1*> \brief \b DOPMTR
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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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dopmtr.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE DOPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK,
22*                          INFO )
23*
24*       .. Scalar Arguments ..
25*       CHARACTER          SIDE, TRANS, UPLO
26*       INTEGER            INFO, LDC, M, N
27*       ..
28*       .. Array Arguments ..
29*       DOUBLE PRECISION   AP( * ), C( LDC, * ), TAU( * ), WORK( * )
30*       ..
31*
32*
33*> \par Purpose:
34*  =============
35*>
36*> \verbatim
37*>
38*> DOPMTR 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 DSPTRD using packed
47*> storage:
48*>
49*> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
50*>
51*> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
52*> \endverbatim
53*
54*  Arguments:
55*  ==========
56*
57*> \param[in] SIDE
58*> \verbatim
59*>          SIDE is CHARACTER*1
60*>          = 'L': apply Q or Q**T from the Left;
61*>          = 'R': apply Q or Q**T from the Right.
62*> \endverbatim
63*>
64*> \param[in] UPLO
65*> \verbatim
66*>          UPLO is CHARACTER*1
67*>          = 'U': Upper triangular packed storage used in previous
68*>                 call to DSPTRD;
69*>          = 'L': Lower triangular packed storage used in previous
70*>                 call to DSPTRD.
71*> \endverbatim
72*>
73*> \param[in] TRANS
74*> \verbatim
75*>          TRANS is CHARACTER*1
76*>          = 'N':  No transpose, apply Q;
77*>          = 'T':  Transpose, apply Q**T.
78*> \endverbatim
79*>
80*> \param[in] M
81*> \verbatim
82*>          M is INTEGER
83*>          The number of rows of the matrix C. M >= 0.
84*> \endverbatim
85*>
86*> \param[in] N
87*> \verbatim
88*>          N is INTEGER
89*>          The number of columns of the matrix C. N >= 0.
90*> \endverbatim
91*>
92*> \param[in] AP
93*> \verbatim
94*>          AP is DOUBLE PRECISION array, dimension
95*>                               (M*(M+1)/2) if SIDE = 'L'
96*>                               (N*(N+1)/2) if SIDE = 'R'
97*>          The vectors which define the elementary reflectors, as
98*>          returned by DSPTRD.  AP is modified by the routine but
99*>          restored on exit.
100*> \endverbatim
101*>
102*> \param[in] TAU
103*> \verbatim
104*>          TAU is DOUBLE PRECISION array, dimension (M-1) if SIDE = 'L'
105*>                                     or (N-1) if SIDE = 'R'
106*>          TAU(i) must contain the scalar factor of the elementary
107*>          reflector H(i), as returned by DSPTRD.
108*> \endverbatim
109*>
110*> \param[in,out] C
111*> \verbatim
112*>          C is DOUBLE PRECISION array, dimension (LDC,N)
113*>          On entry, the M-by-N matrix C.
114*>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
115*> \endverbatim
116*>
117*> \param[in] LDC
118*> \verbatim
119*>          LDC is INTEGER
120*>          The leading dimension of the array C. LDC >= max(1,M).
121*> \endverbatim
122*>
123*> \param[out] WORK
124*> \verbatim
125*>          WORK is DOUBLE PRECISION array, dimension
126*>                                   (N) if SIDE = 'L'
127*>                                   (M) if SIDE = 'R'
128*> \endverbatim
129*>
130*> \param[out] INFO
131*> \verbatim
132*>          INFO is INTEGER
133*>          = 0:  successful exit
134*>          < 0:  if INFO = -i, the i-th argument had an illegal value
135*> \endverbatim
136*
137*  Authors:
138*  ========
139*
140*> \author Univ. of Tennessee
141*> \author Univ. of California Berkeley
142*> \author Univ. of Colorado Denver
143*> \author NAG Ltd.
144*
145*> \ingroup doubleOTHERcomputational
146*
147*  =====================================================================
148      SUBROUTINE DOPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK,
149     $                   INFO )
150*
151*  -- LAPACK computational routine --
152*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
153*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
154*
155*     .. Scalar Arguments ..
156      CHARACTER          SIDE, TRANS, UPLO
157      INTEGER            INFO, LDC, M, N
158*     ..
159*     .. Array Arguments ..
160      DOUBLE PRECISION   AP( * ), C( LDC, * ), TAU( * ), WORK( * )
161*     ..
162*
163*  =====================================================================
164*
165*     .. Parameters ..
166      DOUBLE PRECISION   ONE
167      PARAMETER          ( ONE = 1.0D+0 )
168*     ..
169*     .. Local Scalars ..
170      LOGICAL            FORWRD, LEFT, NOTRAN, UPPER
171      INTEGER            I, I1, I2, I3, IC, II, JC, MI, NI, NQ
172      DOUBLE PRECISION   AII
173*     ..
174*     .. External Functions ..
175      LOGICAL            LSAME
176      EXTERNAL           LSAME
177*     ..
178*     .. External Subroutines ..
179      EXTERNAL           DLARF, XERBLA
180*     ..
181*     .. Intrinsic Functions ..
182      INTRINSIC          MAX
183*     ..
184*     .. Executable Statements ..
185*
186*     Test the input arguments
187*
188      INFO = 0
189      LEFT = LSAME( SIDE, 'L' )
190      NOTRAN = LSAME( TRANS, 'N' )
191      UPPER = LSAME( UPLO, 'U' )
192*
193*     NQ is the order of Q
194*
195      IF( LEFT ) THEN
196         NQ = M
197      ELSE
198         NQ = N
199      END IF
200      IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
201         INFO = -1
202      ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
203         INFO = -2
204      ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
205         INFO = -3
206      ELSE IF( M.LT.0 ) THEN
207         INFO = -4
208      ELSE IF( N.LT.0 ) THEN
209         INFO = -5
210      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
211         INFO = -9
212      END IF
213      IF( INFO.NE.0 ) THEN
214         CALL XERBLA( 'DOPMTR', -INFO )
215         RETURN
216      END IF
217*
218*     Quick return if possible
219*
220      IF( M.EQ.0 .OR. N.EQ.0 )
221     $   RETURN
222*
223      IF( UPPER ) THEN
224*
225*        Q was determined by a call to DSPTRD with UPLO = 'U'
226*
227         FORWRD = ( LEFT .AND. NOTRAN ) .OR.
228     $            ( .NOT.LEFT .AND. .NOT.NOTRAN )
229*
230         IF( FORWRD ) THEN
231            I1 = 1
232            I2 = NQ - 1
233            I3 = 1
234            II = 2
235         ELSE
236            I1 = NQ - 1
237            I2 = 1
238            I3 = -1
239            II = NQ*( NQ+1 ) / 2 - 1
240         END IF
241*
242         IF( LEFT ) THEN
243            NI = N
244         ELSE
245            MI = M
246         END IF
247*
248         DO 10 I = I1, I2, I3
249            IF( LEFT ) THEN
250*
251*              H(i) is applied to C(1:i,1:n)
252*
253               MI = I
254            ELSE
255*
256*              H(i) is applied to C(1:m,1:i)
257*
258               NI = I
259            END IF
260*
261*           Apply H(i)
262*
263            AII = AP( II )
264            AP( II ) = ONE
265            CALL DLARF( SIDE, MI, NI, AP( II-I+1 ), 1, TAU( I ), C, LDC,
266     $                  WORK )
267            AP( II ) = AII
268*
269            IF( FORWRD ) THEN
270               II = II + I + 2
271            ELSE
272               II = II - I - 1
273            END IF
274   10    CONTINUE
275      ELSE
276*
277*        Q was determined by a call to DSPTRD with UPLO = 'L'.
278*
279         FORWRD = ( LEFT .AND. .NOT.NOTRAN ) .OR.
280     $            ( .NOT.LEFT .AND. NOTRAN )
281*
282         IF( FORWRD ) THEN
283            I1 = 1
284            I2 = NQ - 1
285            I3 = 1
286            II = 2
287         ELSE
288            I1 = NQ - 1
289            I2 = 1
290            I3 = -1
291            II = NQ*( NQ+1 ) / 2 - 1
292         END IF
293*
294         IF( LEFT ) THEN
295            NI = N
296            JC = 1
297         ELSE
298            MI = M
299            IC = 1
300         END IF
301*
302         DO 20 I = I1, I2, I3
303            AII = AP( II )
304            AP( II ) = ONE
305            IF( LEFT ) THEN
306*
307*              H(i) is applied to C(i+1:m,1:n)
308*
309               MI = M - I
310               IC = I + 1
311            ELSE
312*
313*              H(i) is applied to C(1:m,i+1:n)
314*
315               NI = N - I
316               JC = I + 1
317            END IF
318*
319*           Apply H(i)
320*
321            CALL DLARF( SIDE, MI, NI, AP( II ), 1, TAU( I ),
322     $                  C( IC, JC ), LDC, WORK )
323            AP( II ) = AII
324*
325            IF( FORWRD ) THEN
326               II = II + NQ - I + 1
327            ELSE
328               II = II - NQ + I - 2
329            END IF
330   20    CONTINUE
331      END IF
332      RETURN
333*
334*     End of DOPMTR
335*
336      END
337