LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches
dorgtr.f
Go to the documentation of this file.
1*> \brief \b DORGTR
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/dorgtr.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorgtr.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorgtr.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE DORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
22*
23* .. Scalar Arguments ..
24* CHARACTER UPLO
25* INTEGER INFO, LDA, LWORK, N
26* ..
27* .. Array Arguments ..
28* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
29* ..
30*
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> DORGTR generates a real orthogonal matrix Q which is defined as the
38*> product of n-1 elementary reflectors of order N, as returned by
39*> DSYTRD:
40*>
41*> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
42*>
43*> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
44*> \endverbatim
45*
46* Arguments:
47* ==========
48*
49*> \param[in] UPLO
50*> \verbatim
51*> UPLO is CHARACTER*1
52*> = 'U': Upper triangle of A contains elementary reflectors
53*> from DSYTRD;
54*> = 'L': Lower triangle of A contains elementary reflectors
55*> from DSYTRD.
56*> \endverbatim
57*>
58*> \param[in] N
59*> \verbatim
60*> N is INTEGER
61*> The order of the matrix Q. N >= 0.
62*> \endverbatim
63*>
64*> \param[in,out] A
65*> \verbatim
66*> A is DOUBLE PRECISION array, dimension (LDA,N)
67*> On entry, the vectors which define the elementary reflectors,
68*> as returned by DSYTRD.
69*> On exit, the N-by-N orthogonal matrix Q.
70*> \endverbatim
71*>
72*> \param[in] LDA
73*> \verbatim
74*> LDA is INTEGER
75*> The leading dimension of the array A. LDA >= max(1,N).
76*> \endverbatim
77*>
78*> \param[in] TAU
79*> \verbatim
80*> TAU is DOUBLE PRECISION array, dimension (N-1)
81*> TAU(i) must contain the scalar factor of the elementary
82*> reflector H(i), as returned by DSYTRD.
83*> \endverbatim
84*>
85*> \param[out] WORK
86*> \verbatim
87*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
88*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
89*> \endverbatim
90*>
91*> \param[in] LWORK
92*> \verbatim
93*> LWORK is INTEGER
94*> The dimension of the array WORK. LWORK >= max(1,N-1).
95*> For optimum performance LWORK >= (N-1)*NB, where NB is
96*> the optimal blocksize.
97*>
98*> If LWORK = -1, then a workspace query is assumed; the routine
99*> only calculates the optimal size of the WORK array, returns
100*> this value as the first entry of the WORK array, and no error
101*> message related to LWORK is issued by XERBLA.
102*> \endverbatim
103*>
104*> \param[out] INFO
105*> \verbatim
106*> INFO is INTEGER
107*> = 0: successful exit
108*> < 0: if INFO = -i, the i-th argument had an illegal value
109*> \endverbatim
110*
111* Authors:
112* ========
113*
114*> \author Univ. of Tennessee
115*> \author Univ. of California Berkeley
116*> \author Univ. of Colorado Denver
117*> \author NAG Ltd.
118*
119*> \ingroup doubleOTHERcomputational
120*
121* =====================================================================
122 SUBROUTINE dorgtr( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
123*
124* -- LAPACK computational routine --
125* -- LAPACK is a software package provided by Univ. of Tennessee, --
126* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
127*
128* .. Scalar Arguments ..
129 CHARACTER UPLO
130 INTEGER INFO, LDA, LWORK, N
131* ..
132* .. Array Arguments ..
133 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
134* ..
135*
136* =====================================================================
137*
138* .. Parameters ..
139 DOUBLE PRECISION ZERO, ONE
140 parameter( zero = 0.0d+0, one = 1.0d+0 )
141* ..
142* .. Local Scalars ..
143 LOGICAL LQUERY, UPPER
144 INTEGER I, IINFO, J, LWKOPT, NB
145* ..
146* .. External Functions ..
147 LOGICAL LSAME
148 INTEGER ILAENV
149 EXTERNAL lsame, ilaenv
150* ..
151* .. External Subroutines ..
152 EXTERNAL dorgql, dorgqr, xerbla
153* ..
154* .. Intrinsic Functions ..
155 INTRINSIC max
156* ..
157* .. Executable Statements ..
158*
159* Test the input arguments
160*
161 info = 0
162 lquery = ( lwork.EQ.-1 )
163 upper = lsame( uplo, 'U' )
164 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
165 info = -1
166 ELSE IF( n.LT.0 ) THEN
167 info = -2
168 ELSE IF( lda.LT.max( 1, n ) ) THEN
169 info = -4
170 ELSE IF( lwork.LT.max( 1, n-1 ) .AND. .NOT.lquery ) THEN
171 info = -7
172 END IF
173*
174 IF( info.EQ.0 ) THEN
175 IF( upper ) THEN
176 nb = ilaenv( 1, 'DORGQL', ' ', n-1, n-1, n-1, -1 )
177 ELSE
178 nb = ilaenv( 1, 'DORGQR', ' ', n-1, n-1, n-1, -1 )
179 END IF
180 lwkopt = max( 1, n-1 )*nb
181 work( 1 ) = lwkopt
182 END IF
183*
184 IF( info.NE.0 ) THEN
185 CALL xerbla( 'DORGTR', -info )
186 RETURN
187 ELSE IF( lquery ) THEN
188 RETURN
189 END IF
190*
191* Quick return if possible
192*
193 IF( n.EQ.0 ) THEN
194 work( 1 ) = 1
195 RETURN
196 END IF
197*
198 IF( upper ) THEN
199*
200* Q was determined by a call to DSYTRD with UPLO = 'U'
201*
202* Shift the vectors which define the elementary reflectors one
203* column to the left, and set the last row and column of Q to
204* those of the unit matrix
205*
206 DO 20 j = 1, n - 1
207 DO 10 i = 1, j - 1
208 a( i, j ) = a( i, j+1 )
209 10 CONTINUE
210 a( n, j ) = zero
211 20 CONTINUE
212 DO 30 i = 1, n - 1
213 a( i, n ) = zero
214 30 CONTINUE
215 a( n, n ) = one
216*
217* Generate Q(1:n-1,1:n-1)
218*
219 CALL dorgql( n-1, n-1, n-1, a, lda, tau, work, lwork, iinfo )
220*
221 ELSE
222*
223* Q was determined by a call to DSYTRD with UPLO = 'L'.
224*
225* Shift the vectors which define the elementary reflectors one
226* column to the right, and set the first row and column of Q to
227* those of the unit matrix
228*
229 DO 50 j = n, 2, -1
230 a( 1, j ) = zero
231 DO 40 i = j + 1, n
232 a( i, j ) = a( i, j-1 )
233 40 CONTINUE
234 50 CONTINUE
235 a( 1, 1 ) = one
236 DO 60 i = 2, n
237 a( i, 1 ) = zero
238 60 CONTINUE
239 IF( n.GT.1 ) THEN
240*
241* Generate Q(2:n,2:n)
242*
243 CALL dorgqr( n-1, n-1, n-1, a( 2, 2 ), lda, tau, work,
244 \$ lwork, iinfo )
245 END IF
246 END IF
247 work( 1 ) = lwkopt
248 RETURN
249*
250* End of DORGTR
251*
252 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dorgqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
DORGQR
Definition: dorgqr.f:128
subroutine dorgql(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
DORGQL
Definition: dorgql.f:128
subroutine dorgtr(UPLO, N, A, LDA, TAU, WORK, LWORK, INFO)
DORGTR
Definition: dorgtr.f:123