CXML
        	    
LAPACK version 3.0
sptrfs(3)

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

SYNTAX
  SUBROUTINE SPTRFS( N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK,
		     INFO )

      INTEGER	     INFO, LDB, LDX, N, NRHS

      REAL	     B( LDB, * ), BERR( * ), D( * ), DF( * ), E( * ), EF( *
		     ), FERR( * ), WORK( * ), X( LDX, * )

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

ARGUMENTS
  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.

  D	  (input) REAL array, dimension (N)
	  The n diagonal elements of the tridiagonal matrix A.

  E	  (input) REAL array, dimension (N-1)
	  The (n-1) subdiagonal elements of the tridiagonal matrix A.

  DF	  (input) REAL array, dimension (N)
	  The n diagonal elements of the diagonal matrix D from the
	  factorization computed by SPTTRF.

  EF	  (input) REAL array, dimension (N-1)
	  The (n-1) subdiagonal elements of the unit bidiagonal factor L from
	  the factorization computed by SPTTRF.

  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 SPTTRS.  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 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).

  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 (2*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.