NAME

       zpbcon.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zpbcon (UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, RWORK, INFO)
           ZPBCON

Function/Subroutine Documentation

   subroutine zpbcon (character UPLO, integer N, integer KD, complex*16, dimension( ldab, * ) AB,
       integer LDAB, double precision ANORM, double precision RCOND, complex*16, dimension( * )
       WORK, double precision, dimension( * ) RWORK, integer INFO)
       ZPBCON

       Purpose:

            ZPBCON estimates the reciprocal of the condition number (in the
            1-norm) of a complex Hermitian positive definite band matrix using
            the Cholesky factorization A = U**H*U or A = L*L**H computed by
            ZPBTRF.

            An estimate is obtained for norm(inv(A)), and the reciprocal of the
            condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     = 'U':  Upper triangular factor stored in AB;
                     = 'L':  Lower triangular factor stored in AB.

           N

                     N is INTEGER
                     The order of the matrix A.  N >= 0.

           KD

                     KD is INTEGER
                     The number of superdiagonals of the matrix A if UPLO = 'U',
                     or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.

           AB

                     AB is COMPLEX*16 array, dimension (LDAB,N)
                     The triangular factor U or L from the Cholesky factorization
                     A = U**H*U or A = L*L**H of the band matrix A, stored in the
                     first KD+1 rows of the array.  The j-th column of U or L is
                     stored in the j-th column of the array AB as follows:
                     if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
                     if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).

           LDAB

                     LDAB is INTEGER
                     The leading dimension of the array AB.  LDAB >= KD+1.

           ANORM

                     ANORM is DOUBLE PRECISION
                     The 1-norm (or infinity-norm) of the Hermitian band matrix A.

           RCOND

                     RCOND is DOUBLE PRECISION
                     The reciprocal of the condition number of the matrix A,
                     computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
                     estimate of the 1-norm of inv(A) computed in this routine.

           WORK

                     WORK is COMPLEX*16 array, dimension (2*N)

           RWORK

                     RWORK is DOUBLE PRECISION array, dimension (N)

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

Author

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