Re: More weird integration issues...

*To*: mathgroup at smc.vnet.net*Subject*: [mg35773] Re: More weird integration issues...*From*: Binesh Bannerjee <binesh-dated-1028572681.02012b at hex21.com>*Date*: Tue, 30 Jul 2002 07:22:29 -0400 (EDT)*References*: <ai2pua$5l9$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Andrzej Kozlowski <andrzej at tuins.ac.jp> wrote: : There does sem to be a bug here, but it is not quite what you think. : It's the first answer that you get that is probably wrong. On the other : hand, in the second case it is very unlikely that Mathematica enters an : infinite loop, rather it is still trying to arrive at the answer and : there is no guarantee that it will reach one after, say a week or a : month. : As for first case, the reason why the answer is probably this. Evaluate : the formula: Thanks for your response! And, sorry about the TMDA hoops! I forgot to put in a dated address on the post! Hmmm... I'm not so sure... (I cut and pasted from your post, just so it will all be directly cut and pastable in Mathematica) F[a_,b_,c_,d_,e_,f_,X_] := (a + b X + c X^2 + d X^3 + e X^4 + f X^5) * (Exp[-(((X-m)/sd)^2)/2]/(Sqrt[2Pi]sd)) (* Your formula *) formula=Integrate[F[Subscript[p, 0], Subscript[p, 1], Subscript[p, 2], Subscript[p, 3], Subscript[p, 4], Subscript[p, 5], X]*((X - m)/sd)^5, {X, -Infinity, Infinity}] (* I assume you do {i,1,5} instead of {i,0,5} because the result of * the calculation above doesn't include p sub zero *) Evaluate[Table[Subscript[p, i], {i, 1, 5}]] = Table[Random[], {5}] sd = Random[]; m = Random[]; Andrzej = Integrate[F[Subscript[p, 0], Subscript[p, 1], Subscript[p, 2], Subscript[p, 3], Subscript[p, 4], Subscript[p, 5], X]*((X - m)/sd)^5, {X, -Infinity, Infinity}] Chop[Andrzej] formula This yields for me: p = {0.76938, 0.670623, 0.624459, 0.386326, 0.773623} Andrzej = 26.036 * (2.08162+(1.66533*10^-16)p0) Chop[Andrzej] = 54.1961 formula = 54.1961 If you just ExpandAll[Andrzej] , you get 54.1961-(4.3358*10^-15)p0 So, I think it's doing the right thing with the p array, it just goes off into some loop with the a,b,c,d,e,f... Is that reasoning sound, or am I missing something? Perhaps I'm missing a point, and they shouldn't be different _at all_... I dunno... Is that safely negligible as machine precision error? Binesh : You will almost certainly get different answers, while they clearly : ought to be the same. It seems that it is nto the fact that the names : you are suing are different that leads to different results in both of : your integrals but the fact that the names of the parameters in the : first case are not symbols. "Officially" there is no reason why they : should be, but in practice using non-symbols in formulas makes them more : complicated and is more likely to result in errors. : The really bad news as far as your problem is concerned is that it is : the 6 hour fruitless computation that appears to be the correct one ... : Andrzej Kozlowski : Toyama International University : JAPAN : http://platon.c.u-tokyo.ac.jp/andrzej/ : On Saturday, July 27, 2002, at 07:43 PM, Binesh Bannerjee wrote: :> Hi. I'm trying to compute the 5th moment of a tweak to the normal pdf. :> Here's what I have: :> :> F[a_, b_, c_, d_, e_, f_, X_] := (a + b X + c X^2 + d X^3 + e X^4 + f :> X^5)* :> Exp[-(((X - m)/sd)^2)/2]/(Sqrt[2Pi]sd) :> :> The strange thing, and I'd appreciate someone shedding some light on :> this, :> is that this: :> :> \!\(Integrate[ :> F[p\_0, p\_1, p\_2, p\_3, p\_4, p\_5, :> X]*\((\((X - m)\)/sd)\)^5, {X, \(-Infinity\), Infinity}, :> Assumptions -> {sd > 0}]\) :> :> (I cut and pasted that it looks like it works) :> :> Anyway, THAT gives me an answer really quickly... (within 5 minutes on :> my box) :> :> JUST changing it from p0..5 to a,b,c,d,e,f like so: :> :> Integrate[F[a, b, c, d, e, f, X]*((X - m)/sd)^5, {X, -Infinity, :> Infinity}, :> Assumptions -> {sd > 0}] :> :> Causes mathematica to go into an infinite loop (seemingly after 6 :> hours). :> :> This ... sucks. How am I to know if a certain equation is solvable, if :> only I choose the right variables?? :> :> Binesh Bannerjee :> :> -- :> "For in much wisdom is much grief, and he that increaseth knowledge :> increaseth sorrow." -- Ecclesiastes 1:18 :> :> PGP Key: http://www.hex21.com/~binesh/binesh-public.asc :> SSH2 Key: http://www.hex21.com/~binesh/binesh-ssh2.pub :> SSH1 Key: http://www.hex21.com/~binesh/binesh-ssh1.pub :> OpenSSH Key: http://www.hex21.com/~binesh/binesh-openssh.pub :> :> :> -- 'One of the cultural barriers that separates computer scientists from "regular" scientists and engineers is ... the practical scientist is trying to solve tomorrow's problem with yesterday's computer; the computer scientist, we think, often has it the other way around.' -- Numerical Recipes in C PGP Key: http://www.hex21.com/~binesh/binesh-public.asc SSH2 Key: http://www.hex21.com/~binesh/binesh-ssh2.pub SSH1 Key: http://www.hex21.com/~binesh/binesh-ssh1.pub OpenSSH Key: http://www.hex21.com/~binesh/binesh-openssh.pub

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