Re: graphing traces of complicated evaluations (improved)

*To*: mathgroup at smc.vnet.net*Subject*: [mg80625] Re: graphing traces of complicated evaluations (improved)*From*: Chris Chiasson <chris.chiasson at gmail.com>*Date*: Sun, 26 Aug 2007 23:24:01 -0400 (EDT)*References*: <f7si68$28u$1@smc.vnet.net><f8n22c$kj0$1@smc.vnet.net>

On Jul 31, 5:14 am, Chris Chiasson <chris.chias... at gmail.com> wrote: > On Jul 21, 4:04 am, chuck009 <dmili... at comcast.com> wrote: > > > Suppose I'm tenacious. Really I'm just not satisfied with Integrate returning Pi^2/6 for this integral. I know it's a bug but aren't they just curious why it's giving this answer? > > > In[15]:= > > Integrate[Log[1 + Exp[-z]/Sqrt[z]], {z, 0, Infinity}] > > > Out[15]= > > Pi^2/6 > > > I tried using your code to trace it but to no avail. Any suggestions? > > > > Previously, I released code that could help with the > > > tracing of > > > evaluations, > > Hey, google groups wasn't showing this thread a few days ago (or I am > mentally blind, which I would not put past myself). Otherwise, I would > have responded sooner. > > If you really want to get to the bottom of this, there are several > tools at your disposal. > > 1. Contexts[] > Evaluate this command when you start mathematica. Then evaluate it > after your integral. The contexts that have been added (use > Complement) are ones that were loaded especially for your evaluation. > > I got: > {Integrate`EllipticTrig`,Integrate`QuickLookUpDump`,Integrate`TableDump`,Integrate`TableDumpExp`,Integrate`TableDumpSpec`,Integrate`TableDumpTrig`,Internal`HypergeometricPFQ`,Internal`Integrate`,System`EllipticDump`,System`FibonacciDump`,System`GroebnerBasisDump`,System`HypergeometricDump`,System`InverseFunctionDump`,System`MeijerGDump`,System`NielsenDump`,System`TrigExpIntegralDump`} > > 2. Trace and TraceDialog > The contexts used above can be use to select the symbols you might > like to monitor. This is important, because the trace output for the > full evaluation is likely to be more than a typical computer could > handle (and certainly more than could be graphed easily). > > 3. Stack (with no argument or with a pattern) and StackComplete (wrap > the Trace or TraceDialog with this) > Stack with no arguments gives the tags (symbols associated with > DownValues, UpValues, and OwnValues) that are currently executing. > This is useful in the right hand side of a transformation rule in the > second argument of Trace or as a command issued inside a Dialog > initiated by Trace dialog. If you feed in a pattern instead, it will > match against the expressions that are evaluating and return only > those. StackComplete has the effect of making Stack work on the > sequence of expressions used to arrive at the current expression, not > just the sequence of expressions that are currently evaluating (if > this doesn't make sense, look at the corresponding help browser > entry). > > Let's use #s 1 and 2 to get an idea of what is happening in the newly > loaded contexts: > > integralTrace=Trace[Integrate[Log[1+Exp[-z]/Sqrt[z]],z],xpr_/;! > FreeQ[Unevaluated@xpr,symb_Symbol/;AtomQ@Unevaluated@symb&&MemberQ[{"Integrate`EllipticTrig`","Integrate`QuickLookUpDump`","Integrate`TableDump`","Integrate`TableDumpExp`","Integrate`TableDumpSpec`","Integrate`TableDumpTrig`","Internal`HypergeometricPFQ`","Internal`Integrate`","System`EllipticDump`","System`FibonacciDump`","System`GroebnerBasisDump`","System`HypergeometricDump`","System`InverseFunctionDump`","System`MeijerGDump`","System`NielsenDump`","System`TrigExpIntegralDump`"},Context@Unevaluated@symb]],TraceInternal- > > >True]; > > With[{gr=traceToTree[DeleteCases[integralTrace, > {HoldForm[_Message],___},Infinity]]},TreePlot[gr,Left,gr[[1,1]],VertexRenderingFunction- > > >Function@Tooltip[{Blue,Point@#},#2[[-1]]]]] > > Mousing over the nodes in the graph should give you an idea of which > functions you may want to trace and explore further. > > Of course, I don't know what is wrong with the answer Integrate is > giving, so I don't know what to look for, but perhaps you do? > > Here is a version of the tracing code that changes HoldFormComplete so > that it is stored in a TagBox and that changes the toVertex function > to show more lines of Short output (5 instead of whatever the default > is): > > (Attributes@#={HoldAllComplete})&/ > @{traceToTreeAux,toVertex,HoldFormComplete} > MakeBoxes[HoldFormComplete[arg_],form_]:=TagBox[MakeBoxes[arg,form],HoldFormComplete] > MakeBoxes[HoldFormComplete[args___],form_]:=TagBox[MakeBoxes[Sequence@args,form],HoldFormComplete] > edge[{head1_,pos1_,xpr1_}, > {head2_,pos2_,xpr2_}]:=Quiet[Rule[{head1,vertexNumberFunction@pos1,xpr1}, > {head2,vertexNumberFunction@pos2,xpr2}],{Rule::"rhs"}] > toVertex[traceToTreeAux[HoldForm[heldXpr_],pos_]]:=toVertex[heldXpr] > toVertex[traceToTreeAux[HoldForm[heldXprs___],pos_]]:=toVertex@traceToTreeAux[Sequence[],pos] > (*this code is strong enough to not need the ToString commands,but > some of the resulting graph vertices give trouble to thegraphing > routines*) > toVertex[traceToTreeAux[xpr_,pos_]]:={ToString[Short[Extract[Unevaluated@xpr, > 0,HoldFormComplete], > 5],StandardForm],pos,ToString[Short[First@originalTraceExtract@{pos}, > 5],StandardForm]} > traceToTreeAux[xpr_/;AtomQ@Unevaluated@xpr,___]:=Sequence[] > traceToTreeAux[_HoldForm,___]:=Sequence[] > traceToTreeAux[xpr_,pos_]:=With[{lhs=toVertex@traceToTreeAux[xpr,pos],args=HoldComplete@@Unevaluated@xpr},Identity[Sequence] > [ReleaseHold[Function[Null,edge[lhs,toVertex@#],HoldAllComplete]/ > @args],ReleaseHold@args]] > traceToTree[xpr_]:=Block[{vertexNumber=-1,vertexNumberFunction,originalTraceExtract},vertexNumberFunction[arg_]:=vertexNumberFunction[arg]= > + > +vertexNumber;originalTraceExtract[pos_]:=Extract[Unevaluated@xpr,pos,HoldFormComplete]; > {MapIndexed[traceToTreeAux,Unevaluated@xpr,{0,Infinity}]}] > TraceTreeFormPlot[trace_,opts___]:=Block[{$traceExpressionToTree=True},Through@{Unprotect,Update}@SparseArray`ExpressionToTree;SparseArray`ExpressionToTree[trace,Infinity]=traceToTree@trace;With[{result=ToExpression@ToBoxes@TreeForm[trace,opts]},Through@{Unprotect,Update}@SparseArray`ExpressionToTree;SparseArray`ExpressionToTree[trace,Infinity]=.;Through@{Update,Protect,Update}@SparseArray`ExpressionToTree;result]] I just noticed that the combination of transmission over the newsgroup and pasting back into mathematica screws up this code: vertexNumberFunction[arg_]:=vertexNumberFunction[arg]=++vertexNumber; I dunno what to say...