Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3 - provides error bounds and backward error estimates for the solution to a system
       of linear equations with a triangular 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, * )

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.

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 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 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) 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 illegal value

 LAPACK routine (version 3.3.1)             April 2011                            DTBRFS(3lapack)