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

mfmorss at aep.com mfmorss at aep.com
Thu Jun 29 08:16:38 CDT 2006


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 at gmail.                                             
             com>                                                       To 
             Sent by:                  "Robert Kern"                       
             numpy-discussion-         <robert.kern at gmail.com>             
             bounces at lists.sou                                          cc 
             rceforge.net              numpy-discussion at lists.sourceforge. 
                                       net                                 
                                                                   Subject 
             06/27/2006 11:25          Re: [Numpy-discussion] Should       
             PM                        cholesky return upper or            
                                       lowertriangular matrix?             
                                                                           
                                                                           
                                                                           
                                                                           
                                                                           
                                                                           




On 6/27/06, Robert Kern <robert.kern at gmail.com> 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.

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