*> \brief \b DORGRQ * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DORGRQ + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DORGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, K, LDA, LWORK, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DORGRQ generates an M-by-N real matrix Q with orthonormal rows, *> which is defined as the last M rows of a product of K elementary *> reflectors of order N *> *> Q = H(1) H(2) . . . H(k) *> *> as returned by DGERQF. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix Q. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix Q. N >= M. *> \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,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the (m-k+i)-th row must contain the vector which *> defines the elementary reflector H(i), for i = 1,2,...,k, as *> returned by DGERQF in the last k rows of its array argument *> A. *> On exit, the M-by-N matrix Q. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The first dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is DOUBLE PRECISION array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by DGERQF. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION 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. LWORK >= max(1,M). *> For optimum performance LWORK >= M*NB, where NB is the *> optimal blocksize. *> *> 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 has an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup doubleOTHERcomputational * * ===================================================================== SUBROUTINE DORGRQ( M, N, K, A, LDA, TAU, 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 .. INTEGER INFO, K, LDA, LWORK, M, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. * .. Local Scalars .. LOGICAL LQUERY INTEGER I, IB, II, IINFO, IWS, J, KK, L, LDWORK, \$ LWKOPT, NB, NBMIN, NX * .. * .. External Subroutines .. EXTERNAL DLARFB, DLARFT, DORGR2, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 LQUERY = ( LWORK.EQ.-1 ) IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.M ) THEN INFO = -2 ELSE IF( K.LT.0 .OR. K.GT.M ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -5 END IF * IF( INFO.EQ.0 ) THEN IF( M.LE.0 ) THEN LWKOPT = 1 ELSE NB = ILAENV( 1, 'DORGRQ', ' ', M, N, K, -1 ) LWKOPT = M*NB END IF WORK( 1 ) = LWKOPT * IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN INFO = -8 END IF END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DORGRQ', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( M.LE.0 ) THEN RETURN END IF * NBMIN = 2 NX = 0 IWS = M IF( NB.GT.1 .AND. NB.LT.K ) THEN * * Determine when to cross over from blocked to unblocked code. * NX = MAX( 0, ILAENV( 3, 'DORGRQ', ' ', M, N, K, -1 ) ) IF( NX.LT.K ) THEN * * Determine if workspace is large enough for blocked code. * LDWORK = M IWS = LDWORK*NB IF( LWORK.LT.IWS ) THEN * * Not enough workspace to use optimal NB: reduce NB and * determine the minimum value of NB. * NB = LWORK / LDWORK NBMIN = MAX( 2, ILAENV( 2, 'DORGRQ', ' ', M, N, K, -1 ) ) END IF END IF END IF * IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN * * Use blocked code after the first block. * The last kk rows are handled by the block method. * KK = MIN( K, ( ( K-NX+NB-1 ) / NB )*NB ) * * Set A(1:m-kk,n-kk+1:n) to zero. * DO 20 J = N - KK + 1, N DO 10 I = 1, M - KK A( I, J ) = ZERO 10 CONTINUE 20 CONTINUE ELSE KK = 0 END IF * * Use unblocked code for the first or only block. * CALL DORGR2( M-KK, N-KK, K-KK, A, LDA, TAU, WORK, IINFO ) * IF( KK.GT.0 ) THEN * * Use blocked code * DO 50 I = K - KK + 1, K, NB IB = MIN( NB, K-I+1 ) II = M - K + I IF( II.GT.1 ) THEN * * Form the triangular factor of the block reflector * H = H(i+ib-1) . . . H(i+1) H(i) * CALL DLARFT( 'Backward', 'Rowwise', N-K+I+IB-1, IB, \$ A( II, 1 ), LDA, TAU( I ), WORK, LDWORK ) * * Apply H**T to A(1:m-k+i-1,1:n-k+i+ib-1) from the right * CALL DLARFB( 'Right', 'Transpose', 'Backward', 'Rowwise', \$ II-1, N-K+I+IB-1, IB, A( II, 1 ), LDA, WORK, \$ LDWORK, A, LDA, WORK( IB+1 ), LDWORK ) END IF * * Apply H**T to columns 1:n-k+i+ib-1 of current block * CALL DORGR2( IB, N-K+I+IB-1, IB, A( II, 1 ), LDA, TAU( I ), \$ WORK, IINFO ) * * Set columns n-k+i+ib:n of current block to zero * DO 40 L = N - K + I + IB, N DO 30 J = II, II + IB - 1 A( J, L ) = ZERO 30 CONTINUE 40 CONTINUE 50 CONTINUE END IF * WORK( 1 ) = IWS RETURN * * End of DORGRQ * END