STBRFS - provide error bounds and backward error estimates
       for the solution to a system of linear  equations  with  a
       triangular band coefficient matrix


SYNOPSIS

       SUBROUTINE STBRFS( 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( * )

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


PURPOSE

       STBRFS provides error bounds and backward error  estimates
       for  the  solution  to a system of linear equations with a
       triangular band coefficient matrix.  The solution matrix X
       must  be  computed  by  STBTRS  or some other means before
       entering this  routine.   STBRFS  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  =
               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


       AB      (input) REAL 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) REAL 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) REAL 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 bound for each solu­
               tion vector X(j) (the j-th column of the  solution
               matrix  X).   If XTRUE is the true solution corre­
               sponding to X(j), FERR(j) is  an  estimated  upper
               bound  for the magnitude of the largest element in
               (X(j) - XTRUE) divided by  the  magnitude  of  the
               largest element in X(j).  The estimate is as reli­
               able as the estimate  for  RCOND,  and  is  almost
               always a slight overestimate of the true error.

       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 element of A or B that makes X(j) an
               exact solution).

       WORK    (workspace) REAL 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



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