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|
*> \brief \b CUNMRZ
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CUNMRZ + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cunmrz.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cunmrz.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cunmrz.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CUNMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
*
* .. Scalar Arguments ..
* CHARACTER SIDE, TRANS
* INTEGER INFO, K, L, LDA, LDC, LWORK, M, N
* ..
* .. Array Arguments ..
* COMPLEX A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CUNMRZ 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 k
*> elementary reflectors
*>
*> Q = H(1) H(2) . . . H(k)
*>
*> as returned by CTZRZF. Q is of order M if SIDE = 'L' and of order N
*> if SIDE = 'R'.
*> \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.
*> If SIDE = 'L', M >= K >= 0;
*> if SIDE = 'R', N >= K >= 0.
*> \endverbatim
*>
*> \param[in] L
*> \verbatim
*> L is INTEGER
*> The number of columns of the matrix A containing
*> the meaningful part of the Householder reflectors.
*> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX array, dimension
*> (LDA,M) if SIDE = 'L',
*> (LDA,N) if SIDE = 'R'
*> The i-th row must contain the vector which defines the
*> elementary reflector H(i), for i = 1,2,...,k, as returned by
*> CTZRZF in the last k rows of its array argument A.
*> A is modified by the routine but restored on exit.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,K).
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is COMPLEX array, dimension (K)
*> TAU(i) must contain the scalar factor of the elementary
*> reflector H(i), as returned by CTZRZF.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is COMPLEX 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
*> WORK is COMPLEX array, dimension (MAX(1,LWORK))
*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The dimension of the array WORK.
*> If SIDE = 'L', LWORK >= max(1,N);
*> if SIDE = 'R', LWORK >= max(1,M).
*> For good performance, LWORK should generally be larger.
*>
*> 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.
*
*> \date December 2016
*
*> \ingroup complexOTHERcomputational
*
*> \par Contributors:
* ==================
*>
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*> \endverbatim
*>
* =====================================================================
SUBROUTINE CUNMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
$ WORK, LWORK, INFO )
*
* -- 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 SIDE, TRANS
INTEGER INFO, K, L, LDA, LDC, LWORK, M, N
* ..
* .. Array Arguments ..
COMPLEX A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
INTEGER NBMAX, LDT, TSIZE
PARAMETER ( NBMAX = 64, LDT = NBMAX+1,
$ TSIZE = LDT*NBMAX )
* ..
* .. Local Scalars ..
LOGICAL LEFT, LQUERY, NOTRAN
CHARACTER TRANST
INTEGER I, I1, I2, I3, IB, IC, IINFO, IWT, JA, JC,
$ LDWORK, LWKOPT, MI, NB, NBMIN, NI, NQ, NW
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV
EXTERNAL LSAME, ILAENV
* ..
* .. External Subroutines ..
EXTERNAL CLARZB, CLARZT, CUNMR3, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* Test the input arguments
*
INFO = 0
LEFT = LSAME( SIDE, 'L' )
NOTRAN = LSAME( TRANS, 'N' )
LQUERY = ( LWORK.EQ.-1 )
*
* NQ is the order of Q and NW is the minimum dimension of WORK
*
IF( LEFT ) THEN
NQ = M
NW = MAX( 1, N )
ELSE
NQ = N
NW = MAX( 1, M )
END IF
IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
INFO = -1
ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
INFO = -2
ELSE IF( M.LT.0 ) THEN
INFO = -3
ELSE IF( N.LT.0 ) THEN
INFO = -4
ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
INFO = -5
ELSE IF( L.LT.0 .OR. ( LEFT .AND. ( L.GT.M ) ) .OR.
$ ( .NOT.LEFT .AND. ( L.GT.N ) ) ) THEN
INFO = -6
ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
INFO = -8
ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
INFO = -11
ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
INFO = -13
END IF
*
IF( INFO.EQ.0 ) THEN
*
* Compute the workspace requirements
*
IF( M.EQ.0 .OR. N.EQ.0 ) THEN
LWKOPT = 1
ELSE
NB = MIN( NBMAX, ILAENV( 1, 'CUNMRQ', SIDE // TRANS, M, N,
$ K, -1 ) )
LWKOPT = NW*NB + TSIZE
END IF
WORK( 1 ) = LWKOPT
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CUNMRZ', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Quick return if possible
*
IF( M.EQ.0 .OR. N.EQ.0 ) THEN
RETURN
END IF
*
* Determine the block size.
*
NB = MIN( NBMAX, ILAENV( 1, 'CUNMRQ', SIDE // TRANS, M, N, K,
$ -1 ) )
NBMIN = 2
LDWORK = NW
IF( NB.GT.1 .AND. NB.LT.K ) THEN
IF( LWORK.LT.NW*NB+TSIZE ) THEN
NB = (LWORK-TSIZE) / LDWORK
NBMIN = MAX( 2, ILAENV( 2, 'CUNMRQ', SIDE // TRANS, M, N, K,
$ -1 ) )
END IF
END IF
*
IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
*
* Use unblocked code
*
CALL CUNMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
$ WORK, IINFO )
ELSE
*
* Use blocked code
*
IWT = 1 + NW*NB
IF( ( LEFT .AND. .NOT.NOTRAN ) .OR.
$ ( .NOT.LEFT .AND. NOTRAN ) ) THEN
I1 = 1
I2 = K
I3 = NB
ELSE
I1 = ( ( K-1 ) / NB )*NB + 1
I2 = 1
I3 = -NB
END IF
*
IF( LEFT ) THEN
NI = N
JC = 1
JA = M - L + 1
ELSE
MI = M
IC = 1
JA = N - L + 1
END IF
*
IF( NOTRAN ) THEN
TRANST = 'C'
ELSE
TRANST = 'N'
END IF
*
DO 10 I = I1, I2, I3
IB = MIN( NB, K-I+1 )
*
* Form the triangular factor of the block reflector
* H = H(i+ib-1) . . . H(i+1) H(i)
*
CALL CLARZT( 'Backward', 'Rowwise', L, IB, A( I, JA ), LDA,
$ TAU( I ), WORK( IWT ), LDT )
*
IF( LEFT ) THEN
*
* H or H**H is applied to C(i:m,1:n)
*
MI = M - I + 1
IC = I
ELSE
*
* H or H**H is applied to C(1:m,i:n)
*
NI = N - I + 1
JC = I
END IF
*
* Apply H or H**H
*
CALL CLARZB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI,
$ IB, L, A( I, JA ), LDA, WORK( IWT ), LDT,
$ C( IC, JC ), LDC, WORK, LDWORK )
10 CONTINUE
*
END IF
*
WORK( 1 ) = LWKOPT
*
RETURN
*
* End of CUNMRZ
*
END
|
