NAME

       spbrfs.f -

SYNOPSIS

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

Function/Subroutine Documentation

   subroutine spbrfs (character UPLO, integer N, integer KD, integer NRHS, real, dimension( ldab,
       * ) AB, integer LDAB, real, dimension( ldafb, * ) AFB, integer LDAFB, real, dimension(
       ldb, * ) B, integer LDB, real, dimension( ldx, * ) X, integer LDX, real, dimension( * )
       FERR, real, dimension( * ) BERR, real, dimension( * ) WORK, integer, dimension( * ) IWORK,
       integer INFO)
       SPBRFS

       Purpose:

            SPBRFS improves the computed solution to a system of linear
            equations when the coefficient matrix is symmetric 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 REAL array, dimension (LDAB,N)
                     The upper or lower triangle of the symmetric 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 REAL array, dimension (LDAFB,N)
                     The triangular factor U or L from the Cholesky factorization
                     A = U**T*U or A = L*L**T of the band matrix A as computed by
                     SPBTRF, 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 REAL 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 REAL array, dimension (LDX,NRHS)
                     On entry, the solution matrix X, as computed by SPBTRS.
                     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 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.

           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).

           WORK

                     WORK is REAL array, dimension (3*N)

           IWORK

                     IWORK is INTEGER 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

Author

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