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NAME
     dtbrfs - 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 DTBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB,
               B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )

     CHARACTER DIAG, TRANS, UPLO

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

     INTEGER IWORK( * )

     DOUBLE PRECISION AB( LDAB, * ), B( LDB,  *  ),  BERR(  *  ),
               FERR( * ), WORK( * ), X( LDX, * )



     #include <sunperf.h>

     void dtbrfs(char uplo, char trans, char diag, int n, int kd,
               int  nrhs,  double *dab, int ldab, double *db, int
               ldb, double *dx, int  ldx,  double  *ferr,  double
               *berr, int *info) ;

PURPOSE
     DTBRFS 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  DTBTRS  or  some
     other  means  before entering this routine.  DTBRFS 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 = Tran-
               spose)

     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) DOUBLE PRECISION 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)   DOUBLE   PRECISION   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)   DOUBLE   PRECISION   array,    dimension
               (LDX,NRHS)
               The solution matrix X.

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

     FERR      (output) DOUBLE PRECISION array, dimension (NRHS)
               The estimated forward error bound for  each  solu-
               tion  vector X(j) (the j-th column of the solution
               matrix  X).   If  XTRUE  is  the   true   solution
               corresponding  to  X(j),  FERR(j)  is an estimated
               upper bound for the magnitude of the largest  ele-
               ment in (X(j) - XTRUE) divided by the magnitude of
               the largest element in X(j).  The estimate  is  as
               reliable  as the estimate for RCOND, and is almost
               always a slight overestimate of the true error.

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

     WORK      (workspace)  DOUBLE  PRECISION  array,   dimension
               (3*N)

     IWORK     (workspace) INTEGER array, dimension (N)

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

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