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

NAME

       LAPACK-3  -  improves  the  computed  solution  to  a  system of linear equations when the
       coefficient matrix is banded, and provides error bounds and backward error  estimates  for
       the solution

SYNOPSIS

       SUBROUTINE ZGBRFS( TRANS,  N,  KL,  KU,  NRHS, AB, LDAB, AFB, LDAFB, IPIV, B, LDB, X, LDX,
                          FERR, BERR, WORK, RWORK, INFO )

           CHARACTER      TRANS

           INTEGER        INFO, KL, KU, LDAB, LDAFB, LDB, LDX, N, NRHS

           INTEGER        IPIV( * )

           DOUBLE         PRECISION BERR( * ), FERR( * ), RWORK( * )

           COMPLEX*16     AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), WORK( * ), X( LDX, * )

PURPOSE

       ZGBRFS improves the computed solution to a system of linear equations when the coefficient
       matrix is banded, and provides error bounds and backward error estimates for the solution.

ARGUMENTS

        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)

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

        KL      (input) INTEGER
                The number of subdiagonals within the band of A.  KL >= 0.

        KU      (input) INTEGER
                The number of superdiagonals within the band of A.  KU >= 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) COMPLEX*16 array, dimension (LDAB,N)
                The original band matrix A, stored in rows 1 to KL+KU+1.
                The j-th column of A is stored in the j-th column of the
                array AB as follows:
                AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).

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

        AFB     (input) COMPLEX*16 array, dimension (LDAFB,N)
                Details of the LU factorization of the band matrix A, as
                computed by ZGBTRF.  U is stored as an upper triangular band
                matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
                the multipliers used during the factorization are stored in
                rows KL+KU+2 to 2*KL+KU+1.

        LDAFB   (input) INTEGER
                The leading dimension of the array AFB.  LDAFB >= 2*KL*KU+1.

        IPIV    (input) INTEGER array, dimension (N)
                The pivot indices from ZGBTRF; for 1<=i<=N, row i of the
                matrix was interchanged with row IPIV(i).

        B       (input) COMPLEX*16 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/output) COMPLEX*16 array, dimension (LDX,NRHS)
                On entry, the solution matrix X, as computed by ZGBTRS.
                On exit, the improved 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) COMPLEX*16 array, dimension (2*N)

        RWORK   (workspace) DOUBLE PRECISION array, dimension (N)

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

PARAMETERS

        ITMAX is the maximum number of steps of iterative refinement.

 LAPACK routine (version 3.2)               April 2011                            ZGBRFS(3lapack)