1*> \brief \b SORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm).
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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14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sorg2l.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE SORG2L( M, N, K, A, LDA, TAU, WORK, INFO )
22*
23*       .. Scalar Arguments ..
24*       INTEGER            INFO, K, LDA, M, N
25*       ..
26*       .. Array Arguments ..
27*       REAL               A( LDA, * ), TAU( * ), WORK( * )
28*       ..
29*
30*
31*> \par Purpose:
32*  =============
33*>
34*> \verbatim
35*>
36*> SORG2L generates an m by n real matrix Q with orthonormal columns,
37*> which is defined as the last n columns of a product of k elementary
38*> reflectors of order m
39*>
40*>       Q  =  H(k) . . . H(2) H(1)
41*>
42*> as returned by SGEQLF.
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. M >= N >= 0.
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. N >= K >= 0.
65*> \endverbatim
66*>
67*> \param[in,out] A
68*> \verbatim
69*>          A is REAL array, dimension (LDA,N)
70*>          On entry, the (n-k+i)-th column must contain the vector which
71*>          defines the elementary reflector H(i), for i = 1,2,...,k, as
72*>          returned by SGEQLF in the last k columns of its array
73*>          argument A.
74*>          On exit, the m by n matrix Q.
75*> \endverbatim
76*>
77*> \param[in] LDA
78*> \verbatim
79*>          LDA is INTEGER
80*>          The first dimension of the array A. LDA >= max(1,M).
81*> \endverbatim
82*>
83*> \param[in] TAU
84*> \verbatim
85*>          TAU is REAL array, dimension (K)
86*>          TAU(i) must contain the scalar factor of the elementary
87*>          reflector H(i), as returned by SGEQLF.
88*> \endverbatim
89*>
90*> \param[out] WORK
91*> \verbatim
92*>          WORK is REAL array, dimension (N)
93*> \endverbatim
94*>
95*> \param[out] INFO
96*> \verbatim
97*>          INFO is INTEGER
98*>          = 0: successful exit
99*>          < 0: if INFO = -i, the i-th argument has an illegal value
100*> \endverbatim
101*
102*  Authors:
103*  ========
104*
105*> \author Univ. of Tennessee
106*> \author Univ. of California Berkeley
107*> \author Univ. of Colorado Denver
108*> \author NAG Ltd.
109*
110*> \date September 2012
111*
112*> \ingroup realOTHERcomputational
113*
114*  =====================================================================
115      SUBROUTINE SORG2L( M, N, K, A, LDA, TAU, WORK, INFO )
116*
117*  -- LAPACK computational routine (version 3.4.2) --
118*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
119*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
120*     September 2012
121*
122*     .. Scalar Arguments ..
123      INTEGER            INFO, K, LDA, M, N
124*     ..
125*     .. Array Arguments ..
126      REAL               A( LDA, * ), TAU( * ), WORK( * )
127*     ..
128*
129*  =====================================================================
130*
131*     .. Parameters ..
132      REAL               ONE, ZERO
133      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
134*     ..
135*     .. Local Scalars ..
136      INTEGER            I, II, J, L
137*     ..
138*     .. External Subroutines ..
139      EXTERNAL           SLARF, SSCAL, XERBLA
140*     ..
141*     .. Intrinsic Functions ..
142      INTRINSIC          MAX
143*     ..
144*     .. Executable Statements ..
145*
146*     Test the input arguments
147*
148      INFO = 0
149      IF( M.LT.0 ) THEN
150         INFO = -1
151      ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
152         INFO = -2
153      ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
154         INFO = -3
155      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
156         INFO = -5
157      END IF
158      IF( INFO.NE.0 ) THEN
159         CALL XERBLA( 'SORG2L', -INFO )
160         RETURN
161      END IF
162*
163*     Quick return if possible
164*
165      IF( N.LE.0 )
166     $   RETURN
167*
168*     Initialise columns 1:n-k to columns of the unit matrix
169*
170      DO 20 J = 1, N - K
171         DO 10 L = 1, M
172            A( L, J ) = ZERO
173   10    CONTINUE
174         A( M-N+J, J ) = ONE
175   20 CONTINUE
176*
177      DO 40 I = 1, K
178         II = N - K + I
179*
180*        Apply H(i) to A(1:m-k+i,1:n-k+i) from the left
181*
182         A( M-N+II, II ) = ONE
183         CALL SLARF( 'Left', M-N+II, II-1, A( 1, II ), 1, TAU( I ), A,
184     $               LDA, WORK )
185         CALL SSCAL( M-N+II-1, -TAU( I ), A( 1, II ), 1 )
186         A( M-N+II, II ) = ONE - TAU( I )
187*
188*        Set A(m-k+i+1:m,n-k+i) to zero
189*
190         DO 30 L = M - N + II + 1, M
191            A( L, II ) = ZERO
192   30    CONTINUE
193   40 CONTINUE
194      RETURN
195*
196*     End of SORG2L
197*
198      END
199