RE: friendly challenge 3
- To: mathgroup at smc.vnet.net
- Subject: [mg35112] RE: [mg35076] friendly challenge 3
- From: "DrBob" <majort at cox-internet.com>
- Date: Tue, 25 Jun 2002 03:41:05 -0400 (EDT)
- Reply-to: <drbob at bigfoot.com>
- Sender: owner-wri-mathgroup at wolfram.com
How's this?
Needs["Statistics`DescriptiveStatistics`"]
ClearAll[sign2, bt, tst]
sign2[M_?MatrixQ] :=
Count[Eigenvalues[M], _?(# > 0 &)] - Count[Eigenvalues[M], _?(# < 0
&)]
bt[M_?MatrixQ] := Plus @@ (Sign /@ Eigenvalues[M])
tst[k_Integer] := (m = Table[Random[Integer, {1, 9}], {k}, {k}];
n = m + Transpose[m];
First[Timing[#[n]]] & /@ {sign2, bt}
)
tst[k_Integer, i_Integer] := Module[{t},
t = Mean /@ Transpose[tst[k] & /@ Range[i]];
{t, t[[1]]/t[[2]]}
]
tst[30, 10]
{{0.808 Second, 0.3344 Second}, 2.41627}
tst[40, 20]
{{2.5693 Second, 1.15175 Second}, 2.23078}
tst[50, 10]
{{7.1828 Second, 3.1859 Second}, 2.25456}
Bobby Treat
-----Original Message-----
From: Andrzej Kozlowski [mailto:andrzej at platon.c.u-tokyo.ac.jp]
To: mathgroup at smc.vnet.net
Subject: [mg35112] [mg35076] friendly challenge 3
While the season for "friendly challenges" lasts, here is something that
has just come up in my own work. Let's define the signature of a
symmetric matrix as the number of positive eigenvalues - the number of
negative ones. I need an efficient function to compute this.
There is the obvious and rather pedestrian one:
sign2[M_?MatrixQ] :=
Count[Eigenvalues[M], _?(# > 0 &)] - Count[Eigenvalues[M], _?(# < 0
&)]
For example, let's construct a symmetric matrix of random integers (all
matrices I am considering have integer entries):
m = Table[Random[Integer, {1, 9}], {30}, {30}]; n = m + Transpose[m];
the above sign2 gives:
In[4]:=
sign2[n]//Timing
Out[4]=
{3.5 Second,0}
My best function, sign1 gives (on 400 mghz PowerBOok G4)
In[5]:=
sign1[n]//Timing
Out[5]=
{1.44 Second,0}
Nearly two and a half times as fast. Can anyone do better?
Andrzej