Re: covariance, eigenvalues

*To*: mathgroup at smc.vnet.net*Subject*: [mg51861] Re: [mg51843] covariance, eigenvalues*From*: Tomas Garza <tgarza01 at prodigy.net.mx>*Date*: Thu, 4 Nov 2004 01:49:02 -0500 (EST)*References*: <200411030625.BAA08378@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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. In[1]:= << "Statistics`MultiDescriptiveStatistics`"; In[15]:= x = Table[Random[], {130}, {1500}]; In[16]:= AbsoluteTiming[m = CovarianceMatrix[x]; ] Out[16]= {117.Second, Null} Same goes for the eigenvalues and eigenvectors. In[18]:= Eigenvalues[m];//AbsoluteTiming Out[18]= {9.0000000 Second,Null} In[20]:= Eigenvectors[m];//AbsoluteTiming Out[20]= {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 yahoo.com> To: mathgroup at smc.vnet.net 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 > >

**References**:**covariance, eigenvalues***From:*cagdaskafali@yahoo.com (cagdas)