Numerical Integration
in [Matlab]
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From: KAMAL ABAZA on 8 May 2010 13:18 Hello Guys, I'm Having a problem at integration a function on matlab the function is as follow : Integral = ∫[ϕ(ω) e^(-jωE) dω] " integration from -∞ to +∞ " Where: ϕ(ω)=∏[(1-j2ωλ(i))]^(-1) "multiplication" λ is vector of eigen values KNOWN (the whole vector is available) E is also known ω is a variable unknown and I want to integrate on . hope that the equations are clear enough how can integrate this function numerically ???? !!!! thanks in Advance
From: Roger Stafford on 8 May 2010 16:13 "KAMAL ABAZA" <abaza_kamal(a)yahoo.com> wrote in message <hs46cc$ndc$1(a)fred.mathworks.com>... > Hello Guys, > I'm Having a problem at integration a function on matlab the function is as follow : > Integral = ∫[ϕ(ω) e^(-jωE) dω] " integration from -∞ to +∞ " > Where: ϕ(ω)=∏[(1-j2ωλ(i))]^(-1) "multiplication" > λ is vector of eigen values KNOWN (the whole vector is available) > E is also known > ω is a variable unknown and I want to integrate on . > hope that the equations are clear enough > how can integrate this function numerically ???? !!!! > thanks in Advance - - - - - - - - Use 'quadgk', which accepts infinite limits of integration. You will need to write a function for your integrand which accepts vector arguments, and it will need to accept the known parameters E and vector lambda. I assume that some of the eigenvalues in lambda are complex-valued in appropriate ways. Otherwise the function would not be integrable. Roger Stafford
From: Bruno Luong on 8 May 2010 17:18 "KAMAL ABAZA" <abaza_kamal(a)yahoo.com> wrote in message <hs46cc$ndc$1(a)fred.mathworks.com>... > Hello Guys, > I'm Having a problem at integration a function on matlab the function is as follow : > Integral = ∫[ϕ(ω) e^(-jωE) dω] " integration from -∞ to +∞ " > Where: ϕ(ω)=∏[(1-j2ωλ(i))]^(-1) "multiplication" > λ is vector of eigen values KNOWN (the whole vector is available) > E is also known > ω is a variable unknown and I want to integrate on . > hope that the equations are clear enough > how can integrate this function numerically ???? !!!! It seems like you can use Residue Theorem to compute such thing almost by hand. Bruno
From: Roger Stafford on 8 May 2010 17:41 "Bruno Luong" <b.luong(a)fogale.findmycountry> wrote in message <hs4kef$c9p$1(a)fred.mathworks.com>... > It seems like you can use Residue Theorem to compute such thing almost by hand. > > Bruno I agree, Bruno! Roger Stafford
From: Patricia Rosales on 10 May 2010 03:35 Thank you for your help. Best wishes "John D'Errico" <woodchips(a)rochester.rr.com> wrote in message <hs12j9$7h6$1(a)fred.mathworks.com>... > "Patricia Rosales" <proslop(a)oc.mde.es> wrote in message <hrmnul$qv9$1(a)fred.mathworks.com>... > > Hello, > > > > I have an image that is a matrix of 508x640 values of a physical magnitude(radiance). > > In order to obtain the whole radiance of the image, i want to integrate all the values in the whole image. But this means to perform an integration where the integrand is a set of values, not a function. Could anyone to help me with this? > > > > Thank you! > > Let me try again. trapz is the tool to integrate an array > or vector of numbers. > > Perhaps you are confused in that trapz did not give you > a SINGLE number. > > Perhaps you do not understand that an integration is > applied to a SINGLE variable at once. Since an array > (an image) is a two dimensional thing, you will need > to do two integrations. > > How do you do two integrations, one on each variable? > > Call trapz twice! > > If this is not the answer to your problem, then you need > to seriously learn to explain your problems better and > more clearly. Learn to explain problems in mathematics > by using mathematics. > > John
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