From help-request at octave dot org Mon Aug 16 20:50:59 2004
Subject: Re: chol: matrix not positive definite
From: "Henry F. Mollet" <mollet at pacbell dot net>
To: Geordie McBain <geordie dot mcbain at aeromech dot usyd dot edu dot au>,         "Pascal A. Dupuis" <Pascal.Dupuis@esat.kuleuven.ac.be>
CC: Octave_post <help at octave dot org>
Date: Mon, 16 Aug 2004 18:46:23 -0700

As far as I know 
" ' " is the conjugate transpose operator, whereas
" .' " is the non-cojugate transpose operator.

Perhaps difficult to understand that the former (one symbol) does more than
the latter (two symbols)?
Henry


on 8/17/04 6:51 AM, Geordie McBain at geordie dot mcbain at aeromech dot usyd dot edu dot au
wrote:

> Hello,
> 
> I think the assuredly positive Hermitian matrices should be formed
> with X'*X rather than X.'*X
> 
> I don't understand the latter (dot prime star).  What does it do?
> 
> With A=rand(3)+1i*rand(3), A'*A is positive Hermitian but A.'*A isn't.
> 
> Geordie McBain
> 
> 
> On Mon, 2004-08-16 at 10:50, Pascal A. Dupuis wrote:
>> Hello,
>> 
>> I generate a spare matrix X the following way:
>> 
>> X=[ C0 0  0  0  0
>>     C1 C0 0  0  0
>>     C2 C1 C0 0  0
>>     ...
>>           C2 C1 C0]
>> 
>> with a size of N, N-2 (N >> 2), and C0+C1+C2=0; ||(C0,C1,C2)|| = 1.
>> 
>> then I compute:
>> 
>> xinv = inv(X.'*X);
>> H = chol(xinv);
>> 
>> which results in:  chol: matrix not positive definite
>> 
>> But by construction the matrix should be positive definite, as
>> range(X)=N-2. OTOH, X is also badly conditionned:
>> 
>> [dummy, rcond]=inv(X.'*X);
>> rcond =  1.0498e-10
>> 
>> 
>> If I check the eigenvalues of X.'*X, they are all  > 0, although some
>> of them are very small. (~= 1e-10). So, is it a problem of numerical
>> inaccuracy in the computation of chol ? Or should I instead compute
>> H = chol(pinv(X.'*X))
>> 
>> TIA
>> 
>> Pascal Dupuis
> 
> 
> 
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