1*> \brief \b SORGHR
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 SORGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
22*
23*       .. Scalar Arguments ..
24*       INTEGER            IHI, ILO, INFO, LDA, LWORK, N
25*       ..
26*       .. Array Arguments ..
27*       REAL               A( LDA, * ), TAU( * ), WORK( * )
28*       ..
29*
30*
31*> \par Purpose:
32*  =============
33*>
34*> \verbatim
35*>
36*> SORGHR generates a real orthogonal matrix Q which is defined as the
37*> product of IHI-ILO elementary reflectors of order N, as returned by
38*> SGEHRD:
39*>
40*> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
41*> \endverbatim
42*
43*  Arguments:
44*  ==========
45*
46*> \param[in] N
47*> \verbatim
48*>          N is INTEGER
49*>          The order of the matrix Q. N >= 0.
50*> \endverbatim
51*>
52*> \param[in] ILO
53*> \verbatim
54*>          ILO is INTEGER
55*> \endverbatim
56*>
57*> \param[in] IHI
58*> \verbatim
59*>          IHI is INTEGER
60*>
61*>          ILO and IHI must have the same values as in the previous call
62*>          of SGEHRD. Q is equal to the unit matrix except in the
63*>          submatrix Q(ilo+1:ihi,ilo+1:ihi).
64*>          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
65*> \endverbatim
66*>
67*> \param[in,out] A
68*> \verbatim
69*>          A is REAL array, dimension (LDA,N)
70*>          On entry, the vectors which define the elementary reflectors,
71*>          as returned by SGEHRD.
72*>          On exit, the N-by-N orthogonal matrix Q.
73*> \endverbatim
74*>
75*> \param[in] LDA
76*> \verbatim
77*>          LDA is INTEGER
78*>          The leading dimension of the array A. LDA >= max(1,N).
79*> \endverbatim
80*>
81*> \param[in] TAU
82*> \verbatim
83*>          TAU is REAL array, dimension (N-1)
84*>          TAU(i) must contain the scalar factor of the elementary
85*>          reflector H(i), as returned by SGEHRD.
86*> \endverbatim
87*>
88*> \param[out] WORK
89*> \verbatim
90*>          WORK is REAL array, dimension (MAX(1,LWORK))
91*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
92*> \endverbatim
93*>
94*> \param[in] LWORK
95*> \verbatim
96*>          LWORK is INTEGER
97*>          The dimension of the array WORK. LWORK >= IHI-ILO.
98*>          For optimum performance LWORK >= (IHI-ILO)*NB, where NB is
99*>          the optimal blocksize.
100*>
101*>          If LWORK = -1, then a workspace query is assumed; the routine
102*>          only calculates the optimal size of the WORK array, returns
103*>          this value as the first entry of the WORK array, and no error
104*>          message related to LWORK is issued by XERBLA.
105*> \endverbatim
106*>
107*> \param[out] INFO
108*> \verbatim
109*>          INFO is INTEGER
110*>          = 0:  successful exit
111*>          < 0:  if INFO = -i, the i-th argument had an illegal value
112*> \endverbatim
113*
114*  Authors:
115*  ========
116*
117*> \author Univ. of Tennessee
118*> \author Univ. of California Berkeley
119*> \author Univ. of Colorado Denver
120*> \author NAG Ltd.
121*
122*> \date November 2011
123*
124*> \ingroup realOTHERcomputational
125*
126*  =====================================================================
127      SUBROUTINE SORGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
128*
129*  -- LAPACK computational routine (version 3.4.0) --
130*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
131*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132*     November 2011
133*
134*     .. Scalar Arguments ..
135      INTEGER            IHI, ILO, INFO, LDA, LWORK, N
136*     ..
137*     .. Array Arguments ..
138      REAL               A( LDA, * ), TAU( * ), WORK( * )
139*     ..
140*
141*  =====================================================================
142*
143*     .. Parameters ..
144      REAL               ZERO, ONE
145      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
146*     ..
147*     .. Local Scalars ..
148      LOGICAL            LQUERY
149      INTEGER            I, IINFO, J, LWKOPT, NB, NH
150*     ..
151*     .. External Subroutines ..
152      EXTERNAL           SORGQR, XERBLA
153*     ..
154*     .. External Functions ..
155      INTEGER            ILAENV
156      EXTERNAL           ILAENV
157*     ..
158*     .. Intrinsic Functions ..
159      INTRINSIC          MAX, MIN
160*     ..
161*     .. Executable Statements ..
162*
163*     Test the input arguments
164*
165      INFO = 0
166      NH = IHI - ILO
167      LQUERY = ( LWORK.EQ.-1 )
168      IF( N.LT.0 ) THEN
169         INFO = -1
170      ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN
171         INFO = -2
172      ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN
173         INFO = -3
174      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
175         INFO = -5
176      ELSE IF( LWORK.LT.MAX( 1, NH ) .AND. .NOT.LQUERY ) THEN
177         INFO = -8
178      END IF
179*
180      IF( INFO.EQ.0 ) THEN
181         NB = ILAENV( 1, 'SORGQR', ' ', NH, NH, NH, -1 )
182         LWKOPT = MAX( 1, NH )*NB
183         WORK( 1 ) = LWKOPT
184      END IF
185*
186      IF( INFO.NE.0 ) THEN
187         CALL XERBLA( 'SORGHR', -INFO )
188         RETURN
189      ELSE IF( LQUERY ) THEN
190         RETURN
191      END IF
192*
193*     Quick return if possible
194*
195      IF( N.EQ.0 ) THEN
196         WORK( 1 ) = 1
197         RETURN
198      END IF
199*
200*     Shift the vectors which define the elementary reflectors one
201*     column to the right, and set the first ilo and the last n-ihi
202*     rows and columns to those of the unit matrix
203*
204      DO 40 J = IHI, ILO + 1, -1
205         DO 10 I = 1, J - 1
206            A( I, J ) = ZERO
207   10    CONTINUE
208         DO 20 I = J + 1, IHI
209            A( I, J ) = A( I, J-1 )
210   20    CONTINUE
211         DO 30 I = IHI + 1, N
212            A( I, J ) = ZERO
213   30    CONTINUE
214   40 CONTINUE
215      DO 60 J = 1, ILO
216         DO 50 I = 1, N
217            A( I, J ) = ZERO
218   50    CONTINUE
219         A( J, J ) = ONE
220   60 CONTINUE
221      DO 80 J = IHI + 1, N
222         DO 70 I = 1, N
223            A( I, J ) = ZERO
224   70    CONTINUE
225         A( J, J ) = ONE
226   80 CONTINUE
227*
228      IF( NH.GT.0 ) THEN
229*
230*        Generate Q(ilo+1:ihi,ilo+1:ihi)
231*
232         CALL SORGQR( NH, NH, NH, A( ILO+1, ILO+1 ), LDA, TAU( ILO ),
233     $                WORK, LWORK, IINFO )
234      END IF
235      WORK( 1 ) = LWKOPT
236      RETURN
237*
238*     End of SORGHR
239*
240      END
241