ZPTRFS (3lapack)

improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution

SYNOPSIS

  SUBROUTINE ZPTRFS( UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR,
                     WORK, RWORK, INFO )

      CHARACTER      UPLO

      INTEGER        INFO, LDB, LDX, N, NRHS

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

      COMPLEX*16     B( LDB, * ), E( * ), EF( * ), WORK( * ), X( LDX, * )

PURPOSE

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

ARGUMENTS

  UPLO    (input) CHARACTER*1
          Specifies whether the superdiagonal or the subdiagonal of the
          tridiagonal matrix A is stored and the form of the factorization:
          = 'U':  E is the superdiagonal of A, and A = U**H*D*U;
          = 'L':  E is the subdiagonal of A, and A = L*D*L**H.  (The two
          forms are equivalent if A is real.)

  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
          matrix B.  NRHS >= 0.

  D       (input) DOUBLE PRECISION array, dimension (N)
          The n real diagonal elements of the tridiagonal matrix A.

  E       (input) COMPLEX*16 array, dimension (N-1)
          The (n-1) off-diagonal elements of the tridiagonal matrix A (see
          UPLO).

  DF      (input) DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the diagonal matrix D from the
          factorization computed by ZPTTRF.

  EF      (input) COMPLEX*16 array, dimension (N-1)
          The (n-1) off-diagonal elements of the unit bidiagonal factor U or
          L from the factorization computed by ZPTTRF (see UPLO).

  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 ZPTTRS.  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 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).

  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 (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.