ZPPRFS (3lapack)

improve 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

SYNOPSIS

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

      CHARACTER      UPLO

      INTEGER        INFO, LDB, LDX, N, NRHS

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

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

PURPOSE

  ZPPRFS 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.

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)*(2n-j)/2) = A(i,j) for
          j<=i<=n.

  AFP     (input) COMPLEX*16 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 DPPTRF/ZPPTRF, packed
          columnwise in a linear array in the same format as A (see AP).

  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 ZPPTRS.  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.