cgtrfs(3F)

NAME
     CGTRFS - 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 CGTRFS( 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( * )

         REAL           BERR( * ), FERR( * ), RWORK( * )

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

PURPOSE
     CGTRFS 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 array, dimension (N-1)
             The (n-1) subdiagonal elements of A.

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

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

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

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

     DU2     (input) COMPLEX 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 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 array, dimension (LDX,NRHS)
             On entry, the solution matrix X, as computed by CGTTRS.  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 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) 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) COMPLEX array, dimension (2*N)

     RWORK   (workspace) REAL 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.