Re: Is it possible to access internal variables? [CompoundExpression]

*To*: mathgroup at smc.vnet.net*Subject*: [mg34794] Re: Is it possible to access internal variables? [CompoundExpression]*From*: "Allan Hayes" <hay at haystack.demon.co.uk>*Date*: Fri, 7 Jun 2002 01:08:57 -0400 (EDT)*References*: <admtj1$ekh$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Dear Hartmut, The description of the evaluation of CompoundExpression in http://library.wolfram.com/mathgroup/archive/1999/Feb/msg00460.html was corrected in http://library.wolfram.com/mathgroup/archive/1999/Feb/msg00440.html (although the latter was sent a day later, for some reason it appears earlier in the MathGroup numbering). Here is a sketch of the evaluation ( e* denotes the value of e) CompoundExpression[e1, Evaluate[e2], e3] CompoundExpression[e1, e2*, e3] (*evaluate Evaluate[.].. in order*) CompoundExpression[e1*, e2*, e3](*restart; evaluate entries in order*) CompoundExpression[e1*, e2**, e3] CompoundExpression[e1*, e2**, e3*] e3* e3** (*evaluate e3* since it is not the same as CompoundExpression[e1*, e2**, e3*] *) SUPPORTING EVIDENCE ( I have added comments to the output) Clear[pr,a]; CompoundExpression[ Print[pr = Print], Evaluate[pr[Print[2]]], {a, a = 4} ] 2 (* from evaluating Evaluate[...] to pr[Null] *) Print (* from evaluating Print[pr = Print] *) Null (* from evaluating pr[Null] *) {4,4} (* from the evaluation of {a, 4} , after evaluating a=4*) SIMULATION with CE SetAttributes[CE, HoldAll] CE[x__]:= Last[{x}] CE[]:=Null Clear[pr,a]; CE[ Print[pr = Print], Evaluate[pr[Print[2]]], {a,a=4} ] 2 Print Null {4,4} -- Allan --------------------- Allan Hayes Mathematica Training and Consulting Leicester UK www.haystack.demon.co.uk hay at haystack.demon.co.uk Voice: +44 (0)116 271 4198 Fax: +44 (0)870 164 0565 "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com> wrote in message news:admtj1$ekh$1 at smc.vnet.net... > > Hello Bobby, > > Two things: (1) as Hob Hanlon has pointed out, I missed to assign to v at > definiton of h[x_], which of course explains everything. Aside from being > this my standard blunder mixing up Append with AppendTo in my mind from my > first day on with Mathematica, I did not look close enough, and finally: > there are no mysteries. Sorry for disturbing you. > > (2) What considers CompoundExpression: this is no bug for shure; instead we > simply have to recognize the precise semantics of (e1; e2; ...; en) > > The expressions e1, e2, up to en are executed in order, then the result of > en is assigned to CompoundExpression[e1, e2, ..., en] and then this is > evaluated again. Normaly, this has no visible effect since the execution > environment of en when evaluated within the CompoundExpression is the same > as that of the CompoundExpression when it returns; yet this is not enough. > Here, since FindMinimum fails it returns itself unevaluated (a standard > behaviour), this now becomes the value of CompoundExpression and such > FindMinimum will start anew. > > This all conforms to the execution sequence as specified for Mathematica. We > certainly should have internalized this precisely and permanently (as a > morning prayer). However, we are human beings, and build up our own rules in > our heads and take many shortcuts. It's there where we often become > irritated. We just have concede that > > In[1]:= expr1 > > In[2]:= expr2 > > is *not* the same as > > In[1]:= expr1; > expr2 > > As I mentioned I've seen a prior thread to this theme with a prominent > contribution of Allan Hayes, e.g. > http://library.wolfram.com/mathgroup/archive/1999/Feb/msg00460.html or see > also my reply to Allan at another thread > http://library.wolfram.com/mathgroup/archive/2000/Jul/msg00115.html . > > BTW esp. with Block, things are quite the same, and quite common here, since > the execution > environment within Block almost always differs form that one outside: we > have to anticipate the transformations to the _result_ of Block, as here to > the _result_ of CompoundExpression. > > -- > Hartmut > > > > -----Original Message----- > > From: DrBob [mailto:majort at cox-internet.com] To: mathgroup at smc.vnet.net > > Sent: Tuesday, June 04, 2002 5:59 PM > > Cc: 'David Park'; BobHanlon at aol.com > > Subject: [mg34794] RE: Is it possible to > > access internal variables? > > > > > > 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: [mg34794] 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 > > > > 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: [mg34794] 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 > > > > > > > > > >