*> \brief \b ZLAMSWLQ
*
* Definition:
* ===========
*
* SUBROUTINE ZLAMSWLQ( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T,
* $ LDT, C, LDC, WORK, LWORK, INFO )
*
*
* .. Scalar Arguments ..
* CHARACTER SIDE, TRANS
* INTEGER INFO, LDA, M, N, K, MB, NB, LDT, LWORK, LDC
* ..
* .. Array Arguments ..
* COMPLEX*16 A( LDA, * ), WORK( * ), C(LDC, * ),
* $ T( LDT, * )
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZLAMSWLQ overwrites the general complex M-by-N matrix C with
*>
*>
*> SIDE = 'L' SIDE = 'R'
*> TRANS = 'N': Q * C C * Q
*> TRANS = 'C': Q**H * C C * Q**H
*> where Q is a complex unitary matrix defined as the product of blocked
*> elementary reflectors computed by short wide LQ
*> factorization (ZLASWLQ)
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] SIDE
*> \verbatim
*> SIDE is CHARACTER*1
*> = 'L': apply Q or Q**H from the Left;
*> = 'R': apply Q or Q**H from the Right.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> = 'N': No transpose, apply Q;
*> = 'C': Conjugate Transpose, apply Q**H.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix C. M >=0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix C. N >= 0.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*> K is INTEGER
*> The number of elementary reflectors whose product defines
*> the matrix Q.
*> M >= K >= 0;
*>
*> \endverbatim
*> \param[in] MB
*> \verbatim
*> MB is INTEGER
*> The row block size to be used in the blocked LQ.
*> M >= MB >= 1
*> \endverbatim
*>
*> \param[in] NB
*> \verbatim
*> NB is INTEGER
*> The column block size to be used in the blocked LQ.
*> NB > M.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX*16 array, dimension
*> (LDA,M) if SIDE = 'L',
*> (LDA,N) if SIDE = 'R'
*> The i-th row must contain the vector which defines the blocked
*> elementary reflector H(i), for i = 1,2,...,k, as returned by
*> ZLASWLQ in the first k rows of its array argument A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= MAX(1,K).
*> \endverbatim
*>
*> \param[in] T
*> \verbatim
*> T is COMPLEX*16 array, dimension
*> ( M * Number of blocks(CEIL(N-K/NB-K)),
*> The blocked upper triangular block reflectors stored in compact form
*> as a sequence of upper triangular blocks. See below
*> for further details.
*> \endverbatim
*>
*> \param[in] LDT
*> \verbatim
*> LDT is INTEGER
*> The leading dimension of the array T. LDT >= MB.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is COMPLEX*16 array, dimension (LDC,N)
*> On entry, the M-by-N matrix C.
*> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*> LDC is INTEGER
*> The leading dimension of the array C. LDC >= max(1,M).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The dimension of the array WORK.
*> If SIDE = 'L', LWORK >= max(1,NB) * MB;
*> if SIDE = 'R', LWORK >= max(1,M) * MB.
*> If LWORK = -1, then a workspace query is assumed; the routine
*> only calculates the optimal size of the WORK array, returns
*> this value as the first entry of the WORK array, and no error
*> message related to LWORK is issued by XERBLA.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*> Short-Wide LQ (SWLQ) performs LQ by a sequence of unitary transformations,
*> representing Q as a product of other unitary matrices
*> Q = Q(1) * Q(2) * . . . * Q(k)
*> where each Q(i) zeros out upper diagonal entries of a block of NB rows of A:
*> Q(1) zeros out the upper diagonal entries of rows 1:NB of A
*> Q(2) zeros out the bottom MB-N rows of rows [1:M,NB+1:2*NB-M] of A
*> Q(3) zeros out the bottom MB-N rows of rows [1:M,2*NB-M+1:3*NB-2*M] of A
*> . . .
*>
*> Q(1) is computed by GELQT, which represents Q(1) by Householder vectors
*> stored under the diagonal of rows 1:MB of A, and by upper triangular
*> block reflectors, stored in array T(1:LDT,1:N).
*> For more information see Further Details in GELQT.
*>
*> Q(i) for i>1 is computed by TPLQT, which represents Q(i) by Householder vectors
*> stored in columns [(i-1)*(NB-M)+M+1:i*(NB-M)+M] of A, and by upper triangular
*> block reflectors, stored in array T(1:LDT,(i-1)*M+1:i*M).
*> The last Q(k) may use fewer rows.
*> For more information see Further Details in TPLQT.
*>
*> For more details of the overall algorithm, see the description of
*> Sequential TSQR in Section 2.2 of [1].
*>
*> [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,”
*> J. Demmel, L. Grigori, M. Hoemmen, J. Langou,
*> SIAM J. Sci. Comput, vol. 34, no. 1, 2012
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZLAMSWLQ( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T,
$ LDT, C, LDC, WORK, LWORK, INFO )
*
* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
CHARACTER SIDE, TRANS
INTEGER INFO, LDA, M, N, K, MB, NB, LDT, LWORK, LDC
* ..
* .. Array Arguments ..
COMPLEX*16 A( LDA, * ), WORK( * ), C(LDC, * ),
$ T( LDT, * )
* ..
*
* =====================================================================
*
* ..
* .. Local Scalars ..
LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
INTEGER I, II, KK, LW, CTR
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* .. External Subroutines ..
EXTERNAL ZTPMLQT, ZGEMLQT, XERBLA
* ..
* .. Executable Statements ..
*
* Test the input arguments
*
LQUERY = LWORK.LT.0
NOTRAN = LSAME( TRANS, 'N' )
TRAN = LSAME( TRANS, 'C' )
LEFT = LSAME( SIDE, 'L' )
RIGHT = LSAME( SIDE, 'R' )
IF (LEFT) THEN
LW = N * MB
ELSE
LW = M * MB
END IF
*
INFO = 0
IF( .NOT.LEFT .AND. .NOT.RIGHT ) THEN
INFO = -1
ELSE IF( .NOT.TRAN .AND. .NOT.NOTRAN ) THEN
INFO = -2
ELSE IF( K.LT.0 ) THEN
INFO = -5
ELSE IF( M.LT.K ) THEN
INFO = -3
ELSE IF( N.LT.0 ) THEN
INFO = -4
ELSE IF( K.LT.MB .OR. MB.LT.1) THEN
INFO = -6
ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
INFO = -9
ELSE IF( LDT.LT.MAX( 1, MB) ) THEN
INFO = -11
ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
INFO = -13
ELSE IF(( LWORK.LT.MAX(1,LW)).AND.(.NOT.LQUERY)) THEN
INFO = -15
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZLAMSWLQ', -INFO )
WORK(1) = LW
RETURN
ELSE IF (LQUERY) THEN
WORK(1) = LW
RETURN
END IF
*
* Quick return if possible
*
IF( MIN(M,N,K).EQ.0 ) THEN
RETURN
END IF
*
IF((NB.LE.K).OR.(NB.GE.MAX(M,N,K))) THEN
CALL ZGEMLQT( SIDE, TRANS, M, N, K, MB, A, LDA,
$ T, LDT, C, LDC, WORK, INFO)
RETURN
END IF
*
IF(LEFT.AND.TRAN) THEN
*
* Multiply Q to the last block of C
*
KK = MOD((M-K),(NB-K))
CTR = (M-K)/(NB-K)
*
IF (KK.GT.0) THEN
II=M-KK+1
CALL ZTPMLQT('L','C',KK , N, K, 0, MB, A(1,II), LDA,
$ T(1,CTR*K+1), LDT, C(1,1), LDC,
$ C(II,1), LDC, WORK, INFO )
ELSE
II=M+1
END IF
*
DO I=II-(NB-K),NB+1,-(NB-K)
*
* Multiply Q to the current block of C (1:M,I:I+NB)
*
CTR = CTR - 1
CALL ZTPMLQT('L','C',NB-K , N, K, 0,MB, A(1,I), LDA,
$ T(1,CTR*K+1),LDT, C(1,1), LDC,
$ C(I,1), LDC, WORK, INFO )
END DO
*
* Multiply Q to the first block of C (1:M,1:NB)
*
CALL ZGEMLQT('L','C',NB , N, K, MB, A(1,1), LDA, T
$ ,LDT ,C(1,1), LDC, WORK, INFO )
*
ELSE IF (LEFT.AND.NOTRAN) THEN
*
* Multiply Q to the first block of C
*
KK = MOD((M-K),(NB-K))
II=M-KK+1
CTR = 1
CALL ZGEMLQT('L','N',NB , N, K, MB, A(1,1), LDA, T
$ ,LDT ,C(1,1), LDC, WORK, INFO )
*
DO I=NB+1,II-NB+K,(NB-K)
*
* Multiply Q to the current block of C (I:I+NB,1:N)
*
CALL ZTPMLQT('L','N',NB-K , N, K, 0,MB, A(1,I), LDA,
$ T(1, CTR * K + 1), LDT, C(1,1), LDC,
$ C(I,1), LDC, WORK, INFO )
CTR = CTR + 1
*
END DO
IF(II.LE.M) THEN
*
* Multiply Q to the last block of C
*
CALL ZTPMLQT('L','N',KK , N, K, 0, MB, A(1,II), LDA,
$ T(1, CTR * K + 1), LDT, C(1,1), LDC,
$ C(II,1), LDC, WORK, INFO )
*
END IF
*
ELSE IF(RIGHT.AND.NOTRAN) THEN
*
* Multiply Q to the last block of C
*
KK = MOD((N-K),(NB-K))
CTR = (N-K)/(NB-K)
IF (KK.GT.0) THEN
II=N-KK+1
CALL ZTPMLQT('R','N',M , KK, K, 0, MB, A(1, II), LDA,
$ T(1, CTR * K + 1), LDT, C(1,1), LDC,
$ C(1,II), LDC, WORK, INFO )
ELSE
II=N+1
END IF
*
DO I=II-(NB-K),NB+1,-(NB-K)
*
* Multiply Q to the current block of C (1:M,I:I+MB)
*
CTR = CTR - 1
CALL ZTPMLQT('R','N', M, NB-K, K, 0, MB, A(1, I), LDA,
$ T(1, CTR * K + 1), LDT, C(1,1), LDC,
$ C(1,I), LDC, WORK, INFO )
END DO
*
* Multiply Q to the first block of C (1:M,1:MB)
*
CALL ZGEMLQT('R','N',M , NB, K, MB, A(1,1), LDA, T
$ ,LDT ,C(1,1), LDC, WORK, INFO )
*
ELSE IF (RIGHT.AND.TRAN) THEN
*
* Multiply Q to the first block of C
*
KK = MOD((N-K),(NB-K))
II=N-KK+1
CALL ZGEMLQT('R','C',M , NB, K, MB, A(1,1), LDA, T
$ ,LDT ,C(1,1), LDC, WORK, INFO )
CTR = 1
*
DO I=NB+1,II-NB+K,(NB-K)
*
* Multiply Q to the current block of C (1:M,I:I+MB)
*
CALL ZTPMLQT('R','C',M , NB-K, K, 0,MB, A(1,I), LDA,
$ T(1,CTR *K+1), LDT, C(1,1), LDC,
$ C(1,I), LDC, WORK, INFO )
CTR = CTR + 1
*
END DO
IF(II.LE.N) THEN
*
* Multiply Q to the last block of C
*
CALL ZTPMLQT('R','C',M , KK, K, 0,MB, A(1,II), LDA,
$ T(1, CTR * K + 1),LDT, C(1,1), LDC,
$ C(1,II), LDC, WORK, INFO )
*
END IF
*
END IF
*
WORK(1) = LW
RETURN
*
* End of ZLAMSWLQ
*
END