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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, * )



     #include <sunperf.h>

     void cgtrfs(char trans, int n, int nrhs, complex  *dl,  com-
               plex  *d,  complex *du, complex *dlf, complex *df,
               complex *duf, complex *du2, int  *ipivot,  complex
               *cb,  int  ldb, complex *cx, int ldx, float *ferr,
               float *berr, int *info) ;

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  indi-
               cates 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  solu-
               tion  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  ele-
               ment 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 ille-
               gal value

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