NAME

       sgbrfs.f -

SYNOPSIS

   Functions/Subroutines
       subroutine sgbrfs (TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, IPIV, B, LDB, X, LDX,
           FERR, BERR, WORK, IWORK, INFO)
           SGBRFS

Function/Subroutine Documentation

   subroutine sgbrfs (characterTRANS, integerN, integerKL, integerKU, integerNRHS, real,
       dimension( ldab, * )AB, integerLDAB, real, dimension( ldafb, * )AFB, integerLDAFB,
       integer, dimension( * )IPIV, real, dimension( ldb, * )B, integerLDB, real, dimension( ldx,
       * )X, integerLDX, real, dimension( * )FERR, real, dimension( * )BERR, real, dimension( *
       )WORK, integer, dimension( * )IWORK, integerINFO)
       SGBRFS

       Purpose:

            SGBRFS improves the computed solution to a system of linear
            equations when the coefficient matrix is banded, and provides
            error bounds and backward error estimates for the solution.

       Parameters:
           TRANS

                     TRANS is CHARACTER*1
                     Specifies the form of the system of equations:
                     = 'N':  A * X = B     (No transpose)
                     = 'T':  A**T * X = B  (Transpose)
                     = 'C':  A**H * X = B  (Conjugate transpose = Transpose)

           N

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

           KL

                     KL is INTEGER
                     The number of subdiagonals within the band of A.  KL >= 0.

           KU

                     KU is INTEGER
                     The number of superdiagonals within the band of A.  KU >= 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 original band matrix A, stored in rows 1 to KL+KU+1.
                     The j-th column of A is stored in the j-th column of the
                     array AB as follows:
                     AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).

           LDAB

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

           AFB

                     AFB is REAL array, dimension (LDAFB,N)
                     Details of the LU factorization of the band matrix A, as
                     computed by SGBTRF.  U is stored as an upper triangular band
                     matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
                     the multipliers used during the factorization are stored in
                     rows KL+KU+2 to 2*KL+KU+1.

           LDAFB

                     LDAFB is INTEGER
                     The leading dimension of the array AFB.  LDAFB >= 2*KL*KU+1.

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     The pivot indices from SGBTRF; for 1<=i<=N, row i of the
                     matrix was interchanged with row IPIV(i).

           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 SGBTRS.
                     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

       Definition at line 204 of file sgbrfs.f.

Author

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