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.

 

[alphy]

I would suggest using the function "trapz" to integrate your data curve. However, in order to specify an integration interval, you will need to provide both the x-axis values and the corresponding y-axis values to the function. In this case, you can use the following code:

trapz(t(1:5),Cp(1:5))

This will integrate from the first data point to the fifth data point on your curve. You can adjust the indices to specify any interval you desire.

Additionally, you can also use the "cumtrapz" function to perform a cumulative integration on your data, which will give you the area under the curve up to each data point. This can be useful for visualizing the changing integral over time.

I would also recommend checking the documentation for both "trapz" and "cumtrapz" to ensure that your data is in the correct format and that you are using the functions correctly. If you continue to encounter error messages, it may be helpful to consult with a more experienced MATLAB user or seek assistance from the MATLAB community forums.