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help in speeding up code involving a recursive function

• To: mathgroup at smc.vnet.net
• Subject: [mg43907] help in speeding up code involving a recursive function
• From: "Salman Durrani" <s4001586 at student.uq.edu.au>
• Date: Fri, 10 Oct 2003 03:06:39 -0400 (EDT)
• Organization: The University of Queensland, Australia
• Reply-to: "Salman Durrani" <s4001586 at student.uq.edu.au>
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

In the code below, the input variables are L and a.

The code executes correctly and almost instantaneously for L=1 and a=5.

However when I run it for L=2 and a=5, the execution is very slow.

I ran it on a 2.5 GHz machine for L=2 and a=5 for over 48 hours, without the
execution finishing.
In the end, I was forced to abort the execution.

Can someone please suggest how to speed up the execution.

The code can also be downloaded from
http://www.itee.uq.edu.au/~dsalman/_downloads/test.nb

Thanks in advance.

Salman



\!\(\(betacoeff =
      Function[{k, r, L}, \[IndentingNewLine]If[k == 0,
          outp = 1, \[IndentingNewLine]\(If[r == 1,
              outp = 1\/\(k!\), \[IndentingNewLine]\(If[k == 1,
                  outp = r, \[IndentingNewLine]\(outp =
                      Sum[betacoeff[i, r - 1, L]\ 1\/\(\((k - i)\)!\)\ If[
                            i >= 0 && i <= \((\((r - 1)\)\ \((L - 1)\))\),
1,
                            0], {i, k - \((L - 1)\),

k}];\)\[IndentingNewLine]];\)\[IndentingNewLine]];\)\
\[IndentingNewLine]]; \[IndentingNewLine]outp\[IndentingNewLine]];\)\)
\!\(\(ansOUT = {};\)\[IndentingNewLine]
  \(For[a = 5, a <= 15,
      a += 5\/1, \[IndentingNewLine]L = 1; \[IndentingNewLine]y =
        10; \[IndentingNewLine]x =
        N[10\^\(y\/10\), 64]; \[IndentingNewLine]M =
        64; \[IndentingNewLine]m = 1; \[IndentingNewLine]K =
        Log[2, M]; \[IndentingNewLine]Ku = a; \[IndentingNewLine]Nc =
        256; \[IndentingNewLine]X = K\/L\ x; \[IndentingNewLine]rho\  =
        X\/\(1 + \(2\/\(3\ Nc\)\) X\ \((Ku\ L - 1)\)\); \[IndentingNewLine]p
\
= \(\(M/2\)\/\(M - 1\)\)
          1\/Gamma[m\ L]\ Sum[\ \((\(-1\))\)\^\(n + 1\)\ \((Binomial[M - 1,
                  n])\)\ \((m\/\(\((\(n\/\(n + 1\)\) rho)\) + m\))\)\^\(m\ \
L\)\ \ Sum[\ Sum[\[IndentingNewLine]\ \((Binomial[k, i])\) \((betacoeff[k,
n,
                        L])\)\ \((\(Gamma[L + k]\ Gamma[\((m\ L)\)\  + \
i]\)\
\/\(\((n + 1)\)\^\(L + k\)\ Gamma[L + i]\))\) \((rho\/\(n \((rho + m)\) + \
m\
\))\)\^i, {i, \ 0, \ k}], {k, 0, n \((L - 1)\)}], {n, 1,
              M - 1}]; \[IndentingNewLine]AppendTo[
        ansOUT, {N[a, 4], N[p, 8]}];\[IndentingNewLine]];\)\)
TableForm[ansOUT]
\!\(\*
  TagBox[GridBox[{
        {"5.`", "0.059290035286915295`"},
        {"10.`", "0.08414846730969132`"},
        {"15.`", "0.10697647648324377`"}
        },
      RowSpacings->1,
      ColumnSpacings->3,
      RowAlignments->Baseline,
      ColumnAlignments->{Left}],
    (TableForm[ #]&)]\)