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Re: Plot problem with function

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Joe Riel wrote:
> "I.N. Galidakis" <morpheus@olympus.mons> writes:
>
>> I am having some problems with Maple 9 when plotting a certain
>> function. The function is:
>>
>>> HW:=proc()
>>> local y,n,c,s,p,sol,i,aprx,dy,dist,r,oldr,newr,fun,dfun,eps;
>>> if nargs<2 then ERROR("At least two arguments required.") fi;
>>> n:= args[-1];y:=args[-2];c:= [args[1..-3]];
>>> if y=0 then 0 else
>>>  dist:=infinity;
>>>  eps:=1e-32;
>>>  fun:= 1;
>>>  for i from 1 to nargs-2 do fun:= exp(c[i]*fun) od;
>>>  fun:= z*fun-y;
>>>  dfun:=diff(fun,z);
>>>  s:=series(fun,z,n);
>>>  p:=convert(s,polynom);
>>>  sol:={fsolve(p=0,z,complex)}; #complex?
>>>  for i from 1 to nops(sol) do
>>>   aprx:=evalf(subs(z=op(i,sol),fun));
>>>   dy:=evalf(abs(aprx));
>>>   if dy<=dist then r:=op(i,sol);dist:=dy;fi;
>>>  od;
>>> #start Newton with approximate zero found.
>>>  oldr:=r;
>>>  newr:=r-evalf(subs(z=r,fun)/subs(z=r,dfun));
>>>  for i from 1 to 1000 while (abs((oldr-newr)/oldr)>eps) do
>>>   oldr:=newr;
>>>   newr:=newr-evalf(subs(z=newr,fun)/subs(z=newr,dfun));
>>>  od;
>>> newr;
>>> fi;
>>> end:
>>
>> When I try to plot it (in this case the arguments make it equivalent
>> to arcsin) I get:
>>
>>> with(plots):
>>> plot(HW(log(sin(z)/z),y,10),y=-1..1);
>> Error, (in fsolve) y is in the equation, and is not solved for
>>
>> while if I do a:
>>
>>> N:=50;x1:=-1;x2:=1;
>>> x:=n->x1+abs(x2-x1)/N*n;
>>> L:=[seq([x(n),HW(log(sin(z)/z),x(n),10)],n=0..N)]:
>>> plot(L,scaling=constrained);
>>
>> It works (shows the graph of arcsin).
>>
>> Individual values seem to be calculated correctly. For example:
>>
>>> HW(log(sin(z)/z),0.245,10);
>> .247519692533815916885429116210
>>
>> Does anyone know why the plot command doesn't work with this
>> function?
>
> The cause is premature evaluation.  The plot procedures (as most Maple
> procedures) first evaluates its arguments.   But
>
> HW(log(sin(z)/z),y,10);
>
> raises the error because y is not numeric.  An easy solution is
> to delay the evaluation of HW.  You can do that via
>
>  plot('HW'(log(sin(z)/z),y,10),y=-1..1);

Thanks. I thought of premature evaluation, but I didn't know what delimiters to 
put around HW. On Maple V rel 5, it was `HW`(..) so I tried that and it didn't 
work.

Now it seems to be 'HW'(...).
-- 
I. 

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Thread

Plot problem with function "I.N. Galidakis" <morpheus@olympus.mons> - 2011-07-28 22:09 +0300
  Re: Plot problem with function Joe Riel <joer@san.rr.com> - 2011-07-28 12:18 -0700
    Re: Plot problem with function "I.N. Galidakis" <morpheus@olympus.mons> - 2011-07-29 00:11 +0300
      Re: Plot problem with function Joe Riel <joer@san.rr.com> - 2011-07-28 14:31 -0700

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