Difference between revisions of "Decompose"

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Cholesky decomposition computes a lower diagonal matrix L
 
Cholesky decomposition computes a lower diagonal matrix L
 
such that L * L' = C, where L' is the transpose of L.
 
such that L * L' = C, where L' is the transpose of L.
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= Testing for Positive Definiteness =
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To avoid an error, the following [[User-Defined Functions|UDF]] can be used to test for positive definiteness:
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Function IsPosDefinite( A : Number[I,J] ; I,J : Index )
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Description: Returns true (1) if A is positive-definite, 0 (false) otherwise.
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Definition: min([[EigenDecomp]](A+[[Transpose]](A,I,J),I,J)[.Item='value'],J)>0
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= See Also =
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* [[SingularValueDecomp]]
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* [[EigenDecomp]]

Revision as of 14:08, 11 October 2007


Decompose(C,I,J)

Returns the Cholesky decomposition (square root) matrix of matrix C along dimensions I and J. Matrix C must be symmetric and positive-definite. (Positive-definite means that v * C * v > 0, for all vectors v.)

Cholesky decomposition computes a lower diagonal matrix L such that L * L' = C, where L' is the transpose of L.

Testing for Positive Definiteness

To avoid an error, the following UDF can be used to test for positive definiteness: 

Function IsPosDefinite( A : Number[I,J] ; I,J : Index ) 
Description: Returns true (1) if A is positive-definite, 0 (false) otherwise.
Definition: min(EigenDecomp(A+Transpose(A,I,J),I,J)[.Item='value'],J)>0

See Also

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