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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