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*> \brief \b CUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CUNGL2 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cungl2.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cungl2.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cungl2.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CUNGL2( M, N, K, A, LDA, TAU, WORK, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, K, LDA, M, N
* ..
* .. Array Arguments ..
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CUNGL2 generates an m-by-n complex matrix Q with orthonormal rows,
*> which is defined as the first m rows of a product of k elementary
*> reflectors of order n
*>
*> Q = H(k)**H . . . H(2)**H H(1)**H
*>
*> as returned by CGELQF.
*> \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 COMPLEX array, dimension (LDA,N)
*> On entry, the i-th row must contain the vector which defines
*> the elementary reflector H(i), for i = 1,2,...,k, as returned
*> by CGELQF in the first 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 COMPLEX array, dimension (K)
*> TAU(i) must contain the scalar factor of the elementary
*> reflector H(i), as returned by CGELQF.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX 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 complexOTHERcomputational
*
* =====================================================================
SUBROUTINE CUNGL2( 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 ..
COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX ONE, ZERO
PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ),
$ ZERO = ( 0.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
INTEGER I, J, L
* ..
* .. External Subroutines ..
EXTERNAL CLACGV, CLARF, CSCAL, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG, 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( 'CUNGL2', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( M.LE.0 )
$ RETURN
*
IF( K.LT.M ) THEN
*
* Initialise rows k+1:m to rows of the unit matrix
*
DO 20 J = 1, N
DO 10 L = K + 1, M
A( L, J ) = ZERO
10 CONTINUE
IF( J.GT.K .AND. J.LE.M )
$ A( J, J ) = ONE
20 CONTINUE
END IF
*
DO 40 I = K, 1, -1
*
* Apply H(i)**H to A(i:m,i:n) from the right
*
IF( I.LT.N ) THEN
CALL CLACGV( N-I, A( I, I+1 ), LDA )
IF( I.LT.M ) THEN
A( I, I ) = ONE
CALL CLARF( 'Right', M-I, N-I+1, A( I, I ), LDA,
$ CONJG( TAU( I ) ), A( I+1, I ), LDA, WORK )
END IF
CALL CSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA )
CALL CLACGV( N-I, A( I, I+1 ), LDA )
END IF
A( I, I ) = ONE - CONJG( TAU( I ) )
*
* Set A(i,1:i-1,i) to zero
*
DO 30 L = 1, I - 1
A( I, L ) = ZERO
30 CONTINUE
40 CONTINUE
RETURN
*
* End of CUNGL2
*
END
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