sgbrfs.f(3)							      LAPACK							       sgbrfs.f(3)

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
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       sgbrfs.f(3)