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MathGroup Archive 2001

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Help with Fold/outer one-liner (II)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg28227] Help with Fold/outer one-liner (II)
  • From: "Emilio Martin-Serrano Sobrino" <emilio.martin at sema.es>
  • Date: Thu, 5 Apr 2001 03:00:42 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

  Hi:

Sorry for bothering you again.

Finally, I think I solved my "Fold/Outer/Function-application" problem; Find
it in the attached notebook . Anyway, now my question is: I am there is a
more elegant way to the solution; any clue?

Emilio Martin-Serrano



 ReJacobian.nb

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(************** Content-type: application/mathematica **************

                    Mathematica-Compatible Notebook

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Notebook[{
Cell[BoxData[
    \( (*\ These\ are\ the\ matrices\ to\ differentiate*) \)], "Input"],

Cell[BoxData[
    \(a1 = {Sin[x[1]]\ Cos[x[2]], \ Sin[x[2]]\ Sin[x[3]]^2,
        x[3]\ \ Tan[x[3]]}\)], "Input"],

Cell[BoxData[
    \(a2 = {Cos[x[1]]\ Cos[x[2]], \ Cos[x[2]]\ Sin[x[3]]^2, \
        Cos[x[3]\ ]\ Tan[x[3]]}\)], "Input"],

Cell[BoxData[
    \(a3 = {Cos[x[2]]\ Cos[x[2]], \ Cos[x[2]]\ Sin[x[1]]^2, \
        Cos[x[3]\ ]\ Tan[x[2]]}\)], "Input"],

Cell[BoxData[
    \(a4 = {Cos[x[1]]\ Cos[x[1]], \ Cos[x[2]]\ Sin[x[2]]^2, \
        Cos[x[1]\ ]\ Tan[x[1]]}\)], "Input"],

Cell[BoxData[
    \( (*\
      This\ is\ a\ function\ definition\ to\ perform\ the\ task*) \)], 
"Input"],

Cell[BoxData[
    \(fCont[f_List] :=
      With[{vars = Array[x, Take[Dimensions[First[f]]]]},
        Fold[Outer[D, #, vars] &, First[f], Drop[f, 1]]]\)], "Input"],

Cell[BoxData[
    \(fCont[{a1, a2, a3, a4}]\)], "Input"],

Cell[BoxData[
    \( (*\ This\ is\ an\ expresion\ equivalent\ to\ the\ previous\ one, 
\
      it\ yields\ the\ same\ \ \ *) \)], "Input"],

Cell[BoxData[
    \(With[{vars = Array[x, Take[Dimensions[a1]]]},
      Fold[Outer[D, #, vars] &, a1, {a2, a3, a4}]]\)], "Input"],

Cell[BoxData[
    \( (*\ and\ finally, \ this\ is\ what\ I\ wanted\ *) \)], "Input"],

Cell[BoxData[
    \(\(With[{vars = Array[x, Take[Dimensions[First[#]]]]},
          Fold[Outer[D, #, vars] &, First[#], Drop[#, 1]]] &\)[{a1, a2, 
a3,
        a4}]\)], "Input"]
},
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(*******************************************************************
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