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MathGroup Archive 2002

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Re: RE: Re: Is it possible to access internal variables?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg34767] Re: [mg34749] RE: [mg34709] Re: [mg34705] Is it possible to access internal variables?
  • From: BobHanlon at aol.com
  • Date: Wed, 5 Jun 2002 03:38:29 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

My response failed to extract the final (failed) value with the constraints.  
My bad.

However, the definition of g is not behaving differently from that for h due 
to anything other than different definitions.  The definition of h does not 
assign v a new value.  Copied from below:

h[x_] := Module[{t = f[x]}, Append[v, {x, t}]; t];

With the assignment included it will behave similarly, i.e., still won't do 
what was requested.

Bob

In a message dated 6/4/02 11:59:59 AM, majort at cox-internet.com writes:

>If compound expressions are not evaluated in order, how can Modules or
>Blocks work?  Aren't they compound expressions?  What makes g and h
>different?
>
>These are serious bugs.
>
>I feel like we're walking on quicksand, now.
>
>Bobby
>
>-----Original Message-----
>From: Wolf, Hartmut [mailto:Hartmut.Wolf at t-systems.com] 
To: mathgroup at smc.vnet.net
>Sent: Tuesday, June 04, 2002 3:45 AM
>Subject: [mg34767] [mg34749] RE: [mg34709] Re: [mg34705] Is it possible to access
>internal variables?
>
>
>Hello Bob,
>
>there is something mysterious with your proposal that disturbs me
>somewhat.
>See my records:
>
>In[1]:= f[x_] := (x - 3)(x - 4)
> 
>In[2]:= g[x_] := Module[{t = f[x]}, v = Append[v, {x, t}]; t];
>In[3]:= v = {}; FindMinimum[g[x], {x, 2, 1, 3}]
>>From In[3]:=
>FindMinimum::"regex": "Reached the point \!\({3.5000000000000018`}\)
>which
>is \
>outside the region \!\({\({1.`, 3.`}\)}\)."
>>From In[3]:=
>FindMinimum::"regex": "Reached the point \!\({3.5000000000000018`}\)
>which
>is \
>outside the region \!\({\({1.`, 3.`}\)}\)."
>Out[3]=
>FindMinimum[g[x], {x, 2, 1, 3}]
>
>In[4]:= v
>Out[4]=
>{{2., 2.}, {2., 2.}, {2.03136, 1.9069}, {2.05074, 1.85035}, {2.18642, 
>    1.4755}, {3., 0.}, {2., 2.}, {2., 2.}, {2.03136, 1.9069}, {2.05074,
>
>    1.85035}, {2.18642, 1.4755}, {3., 0.}}
>
>In[5]:= g[x]
>Out[5]= (-4 + x) (-3 + x)
>
>In[6]:= ?g
>Global`g
>g[x_] := Module[{t = f[x]}, v = Append[v, {x, t}]; t]
>
>Apart from the fact that FindMinimum is restarted and that the first
>value
>appears twice, this seems to be what you intended. It doesn't help Arny
>though, as the minimum value -- what he supposed to be that x occuring
>in
>the error message -- is not included in that list v.
>
>But there seems to be something special with g, if I try with h it
>doesn't
>work:
> 
>In[7]:= h[x_] := Module[{t = f[x]}, Append[v, {x, t}]; t];
>In[8]:= v = {}; FindMinimum[h[x], {x, 2, 1, 3}]
>>From In[8]:=
>FindMinimum::"regex": "Reached the point \!\({3.5000000000000018`}\)
>which
>is \
>outside the region \!\({\({1.`, 3.`}\)}\)."
>>From In[8]:=
>FindMinimum::"regex": "Reached the point \!\({3.5000000000000018`}\)
>which
>is \
>outside the region \!\({\({1.`, 3.`}\)}\)."
>Out[8]=
>FindMinimum[h[x], {x, 2, 1, 3}]
>
>In[9]:= v     (* v is empty *)
>Out[9]= {}       
>
>In[10]:= h[x]
>Out[10]= (-4 + x) (-3 + x)
>
>In[11]:= ?h
>Global`h
>h[x_] := Module[{t = f[x]}, Append[v, {x, t}]; t]
>
>
>Now observe:
>
>In[12]:= FindMinimum[Print[x]; f[x], {x, 2, 1, 3}]
>>From In[12]:= x
>>From In[12]:= 2.
>>From In[12]:= 2.03136
>>From In[12]:= 2.05074
>>From In[12]:= 2.18642
>>From In[12]:= 3.
>>From In[12]:= FindMinimum::"regex": "Reached the point
>\!\({3.5000000000000018`}\) which is \
>outside the region \!\({\({1.`, 3.`}\)}\)."
>Out[12]= FindMinimum[Print[x]; f[x], {x, 2, 1, 3}]
>
>The Argument of FindMinimum is evaluated first with symbolic x (to get
>at
>the derivative I suppose), later, at the second call, it and such also
>t
>=
>(-4 + x) (-3 + x) get a numeric value, and therefore the values are
>introduced into v when appending {x,t}, so the start value gets doubled.
>
>
>The restart of the minimization seems to be triggered by the compound
>expression v = {}; FindMinimum[...] in the main loop (not within Find
>Minimum)
> 
>In[19]:= h5[x_] := Module[{t = f[x]}, Print[x]; t];
>
>In[20]:= v = {}; FindMinimum[h5[x], {x, 2, 1, 3}]
>>From In[20]:= x
>>From In[20]:= 2.
>>From In[20]:= 2.03136
>>From In[20]:= 2.05074
>>From In[20]:= 2.18642
>>From In[20]:= 3.
>>From In[20]:= 
>FindMinimum::"regex": "Reached the point \!\({3.5000000000000018`}\)
>which
>is \
>outside the region \!\({\({1.`, 3.`}\)}\)."
>>From In[20]:= x
>>From In[20]:= 2.
>>From In[20]:= 2.03136
>>From In[20]:= 2.05074
>>From In[20]:= 2.18642
>>From In[20]:= 3.
>>From In[20]:=
>FindMinimum::"regex": "Reached the point \!\({3.5000000000000018`}\)
>which
>is \
>outside the region \!\({\({1.`, 3.`}\)}\)."
>Out[20]= FindMinimum[h5[x], {x, 2, 1, 3}]
>
>Any expression e.g. (3; FindMinimum[...]) does that too; conversely if
>you
>initialize v in an extra line, there will be no restart. This may have
>something to do with peculiarities of compound expression, sometimes
>starting a re-evaluation. (This had been reported by Allan Hayes some
>years
>ago.) See:
>
>In[65]:= x = 5;
>
>In[66]:= x =.; Print[x]; {x, x = 3, x}
>>From In[66]:= x
>Out[66]= {3, 3, 3}
>
>In[67]:= x =.
>In[68]:= {x, x = 3, x}
>Out[68]= {x, 3, 3}
>
>Anyways, as shown above, Arny's desire to get at 'internal values' of
>FindMinimum seems to be hopeless. My advice would be to check for the
>error
>message and then possibly increase the search range (by a certain
>tolerance)
>and restart (only a finite number of times).
>
>--
>Hartmut
>
>
>> -----Original Message-----
>> From: BobHanlon at aol.com [mailto:BobHanlon at aol.com]
To: mathgroup at smc.vnet.net
>> Sent: Sunday, June 02, 2002 7:15 AM
>> Subject: [mg34767] [mg34749] [mg34709] Re: [mg34705] Is it possible to access
>internal
>> variables?
>> 
>> 
>> 
>> In a message dated 6/1/02 6:18:58 AM, 
>> someone at somewhere.sometime writes:
>> 
>> >I am minimizing a function which only has real values 
>> >between 1 and -1, 
>> most
>> >of the time... occasionally its range is different and 
>> unknown, (but anyway
>> >not far from 1 and -1).  I could write a routine using Check 
>> to catch errors
>> >and then expand the range over which FindMinimum is allowed 
>> to search,
>> >but
>> >since FindMinimum seems to be getting the appropriate values 
>> anyway - it
>> >tells me the values in its error message -  I was wondering 
>> if there weren't
>> >some way to get at those values and use them without 
>> bothering to write
>> >said routine.  I was thinking of analysing 'MessageList' or 
>> '$MessageList',
>> >but was thinking there might be some easier way.
>> >
>> >Aren't variables within packages accessible via their long 
>> names, e.g.
>> >`package`private`variablename or something like that?  Does 
>> anyone have
>> >any suggestions?
>> >
>> 
>> f[x_] := (x-3)(x-4);
>> 
>> g[x_] := Module[{t = f[x]}, v=Append[v, {x,t}]; t];
>> 
>> g is the same function as f except that calls to g are recorded in v
>> 
>> v={}; FindMinimum[g[x], {x, 2}]
>> 
>> {-0.25, {x -> 3.5}}
>> 
>> FindMinimum called g at the following values of x:
>> 
>> v[[All,1]]
>> 
>> {2., 2., 2.0313609375, 2.0507430627940644,
>>  
>>   2.1864179398525154, 3.136142079261673, 3.500000000000001,
>>  
>>   3.838316500294484, 3.5, 3.3180710396308366,
>>  
>>   3.4999904004703097, 3.5, 3.499999994722301}
>> 
>> 
>> Bob Hanlon
>> Chantilly, VA  USA


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