MaplePrimes - answers and comments on Question, inconsisten numerical answers between evalf and plot

Change Digits

Joe Riel — Sat, 15 Dec 2007 11:43:16 Z

Your function is too wide for the screen. Try evalf[20](ratio); (the 20 is the number of digits used in the numerical computation).

start over ...

Axel Vogt — Sat, 15 Dec 2007 15:11:02 Z

Your expression is about 20 pages long and you seem to use 10 Digits of precision. It sounds like brute force and it is very likely you are killed by rounding errors. Additionally it contains complex values, what should be plotted? Try to plot x + I*1e-10 to see ... Being not sure whether 'ratio' is a reserved word I call it the Ratio. Now fnormal(theRatio) returns Float(undefined)*Pi*f0^2. This indicates numerical division by 0 or a singularity with 'jumps'. BTW: your variable seems to be actually Pi*f0. If you want a reasonable answer you may want to upload a sheet or text file showing the steps and not only the final result, so may get hints how to proceed better. PS: you also should edit your post (if possible) and delete your expression, otherwise the replies may not be readable.

Precision

gkokovidis — Sat, 15 Dec 2007 17:06:34 Z

As mentioned above, this is a precision issue. The attached worksheet correlates with the answer from your plot. View 221_ratio.mw on MapleNet or Download 221_ratio.mw
Regards, Georgios Kokovidis Dräger Medical

some dirty hack

Axel Vogt — Sat, 15 Dec 2007 20:33:21 Z

naming your expression 'theRatio' the following might do:

  restart; interface(version);
  Digits:=30;
  read "D:\\_Work\\Maple_Work\\ratio.txt": # read from file
  length(theRatio): evalf[2](%/80/60);     # 19 pages
  indets(theRatio,atomic): indets(%);      # check: actual depends on f0 only
  fnormal(theRatio,14);                    # check: nonsense with low precision, needs at leat 16
  
  
  
  convert(theRatio, rational):
  eval(%, f0=g0/Pi):
  eval(%, g0=a^2):
  R:=%:
  ``;
  R1:=simplify(R,size): 
  #length(%): evalf[2](%/80/60);
  
  Digits:=16;
  evalf[16](R1): evalc(Re(%)):
  codegen[makeproc](%,a):
  p:=codegen[optimize] (%,tryhard):
  
  length(p(a)): evalf[2](%/80/60);
  
  
  #q:=proc(f0) p(sqrt(Pi*f0)); subs(pow=`^`,%); evalhf( % ) end proc;
  q:=proc(f0) subs( pow(1/(a^2),1/2) = 1/a,p(a)); subs(a=sqrt(Pi*f0),%); subs(pow=`^`,%); evalf( % ) end proc;
  q(5.0e9);
  
  
  #plots[semilogplot]('q'(f0),f0=5e9..1e12);
  plots[semilogplot]('q'(f0),f0=5e9..1e12,color=magenta,numpoints=1000,axis[1] =
  [tickmarks=[4,subticks=8]],axis[2] = [tickmarks=[4,subticks=5]],
  view=[1.0e9..1.0e12,0.40..1.00]);

Thanks very much for your help!

tintin — Sun, 16 Dec 2007 13:01:50 Z

OK thanks everyone for pointing out the reason for the inconsistent numerical answers. Sorry again for the really long expression on my post. I am not too experienced in posting on this format. I will perform calculations using evalf[20] as suggested. Cheers, -Dan

precision

DJKeenan — Sun, 16 Dec 2007 17:57:39 Z

You can see the effects of increasing Digits using something like this:

for d from 8 to 20 do evalf[d](eval(theRatio, f0=5e9)) end do;

84.533996 2.76902582 0.3832106715 0.45853662433 0.456853381170 0.4560144647218 0.45601446472291 0.456016978775341 0.4560168949732729 0.45601697877528942 0.456016982965391820 0.4560169819597674829 0.45601698196814768301 There is a related issue. It might be that the constants in your expression need to be specified to greater precision, in order to get an accurate final answer. As a partial test of this, I replaced each occurrence of 0.6666666666e-14 with ((2/3)*10^(-14)), and got the following: 96.518370 2.76902582 0.3832106715 0.47576578081 0.475765780540 0.4740104054132 0.47395785560670 0.473963986083011 0.4739638985041114 0.47396393353565157 0.473963946672481361 0.4739639466724813721 0.47396394663744982527 Several other constants in your expression also appear to be truncations of exact numbers. I do not believe that you can accurately evaluate the expression without increasing the precision of the constants. (Where did the constants come from?)