Should cholesky return upper or lower triangular matrix?
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
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
On 6/27/06, Robert Kern <robert.kern@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.
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- <robert.kern@gmail.com> bounces@lists.sou cc rceforge.net numpy-discussion@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@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. 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 Numpy-discussion@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/numpy-discussion
All, On 6/29/06, mfmorss@aep.com <mfmorss@aep.com> 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
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
participants (5)
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Charles R Harris -
Jon Wright -
Keith Goodman -
mfmorss＠aep.com -
Robert Kern