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OpenBLAS/lapack-netlib/SRC/dlarzb.f

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*> \brief \b DLARZB applies a block reflector or its transpose to a general matrix.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLARZB + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarzb.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarzb.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarzb.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
* LDV, T, LDT, C, LDC, WORK, LDWORK )
*
* .. Scalar Arguments ..
* CHARACTER DIRECT, SIDE, STOREV, TRANS
* INTEGER K, L, LDC, LDT, LDV, LDWORK, M, N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ),
* $ WORK( LDWORK, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLARZB applies a real block reflector H or its transpose H**T to
*> a real distributed M-by-N C from the left or the right.
*>
*> Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] SIDE
*> \verbatim
*> SIDE is CHARACTER*1
*> = 'L': apply H or H**T from the Left
*> = 'R': apply H or H**T from the Right
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> = 'N': apply H (No transpose)
*> = 'C': apply H**T (Transpose)
*> \endverbatim
*>
*> \param[in] DIRECT
*> \verbatim
*> DIRECT is CHARACTER*1
*> Indicates how H is formed from a product of elementary
*> reflectors
*> = '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
*> Indicates how the vectors which define the elementary
*> reflectors are stored:
*> = 'C': Columnwise (not supported yet)
*> = 'R': Rowwise
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix C.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix C.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*> K is INTEGER
*> The order of the matrix T (= the number of elementary
*> reflectors whose product defines the block reflector).
*> \endverbatim
*>
*> \param[in] L
*> \verbatim
*> L is INTEGER
*> The number of columns of the matrix V containing the
*> meaningful part of the Householder reflectors.
*> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
*> \endverbatim
*>
*> \param[in] V
*> \verbatim
*> V is DOUBLE PRECISION array, dimension (LDV,NV).
*> If STOREV = 'C', NV = K; if STOREV = 'R', NV = L.
*> \endverbatim
*>
*> \param[in] LDV
*> \verbatim
*> LDV is INTEGER
*> The leading dimension of the array V.
*> If STOREV = 'C', LDV >= L; if STOREV = 'R', LDV >= K.
*> \endverbatim
*>
*> \param[in] T
*> \verbatim
*> T is DOUBLE PRECISION array, dimension (LDT,K)
*> The triangular K-by-K matrix T in the representation of the
*> block reflector.
*> \endverbatim
*>
*> \param[in] LDT
*> \verbatim
*> LDT is INTEGER
*> The leading dimension of the array T. LDT >= K.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is DOUBLE PRECISION array, dimension (LDC,N)
*> On entry, the M-by-N matrix C.
*> On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T.
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*> LDC is INTEGER
*> The leading dimension of the array C. LDC >= max(1,M).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (LDWORK,K)
*> \endverbatim
*>
*> \param[in] LDWORK
*> \verbatim
*> LDWORK is INTEGER
*> The leading dimension of the array WORK.
*> If SIDE = 'L', LDWORK >= max(1,N);
*> if SIDE = 'R', LDWORK >= max(1,M).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup doubleOTHERcomputational
*
*> \par Contributors:
* ==================
*>
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*> \endverbatim
*>
* =====================================================================
SUBROUTINE DLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
$ LDV, T, LDT, C, LDC, WORK, LDWORK )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
CHARACTER DIRECT, SIDE, STOREV, TRANS
INTEGER K, L, LDC, LDT, LDV, LDWORK, M, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ),
$ WORK( LDWORK, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
CHARACTER TRANST
INTEGER I, INFO, J
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL DCOPY, DGEMM, DTRMM, XERBLA
* ..
* .. Executable Statements ..
*
* Quick return if possible
*
IF( M.LE.0 .OR. N.LE.0 )
$ RETURN
*
* Check for currently supported options
*
INFO = 0
IF( .NOT.LSAME( DIRECT, 'B' ) ) THEN
INFO = -3
ELSE IF( .NOT.LSAME( STOREV, 'R' ) ) THEN
INFO = -4
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DLARZB', -INFO )
RETURN
END IF
*
IF( LSAME( TRANS, 'N' ) ) THEN
TRANST = 'T'
ELSE
TRANST = 'N'
END IF
*
IF( LSAME( SIDE, 'L' ) ) THEN
*
* Form H * C or H**T * C
*
* W( 1:n, 1:k ) = C( 1:k, 1:n )**T
*
DO 10 J = 1, K
CALL DCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
10 CONTINUE
*
* W( 1:n, 1:k ) = W( 1:n, 1:k ) + ...
* C( m-l+1:m, 1:n )**T * V( 1:k, 1:l )**T
*
IF( L.GT.0 )
$ CALL DGEMM( 'Transpose', 'Transpose', N, K, L, ONE,
$ C( M-L+1, 1 ), LDC, V, LDV, ONE, WORK, LDWORK )
*
* W( 1:n, 1:k ) = W( 1:n, 1:k ) * T**T or W( 1:m, 1:k ) * T
*
CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, ONE, T,
$ LDT, WORK, LDWORK )
*
* C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )**T
*
DO 30 J = 1, N
DO 20 I = 1, K
C( I, J ) = C( I, J ) - WORK( J, I )
20 CONTINUE
30 CONTINUE
*
* C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
* V( 1:k, 1:l )**T * W( 1:n, 1:k )**T
*
IF( L.GT.0 )
$ CALL DGEMM( 'Transpose', 'Transpose', L, N, K, -ONE, V, LDV,
$ WORK, LDWORK, ONE, C( M-L+1, 1 ), LDC )
*
ELSE IF( LSAME( SIDE, 'R' ) ) THEN
*
* Form C * H or C * H**T
*
* W( 1:m, 1:k ) = C( 1:m, 1:k )
*
DO 40 J = 1, K
CALL DCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 )
40 CONTINUE
*
* W( 1:m, 1:k ) = W( 1:m, 1:k ) + ...
* C( 1:m, n-l+1:n ) * V( 1:k, 1:l )**T
*
IF( L.GT.0 )
$ CALL DGEMM( 'No transpose', 'Transpose', M, K, L, ONE,
$ C( 1, N-L+1 ), LDC, V, LDV, ONE, WORK, LDWORK )
*
* W( 1:m, 1:k ) = W( 1:m, 1:k ) * T or W( 1:m, 1:k ) * T**T
*
CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, ONE, T,
$ LDT, WORK, LDWORK )
*
* C( 1:m, 1:k ) = C( 1:m, 1:k ) - W( 1:m, 1:k )
*
DO 60 J = 1, K
DO 50 I = 1, M
C( I, J ) = C( I, J ) - WORK( I, J )
50 CONTINUE
60 CONTINUE
*
* C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
* W( 1:m, 1:k ) * V( 1:k, 1:l )
*
IF( L.GT.0 )
$ CALL DGEMM( 'No transpose', 'No transpose', M, L, K, -ONE,
$ WORK, LDWORK, V, LDV, ONE, C( 1, N-L+1 ), LDC )
*
END IF
*
RETURN
*
* End of DLARZB
*
END
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