1      SUBROUTINE CGERQ2( M, N, A, LDA, TAU, WORK, INFO )
2*
3*  -- LAPACK routine (version 3.0) --
4*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
5*     Courant Institute, Argonne National Lab, and Rice University
6*     September 30, 1994
7*
8*     .. Scalar Arguments ..
9      INTEGER            INFO, LDA, M, N
10*     ..
11*     .. Array Arguments ..
12      COMPLEX            A( LDA, * ), TAU( * ), WORK( * )
13*     ..
14*
15*  Purpose
16*  =======
17*
18*  CGERQ2 computes an RQ factorization of a complex m by n matrix A:
19*  A = R * Q.
20*
21*  Arguments
22*  =========
23*
24*  M       (input) INTEGER
25*          The number of rows of the matrix A.  M >= 0.
26*
27*  N       (input) INTEGER
28*          The number of columns of the matrix A.  N >= 0.
29*
30*  A       (input/output) COMPLEX array, dimension (LDA,N)
31*          On entry, the m by n matrix A.
32*          On exit, if m <= n, the upper triangle of the subarray
33*          A(1:m,n-m+1:n) contains the m by m upper triangular matrix R;
34*          if m >= n, the elements on and above the (m-n)-th subdiagonal
35*          contain the m by n upper trapezoidal matrix R; the remaining
36*          elements, with the array TAU, represent the unitary matrix
37*          Q as a product of elementary reflectors (see Further
38*          Details).
39*
40*  LDA     (input) INTEGER
41*          The leading dimension of the array A.  LDA >= max(1,M).
42*
43*  TAU     (output) COMPLEX array, dimension (min(M,N))
44*          The scalar factors of the elementary reflectors (see Further
45*          Details).
46*
47*  WORK    (workspace) COMPLEX array, dimension (M)
48*
49*  INFO    (output) INTEGER
50*          = 0: successful exit
51*          < 0: if INFO = -i, the i-th argument had an illegal value
52*
53*  Further Details
54*  ===============
55*
56*  The matrix Q is represented as a product of elementary reflectors
57*
58*     Q = H(1)' H(2)' . . . H(k)', where k = min(m,n).
59*
60*  Each H(i) has the form
61*
62*     H(i) = I - tau * v * v'
63*
64*  where tau is a complex scalar, and v is a complex vector with
65*  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
66*  exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).
67*
68*  =====================================================================
69*
70*     .. Parameters ..
71      COMPLEX            ONE
72      PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ) )
73*     ..
74*     .. Local Scalars ..
75      INTEGER            I, K
76      COMPLEX            ALPHA
77*     ..
78*     .. External Subroutines ..
79      EXTERNAL           CLACGV, CLARF, CLARFG, XERBLA
80*     ..
81*     .. Intrinsic Functions ..
82      INTRINSIC          MAX, MIN
83*     ..
84*     .. Executable Statements ..
85*
86*     Test the input arguments
87*
88      INFO = 0
89      IF( M.LT.0 ) THEN
90         INFO = -1
91      ELSE IF( N.LT.0 ) THEN
92         INFO = -2
93      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
94         INFO = -4
95      END IF
96      IF( INFO.NE.0 ) THEN
97         CALL XERBLA( 'CGERQ2', -INFO )
98         RETURN
99      END IF
100*
101      K = MIN( M, N )
102*
103      DO 10 I = K, 1, -1
104*
105*        Generate elementary reflector H(i) to annihilate
106*        A(m-k+i,1:n-k+i-1)
107*
108         CALL CLACGV( N-K+I, A( M-K+I, 1 ), LDA )
109         ALPHA = A( M-K+I, N-K+I )
110         CALL CLARFG( N-K+I, ALPHA, A( M-K+I, 1 ), LDA,
111     $                TAU( I ) )
112*
113*        Apply H(i) to A(1:m-k+i-1,1:n-k+i) from the right
114*
115         A( M-K+I, N-K+I ) = ONE
116         CALL CLARF( 'Right', M-K+I-1, N-K+I, A( M-K+I, 1 ), LDA,
117     $               TAU( I ), A, LDA, WORK )
118         A( M-K+I, N-K+I ) = ALPHA
119         CALL CLACGV( N-K+I-1, A( M-K+I, 1 ), LDA )
120   10 CONTINUE
121      RETURN
122*
123*     End of CGERQ2
124*
125      END
126