LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches
sorgbr.f
Go to the documentation of this file.
1*> \brief \b SORGBR
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/sorgbr.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sorgbr.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sorgbr.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE SORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
22*
23* .. Scalar Arguments ..
24* CHARACTER VECT
25* INTEGER INFO, K, LDA, LWORK, M, N
26* ..
27* .. Array Arguments ..
28* REAL A( LDA, * ), TAU( * ), WORK( * )
29* ..
30*
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> SORGBR generates one of the real orthogonal matrices Q or P**T
38*> determined by SGEBRD when reducing a real matrix A to bidiagonal
39*> form: A = Q * B * P**T. Q and P**T are defined as products of
40*> elementary reflectors H(i) or G(i) respectively.
41*>
42*> If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
43*> is of order M:
44*> if m >= k, Q = H(1) H(2) . . . H(k) and SORGBR returns the first n
45*> columns of Q, where m >= n >= k;
46*> if m < k, Q = H(1) H(2) . . . H(m-1) and SORGBR returns Q as an
47*> M-by-M matrix.
48*>
49*> If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T
50*> is of order N:
51*> if k < n, P**T = G(k) . . . G(2) G(1) and SORGBR returns the first m
52*> rows of P**T, where n >= m >= k;
53*> if k >= n, P**T = G(n-1) . . . G(2) G(1) and SORGBR returns P**T as
54*> an N-by-N matrix.
55*> \endverbatim
56*
57* Arguments:
58* ==========
59*
60*> \param[in] VECT
61*> \verbatim
62*> VECT is CHARACTER*1
63*> Specifies whether the matrix Q or the matrix P**T is
64*> required, as defined in the transformation applied by SGEBRD:
65*> = 'Q': generate Q;
66*> = 'P': generate P**T.
67*> \endverbatim
68*>
69*> \param[in] M
70*> \verbatim
71*> M is INTEGER
72*> The number of rows of the matrix Q or P**T to be returned.
73*> M >= 0.
74*> \endverbatim
75*>
76*> \param[in] N
77*> \verbatim
78*> N is INTEGER
79*> The number of columns of the matrix Q or P**T to be returned.
80*> N >= 0.
81*> If VECT = 'Q', M >= N >= min(M,K);
82*> if VECT = 'P', N >= M >= min(N,K).
83*> \endverbatim
84*>
85*> \param[in] K
86*> \verbatim
87*> K is INTEGER
88*> If VECT = 'Q', the number of columns in the original M-by-K
89*> matrix reduced by SGEBRD.
90*> If VECT = 'P', the number of rows in the original K-by-N
91*> matrix reduced by SGEBRD.
92*> K >= 0.
93*> \endverbatim
94*>
95*> \param[in,out] A
96*> \verbatim
97*> A is REAL array, dimension (LDA,N)
98*> On entry, the vectors which define the elementary reflectors,
99*> as returned by SGEBRD.
100*> On exit, the M-by-N matrix Q or P**T.
101*> \endverbatim
102*>
103*> \param[in] LDA
104*> \verbatim
105*> LDA is INTEGER
106*> The leading dimension of the array A. LDA >= max(1,M).
107*> \endverbatim
108*>
109*> \param[in] TAU
110*> \verbatim
111*> TAU is REAL array, dimension
112*> (min(M,K)) if VECT = 'Q'
113*> (min(N,K)) if VECT = 'P'
114*> TAU(i) must contain the scalar factor of the elementary
115*> reflector H(i) or G(i), which determines Q or P**T, as
116*> returned by SGEBRD in its array argument TAUQ or TAUP.
117*> \endverbatim
118*>
119*> \param[out] WORK
120*> \verbatim
121*> WORK is REAL array, dimension (MAX(1,LWORK))
122*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
123*> \endverbatim
124*>
125*> \param[in] LWORK
126*> \verbatim
127*> LWORK is INTEGER
128*> The dimension of the array WORK. LWORK >= max(1,min(M,N)).
129*> For optimum performance LWORK >= min(M,N)*NB, where NB
130*> is the optimal blocksize.
131*>
132*> If LWORK = -1, then a workspace query is assumed; the routine
133*> only calculates the optimal size of the WORK array, returns
134*> this value as the first entry of the WORK array, and no error
135*> message related to LWORK is issued by XERBLA.
136*> \endverbatim
137*>
138*> \param[out] INFO
139*> \verbatim
140*> INFO is INTEGER
141*> = 0: successful exit
142*> < 0: if INFO = -i, the i-th argument had an illegal value
143*> \endverbatim
144*
145* Authors:
146* ========
147*
148*> \author Univ. of Tennessee
149*> \author Univ. of California Berkeley
150*> \author Univ. of Colorado Denver
151*> \author NAG Ltd.
152*
153*> \ingroup realGBcomputational
154*
155* =====================================================================
156 SUBROUTINE sorgbr( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
157*
158* -- LAPACK computational routine --
159* -- LAPACK is a software package provided by Univ. of Tennessee, --
160* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
161*
162* .. Scalar Arguments ..
163 CHARACTER VECT
164 INTEGER INFO, K, LDA, LWORK, M, N
165* ..
166* .. Array Arguments ..
167 REAL A( LDA, * ), TAU( * ), WORK( * )
168* ..
169*
170* =====================================================================
171*
172* .. Parameters ..
173 REAL ZERO, ONE
174 parameter( zero = 0.0e+0, one = 1.0e+0 )
175* ..
176* .. Local Scalars ..
177 LOGICAL LQUERY, WANTQ
178 INTEGER I, IINFO, J, LWKOPT, MN
179* ..
180* .. External Functions ..
181 LOGICAL LSAME
182 EXTERNAL lsame
183* ..
184* .. External Subroutines ..
185 EXTERNAL sorglq, sorgqr, xerbla
186* ..
187* .. Intrinsic Functions ..
188 INTRINSIC max, min
189* ..
190* .. Executable Statements ..
191*
192* Test the input arguments
193*
194 info = 0
195 wantq = lsame( vect, 'Q' )
196 mn = min( m, n )
197 lquery = ( lwork.EQ.-1 )
198 IF( .NOT.wantq .AND. .NOT.lsame( vect, 'P' ) ) THEN
199 info = -1
200 ELSE IF( m.LT.0 ) THEN
201 info = -2
202 ELSE IF( n.LT.0 .OR. ( wantq .AND. ( n.GT.m .OR. n.LT.min( m,
203 \$ k ) ) ) .OR. ( .NOT.wantq .AND. ( m.GT.n .OR. m.LT.
204 \$ min( n, k ) ) ) ) THEN
205 info = -3
206 ELSE IF( k.LT.0 ) THEN
207 info = -4
208 ELSE IF( lda.LT.max( 1, m ) ) THEN
209 info = -6
210 ELSE IF( lwork.LT.max( 1, mn ) .AND. .NOT.lquery ) THEN
211 info = -9
212 END IF
213*
214 IF( info.EQ.0 ) THEN
215 work( 1 ) = 1
216 IF( wantq ) THEN
217 IF( m.GE.k ) THEN
218 CALL sorgqr( m, n, k, a, lda, tau, work, -1, iinfo )
219 ELSE
220 IF( m.GT.1 ) THEN
221 CALL sorgqr( m-1, m-1, m-1, a, lda, tau, work, -1,
222 \$ iinfo )
223 END IF
224 END IF
225 ELSE
226 IF( k.LT.n ) THEN
227 CALL sorglq( m, n, k, a, lda, tau, work, -1, iinfo )
228 ELSE
229 IF( n.GT.1 ) THEN
230 CALL sorglq( n-1, n-1, n-1, a, lda, tau, work, -1,
231 \$ iinfo )
232 END IF
233 END IF
234 END IF
235 lwkopt = int( work( 1 ) )
236 lwkopt = max(lwkopt, mn)
237 END IF
238*
239 IF( info.NE.0 ) THEN
240 CALL xerbla( 'SORGBR', -info )
241 RETURN
242 ELSE IF( lquery ) THEN
243 work( 1 ) = lwkopt
244 RETURN
245 END IF
246*
247* Quick return if possible
248*
249 IF( m.EQ.0 .OR. n.EQ.0 ) THEN
250 work( 1 ) = 1
251 RETURN
252 END IF
253*
254 IF( wantq ) THEN
255*
256* Form Q, determined by a call to SGEBRD to reduce an m-by-k
257* matrix
258*
259 IF( m.GE.k ) THEN
260*
261* If m >= k, assume m >= n >= k
262*
263 CALL sorgqr( m, n, k, a, lda, tau, work, lwork, iinfo )
264*
265 ELSE
266*
267* If m < k, assume m = n
268*
269* Shift the vectors which define the elementary reflectors one
270* column to the right, and set the first row and column of Q
271* to those of the unit matrix
272*
273 DO 20 j = m, 2, -1
274 a( 1, j ) = zero
275 DO 10 i = j + 1, m
276 a( i, j ) = a( i, j-1 )
277 10 CONTINUE
278 20 CONTINUE
279 a( 1, 1 ) = one
280 DO 30 i = 2, m
281 a( i, 1 ) = zero
282 30 CONTINUE
283 IF( m.GT.1 ) THEN
284*
285* Form Q(2:m,2:m)
286*
287 CALL sorgqr( m-1, m-1, m-1, a( 2, 2 ), lda, tau, work,
288 \$ lwork, iinfo )
289 END IF
290 END IF
291 ELSE
292*
293* Form P**T, determined by a call to SGEBRD to reduce a k-by-n
294* matrix
295*
296 IF( k.LT.n ) THEN
297*
298* If k < n, assume k <= m <= n
299*
300 CALL sorglq( m, n, k, a, lda, tau, work, lwork, iinfo )
301*
302 ELSE
303*
304* If k >= n, assume m = n
305*
306* Shift the vectors which define the elementary reflectors one
307* row downward, and set the first row and column of P**T to
308* those of the unit matrix
309*
310 a( 1, 1 ) = one
311 DO 40 i = 2, n
312 a( i, 1 ) = zero
313 40 CONTINUE
314 DO 60 j = 2, n
315 DO 50 i = j - 1, 2, -1
316 a( i, j ) = a( i-1, j )
317 50 CONTINUE
318 a( 1, j ) = zero
319 60 CONTINUE
320 IF( n.GT.1 ) THEN
321*
322* Form P**T(2:n,2:n)
323*
324 CALL sorglq( n-1, n-1, n-1, a( 2, 2 ), lda, tau, work,
325 \$ lwork, iinfo )
326 END IF
327 END IF
328 END IF
329 work( 1 ) = lwkopt
330 RETURN
331*
332* End of SORGBR
333*
334 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine sorgbr(VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGBR
Definition: sorgbr.f:157
subroutine sorglq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGLQ
Definition: sorglq.f:127
subroutine sorgqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGQR
Definition: sorgqr.f:128