zgtrfs(3F)

NAME
     ZGTRFS - improve 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 ZGTRFS( TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B,
                        LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )

         CHARACTER      TRANS

         INTEGER        INFO, LDB, LDX, N, NRHS

         INTEGER        IPIV( * )

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

         COMPLEX*16     B( LDB, * ), D( * ), DF( * ), DL( * ), DLF( * ), DU( *
                        ), DU2( * ), DUF( * ), WORK( * ), X( LDX, * )

PURPOSE
     ZGTRFS 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)

     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) COMPLEX*16 array, dimension (N-1)
             The (n-1) subdiagonal elements of A.

     D       (input) COMPLEX*16 array, dimension (N)
             The diagonal elements of A.

     DU      (input) COMPLEX*16 array, dimension (N-1)
             The (n-1) superdiagonal elements of A.

     DLF     (input) COMPLEX*16 array, dimension (N-1)
             The (n-1) multipliers that define the matrix L from the LU
             factorization of A as computed by ZGTTRF.
     DF      (input) COMPLEX*16 array, dimension (N)
             The n diagonal elements of the upper triangular matrix U from the
             LU factorization of A.

     DUF     (input) COMPLEX*16 array, dimension (N-1)
             The (n-1) elements of the first superdiagonal of U.

     DU2     (input) COMPLEX*16 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) 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 ZGTTRS.  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 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) COMPLEX*16 array, dimension (2*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.