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MathGroup Archive 2003

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Dot - mystery consumption time

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44012] Dot - mystery consumption time
  • From: kujanp at fel.cvut.cz (Petr Kujan)
  • Date: Fri, 17 Oct 2003 05:14:42 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hello MathGroup,

I would be grateful if someone could explain the difference in 
consumption time. I redefine function Dot[].

Here is a Mathematica document with comments.

Thank in advance for all your help.
Best regards,
    Petr.


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Notebook[{
Cell["\<\
I use  Mathematica 5.0 ->  SparseArray[ ] for fast generating zero
matrix in \
function sm[].
PC with Duron 750GHz, 256MB,  Win2k \
\>", "Text"],

Cell["Auxiliary function", "Text"],

Cell[BoxData[{
    \(\(\(prand[deg_, rowcol_, var_] :=
        pm[Table[Random[Real, {\(-2\), 2}],
              Evaluate[{deg + 1}, {rowcol}, {rowcol}]] //
ToPackedArray, var,
          deg];\)\(\[IndentingNewLine]\)
    \)\), "\[IndentingNewLine]",
    \(\(\(size[pol : pm[pmc_, var_, deg_]] :=
        Dimensions[pmc[\([1]\)]];\)\(\[IndentingNewLine]\)
    \)\), "\[IndentingNewLine]",
    \(\(\(droplzer[dat_] :=
        Module[{lendat = Length[dat], i},
          i = lendat; \[IndentingNewLine]While[
            And @@ \(ZeroQ /@ \(Hold @@ Flatten[dat[\([i]\)]]\)\), \(i =
                i - 1;\)]; \[IndentingNewLine]Drop[
            dat, \(-\((lendat - i)\)\)]];\)\(\[IndentingNewLine]\)
    \)\), "\[IndentingNewLine]",
    \(\(prepmat[r_Integer, c_Integer,
            ini : \(\((_?NumericQ)\) : 0. \)] /; \((r > 0 && c > 0)\) :=
        If[$VersionNumber < 5, Table[ini, {r}, {c}],
          Normal[SparseArray[{1, 1} -> ini, {r, c},
              ini]]];\)\[IndentingNewLine]\), "\[IndentingNewLine]",
    \(\(sm[A : pm[pmcA_, var_, deg_], col_?Positive] :=
        Module[{m, n, mat, flatpmcA, prepnum}, {m, n} =
            size[A]; \[IndentingNewLine]flatpmcA =
            Flatten[pmcA, 1]; \[IndentingNewLine]mat =
            prepmat[m*\((col + deg)\), col*n, 0. ]; \[IndentingNewLine]Do[
            mat[\([Range[\((i - 1)\)*m + 1, \((i + deg)\)*m],
                  Range[\((i - 1)\)*n + 1, i*n]]\)] = flatpmcA, {i,
              col}]; \[IndentingNewLine]mat];\)\)}], "Input"],

Cell["Redefine standard function Dot[] for my object pm[]", "Text"],

Cell["\<\
Fast computation - OK
!! now computation Chop[ ] and droplzer[ ] is commentary\
\>", "Text"],

Cell[BoxData[
    \(pm /:
      Dot[A : pm[pmcA_, varA_, degA_],
        B : pm[pmcB_, varB_, degB_]] := \[IndentingNewLine]Module[{me, zer,
          pmc, pardot, cho, s1,
          s2}, \[IndentingNewLine] (*zeroing\ data*)
\[IndentingNewLine] (*me \
= NonZeroMin[{pmcA, pmcB}];  (*\(! \(! slow\)\)*) *) \[IndentingNewLine]me =
          0. ; \[IndentingNewLine]zer =
          10. ^\(-10\); \[IndentingNewLine]Print["\<---------\>"]; \
\[IndentingNewLine]Print["\<s1: \>",
          Timing[\[IndentingNewLine]\(s1 =
                sm[A, degB +
                    1];\)\[IndentingNewLine]]]; \
\[IndentingNewLine]Print["\<s2: \>",
          Timing[\[IndentingNewLine]\(s2 =
                sm[B, 1];\)\[IndentingNewLine]]]; \
\[IndentingNewLine]Print["\<pardot: \>",
          Timing[\[IndentingNewLine]\(pardot =
                Partition[
                  s1 . s2, \(size[
                      A]\)[\([1]\)]];\)\[IndentingNewLine]]]; \
\[IndentingNewLine] (*\ \(\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\(\
\[IndentingNewLine]\)\(Print["\<chop: \>",
              Timing[\[IndentingNewLine]\(cho =
                    Chop[par,
                      me*zer];\)\[IndentingNewLine]]]\)\); \
\[IndentingNewLine]\(Print["\<droplzer\>",
              Timing[\[IndentingNewLine]\(pmc =
                    droplzer[
                      cho];\)\[IndentingNewLine]]];\[IndentingNewLine]
**  **  \
**  **  **  **  ** \)\ *) \[IndentingNewLine]pm[pardot, varA,
          Length[pardot] - 1]\[IndentingNewLine]]\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[{
    \(SeedRandom[1]\), "\[IndentingNewLine]",
    \(\(a = prand[20, 50, s];\)\), "\[IndentingNewLine]",
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Cell[BoxData[
    InterpretationBox[\("s1: "\[InvisibleSpace]{0.3309999999999995`\
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      SequenceForm[ "s1: ", {
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        Times[ .63100000000000023, Second], Null}],
      Editable->False]], "Print"],

Cell[BoxData[
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}, Open  ]],

Cell["\<\
small consumption time for computation
s1=sm[..]: 0.37
s2=sm[..]: 0.01
pardot: 0.631\
\>", "Text"],

Cell["\<\
!! now only uncommentary last functions Chop[] and droplzer[]
and consumption time for computation s1, s2 and pardot is larger !!
s1=sm[..]: 0.37 -> 0.64
s2=sm[..]: 0.01 -> 0.02
pardot: 0.631 -> 1.112

I expect time increasing only 0.14 second
Chop[..]: 0.14
droplzer: 0\
\>", "Text"],

Cell[BoxData[{
    \(\(Clear[pm];\)\), "\[IndentingNewLine]",
    \(pm /:
      Dot[A : pm[pmcA_, varA_, degA_],
        B : pm[pmcB_, varB_, degB_]] := \[IndentingNewLine]Module[{me, zer,
          pmc, pardot, cho, s1,
          s2}, \[IndentingNewLine] (*zeroing\ data*)
\[IndentingNewLine] (*me \
= NonZeroMin[{pmcA, pmcB}];  (*\(! \(! slow\)\)*) *) \[IndentingNewLine]me =
          0. ; \[IndentingNewLine]zer =
          10. ^\(-10\); \[IndentingNewLine]Print["\<---------\>"]; \
\[IndentingNewLine]Print["\<s1: \>",
          Timing[\[IndentingNewLine]\(s1 =
                sm[A, degB +
                    1];\)\[IndentingNewLine]]]; \
\[IndentingNewLine]Print["\<s2: \>",
          Timing[\[IndentingNewLine]\(s2 =
                sm[B, 1];\)\[IndentingNewLine]]]; \
\[IndentingNewLine]Print["\<dot: \>",
          Timing[\[IndentingNewLine]\(pardot =
                Partition[
                  s1 . s2, \(size[
                      A]\)[\([1]\)]];\)\[IndentingNewLine]]]; \
\[IndentingNewLine]Print["\<chop: \>",
          Timing[\[IndentingNewLine]\(cho =
                Chop[pardot,
                  me*zer];\)\[IndentingNewLine]]];
\[IndentingNewLine]Print["\
\<droplzer\>",
          Timing[\[IndentingNewLine]\(pmc =
                droplzer[cho];\)\[IndentingNewLine]]];
\[IndentingNewLine]pm[
          pmc, varA, Length[pmc] - 1]\[IndentingNewLine]]\)}], "Input"],

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    \(SeedRandom[1]\), "\[IndentingNewLine]",
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      Editable->False]], "Print"],

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      SequenceForm[ "chop: ", {
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      Editable->False]], "Print"],

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      SequenceForm[ "droplzer", {
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      Editable->False]], "Print"],

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