Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2002
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2002

[Date Index] [Thread Index] [Author Index]

Search the Archive

friendly challenge 3

  • To: mathgroup at smc.vnet.net
  • Subject: [mg35076] friendly challenge 3
  • From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
  • Date: Mon, 24 Jun 2002 03:21:01 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

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



  • Prev by Date: Problem with entering text into a mathematica notebook by VB or QuicKeys
  • Next by Date: Strange thing with exporting to PDF.
  • Previous by thread: Re: FrameTick Problem
  • Next by thread: Re: friendly challenge 3