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