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version 1.7, 2010/12/21 13:53:45 version 1.8, 2011/11/21 20:43:11
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   *> \brief \b ZGTTRF
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZGTTRF + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgttrf.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgttrf.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgttrf.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
   * 
   *       .. Scalar Arguments ..
   *       INTEGER            INFO, N
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IPIV( * )
   *       COMPLEX*16         D( * ), DL( * ), DU( * ), DU2( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZGTTRF computes an LU factorization of a complex tridiagonal matrix A
   *> using elimination with partial pivoting and row interchanges.
   *>
   *> The factorization has the form
   *>    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.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix A.
   *> \endverbatim
   *>
   *> \param[in,out] DL
   *> \verbatim
   *>          DL is COMPLEX*16 array, dimension (N-1)
   *>          On entry, DL must contain the (n-1) sub-diagonal elements of
   *>          A.
   *>
   *>          On exit, DL is overwritten by the (n-1) multipliers that
   *>          define the matrix L from the LU factorization of A.
   *> \endverbatim
   *>
   *> \param[in,out] D
   *> \verbatim
   *>          D is COMPLEX*16 array, dimension (N)
   *>          On entry, D must contain the diagonal elements of A.
   *>
   *>          On exit, D is overwritten by the n diagonal elements of the
   *>          upper triangular matrix U from the LU factorization of A.
   *> \endverbatim
   *>
   *> \param[in,out] DU
   *> \verbatim
   *>          DU is COMPLEX*16 array, dimension (N-1)
   *>          On entry, DU must contain the (n-1) super-diagonal elements
   *>          of A.
   *>
   *>          On exit, DU is overwritten by the (n-1) elements of the first
   *>          super-diagonal of U.
   *> \endverbatim
   *>
   *> \param[out] DU2
   *> \verbatim
   *>          DU2 is COMPLEX*16 array, dimension (N-2)
   *>          On exit, DU2 is overwritten by the (n-2) elements of the
   *>          second super-diagonal of U.
   *> \endverbatim
   *>
   *> \param[out] IPIV
   *> \verbatim
   *>          IPIV is 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 indicates a row interchange was not
   *>          required.
   *> \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, U(k,k) is exactly zero. The factorization
   *>                has been completed, but the factor U is exactly
   *>                singular, and division by zero will occur if it is used
   *>                to solve a system of equations.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup complex16OTHERcomputational
   *
   *  =====================================================================
       SUBROUTINE ZGTTRF( N, DL, D, DU, DU2, IPIV, INFO )        SUBROUTINE ZGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
 *  *
 *  -- LAPACK routine (version 3.2) --  *  -- LAPACK computational routine (version 3.4.0) --
 *  -- 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  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            INFO, N        INTEGER            INFO, N
Line 13 Line 137
       COMPLEX*16         D( * ), DL( * ), DU( * ), DU2( * )        COMPLEX*16         D( * ), DL( * ), DU( * ), DU2( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZGTTRF computes an LU factorization of a complex tridiagonal matrix A  
 *  using elimination with partial pivoting and row interchanges.  
 *  
 *  The factorization has the form  
 *     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.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrix A.  
 *  
 *  DL      (input/output) COMPLEX*16 array, dimension (N-1)  
 *          On entry, DL must contain the (n-1) sub-diagonal elements of  
 *          A.  
 *  
 *          On exit, DL is overwritten by the (n-1) multipliers that  
 *          define the matrix L from the LU factorization of A.  
 *  
 *  D       (input/output) COMPLEX*16 array, dimension (N)  
 *          On entry, D must contain the diagonal elements of A.  
 *  
 *          On exit, D is overwritten by the n diagonal elements of the  
 *          upper triangular matrix U from the LU factorization of A.  
 *  
 *  DU      (input/output) COMPLEX*16 array, dimension (N-1)  
 *          On entry, DU must contain the (n-1) super-diagonal elements  
 *          of A.  
 *  
 *          On exit, DU is overwritten by the (n-1) elements of the first  
 *          super-diagonal of U.  
 *  
 *  DU2     (output) COMPLEX*16 array, dimension (N-2)  
 *          On exit, DU2 is overwritten by the (n-2) elements of the  
 *          second super-diagonal of U.  
 *  
 *  IPIV    (output) 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 indicates a row interchange was not  
 *          required.  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit  
 *          < 0:  if INFO = -k, the k-th argument had an illegal value  
 *          > 0:  if INFO = k, U(k,k) is exactly zero. The factorization  
 *                has been completed, but the factor U is exactly  
 *                singular, and division by zero will occur if it is used  
 *                to solve a system of equations.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.7  
changed lines
  Added in v.1.8

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