STBRFS(3)      LAPACK routine of NEC Numeric Library Collection      STBRFS(3)



NAME
       STBRFS

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



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

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

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

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

           NRHS      (input)
                     NRHS is INTEGER
                     The number of right hand sides, i.e., the number of columns
                     of the matrices B and X.  NRHS >= 0.

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

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

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

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

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

           FERR      (output)
                     FERR is REAL array, dimension (NRHS)
                     The estimated forward error bound for each solution 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
                     element 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)
                     BERR is 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      (output)
                     WORK is REAL array, dimension (3*N)

           IWORK     (output)
                     IWORK is INTEGER array, dimension (N)

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



LAPACK routine                  31 October 2017                      STBRFS(3)