RE: Is it possible to access internal variables? [CompoundExpression]
- To: mathgroup at smc.vnet.net
- Subject: [mg34797] RE: Is it possible to access internal variables? [CompoundExpression]
- From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
- Date: Fri, 7 Jun 2002 01:09:01 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Dear Allan,
you might be interested in this device to check for the evaluation sequence:
In[1]:= v[n_] := Nest["*" <> # &, "", n]
In[2]:= e1 /; (Print["e1", v[++c1]]; False) = Null
In[3]:= e2 /; (Print["e2", v[++c2]]; False) = Null
In[4]:= e3 /; (Print["e3", v[++c3]]; False) = Null
normal execution of CompoundExpression:
In[5]:= c1 = c2 = c3 = 0;
In[6]:= e1; e2; e3
>From In[6]:= e1*
>From In[6]:= e2*
>From In[6]:= e3*
>From In[6]:= e3**
Out[6]= e3
pushing e3:
In[7]:= c1 = c2 = c3 = 0;
In[8]:= e1; e2; Evaluate[e3]
>From In[8]:= e3*
>From In[8]:= e1*
>From In[8]:= e2*
>From In[8]:= e3**
>From In[8]:= e3***
Out[8]= e3
conversely:
In[9]:= c1 = c2 = c3 = 0;
In[10]:= e1; e2; {e3}
>From In[10]:= e1*
>From In[10]:= e2*
>From In[10]:= e3*
Out[10]= {e3}
... "lists are inert"
equally:
In[11]:= c1 = c2 = c3 = 0;
In[12]:= e1; {e2, e3}
>From In[12]:= e1*
>From In[12]:= e2*
>From In[12]:= e3*
Out[12]= {e2, e3}
also
In[13]:= c1 = c2 = c3 = 0;
In[14]:= (e1; Evaluate[{e2, e3}])
>From In[14]:= e2*
>From In[14]:= e3*
>From In[14]:= e1*
Out[14]= {e2, e3}
sandwiching
In[15]:= c1 = c2 = c3 = 0;
In[16]:= (e1; Evaluate[{Hold[e2], e3}]) // ReleaseHold
>From In[16]:= e3*
>From In[16]:= e1*
>From In[16]:= e2*
>From In[16]:= e3**
Out[16]= {e2, e3}
In[17]:= c1 = c2 = c3 = 0;
In[18]:= (e1; Evaluate[e2; e3])
>From In[18]:= e2*
>From In[18]:= e3*
>From In[18]:= e3**
>From In[18]:= e1*
>From In[18]:= e3***
>From In[18]:= e3****
Out[18]= e3
In[19]:= c1 = c2 = c3 = 0;
In[20]:= (e1; Evaluate[Hold[e2]; e3]) // ReleaseHold
>From In[20]:= e3*
>From In[20]:= e3**
>From In[20]:= e1*
>From In[20]:= e3***
>From In[20]:= e3****
>From In[20]:= e3*****
Out[20]= e3
I'd call this a 5 star evaluation
--
Hartmut
> -----Original Message-----
> From: Allan Hayes [mailto:hay at haystack.demon.co.uk]
To: mathgroup at smc.vnet.net
> Sent: Thursday, June 06, 2002 1:34 PM
> Subject: [mg34797] Re: Is it possible to access internal variables?
> [CompoundExpression]
>
>
> 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: [mg34797] 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: [mg34797] 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: [mg34797] 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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<P><FONT SIZE=2>Dear Allan,</FONT>
</P>
<P><FONT SIZE=2>you might be interested in this device to check for the evaluation sequence:</FONT>
<BR><FONT SIZE=2> </FONT>
<BR><FONT SIZE=2>In[1]:= v[n_] := Nest["*" <> # &, "", n]</FONT>
</P>
<P><FONT SIZE=2>In[2]:= e1 /; (Print["e1", v[++c1]]; False) = Null</FONT>
<BR><FONT SIZE=2>In[3]:= e2 /; (Print["e2", v[++c2]]; False) = Null</FONT>
<BR><FONT SIZE=2>In[4]:= e3 /; (Print["e3", v[++c3]]; False) = Null</FONT>
</P>
<P><FONT SIZE=2> normal execution of CompoundExpression:</FONT>
</P>
<P><FONT SIZE=2>In[5]:= c1 = c2 = c3 = 0;</FONT>
<BR><FONT SIZE=2>In[6]:= e1; e2; e3</FONT>
<BR><FONT SIZE=2>From In[6]:= e1*</FONT>
<BR><FONT SIZE=2>From In[6]:= e2*</FONT>
<BR><FONT SIZE=2>From In[6]:= e3*</FONT>
<BR><FONT SIZE=2>From In[6]:= e3**</FONT>
<BR><FONT SIZE=2>Out[6]= e3</FONT>
</P>
<P><FONT SIZE=2> pushing e3:</FONT>
</P>
<P><FONT SIZE=2>In[7]:= c1 = c2 = c3 = 0;</FONT>
<BR><FONT SIZE=2>In[8]:= e1; e2; Evaluate[e3]</FONT>
<BR><FONT SIZE=2>From In[8]:= e3*</FONT>
<BR><FONT SIZE=2>From In[8]:= e1*</FONT>
<BR><FONT SIZE=2>From In[8]:= e2*</FONT>
<BR><FONT SIZE=2>From In[8]:= e3**</FONT>
<BR><FONT SIZE=2>From In[8]:= e3***</FONT>
<BR><FONT SIZE=2>Out[8]= e3</FONT>
</P>
<P><FONT SIZE=2> conversely:</FONT>
</P>
<P><FONT SIZE=2>In[9]:= c1 = c2 = c3 = 0;</FONT>
<BR><FONT SIZE=2>In[10]:= e1; e2; {e3}</FONT>
<BR><FONT SIZE=2>From In[10]:= e1*</FONT>
<BR><FONT SIZE=2>From In[10]:= e2*</FONT>
<BR><FONT SIZE=2>From In[10]:= e3*</FONT>
<BR><FONT SIZE=2>Out[10]= {e3}</FONT>
</P>
<P><FONT SIZE=2>... "lists are inert"</FONT>
</P>
<P><FONT SIZE=2> equally:</FONT>
</P>
<P><FONT SIZE=2>In[11]:= c1 = c2 = c3 = 0;</FONT>
<BR><FONT SIZE=2>In[12]:= e1; {e2, e3}</FONT>
<BR><FONT SIZE=2>From In[12]:= e1*</FONT>
<BR><FONT SIZE=2>From In[12]:= e2*</FONT>
<BR><FONT SIZE=2>From In[12]:= e3*</FONT>
<BR><FONT SIZE=2>Out[12]= {e2, e3}</FONT>
</P>
<P><FONT SIZE=2> also</FONT>
</P>
<P><FONT SIZE=2>In[13]:= c1 = c2 = c3 = 0;</FONT>
<BR><FONT SIZE=2>In[14]:= (e1; Evaluate[{e2, e3}])</FONT>
<BR><FONT SIZE=2>From In[14]:= e2*</FONT>
<BR><FONT SIZE=2>From In[14]:= e3*</FONT>
<BR><FONT SIZE=2>From In[14]:= e1*</FONT>
<BR><FONT SIZE=2>Out[14]= {e2, e3}</FONT>
</P>
<P><FONT SIZE=2> sandwiching</FONT>
<BR><FONT SIZE=2> </FONT>
<BR><FONT SIZE=2>In[15]:= c1 = c2 = c3 = 0;</FONT>
<BR><FONT SIZE=2>In[16]:= (e1; Evaluate[{Hold[e2], e3}]) // ReleaseHold</FONT>
<BR><FONT SIZE=2>From In[16]:= e3*</FONT>
<BR><FONT SIZE=2>From In[16]:= e1*</FONT>
<BR><FONT SIZE=2>From In[16]:= e2*</FONT>
<BR><FONT SIZE=2>From In[16]:= e3**</FONT>
<BR><FONT SIZE=2>Out[16]= {e2, e3}</FONT>
<BR><FONT SIZE=2> </FONT>
<BR><FONT SIZE=2>In[17]:= c1 = c2 = c3 = 0;</FONT>
<BR><FONT SIZE=2>In[18]:= (e1; Evaluate[e2; e3])</FONT>
<BR><FONT SIZE=2>From In[18]:= e2*</FONT>
<BR><FONT SIZE=2>From In[18]:= e3*</FONT>
<BR><FONT SIZE=2>From In[18]:= e3**</FONT>
<BR><FONT SIZE=2>From In[18]:= e1*</FONT>
<BR><FONT SIZE=2>From In[18]:= e3***</FONT>
<BR><FONT SIZE=2>From In[18]:= e3****</FONT>
<BR><FONT SIZE=2>Out[18]= e3</FONT>
<BR><FONT SIZE=2> </FONT>
<BR><FONT SIZE=2>In[19]:= c1 = c2 = c3 = 0;</FONT>
<BR><FONT SIZE=2>In[20]:= (e1; Evaluate[Hold[e2]; e3]) // ReleaseHold</FONT>
<BR><FONT SIZE=2>From In[20]:= e3*</FONT>
<BR><FONT SIZE=2>From In[20]:= e3**</FONT>
<BR><FONT SIZE=2>From In[20]:= e1*</FONT>
<BR><FONT SIZE=2>From In[20]:= e3***</FONT>
<BR><FONT SIZE=2>From In[20]:= e3****</FONT>
<BR><FONT SIZE=2>From In[20]:= e3*****</FONT>
<BR><FONT SIZE=2>Out[20]= e3</FONT>
</P>
<P><FONT SIZE=2>I'd call this a 5 star evaluation</FONT>
</P>
<P><FONT SIZE=2>--</FONT>
<BR><FONT SIZE=2>Hartmut</FONT>
</P>
<BR>
<P><FONT SIZE=2>> -----Original Message-----</FONT>
<BR><FONT SIZE=2>> From: Allan Hayes [<A HREF="mailto:hay at haystack.demon.co.uk">mailto:hay at haystack.demon.co.uk</A>]</FONT>
To: mathgroup at smc.vnet.net
<BR><FONT SIZE=2>> Sent: Thursday, June 06, 2002 1:34 PM</FONT>
<BR><FONT SIZE=2>> To: Wolf, Hartmut; majort at cox-internet.com; Bob Hanlon; David Park</FONT>
<BR><FONT SIZE=2>> Subject: [mg34797] Re: Is it possible to access internal variables?</FONT>
<BR><FONT SIZE=2>> [CompoundExpression]</FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> Dear Hartmut,</FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> The description of the evaluation of CompoundExpression in</FONT>
<BR><FONT SIZE=2>> <A HREF="http://library.wolfram.com/mathgroup/archive/1999/Feb/msg00460.html"; TARGET="_blank">http://library.wolfram.com/mathgroup/archive/1999/Feb/msg00460.html</A></FONT>
<BR><FONT SIZE=2>> was corrected in</FONT>
<BR><FONT SIZE=2>> <A HREF="http://library.wolfram.com/mathgroup/archive/1999/Feb/msg00440.html"; TARGET="_blank">http://library.wolfram.com/mathgroup/archive/1999/Feb/msg00440.html</A></FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> (although the latter was sent a day later, for some reason it appears</FONT>
<BR><FONT SIZE=2>> earlier in the MathGroup numbering).</FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> Here is a sketch of the evaluation ( e* denotes the value of e)</FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> CompoundExpression[e1, Evaluate[e2], e3]</FONT>
<BR><FONT SIZE=2>> CompoundExpression[e1, e2*, e3] (*evaluate Evaluate[.].. in order*)</FONT>
<BR><FONT SIZE=2>> CompoundExpression[e1*, e2*, e3](*restart; evaluate entries </FONT>
<BR><FONT SIZE=2>> in order*)</FONT>
<BR><FONT SIZE=2>> CompoundExpression[e1*, e2**, e3]</FONT>
<BR><FONT SIZE=2>> CompoundExpression[e1*, e2**, e3*]</FONT>
<BR><FONT SIZE=2>> e3*</FONT>
<BR><FONT SIZE=2>> e3** (*evaluate e3* since it is not the same as</FONT>
<BR><FONT SIZE=2>> CompoundExpression[e1*, e2**, e3*]</FONT>
<BR><FONT SIZE=2>> *)</FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> SUPPORTING EVIDENCE ( I have added comments to the output)</FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> Clear[pr,a];</FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> CompoundExpression[</FONT>
<BR><FONT SIZE=2>> Print[pr = Print], Evaluate[pr[Print[2]]], {a, a = 4}</FONT>
<BR><FONT SIZE=2>> ]</FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> 2 (* from evaluating Evaluate[...] to pr[Null] *)</FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> Print (* from evaluating Print[pr = Print] *)</FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> Null (* from evaluating pr[Null] *)</FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> {4,4} (* from the evaluation of {a, 4} , after </FONT>
<BR><FONT SIZE=2>> evaluating a=4*)</FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> SIMULATION with CE</FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> SetAttributes[CE, HoldAll]</FONT>
<BR><FONT SIZE=2>> CE[x__]:= Last[{x}]</FONT>
<BR><FONT SIZE=2>> CE[]:=Null</FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> Clear[pr,a];</FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> CE[</FONT>
<BR><FONT SIZE=2>> Print[pr = Print], Evaluate[pr[Print[2]]], {a,a=4}</FONT>
<BR><FONT SIZE=2>> ]</FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> 2</FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> Print</FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> Null</FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> {4,4}</FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> --</FONT>
<BR><FONT SIZE=2>> Allan</FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> ---------------------</FONT>
<BR><FONT SIZE=2>> Allan Hayes</FONT>
<BR><FONT SIZE=2>> Mathematica Training and Consulting</FONT>
<BR><FONT SIZE=2>> Leicester UK</FONT>
<BR><FONT SIZE=2>> www.haystack.demon.co.uk</FONT>
<BR><FONT SIZE=2>> hay at haystack.demon.co.uk</FONT>
<BR><FONT SIZE=2>> Voice: +44 (0)116 271 4198</FONT>
<BR><FONT SIZE=2>> Fax: +44 (0)870 164 0565</FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com> wrote in message</FONT>
<BR><FONT SIZE=2>> <A HREF="news:admtj1$ekh$1 at smc.vnet.net" TARGET="_blank">news:admtj1$ekh$1 at smc.vnet.net</A>...</FONT>
<BR><FONT SIZE=2>> ></FONT>
<BR><FONT SIZE=2>> > Hello Bobby,</FONT>
<BR><FONT SIZE=2>> ></FONT>
<BR><FONT SIZE=2>> > Two things: (1) as Hob Hanlon has pointed out, I missed to </FONT>
<BR><FONT SIZE=2>> assign to v at</FONT>
<BR><FONT SIZE=2>> > definiton of h[x_], which of course explains everything. </FONT>
<BR><FONT SIZE=2>> Aside from being</FONT>
<BR><FONT SIZE=2>> > this my standard blunder mixing up Append with AppendTo in </FONT>
<BR><FONT SIZE=2>> my mind from my</FONT>
<BR><FONT SIZE=2>> > first day on with Mathematica, I did not look close enough, </FONT>
<BR><FONT SIZE=2>> and finally:</FONT>
<BR><FONT SIZE=2>> > there are no mysteries. Sorry for disturbing you.</FONT>
<BR><FONT SIZE=2>> ></FONT>
<BR><FONT SIZE=2>> > (2) What considers CompoundExpression: this is no bug for </FONT>
<BR><FONT SIZE=2>> shure; instead</FONT>
<BR><FONT SIZE=2>> we</FONT>
<BR><FONT SIZE=2>> > simply have to recognize the precise semantics of (e1; e2; ...; en)</FONT>
<BR><FONT SIZE=2>> ></FONT>
<BR><FONT SIZE=2>> > The expressions e1, e2, up to en are executed in order, </FONT>
<BR><FONT SIZE=2>> then the result of</FONT>
<BR><FONT SIZE=2>> > en is assigned to CompoundExpression[e1, e2, ..., en] and </FONT>
<BR><FONT SIZE=2>> then this is</FONT>
<BR><FONT SIZE=2>> > evaluated again. Normaly, this has no visible effect since </FONT>
<BR><FONT SIZE=2>> the execution</FONT>
<BR><FONT SIZE=2>> > environment of en when evaluated within the </FONT>
<BR><FONT SIZE=2>> CompoundExpression is the same</FONT>
<BR><FONT SIZE=2>> > as that of the CompoundExpression when it returns; yet this </FONT>
<BR><FONT SIZE=2>> is not enough.</FONT>
<BR><FONT SIZE=2>> > Here, since FindMinimum fails it returns itself unevaluated </FONT>
<BR><FONT SIZE=2>> (a standard</FONT>
<BR><FONT SIZE=2>> > behaviour), this now becomes the value of </FONT>
<BR><FONT SIZE=2>> CompoundExpression and such</FONT>
<BR><FONT SIZE=2>> > FindMinimum will start anew.</FONT>
<BR><FONT SIZE=2>> ></FONT>
<BR><FONT SIZE=2>> > This all conforms to the execution sequence as specified </FONT>
<BR><FONT SIZE=2>> for Mathematica.</FONT>
<BR><FONT SIZE=2>> We</FONT>
<BR><FONT SIZE=2>> > certainly should have internalized this precisely and </FONT>
<BR><FONT SIZE=2>> permanently (as a</FONT>
<BR><FONT SIZE=2>> > morning prayer). However, we are human beings, and build up </FONT>
<BR><FONT SIZE=2>> our own rules</FONT>
<BR><FONT SIZE=2>> in</FONT>
<BR><FONT SIZE=2>> > our heads and take many shortcuts. It's there where we often become</FONT>
<BR><FONT SIZE=2>> > irritated. We just have concede that</FONT>
<BR><FONT SIZE=2>> ></FONT>
<BR><FONT SIZE=2>> > In[1]:= expr1</FONT>
<BR><FONT SIZE=2>> ></FONT>
<BR><FONT SIZE=2>> > In[2]:= expr2</FONT>
<BR><FONT SIZE=2>> ></FONT>
<BR><FONT SIZE=2>> > is *not* the same as</FONT>
<BR><FONT SIZE=2>> ></FONT>
<BR><FONT SIZE=2>> > In[1]:= expr1;</FONT>
<BR><FONT SIZE=2>> > expr2</FONT>
<BR><FONT SIZE=2>> ></FONT>
<BR><FONT SIZE=2>> > As I mentioned I've seen a prior thread to this theme with </FONT>
<BR><FONT SIZE=2>> a prominent</FONT>
<BR><FONT SIZE=2>> > contribution of Allan Hayes, e.g.</FONT>
<BR><FONT SIZE=2>> > </FONT>
<BR><FONT SIZE=2>> <A HREF="http://library.wolfram.com/mathgroup/archive/1999/Feb/msg00460"; TARGET="_blank">http://library.wolfram.com/mathgroup/archive/1999/Feb/msg00460</A></FONT>
<BR><FONT SIZE=2>> .html or see</FONT>
<BR><FONT SIZE=2>> > also my reply to Allan at another thread</FONT>
<BR><FONT SIZE=2>> > </FONT>
<BR><FONT SIZE=2>> <A HREF="http://library.wolfram.com/mathgroup/archive/2000/Jul/msg00115.html"; TARGET="_blank">http://library.wolfram.com/mathgroup/archive/2000/Jul/msg00115.html</A> .</FONT>
<BR><FONT SIZE=2>> ></FONT>
<BR><FONT SIZE=2>> > BTW esp. with Block, things are quite the same, and quite </FONT>
<BR><FONT SIZE=2>> common here,</FONT>
<BR><FONT SIZE=2>> since</FONT>
<BR><FONT SIZE=2>> > the execution</FONT>
<BR><FONT SIZE=2>> > environment within Block almost always differs form that </FONT>
<BR><FONT SIZE=2>> one outside: we</FONT>
<BR><FONT SIZE=2>> > have to anticipate the transformations to the _result_ of </FONT>
<BR><FONT SIZE=2>> Block, as here</FONT>
<BR><FONT SIZE=2>> to</FONT>
<BR><FONT SIZE=2>> > the _result_ of CompoundExpression.</FONT>
<BR><FONT SIZE=2>> ></FONT>
<BR><FONT SIZE=2>> > --</FONT>
<BR><FONT SIZE=2>> > Hartmut</FONT>
<BR><FONT SIZE=2>> ></FONT>
<BR><FONT SIZE=2>> ></FONT>
<BR><FONT SIZE=2>> > > -----Original Message-----</FONT>
<BR><FONT SIZE=2>> > > From: DrBob [<A HREF="mailto:majort at cox-internet.com">mailto:majort at cox-internet.com</A>]</FONT>
To: mathgroup at smc.vnet.net
<BR><FONT SIZE=2>> > > Sent: Tuesday, June 04, 2002 5:59 PM</FONT>
<BR><FONT SIZE=2>> > > Cc: 'David Park'; BobHanlon at aol.com</FONT>
<BR><FONT SIZE=2>> > > Subject: [mg34797] RE: Is it possible to</FONT>
<BR><FONT SIZE=2>> > > access internal variables?</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > If compound expressions are not evaluated in order, how </FONT>
<BR><FONT SIZE=2>> can Modules or</FONT>
<BR><FONT SIZE=2>> > > Blocks work? Aren't they compound expressions? What </FONT>
<BR><FONT SIZE=2>> makes g and h</FONT>
<BR><FONT SIZE=2>> > > different?</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > These are serious bugs.</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > I feel like we're walking on quicksand, now.</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > Bobby</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > -----Original Message-----</FONT>
<BR><FONT SIZE=2>> > > From: Wolf, Hartmut [<A HREF="mailto:Hartmut.Wolf at t-systems.com">mailto:Hartmut.Wolf at t-systems.com</A>]</FONT>
To: mathgroup at smc.vnet.net
<BR><FONT SIZE=2>> > > Sent: Tuesday, June 04, 2002 3:45 AM</FONT>
<BR><FONT SIZE=2>> > > Subject: Is it possible</FONT>
<BR><FONT SIZE=2>> > > to access</FONT>
<BR><FONT SIZE=2>> > > internal variables?</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > Hello Bob,</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > there is something mysterious with your proposal that disturbs me</FONT>
<BR><FONT SIZE=2>> > > somewhat.</FONT>
<BR><FONT SIZE=2>> > > See my records:</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > In[1]:= f[x_] := (x - 3)(x - 4)</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > In[2]:= g[x_] := Module[{t = f[x]}, v = Append[v, {x, t}]; t];</FONT>
<BR><FONT SIZE=2>> > > In[3]:= v = {}; FindMinimum[g[x], {x, 2, 1, 3}]</FONT>
<BR><FONT SIZE=2>> > > >From In[3]:=</FONT>
<BR><FONT SIZE=2>> > > FindMinimum::"regex": "Reached the point </FONT>
<BR><FONT SIZE=2>> \!\({3.5000000000000018`}\)</FONT>
<BR><FONT SIZE=2>> > > which</FONT>
<BR><FONT SIZE=2>> > > is \</FONT>
<BR><FONT SIZE=2>> > > outside the region \!\({\({1.`, 3.`}\)}\)."</FONT>
<BR><FONT SIZE=2>> > > >From In[3]:=</FONT>
<BR><FONT SIZE=2>> > > FindMinimum::"regex": "Reached the point </FONT>
<BR><FONT SIZE=2>> \!\({3.5000000000000018`}\)</FONT>
<BR><FONT SIZE=2>> > > which</FONT>
<BR><FONT SIZE=2>> > > is \</FONT>
<BR><FONT SIZE=2>> > > outside the region \!\({\({1.`, 3.`}\)}\)."</FONT>
<BR><FONT SIZE=2>> > > Out[3]=</FONT>
<BR><FONT SIZE=2>> > > FindMinimum[g[x], {x, 2, 1, 3}]</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > In[4]:= v</FONT>
<BR><FONT SIZE=2>> > > Out[4]=</FONT>
<BR><FONT SIZE=2>> > > {{2., 2.}, {2., 2.}, {2.03136, 1.9069}, {2.05074, </FONT>
<BR><FONT SIZE=2>> 1.85035}, {2.18642,</FONT>
<BR><FONT SIZE=2>> > > 1.4755}, {3., 0.}, {2., 2.}, {2., 2.}, {2.03136, 1.9069},</FONT>
<BR><FONT SIZE=2>> > > {2.05074,</FONT>
<BR><FONT SIZE=2>> > > 1.85035}, {2.18642, 1.4755}, {3., 0.}}</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > In[5]:= g[x]</FONT>
<BR><FONT SIZE=2>> > > Out[5]= (-4 + x) (-3 + x)</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > In[6]:= ?g</FONT>
<BR><FONT SIZE=2>> > > Global`g</FONT>
<BR><FONT SIZE=2>> > > g[x_] := Module[{t = f[x]}, v = Append[v, {x, t}]; t]</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > Apart from the fact that FindMinimum is restarted and </FONT>
<BR><FONT SIZE=2>> that the first</FONT>
<BR><FONT SIZE=2>> > > value</FONT>
<BR><FONT SIZE=2>> > > appears twice, this seems to be what you intended. It doesn't</FONT>
<BR><FONT SIZE=2>> > > help Arny</FONT>
<BR><FONT SIZE=2>> > > though, as the minimum value -- what he supposed to be </FONT>
<BR><FONT SIZE=2>> that x occuring</FONT>
<BR><FONT SIZE=2>> > > in</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > But there seems to be something special with g, if I try with h it</FONT>
<BR><FONT SIZE=2>> > > doesn't</FONT>
<BR><FONT SIZE=2>> > > work:</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > In[7]:= h[x_] := Module[{t = f[x]}, Append[v, {x, t}]; t];</FONT>
<BR><FONT SIZE=2>> > > In[8]:= v = {}; FindMinimum[h[x], {x, 2, 1, 3}]</FONT>
<BR><FONT SIZE=2>> > > >From In[8]:=</FONT>
<BR><FONT SIZE=2>> > > FindMinimum::"regex": "Reached the point </FONT>
<BR><FONT SIZE=2>> \!\({3.5000000000000018`}\)</FONT>
<BR><FONT SIZE=2>> > > which</FONT>
<BR><FONT SIZE=2>> > > is \</FONT>
<BR><FONT SIZE=2>> > > outside the region \!\({\({1.`, 3.`}\)}\)."</FONT>
<BR><FONT SIZE=2>> > > >From In[8]:=</FONT>
<BR><FONT SIZE=2>> > > FindMinimum::"regex": "Reached the point </FONT>
<BR><FONT SIZE=2>> \!\({3.5000000000000018`}\)</FONT>
<BR><FONT SIZE=2>> > > which</FONT>
<BR><FONT SIZE=2>> > > is \</FONT>
<BR><FONT SIZE=2>> > > outside the region \!\({\({1.`, 3.`}\)}\)."</FONT>
<BR><FONT SIZE=2>> > > Out[8]=</FONT>
<BR><FONT SIZE=2>> > > FindMinimum[h[x], {x, 2, 1, 3}]</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > In[9]:= v (* v is empty *)</FONT>
<BR><FONT SIZE=2>> > > Out[9]= {}</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > In[10]:= h[x]</FONT>
<BR><FONT SIZE=2>> > > Out[10]= (-4 + x) (-3 + x)</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > In[11]:= ?h</FONT>
<BR><FONT SIZE=2>> > > Global`h</FONT>
<BR><FONT SIZE=2>> > > h[x_] := Module[{t = f[x]}, Append[v, {x, t}]; t]</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > Now observe:</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > In[12]:= FindMinimum[Print[x]; f[x], {x, 2, 1, 3}]</FONT>
<BR><FONT SIZE=2>> > > >From In[12]:= x</FONT>
<BR><FONT SIZE=2>> > > >From In[12]:= 2.</FONT>
<BR><FONT SIZE=2>> > > >From In[12]:= 2.03136</FONT>
<BR><FONT SIZE=2>> > > >From In[12]:= 2.05074</FONT>
<BR><FONT SIZE=2>> > > >From In[12]:= 2.18642</FONT>
<BR><FONT SIZE=2>> > > >From In[12]:= 3.</FONT>
<BR><FONT SIZE=2>> > > >From In[12]:= FindMinimum::"regex": "Reached the point</FONT>
<BR><FONT SIZE=2>> > > \!\({3.5000000000000018`}\) which is \</FONT>
<BR><FONT SIZE=2>> > > outside the region \!\({\({1.`, 3.`}\)}\)."</FONT>
<BR><FONT SIZE=2>> > > Out[12]= FindMinimum[Print[x]; f[x], {x, 2, 1, 3}]</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > The Argument of FindMinimum is evaluated first with </FONT>
<BR><FONT SIZE=2>> symbolic x (to get</FONT>
<BR><FONT SIZE=2>> > > at</FONT>
<BR><FONT SIZE=2>> > > the derivative I suppose), later, at the second call, it and</FONT>
<BR><FONT SIZE=2>> > > such also t</FONT>
<BR><FONT SIZE=2>> > > =</FONT>
<BR><FONT SIZE=2>> > > (-4 + x) (-3 + x) get a numeric value, and therefore the </FONT>
<BR><FONT SIZE=2>> values are</FONT>
<BR><FONT SIZE=2>> > > introduced into v when appending {x,t}, so the start value</FONT>
<BR><FONT SIZE=2>> > > gets doubled.</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > The restart of the minimization seems to be triggered by </FONT>
<BR><FONT SIZE=2>> the compound</FONT>
<BR><FONT SIZE=2>> > > expression v = {}; FindMinimum[...] in the main loop (not </FONT>
<BR><FONT SIZE=2>> within Find</FONT>
<BR><FONT SIZE=2>> > > Minimum)</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > In[19]:= h5[x_] := Module[{t = f[x]}, Print[x]; t];</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > In[20]:= v = {}; FindMinimum[h5[x], {x, 2, 1, 3}]</FONT>
<BR><FONT SIZE=2>> > > >From In[20]:= x</FONT>
<BR><FONT SIZE=2>> > > >From In[20]:= 2.</FONT>
<BR><FONT SIZE=2>> > > >From In[20]:= 2.03136</FONT>
<BR><FONT SIZE=2>> > > >From In[20]:= 2.05074</FONT>
<BR><FONT SIZE=2>> > > >From In[20]:= 2.18642</FONT>
<BR><FONT SIZE=2>> > > >From In[20]:= 3.</FONT>
<BR><FONT SIZE=2>> > > >From In[20]:=</FONT>
<BR><FONT SIZE=2>> > > FindMinimum::"regex": "Reached the point </FONT>
<BR><FONT SIZE=2>> \!\({3.5000000000000018`}\)</FONT>
<BR><FONT SIZE=2>> > > which</FONT>
<BR><FONT SIZE=2>> > > is \</FONT>
<BR><FONT SIZE=2>> > > outside the region \!\({\({1.`, 3.`}\)}\)."</FONT>
<BR><FONT SIZE=2>> > > >From In[20]:= x</FONT>
<BR><FONT SIZE=2>> > > >From In[20]:= 2.</FONT>
<BR><FONT SIZE=2>> > > >From In[20]:= 2.03136</FONT>
<BR><FONT SIZE=2>> > > >From In[20]:= 2.05074</FONT>
<BR><FONT SIZE=2>> > > >From In[20]:= 2.18642</FONT>
<BR><FONT SIZE=2>> > > >From In[20]:= 3.</FONT>
<BR><FONT SIZE=2>> > > >From In[20]:=</FONT>
<BR><FONT SIZE=2>> > > FindMinimum::"regex": "Reached the point </FONT>
<BR><FONT SIZE=2>> \!\({3.5000000000000018`}\)</FONT>
<BR><FONT SIZE=2>> > > which</FONT>
<BR><FONT SIZE=2>> > > is \</FONT>
<BR><FONT SIZE=2>> > > outside the region \!\({\({1.`, 3.`}\)}\)."</FONT>
<BR><FONT SIZE=2>> > > Out[20]= FindMinimum[h5[x], {x, 2, 1, 3}]</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > Any expression e.g. (3; FindMinimum[...]) does that too; </FONT>
<BR><FONT SIZE=2>> conversely if</FONT>
<BR><FONT SIZE=2>> > > you</FONT>
<BR><FONT SIZE=2>> > > initialize v in an extra line, there will be no restart. </FONT>
<BR><FONT SIZE=2>> This may have</FONT>
<BR><FONT SIZE=2>> > > something to do with peculiarities of compound </FONT>
<BR><FONT SIZE=2>> expression, sometimes</FONT>
<BR><FONT SIZE=2>> > > starting a re-evaluation. (This had been reported by </FONT>
<BR><FONT SIZE=2>> Allan Hayes some</FONT>
<BR><FONT SIZE=2>> > > years</FONT>
<BR><FONT SIZE=2>> > > ago.) See:</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > In[65]:= x = 5;</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > In[66]:= x =.; Print[x]; {x, x = 3, x}</FONT>
<BR><FONT SIZE=2>> > > >From In[66]:= x</FONT>
<BR><FONT SIZE=2>> > > Out[66]= {3, 3, 3}</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > In[67]:= x =.</FONT>
<BR><FONT SIZE=2>> > > In[68]:= {x, x = 3, x}</FONT>
<BR><FONT SIZE=2>> > > Out[68]= {x, 3, 3}</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > Anyways, as shown above, Arny's desire to get at </FONT>
<BR><FONT SIZE=2>> 'internal values' of</FONT>
<BR><FONT SIZE=2>> > > FindMinimum seems to be hopeless. My advice would be to </FONT>
<BR><FONT SIZE=2>> check for the</FONT>
<BR><FONT SIZE=2>> > > error</FONT>
<BR><FONT SIZE=2>> > > message and then possibly increase the search range (by a certain</FONT>
<BR><FONT SIZE=2>> > > tolerance)</FONT>
<BR><FONT SIZE=2>> > > and restart (only a finite number of times).</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > --</FONT>
<BR><FONT SIZE=2>> > > Hartmut</FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > > > -----Original Message-----</FONT>
<BR><FONT SIZE=2>> > > > From: BobHanlon at aol.com [<A HREF="mailto:BobHanlon at aol.com">mailto:BobHanlon at aol.com</A>]</FONT>
To: mathgroup at smc.vnet.net
<BR><FONT SIZE=2>> > > > Sent: Sunday, June 02, 2002 7:15 AM</FONT>
<BR><FONT SIZE=2>> > > > Subject: Is it possible to access</FONT>
<BR><FONT SIZE=2>> > > internal</FONT>
<BR><FONT SIZE=2>> > > > variables?</FONT>
<BR><FONT SIZE=2>> > > ></FONT>
<BR><FONT SIZE=2>> > > ></FONT>
<BR><FONT SIZE=2>> > > ></FONT>
<BR><FONT SIZE=2>> > > > In a message dated 6/1/02 6:18:58 AM,</FONT>
<BR><FONT SIZE=2>> > > > someone at somewhere.sometime writes:</FONT>
<BR><FONT SIZE=2>> > > ></FONT>
<BR><FONT SIZE=2>> > > > >I am minimizing a function which only has real values</FONT>
<BR><FONT SIZE=2>> > > > >between 1 and -1,</FONT>
<BR><FONT SIZE=2>> > > > most</FONT>
<BR><FONT SIZE=2>> > > > >of the time... occasionally its range is different and</FONT>
<BR><FONT SIZE=2>> > > > unknown, (but anyway</FONT>
<BR><FONT SIZE=2>> > > > >not far from 1 and -1). I could write a routine using Check</FONT>
<BR><FONT SIZE=2>> > > > to catch errors</FONT>
<BR><FONT SIZE=2>> > > > >and then expand the range over which FindMinimum is allowed</FONT>
<BR><FONT SIZE=2>> > > > to search,</FONT>
<BR><FONT SIZE=2>> > > > >but</FONT>
<BR><FONT SIZE=2>> > > > >since FindMinimum seems to be getting the appropriate values</FONT>
<BR><FONT SIZE=2>> > > > anyway - it</FONT>
<BR><FONT SIZE=2>> > > > >tells me the values in its error message - I was wondering</FONT>
<BR><FONT SIZE=2>> > > > if there weren't</FONT>
<BR><FONT SIZE=2>> > > > >some way to get at those values and use them without</FONT>
<BR><FONT SIZE=2>> > > > bothering to write</FONT>
<BR><FONT SIZE=2>> > > > >said routine. I was thinking of analysing 'MessageList' or</FONT>
<BR><FONT SIZE=2>> > > > '$MessageList',</FONT>
<BR><FONT SIZE=2>> > > > >but was thinking there might be some easier way.</FONT>
<BR><FONT SIZE=2>> > > > ></FONT>
<BR><FONT SIZE=2>> > > > >Aren't variables within packages accessible via their long</FONT>
<BR><FONT SIZE=2>> > > > names, e.g.</FONT>
<BR><FONT SIZE=2>> > > > >`package`private`variablename or something like that? Does</FONT>
<BR><FONT SIZE=2>> > > > anyone have</FONT>
<BR><FONT SIZE=2>> > > > >any suggestions?</FONT>
<BR><FONT SIZE=2>> > > > ></FONT>
<BR><FONT SIZE=2>> > > ></FONT>
<BR><FONT SIZE=2>> > > > f[x_] := (x-3)(x-4);</FONT>
<BR><FONT SIZE=2>> > > ></FONT>
<BR><FONT SIZE=2>> > > > g[x_] := Module[{t = f[x]}, v=Append[v, {x,t}]; t];</FONT>
<BR><FONT SIZE=2>> > > ></FONT>
<BR><FONT SIZE=2>> > > > g is the same function as f except that calls to g are </FONT>
<BR><FONT SIZE=2>> recorded in v</FONT>
<BR><FONT SIZE=2>> > > ></FONT>
<BR><FONT SIZE=2>> > > > v={}; FindMinimum[g[x], {x, 2}]</FONT>
<BR><FONT SIZE=2>> > > ></FONT>
<BR><FONT SIZE=2>> > > > {-0.25, {x -> 3.5}}</FONT>
<BR><FONT SIZE=2>> > > ></FONT>
<BR><FONT SIZE=2>> > > > FindMinimum called g at the following values of x:</FONT>
<BR><FONT SIZE=2>> > > ></FONT>
<BR><FONT SIZE=2>> > > > v[[All,1]]</FONT>
<BR><FONT SIZE=2>> > > ></FONT>
<BR><FONT SIZE=2>> > > > {2., 2., 2.0313609375, 2.0507430627940644,</FONT>
<BR><FONT SIZE=2>> > > ></FONT>
<BR><FONT SIZE=2>> > > > 2.1864179398525154, 3.136142079261673, 3.500000000000001,</FONT>
<BR><FONT SIZE=2>> > > ></FONT>
<BR><FONT SIZE=2>> > > > 3.838316500294484, 3.5, 3.3180710396308366,</FONT>
<BR><FONT SIZE=2>> > > ></FONT>
<BR><FONT SIZE=2>> > > > 3.4999904004703097, 3.5, 3.499999994722301}</FONT>
<BR><FONT SIZE=2>> > > ></FONT>
<BR><FONT SIZE=2>> > > ></FONT>
<BR><FONT SIZE=2>> > > > Bob Hanlon</FONT>
<BR><FONT SIZE=2>> > > > Chantilly, VA USA</FONT>
<BR><FONT SIZE=2>> > > ></FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> > ></FONT>
<BR><FONT SIZE=2>> ></FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> </FONT>
<BR><FONT SIZE=2>> </FONT>
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