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*> \brief \b DORGR2 generates all or part of the orthogonal matrix Q from an RQ factorization determined by sgerqf (unblocked algorithm).
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DORGR2 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorgr2.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorgr2.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorgr2.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DORGR2( M, N, K, A, LDA, TAU, WORK, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, K, LDA, M, N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DORGR2 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 (M)
*> \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.
*
*> \date December 2016
*
*> \ingroup doubleOTHERcomputational
*
* =====================================================================
SUBROUTINE DORGR2( M, N, K, A, LDA, TAU, 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, K, LDA, M, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, II, J, L
* ..
* .. External Subroutines ..
EXTERNAL DLARF, DSCAL, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input arguments
*
INFO = 0
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.NE.0 ) THEN
CALL XERBLA( 'DORGR2', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( M.LE.0 )
$ RETURN
*
IF( K.LT.M ) THEN
*
* Initialise rows 1:m-k to rows of the unit matrix
*
DO 20 J = 1, N
DO 10 L = 1, M - K
A( L, J ) = ZERO
10 CONTINUE
IF( J.GT.N-M .AND. J.LE.N-K )
$ A( M-N+J, J ) = ONE
20 CONTINUE
END IF
*
DO 40 I = 1, K
II = M - K + I
*
* Apply H(i) to A(1:m-k+i,1:n-k+i) from the right
*
A( II, N-M+II ) = ONE
CALL DLARF( 'Right', II-1, N-M+II, A( II, 1 ), LDA, TAU( I ),
$ A, LDA, WORK )
CALL DSCAL( N-M+II-1, -TAU( I ), A( II, 1 ), LDA )
A( II, N-M+II ) = ONE - TAU( I )
*
* Set A(m-k+i,n-k+i+1:n) to zero
*
DO 30 L = N - M + II + 1, N
A( II, L ) = ZERO
30 CONTINUE
40 CONTINUE
RETURN
*
* End of DORGR2
*
END
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