[Fwd: RE: Cholesky Decomposition in JAMA vs Matlab]

[Ron Boisvert <boisvert@nist.gov>]

Sender: "Cleve Moler" <Cleve.Moler@mathworks.com>
Subject: RE: Cholesky Decomposition in JAMA vs Matlab


Your matrix is not symmetric.  JAMA checks for symmetry.  MATLAB looks
at only the upper triangle and assumes that the lower triangle is the
reflection of the upper.  Please read the comments at the beginning of
the Java code and the MATLAB help message carefully.
  -- Cleve

-----Original Message-----
From: jama@nist.gov [mailto:jama@nist.gov] On Behalf Of Sione
Sent: Wednesday, April 02, 2008 8:45 AM
To: Multiple recipients of list
Subject: Re: Cholesky Decomposition in JAMA vs Matlab

I have this  [2 x 2]  matrix below :
--------------------------------

double[][] array = {{0.0442 ,  -0.0232},  {-0.0233 ,   0.0222}};
Matrix A = new Matrix(array);
CholeskyDecomposition  cholesky = new CholeskyDecomposition(A);
System.out.println(" Symmetric and positive definite =
"+cholesky.isSPD());

-------------------------------
where the  isSPD method return a false, ie, matrix  A is   NOT   
"Symmetric and positive definite".

In  Matlab , the same matrix gives  a   "p = 0" , which means that  
matrix  A  is
"Symmetric and positive definite".

Why is the difference  Cleve ?

Any hint would be appreciated.

Cheers,
Sione.


Cleve Moler wrote:
> Yes, I can see why you were confused.
> You can always look at the result and see if R'*R is equal to A.
>  -- Cleve
>
> -----Original Message-----
> From: jama@nist.gov [mailto:jama@nist.gov] On Behalf Of Sione
> Sent: Monday, March 03, 2008 2:09 PM
> To: Multiple recipients of list
> Subject: Re: Cholesky Decomposition in JAMA vs Matlab
>
> I have just read the matlab user-guide carefully and concluded that :
>
> p = 0  in Cholesky to mean that  matrix  A is symmetric and positive 
> definite which is "true" instead of being "false" (where a zero in 
> matlab traditionally means "false").  So, the cholesky in JAMA has 
> exactly the same output as in cholesky in Matlab, therefore my own 
> question has been sorted.
>
> Cheers,
> Sione.
>
>
> Sione wrote:
>> Please discard my previous message as my example matrix was wrong. 
>> Here is the correct codes:
>>
>> Does anyone know why the following output in JAMA is different from 
>> that in Matlab for cholesky decomposition?
>>
>> JAMA:
>> ----
>> public static void main(String[] args){
>>    double[][] d = {{1,    -1},{ -1,     2}};
>>    Matrix A = new Matrix(d);
>>    CholeskyDecomposition chol = new CholeskyDecomposition(A);
>>    Matrix R = chol.getL();
>>    System.out.println(" chol.isSPD = "+chol.isSPD());
>>  }
>>
>> The output is :==>  "chol.isSPD = true"
>>
>>
>> Matlab:
>> ------
>>
>> A = [1    -1; -1     2];
>> [R,p] = chol(A);
>>
>> The output for 'p' is :==>  p = 0
>>
>>
>> In Matlab, anything that is zero is regarded as  false (logical 
>> value), and this means that  'chol' function in matlab returns a 
>> "FALSE" (ie, p=0)  that A is not symmetric and positive definite,  
>> while that of  JAMA returns "TRUE".
>>
>> Is my interpretation of both the outputs in JAMA vs Matlab is correct

>> here, that they are different for the same matrix A?
>>
>> Any hint (perhaps from Cleve Moler) would be appreciated.
>>
>> Cheers,
>> Sione.
>>
>>
>>
>>
>>
>>
>
>
>
>
>
>
>
>