## 5018 Reputation

15 years, 305 days
Munich, Germany

## if i call your set of...

if i call your set of unknowns by unk, then there are 22, yes. but indets(eqns,atomic): indets(%): % minus unk; nops(%); shows {s1, s2, v0, s0, vQX, vQY, v1, v2, RT1_FR, RT2_FR, RL1_LS, RL2_LS, PaQv} so your input produces 13 new variables ... what is s1, s2 etc? May be a careful input may solve your problem?

## That would be fine ... but...

That would be fine ... but they would have done, if they think it time to release it. And it might not help you - why 50 digits (I think Bailey has special software for quadrature of high precision)? Plotting shows the problem is at the boundary. Some thoughts ... as you do not state all you know for your special case and I see - 2 variables (could there be more? - that may be a show stopper) - coeffs sum to 0 in (x,y)=(0,0), so re-scaling possible? - there is only 1 mixed term - staring at the powers: one can reduce to degree 2 Int(Int(sqrt(R)/xi^(99/100)/eta^(1410/1411),xi = 0 .. bX^100), eta = 0 .. bY^1411)/176375000 where bX, bY are the bounds and R:=1562500+7582500*eta+9199089*xi^2+7582500*xi+9199089*eta^2 -33563178*xi*eta Then the problems for the integrator are at 0. Note that order of integration numerical could make a difference, if the powers are of different size (as in your case, bounds^m --> 0 with m large) and one of the bounds is not very close to 1. Now i looked in Gradsteyn et al ... 2.260.1 has a recursive formula for Int( x^m * srqt(R), x). One might try to write the denominators as Taylor series (may be after xi -> 1 - mu etc) and try to write down a recursion, so the problem becomes an infinite series in applying the outer integration numerical (plus some stopping, I do not have a good feeling for convergence rates ...). But for higher dimension this approach will be quite hopeless and it reminds me a bit to calculate a (bi-variate) cumulative normal where correlations ~ +-1 cause problems, but can be settled in the 2 dim case (only) by recursive computations. But it's just an idea, not a solution.

## well ......

you just type the formulae in a sheet ... and for all software new to you: contact the manual for first steps ... sounds sarcastic, I know, but either i do not understand your question ... or you have not looked into the manual or the only help (just mark in with the mouse and hit F1 key

## what do you mean by that?...

could you say what you want to do exactly?

## There is the possibility to...

There is the possibility to tell Maple to use a default type for the variables. The other - quite lame - thing I sometimes do is to work with an editor or just Win Word (which often is easier than to look up commands, especially if one wants arrays in readable form or other formatings): copy your definitions to the editor and replace "t" by "float t" using the editor's ability. But the proper way is to look at some of the examples at the online help.

## this is not a function of P_m...

This is not a function of P_m, since that is your integration variable. If the others are constant that is a real number (or undefined) and I doubt that Maple plots it - what is your input for that?

## unacceptable...

Even if I accept licence checking as a good thing that is either an unacceptable behaviour or a bonelazy answer you got. Or both. Of course I have files which are created in future ... I do not use my PC for Maple alone.

It is not quite clear for me which constants you use and it may be you cut off to early (where the exp term is still contributing), but I would do it this way: Your integral writes as Int(erfc(b*sqrt(xi/(xi+1))) *exp(-a*xi)*a,xi=0..infinity) for b = B^2, a = 1/gamav. Here xi/(xi+1) approaches 1 from below for large xi and beyond xi = 1/epsilon-1 differs at most by epsilon from 1. Then split the integration at this point into Int(a*erfc(b*(xi/(xi+1))^(1/2))*exp(-a*xi),xi = 0 .. 1/epsilon-1) + Int(a*erfc(b)*exp(-a*xi),xi = 1/epsilon-1 .. infinity); The last is erfc(b)*exp(-a*(1/epsilon-1)) and the first should be done by working numerical. May be you refine that suggestion.

since nobody answers: you may add your hardware and operating system and may be graphical interface (and personally i just would reinstall instead of doing anything else ... and de-install first ... and if you do it try to avoid the blank in the directory name, overwrite it by Maple10 or similar within the installation dialog ... and if you have and old OS like WinME - do not use the standard interface)

sigh ...

## concrete example?...

would you mind to post that example? evalf(Int(f,t=0..1)) uses the NAG library i think ...

## for example...

```randomize():
B:=[stats[random,normald[0,1]](N+1)]:
W:=[stats[random,normald[0,1]](N+1)]:
Z:= zip((x,y) -> evalf( rho*x+sqrt(1-rho^2)*y ),B,W): # or evalhf?
```
Then Z and B will do, where rho is the desired correlation. In Maple 10 it is a bit different, but much (!) faster.

## Ooura's method...

Once i translated Ooura's double exponential integration into Maple (find it uploaded, but i have neither cleaned up that port nor tested it carefully). That method is quite robust. So you can use Maple's new ability to generate a DLL and use that as a function directly in Maple. This might give you some of the speed improvements you are looking for. The additional advantage is: you can test values against Maple if you have some doubts. For distributions usually a Gauss-Legendre method also works well (using fixed numbers of sub-divisions), 16 point suffice. What i can not see is your chi^2, i thought it contains an exp in the integrand? Just a last thought: when i try to fit some pdf against data (to get parameters) i pass to the logarithm (and refine later if neccessary). If you want to fit against a cdf then i can imagine troubles (i am not sure whether this is a stable approach, especially if you are not absolutely convinced that your cdf is the correct one). PS: as i do not recognize how to attach files use that link http://www.axelvogt.de/axalom/maple/Ooura_DoubleExp_Integration.mws

## the only thing i can imagine...

the only thing i can imagine is that Maple methods can be worked out ... having not traced through the procs it is clear that they involve external callings for NAG routines what exactly are you looking for?
 First 84 85 86 Page 86 of 86
﻿