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Topic: What's wrong with cumtrapz?
Replies: 7   Last Post: Jun 17, 2013 10:52 AM

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Yuji

Posts: 30
Registered: 6/27/11
Re: What's wrong with cumtrapz?
Posted: Jun 16, 2013 1:33 AM
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nice explanation!

Rick, there is:
if F'(x) = f(x), then
integral f(x) dx = F(x) + C C is any constant

so the integral result has some shift along y axis. The shift should be determined by boundary conditions.



"Timothy E. Vaughan" <tvaughan@_NO_SPAM_bwh.harvard.edu> wrote in message <9cu9jh$doh$1@plato.harvard.edu>...
>
> ""Leung, Randolph [COPE/HKG]"" <RckLeung@Copeland-Corp.com> wrote in message
> news:9B636583813BD311BE6400508B10481F6C5274@fs83.hk.copeland-sid.com...

> >
> > I have some experimental time traces to integrate. CUMTRAPZ seems
> > to be a simple and easy option for me. To test it, I tried to integrate a
> > simple SIN(X) time trace as follows,
> >
> > x = 0:pi/100:4*pi];
> > y = sin( 2*pi*x).
> >
> > inty = cumtrapz( x', y' );
> >
> > I would expect a COS(X) time trace after CUMTRAPZ. The integrated
> > time trace gave a cos pattern of variation, correct amplitude BUT was
> > wrong in phase and shifted upwards, i.e. it is greater than zero for all
> > x and gives 0, rather than 1, at x = 0. I am very confused with the
> > results.

>
> It seems you may be forgetting a bit of your calculus. You are numerically
> taking the INDEFINITE integral of your function. In that case, you must be
> prepared to add a constant to your solution. [I think it is really only
> shifted "upward", and not really wrong in phase.] You need to determine the
> appropriate constant from other conditions of your problem.
>
> Tim
>
>
>




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