Digits

acer — Mon, 25 Jul 2011 13:22:12 Z

Since the upper limit of your integral will evaluate to a float (for nice numeric delta) then `int` will call out to do numeric quadrature. But better to keep things straight and use `Int`, so as to ensure that `int` never wastes time trying to do a mixed symbolic-float integral in some "exact" way (which is often a Bad Idea, as well as time wasting when it fails).

Also, NextZero may try an bump up Digits, which can be unfortunate for evalf(Int(...)) if it makes Digits too high for fast double precision computation, or it this interferes with the convergence acceptance. So I use a proc `fdf` which forces Digits=15 each time its called.

I find that these times below can vary from run to run, even when trying to measure the timings while clearing remember tables. (I suspect there may be a remember table that I am not always clearing.)

f:=Int((50-50*delta)*(50+50*delta)*(0.3e-1+(.36*(1-exp(-.39*t)))
       /(12.00000000*exp(-.39*t)+1))
       *(1-(1-exp(-.39*t))/(12.00000000*exp(-.39*t)+1))/1.08^t,
       t = 0 .. -2.564102564*ln((1.+5.*delta)/(53.+5.*delta)))
     +(500.*(-1.-5.*delta))*(-(1.*(1.+4.*ga))/(-53.+48.*ga))^.197336002905
      /((-1.+1.*ga)*(1.+delta)*((1.+5.*delta)/(53.+5.*delta))^.197336002905):

#plots:-display(seq(plot(eval(f,ga=m),delta=0..2),m=0.1..0.8,0.1));

df:=diff(eval(f,ga=0.1),delta):

forget(evalf); forget(`evalf/int`):st:=time():
fsolve(df=0,delta=0..1);
                          0.1706030333
time()-st;
                             0.219

fdf:=proc(m) Digits:=15: eval(df,delta=m); end proc:

forget(evalf); forget(`evalf/int`):st:=time():
RootFinding:-NextZero(fdf,0.0);
                          0.1706030333
time()-st;
                             0.156

forget(evalf); forget(`evalf/int`):st:=time():
fsolve(fdf,0..1);
                          0.1706030333
time()-st;
                             0.187

A little more time (maybe 15% off those times above) could be saved by specifying some evalf/Int options (such as method=_d01ajc, and maybe digits=15 and epsilon=1e-13). But it's awkward to get these optiona into the Int() call, since they muck with the `diff` call if they are present in the original `f`.

acer

with DirectSearch

mois — Mon, 25 Jul 2011 18:30:59 Z

I try solve problem by DirectSearch package v.2. I cannot find any problem to maximize function f and to solve equation df=0.

with(DirectSearch);

seq(Search(eval(f,ga=m),maximize),m=0.1..0.8,0.1);

SolveEquations(df=0);

Great. That helps a lot acer - thanks !

longrob — Mon, 25 Jul 2011 13:44:02 Z

Great. That helps a lot acer - thanks !

MaplePrimes - answers and comments on Question, Root Finding again

Digits

with DirectSearch

Great. That helps a lot acer - thanks !