overlooked

acer — Tue, 06 Jul 2010 18:54:40 Z

You are overlooking the effects of round-off error during the floating-point computation (ie. during the evaluations of diff(sCARA4,mu) at floating-point values). Remember that the Digits environment variable controls the working precision and is not a target accuracy tolerance.

> restart:

> sCARA4 := -ln(-(mu/sigma^2)^(mu^2/(mu-sigma^2))*(sigma^2/mu)^(mu^2/(mu-sigma^2))
>    +(sigma^2/mu)^(mu^2/(mu-sigma^2))*((exp(phi)*sigma^2+mu-sigma^2)
>    *exp(-phi)/sigma^2)^(mu^2/(mu-sigma^2))+1)/phi:

> dsCARA4:=diff(sCARA4,mu):

> eval(dsCARA4,[mu=29.38,phi=1.0,sigma=1.0]);
                          -2.499130625

> evalf[20](eval(dsCARA4,[mu=29.38,phi=1.0,sigma=1.0]));
                     0.99919104807402453122

Note also that, even though simplification (using `simplify`, with or without assumptions) seems to help below, there is no guarantee in general that it will generate a form of a symbolic expression with better conditioning during floating-point evaluation.

> eval(dsCARA4,[mu=29.38,phi=1.0,sigma=1.0]);
                          -2.499130625
> eval(simplify(dsCARA4),[mu=29.38,phi=1.0,sigma=1.0]);
                          1.204768329
> eval(simplify(dsCARA4),[mu=29.38,phi=1.0,sigma=1.0]) assuming positive;
                          0.9991907685

You can also look at ?evalr

You are overlooking analysis during the simplification of sCARA4. You might compare output from these,

simplify(sCARA4);

simplify(sCARA4) assuming positive;
acer

learned something new

afeddersen — Wed, 07 Jul 2010 14:00:01 Z

Thanks acer,

I learned something new. In fact I didn´t know, that the Digits environment variable controls the working precision and that the effect of round-off error could be that significant.

So may I also manipulate the working precision of the 'Explore' option by setting 'Digits' to another value (say 20) or is there another way of minimizing the round-off error effects when using 'Explore'?

MaplePrimes - answers and comments on Question, A matter of trust?

overlooked

learned something new