      SUBROUTINE DPTSVX( FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX,
     $                   RCOND, FERR, BERR, WORK, INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     June 30, 1999
*
*     .. Scalar Arguments ..
      CHARACTER          FACT
      INTEGER            INFO, LDB, LDX, N, NRHS
      DOUBLE PRECISION   RCOND
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   B( LDB, * ), BERR( * ), D( * ), DF( * ),
     $                   E( * ), EF( * ), FERR( * ), WORK( * ),
     $                   X( LDX, * )
*     ..
*
*  Purpose
*  =======
*
*  DPTSVX uses the factorization A = L*D*L**T to compute the solution
*  to a real system of linear equations A*X = B, where A is an N-by-N
*  symmetric positive definite tridiagonal matrix 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 matrix A is factored as A = L*D*L**T, where L
*     is a unit lower bidiagonal matrix and D is diagonal.  The
*     factorization can also be regarded as having the form
*     A = U**T*D*U.
*
*  2. If the leading i-by-i principal minor is not positive definite,
*     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':  On entry, DF and EF contain the factored form of A.
*                  D, E, DF, and EF will not be modified.
*          = 'N':  The matrix A will be copied to DF and EF and
*                  factored.
*
*  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 matrices B and X.  NRHS >= 0.
*
*  D       (input) DOUBLE PRECISION array, dimension (N)
*          The n diagonal elements of the tridiagonal matrix A.
*
*  E       (input) DOUBLE PRECISION array, dimension (N-1)
*          The (n-1) subdiagonal elements of the tridiagonal matrix 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 diagonal matrix D
*          from the L*D*L**T factorization of A.
*          If FACT = 'N', then DF is an output argument and on exit
*          contains the n diagonal elements of the diagonal matrix D
*          from the L*D*L**T factorization of A.
*
*  EF      (input or output) DOUBLE PRECISION array, dimension (N-1)
*          If FACT = 'F', then EF is an input argument and on entry
*          contains the (n-1) subdiagonal elements of the unit
*          bidiagonal factor L from the L*D*L**T factorization of A.
*          If FACT = 'N', then EF is an output argument and on exit
*          contains the (n-1) subdiagonal elements of the unit
*          bidiagonal factor L from the L*D*L**T factorization of A.
*
*  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 of 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 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 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).
*
*  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 (2*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:  the leading minor of order i of A is
*                       not positive definite, so the factorization
*                       could not be completed, and the solution has not
*                       been 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
      DOUBLE PRECISION   ANORM
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   DLAMCH, DLANST
      EXTERNAL           LSAME, DLAMCH, DLANST
*     ..
*     .. External Subroutines ..
      EXTERNAL           DCOPY, DLACPY, DPTCON, DPTRFS, DPTTRF, DPTTRS,
     $                   XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      NOFACT = LSAME( FACT, 'N' )
      IF( .NOT.NOFACT .AND. .NOT.LSAME( FACT, 'F' ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( NRHS.LT.0 ) THEN
         INFO = -3
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -9
      ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
         INFO = -11
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DPTSVX', -INFO )
         RETURN
      END IF
*
      IF( NOFACT ) THEN
*
*        Compute the L*D*L' (or U'*D*U) factorization of A.
*
         CALL DCOPY( N, D, 1, DF, 1 )
         IF( N.GT.1 )
     $      CALL DCOPY( N-1, E, 1, EF, 1 )
         CALL DPTTRF( N, DF, EF, INFO )
*
*        Return if INFO is non-zero.
*
         IF( INFO.NE.0 ) THEN
            IF( INFO.GT.0 )
     $         RCOND = ZERO
            RETURN
         END IF
      END IF
*
*     Compute the norm of the matrix A.
*
      ANORM = DLANST( '1', N, D, E )
*
*     Compute the reciprocal of the condition number of A.
*
      CALL DPTCON( N, DF, EF, ANORM, RCOND, WORK, INFO )
*
*     Set INFO = N+1 if the matrix is singular to working precision.
*
      IF( RCOND.LT.DLAMCH( 'Epsilon' ) )
     $   INFO = N + 1
*
*     Compute the solution vectors X.
*
      CALL DLACPY( 'Full', N, NRHS, B, LDB, X, LDX )
      CALL DPTTRS( N, NRHS, DF, EF, X, LDX, INFO )
*
*     Use iterative refinement to improve the computed solutions and
*     compute error bounds and backward error estimates for them.
*
      CALL DPTRFS( N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR,
     $             WORK, INFO )
*
      RETURN
*
*     End of DPTSVX
*
      END
