sgbrfs.f3

!>
!> 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.
!> 

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
!> 

!>  ITMAX is the maximum number of steps of iterative refinement.
!> 

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