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DGTRFS(l)					)					DGTRFS(l)

NAME
       DGTRFS  -  improve  the computed solution to a system of linear equations when the coeffi-
       cient matrix is tridiagonal, and provides error bounds and backward  error  estimates  for
       the solution

SYNOPSIS
       SUBROUTINE DGTRFS( 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( * )

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

PURPOSE
       DGTRFS 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) DOUBLE PRECISION array, dimension (N-1)
	       The (n-1) subdiagonal elements of A.

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

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

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

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

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

       DU2     (input) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDX,NRHS)
	       On entry, the solution matrix X, as computed by DGTTRS.	 On  exit,  the  improved
	       solution matrix X.

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

       FERR    (output) DOUBLE PRECISION 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 esti-
	       mate is as reliable as the estimate for RCOND, and is almost always a slight over-
	       estimate of the true error.

       BERR    (output) DOUBLE PRECISION 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 solu-
	       tion).

       WORK    (workspace) DOUBLE PRECISION 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 				DGTRFS(l)
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