Fwd: Re: CholeskyDecomposition

[boisvert@nist.gov]

Sender: Sione <sionep@xtra.co.nz>
Subject: Re: CholeskyDecomposition



I found this matlab script on the internet which agrees with the  
'chol'  command in matlab for testing  'positive definite'.
In testing the matrix,

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

with this script it gives the same answer as that of the matlab 'chol' 
command, which is true that  H is positive definite. I am including this 
matlab script in the "Maths" class in JAMA as a utility function.

"Positive-Definite Matrices"
http://www.ece.uwaterloo.ca/~ece204/TheBook/04LinearAlgebra/posdef/matlab.html

Sione.


Sione wrote:
> 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 -----
>>>
>>>
>>>
>>>     
>>>       
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>>
>>
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>>
>>   
>>     
>
>
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