ZPTRFS(3)                  MathKeisan LAPACK routine                 ZPTRFS(3)



NAME
       ZPTRFS - the computed solution to a system of linear equations when the
       coefficient matrix is Hermitian positive definite and tridiagonal,  and
       provides error bounds and backward error estimates for the solution

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

           CHARACTER      UPLO

           INTEGER        INFO, LDB, LDX, N, NRHS

           DOUBLE         PRECISION BERR( * ), D( * ), DF( *  ),  FERR(  *  ),
                          RWORK( * )

           COMPLEX*16     B( LDB, * ), E( * ), EF( * ), WORK( * ), X( LDX, * )

PURPOSE
       ZPTRFS improves the computed solution to a system of  linear  equations
       when the coefficient matrix is Hermitian positive definite and tridiag-
       onal, and provides error bounds and backward error  estimates  for  the
       solution.


ARGUMENTS
       UPLO    (input) CHARACTER*1
               Specifies  whether  the superdiagonal or the subdiagonal of the
               tridiagonal matrix A is stored and the form of  the  factoriza-
               tion:
               = 'U':  E is the superdiagonal of A, and A = U**H*D*U;
               =  'L':  E is the subdiagonal of A, and A = L*D*L**H.  (The two
               forms are equivalent if A is real.)

       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 real diagonal elements of the tridiagonal matrix A.

       E       (input) COMPLEX*16 array, dimension (N-1)
               The  (n-1)  off-diagonal  elements  of the tridiagonal matrix A
               (see UPLO).

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

       EF      (input) COMPLEX*16 array, dimension (N-1)
               The (n-1) off-diagonal elements of the unit bidiagonal factor U
               or L from the factorization computed by ZPTTRF (see UPLO).

       B       (input) COMPLEX*16 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) COMPLEX*16 array, dimension (LDX,NRHS)
               On entry, the solution matrix X, as  computed  by  ZPTTRS.   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) COMPLEX*16 array, dimension (N)

       RWORK   (workspace) DOUBLE PRECISION 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 3.1)    November 2006                       ZPTRFS(3)