zpbrfs.f(3)

NAME
zpbrfs.f -

SYNOPSIS

  Functions/Subroutines
subroutine ZPBRFS (UPLO, N, KD, NRHS, AB, LDAB, AFB, LDAFB, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
ZPBRFS

Function/Subroutine Documentation

  subroutine ZPBRFS (CHARACTERUPLO, INTEGERN, INTEGERKD, INTEGERNRHS, COMPLEX*16, dimension( ldab, * )AB, INTEGERLDAB, COMPLEX*16, dimension( ldafb, * )AFB, INTEGERLDAFB, COMPLEX*16, dimension( ldb, * )B, INTEGERLDB, COMPLEX*16, dimension( ldx, * )X, INTEGERLDX, DOUBLE PRECISION, dimension( * )FERR, DOUBLE PRECISION, dimension( * )BERR, COMPLEX*16, dimension( * )WORK, DOUBLE PRECISION, dimension( * )RWORK, INTEGERINFO)

ZPBRFS

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:
    UPLO

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

    N

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

    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.

    NRHS

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

    AB

              AB is DOUBLE PRECISION 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).

    LDAB

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

    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).

    LDAFB

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

    B

              B is COMPLEX*16 array, dimension (LDB,NRHS)
              The right hand side matrix B.

    LDB

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

    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.

    LDX

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

    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.

    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).

    WORK

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

    RWORK

              RWORK is DOUBLE PRECISION array, dimension (N)

    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'.

Date:
    November 2011

Definition at line 189 of file zpbrfs.f'.

Author

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