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version 1.8, 2011/07/22 07:38:18 version 1.9, 2011/11/21 20:43:17
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   *> \brief \b ZLARFT
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZLARFT + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarft.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlarft.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarft.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          DIRECT, STOREV
   *       INTEGER            K, LDT, LDV, N
   *       ..
   *       .. Array Arguments ..
   *       COMPLEX*16         T( LDT, * ), TAU( * ), V( LDV, * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZLARFT forms the triangular factor T of a complex block reflector H
   *> of order n, which is defined as a product of k elementary reflectors.
   *>
   *> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;
   *>
   *> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.
   *>
   *> If STOREV = 'C', the vector which defines the elementary reflector
   *> H(i) is stored in the i-th column of the array V, and
   *>
   *>    H  =  I - V * T * V**H
   *>
   *> If STOREV = 'R', the vector which defines the elementary reflector
   *> H(i) is stored in the i-th row of the array V, and
   *>
   *>    H  =  I - V**H * T * V
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] DIRECT
   *> \verbatim
   *>          DIRECT is CHARACTER*1
   *>          Specifies the order in which the elementary reflectors are
   *>          multiplied to form the block reflector:
   *>          = 'F': H = H(1) H(2) . . . H(k) (Forward)
   *>          = 'B': H = H(k) . . . H(2) H(1) (Backward)
   *> \endverbatim
   *>
   *> \param[in] STOREV
   *> \verbatim
   *>          STOREV is CHARACTER*1
   *>          Specifies how the vectors which define the elementary
   *>          reflectors are stored (see also Further Details):
   *>          = 'C': columnwise
   *>          = 'R': rowwise
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the block reflector H. N >= 0.
   *> \endverbatim
   *>
   *> \param[in] K
   *> \verbatim
   *>          K is INTEGER
   *>          The order of the triangular factor T (= the number of
   *>          elementary reflectors). K >= 1.
   *> \endverbatim
   *>
   *> \param[in,out] V
   *> \verbatim
   *>          V is COMPLEX*16 array, dimension
   *>                               (LDV,K) if STOREV = 'C'
   *>                               (LDV,N) if STOREV = 'R'
   *>          The matrix V. See further details.
   *> \endverbatim
   *>
   *> \param[in] LDV
   *> \verbatim
   *>          LDV is INTEGER
   *>          The leading dimension of the array V.
   *>          If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
   *> \endverbatim
   *>
   *> \param[in] TAU
   *> \verbatim
   *>          TAU is COMPLEX*16 array, dimension (K)
   *>          TAU(i) must contain the scalar factor of the elementary
   *>          reflector H(i).
   *> \endverbatim
   *>
   *> \param[out] T
   *> \verbatim
   *>          T is COMPLEX*16 array, dimension (LDT,K)
   *>          The k by k triangular factor T of the block reflector.
   *>          If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is
   *>          lower triangular. The rest of the array is not used.
   *> \endverbatim
   *>
   *> \param[in] LDT
   *> \verbatim
   *>          LDT is INTEGER
   *>          The leading dimension of the array T. LDT >= K.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup complex16OTHERauxiliary
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  The shape of the matrix V and the storage of the vectors which define
   *>  the H(i) is best illustrated by the following example with n = 5 and
   *>  k = 3. The elements equal to 1 are not stored; the corresponding
   *>  array elements are modified but restored on exit. The rest of the
   *>  array is not used.
   *>
   *>  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':
   *>
   *>               V = (  1       )                 V = (  1 v1 v1 v1 v1 )
   *>                   ( v1  1    )                     (     1 v2 v2 v2 )
   *>                   ( v1 v2  1 )                     (        1 v3 v3 )
   *>                   ( v1 v2 v3 )
   *>                   ( v1 v2 v3 )
   *>
   *>  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':
   *>
   *>               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )
   *>                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )
   *>                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
   *>                   (     1 v3 )
   *>                   (        1 )
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )        SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
 *  *
 *  -- LAPACK auxiliary routine (version 3.3.1) --  *  -- LAPACK auxiliary 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..--
 *  -- April 2011                                                      --  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          DIRECT, STOREV        CHARACTER          DIRECT, STOREV
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       COMPLEX*16         T( LDT, * ), TAU( * ), V( LDV, * )        COMPLEX*16         T( LDT, * ), TAU( * ), V( LDV, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZLARFT forms the triangular factor T of a complex block reflector H  
 *  of order n, which is defined as a product of k elementary reflectors.  
 *  
 *  If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;  
 *  
 *  If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.  
 *  
 *  If STOREV = 'C', the vector which defines the elementary reflector  
 *  H(i) is stored in the i-th column of the array V, and  
 *  
 *     H  =  I - V * T * V**H  
 *  
 *  If STOREV = 'R', the vector which defines the elementary reflector  
 *  H(i) is stored in the i-th row of the array V, and  
 *  
 *     H  =  I - V**H * T * V  
 *  
 *  Arguments  
 *  =========  
 *  
 *  DIRECT  (input) CHARACTER*1  
 *          Specifies the order in which the elementary reflectors are  
 *          multiplied to form the block reflector:  
 *          = 'F': H = H(1) H(2) . . . H(k) (Forward)  
 *          = 'B': H = H(k) . . . H(2) H(1) (Backward)  
 *  
 *  STOREV  (input) CHARACTER*1  
 *          Specifies how the vectors which define the elementary  
 *          reflectors are stored (see also Further Details):  
 *          = 'C': columnwise  
 *          = 'R': rowwise  
 *  
 *  N       (input) INTEGER  
 *          The order of the block reflector H. N >= 0.  
 *  
 *  K       (input) INTEGER  
 *          The order of the triangular factor T (= the number of  
 *          elementary reflectors). K >= 1.  
 *  
 *  V       (input/output) COMPLEX*16 array, dimension  
 *                               (LDV,K) if STOREV = 'C'  
 *                               (LDV,N) if STOREV = 'R'  
 *          The matrix V. See further details.  
 *  
 *  LDV     (input) INTEGER  
 *          The leading dimension of the array V.  
 *          If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.  
 *  
 *  TAU     (input) COMPLEX*16 array, dimension (K)  
 *          TAU(i) must contain the scalar factor of the elementary  
 *          reflector H(i).  
 *  
 *  T       (output) COMPLEX*16 array, dimension (LDT,K)  
 *          The k by k triangular factor T of the block reflector.  
 *          If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is  
 *          lower triangular. The rest of the array is not used.  
 *  
 *  LDT     (input) INTEGER  
 *          The leading dimension of the array T. LDT >= K.  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  The shape of the matrix V and the storage of the vectors which define  
 *  the H(i) is best illustrated by the following example with n = 5 and  
 *  k = 3. The elements equal to 1 are not stored; the corresponding  
 *  array elements are modified but restored on exit. The rest of the  
 *  array is not used.  
 *  
 *  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':  
 *  
 *               V = (  1       )                 V = (  1 v1 v1 v1 v1 )  
 *                   ( v1  1    )                     (     1 v2 v2 v2 )  
 *                   ( v1 v2  1 )                     (        1 v3 v3 )  
 *                   ( v1 v2 v3 )  
 *                   ( v1 v2 v3 )  
 *  
 *  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':  
 *  
 *               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )  
 *                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )  
 *                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )  
 *                   (     1 v3 )  
 *                   (        1 )  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.8  
changed lines
  Added in v.1.9

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