1*> \brief \b CUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cungl2.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE CUNGL2( M, N, K, A, LDA, TAU, WORK, INFO )
22*
23*       .. Scalar Arguments ..
24*       INTEGER            INFO, K, LDA, M, N
25*       ..
26*       .. Array Arguments ..
27*       COMPLEX            A( LDA, * ), TAU( * ), WORK( * )
28*       ..
29*
30*
31*> \par Purpose:
32*  =============
33*>
34*> \verbatim
35*>
36*> CUNGL2 generates an m-by-n complex matrix Q with orthonormal rows,
37*> which is defined as the first m rows of a product of k elementary
38*> reflectors of order n
39*>
40*>       Q  =  H(k)**H . . . H(2)**H H(1)**H
41*>
42*> as returned by CGELQF.
43*> \endverbatim
44*
45*  Arguments:
46*  ==========
47*
48*> \param[in] M
49*> \verbatim
50*>          M is INTEGER
51*>          The number of rows of the matrix Q. M >= 0.
52*> \endverbatim
53*>
54*> \param[in] N
55*> \verbatim
56*>          N is INTEGER
57*>          The number of columns of the matrix Q. N >= M.
58*> \endverbatim
59*>
60*> \param[in] K
61*> \verbatim
62*>          K is INTEGER
63*>          The number of elementary reflectors whose product defines the
64*>          matrix Q. M >= K >= 0.
65*> \endverbatim
66*>
67*> \param[in,out] A
68*> \verbatim
69*>          A is COMPLEX array, dimension (LDA,N)
70*>          On entry, the i-th row must contain the vector which defines
71*>          the elementary reflector H(i), for i = 1,2,...,k, as returned
72*>          by CGELQF in the first k rows of its array argument A.
73*>          On exit, the m by n matrix Q.
74*> \endverbatim
75*>
76*> \param[in] LDA
77*> \verbatim
78*>          LDA is INTEGER
79*>          The first dimension of the array A. LDA >= max(1,M).
80*> \endverbatim
81*>
82*> \param[in] TAU
83*> \verbatim
84*>          TAU is COMPLEX array, dimension (K)
85*>          TAU(i) must contain the scalar factor of the elementary
86*>          reflector H(i), as returned by CGELQF.
87*> \endverbatim
88*>
89*> \param[out] WORK
90*> \verbatim
91*>          WORK is COMPLEX array, dimension (M)
92*> \endverbatim
93*>
94*> \param[out] INFO
95*> \verbatim
96*>          INFO is INTEGER
97*>          = 0: successful exit
98*>          < 0: if INFO = -i, the i-th argument has an illegal value
99*> \endverbatim
100*
101*  Authors:
102*  ========
103*
104*> \author Univ. of Tennessee
105*> \author Univ. of California Berkeley
106*> \author Univ. of Colorado Denver
107*> \author NAG Ltd.
108*
109*> \ingroup complexOTHERcomputational
110*
111*  =====================================================================
112      SUBROUTINE CUNGL2( M, N, K, A, LDA, TAU, WORK, INFO )
113*
114*  -- LAPACK computational routine --
115*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
116*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
117*
118*     .. Scalar Arguments ..
119      INTEGER            INFO, K, LDA, M, N
120*     ..
121*     .. Array Arguments ..
122      COMPLEX            A( LDA, * ), TAU( * ), WORK( * )
123*     ..
124*
125*  =====================================================================
126*
127*     .. Parameters ..
128      COMPLEX            ONE, ZERO
129      PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ),
130     $                   ZERO = ( 0.0E+0, 0.0E+0 ) )
131*     ..
132*     .. Local Scalars ..
133      INTEGER            I, J, L
134*     ..
135*     .. External Subroutines ..
136      EXTERNAL           CLACGV, CLARF, CSCAL, XERBLA
137*     ..
138*     .. Intrinsic Functions ..
139      INTRINSIC          CONJG, MAX
140*     ..
141*     .. Executable Statements ..
142*
143*     Test the input arguments
144*
145      INFO = 0
146      IF( M.LT.0 ) THEN
147         INFO = -1
148      ELSE IF( N.LT.M ) THEN
149         INFO = -2
150      ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
151         INFO = -3
152      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
153         INFO = -5
154      END IF
155      IF( INFO.NE.0 ) THEN
156         CALL XERBLA( 'CUNGL2', -INFO )
157         RETURN
158      END IF
159*
160*     Quick return if possible
161*
162      IF( M.LE.0 )
163     $   RETURN
164*
165      IF( K.LT.M ) THEN
166*
167*        Initialise rows k+1:m to rows of the unit matrix
168*
169         DO 20 J = 1, N
170            DO 10 L = K + 1, M
171               A( L, J ) = ZERO
172   10       CONTINUE
173            IF( J.GT.K .AND. J.LE.M )
174     $         A( J, J ) = ONE
175   20    CONTINUE
176      END IF
177*
178      DO 40 I = K, 1, -1
179*
180*        Apply H(i)**H to A(i:m,i:n) from the right
181*
182         IF( I.LT.N ) THEN
183            CALL CLACGV( N-I, A( I, I+1 ), LDA )
184            IF( I.LT.M ) THEN
185               A( I, I ) = ONE
186               CALL CLARF( 'Right', M-I, N-I+1, A( I, I ), LDA,
187     $                     CONJG( TAU( I ) ), A( I+1, I ), LDA, WORK )
188            END IF
189            CALL CSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA )
190            CALL CLACGV( N-I, A( I, I+1 ), LDA )
191         END IF
192         A( I, I ) = ONE - CONJG( TAU( I ) )
193*
194*        Set A(i,1:i-1,i) to zero
195*
196         DO 30 L = 1, I - 1
197            A( I, L ) = ZERO
198   30    CONTINUE
199   40 CONTINUE
200      RETURN
201*
202*     End of CUNGL2
203*
204      END
205