1*> \brief \b CGEQRS
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*  Definition:
9*  ===========
10*
11*       SUBROUTINE CGEQRS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
12*                          INFO )
13*
14*       .. Scalar Arguments ..
15*       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS
16*       ..
17*       .. Array Arguments ..
18*       COMPLEX            A( LDA, * ), B( LDB, * ), TAU( * ),
19*      $                   WORK( LWORK )
20*       ..
21*
22*
23*> \par Purpose:
24*  =============
25*>
26*> \verbatim
27*>
28*> Solve the least squares problem
29*>     min || A*X - B ||
30*> using the QR factorization
31*>     A = Q*R
32*> computed by CGEQRF.
33*> \endverbatim
34*
35*  Arguments:
36*  ==========
37*
38*> \param[in] M
39*> \verbatim
40*>          M is INTEGER
41*>          The number of rows of the matrix A.  M >= 0.
42*> \endverbatim
43*>
44*> \param[in] N
45*> \verbatim
46*>          N is INTEGER
47*>          The number of columns of the matrix A.  M >= N >= 0.
48*> \endverbatim
49*>
50*> \param[in] NRHS
51*> \verbatim
52*>          NRHS is INTEGER
53*>          The number of columns of B.  NRHS >= 0.
54*> \endverbatim
55*>
56*> \param[in] A
57*> \verbatim
58*>          A is COMPLEX array, dimension (LDA,N)
59*>          Details of the QR factorization of the original matrix A as
60*>          returned by CGEQRF.
61*> \endverbatim
62*>
63*> \param[in] LDA
64*> \verbatim
65*>          LDA is INTEGER
66*>          The leading dimension of the array A.  LDA >= M.
67*> \endverbatim
68*>
69*> \param[in] TAU
70*> \verbatim
71*>          TAU is COMPLEX array, dimension (N)
72*>          Details of the orthogonal matrix Q.
73*> \endverbatim
74*>
75*> \param[in,out] B
76*> \verbatim
77*>          B is COMPLEX array, dimension (LDB,NRHS)
78*>          On entry, the m-by-nrhs right hand side matrix B.
79*>          On exit, the n-by-nrhs solution matrix X.
80*> \endverbatim
81*>
82*> \param[in] LDB
83*> \verbatim
84*>          LDB is INTEGER
85*>          The leading dimension of the array B. LDB >= M.
86*> \endverbatim
87*>
88*> \param[out] WORK
89*> \verbatim
90*>          WORK is COMPLEX array, dimension (LWORK)
91*> \endverbatim
92*>
93*> \param[in] LWORK
94*> \verbatim
95*>          LWORK is INTEGER
96*>          The length of the array WORK.  LWORK must be at least NRHS,
97*>          and should be at least NRHS*NB, where NB is the block size
98*>          for this environment.
99*> \endverbatim
100*>
101*> \param[out] INFO
102*> \verbatim
103*>          INFO is INTEGER
104*>          = 0: successful exit
105*>          < 0: if INFO = -i, the i-th argument had an illegal value
106*> \endverbatim
107*
108*  Authors:
109*  ========
110*
111*> \author Univ. of Tennessee
112*> \author Univ. of California Berkeley
113*> \author Univ. of Colorado Denver
114*> \author NAG Ltd.
115*
116*> \ingroup complex_lin
117*
118*  =====================================================================
119      SUBROUTINE CGEQRS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
120     $                   INFO )
121*
122*  -- LAPACK test routine --
123*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
124*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125*
126*     .. Scalar Arguments ..
127      INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS
128*     ..
129*     .. Array Arguments ..
130      COMPLEX            A( LDA, * ), B( LDB, * ), TAU( * ),
131     $                   WORK( LWORK )
132*     ..
133*
134*  =====================================================================
135*
136*     .. Parameters ..
137      COMPLEX            ONE
138      PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ) )
139*     ..
140*     .. External Subroutines ..
141      EXTERNAL           CTRSM, CUNMQR, XERBLA
142*     ..
143*     .. Intrinsic Functions ..
144      INTRINSIC          MAX
145*     ..
146*     .. Executable Statements ..
147*
148*     Test the input arguments.
149*
150      INFO = 0
151      IF( M.LT.0 ) THEN
152         INFO = -1
153      ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
154         INFO = -2
155      ELSE IF( NRHS.LT.0 ) THEN
156         INFO = -3
157      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
158         INFO = -5
159      ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
160         INFO = -8
161      ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 )
162     $          THEN
163         INFO = -10
164      END IF
165      IF( INFO.NE.0 ) THEN
166         CALL XERBLA( 'CGEQRS', -INFO )
167         RETURN
168      END IF
169*
170*     Quick return if possible
171*
172      IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 )
173     $   RETURN
174*
175*     B := Q' * B
176*
177      CALL CUNMQR( 'Left', 'Conjugate transpose', M, NRHS, N, A, LDA,
178     $             TAU, B, LDB, WORK, LWORK, INFO )
179*
180*     Solve R*X = B(1:n,:)
181*
182      CALL CTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', N, NRHS,
183     $            ONE, A, LDA, B, LDB )
184*
185      RETURN
186*
187*     End of CGEQRS
188*
189      END
190