*> \brief \b DGELQT * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DGEQRT + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DGELQT( M, N, MB, A, LDA, T, LDT, WORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, LDT, M, N, MB * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), T( LDT, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DGELQT computes a blocked LQ factorization of a real M-by-N matrix A *> using the compact WY representation of 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 >= 0. *> \endverbatim *> *> \param[in] MB *> \verbatim *> MB is INTEGER *> The block size to be used in the blocked QR. MIN(M,N) >= MB >= 1. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the M-by-N matrix A. *> On exit, the elements on and below the diagonal of the array *> contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is *> lower triangular if M <= N); the elements above the diagonal *> are the rows of V. *> \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 DOUBLE PRECISION array, dimension (LDT,MIN(M,N)) *> The 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 >= MB. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (MB*N) *> \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 June 2017 * *> \ingroup doubleGEcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> The matrix V stores the elementary reflectors H(i) in the i-th row *> above the diagonal. For example, if M=5 and N=3, the matrix V is *> *> V = ( 1 v1 v1 v1 v1 ) *> ( 1 v2 v2 v2 ) *> ( 1 v3 v3 ) *> *> *> where the vi's represent the vectors which define H(i), which are returned *> in the matrix A. The 1's along the diagonal of V are not stored in A. *> Let K=MIN(M,N). The number of blocks is B = ceiling(K/MB), where each *> block is of order MB except for the last block, which is of order *> IB = K - (B-1)*MB. For each of the B blocks, a upper triangular block *> reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB *> for the last block) T's are stored in the MB-by-K matrix T as *> *> T = (T1 T2 ... TB). *> \endverbatim *> * ===================================================================== SUBROUTINE DGELQT( M, N, MB, A, LDA, T, LDT, WORK, INFO ) * * -- LAPACK computational routine (version 3.7.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2017 * * .. Scalar Arguments .. INTEGER INFO, LDA, LDT, M, N, MB * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), T( LDT, * ), WORK( * ) * .. * * ===================================================================== * * .. * .. Local Scalars .. INTEGER I, IB, IINFO, K * .. * .. External Subroutines .. EXTERNAL DGEQRT2, DGEQRT3, DLARFB, XERBLA * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( MB.LT.1 .OR. ( MB.GT.MIN(M,N) .AND. MIN(M,N).GT.0 ) )THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -5 ELSE IF( LDT.LT.MB ) THEN INFO = -7 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DGELQT', -INFO ) RETURN END IF * * Quick return if possible * K = MIN( M, N ) IF( K.EQ.0 ) RETURN * * Blocked loop of length K * DO I = 1, K, MB IB = MIN( K-I+1, MB ) * * Compute the LQ factorization of the current block A(I:M,I:I+IB-1) * CALL DGELQT3( IB, N-I+1, A(I,I), LDA, T(1,I), LDT, IINFO ) IF( I+IB.LE.M ) THEN * * Update by applying H**T to A(I:M,I+IB:N) from the right * CALL DLARFB( 'R', 'N', 'F', 'R', M-I-IB+1, N-I+1, IB, \$ A( I, I ), LDA, T( 1, I ), LDT, \$ A( I+IB, I ), LDA, WORK , M-I-IB+1 ) END IF END DO RETURN * * End of DGELQT * END