Previous: zsytrs Up: ../lapack-z.html Next: ztbrfs

ztbcon

 NAME
      ZTBCON - estimate the reciprocal of the condition number of
      a triangular band matrix A, in either the 1-norm or the
      infinity-norm

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

          CHARACTER      DIAG, NORM, UPLO

          INTEGER        INFO, KD, LDAB, N

          DOUBLE         PRECISION RCOND

          DOUBLE         PRECISION RWORK( * )

          COMPLEX*16     AB( LDAB, * ), WORK( * )

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

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

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

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

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

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

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

      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