418 lines
12 KiB
Fortran
418 lines
12 KiB
Fortran
*> \brief \b CLAMTSQR
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE CLAMTSQR( 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 A( LDA, * ), WORK( * ), C(LDC, * ),
|
|
* $ T( LDT, * )
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> CLAMTSQR 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 tall skinny
|
|
*> QR factorization (CLATSQR)
|
|
*> \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 A. 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 block size to be used in the blocked QR.
|
|
*> MB > N. (must be the same as CLATSQR)
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] NB
|
|
*> \verbatim
|
|
*> NB is INTEGER
|
|
*> The column block size to be used in the blocked QR.
|
|
*> N >= NB >= 1.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] A
|
|
*> \verbatim
|
|
*> A is COMPLEX array, dimension (LDA,K)
|
|
*> The i-th column must contain the vector which defines the
|
|
*> blockedelementary reflector H(i), for i = 1,2,...,k, as
|
|
*> returned by CLATSQR in the first k columns of
|
|
*> its array argument A.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDA
|
|
*> \verbatim
|
|
*> LDA is INTEGER
|
|
*> The leading dimension of the array A.
|
|
*> If SIDE = 'L', LDA >= max(1,M);
|
|
*> if SIDE = 'R', LDA >= max(1,N).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] T
|
|
*> \verbatim
|
|
*> T is COMPLEX array, dimension
|
|
*> ( N * Number of blocks(CEIL(M-K/MB-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 >= NB.
|
|
*> \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
|
|
*> (workspace) COMPLEX 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,N)*NB;
|
|
*> if SIDE = 'R', LWORK >= max(1,MB)*NB.
|
|
*> 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
|
|
*> Tall-Skinny QR (TSQR) performs QR 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 subdiagonal entries of a block of MB rows of A:
|
|
*> Q(1) zeros out the subdiagonal entries of rows 1:MB of A
|
|
*> Q(2) zeros out the bottom MB-N rows of rows [1:N,MB+1:2*MB-N] of A
|
|
*> Q(3) zeros out the bottom MB-N rows of rows [1:N,2*MB-N+1:3*MB-2*N] of A
|
|
*> . . .
|
|
*>
|
|
*> Q(1) is computed by GEQRT, 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 GEQRT.
|
|
*>
|
|
*> Q(i) for i>1 is computed by TPQRT, which represents Q(i) by Householder vectors
|
|
*> stored in rows [(i-1)*(MB-N)+N+1:i*(MB-N)+N] of A, and by upper triangular
|
|
*> block reflectors, stored in array T(1:LDT,(i-1)*N+1:i*N).
|
|
*> The last Q(k) may use fewer rows.
|
|
*> For more information see Further Details in TPQRT.
|
|
*>
|
|
*> 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 CLAMTSQR( 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 A( LDA, * ), WORK( * ), C(LDC, * ),
|
|
$ T( LDT, * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* ..
|
|
* .. Local Scalars ..
|
|
LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
|
|
INTEGER I, II, KK, LW, CTR, Q
|
|
* ..
|
|
* .. External Functions ..
|
|
LOGICAL LSAME
|
|
EXTERNAL LSAME
|
|
* .. External Subroutines ..
|
|
EXTERNAL CGEMQRT, CTPMQRT, 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 * NB
|
|
Q = M
|
|
ELSE
|
|
LW = M * NB
|
|
Q = N
|
|
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( M.LT.K ) THEN
|
|
INFO = -3
|
|
ELSE IF( N.LT.0 ) THEN
|
|
INFO = -4
|
|
ELSE IF( K.LT.0 ) THEN
|
|
INFO = -5
|
|
ELSE IF( K.LT.NB .OR. NB.LT.1 ) THEN
|
|
INFO = -7
|
|
ELSE IF( LDA.LT.MAX( 1, Q ) ) THEN
|
|
INFO = -9
|
|
ELSE IF( LDT.LT.MAX( 1, NB) ) 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
|
|
*
|
|
* Determine the block size if it is tall skinny or short and wide
|
|
*
|
|
IF( INFO.EQ.0) THEN
|
|
WORK(1) = LW
|
|
END IF
|
|
*
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL XERBLA( 'CLAMTSQR', -INFO )
|
|
RETURN
|
|
ELSE IF (LQUERY) THEN
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Quick return if possible
|
|
*
|
|
IF( MIN(M,N,K).EQ.0 ) THEN
|
|
RETURN
|
|
END IF
|
|
*
|
|
IF((MB.LE.K).OR.(MB.GE.MAX(M,N,K))) THEN
|
|
CALL CGEMQRT( SIDE, TRANS, M, N, K, NB, A, LDA,
|
|
$ T, LDT, C, LDC, WORK, INFO)
|
|
RETURN
|
|
END IF
|
|
*
|
|
IF(LEFT.AND.NOTRAN) THEN
|
|
*
|
|
* Multiply Q to the last block of C
|
|
*
|
|
KK = MOD((M-K),(MB-K))
|
|
CTR = (M-K)/(MB-K)
|
|
IF (KK.GT.0) THEN
|
|
II=M-KK+1
|
|
CALL CTPMQRT('L','N',KK , N, K, 0, NB, A(II,1), 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-(MB-K),MB+1,-(MB-K)
|
|
*
|
|
* Multiply Q to the current block of C (I:I+MB,1:N)
|
|
*
|
|
CTR = CTR - 1
|
|
CALL CTPMQRT('L','N',MB-K , N, K, 0,NB, A(I,1), 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:MB,1:N)
|
|
*
|
|
CALL CGEMQRT('L','N',MB , N, K, NB, A(1,1), LDA, T
|
|
$ ,LDT ,C(1,1), LDC, WORK, INFO )
|
|
*
|
|
ELSE IF (LEFT.AND.TRAN) THEN
|
|
*
|
|
* Multiply Q to the first block of C
|
|
*
|
|
KK = MOD((M-K),(MB-K))
|
|
II=M-KK+1
|
|
CTR = 1
|
|
CALL CGEMQRT('L','C',MB , N, K, NB, A(1,1), LDA, T
|
|
$ ,LDT ,C(1,1), LDC, WORK, INFO )
|
|
*
|
|
DO I=MB+1,II-MB+K,(MB-K)
|
|
*
|
|
* Multiply Q to the current block of C (I:I+MB,1:N)
|
|
*
|
|
CALL CTPMQRT('L','C',MB-K , N, K, 0,NB, A(I,1), 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 CTPMQRT('L','C',KK , N, K, 0,NB, A(II,1), LDA,
|
|
$ T(1,CTR*K+1), LDT, C(1,1), LDC,
|
|
$ C(II,1), LDC, WORK, INFO )
|
|
*
|
|
END IF
|
|
*
|
|
ELSE IF(RIGHT.AND.TRAN) THEN
|
|
*
|
|
* Multiply Q to the last block of C
|
|
*
|
|
KK = MOD((N-K),(MB-K))
|
|
CTR = (N-K)/(MB-K)
|
|
IF (KK.GT.0) THEN
|
|
II=N-KK+1
|
|
CALL CTPMQRT('R','C',M , KK, K, 0, NB, A(II,1), 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-(MB-K),MB+1,-(MB-K)
|
|
*
|
|
* Multiply Q to the current block of C (1:M,I:I+MB)
|
|
*
|
|
CTR = CTR - 1
|
|
CALL CTPMQRT('R','C',M , MB-K, K, 0,NB, A(I,1), 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 CGEMQRT('R','C',M , MB, K, NB, A(1,1), LDA, T
|
|
$ ,LDT ,C(1,1), LDC, WORK, INFO )
|
|
*
|
|
ELSE IF (RIGHT.AND.NOTRAN) THEN
|
|
*
|
|
* Multiply Q to the first block of C
|
|
*
|
|
KK = MOD((N-K),(MB-K))
|
|
II=N-KK+1
|
|
CTR = 1
|
|
CALL CGEMQRT('R','N', M, MB , K, NB, A(1,1), LDA, T
|
|
$ ,LDT ,C(1,1), LDC, WORK, INFO )
|
|
*
|
|
DO I=MB+1,II-MB+K,(MB-K)
|
|
*
|
|
* Multiply Q to the current block of C (1:M,I:I+MB)
|
|
*
|
|
CALL CTPMQRT('R','N', M, MB-K, K, 0,NB, A(I,1), 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 CTPMQRT('R','N', M, KK , K, 0,NB, A(II,1), 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 CLAMTSQR
|
|
*
|
|
END
|