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* Definition:
* ===========
*
* SUBROUTINE SGELQT( M, N, MB, A, LDA, T, LDT, WORK, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, LDT, M, N, MB
* ..
* .. Array Arguments ..
* REAL 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 REAL 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 REAL 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 REAL 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 SGELQT( 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 ..
REAL A( LDA, * ), T( LDT, * ), WORK( * )
* ..
*
* =====================================================================
*
* ..
* .. Local Scalars ..
INTEGER I, IB, IINFO, K
* ..
* .. External Subroutines ..
EXTERNAL SGEQRT2, SGEQRT3, SLARFB, 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( 'SGELQT', -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 SGELQT3( 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 SLARFB( '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 SGELQT
*
END
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