- SUBROUTINE ZPTCON(
- N, D, E, ANORM, RCOND, RWORK, INFO )
- INTEGER INFO, N
- DOUBLE PRECISION ANORM, RCOND
- DOUBLE PRECISION D( * ), RWORK( * )
- COMPLEX*16 E( * )
PURPOSEZPTCON computes the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by ZPTTRF. Norm(inv(A)) is computed by a direct method, and the reciprocal of the condition number is computed as
RCOND = 1 / (ANORM * norm(inv(A))).
- N (input) INTEGER
- The order of the matrix A. N >= 0.
- D (input) DOUBLE PRECISION array, dimension (N)
- The n diagonal elements of the diagonal matrix D from the factorization of A, as computed by ZPTTRF.
- E (input) COMPLEX*16 array, dimension (N-1)
- The (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization of A, as computed by ZPTTRF.
- ANORM (input) DOUBLE PRECISION
- The 1-norm of the original matrix A.
- RCOND (output) DOUBLE PRECISION
- The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the 1-norm of inv(A) computed in this routine.
- RWORK (workspace) DOUBLE PRECISION array, dimension (N)
- INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
FURTHER DETAILSThe method used is described in Nicholas J. Higham, "Efficient Algorithms for Computing the Condition Number of a Tridiagonal Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.