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stbrfs.f(3)				      LAPACK				      stbrfs.f(3)

NAME
       stbrfs.f -

SYNOPSIS
   Functions/Subroutines
       subroutine stbrfs (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX, FERR, BERR,
	   WORK, IWORK, INFO)
	   STBRFS

Function/Subroutine Documentation
   subroutine stbrfs (characterUPLO, characterTRANS, characterDIAG, integerN, integerKD,
       integerNRHS, real, dimension( ldab, * )AB, integerLDAB, real, dimension( ldb, * )B,
       integerLDB, real, dimension( ldx, * )X, integerLDX, real, dimension( * )FERR, real,
       dimension( * )BERR, real, dimension( * )WORK, integer, dimension( * )IWORK, integerINFO)
       STBRFS

       Purpose:

	    STBRFS provides error bounds and backward error estimates for the
	    solution to a system of linear equations with a triangular band
	    coefficient matrix.

	    The solution matrix X must be computed by STBTRS or some other
	    means before entering this routine.  STBRFS does not do iterative
	    refinement because doing so cannot improve the backward error.

       Parameters:
	   UPLO

		     UPLO is CHARACTER*1
		     = 'U':  A is upper triangular;
		     = 'L':  A is lower triangular.

	   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)

	   DIAG

		     DIAG is CHARACTER*1
		     = 'N':  A is non-unit triangular;
		     = 'U':  A is unit triangular.

	   N

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

	   KD

		     KD is INTEGER
		     The number of superdiagonals or subdiagonals of the
		     triangular band matrix A.	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 triangular 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).
		     If DIAG = 'U', the diagonal elements of A are not referenced
		     and are assumed to be 1.

	   LDAB

		     LDAB is INTEGER
		     The leading dimension of the array AB.  LDAB >= 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)
		     The 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

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Definition at line 188 of file stbrfs.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

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