[Numpy-discussion] Should cholesky return upper or lowertriangularmatrix? (original) (raw)

mfmorss at aep.com mfmorss at aep.com
Thu Jun 29 09:16:38 EDT 2006

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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"                                               
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         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/Choleskydecomposition 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/choleskyfactorization.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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