1*> \brief \b DORMTR
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download DORMTR + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dormtr.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dormtr.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dormtr.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE DORMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC,
22*                          WORK, LWORK, INFO )
23*
24*       .. Scalar Arguments ..
25*       CHARACTER          SIDE, TRANS, UPLO
26*       INTEGER            INFO, LDA, LDC, LWORK, M, N
27*       ..
28*       .. Array Arguments ..
29*       DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
30*       ..
31*
32*
33*> \par Purpose:
34*  =============
35*>
36*> \verbatim
37*>
38*> DORMTR overwrites the general real M-by-N matrix C with
39*>
40*>                 SIDE = 'L'     SIDE = 'R'
41*> TRANS = 'N':      Q * C          C * Q
42*> TRANS = 'T':      Q**T * C       C * Q**T
43*>
44*> where Q is a real orthogonal matrix of order nq, with nq = m if
45*> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
46*> nq-1 elementary reflectors, as returned by DSYTRD:
47*>
48*> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
49*>
50*> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
51*> \endverbatim
52*
53*  Arguments:
54*  ==========
55*
56*> \param[in] SIDE
57*> \verbatim
58*>          SIDE is CHARACTER*1
59*>          = 'L': apply Q or Q**T from the Left;
60*>          = 'R': apply Q or Q**T from the Right.
61*> \endverbatim
62*>
63*> \param[in] UPLO
64*> \verbatim
65*>          UPLO is CHARACTER*1
66*>          = 'U': Upper triangle of A contains elementary reflectors
67*>                 from DSYTRD;
68*>          = 'L': Lower triangle of A contains elementary reflectors
69*>                 from DSYTRD.
70*> \endverbatim
71*>
72*> \param[in] TRANS
73*> \verbatim
74*>          TRANS is CHARACTER*1
75*>          = 'N':  No transpose, apply Q;
76*>          = 'T':  Transpose, apply Q**T.
77*> \endverbatim
78*>
79*> \param[in] M
80*> \verbatim
81*>          M is INTEGER
82*>          The number of rows of the matrix C. M >= 0.
83*> \endverbatim
84*>
85*> \param[in] N
86*> \verbatim
87*>          N is INTEGER
88*>          The number of columns of the matrix C. N >= 0.
89*> \endverbatim
90*>
91*> \param[in] A
92*> \verbatim
93*>          A is DOUBLE PRECISION array, dimension
94*>                               (LDA,M) if SIDE = 'L'
95*>                               (LDA,N) if SIDE = 'R'
96*>          The vectors which define the elementary reflectors, as
97*>          returned by DSYTRD.
98*> \endverbatim
99*>
100*> \param[in] LDA
101*> \verbatim
102*>          LDA is INTEGER
103*>          The leading dimension of the array A.
104*>          LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
105*> \endverbatim
106*>
107*> \param[in] TAU
108*> \verbatim
109*>          TAU is DOUBLE PRECISION array, dimension
110*>                               (M-1) if SIDE = 'L'
111*>                               (N-1) if SIDE = 'R'
112*>          TAU(i) must contain the scalar factor of the elementary
113*>          reflector H(i), as returned by DSYTRD.
114*> \endverbatim
115*>
116*> \param[in,out] C
117*> \verbatim
118*>          C is DOUBLE PRECISION array, dimension (LDC,N)
119*>          On entry, the M-by-N matrix C.
120*>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
121*> \endverbatim
122*>
123*> \param[in] LDC
124*> \verbatim
125*>          LDC is INTEGER
126*>          The leading dimension of the array C. LDC >= max(1,M).
127*> \endverbatim
128*>
129*> \param[out] WORK
130*> \verbatim
131*>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
132*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
133*> \endverbatim
134*>
135*> \param[in] LWORK
136*> \verbatim
137*>          LWORK is INTEGER
138*>          The dimension of the array WORK.
139*>          If SIDE = 'L', LWORK >= max(1,N);
140*>          if SIDE = 'R', LWORK >= max(1,M).
141*>          For optimum performance LWORK >= N*NB if SIDE = 'L', and
142*>          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
143*>          blocksize.
144*>
145*>          If LWORK = -1, then a workspace query is assumed; the routine
146*>          only calculates the optimal size of the WORK array, returns
147*>          this value as the first entry of the WORK array, and no error
148*>          message related to LWORK is issued by XERBLA.
149*> \endverbatim
150*>
151*> \param[out] INFO
152*> \verbatim
153*>          INFO is INTEGER
154*>          = 0:  successful exit
155*>          < 0:  if INFO = -i, the i-th argument had an illegal value
156*> \endverbatim
157*
158*  Authors:
159*  ========
160*
161*> \author Univ. of Tennessee
162*> \author Univ. of California Berkeley
163*> \author Univ. of Colorado Denver
164*> \author NAG Ltd.
165*
166*> \ingroup doubleOTHERcomputational
167*
168*  =====================================================================
169      SUBROUTINE DORMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC,
170     $                   WORK, LWORK, INFO )
171*
172*  -- LAPACK computational routine --
173*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
174*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
175*
176*     .. Scalar Arguments ..
177      CHARACTER          SIDE, TRANS, UPLO
178      INTEGER            INFO, LDA, LDC, LWORK, M, N
179*     ..
180*     .. Array Arguments ..
181      DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
182*     ..
183*
184*  =====================================================================
185*
186*     .. Local Scalars ..
187      LOGICAL            LEFT, LQUERY, UPPER
188      INTEGER            I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
189*     ..
190*     .. External Functions ..
191      LOGICAL            LSAME
192      INTEGER            ILAENV
193      EXTERNAL           LSAME, ILAENV
194*     ..
195*     .. External Subroutines ..
196      EXTERNAL           DORMQL, DORMQR, XERBLA
197*     ..
198*     .. Intrinsic Functions ..
199      INTRINSIC          MAX
200*     ..
201*     .. Executable Statements ..
202*
203*     Test the input arguments
204*
205      INFO = 0
206      LEFT = LSAME( SIDE, 'L' )
207      UPPER = LSAME( UPLO, 'U' )
208      LQUERY = ( LWORK.EQ.-1 )
209*
210*     NQ is the order of Q and NW is the minimum dimension of WORK
211*
212      IF( LEFT ) THEN
213         NQ = M
214         NW = MAX( 1, N )
215      ELSE
216         NQ = N
217         NW = MAX( 1, M )
218      END IF
219      IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
220         INFO = -1
221      ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
222         INFO = -2
223      ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.LSAME( TRANS, 'T' ) )
224     $          THEN
225         INFO = -3
226      ELSE IF( M.LT.0 ) THEN
227         INFO = -4
228      ELSE IF( N.LT.0 ) THEN
229         INFO = -5
230      ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN
231         INFO = -7
232      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
233         INFO = -10
234      ELSE IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN
235         INFO = -12
236      END IF
237*
238      IF( INFO.EQ.0 ) THEN
239         IF( UPPER ) THEN
240            IF( LEFT ) THEN
241               NB = ILAENV( 1, 'DORMQL', SIDE // TRANS, M-1, N, M-1,
242     $              -1 )
243            ELSE
244               NB = ILAENV( 1, 'DORMQL', SIDE // TRANS, M, N-1, N-1,
245     $              -1 )
246            END IF
247         ELSE
248            IF( LEFT ) THEN
249               NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M-1, N, M-1,
250     $              -1 )
251            ELSE
252               NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M, N-1, N-1,
253     $              -1 )
254            END IF
255         END IF
256         LWKOPT = NW*NB
257         WORK( 1 ) = LWKOPT
258      END IF
259*
260      IF( INFO.NE.0 ) THEN
261         CALL XERBLA( 'DORMTR', -INFO )
262         RETURN
263      ELSE IF( LQUERY ) THEN
264         RETURN
265      END IF
266*
267*     Quick return if possible
268*
269      IF( M.EQ.0 .OR. N.EQ.0 .OR. NQ.EQ.1 ) THEN
270         WORK( 1 ) = 1
271         RETURN
272      END IF
273*
274      IF( LEFT ) THEN
275         MI = M - 1
276         NI = N
277      ELSE
278         MI = M
279         NI = N - 1
280      END IF
281*
282      IF( UPPER ) THEN
283*
284*        Q was determined by a call to DSYTRD with UPLO = 'U'
285*
286         CALL DORMQL( SIDE, TRANS, MI, NI, NQ-1, A( 1, 2 ), LDA, TAU, C,
287     $                LDC, WORK, LWORK, IINFO )
288      ELSE
289*
290*        Q was determined by a call to DSYTRD with UPLO = 'L'
291*
292         IF( LEFT ) THEN
293            I1 = 2
294            I2 = 1
295         ELSE
296            I1 = 1
297            I2 = 2
298         END IF
299         CALL DORMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU,
300     $                C( I1, I2 ), LDC, WORK, LWORK, IINFO )
301      END IF
302      WORK( 1 ) = LWKOPT
303      RETURN
304*
305*     End of DORMTR
306*
307      END
308