1*> \brief \b SORMHR
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 SORMHR( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C,
22*                          LDC, WORK, LWORK, INFO )
23*
24*       .. Scalar Arguments ..
25*       CHARACTER          SIDE, TRANS
26*       INTEGER            IHI, ILO, INFO, LDA, LDC, LWORK, M, N
27*       ..
28*       .. Array Arguments ..
29*       REAL               A( LDA, * ), C( LDC, * ), TAU( * ),
30*      $                   WORK( * )
31*       ..
32*
33*
34*> \par Purpose:
35*  =============
36*>
37*> \verbatim
38*>
39*> SORMHR overwrites the general real M-by-N matrix C with
40*>
41*>                 SIDE = 'L'     SIDE = 'R'
42*> TRANS = 'N':      Q * C          C * Q
43*> TRANS = 'T':      Q**T * C       C * Q**T
44*>
45*> where Q is a real orthogonal matrix of order nq, with nq = m if
46*> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
47*> IHI-ILO elementary reflectors, as returned by SGEHRD:
48*>
49*> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
50*> \endverbatim
51*
52*  Arguments:
53*  ==========
54*
55*> \param[in] SIDE
56*> \verbatim
57*>          SIDE is CHARACTER*1
58*>          = 'L': apply Q or Q**T from the Left;
59*>          = 'R': apply Q or Q**T from the Right.
60*> \endverbatim
61*>
62*> \param[in] TRANS
63*> \verbatim
64*>          TRANS is CHARACTER*1
65*>          = 'N':  No transpose, apply Q;
66*>          = 'T':  Transpose, apply Q**T.
67*> \endverbatim
68*>
69*> \param[in] M
70*> \verbatim
71*>          M is INTEGER
72*>          The number of rows of the matrix C. M >= 0.
73*> \endverbatim
74*>
75*> \param[in] N
76*> \verbatim
77*>          N is INTEGER
78*>          The number of columns of the matrix C. N >= 0.
79*> \endverbatim
80*>
81*> \param[in] ILO
82*> \verbatim
83*>          ILO is INTEGER
84*> \endverbatim
85*>
86*> \param[in] IHI
87*> \verbatim
88*>          IHI is INTEGER
89*>
90*>          ILO and IHI must have the same values as in the previous call
91*>          of SGEHRD. Q is equal to the unit matrix except in the
92*>          submatrix Q(ilo+1:ihi,ilo+1:ihi).
93*>          If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and
94*>          ILO = 1 and IHI = 0, if M = 0;
95*>          if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and
96*>          ILO = 1 and IHI = 0, if N = 0.
97*> \endverbatim
98*>
99*> \param[in] A
100*> \verbatim
101*>          A is REAL array, dimension
102*>                               (LDA,M) if SIDE = 'L'
103*>                               (LDA,N) if SIDE = 'R'
104*>          The vectors which define the elementary reflectors, as
105*>          returned by SGEHRD.
106*> \endverbatim
107*>
108*> \param[in] LDA
109*> \verbatim
110*>          LDA is INTEGER
111*>          The leading dimension of the array A.
112*>          LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
113*> \endverbatim
114*>
115*> \param[in] TAU
116*> \verbatim
117*>          TAU is REAL array, dimension
118*>                               (M-1) if SIDE = 'L'
119*>                               (N-1) if SIDE = 'R'
120*>          TAU(i) must contain the scalar factor of the elementary
121*>          reflector H(i), as returned by SGEHRD.
122*> \endverbatim
123*>
124*> \param[in,out] C
125*> \verbatim
126*>          C is REAL array, dimension (LDC,N)
127*>          On entry, the M-by-N matrix C.
128*>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
129*> \endverbatim
130*>
131*> \param[in] LDC
132*> \verbatim
133*>          LDC is INTEGER
134*>          The leading dimension of the array C. LDC >= max(1,M).
135*> \endverbatim
136*>
137*> \param[out] WORK
138*> \verbatim
139*>          WORK is REAL array, dimension (MAX(1,LWORK))
140*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
141*> \endverbatim
142*>
143*> \param[in] LWORK
144*> \verbatim
145*>          LWORK is INTEGER
146*>          The dimension of the array WORK.
147*>          If SIDE = 'L', LWORK >= max(1,N);
148*>          if SIDE = 'R', LWORK >= max(1,M).
149*>          For optimum performance LWORK >= N*NB if SIDE = 'L', and
150*>          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
151*>          blocksize.
152*>
153*>          If LWORK = -1, then a workspace query is assumed; the routine
154*>          only calculates the optimal size of the WORK array, returns
155*>          this value as the first entry of the WORK array, and no error
156*>          message related to LWORK is issued by XERBLA.
157*> \endverbatim
158*>
159*> \param[out] INFO
160*> \verbatim
161*>          INFO is INTEGER
162*>          = 0:  successful exit
163*>          < 0:  if INFO = -i, the i-th argument had an illegal value
164*> \endverbatim
165*
166*  Authors:
167*  ========
168*
169*> \author Univ. of Tennessee
170*> \author Univ. of California Berkeley
171*> \author Univ. of Colorado Denver
172*> \author NAG Ltd.
173*
174*> \date November 2011
175*
176*> \ingroup realOTHERcomputational
177*
178*  =====================================================================
179      SUBROUTINE SORMHR( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C,
180     $                   LDC, WORK, LWORK, INFO )
181*
182*  -- LAPACK computational routine (version 3.4.0) --
183*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
184*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
185*     November 2011
186*
187*     .. Scalar Arguments ..
188      CHARACTER          SIDE, TRANS
189      INTEGER            IHI, ILO, INFO, LDA, LDC, LWORK, M, N
190*     ..
191*     .. Array Arguments ..
192      REAL               A( LDA, * ), C( LDC, * ), TAU( * ),
193     $                   WORK( * )
194*     ..
195*
196*  =====================================================================
197*
198*     .. Local Scalars ..
199      LOGICAL            LEFT, LQUERY
200      INTEGER            I1, I2, IINFO, LWKOPT, MI, NB, NH, NI, NQ, NW
201*     ..
202*     .. External Functions ..
203      LOGICAL            LSAME
204      INTEGER            ILAENV
205      EXTERNAL           ILAENV, LSAME
206*     ..
207*     .. External Subroutines ..
208      EXTERNAL           SORMQR, XERBLA
209*     ..
210*     .. Intrinsic Functions ..
211      INTRINSIC          MAX, MIN
212*     ..
213*     .. Executable Statements ..
214*
215*     Test the input arguments
216*
217      INFO = 0
218      NH = IHI - ILO
219      LEFT = LSAME( SIDE, 'L' )
220      LQUERY = ( LWORK.EQ.-1 )
221*
222*     NQ is the order of Q and NW is the minimum dimension of WORK
223*
224      IF( LEFT ) THEN
225         NQ = M
226         NW = N
227      ELSE
228         NQ = N
229         NW = M
230      END IF
231      IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
232         INFO = -1
233      ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.LSAME( TRANS, 'T' ) )
234     $          THEN
235         INFO = -2
236      ELSE IF( M.LT.0 ) THEN
237         INFO = -3
238      ELSE IF( N.LT.0 ) THEN
239         INFO = -4
240      ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, NQ ) ) THEN
241         INFO = -5
242      ELSE IF( IHI.LT.MIN( ILO, NQ ) .OR. IHI.GT.NQ ) THEN
243         INFO = -6
244      ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN
245         INFO = -8
246      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
247         INFO = -11
248      ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
249         INFO = -13
250      END IF
251*
252      IF( INFO.EQ.0 ) THEN
253         IF( LEFT ) THEN
254            NB = ILAENV( 1, 'SORMQR', SIDE // TRANS, NH, N, NH, -1 )
255         ELSE
256            NB = ILAENV( 1, 'SORMQR', SIDE // TRANS, M, NH, NH, -1 )
257         END IF
258         LWKOPT = MAX( 1, NW )*NB
259         WORK( 1 ) = LWKOPT
260      END IF
261*
262      IF( INFO.NE.0 ) THEN
263         CALL XERBLA( 'SORMHR', -INFO )
264         RETURN
265      ELSE IF( LQUERY ) THEN
266         RETURN
267      END IF
268*
269*     Quick return if possible
270*
271      IF( M.EQ.0 .OR. N.EQ.0 .OR. NH.EQ.0 ) THEN
272         WORK( 1 ) = 1
273         RETURN
274      END IF
275*
276      IF( LEFT ) THEN
277         MI = NH
278         NI = N
279         I1 = ILO + 1
280         I2 = 1
281      ELSE
282         MI = M
283         NI = NH
284         I1 = 1
285         I2 = ILO + 1
286      END IF
287*
288      CALL SORMQR( SIDE, TRANS, MI, NI, NH, A( ILO+1, ILO ), LDA,
289     $             TAU( ILO ), C( I1, I2 ), LDC, WORK, LWORK, IINFO )
290*
291      WORK( 1 ) = LWKOPT
292      RETURN
293*
294*     End of SORMHR
295*
296      END
297