Computing the Inverse of a Positive Definite Matrix (potri)

potri computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization computed by trf_.

Real Variant

The Cholesky factorization reads \( A = U^T U \) or \( A = L L^T \).

A

(input/output) real valued SyMatrix
The triangular factor \( U \) or \( L \) from the Cholesky factorization \( A = U^T U \) or \( A = L L^T \), as computed by potrf.

Return value:

i=0

Successful exit.

i>0

The \( i \)-th diagonal element of the factor \( U \) or \( L \) is zero, and the inverse could not be computed.

Complex Variant

The Cholesky factorization reads \( A = U^H U \) or \( A = L L^H \).

A

(input/output) complex valued HeMatrix
The triangular factor \( U \) or \( L \) from the Cholesky factorization \( A = U^H U \) or \( A = L L^H \), as computed by potrf.

Return value:

i=0

Successful exit.

i>0

The \( i \)-th diagonal element of the factor \( U \) or \( L \) is zero, and the inverse could not be computed.