You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
381 lines
10 KiB
381 lines
10 KiB
2 years ago
|
*> \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.
|
||
|
|
*
|
||
|
|
*> \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 --
|
||
|
|
* -- 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, 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.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.LWKOPT ) 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
|