1*> \brief \b ZUNG2R
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
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16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE ZUNG2R( 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*16         A( LDA, * ), TAU( * ), WORK( * )
28*       ..
29*
30*
31*> \par Purpose:
32*  =============
33*>
34*> \verbatim
35*>
36*> ZUNG2R generates an m by n complex matrix Q with orthonormal columns,
37*> which is defined as the first n columns of a product of k elementary
38*> reflectors of order m
39*>
40*>       Q  =  H(1) H(2) . . . H(k)
41*>
42*> as returned by ZGEQRF.
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. M >= N >= 0.
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. N >= K >= 0.
65*> \endverbatim
66*>
67*> \param[in,out] A
68*> \verbatim
69*>          A is COMPLEX*16 array, dimension (LDA,N)
70*>          On entry, the i-th column must contain the vector which
71*>          defines the elementary reflector H(i), for i = 1,2,...,k, as
72*>          returned by ZGEQRF in the first k columns of its array
73*>          argument A.
74*>          On exit, the m by n matrix Q.
75*> \endverbatim
76*>
77*> \param[in] LDA
78*> \verbatim
79*>          LDA is INTEGER
80*>          The first dimension of the array A. LDA >= max(1,M).
81*> \endverbatim
82*>
83*> \param[in] TAU
84*> \verbatim
85*>          TAU is COMPLEX*16 array, dimension (K)
86*>          TAU(i) must contain the scalar factor of the elementary
87*>          reflector H(i), as returned by ZGEQRF.
88*> \endverbatim
89*>
90*> \param[out] WORK
91*> \verbatim
92*>          WORK is COMPLEX*16 array, dimension (N)
93*> \endverbatim
94*>
95*> \param[out] INFO
96*> \verbatim
97*>          INFO is INTEGER
98*>          = 0: successful exit
99*>          < 0: if INFO = -i, the i-th argument has an illegal value
100*> \endverbatim
101*
102*  Authors:
103*  ========
104*
105*> \author Univ. of Tennessee
106*> \author Univ. of California Berkeley
107*> \author Univ. of Colorado Denver
108*> \author NAG Ltd.
109*
110*> \ingroup complex16OTHERcomputational
111*
112*  =====================================================================
113      SUBROUTINE ZUNG2R( M, N, K, A, LDA, TAU, WORK, INFO )
114*
115*  -- LAPACK computational routine --
116*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
117*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
118*
119*     .. Scalar Arguments ..
120      INTEGER            INFO, K, LDA, M, N
121*     ..
122*     .. Array Arguments ..
123      COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
124*     ..
125*
126*  =====================================================================
127*
128*     .. Parameters ..
129      COMPLEX*16         ONE, ZERO
130      PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ),
131     $                   ZERO = ( 0.0D+0, 0.0D+0 ) )
132*     ..
133*     .. Local Scalars ..
134      INTEGER            I, J, L
135*     ..
136*     .. External Subroutines ..
137      EXTERNAL           XERBLA, ZLARF, ZSCAL
138*     ..
139*     .. Intrinsic Functions ..
140      INTRINSIC          MAX
141*     ..
142*     .. Executable Statements ..
143*
144*     Test the input arguments
145*
146      INFO = 0
147      IF( M.LT.0 ) THEN
148         INFO = -1
149      ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
150         INFO = -2
151      ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
152         INFO = -3
153      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
154         INFO = -5
155      END IF
156      IF( INFO.NE.0 ) THEN
157         CALL XERBLA( 'ZUNG2R', -INFO )
158         RETURN
159      END IF
160*
161*     Quick return if possible
162*
163      IF( N.LE.0 )
164     $   RETURN
165*
166*     Initialise columns k+1:n to columns of the unit matrix
167*
168      DO 20 J = K + 1, N
169         DO 10 L = 1, M
170            A( L, J ) = ZERO
171   10    CONTINUE
172         A( J, J ) = ONE
173   20 CONTINUE
174*
175      DO 40 I = K, 1, -1
176*
177*        Apply H(i) to A(i:m,i:n) from the left
178*
179         IF( I.LT.N ) THEN
180            A( I, I ) = ONE
181            CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ),
182     $                  A( I, I+1 ), LDA, WORK )
183         END IF
184         IF( I.LT.M )
185     $      CALL ZSCAL( M-I, -TAU( I ), A( I+1, I ), 1 )
186         A( I, I ) = ONE - TAU( I )
187*
188*        Set A(1:i-1,i) to zero
189*
190         DO 30 L = 1, I - 1
191            A( L, I ) = ZERO
192   30    CONTINUE
193   40 CONTINUE
194      RETURN
195*
196*     End of ZUNG2R
197*
198      END
199