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

Complex numbers

new in Analytica 4.5. When «C» contains complex numbers, then the matrix must be Hermitian and positive definite. The Hermitian condition is the same as the symmetric condition for real-valued matrices, but requires the transpose to be the complex conjugate of the matrix.

See Also

• SingularValueDecomp
• EigenDecomp