Decompose

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

• SingularValueDecomp
• EigenDecomp