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diff --git a/SRC/zlaswlq.f b/SRC/zlaswlq.f new file mode 100644 index 00000000..67178c29 --- /dev/null +++ b/SRC/zlaswlq.f @@ -0,0 +1,258 @@ +* +* Definition: +* =========== +* +* SUBROUTINE ZLASWLQ( M, N, MB, NB, A, LDA, T, LDT, WORK, +* LWORK, INFO) +* +* .. Scalar Arguments .. +* INTEGER INFO, LDA, M, N, MB, NB, LDT, LWORK +* .. +* .. Array Arguments .. +* COMPLEX*16 A( LDA, * ), T( LDT, * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZLASWLQ computes a blocked Short-Wide LQ factorization of a +*> M-by-N matrix A, where N >= M: +*> A = L * Q +*> \endverbatim +* +* Arguments: +* ========== +* +*> \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 A. N >= M >= 0. +*> \endverbatim +*> +*> \param[in] MB +*> \verbatim +*> MB is INTEGER +*> The row block size to be used in the blocked QR. +*> M >= MB >= 1 +*> \endverbatim +*> \param[in] NB +*> \verbatim +*> NB is INTEGER +*> The column block size to be used in the blocked QR. +*> NB > M. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX*16 array, dimension (LDA,N) +*> On entry, the M-by-N matrix A. +*> On exit, the elements on and bleow the diagonal +*> of the array contain the N-by-N lower triangular matrix L; +*> the elements above the diagonal represent Q by the rows +*> of blocked V (see Further Details). +*> +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +*> +*> \param[out] T +*> \verbatim +*> T is COMPLEX*16 array, +*> dimension (LDT, N * Number_of_row_blocks) +*> where Number_of_row_blocks = CEIL((N-M)/(NB-M)) +*> The blocked upper triangular block reflectors stored in compact form +*> as a sequence of upper triangular blocks. +*> See Further Details below. +*> \endverbatim +*> +*> \param[in] LDT +*> \verbatim +*> LDT is INTEGER +*> The leading dimension of the array T. LDT >= MB. +*> \endverbatim +*> +*> +*> \param[out] WORK +*> \verbatim +*> (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) +*> +*> \endverbatim +*> \param[in] LWORK +*> \verbatim +*> The dimension of the array WORK. LWORK >= MB*M. +*> 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 orthogonal transformations, +*> representing Q as a product of other orthogonal 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 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 ZLASWLQ( M, N, MB, NB, A, LDA, T, LDT, WORK, LWORK, + $ INFO) +* +* -- LAPACK computational routine (version 3.5.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd. -- +* November 2013 +* +* .. Scalar Arguments .. + INTEGER INFO, LDA, M, N, MB, NB, LWORK, LDT +* .. +* .. Array Arguments .. + COMPLEX*16 A( LDA, * ), WORK( * ), T( LDT, *) +* .. +* +* ===================================================================== +* +* .. +* .. Local Scalars .. + LOGICAL LQUERY + INTEGER I, II, KK, CTR +* .. +* .. EXTERNAL FUNCTIONS .. + LOGICAL LSAME + EXTERNAL LSAME +* .. EXTERNAL SUBROUTINES .. + EXTERNAL ZGELQT, ZTPLQT, XERBLA +* .. INTRINSIC FUNCTIONS .. + INTRINSIC MAX, MIN, MOD +* .. +* .. EXECUTABLE STATEMENTS .. +* +* TEST THE INPUT ARGUMENTS +* + INFO = 0 +* + LQUERY = ( LWORK.EQ.-1 ) +* + IF( M.LT.0 ) THEN + INFO = -1 + ELSE IF( N.LT.0 .OR. N.LT.M ) THEN + INFO = -2 + ELSE IF( MB.LT.1 .OR. ( MB.GT.M .AND. M.GT.0 )) THEN + INFO = -3 + ELSE IF( NB.LE.M ) THEN + INFO = -4 + ELSE IF( LDA.LT.MAX( 1, M ) ) THEN + INFO = -5 + ELSE IF( LDT.LT.MB ) THEN + INFO = -8 + ELSE IF( ( LWORK.LT.M*MB) .AND. (.NOT.LQUERY) ) THEN + INFO = -10 + END IF + IF( INFO.EQ.0) THEN + WORK(1) = MB*M + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'ZLASWLQ', -INFO ) + RETURN + ELSE IF (LQUERY) THEN + RETURN + END IF +* +* Quick return if possible +* + IF( MIN(M,N).EQ.0 ) THEN + RETURN + END IF +* +* The LQ Decomposition +* + IF((M.GE.N).OR.(NB.LE.M).OR.(NB.GE.N)) THEN + CALL ZGELQT( M, N, MB, A, LDA, T, LDT, WORK, INFO) + RETURN + END IF +* + KK = MOD((N-M),(NB-M)) + II=N-KK+1 +* +* Compute the LQ factorization of the first block A(1:M,1:NB) +* + CALL ZGELQT( M, NB, MB, A(1,1), LDA, T, LDT, WORK, INFO) + CTR = 1 +* + DO I = NB+1, II-NB+M , (NB-M) +* +* Compute the QR factorization of the current block A(1:M,I:I+NB-M) +* + CALL ZTPLQT( M, NB-M, 0, MB, A(1,1), LDA, A( 1, I ), + $ LDA, T(1, CTR * M + 1), + $ LDT, WORK, INFO ) + CTR = CTR + 1 + END DO +* +* Compute the QR factorization of the last block A(1:M,II:N) +* + IF (II.LE.N) THEN + CALL ZTPLQT( M, KK, 0, MB, A(1,1), LDA, A( 1, II ), + $ LDA, T(1, CTR * M + 1), LDT, + $ WORK, INFO ) + END IF +* + WORK( 1 ) = M * MB + RETURN +* +* End of ZLASWLQ +* + END
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