Re: friendly challenge 3
- To: mathgroup at smc.vnet.net
- Subject: [mg35094] Re: friendly challenge 3
- From: "Allan Hayes" <hay at haystack.demon.co.uk>
- Date: Tue, 25 Jun 2002 03:39:31 -0400 (EDT)
- References: <af6hk6$lkc$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Andrzej,
m = Table[Random[Integer, {1, 9}], {30}, {30}]; n = m + Transpose[m];
sign2[M_?MatrixQ] :=
Count[Eigenvalues[M], _?(# > 0 &)] - Count[Eigenvalues[M], _?(# < 0 &)]
sign3[M_?MatrixQ] :=Plus@@Sign[Eigenvalues[M]]
sign4[M_?MatrixQ] :=Plus@@Sign[Eigenvalues[N[M]]]
Timings,
sign2[n]//Timing
{18.4 Second,2}
sign3[n]//Timing
{8.9 Second,2}
sign4[n]//Timing
{0.05 Second,2}
--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565
"Andrzej Kozlowski" <andrzej at platon.c.u-tokyo.ac.jp> wrote in message
news:af6hk6$lkc$1 at smc.vnet.net...
> 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
>
>