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version 1.1, 2010/01/26 15:22:45 version 1.14, 2016/08/27 15:34:23
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   *> \brief \b DGETRF
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DGETRF + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgetrf.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgetrf.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgetrf.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO )
   * 
   *       .. Scalar Arguments ..
   *       INTEGER            INFO, LDA, M, N
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IPIV( * )
   *       DOUBLE PRECISION   A( LDA, * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DGETRF computes an LU factorization of a general M-by-N matrix A
   *> using partial pivoting with row interchanges.
   *>
   *> The factorization has the form
   *>    A = P * L * U
   *> where P is a permutation matrix, L is lower triangular with unit
   *> diagonal elements (lower trapezoidal if m > n), and U is upper
   *> triangular (upper trapezoidal if m < n).
   *>
   *> This is the right-looking Level 3 BLAS version of the algorithm.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] M
   *> \verbatim
   *>          M is INTEGER
   *>          The number of rows of the matrix A.  M >= 0.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The number of columns of the matrix A.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in,out] A
   *> \verbatim
   *>          A is DOUBLE PRECISION array, dimension (LDA,N)
   *>          On entry, the M-by-N matrix to be factored.
   *>          On exit, the factors L and U from the factorization
   *>          A = P*L*U; the unit diagonal elements of L are not stored.
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>          The leading dimension of the array A.  LDA >= max(1,M).
   *> \endverbatim
   *>
   *> \param[out] IPIV
   *> \verbatim
   *>          IPIV is INTEGER array, dimension (min(M,N))
   *>          The pivot indices; for 1 <= i <= min(M,N), row i of the
   *>          matrix was interchanged with row IPIV(i).
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0:  successful exit
   *>          < 0:  if INFO = -i, the i-th argument had an illegal value
   *>          > 0:  if INFO = i, U(i,i) 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 2015
   *
   *> \ingroup doubleGEcomputational
   *
   *  =====================================================================
       SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO )        SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO )
 *  *
 *  -- LAPACK routine (version 3.2) --  *  -- LAPACK computational routine (version 3.6.0) --
 *  -- 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 2015
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, M, N        INTEGER            INFO, LDA, M, N
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       DOUBLE PRECISION   A( LDA, * )        DOUBLE PRECISION   A( LDA, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DGETRF computes an LU factorization of a general M-by-N matrix A  
 *  using partial pivoting with row interchanges.  
 *  
 *  The factorization has the form  
 *     A = P * L * U  
 *  where P is a permutation matrix, L is lower triangular with unit  
 *  diagonal elements (lower trapezoidal if m > n), and U is upper  
 *  triangular (upper trapezoidal if m < n).  
 *  
 *  This is the right-looking Level 3 BLAS version of the algorithm.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  M       (input) INTEGER  
 *          The number of rows of the matrix A.  M >= 0.  
 *  
 *  N       (input) INTEGER  
 *          The number of columns of the matrix A.  N >= 0.  
 *  
 *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)  
 *          On entry, the M-by-N matrix to be factored.  
 *          On exit, the factors L and U from the factorization  
 *          A = P*L*U; the unit diagonal elements of L are not stored.  
 *  
 *  LDA     (input) INTEGER  
 *          The leading dimension of the array A.  LDA >= max(1,M).  
 *  
 *  IPIV    (output) INTEGER array, dimension (min(M,N))  
 *          The pivot indices; for 1 <= i <= min(M,N), row i of the  
 *          matrix was interchanged with row IPIV(i).  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit  
 *          < 0:  if INFO = -i, the i-th argument had an illegal value  
 *          > 0:  if INFO = i, U(i,i) 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 ..
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       INTEGER            I, IINFO, J, JB, NB        INTEGER            I, IINFO, J, JB, NB
 *     ..  *     ..
 *     .. External Subroutines ..  *     .. External Subroutines ..
       EXTERNAL           DGEMM, DGETF2, DLASWP, DTRSM, XERBLA        EXTERNAL           DGEMM, DGETRF2, DLASWP, DTRSM, XERBLA
 *     ..  *     ..
 *     .. External Functions ..  *     .. External Functions ..
       INTEGER            ILAENV        INTEGER            ILAENV
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 *  *
 *        Use unblocked code.  *        Use unblocked code.
 *  *
          CALL DGETF2( M, N, A, LDA, IPIV, INFO )           CALL DGETRF2( M, N, A, LDA, IPIV, INFO )
       ELSE        ELSE
 *  *
 *        Use blocked code.  *        Use blocked code.
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 *           Factor diagonal and subdiagonal blocks and test for exact  *           Factor diagonal and subdiagonal blocks and test for exact
 *           singularity.  *           singularity.
 *  *
             CALL DGETF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO )              CALL DGETRF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO )
 *  *
 *           Adjust INFO and the pivot indices.  *           Adjust INFO and the pivot indices.
 *  *
Removed from v.1.1  
changed lines
  Added in v.1.14

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