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 Hermitian indefinite, and provides error bounds and  backward  error
       estimates for the solution

SYNOPSIS

       SUBROUTINE ZHERFS( UPLO,  N,  NRHS,  A,  LDA,  AF, LDAF, IPIV, B, LDB, X, LDX, FERR, BERR,
                          WORK, RWORK, INFO )

           CHARACTER      UPLO

           INTEGER        INFO, LDA, LDAF, LDB, LDX, N, NRHS

           INTEGER        IPIV( * )

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

           COMPLEX*16     A( LDA, * ), AF( LDAF, * ), B( LDB, * ), WORK( * ), X( LDX, * )

PURPOSE

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

ARGUMENTS

        UPLO    (input) CHARACTER*1
                = 'U':  Upper triangle of A is stored;
                = 'L':  Lower triangle of A is stored.

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

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

        A       (input) COMPLEX*16 array, dimension (LDA,N)
                The Hermitian matrix A.  If UPLO = 'U', the leading N-by-N
                upper triangular part of A contains the upper triangular part
                of the matrix A, and the strictly lower triangular part of A
                is not referenced.  If UPLO = 'L', the leading N-by-N lower
                triangular part of A contains the lower triangular part of
                the matrix A, and the strictly upper triangular part of A is
                not referenced.

        LDA     (input) INTEGER
                The leading dimension of the array A.  LDA >= max(1,N).

        AF      (input) COMPLEX*16 array, dimension (LDAF,N)
                The factored form of the matrix A.  AF contains the block
                diagonal matrix D and the multipliers used to obtain the
                factor U or L from the factorization A = U*D*U**H or
                A = L*D*L**H as computed by ZHETRF.

        LDAF    (input) INTEGER
                The leading dimension of the array AF.  LDAF >= max(1,N).

        IPIV    (input) INTEGER array, dimension (N)
                Details of the interchanges and the block structure of D
                as determined by ZHETRF.

        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 ZHETRS.
                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                            ZHERFS(3lapack)