CTBCON (3lapack)

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

SYNOPSIS

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

      CHARACTER      DIAG, NORM, UPLO

      INTEGER        INFO, KD, LDAB, N

      REAL           RCOND

      REAL           RWORK( * )

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

PURPOSE

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

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

  RWORK   (workspace) REAL array, dimension (N)

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