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Re: covariance, eigenvalues

  • To: mathgroup at
  • Subject: [mg51861] Re: [mg51843] covariance, eigenvalues
  • From: Tomas Garza <tgarza01 at>
  • Date: Thu, 4 Nov 2004 01:49:02 -0500 (EST)
  • References: <>
  • Sender: owner-wri-mathgroup at

The only problem here is the time needed to complete your computations. Size 
is no problem by itself. As an example, I took 130 samples of a vector of 
length 1,500 (i.e., one-tenth of what you want), and used the inbuilt 
function CovarianceMatrix. It took about 117 seconds on a 2GHz machine with 
512 MB memory.


<< "Statistics`MultiDescriptiveStatistics`";

x = Table[Random[], {130}, {1500}];

AbsoluteTiming[m = CovarianceMatrix[x]; ]
{117.Second, Null}

Same goes for the eigenvalues and eigenvectors.

{9.0000000 Second,Null}

{55.4531250 Second,Null}

If you increase from 1,500 to 15,000 you must expect a very considerable 
increase in computer time to get your results.

Tomas Garza

Mexico City

----- Original Message ----- 
From: "cagdas" <cagdaskafali at>
To: mathgroup at
Subject: [mg51861] [mg51843] covariance, eigenvalues

> Hi,
> I have a random vector of length 15000 by 1. I have 130 samples of
> this vector and I would like to estimate the covariance matrix. Is
> there a built-in function in mathematica to do that ? If there is, can
> it handle a covariance matrix of size 15000 by 15000?
> If I can get that matrix the next step is an eigenvalue decomposition.
> Are there any built-in functions to compute eigenvalues and
> eigenvectors of a given matrix ? and again, is it possible to use
> these functions for a matrix of size 15000 by 15000?
> I would appreciate any suggestions (related to mathematica or some
> other options)
> Thanks
> Cagdas

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