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ctbrfs

 NAME
      CTBRFS - provide error bounds and backward error estimates
      for the solution to a system of linear equations with a tri-
      angular band coefficient matrix

 SYNOPSIS
      SUBROUTINE CTBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB,
                         B, LDB, X, LDX, FERR, BERR, WORK, RWORK,
                         INFO )

          CHARACTER      DIAG, TRANS, UPLO

          INTEGER        INFO, KD, LDAB, LDB, LDX, N, NRHS

          REAL           BERR( * ), FERR( * ), RWORK( * )

          COMPLEX        AB( LDAB, * ), B( LDB, * ), WORK( * ), X(
                         LDX, * )

 PURPOSE
      CTBRFS provides error bounds and backward error estimates
      for the solution to a system of linear equations with a tri-
      angular band coefficient matrix.

      The solution matrix X must be computed by CTBTRS or some
      other means before entering this routine.  CTBRFS does not
      do iterative refinement because doing so cannot improve the
      backward error.

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

      TRANS   (input) CHARACTER*1
              Specifies the form of the system of equations:
              = 'N':  A * X = B     (No transpose)
              = 'T':  A**T * X = B  (Transpose)
              = 'C':  A**H * X = B  (Conjugate transpose)

      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.

      NRHS    (input) INTEGER
              The number of right hand sides, i.e., the number of
              columns of the matrices B and X.  NRHS >= 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.

      B       (input) COMPLEX array, dimension (LDB,NRHS)
              The right hand side matrix B.

      LDB     (input) INTEGER
              The leading dimension of the array B.  LDB >=
              max(1,N).

      X       (input) COMPLEX array, dimension (LDX,NRHS)
              The solution matrix X.

      LDX     (input) INTEGER
              The leading dimension of the array X.  LDX >=
              max(1,N).

      FERR    (output) REAL array, dimension (NRHS)
              The estimated forward error bounds for each solution
              vector X(j) (the j-th column of the solution matrix
              X).  If XTRUE is the true solution, FERR(j) bounds
              the magnitude of the largest entry in (X(j) - XTRUE)
              divided by the magnitude of the largest entry in
              X(j).  The quality of the error bound depends on the
              quality of the estimate of norm(inv(A)) computed in
              the code; if the estimate of norm(inv(A)) is accu-
              rate, the error bound is guaranteed.

      BERR    (output) REAL array, dimension (NRHS)
              The componentwise relative backward error of each
              solution vector X(j) (i.e., the smallest relative
              change in any entry of A or B that makes X(j) an
              exact solution).

      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