1*> \brief \b SORGTR
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
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15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE SORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
22*
23*       .. Scalar Arguments ..
24*       CHARACTER          UPLO
25*       INTEGER            INFO, LDA, LWORK, N
26*       ..
27*       .. Array Arguments ..
28*       REAL               A( LDA, * ), TAU( * ), WORK( * )
29*       ..
30*
31*
32*> \par Purpose:
33*  =============
34*>
35*> \verbatim
36*>
37*> SORGTR generates a real orthogonal matrix Q which is defined as the
38*> product of n-1 elementary reflectors of order N, as returned by
39*> SSYTRD:
40*>
41*> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
42*>
43*> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
44*> \endverbatim
45*
46*  Arguments:
47*  ==========
48*
49*> \param[in] UPLO
50*> \verbatim
51*>          UPLO is CHARACTER*1
52*>          = 'U': Upper triangle of A contains elementary reflectors
53*>                 from SSYTRD;
54*>          = 'L': Lower triangle of A contains elementary reflectors
55*>                 from SSYTRD.
56*> \endverbatim
57*>
58*> \param[in] N
59*> \verbatim
60*>          N is INTEGER
61*>          The order of the matrix Q. N >= 0.
62*> \endverbatim
63*>
64*> \param[in,out] A
65*> \verbatim
66*>          A is REAL array, dimension (LDA,N)
67*>          On entry, the vectors which define the elementary reflectors,
68*>          as returned by SSYTRD.
69*>          On exit, the N-by-N orthogonal matrix Q.
70*> \endverbatim
71*>
72*> \param[in] LDA
73*> \verbatim
74*>          LDA is INTEGER
75*>          The leading dimension of the array A. LDA >= max(1,N).
76*> \endverbatim
77*>
78*> \param[in] TAU
79*> \verbatim
80*>          TAU is REAL array, dimension (N-1)
81*>          TAU(i) must contain the scalar factor of the elementary
82*>          reflector H(i), as returned by SSYTRD.
83*> \endverbatim
84*>
85*> \param[out] WORK
86*> \verbatim
87*>          WORK is REAL array, dimension (MAX(1,LWORK))
88*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
89*> \endverbatim
90*>
91*> \param[in] LWORK
92*> \verbatim
93*>          LWORK is INTEGER
94*>          The dimension of the array WORK. LWORK >= max(1,N-1).
95*>          For optimum performance LWORK >= (N-1)*NB, where NB is
96*>          the optimal blocksize.
97*>
98*>          If LWORK = -1, then a workspace query is assumed; the routine
99*>          only calculates the optimal size of the WORK array, returns
100*>          this value as the first entry of the WORK array, and no error
101*>          message related to LWORK is issued by XERBLA.
102*> \endverbatim
103*>
104*> \param[out] INFO
105*> \verbatim
106*>          INFO is INTEGER
107*>          = 0:  successful exit
108*>          < 0:  if INFO = -i, the i-th argument had an illegal value
109*> \endverbatim
110*
111*  Authors:
112*  ========
113*
114*> \author Univ. of Tennessee
115*> \author Univ. of California Berkeley
116*> \author Univ. of Colorado Denver
117*> \author NAG Ltd.
118*
119*> \date November 2011
120*
121*> \ingroup realOTHERcomputational
122*
123*  =====================================================================
124      SUBROUTINE SORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
125*
126*  -- LAPACK computational routine (version 3.4.0) --
127*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
128*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129*     November 2011
130*
131*     .. Scalar Arguments ..
132      CHARACTER          UPLO
133      INTEGER            INFO, LDA, LWORK, N
134*     ..
135*     .. Array Arguments ..
136      REAL               A( LDA, * ), TAU( * ), WORK( * )
137*     ..
138*
139*  =====================================================================
140*
141*     .. Parameters ..
142      REAL               ZERO, ONE
143      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
144*     ..
145*     .. Local Scalars ..
146      LOGICAL            LQUERY, UPPER
147      INTEGER            I, IINFO, J, LWKOPT, NB
148*     ..
149*     .. External Functions ..
150      LOGICAL            LSAME
151      INTEGER            ILAENV
152      EXTERNAL           ILAENV, LSAME
153*     ..
154*     .. External Subroutines ..
155      EXTERNAL           SORGQL, SORGQR, XERBLA
156*     ..
157*     .. Intrinsic Functions ..
158      INTRINSIC          MAX
159*     ..
160*     .. Executable Statements ..
161*
162*     Test the input arguments
163*
164      INFO = 0
165      LQUERY = ( LWORK.EQ.-1 )
166      UPPER = LSAME( UPLO, 'U' )
167      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
168         INFO = -1
169      ELSE IF( N.LT.0 ) THEN
170         INFO = -2
171      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
172         INFO = -4
173      ELSE IF( LWORK.LT.MAX( 1, N-1 ) .AND. .NOT.LQUERY ) THEN
174         INFO = -7
175      END IF
176*
177      IF( INFO.EQ.0 ) THEN
178         IF ( UPPER ) THEN
179           NB = ILAENV( 1, 'SORGQL', ' ', N-1, N-1, N-1, -1 )
180         ELSE
181           NB = ILAENV( 1, 'SORGQR', ' ', N-1, N-1, N-1, -1 )
182         END IF
183         LWKOPT = MAX( 1, N-1 )*NB
184         WORK( 1 ) = LWKOPT
185      END IF
186*
187      IF( INFO.NE.0 ) THEN
188         CALL XERBLA( 'SORGTR', -INFO )
189         RETURN
190      ELSE IF( LQUERY ) THEN
191         RETURN
192      END IF
193*
194*     Quick return if possible
195*
196      IF( N.EQ.0 ) THEN
197         WORK( 1 ) = 1
198         RETURN
199      END IF
200*
201      IF( UPPER ) THEN
202*
203*        Q was determined by a call to SSYTRD with UPLO = 'U'
204*
205*        Shift the vectors which define the elementary reflectors one
206*        column to the left, and set the last row and column of Q to
207*        those of the unit matrix
208*
209         DO 20 J = 1, N - 1
210            DO 10 I = 1, J - 1
211               A( I, J ) = A( I, J+1 )
212   10       CONTINUE
213            A( N, J ) = ZERO
214   20    CONTINUE
215         DO 30 I = 1, N - 1
216            A( I, N ) = ZERO
217   30    CONTINUE
218         A( N, N ) = ONE
219*
220*        Generate Q(1:n-1,1:n-1)
221*
222         CALL SORGQL( N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK, IINFO )
223*
224      ELSE
225*
226*        Q was determined by a call to SSYTRD with UPLO = 'L'.
227*
228*        Shift the vectors which define the elementary reflectors one
229*        column to the right, and set the first row and column of Q to
230*        those of the unit matrix
231*
232         DO 50 J = N, 2, -1
233            A( 1, J ) = ZERO
234            DO 40 I = J + 1, N
235               A( I, J ) = A( I, J-1 )
236   40       CONTINUE
237   50    CONTINUE
238         A( 1, 1 ) = ONE
239         DO 60 I = 2, N
240            A( I, 1 ) = ZERO
241   60    CONTINUE
242         IF( N.GT.1 ) THEN
243*
244*           Generate Q(2:n,2:n)
245*
246            CALL SORGQR( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
247     $                   LWORK, IINFO )
248         END IF
249      END IF
250      WORK( 1 ) = LWKOPT
251      RETURN
252*
253*     End of SORGTR
254*
255      END
256