ZHPRFS (3lapack)

improve 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

SYNOPSIS

  SUBROUTINE ZHPRFS( UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, FERR,
                     BERR, WORK, RWORK, INFO )

      CHARACTER      UPLO

      INTEGER        INFO, LDB, LDX, N, NRHS

      INTEGER        IPIV( * )

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

      COMPLEX*16     AFP( * ), AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )

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.

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.

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

  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 ZHPTRS.  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.