CPTCON (3lapack)

compute 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 CPTTRF

SYNOPSIS

  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 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 CPTTRF.

  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))).

ARGUMENTS

  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 (N-1)
          The (n-1) off-diagonal elements of the unit bidiagonal factor U or
          L from the factorization of A, as computed by CPTTRF.

  ANORM   (input) REAL
          The 1-norm 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 1-norm of inv(A)
          computed in this routine.

  RWORK   (workspace) REAL array, dimension (N)

  INFO    (output) INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th 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.