SGTRFS(l)								 )								 SGTRFS(l)

NAME

       SGTRFS  -  improve  the	computed  solution  to a system of linear equations when the coefficient matrix is tridiagonal, and provides error
       bounds and backward error estimates for the solution

SYNOPSIS

       SUBROUTINE SGTRFS( TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )

	   CHARACTER	  TRANS

	   INTEGER	  INFO, LDB, LDX, N, NRHS

	   INTEGER	  IPIV( * ), IWORK( * )

	   REAL 	  B( LDB, * ), BERR( * ), D( * ), DF( * ), DL( * ), DLF( * ), DU( * ), DU2( * ), DUF( * ), FERR( * ), WORK( * ), X( LDX, *
			  )

PURPOSE

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

ARGUMENTS

       TRANS   (input) 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       (input) INTEGER
	       The order of the matrix A.  N >= 0.

       NRHS    (input) INTEGER
	       The number of right hand sides, i.e., the number of columns of the matrix B.  NRHS >= 0.

       DL      (input) REAL array, dimension (N-1)
	       The (n-1) subdiagonal elements of A.

       D       (input) REAL array, dimension (N)
	       The diagonal elements of A.

       DU      (input) REAL array, dimension (N-1)
	       The (n-1) superdiagonal elements of A.

       DLF     (input) REAL array, dimension (N-1)
	       The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by SGTTRF.

       DF      (input) REAL array, dimension (N)
	       The n diagonal elements of the upper triangular matrix U from the LU factorization of A.

       DUF     (input) REAL array, dimension (N-1)
	       The (n-1) elements of the first superdiagonal of U.

       DU2     (input) REAL array, dimension (N-2)
	       The (n-2) elements of the second superdiagonal of U.

       IPIV    (input) INTEGER array, dimension (N)
	       The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i).  IPIV(i) will always be either i or i+1;
	       IPIV(i) = i indicates a row interchange was not required.

       B       (input) REAL array, dimension (LDB,NRHS)
	       The right hand side matrix B.

       LDB     (input) INTEGER
	       The leading dimension of the array B.  LDB >= max(1,N).

       X       (input/output) REAL array, dimension (LDX,NRHS)
	       On entry, the solution matrix X, as computed by SGTTRS.	On exit, the improved solution matrix X.

       LDX     (input) INTEGER
	       The leading dimension of the array X.  LDX >= max(1,N).

       FERR    (output) 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    (output) 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    (workspace) REAL array, dimension (3*N)

       IWORK   (workspace) INTEGER array, dimension (N)

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value

PARAMETERS

       ITMAX is the maximum number of steps of iterative refinement.

LAPACK version 3.0						   15 June 2000 							 SGTRFS(l)