Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]

Groups > comp.soft-sys.math.mathematica > #2455 > unrolled thread

while loop - numerics

Back to article view | Back to comp.soft-sys.math.mathematica

Contents

  while loop - numerics Anna Kaladze <anna.kaladze@gmail.com> - 2011-05-18 11:17 +0000
    Re: while loop - numerics Peter Pein <petsie@dordos.net> - 2011-05-19 11:43 +0000

#2455 — while loop - numerics

Hi all,



I am new in loop writing in Mathematica, so your help on the following
seemingly simple problem would be appreciated.  I have the following
commands:

-------------------------------------------------

tol=1/100;



DM=9;



yguess=0.5;



x=yguess^2

0.25



yfeedback=x*yguess

0.125



Error=Abs[yfeedback-yguess]

0.375
-------------------------------------------
Without doing any equations solving/substitutions or any algebraic
manipulations, or utilizing Table commands, I need to have a while loop
command applied to the above code, such that for a given yguess value
entered (now it is set to 0.5 for the first iteration), Mathematica would
calculate yfeedback and the Error, every time updating yguess with the
following rule: yguess = the last calculated value of yguess*(1+last
calculated value of Error/DM), until Error in the last iteration is less or
equal tol. And then report what that yguess value is.

For yguess = 0.5, we obviously get after 1st iteration that yfeedback=0.125
and a large resulting Error value 0.375. So, the yguess needs to be updated
as 0.5*(1+0.375/DM), and that would become 0.520833. Now in the second
iteration yguess takes the value of 0.520833, and then the resulting Error
would become 0.379548, and then the updated yguess would become
0.520833*(1+0.379548/DM)= 0.542798 and so on until the stopping criteria is
achieved. (Somewhere when the program calculates yguess close to unity the
program should stop obviously). The question is how to write such a code.

Thanks in advance.

Anna

[toc] | [next] | [standalone]

#2478

Am 18.05.2011 13:17, schrieb Anna Kaladze:
> Hi all,
>
>
>
> I am new in loop writing in Mathematica, so your help on the following
> seemingly simple problem would be appreciated.  I have the following
> commands:
>
> -------------------------------------------------
>
> tol=1/100;
>
>
>
> DM=9;
>
>
>
> yguess=0.5;
>
>
>
> x=yguess^2
>
> 0.25
>
>
>
> yfeedback=x*yguess
>
> 0.125
>
>
>
> Error=Abs[yfeedback-yguess]
>
> 0.375
> -------------------------------------------
> Without doing any equations solving/substitutions or any algebraic
> manipulations, or utilizing Table commands, I need to have a while loop
> command applied to the above code, such that for a given yguess value
> entered (now it is set to 0.5 for the first iteration), Mathematica would
> calculate yfeedback and the Error, every time updating yguess with the
> following rule: yguess = the last calculated value of yguess*(1+last
> calculated value of Error/DM), until Error in the last iteration is less or
> equal tol. And then report what that yguess value is.
>
> For yguess = 0.5, we obviously get after 1st iteration that yfeedback=0.125
> and a large resulting Error value 0.375. So, the yguess needs to be updated
> as 0.5*(1+0.375/DM), and that would become 0.520833. Now in the second
> iteration yguess takes the value of 0.520833, and then the resulting Error
> would become 0.379548, and then the updated yguess would become
> 0.520833*(1+0.379548/DM)= 0.542798 and so on until the stopping criteria is
> achieved. (Somewhere when the program calculates yguess close to unity the
> program should stop obviously). The question is how to write such a code.
>
> Thanks in advance.
>
> Anna

Hi Anna,

this is a typical problem for "NestWhile[..]". The following function 
will return the pair {yguess, error} when the termination condition is 
satisfied. I built it with two emergency brakes; one restricts the 
number of iterations to 10000 and the other breaks when the error 
becomes greater than 10^10 (iteration diverges):

iterate[yguess_]:=
   Block[{tol = 1/100, DM = 9, tmp},
     NestWhile[{tmp = #[[1]](1 + #[[2]]/DM), Abs[tmp(tmp^2 - 1)]} &,
       {yguess, Abs[yguess(yguess^2 - 1)]},
      10^10 > #[[2]] > tol &,1,10000]
   ]

if you use "NestWhileList" in place of "NestWhile", you'll get a list of 
all calculated {guess, error} - pairs.

hth,
Peter

[toc] | [prev] | [standalone]

Back to top | Article view | comp.soft-sys.math.mathematica

csiph-web