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*> \brief \b SGEQRT
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download SGEQRT + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgeqrt.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgeqrt.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgeqrt.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE SGEQRT( M, N, NB, A, LDA, T, LDT, WORK, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, LDT, M, N, NB
* ..
* .. Array Arguments ..
* REAL A( LDA, * ), T( LDT, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SGEQRT computes a blocked QR 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] NB
*> \verbatim
*> NB is INTEGER
*> The block size to be used in the blocked QR. MIN(M,N) >= NB >= 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 above the diagonal of the array
*> contain the min(M,N)-by-N upper trapezoidal matrix R (R is
*> upper triangular if M >= N); the elements below the diagonal
*> are the columns 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 >= NB.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array, dimension (NB*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 December 2016
*
*> \ingroup realGEcomputational
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> The matrix V stores the elementary reflectors H(i) in the i-th column
*> below the diagonal. For example, if M=5 and N=3, the matrix V is
*>
*> V = ( 1 )
*> ( v1 1 )
*> ( v1 v2 1 )
*> ( v1 v2 v3 )
*> ( v1 v2 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/NB), where each
*> block is of order NB except for the last block, which is of order
*> IB = K - (B-1)*NB. For each of the B blocks, a upper triangular block
*> reflector factor is computed: T1, T2, ..., TB. The NB-by-NB (and IB-by-IB
*> for the last block) T's are stored in the NB-by-N matrix T as
*>
*> T = (T1 T2 ... TB).
*> \endverbatim
*>
* =====================================================================
SUBROUTINE SGEQRT( M, N, NB, A, LDA, T, LDT, WORK, INFO )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDT, M, N, NB
* ..
* .. Array Arguments ..
REAL A( LDA, * ), T( LDT, * ), WORK( * )
* ..
*
* =====================================================================
*
* ..
* .. Local Scalars ..
INTEGER I, IB, IINFO, K
LOGICAL USE_RECURSIVE_QR
PARAMETER( USE_RECURSIVE_QR=.TRUE. )
* ..
* .. 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( NB.LT.1 .OR. ( NB.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.NB ) THEN
INFO = -7
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SGEQRT', -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, NB
IB = MIN( K-I+1, NB )
*
* Compute the QR factorization of the current block A(I:M,I:I+IB-1)
*
IF( USE_RECURSIVE_QR ) THEN
CALL SGEQRT3( M-I+1, IB, A(I,I), LDA, T(1,I), LDT, IINFO )
ELSE
CALL SGEQRT2( M-I+1, IB, A(I,I), LDA, T(1,I), LDT, IINFO )
END IF
IF( I+IB.LE.N ) THEN
*
* Update by applying H**T to A(I:M,I+IB:N) from the left
*
CALL SLARFB( 'L', 'T', 'F', 'C', M-I+1, N-I-IB+1, IB,
$ A( I, I ), LDA, T( 1, I ), LDT,
$ A( I, I+IB ), LDA, WORK , N-I-IB+1 )
END IF
END DO
RETURN
*
* End of SGEQRT
*
END
|
