Fwd: RE: CholeskyDecomposition

[boisvert@nist.gov]

Sender: "Cleve Moler" <Cleve.Moler@mathworks.com>
Subject: RE: CholeskyDecomposition


The input matrix should be symmetric.  Yours isn't.  MATLAB and JAMA
only look at half of the matrix.  They're probably looking at different
halves.
  -- Cleve

-----Original Message-----
From: jama@nist.gov [mailto:jama@nist.gov] On Behalf Of Sione
Sent: Thursday, May 03, 2007 12:02 PM
To: Multiple recipients of list
Subject: Re: CholeskyDecomposition

Pete,

Thanks for the tip. Yes, it does when I  transpose the last  L*L' ;

The same matrix 'H', (shown below)  using  Matlab cholesky   'chol'  
command gives an answer that  'H'  is positive definite, while the JAMA

Cholesky gives  a false (not positive definite)?

H = [4532 , 5682 ; 5634 , 7134];

Cheers,
Sione.






G. W. (Pete) Stewart wrote:
> Try computing LL' instead of L'L.
>
> Pete Stewart
>
>
> On Thu, 3 May 2007, Sione wrote:
>
>   
>> Date: Thu, 3 May 2007 10:36:14 -0400 (EDT)
>> From: Sione <sionep@xtra.co.nz>
>> Reply-To: jama@nist.gov
>> To: Multiple recipients of list <jama@nist.gov>
>> Subject: CholeskyDecomposition
>>
>> Hello All,
>>
>> I have a question about the CholeskyDecomposition.  The following
code
>> snippets shows a reconstruction of  a matrix from a
>> CholeskyDecomposition and the result is not the same as the original
one.
>>
>> -------- sample code -----------
>>
>> double[][] h = new double[][]{
>>      {4532 , 5682 },
>>      {5634 ,  7134}
>>    }
>>
>> Matrix H = new Matrix(h);
>>
>> CholeskyDecomposition chol = H.chol();
>>
>> Matrix L = chol.getL();
>>
>> Matrix LtL = L.transpose().times(L);
>>
>>
>> System.out.println("\n =========== H ==========");
>> H.print(6,0);
>>
>> System.out.println("\n =========== L ==========");
>> L.print(6,4);
>>
>> System.out.println("\n =========== L'*L ==========");
>> LtL.print(6,4);
>>
>> --------- end sample code ------------
>>
>>
>>
>> The output gave me this:
>>
>> =========== H ==========
>>
>>  4532  5682
>>
>>  5634  7134
>>
>>
>> =========== L ==========
>>  67.3201   0.0000
>>
>>  83.6897  11.4034
>>
>>
>> =========== L'*L ==========
>> 11535.9620  954.3484
>>
>>   954.3484  130.0380
>>
>>
>> My question is why the reconstruction  L'*L  is not the same as  H ?
>>
>>
>> Cheers,
>> Sione.
>>
>>
>>
>>
>> ----- End forwarded message -----
>>
>>
>>
>>     
>
>
> ----- End forwarded message -----
>
>
>
>
>   


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