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version 1.1, 2010/01/26 15:22:46 version 1.19, 2018/05/29 06:55:22
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   *> \brief \b ZGETC2 computes the LU factorization with complete pivoting of the general n-by-n matrix.
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *> \htmlonly
   *> Download ZGETC2 + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgetc2.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgetc2.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgetc2.f">
   *> [TXT]</a>
   *> \endhtmlonly
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZGETC2( N, A, LDA, IPIV, JPIV, INFO )
   *
   *       .. Scalar Arguments ..
   *       INTEGER            INFO, LDA, N
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IPIV( * ), JPIV( * )
   *       COMPLEX*16         A( LDA, * )
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZGETC2 computes an LU factorization, using complete pivoting, of the
   *> n-by-n matrix A. The factorization has the form A = P * L * U * Q,
   *> where P and Q are permutation matrices, L is lower triangular with
   *> unit diagonal elements and U is upper triangular.
   *>
   *> This is a level 1 BLAS version of the algorithm.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix A. N >= 0.
   *> \endverbatim
   *>
   *> \param[in,out] A
   *> \verbatim
   *>          A is COMPLEX*16 array, dimension (LDA, N)
   *>          On entry, the n-by-n matrix to be factored.
   *>          On exit, the factors L and U from the factorization
   *>          A = P*L*U*Q; the unit diagonal elements of L are not stored.
   *>          If U(k, k) appears to be less than SMIN, U(k, k) is given the
   *>          value of SMIN, giving a nonsingular perturbed system.
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>          The leading dimension of the array A.  LDA >= max(1, N).
   *> \endverbatim
   *>
   *> \param[out] IPIV
   *> \verbatim
   *>          IPIV is INTEGER array, dimension (N).
   *>          The pivot indices; for 1 <= i <= N, row i of the
   *>          matrix has been interchanged with row IPIV(i).
   *> \endverbatim
   *>
   *> \param[out] JPIV
   *> \verbatim
   *>          JPIV is INTEGER array, dimension (N).
   *>          The pivot indices; for 1 <= j <= N, column j of the
   *>          matrix has been interchanged with column JPIV(j).
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>           = 0: successful exit
   *>           > 0: if INFO = k, U(k, k) is likely to produce overflow if
   *>                one tries to solve for x in Ax = b. So U is perturbed
   *>                to avoid the overflow.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee
   *> \author Univ. of California Berkeley
   *> \author Univ. of Colorado Denver
   *> \author NAG Ltd.
   *
   *> \date June 2016
   *
   *> \ingroup complex16GEauxiliary
   *
   *> \par Contributors:
   *  ==================
   *>
   *>     Bo Kagstrom and Peter Poromaa, Department of Computing Science,
   *>     Umea University, S-901 87 Umea, Sweden.
   *
   *  =====================================================================
       SUBROUTINE ZGETC2( N, A, LDA, IPIV, JPIV, INFO )        SUBROUTINE ZGETC2( N, A, LDA, IPIV, JPIV, INFO )
 *  *
 *  -- LAPACK auxiliary routine (version 3.2) --  *  -- LAPACK auxiliary routine (version 3.8.0) --
 *  -- 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  *     June 2016
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, N        INTEGER            INFO, LDA, N
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       COMPLEX*16         A( LDA, * )        COMPLEX*16         A( LDA, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZGETC2 computes an LU factorization, using complete pivoting, of the  
 *  n-by-n matrix A. The factorization has the form A = P * L * U * Q,  
 *  where P and Q are permutation matrices, L is lower triangular with  
 *  unit diagonal elements and U is upper triangular.  
 *  
 *  This is a level 1 BLAS version of the algorithm.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrix A. N >= 0.  
 *  
 *  A       (input/output) COMPLEX*16 array, dimension (LDA, N)  
 *          On entry, the n-by-n matrix to be factored.  
 *          On exit, the factors L and U from the factorization  
 *          A = P*L*U*Q; the unit diagonal elements of L are not stored.  
 *          If U(k, k) appears to be less than SMIN, U(k, k) is given the  
 *          value of SMIN, giving a nonsingular perturbed system.  
 *  
 *  LDA     (input) INTEGER  
 *          The leading dimension of the array A.  LDA >= max(1, N).  
 *  
 *  IPIV    (output) INTEGER array, dimension (N).  
 *          The pivot indices; for 1 <= i <= N, row i of the  
 *          matrix has been interchanged with row IPIV(i).  
 *  
 *  JPIV    (output) INTEGER array, dimension (N).  
 *          The pivot indices; for 1 <= j <= N, column j of the  
 *          matrix has been interchanged with column JPIV(j).  
 *  
 *  INFO    (output) INTEGER  
 *           = 0: successful exit  
 *           > 0: if INFO = k, U(k, k) is likely to produce overflow if  
 *                one tries to solve for x in Ax = b. So U is perturbed  
 *                to avoid the overflow.  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  Based on contributions by  
 *     Bo Kagstrom and Peter Poromaa, Department of Computing Science,  
 *     Umea University, S-901 87 Umea, Sweden.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
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       DOUBLE PRECISION   BIGNUM, EPS, SMIN, SMLNUM, XMAX        DOUBLE PRECISION   BIGNUM, EPS, SMIN, SMLNUM, XMAX
 *     ..  *     ..
 *     .. External Subroutines ..  *     .. External Subroutines ..
       EXTERNAL           ZGERU, ZSWAP        EXTERNAL           ZGERU, ZSWAP, DLABAD
 *     ..  *     ..
 *     .. External Functions ..  *     .. External Functions ..
       DOUBLE PRECISION   DLAMCH        DOUBLE PRECISION   DLAMCH
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 *     ..  *     ..
 *     .. Executable Statements ..  *     .. Executable Statements ..
 *  *
         INFO = 0
   *
   *     Quick return if possible
   *
         IF( N.EQ.0 )
        $   RETURN
   *
 *     Set constants to control overflow  *     Set constants to control overflow
 *  *
       INFO = 0  
       EPS = DLAMCH( 'P' )        EPS = DLAMCH( 'P' )
       SMLNUM = DLAMCH( 'S' ) / EPS        SMLNUM = DLAMCH( 'S' ) / EPS
       BIGNUM = ONE / SMLNUM        BIGNUM = ONE / SMLNUM
       CALL DLABAD( SMLNUM, BIGNUM )        CALL DLABAD( SMLNUM, BIGNUM )
 *  *
   *     Handle the case N=1 by itself
   *
         IF( N.EQ.1 ) THEN
            IPIV( 1 ) = 1
            JPIV( 1 ) = 1
            IF( ABS( A( 1, 1 ) ).LT.SMLNUM ) THEN
               INFO = 1
               A( 1, 1 ) = DCMPLX( SMLNUM, ZERO )
            END IF
            RETURN
         END IF
   *
 *     Factorize A using complete pivoting.  *     Factorize A using complete pivoting.
 *     Set pivots less than SMIN to SMIN  *     Set pivots less than SMIN to SMIN
 *  *
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          INFO = N           INFO = N
          A( N, N ) = DCMPLX( SMIN, ZERO )           A( N, N ) = DCMPLX( SMIN, ZERO )
       END IF        END IF
   *
   *     Set last pivots to N
   *
         IPIV( N ) = N
         JPIV( N ) = N
   *
       RETURN        RETURN
 *  *
 *     End of ZGETC2  *     End of ZGETC2
Removed from v.1.1  
changed lines
  Added in v.1.19

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