MATLAB: Calculating the area under a curve using cell arrays

area under curve cell arraysMATLAB

Afternoon everyone,
I have spent nearly a week trying to fix this problem and I am completely stuck.
Attached is the data set, each row is a node and each column is a time step, what I need to is calculate the area under the curve when y=0 for each row. Within the data, the peaks and troughs are not in fixed positions because of the phase shift, this leads to problem with errors (logical arrays and 0's) when using intrepl and trapz. Another problem in the data is that for certain rows (390-410) around col. 800 there a small peak that gets referenced as a peak and zero crossing point, as its value is soo close to zero.
Fig 1 (area of dPWP) shows is an area plot under each undulation, I need is the area above and below y=0. Fig 2 (area under trapz) is the area that my code is calculating, which is calcuating only the peaks and fig 3 (based vs peaks) shows the relation between the two.
If you would like to see the entire code let me know, but it is long because I have been addressing the errors above and it may require a bit of explaining but is based on Star Striders (https://uk.mathworks.com/matlabcentral/answers/314470-how-can-i-calculate-the-area-under-a-graph-shaded-area)

Best Answer

Try this: 
D = load('pwp_diff.mat');
dPWP = D.PWP_diff;
tv = 0:size(dPWP,2)-1;
tvi = linspace(min(tv), max(tv), numel(tv)*10);                         % Create Finer Grid
dPWPi = interp1(tv, dPWP.', tvi).';                                     % Interpolate To Finer Grid
zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);                    % Returns Approximate Zero-Crossing Indices Of Argument Vector
for k1 = 1:size(dPWPi,1)
    zx{k1} = zci(dPWPi(k1,:));                                          % Zero-Crossings For This Row
    fzx = dPWPi(1,1)*dPWPi(1,end) < 0;
    for k2 = 1:numel(zx{k1})-fzx
        iidx = [max([1, zx{k1}(k2)-1]) min([numel(dPWPi(k1,:)),zx{k1}(k2)+1])];
        x_exct{k1,k2} = interp1(dPWPi(1,iidx),tvi(iidx), 0);            % Interpolated Exact Zero-Crossings
    end
    posidx = dPWPi(k1,:) >= 0;                                          % Logical Index Of Positive Values
    cposint{k1,:} = cumtrapz(tvi(posidx), dPWPi(k1,posidx));            % Cumulative Positive Integral
    cnegint{k1,:} = cumtrapz(tvi(~posidx), dPWPi(k1,~posidx));          % Cumulative Negative Integral
    posint(k1,:) = cposint{k1}(end);                                    % Scalar Positive Integral Result
    negint(k1,:) = cnegint{k1}(end);                                    % Scalar Negative Integral Result
end
figure
plot(tvi, dPWPi(1,:))
hold on
plot(tvi(zx{1}), dPWPi(1,zx{1}), 'r+')
plot([x_exct{1,:}], zeros(size([x_exct{1,:}])), 'gx')
hold off
grid
xlim([0 100])
The plot simply shows that the increased resolution proviede by the interpolation produces almost the exact zero-crossings. It is not necessary for the code.
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