zherfs(3S)

NAME
     ZHERFS - improve 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, * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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.

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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