dpttrf.f

Go to the documentation of this file.

*> \brief \b DPTTRF
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DPTTRF + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpttrf.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpttrf.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpttrf.f">
*> [TXT]</a>
*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE DPTTRF( N, D, E, INFO )
*
*       .. Scalar Arguments ..
*       INTEGER            INFO, N
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   D( * ), E( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DPTTRF computes the L*D*L**T factorization of a real symmetric
*> positive definite tridiagonal matrix A.  The factorization may also
*> be regarded as having the form A = U**T*D*U.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in,out] D
*> \verbatim
*>          D is DOUBLE PRECISION array, dimension (N)
*>          On entry, the n diagonal elements of the tridiagonal matrix
*>          A.  On exit, the n diagonal elements of the diagonal matrix
*>          D from the L*D*L**T factorization of A.
*> \endverbatim
*>
*> \param[in,out] E
*> \verbatim
*>          E is DOUBLE PRECISION array, dimension (N-1)
*>          On entry, the (n-1) subdiagonal elements of the tridiagonal
*>          matrix A.  On exit, the (n-1) subdiagonal elements of the
*>          unit bidiagonal factor L from the L*D*L**T factorization of A.
*>          E can also be regarded as the superdiagonal of the unit
*>          bidiagonal factor U from the U**T*D*U factorization of A.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0: successful exit
*>          < 0: if INFO = -k, the k-th argument had an illegal value
*>          > 0: if INFO = k, the leading principal minor of order k
*>               is not positive; if k < N, the factorization could not
*>               be completed, while if k = N, the factorization was
*>               completed, but D(N) <= 0.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup pttrf
*
*  =====================================================================
      SUBROUTINE dpttrf( N, D, E, INFO )
*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      INTEGER            INFO, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   D( * ), E( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO
      parameter( zero = 0.0d+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, I4
      DOUBLE PRECISION   EI
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          mod
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      IF( n.LT.0 ) THEN
         info = -1
         CALL xerbla( 'DPTTRF', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 )
     $   RETURN
*
*     Compute the L*D*L**T (or U**T*D*U) factorization of A.
*
      i4 = mod( n-1, 4 )
      DO 10 i = 1, i4
         IF( d( i ).LE.zero ) THEN
            info = i
            GO TO 30
         END IF
         ei = e( i )
         e( i ) = ei / d( i )
         d( i+1 ) = d( i+1 ) - e( i )*ei
   10 CONTINUE
*
      DO 20 i = i4 + 1, n - 4, 4
*
*        Drop out of the loop if d(i) <= 0: the matrix is not positive
*        definite.
*
         IF( d( i ).LE.zero ) THEN
            info = i
            GO TO 30
         END IF
*
*        Solve for e(i) and d(i+1).
*
         ei = e( i )
         e( i ) = ei / d( i )
         d( i+1 ) = d( i+1 ) - e( i )*ei
*
         IF( d( i+1 ).LE.zero ) THEN
            info = i + 1
            GO TO 30
         END IF
*
*        Solve for e(i+1) and d(i+2).
*
         ei = e( i+1 )
         e( i+1 ) = ei / d( i+1 )
         d( i+2 ) = d( i+2 ) - e( i+1 )*ei
*
         IF( d( i+2 ).LE.zero ) THEN
            info = i + 2
            GO TO 30
         END IF
*
*        Solve for e(i+2) and d(i+3).
*
         ei = e( i+2 )
         e( i+2 ) = ei / d( i+2 )
         d( i+3 ) = d( i+3 ) - e( i+2 )*ei
*
         IF( d( i+3 ).LE.zero ) THEN
            info = i + 3
            GO TO 30
         END IF
*
*        Solve for e(i+3) and d(i+4).
*
         ei = e( i+3 )
         e( i+3 ) = ei / d( i+3 )
         d( i+4 ) = d( i+4 ) - e( i+3 )*ei
   20 CONTINUE
*
*     Check d(n) for positive definiteness.
*
      IF( d( n ).LE.zero )
     $   info = n
*
   30 CONTINUE
      RETURN
*
*     End of DPTTRF
*
      END