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version 1.5, 2010/08/07 13:22:24 version 1.18, 2018/05/29 07:18:05
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   *> \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 minor of order k is not
   *>               positive definite; 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.
   *
   *> \date December 2016
   *
   *> \ingroup doublePTcomputational
   *
   *  =====================================================================
       SUBROUTINE DPTTRF( N, D, E, INFO )        SUBROUTINE DPTTRF( N, D, E, INFO )
 *  *
 *  -- LAPACK routine (version 3.2) --  *  -- LAPACK computational routine (version 3.7.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     November 2006  *     December 2016
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            INFO, N        INTEGER            INFO, N
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       DOUBLE PRECISION   D( * ), E( * )        DOUBLE PRECISION   D( * ), E( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DPTTRF computes the L*D*L' factorization of a real symmetric  
 *  positive definite tridiagonal matrix A.  The factorization may also  
 *  be regarded as having the form A = U'*D*U.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrix A.  N >= 0.  
 *  
 *  D       (input/output) 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' factorization of A.  
 *  
 *  E       (input/output) 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' factorization of A.  
 *          E can also be regarded as the superdiagonal of the unit  
 *          bidiagonal factor U from the U'*D*U factorization of A.  
 *  
 *  INFO    (output) INTEGER  
 *          = 0: successful exit  
 *          < 0: if INFO = -k, the k-th argument had an illegal value  
 *          > 0: if INFO = k, the leading minor of order k is not  
 *               positive definite; if k < N, the factorization could not  
 *               be completed, while if k = N, the factorization was  
 *               completed, but D(N) <= 0.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
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       IF( N.EQ.0 )        IF( N.EQ.0 )
      $   RETURN       $   RETURN
 *  *
 *     Compute the L*D*L' (or U'*D*U) factorization of A.  *     Compute the L*D*L**T (or U**T*D*U) factorization of A.
 *  *
       I4 = MOD( N-1, 4 )        I4 = MOD( N-1, 4 )
       DO 10 I = 1, I4        DO 10 I = 1, I4
Removed from v.1.5  
changed lines
  Added in v.1.18

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