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]\)
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\(\(prepmat[r_Integer, c_Integer,
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Normal[SparseArray[{1, 1} -> ini, {r, c},
ini]]];\)\[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"],
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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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