numpy-discussion

[Numpy-discussion] Should cholesky return upper or lower triangular matrix?

[Keith G. <kwg...@gm...>]

Isn't the Cholesky decomposition by convention an upper triangular
matrix? I noticed, by porting Octave code, that linalg.cholesky
returns the lower triangular matrix.

References:

http://mathworld.wolfram.com/CholeskyDecomposition.html
http://www.mathworks.com/access/helpdesk/help/techdoc/ref/chol.html

Re: [Numpy-discussion] Should cholesky return upper or lower triangular matrix?

[Robert K. <rob...@gm...>]

Keith Goodman wrote:
> Isn't the Cholesky decomposition by convention an upper triangular
> matrix? I noticed, by porting Octave code, that linalg.cholesky
> returns the lower triangular matrix.
> 
> References:
> 
> http://mathworld.wolfram.com/CholeskyDecomposition.html
> http://www.mathworks.com/access/helpdesk/help/techdoc/ref/chol.html

Lower:
http://en.wikipedia.org/wiki/Cholesky_decomposition
http://www.math-linux.com/spip.php?article43
http://planetmath.org/?op=getobj&from=objects&id=1287
http://rkb.home.cern.ch/rkb/AN16pp/node33.html#SECTION000330000000000000000
http://www.riskglossary.com/link/cholesky_factorization.htm
http://www.library.cornell.edu/nr/bookcpdf/c2-9.pdf

If anything, the convention appears to be lower-triangular.

-- 
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless enigma
  that is made terrible by our own mad attempt to interpret it as though it had
  an underlying truth."
   -- Umberto Eco

Re: [Numpy-discussion] Should cholesky return upper or lower triangular matrix?

[Keith G. <kwg...@gm...>]

On 6/27/06, Robert Kern <rob...@gm...> wrote:
> Keith Goodman wrote:
> > Isn't the Cholesky decomposition by convention an upper triangular
> > matrix? I noticed, by porting Octave code, that linalg.cholesky
> > returns the lower triangular matrix.
> >
> > References:
> >
> > http://mathworld.wolfram.com/CholeskyDecomposition.html
> > http://www.mathworks.com/access/helpdesk/help/techdoc/ref/chol.html
>
> Lower:
> http://en.wikipedia.org/wiki/Cholesky_decomposition
> http://www.math-linux.com/spip.php?article43
> http://planetmath.org/?op=getobj&from=objects&id=1287
> http://rkb.home.cern.ch/rkb/AN16pp/node33.html#SECTION000330000000000000000
> http://www.riskglossary.com/link/cholesky_factorization.htm
> http://www.library.cornell.edu/nr/bookcpdf/c2-9.pdf
>
> If anything, the convention appears to be lower-triangular.

If you give me a second, I'll show you that the wikipedia supports my claim.

OK. Lower it is. It will save me a transpose when I calculate joint
random variables.

Re: [Numpy-discussion] Should cholesky return upper or lowertriangularmatrix?

[<mf...@ae...>]

The SAS IML Cholesky function "root" returns upper triangular.  Quoting the
SAS documentation:

The ROOT function performs the Cholesky decomposition of a matrix (for
example, A) such that
U'U = A
where U is upper triangular. The matrix A must be symmetric and positive
definite.

Mark F. Morss
Principal Analyst, Market Risk
American Electric Power


                                                                           
             "Keith Goodman"                                               
             <kwgoodman@gmail.                                             
             com>                                                       To 
             Sent by:                  "Robert Kern"                       
             numpy-discussion-         <rob...@gm...>             
             bo...@li...u                                          cc 
             rceforge.net              num...@li...urceforge. 
                                       net                                 
                                                                   Subject 
             06/27/2006 11:25          Re: [Numpy-discussion] Should       
             PM                        cholesky return upper or            
                                       lowertriangular matrix?             
                                                                           
                                                                           
                                                                           
                                                                           
                                                                           
                                                                           




On 6/27/06, Robert Kern <rob...@gm...> wrote:
> Keith Goodman wrote:
> > Isn't the Cholesky decomposition by convention an upper triangular
> > matrix? I noticed, by porting Octave code, that linalg.cholesky
> > returns the lower triangular matrix.
> >
> > References:
> >
> > http://mathworld.wolfram.com/CholeskyDecomposition.html
> > http://www.mathworks.com/access/helpdesk/help/techdoc/ref/chol.html
>
> Lower:
> http://en.wikipedia.org/wiki/Cholesky_decomposition
> http://www.math-linux.com/spip.php?article43
> http://planetmath.org/?op=getobj&from=objects&id=1287
>
http://rkb.home.cern.ch/rkb/AN16pp/node33.html#SECTION000330000000000000000
> http://www.riskglossary.com/link/cholesky_factorization.htm
> http://www.library.cornell.edu/nr/bookcpdf/c2-9.pdf
>
> If anything, the convention appears to be lower-triangular.

If you give me a second, I'll show you that the wikipedia supports my
claim.

OK. Lower it is. It will save me a transpose when I calculate joint
random variables.

Using Tomcat but need to do more? Need to support web services, security?
Get stuff done quickly with pre-integrated technology to make your job
easier
Download IBM WebSphere Application Server v.1.0.1 based on Apache Geronimo
http://sel.as-us.falkag.net/sel?cmd=lnk&kid=120709&bid=263057&dat=121642
_______________________________________________
Numpy-discussion mailing list
Num...@li...
https://lists.sourceforge.net/lists/listinfo/numpy-discussion

Re: [Numpy-discussion] Should cholesky return upper or lowertriangularmatrix?

[Charles R H. <cha...@gm...>]

All,

On 6/29/06, mf...@ae... <mf...@ae...> wrote:
>
> The SAS IML Cholesky function "root" returns upper triangular.  Quoting
> the
> SAS documentation:
>
> The ROOT function performs the Cholesky decomposition of a matrix (for
> example, A) such that
> U'U = A
> where U is upper triangular. The matrix A must be symmetric and positive
> definite.


Does it matter whether the lower or upper triangular part is stored? We
should just pick one convention and stick with it. That is simpler than,
say, ATLAS where the choice is one of the parameters passed to the
subroutine. I vote for lower triangular myself, if only because that was my
choice last time I implemented a Cholesky factorization.

Chuck

Re: [Numpy-discussion] Should cholesky return upper or

[Jon W. <wr...@es...>]

> Does it matter whether the lower or upper triangular part is stored? 
> We should just pick one convention and stick with it. That is simpler 
> than, say, ATLAS where the choice is one of the parameters passed to 
> the subroutine. I vote for lower triangular myself, if only because 
> that was my choice last time I implemented a Cholesky factorization.

Wouldn't a keyword argument make more sense, there's a default, but you 
aren't denied access to ATLAS? It matters if you pass the factorisation 
to a legacy code which expects things to be a particular way around.

Jon