Integrating A Vector (Or rather a series of point values)

Firstly I wish to apologise as I know there's a section of the matlab documentation / help files. However I've tried following it and am still stuck, so I was hoping someone here might be able to help me.

I have a series of data taken from (for the purposes of this question) a line. The data is not taken linearly (i.e. the points at which the data is taken along the line are not evenly distributed). I want to integrate the data taken across the length of the line. I know I can do this in matlab, but I just can't seem to work out how I do it.

(The problem below is made up and isn't my actual code, I just want to learn how to do what I want to do so that I can apply it to my actual problem)

Let's say I have a line of length 5m, and I get the following measurements;

(Distance from the start of the line - Data value)

0.6 - 12.6

1.3 - 87.2

2.0 - 74.2

3.0 - 45.3

4.0 - 23.4

5.0 - 14.2

So I want to integrate the values (on the left) along the length of the line. How would I go about doing this? As I said I know I CAN do it, but I'm really lost over how I do it. I've tried following the help files (using trapz) but I ended up getting a value far larger than I expected.

I know this isn't a lot to go on so I understand if nobody is able to help but (as always) any and all help received is greatly appreciated by this newbie to matlab who is trying to demystify it one function at a time :)

Answer 1

[Sean de Wolski]

trapz([0.6 1.3 2:5],[12.6 87.2 74.2 45.3 23.4 14.2])

And to see if it makes sense, look at each trapezoid's contribution:

cumtrapz([0.6 1.3 2:5],[12.6 87.2 74.2 45.3 23.4 14.2])

[Stephen]

Thank you :) I thought it was something like that, but wasn't sure what I had to do for the first part (i.e. if b=trapz(x,y) i wasn't sure what x had to be, although now that I know I feel rather silly for not thinking of that!).

A follow up question, if my line was still 5m but my first data point was at say 0.2m and my last at 4.8m is there away to ensure it integrates along the whole 5m and not just between 0.2m and 4.8m?

This might be getting more into a maths related question than matlab though. If it is, just say and I'll go read up on it, (I probably learnt how to do it years ago and have simply forgot since!)

Thank you very much for the help, I know I say it a lot but it really is appretiated :)

[Sean de Wolski]

Yes. You could add 0 and 5 to the ends of the x vector. However, you will have to come up with y-values to use at these points. If it's known to be zero or something then this is trivial. Otherwise you'll need to either extrapolate or use the last value.

[Stephen]

Ah, thank you very much, makes sense to me. Truth be told that's another one where I feel a bit silly for not thinking of!

Thank you very much Sean, you've been extremly helpful :)

Answer 2

[Jonathan Sullivan]

x = [0.6 1.3 2 3 4 5]; % Your x values
y = [12.6 87.2 74.2 45.3 23.4 14.2]; % Your y values
Area = trapz(x,y) % The area under the curve

For more information you can type

help trapz
doc trapz

[Stephen]

Thank you very much :) I accepted Sean's answer as his was first however you're answer is just as helpful :)

I've posted a follow up question on Sean's answer which I won't repost here, but I will say once again thank you for taking the time to help me out. :)