Integration over discrete data - don't know if trapz works here

Hey,

I'm trying to integrate a set of data.

I already done: plot(energy,photonflux), where energy is a set of not equaly spaced values for photon energy, and photonflux is the actual amount of photons.

I tried integrating the equation setting a dE=energy(i+1)-energy(i) where dE will be used to integrate.

Since my dE, change for every value the only way i got was too calculate the actual dE for every set of two points where i build a rectangle of height y.

This method alows me to integrate my set of data points quite well but not as perfectly as i would want. The first value for J should be around 66 or 67. And I'm getting about 61. Can i use trapz on this?

q=elementary electron charge.

I want to integrate the black data points.

for i=1:1:length(energy)-1
area=area+photonflux(i)*dE
end
J=area*q

[Mathieu NOE]

hello

yes , trapz is what you need to do a better integration

if your data are not equally sampled, conidesr interp1 to resample the data

[Tiago Fernandes]

Yeah thanks, I will try it.

After writting the doubt here I remembered that I possibly could do the trapz method manually. I think that I will try it.

Thanks a lot.

[Star Strider]

If you have data that are not regularly-sampled (the sampling intervals are not all the same), and you have the independent variable of the sampling intervals, use that independent variable as the first argument to trapz. It will use that vector to calculate the integral correctly.

[Tiago Fernandes]

I tried to do: trapz(energy,photonflux) and it gave me an error: "Second and third argument must either be variables or a variable and a nonnegative integer specifying the number of differentiations."

Don't know what to do.

[Jan]

With dE=energy(i+1)-energy(i), dE it is a vector. Then you need:

area = 0;
for i = 1:length(energy)-1
  area = area + photonflux(i) * dE(i);
  %                               ^^^
end

Please post the complete error message in all cases. "Second and third argument must either be variables or a variable and a nonnegative integer specifying the number of differentiations." looks strange, because the third argument of TRAPZ can be the dimension only and not the number of differentiations. This looks, lkike you have called aother function. The complete error message should clarify this directly.

[Tiago Fernandes]

if you calculate dE=energy(i+1)-energy(i), dE is going to be a scallar for every iteration.

Because i calculate dE before area.

The error was:

Error using sym/diff (line 36)
Second and third argument must either be variables or a variable and a nonnegative
integer specifying the number of differentiations.

Error in trapz (line 79)
    z = diff(x,1,1).' * (y(1:end-1,:) + y(2:end,:))/2;
 

Answer 1

[Jan]

Using trapz check input sizes and cares for matrices also. But if x and y are vectors, this can be done manually also. The trapezoid sum uses an easy formula:

A = sum(diff(x) .* (y(1:end-1) + y(2:end)) / 2)

Or:

y = y(:);
A = diff(x(:)).' * (y(1:end-1) + y(2:end)) / 2;

[Tiago Fernandes]

I will try to do that mannualy thanks.