SRC/zhprfs.f(3)

NAME
SRC/zhprfs.f

SYNOPSIS

  Functions/Subroutines
subroutine zhprfs (uplo, n, nrhs, ap, afp, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
ZHPRFS

Function/Subroutine Documentation

  subroutine zhprfs (character uplo, integer n, integer nrhs, complex*16, dimension( * ) ap, complex*16, dimension( * ) afp, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldx, * ) x, integer ldx, double precision, dimension( * ) ferr, double precision, dimension( * ) berr, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)

ZHPRFS

Purpose:

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

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  Lower triangle of A is stored.
    !>

    N

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

    AP

    !>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
    !>          The upper or lower triangle of the Hermitian matrix A, packed
    !>          columnwise in a linear array.  The j-th column of A is stored
    !>          in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
    !>

    AFP

    !>          AFP is COMPLEX*16 array, dimension (N*(N+1)/2)
    !>          The factored form of the matrix A.  AFP 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 ZHPTRF, stored as a packed
    !>          triangular matrix.
    !>

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the block structure of D
    !>          as determined by ZHPTRF.
    !>

    B

    !>          B is COMPLEX*16 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 COMPLEX*16 array, dimension (LDX,NRHS)
    !>          On entry, the solution matrix X, as computed by ZHPTRS.
    !>          On exit, the improved 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 COMPLEX*16 array, dimension (2*N)
    !>

    RWORK

    !>          RWORK is DOUBLE PRECISION array, dimension (N)
    !>

    INFO

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

Internal Parameters:

    !>  ITMAX is the maximum number of steps of iterative refinement.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 178 of file zhprfs.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.