Integrating a Discrete Function in MATLAB

[tramar]

I have a data curve with discrete time points that I imported into MATLAB. The x-axis is an array named t:

t =

  1.0e+003 *

    0.0319
    0.0505
    0.0851
    0.1037
    0.1356
    0.1648
    0.2021
    0.2313
    0.3616
    0.5823
    0.8880
    1.1778
    1.4996
    1.7814

The y-axis named Cp:

Cp =

  1.0e+004 *

    0.0077
    0.7846
    3.7077
    3.2923
    1.8769
    1.3769
    1.0539
    0.7769
    0.5462
    0.3923
    0.2692
    0.1846
    0.1462
    0.1385

The plot of the curve looks like this:

[PLAIN]http://dl.dropbox.com/u/11932911/Cp.jpg

Essentially I want to integrate the function from zero to one of the time points. I tried using the functions quad and trapz but they seem to return red error messages. The function trapz works when I integrate over the entire curve (trapz(Cp)) but it won't let me specify an integration interval.

 

[MATLABdude]

Trapz implements the trapezoid rule--if this is what you're looking for, that's great (but since you're not putting in the t-values, you're just getting the sum of x, which may or may not be what you're looking for):
http://www.mathworks.com/help/techdoc/ref/trapz.html

If you want to integrate only a portion of the data, put in only a portion of the vectors!

For instance, to extract the 1st through 5th values of x, you'd type in:
>> extract=x(1:5)

More on array indexing (including the colon operator used above):
http://www.mathworks.com/help/techdoc/learn_matlab/f2-12841.html#f2-428

As per the examples under trapz above, as long as the two input vectors are the same size, trapz should produce something--not sure what the error message is, but if you'd post it, we may be able to help you.

 

[tramar]

I should have posed the question in a better way... Based on the research I've done I think Simpson's rule is more efficient. I was initially trying to use the quad function:

quad(Cp, 0, t(1))
? Error using ==> fcnchk at 108
FUN must be a function, a valid string expression, or an inline function object.

Error in ==> quad at 66
f = fcnchk(funfcn);

I'm guessing that the error is because Cp is a discrete function and not a definite function of x. Essentially I need to know how to integrate this curve with Simpson's rule for a certain interval. Is there a way to do it directly or would I need to use the extract=x(..) function?

 

[MATLABdude]

The Simpson's rule implementation in MATLAB requires a function handle. Since you have a collection of data points, this won't work. And as you don't have a huge number of datapoints, efficiency isn't terribly relevant.
http://www.mathworks.com/help/techdoc/ref/function_handle.html

I'd suggest you stick with the trapezoid rule and use the subset extraction method I linked to earlier.