1*> \brief \b DORGL2
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download DORGL2 + dependencies
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14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorgl2.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE DORGL2( M, N, K, A, LDA, TAU, WORK, INFO )
22*
23*       .. Scalar Arguments ..
24*       INTEGER            INFO, K, LDA, M, N
25*       ..
26*       .. Array Arguments ..
27*       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
28*       ..
29*
30*
31*> \par Purpose:
32*  =============
33*>
34*> \verbatim
35*>
36*> DORGL2 generates an m by n real 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(2) H(1)
41*>
42*> as returned by DGELQF.
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 DOUBLE PRECISION 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 DGELQF 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 DOUBLE PRECISION array, dimension (K)
85*>          TAU(i) must contain the scalar factor of the elementary
86*>          reflector H(i), as returned by DGELQF.
87*> \endverbatim
88*>
89*> \param[out] WORK
90*> \verbatim
91*>          WORK is DOUBLE PRECISION 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*> \date December 2016
110*
111*> \ingroup doubleOTHERcomputational
112*
113*  =====================================================================
114      SUBROUTINE DORGL2( M, N, K, A, LDA, TAU, WORK, INFO )
115*
116*  -- LAPACK computational routine (version 3.7.0) --
117*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
118*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
119*     December 2016
120*
121*     .. Scalar Arguments ..
122      INTEGER            INFO, K, LDA, M, N
123*     ..
124*     .. Array Arguments ..
125      DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
126*     ..
127*
128*  =====================================================================
129*
130*     .. Parameters ..
131      DOUBLE PRECISION   ONE, ZERO
132      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
133*     ..
134*     .. Local Scalars ..
135      INTEGER            I, J, L
136*     ..
137*     .. External Subroutines ..
138      EXTERNAL           DLARF, DSCAL, XERBLA
139*     ..
140*     .. Intrinsic Functions ..
141      INTRINSIC          MAX
142*     ..
143*     .. Executable Statements ..
144*
145*     Test the input arguments
146*
147      INFO = 0
148      IF( M.LT.0 ) THEN
149         INFO = -1
150      ELSE IF( N.LT.M ) THEN
151         INFO = -2
152      ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
153         INFO = -3
154      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
155         INFO = -5
156      END IF
157      IF( INFO.NE.0 ) THEN
158         CALL XERBLA( 'DORGL2', -INFO )
159         RETURN
160      END IF
161*
162*     Quick return if possible
163*
164      IF( M.LE.0 )
165     $   RETURN
166*
167      IF( K.LT.M ) THEN
168*
169*        Initialise rows k+1:m to rows of the unit matrix
170*
171         DO 20 J = 1, N
172            DO 10 L = K + 1, M
173               A( L, J ) = ZERO
174   10       CONTINUE
175            IF( J.GT.K .AND. J.LE.M )
176     $         A( J, J ) = ONE
177   20    CONTINUE
178      END IF
179*
180      DO 40 I = K, 1, -1
181*
182*        Apply H(i) to A(i:m,i:n) from the right
183*
184         IF( I.LT.N ) THEN
185            IF( I.LT.M ) THEN
186               A( I, I ) = ONE
187               CALL DLARF( 'Right', M-I, N-I+1, A( I, I ), LDA,
188     $                     TAU( I ), A( I+1, I ), LDA, WORK )
189            END IF
190            CALL DSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA )
191         END IF
192         A( I, I ) = ONE - TAU( I )
193*
194*        Set A(i,1:i-1) 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 DORGL2
203*
204      END
205