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OpenBLAS/lapack-netlib/SRC/zlarzt.f

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*> \brief \b ZLARZT forms the triangular factor T of a block reflector H = I - vtvH.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ZLARZT + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarzt.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlarzt.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarzt.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE ZLARZT( 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
*>
*> ZLARZT 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
*>
*> Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
*> \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, not supported yet)
*> = '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 (not supported yet)
*> = '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 September 2012
*
*> \ingroup complex16OTHERcomputational
*
*> \par Contributors:
* ==================
*>
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
*
*> \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_____
*> ( v1 v2 v3 ) / \
*> ( v1 v2 v3 ) ( v1 v1 v1 v1 v1 . . . . 1 )
*> V = ( v1 v2 v3 ) ( v2 v2 v2 v2 v2 . . . 1 )
*> ( v1 v2 v3 ) ( v3 v3 v3 v3 v3 . . 1 )
*> ( v1 v2 v3 )
*> . . .
*> . . .
*> 1 . .
*> 1 .
*> 1
*>
*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':
*>
*> ______V_____
*> 1 / \
*> . 1 ( 1 . . . . v1 v1 v1 v1 v1 )
*> . . 1 ( . 1 . . . v2 v2 v2 v2 v2 )
*> . . . ( . . 1 . . v3 v3 v3 v3 v3 )
*> . . .
*> ( v1 v2 v3 )
*> ( v1 v2 v3 )
*> V = ( v1 v2 v3 )
*> ( v1 v2 v3 )
*> ( v1 v2 v3 )
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
*
* -- LAPACK computational routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* September 2012
*
* .. Scalar Arguments ..
CHARACTER DIRECT, STOREV
INTEGER K, LDT, LDV, N
* ..
* .. Array Arguments ..
COMPLEX*16 T( LDT, * ), TAU( * ), V( LDV, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX*16 ZERO
PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
INTEGER I, INFO, J
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZGEMV, ZLACGV, ZTRMV
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. Executable Statements ..
*
* Check for currently supported options
*
INFO = 0
IF( .NOT.LSAME( DIRECT, 'B' ) ) THEN
INFO = -1
ELSE IF( .NOT.LSAME( STOREV, 'R' ) ) THEN
INFO = -2
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZLARZT', -INFO )
RETURN
END IF
*
DO 20 I = K, 1, -1
IF( TAU( I ).EQ.ZERO ) THEN
*
* H(i) = I
*
DO 10 J = I, K
T( J, I ) = ZERO
10 CONTINUE
ELSE
*
* general case
*
IF( I.LT.K ) THEN
*
* T(i+1:k,i) = - tau(i) * V(i+1:k,1:n) * V(i,1:n)**H
*
CALL ZLACGV( N, V( I, 1 ), LDV )
CALL ZGEMV( 'No transpose', K-I, N, -TAU( I ),
$ V( I+1, 1 ), LDV, V( I, 1 ), LDV, ZERO,
$ T( I+1, I ), 1 )
CALL ZLACGV( N, V( I, 1 ), LDV )
*
* T(i+1:k,i) = T(i+1:k,i+1:k) * T(i+1:k,i)
*
CALL ZTRMV( 'Lower', 'No transpose', 'Non-unit', K-I,
$ T( I+1, I+1 ), LDT, T( I+1, I ), 1 )
END IF
T( I, I ) = TAU( I )
END IF
20 CONTINUE
RETURN
*
* End of ZLARZT
*
END
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