Definite integral using cumtrapz()

I have a matrix of data points "Y" and want to numerically integrate each ith row of matrix Y from 0 to the ith element of vector "lim" which contains the upper limits of the integral. For example,

Y = 1 2 4 6
    2 4 5 7
    4 5 6 8

lim = [3 2 1]

The cumtrapz function uses unit spacing so I think the columns of Y represent the x-axis from x=0 to x=4. I would like to integrate the first row of Y from x=0 to x=3, the 2nd row from x=0 to x=2 and the 3rd row from x=0 to x=1. Is this possible to do using cumtrapz()? I'm not sure how to specify the limits.

Answer 1

[Star Strider]

I’m not certain what result you want.

Here are two possibilities, the first using trapz, the second using cumtrapz:

Y = [1 2 4 6
     2 4 5 7
     4 5 6 8];

lim = [3 2 1];

for k1 = 1:numel(lim)
    Yint(k1,:) = trapz(Y(k1,1:lim(k1)+1));
end

for k1 = 1:numel(lim)
    Yintc{k1,:} = cumtrapz(Y(k1,1:lim(k1)+1));
end

A loop for each seems to be the only option.

[k.merchant]

The first option works perfectly, I knew I would have to use some sort of loop, but didn't know where to start. Thank you very much for all your help today :) I had been struggling to figure this out for some time now so I really appreciate it!

[Star Strider]

As always, my pleasure!