ZGTRFS(3)      LAPACK routine of NEC Numeric Library Collection      ZGTRFS(3)



NAME
       ZGTRFS

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



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)
                     TRANS is 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)
                     N is INTEGER
                     The order of the matrix A.  N >= 0.

           NRHS      (input)
                     NRHS is INTEGER
                     The number of right hand sides, i.e., the number of columns
                     of the matrix B.  NRHS >= 0.

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

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

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

           DLF       (input)
                     DLF is 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)
                     DF is COMPLEX*16 array, dimension (N)
                     The n diagonal elements of the upper triangular matrix U from
                     the LU factorization of A.

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

           DU2       (input)
                     DU2 is COMPLEX*16 array, dimension (N-2)
                     The (n-2) elements of the second superdiagonal of U.

           IPIV      (input)
                     IPIV is 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)
                     B is COMPLEX*16 array, dimension (LDB,NRHS)
                     The right hand side matrix B.

           LDB       (input)
                     LDB is INTEGER
                     The leading dimension of the array B.  LDB >= max(1,N).

           X         (input/output)
                     X is 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)
                     LDX is INTEGER
                     The leading dimension of the array X.  LDX >= max(1,N).

           FERR      (output)
                     FERR is 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)
                     BERR is 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      (output)
                     WORK is COMPLEX*16 array, dimension (2*N)

           RWORK     (output)
                     RWORK is DOUBLE PRECISION array, dimension (N)

           INFO      (output)
                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value



       Internal Parameters:


             ITMAX is the maximum number of steps of iterative refinement.



LAPACK routine                  31 October 2017                      ZGTRFS(3)