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
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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*> \ingroup doubleOTHERcomputational
110*
111*  =====================================================================
112      SUBROUTINE DORGL2( M, N, K, A, LDA, TAU, WORK, INFO )
113*
114*  -- LAPACK computational routine --
115*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
116*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
117*
118*     .. Scalar Arguments ..
119      INTEGER            INFO, K, LDA, M, N
120*     ..
121*     .. Array Arguments ..
122      DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
123*     ..
124*
125*  =====================================================================
126*
127*     .. Parameters ..
128      DOUBLE PRECISION   ONE, ZERO
129      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
130*     ..
131*     .. Local Scalars ..
132      INTEGER            I, J, L
133*     ..
134*     .. External Subroutines ..
135      EXTERNAL           DLARF, DSCAL, XERBLA
136*     ..
137*     .. Intrinsic Functions ..
138      INTRINSIC          MAX
139*     ..
140*     .. Executable Statements ..
141*
142*     Test the input arguments
143*
144      INFO = 0
145      IF( M.LT.0 ) THEN
146         INFO = -1
147      ELSE IF( N.LT.M ) THEN
148         INFO = -2
149      ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
150         INFO = -3
151      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
152         INFO = -5
153      END IF
154      IF( INFO.NE.0 ) THEN
155         CALL XERBLA( 'DORGL2', -INFO )
156         RETURN
157      END IF
158*
159*     Quick return if possible
160*
161      IF( M.LE.0 )
162     $   RETURN
163*
164      IF( K.LT.M ) THEN
165*
166*        Initialise rows k+1:m to rows of the unit matrix
167*
168         DO 20 J = 1, N
169            DO 10 L = K + 1, M
170               A( L, J ) = ZERO
171   10       CONTINUE
172            IF( J.GT.K .AND. J.LE.M )
173     $         A( J, J ) = ONE
174   20    CONTINUE
175      END IF
176*
177      DO 40 I = K, 1, -1
178*
179*        Apply H(i) to A(i:m,i:n) from the right
180*
181         IF( I.LT.N ) THEN
182            IF( I.LT.M ) THEN
183               A( I, I ) = ONE
184               CALL DLARF( 'Right', M-I, N-I+1, A( I, I ), LDA,
185     $                     TAU( I ), A( I+1, I ), LDA, WORK )
186            END IF
187            CALL DSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA )
188         END IF
189         A( I, I ) = ONE - TAU( I )
190*
191*        Set A(i,1:i-1) to zero
192*
193         DO 30 L = 1, I - 1
194            A( I, L ) = ZERO
195   30    CONTINUE
196   40 CONTINUE
197      RETURN
198*
199*     End of DORGL2
200*
201      END
202