony]

Here's one way to do it by piece-wise integration by checking which interval you are.

tsol = linspace(0,1,9);
ysol = sin(tsol*pi);
errorEst = rand(1,4); %each bar has a length of 0.25;
bar(errorEst); 

errorEst0 = 0; % need to specify initial error at t=0
errorEstLin = zeros(size(tsol));
for i = 1:numel(tsol)
    if i == 1
        errorEstLin(i) = errorEst0;
    else
        errorEstIntervalPrev = ceil(tsol(i-1) / 0.25 + 1e-12); %1e-12 to exclude lower bound of interval from interval
        errorEstIntervalCurr = ceil(tsol(i) / 0.25);
        errorEstLin(i) = errorEstLin(i - 1);
        if errorEstIntervalCurr == errorEstIntervalPrev
            errorEstLin(i) = errorEstLin(i) + (tsol(i) - tsol(i-1)) * errorEst(errorEstIntervalPrev);
        else
            errorEstLin(i) = errorEstLin(i) ...
            + (0.25 * errorEstIntervalPrev - tsol(i-1)) * errorEst(errorEstIntervalPrev) ...
            + sum(0.25 * errorEst(errorEstIntervalPrev + 1 : errorEstIntervalCurr - 1)) ...
            + (tsol(i) - 0.25 * (errorEstIntervalCurr - 1)) * errorEst(errorEstIntervalCurr);
        end
    end
end

yp = ysol + errorEstLin;
ym= ysol -errorEstLin;
plot(tsol', [ysol ; yp ; ym ; errorEstLin]')
legend({'ysol', 'yp', 'ym', 'errorEstLin'})