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NAME

       dtbrfs.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dtbrfs (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X,
           LDX, FERR, BERR, WORK, IWORK, INFO)
           DTBRFS

Function/Subroutine Documentation

   subroutine dtbrfs (characterUPLO, characterTRANS, characterDIAG, integerN,
       integerKD, integerNRHS, double precision, dimension( ldab, * )AB,
       integerLDAB, double precision, dimension( ldb, * )B, integerLDB, double
       precision, dimension( ldx, * )X, integerLDX, double precision,
       dimension( * )FERR, double precision, dimension( * )BERR, double
       precision, dimension( * )WORK, integer, dimension( * )IWORK,
       integerINFO)
       DTBRFS

       Purpose:

            DTBRFS 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 DTBTRS or some other
            means before entering this routine.  DTBRFS does not do iterative
            refinement because doing so cannot improve the backward error.

       Parameters:
           UPLO

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

           TRANS

                     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

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

           N

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

           KD

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

           NRHS

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

           AB

                     AB is 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

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

           B

                     B is DOUBLE PRECISION array, dimension (LDB,NRHS)
                     The right hand side matrix B.

           LDB

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

           X

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

           LDX

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

           FERR

                     FERR is DOUBLE PRECISION 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

                     BERR is 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

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

           IWORK

                     IWORK is INTEGER array, dimension (N)

           INFO

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

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

       Definition at line 188 of file dtbrfs.f.

Author

       Generated automatically by Doxygen for LAPACK from the source code.



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