dptrfs man page on YellowDog

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DPTRFS(l)			       )			     DPTRFS(l)

NAME
       DPTRFS  - improve the computed solution to a system of linear equations
       when the coefficient matrix is symmetric positive definite and tridiag‐
       onal,  and  provides  error bounds and backward error estimates for the
       solution

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

	   INTEGER	  INFO, LDB, LDX, N, NRHS

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

PURPOSE
       DPTRFS improves the computed solution to a system of  linear  equations
       when the coefficient matrix is symmetric positive definite and tridiag‐
       onal, 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) DOUBLE PRECISION array, dimension (N)
	       The n diagonal elements of the tridiagonal matrix A.

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

       DF      (input) DOUBLE PRECISION array, dimension (N)
	       The n diagonal elements of the diagonal matrix D from the  fac‐
	       torization computed by DPTTRF.

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

       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  DPTTRS.   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 forward error bound for each solution vector X(j) (the j-th
	       column of the solution matrix X).  If XTRUE is the  true	 solu‐
	       tion 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) 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 (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.

LAPACK version 3.0		 15 June 2000			     DPTRFS(l)
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