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## cpprfs()

subroutine cpprfs | ( | character | uplo,
|  | integer | n,
|  | integer | nrhs,
|  | complex, dimension( * ) | ap,
|  | complex, dimension( * ) | afp,
|  | complex, dimension( ldb, * ) | b,
|  | integer | ldb,
|  | complex, dimension( ldx, * ) | x,
|  | integer | ldx,
|  | real, dimension( * ) | ferr,
|  | real, dimension( * ) | berr,
|  | complex, dimension( * ) | work,
|  | real, dimension( * ) | rwork,
|  | integer | info )

CPPRFS

Download CPPRFS + dependencies [TGZ] [ZIP] [TXT]

Purpose:

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

Parameters

  [in]

  UPLO

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

  [in]

  N

      !>          N is INTEGER
      !>          The order of the matrix A.  N >= 0.
      !>

  [in]

  NRHS

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

  [in]

  AP

      !>          AP is COMPLEX 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)*(2n-j)/2) = A(i,j) for j<=i<=n.
      !>

  [in]

  AFP

      !>          AFP is COMPLEX array, dimension (N*(N+1)/2)
      !>          The triangular factor U or L from the Cholesky factorization
      !>          A = U**H*U or A = L*L**H, as computed by SPPTRF/CPPTRF,
      !>          packed columnwise in a linear array in the same format as A
      !>          (see AP).
      !>

  [in]

  B

      !>          B is COMPLEX array, dimension (LDB,NRHS)
      !>          The right hand side matrix B.
      !>

  [in]

  LDB

      !>          LDB is INTEGER
      !>          The leading dimension of the array B.  LDB >= max(1,N).
      !>

  [in,out]

  X

      !>          X is COMPLEX array, dimension (LDX,NRHS)
      !>          On entry, the solution matrix X, as computed by CPPTRS.
      !>          On exit, the improved solution matrix X.
      !>

  [in]

  LDX

      !>          LDX is INTEGER
      !>          The leading dimension of the array X.  LDX >= max(1,N).
      !>

  [out]

  FERR

      !>          FERR is REAL 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.
      !>

  [out]

  BERR

      !>          BERR is REAL 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).
      !>

  [out]

  WORK

      !>          WORK is COMPLEX array, dimension (2*N)
      !>

  [out]

  RWORK

      !>          RWORK is REAL array, dimension (N)
      !>

  [out]

  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.