cptcon (l)  Linux Man Pages
cptcon: computes the reciprocal of the condition number (in the 1norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by CPTTRF
NAME
CPTCON  computes the reciprocal of the condition number (in the 1norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by CPTTRFSYNOPSIS
 SUBROUTINE CPTCON(
 N, D, E, ANORM, RCOND, RWORK, INFO )
 INTEGER INFO, N
 REAL ANORM, RCOND
 REAL D( * ), RWORK( * )
 COMPLEX E( * )
PURPOSE
CPTCON computes the reciprocal of the condition number (in the 1norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by CPTTRF. Norm(inv(A)) is computed by a direct method, and the reciprocal of the condition number is computed asARGUMENTS
 N (input) INTEGER
 The order of the matrix A. N >= 0.
 D (input) REAL array, dimension (N)
 The n diagonal elements of the diagonal matrix D from the factorization of A, as computed by CPTTRF.
 E (input) COMPLEX array, dimension (N1)
 The (n1) offdiagonal elements of the unit bidiagonal factor U or L from the factorization of A, as computed by CPTTRF.
 ANORM (input) REAL
 The 1norm of the original matrix A.
 RCOND (output) REAL
 The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the 1norm of inv(A) computed in this routine.
 RWORK (workspace) REAL array, dimension (N)
 INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
FURTHER DETAILS
The 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.