```      SUBROUTINE DGTSVX( FACT, TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF,
\$                   DU2, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR,
\$                   WORK, IWORK, INFO )
*
*  -- LAPACK routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
CHARACTER          FACT, TRANS
INTEGER            INFO, LDB, LDX, N, NRHS
DOUBLE PRECISION   RCOND
*     ..
*     .. Array Arguments ..
INTEGER            IPIV( * ), IWORK( * )
DOUBLE PRECISION   B( LDB, * ), BERR( * ), D( * ), DF( * ),
\$                   DL( * ), DLF( * ), DU( * ), DU2( * ), DUF( * ),
\$                   FERR( * ), WORK( * ), X( LDX, * )
*     ..
*
*  Purpose
*  =======
*
*  DGTSVX uses the LU factorization to compute the solution to a real
*  system of linear equations A * X = B or A**T * X = B,
*  where A is a tridiagonal matrix of order N and X and B are N-by-NRHS
*  matrices.
*
*  Error bounds on the solution and a condition estimate are also
*  provided.
*
*  Description
*  ===========
*
*  The following steps are performed:
*
*  1. If FACT = 'N', the LU decomposition is used to factor the matrix A
*     as A = L * U, where L is a product of permutation and unit lower
*     bidiagonal matrices and U is upper triangular with nonzeros in
*     only the main diagonal and first two superdiagonals.
*
*  2. If some U(i,i)=0, so that U is exactly singular, then the routine
*     returns with INFO = i. Otherwise, the factored form of A is used
*     to estimate the condition number of the matrix A.  If the
*     reciprocal of the condition number is less than machine precision,
*     INFO = N+1 is returned as a warning, but the routine still goes on
*     to solve for X and compute error bounds as described below.
*
*  3. The system of equations is solved for X using the factored form
*     of A.
*
*  4. Iterative refinement is applied to improve the computed solution
*     matrix and calculate error bounds and backward error estimates
*     for it.
*
*  Arguments
*  =========
*
*  FACT    (input) CHARACTER*1
*          Specifies whether or not the factored form of A has been
*          supplied on entry.
*          = 'F':  DLF, DF, DUF, DU2, and IPIV contain the factored
*                  form of A; DL, D, DU, DLF, DF, DUF, DU2 and IPIV
*                  will not be modified.
*          = 'N':  The matrix will be copied to DLF, DF, and DUF
*                  and factored.
*
*  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 = 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) DOUBLE PRECISION array, dimension (N-1)
*          The (n-1) subdiagonal elements of A.
*
*  D       (input) DOUBLE PRECISION array, dimension (N)
*          The n diagonal elements of A.
*
*  DU      (input) DOUBLE PRECISION array, dimension (N-1)
*          The (n-1) superdiagonal elements of A.
*
*  DLF     (input or output) DOUBLE PRECISION array, dimension (N-1)
*          If FACT = 'F', then DLF is an input argument and on entry
*          contains the (n-1) multipliers that define the matrix L from
*          the LU factorization of A as computed by DGTTRF.
*
*          If FACT = 'N', then DLF is an output argument and on exit
*          contains the (n-1) multipliers that define the matrix L from
*          the LU factorization of A.
*
*  DF      (input or output) DOUBLE PRECISION array, dimension (N)
*          If FACT = 'F', then DF is an input argument and on entry
*          contains the n diagonal elements of the upper triangular
*          matrix U from the LU factorization of A.
*
*          If FACT = 'N', then DF is an output argument and on exit
*          contains the n diagonal elements of the upper triangular
*          matrix U from the LU factorization of A.
*
*  DUF     (input or output) DOUBLE PRECISION array, dimension (N-1)
*          If FACT = 'F', then DUF is an input argument and on entry
*          contains the (n-1) elements of the first superdiagonal of U.
*
*          If FACT = 'N', then DUF is an output argument and on exit
*          contains the (n-1) elements of the first superdiagonal of U.
*
*  DU2     (input or output) DOUBLE PRECISION array, dimension (N-2)
*          If FACT = 'F', then DU2 is an input argument and on entry
*          contains the (n-2) elements of the second superdiagonal of
*          U.
*
*          If FACT = 'N', then DU2 is an output argument and on exit
*          contains the (n-2) elements of the second superdiagonal of
*          U.
*
*  IPIV    (input or output) INTEGER array, dimension (N)
*          If FACT = 'F', then IPIV is an input argument and on entry
*          contains the pivot indices from the LU factorization of A as
*          computed by DGTTRF.
*
*          If FACT = 'N', then IPIV is an output argument and on exit
*          contains the pivot indices from the LU factorization of A;
*          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) DOUBLE PRECISION array, dimension (LDB,NRHS)
*          The N-by-NRHS right hand side matrix B.
*
*  LDB     (input) INTEGER
*          The leading dimension of the array B.  LDB >= max(1,N).
*
*  X       (output) DOUBLE PRECISION array, dimension (LDX,NRHS)
*          If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X.
*
*  LDX     (input) INTEGER
*          The leading dimension of the array X.  LDX >= max(1,N).
*
*  RCOND   (output) DOUBLE PRECISION
*          The estimate of the reciprocal condition number of the matrix
*          A.  If RCOND is less than the machine precision (in
*          particular, if RCOND = 0), the matrix is singular to working
*          precision.  This condition is indicated by a return code of
*          INFO > 0.
*
*  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) 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 illegal value
*          > 0:  if INFO = i, and i is
*                <= N:  U(i,i) is exactly zero.  The factorization
*                       has not been completed unless i = N, but the
*                       factor U is exactly singular, so the solution
*                       and error bounds could not be computed.
*                       RCOND = 0 is returned.
*                = N+1: U is nonsingular, but RCOND is less than machine
*                       precision, meaning that the matrix is singular
*                       to working precision.  Nevertheless, the
*                       solution and error bounds are computed because
*                       there are a number of situations where the
*                       computed solution can be more accurate than the
*                       value of RCOND would suggest.
*
*  =====================================================================
*
*     .. Parameters ..
DOUBLE PRECISION   ZERO
PARAMETER          ( ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
LOGICAL            NOFACT, NOTRAN
CHARACTER          NORM
DOUBLE PRECISION   ANORM
*     ..
*     .. External Functions ..
LOGICAL            LSAME
DOUBLE PRECISION   DLAMCH, DLANGT
EXTERNAL           LSAME, DLAMCH, DLANGT
*     ..
*     .. External Subroutines ..
EXTERNAL           DCOPY, DGTCON, DGTRFS, DGTTRF, DGTTRS, DLACPY,
\$                   XERBLA
*     ..
*     .. Intrinsic Functions ..
INTRINSIC          MAX
*     ..
*     .. Executable Statements ..
*
INFO = 0
NOFACT = LSAME( FACT, 'N' )
NOTRAN = LSAME( TRANS, 'N' )
IF( .NOT.NOFACT .AND. .NOT.LSAME( FACT, 'F' ) ) THEN
INFO = -1
ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT.
\$         LSAME( TRANS, 'C' ) ) THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
ELSE IF( NRHS.LT.0 ) THEN
INFO = -4
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -14
ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
INFO = -16
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DGTSVX', -INFO )
RETURN
END IF
*
IF( NOFACT ) THEN
*
*        Compute the LU factorization of A.
*
CALL DCOPY( N, D, 1, DF, 1 )
IF( N.GT.1 ) THEN
CALL DCOPY( N-1, DL, 1, DLF, 1 )
CALL DCOPY( N-1, DU, 1, DUF, 1 )
END IF
CALL DGTTRF( N, DLF, DF, DUF, DU2, IPIV, INFO )
*
*        Return if INFO is non-zero.
*
IF( INFO.GT.0 )THEN
RCOND = ZERO
RETURN
END IF
END IF
*
*     Compute the norm of the matrix A.
*
IF( NOTRAN ) THEN
NORM = '1'
ELSE
NORM = 'I'
END IF
ANORM = DLANGT( NORM, N, DL, D, DU )
*
*     Compute the reciprocal of the condition number of A.
*
CALL DGTCON( NORM, N, DLF, DF, DUF, DU2, IPIV, ANORM, RCOND, WORK,
\$             IWORK, INFO )
*
*     Compute the solution vectors X.
*
CALL DLACPY( 'Full', N, NRHS, B, LDB, X, LDX )
CALL DGTTRS( TRANS, N, NRHS, DLF, DF, DUF, DU2, IPIV, X, LDX,
\$             INFO )
*
*     Use iterative refinement to improve the computed solutions and
*     compute error bounds and backward error estimates for them.
*
CALL DGTRFS( TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV,
\$             B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )
*
*     Set INFO = N+1 if the matrix is singular to working precision.
*
IF( RCOND.LT.DLAMCH( 'Epsilon' ) )
\$   INFO = N + 1
*
RETURN
*
*     End of DGTSVX
*
END

```