LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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dormtr.f
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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
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 unmtr
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
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine dormql(side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
DORMQL
Definition dormql.f:167
subroutine dormqr(side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
DORMQR
Definition dormqr.f:167
subroutine dormtr(side, uplo, trans, m, n, a, lda, tau, c, ldc, work, lwork, info)
DORMTR
Definition dormtr.f:171