ZTBCON(3)      LAPACK routine of NEC Numeric Library Collection      ZTBCON(3)



NAME
       ZTBCON

SYNOPSIS
       SUBROUTINE ZTBCON (NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK,
           RWORK, INFO)



PURPOSE
            ZTBCON estimates the reciprocal of the condition number of a
            triangular band matrix A, in either the 1-norm or the infinity-norm.

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




ARGUMENTS
           NORM      (input)
                     NORM is CHARACTER*1
                     Specifies whether the 1-norm condition number or the
                     infinity-norm condition number is required:
                     = '1' or 'O':  1-norm;
                     = 'I':         Infinity-norm.

           UPLO      (input)
                     UPLO is CHARACTER*1
                     = 'U':  A is upper triangular;
                     = 'L':  A is lower triangular.

           DIAG      (input)
                     DIAG is CHARACTER*1
                     = 'N':  A is non-unit triangular;
                     = 'U':  A is unit triangular.

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

           KD        (input)
                     KD is INTEGER
                     The number of superdiagonals or subdiagonals of the
                     triangular band matrix A.  KD >= 0.

           AB        (input)
                     AB is COMPLEX*16 array, dimension (LDAB,N)
                     The upper or lower triangular band matrix A, stored in the
                     first kd+1 rows of the array. The j-th column of A is stored
                     in the j-th column of the array AB as follows:
                     if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
                     if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
                     If DIAG = 'U', the diagonal elements of A are not referenced
                     and are assumed to be 1.

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

           RCOND     (output)
                     RCOND is DOUBLE PRECISION
                     The reciprocal of the condition number of the matrix A,
                     computed as RCOND = 1/(norm(A) * norm(inv(A))).

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

           RWORK     (output)
                     RWORK is DOUBLE PRECISION array, dimension (N)

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



LAPACK routine                  31 October 2017                      ZTBCON(3)