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DGTRFS(1)		 LAPACK routine (version 3.2)		     DGTRFS(1)

NAME
       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

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 fac‐
	       torization 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 estimate is as reliable as the estimate for RCOND,  and  is
	       almost always a slight overestimate of the true error.

       BERR    (output) DOUBLE PRECISION array, dimension (NRHS)
	       The componentwise relative backward error of each solution vec‐
	       tor X(j) (i.e., the smallest relative change in any element  of
	       A or B that makes X(j) an exact solution).

       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 routine (version 3.2)	 November 2008			     DGTRFS(1)
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