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

     CHARACTER TRANS

     INTEGER INFO, LDB, LDX, N, NRHS

     INTEGER IPIV( * ), IWORK( * )

     DOUBLE PRECISION B( LDB, * ), BERR( * ), D( * ),  DF(  *  ),
               DL(  *  ),  DLF( * ), DU( * ), DU2( * ), DUF( * ),
               FERR( * ), WORK( * ), X( LDX, * )



     #include <sunperf.h>

     void dgtrfs(char trans, int n, int nrhs, double *dl,  double
               *d,  double  *du,  double *dlf, double *df, double
               *duf, double *du2, int *ipivot,  double  *db,  int
               ldb,  double  *dx,  int  ldx, double *ferr, double
               *berr, int *info) ;

PURPOSE
     DGTRFS 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 = Tran-
               spose)

     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) DOUBLE PRECISION array, dimension (N-1)
               The (n-1) subdiagonal elements of A.

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

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

     DLF       (input) DOUBLE PRECISION array, dimension (N-1)
               The (n-1) multipliers that  define  the  matrix  L
               from  the  LU  factorization  of  A as computed by
               DGTTRF.

     DF        (input) DOUBLE PRECISION array, dimension (N)
               The n diagonal elements of  the  upper  triangular
               matrix U from the LU factorization of A.

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

     DU2       (input) DOUBLE PRECISION 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)   DOUBLE   PRECISION   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) DOUBLE PRECISION  array,  dimension
               (LDX,NRHS)
               On entry, the solution matrix X,  as  computed  by
               DGTTRS.  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  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) 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)  DOUBLE  PRECISION  array,   dimension
               (3*N)

     IWORK     (workspace) INTEGER 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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