1*> \brief \b ZGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.
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 ZGEQR2( M, N, A, LDA, TAU, WORK, INFO )
22*
23*       .. Scalar Arguments ..
24*       INTEGER            INFO, 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*> ZGEQR2 computes a QR factorization of a complex m by n matrix A:
37*> A = Q * R.
38*> \endverbatim
39*
40*  Arguments:
41*  ==========
42*
43*> \param[in] M
44*> \verbatim
45*>          M is INTEGER
46*>          The number of rows of the matrix A.  M >= 0.
47*> \endverbatim
48*>
49*> \param[in] N
50*> \verbatim
51*>          N is INTEGER
52*>          The number of columns of the matrix A.  N >= 0.
53*> \endverbatim
54*>
55*> \param[in,out] A
56*> \verbatim
57*>          A is COMPLEX*16 array, dimension (LDA,N)
58*>          On entry, the m by n matrix A.
59*>          On exit, the elements on and above the diagonal of the array
60*>          contain the min(m,n) by n upper trapezoidal matrix R (R is
61*>          upper triangular if m >= n); the elements below the diagonal,
62*>          with the array TAU, represent the unitary matrix Q as a
63*>          product of elementary reflectors (see Further Details).
64*> \endverbatim
65*>
66*> \param[in] LDA
67*> \verbatim
68*>          LDA is INTEGER
69*>          The leading dimension of the array A.  LDA >= max(1,M).
70*> \endverbatim
71*>
72*> \param[out] TAU
73*> \verbatim
74*>          TAU is COMPLEX*16 array, dimension (min(M,N))
75*>          The scalar factors of the elementary reflectors (see Further
76*>          Details).
77*> \endverbatim
78*>
79*> \param[out] WORK
80*> \verbatim
81*>          WORK is COMPLEX*16 array, dimension (N)
82*> \endverbatim
83*>
84*> \param[out] INFO
85*> \verbatim
86*>          INFO is INTEGER
87*>          = 0: successful exit
88*>          < 0: if INFO = -i, the i-th argument had an illegal value
89*> \endverbatim
90*
91*  Authors:
92*  ========
93*
94*> \author Univ. of Tennessee
95*> \author Univ. of California Berkeley
96*> \author Univ. of Colorado Denver
97*> \author NAG Ltd.
98*
99*> \date September 2012
100*
101*> \ingroup complex16GEcomputational
102*
103*> \par Further Details:
104*  =====================
105*>
106*> \verbatim
107*>
108*>  The matrix Q is represented as a product of elementary reflectors
109*>
110*>     Q = H(1) H(2) . . . H(k), where k = min(m,n).
111*>
112*>  Each H(i) has the form
113*>
114*>     H(i) = I - tau * v * v**H
115*>
116*>  where tau is a complex scalar, and v is a complex vector with
117*>  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
118*>  and tau in TAU(i).
119*> \endverbatim
120*>
121*  =====================================================================
122      SUBROUTINE ZGEQR2( M, N, A, LDA, TAU, WORK, INFO )
123*
124*  -- LAPACK computational routine (version 3.4.2) --
125*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
126*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
127*     September 2012
128*
129*     .. Scalar Arguments ..
130      INTEGER            INFO, LDA, M, N
131*     ..
132*     .. Array Arguments ..
133      COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
134*     ..
135*
136*  =====================================================================
137*
138*     .. Parameters ..
139      COMPLEX*16         ONE
140      PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ) )
141*     ..
142*     .. Local Scalars ..
143      INTEGER            I, K
144      COMPLEX*16         ALPHA
145*     ..
146*     .. External Subroutines ..
147      EXTERNAL           XERBLA, ZLARF, ZLARFG
148*     ..
149*     .. Intrinsic Functions ..
150      INTRINSIC          DCONJG, MAX, MIN
151*     ..
152*     .. Executable Statements ..
153*
154*     Test the input arguments
155*
156      INFO = 0
157      IF( M.LT.0 ) THEN
158         INFO = -1
159      ELSE IF( N.LT.0 ) THEN
160         INFO = -2
161      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
162         INFO = -4
163      END IF
164      IF( INFO.NE.0 ) THEN
165         CALL XERBLA( 'ZGEQR2', -INFO )
166         RETURN
167      END IF
168*
169      K = MIN( M, N )
170*
171      DO 10 I = 1, K
172*
173*        Generate elementary reflector H(i) to annihilate A(i+1:m,i)
174*
175         CALL ZLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1,
176     $                TAU( I ) )
177         IF( I.LT.N ) THEN
178*
179*           Apply H(i)**H to A(i:m,i+1:n) from the left
180*
181            ALPHA = A( I, I )
182            A( I, I ) = ONE
183            CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1,
184     $                  DCONJG( TAU( I ) ), A( I, I+1 ), LDA, WORK )
185            A( I, I ) = ALPHA
186         END IF
187   10 CONTINUE
188      RETURN
189*
190*     End of ZGEQR2
191*
192      END
193