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327 lines
9.9 KiB
327 lines
9.9 KiB
*> \brief \b SLARFT
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download SLARFT + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slarft.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slarft.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slarft.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
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*
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* .. Scalar Arguments ..
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* CHARACTER DIRECT, STOREV
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* INTEGER K, LDT, LDV, N
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* ..
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* .. Array Arguments ..
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* REAL T( LDT, * ), TAU( * ), V( LDV, * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SLARFT forms the triangular factor T of a real block reflector H
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*> of order n, which is defined as a product of k elementary reflectors.
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*>
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*> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;
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*>
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*> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.
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*>
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*> If STOREV = 'C', the vector which defines the elementary reflector
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*> H(i) is stored in the i-th column of the array V, and
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*>
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*> H = I - V * T * V**T
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*>
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*> If STOREV = 'R', the vector which defines the elementary reflector
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*> H(i) is stored in the i-th row of the array V, and
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*>
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*> H = I - V**T * T * V
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] DIRECT
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*> \verbatim
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*> DIRECT is CHARACTER*1
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*> Specifies the order in which the elementary reflectors are
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*> multiplied to form the block reflector:
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*> = 'F': H = H(1) H(2) . . . H(k) (Forward)
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*> = 'B': H = H(k) . . . H(2) H(1) (Backward)
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*> \endverbatim
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*>
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*> \param[in] STOREV
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*> \verbatim
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*> STOREV is CHARACTER*1
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*> Specifies how the vectors which define the elementary
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*> reflectors are stored (see also Further Details):
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*> = 'C': columnwise
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*> = 'R': rowwise
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The order of the block reflector H. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] K
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*> \verbatim
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*> K is INTEGER
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*> The order of the triangular factor T (= the number of
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*> elementary reflectors). K >= 1.
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*> \endverbatim
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*>
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*> \param[in] V
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*> \verbatim
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*> V is REAL array, dimension
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*> (LDV,K) if STOREV = 'C'
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*> (LDV,N) if STOREV = 'R'
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*> The matrix V. See further details.
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*> \endverbatim
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*>
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*> \param[in] LDV
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*> \verbatim
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*> LDV is INTEGER
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*> The leading dimension of the array V.
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*> If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
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*> \endverbatim
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*>
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*> \param[in] TAU
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*> \verbatim
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*> TAU is REAL array, dimension (K)
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*> TAU(i) must contain the scalar factor of the elementary
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*> reflector H(i).
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*> \endverbatim
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*>
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*> \param[out] T
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*> \verbatim
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*> T is REAL array, dimension (LDT,K)
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*> The k by k triangular factor T of the block reflector.
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*> If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is
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*> lower triangular. The rest of the array is not used.
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*> \endverbatim
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*>
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*> \param[in] LDT
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*> \verbatim
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*> LDT is INTEGER
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*> The leading dimension of the array T. LDT >= K.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date April 2012
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*
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*> \ingroup realOTHERauxiliary
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*
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*> \par Further Details:
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* =====================
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*>
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*> \verbatim
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*>
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*> The shape of the matrix V and the storage of the vectors which define
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*> the H(i) is best illustrated by the following example with n = 5 and
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*> k = 3. The elements equal to 1 are not stored.
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*>
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*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R':
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*>
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*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 )
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*> ( v1 1 ) ( 1 v2 v2 v2 )
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*> ( v1 v2 1 ) ( 1 v3 v3 )
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*> ( v1 v2 v3 )
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*> ( v1 v2 v3 )
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*>
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*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':
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*>
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*> V = ( v1 v2 v3 ) V = ( v1 v1 1 )
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*> ( v1 v2 v3 ) ( v2 v2 v2 1 )
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*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 )
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*> ( 1 v3 )
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*> ( 1 )
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE SLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
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*
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* -- LAPACK auxiliary routine (version 3.4.1) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* April 2012
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*
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* .. Scalar Arguments ..
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CHARACTER DIRECT, STOREV
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INTEGER K, LDT, LDV, N
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* ..
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* .. Array Arguments ..
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REAL T( LDT, * ), TAU( * ), V( LDV, * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ONE, ZERO
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PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, J, PREVLASTV, LASTV
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* ..
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* .. External Subroutines ..
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EXTERNAL SGEMV, STRMV
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. Executable Statements ..
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*
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* Quick return if possible
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*
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IF( N.EQ.0 )
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$ RETURN
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*
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IF( LSAME( DIRECT, 'F' ) ) THEN
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PREVLASTV = N
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DO I = 1, K
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PREVLASTV = MAX( I, PREVLASTV )
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IF( TAU( I ).EQ.ZERO ) THEN
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*
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* H(i) = I
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*
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DO J = 1, I
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T( J, I ) = ZERO
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END DO
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ELSE
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*
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* general case
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*
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IF( LSAME( STOREV, 'C' ) ) THEN
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* Skip any trailing zeros.
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DO LASTV = N, I+1, -1
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IF( V( LASTV, I ).NE.ZERO ) EXIT
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END DO
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DO J = 1, I-1
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T( J, I ) = -TAU( I ) * V( I , J )
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END DO
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J = MIN( LASTV, PREVLASTV )
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*
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* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i)
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*
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CALL SGEMV( 'Transpose', J-I, I-1, -TAU( I ),
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$ V( I+1, 1 ), LDV, V( I+1, I ), 1, ONE,
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$ T( 1, I ), 1 )
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ELSE
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* Skip any trailing zeros.
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DO LASTV = N, I+1, -1
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IF( V( I, LASTV ).NE.ZERO ) EXIT
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END DO
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DO J = 1, I-1
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T( J, I ) = -TAU( I ) * V( J , I )
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END DO
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J = MIN( LASTV, PREVLASTV )
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*
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* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**T
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*
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CALL SGEMV( 'No transpose', I-1, J-I, -TAU( I ),
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$ V( 1, I+1 ), LDV, V( I, I+1 ), LDV,
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$ ONE, T( 1, I ), 1 )
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END IF
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*
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* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i)
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*
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CALL STRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T,
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$ LDT, T( 1, I ), 1 )
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T( I, I ) = TAU( I )
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IF( I.GT.1 ) THEN
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PREVLASTV = MAX( PREVLASTV, LASTV )
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ELSE
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PREVLASTV = LASTV
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END IF
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END IF
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END DO
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ELSE
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PREVLASTV = 1
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DO I = K, 1, -1
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IF( TAU( I ).EQ.ZERO ) THEN
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*
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* H(i) = I
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*
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DO J = I, K
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T( J, I ) = ZERO
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END DO
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ELSE
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*
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* general case
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*
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IF( I.LT.K ) THEN
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IF( LSAME( STOREV, 'C' ) ) THEN
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* Skip any leading zeros.
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DO LASTV = 1, I-1
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IF( V( LASTV, I ).NE.ZERO ) EXIT
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END DO
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DO J = I+1, K
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T( J, I ) = -TAU( I ) * V( N-K+I , J )
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END DO
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J = MAX( LASTV, PREVLASTV )
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*
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* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**T * V(j:n-k+i,i)
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*
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CALL SGEMV( 'Transpose', N-K+I-J, K-I, -TAU( I ),
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$ V( J, I+1 ), LDV, V( J, I ), 1, ONE,
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$ T( I+1, I ), 1 )
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ELSE
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* Skip any leading zeros.
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DO LASTV = 1, I-1
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IF( V( I, LASTV ).NE.ZERO ) EXIT
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END DO
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DO J = I+1, K
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T( J, I ) = -TAU( I ) * V( J, N-K+I )
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END DO
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J = MAX( LASTV, PREVLASTV )
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*
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* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**T
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*
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CALL SGEMV( 'No transpose', K-I, N-K+I-J,
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$ -TAU( I ), V( I+1, J ), LDV, V( I, J ), LDV,
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$ ONE, T( I+1, I ), 1 )
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END IF
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*
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* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i)
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*
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CALL STRMV( 'Lower', 'No transpose', 'Non-unit', K-I,
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$ T( I+1, I+1 ), LDT, T( I+1, I ), 1 )
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IF( I.GT.1 ) THEN
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PREVLASTV = MIN( PREVLASTV, LASTV )
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ELSE
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PREVLASTV = LASTV
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END IF
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END IF
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T( I, I ) = TAU( I )
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END IF
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END DO
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END IF
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RETURN
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*
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* End of SLARFT
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*
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END
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