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## zpbrfs()

subroutine zpbrfs | ( | character | uplo,
|  | integer | n,
|  | integer | kd,
|  | integer | nrhs,
|  | complex*16, dimension( ldab, * ) | ab,
|  | integer | ldab,
|  | complex*16, dimension( ldafb, * ) | afb,
|  | integer | ldafb,
|  | 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 )

ZPBRFS

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

Purpose:

      !>
      !> ZPBRFS improves the computed solution to a system of linear
      !> equations when the coefficient matrix is Hermitian positive definite
      !> and banded, 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]

  KD

      !>          KD is INTEGER
      !>          The number of superdiagonals of the matrix A if UPLO = 'U',
      !>          or the number of subdiagonals if UPLO = 'L'.  KD >= 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]

  AB

      !>          AB is COMPLEX*16 array, dimension (LDAB,N)
      !>          The upper or lower triangle of the Hermitian band matrix A,
      !>          stored in the first KD+1 rows of the array.  The j-th column
      !>          of A is stored in the j-th column of the array AB as follows:
      !>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
      !>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
      !>

  [in]

  LDAB

      !>          LDAB is INTEGER
      !>          The leading dimension of the array AB.  LDAB >= KD+1.
      !>

  [in]

  AFB

      !>          AFB is COMPLEX*16 array, dimension (LDAFB,N)
      !>          The triangular factor U or L from the Cholesky factorization
      !>          A = U**H*U or A = L*L**H of the band matrix A as computed by
      !>          ZPBTRF, in the same storage format as A (see AB).
      !>

  [in]

  LDAFB

      !>          LDAFB is INTEGER
      !>          The leading dimension of the array AFB.  LDAFB >= KD+1.
      !>

  [in]

  B

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

  [out]

  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).
      !>

  [out]

  WORK

      !>          WORK is COMPLEX*16 array, dimension (2*N)
      !>

  [out]

  RWORK

      !>          RWORK is DOUBLE PRECISION 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.