LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
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
9 *> Download SORGBR + dependencies
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 *> \date April 2012
154 *
155 *> \ingroup realGBcomputational
156 *
157 * =====================================================================
158  SUBROUTINE sorgbr( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
159 *
160 * -- LAPACK computational routine (version 3.7.0) --
161 * -- LAPACK is a software package provided by Univ. of Tennessee, --
162 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
163 * April 2012
164 *
165 * .. Scalar Arguments ..
166  CHARACTER VECT
167  INTEGER INFO, K, LDA, LWORK, M, N
168 * ..
169 * .. Array Arguments ..
170  REAL A( lda, * ), TAU( * ), WORK( * )
171 * ..
172 *
173 * =====================================================================
174 *
175 * .. Parameters ..
176  REAL ZERO, ONE
177  parameter( zero = 0.0e+0, one = 1.0e+0 )
178 * ..
179 * .. Local Scalars ..
180  LOGICAL LQUERY, WANTQ
181  INTEGER I, IINFO, J, LWKOPT, MN
182 * ..
183 * .. External Functions ..
184  LOGICAL LSAME
185  EXTERNAL lsame
186 * ..
187 * .. External Subroutines ..
188  EXTERNAL sorglq, sorgqr, xerbla
189 * ..
190 * .. Intrinsic Functions ..
191  INTRINSIC max, min
192 * ..
193 * .. Executable Statements ..
194 *
195 * Test the input arguments
196 *
197  info = 0
198  wantq = lsame( vect, 'Q' )
199  mn = min( m, n )
200  lquery = ( lwork.EQ.-1 )
201  IF( .NOT.wantq .AND. .NOT.lsame( vect, 'P' ) ) THEN
202  info = -1
203  ELSE IF( m.LT.0 ) THEN
204  info = -2
205  ELSE IF( n.LT.0 .OR. ( wantq .AND. ( n.GT.m .OR. n.LT.min( m,
206  $ k ) ) ) .OR. ( .NOT.wantq .AND. ( m.GT.n .OR. m.LT.
207  $ min( n, k ) ) ) ) THEN
208  info = -3
209  ELSE IF( k.LT.0 ) THEN
210  info = -4
211  ELSE IF( lda.LT.max( 1, m ) ) THEN
212  info = -6
213  ELSE IF( lwork.LT.max( 1, mn ) .AND. .NOT.lquery ) THEN
214  info = -9
215  END IF
216 *
217  IF( info.EQ.0 ) THEN
218  work( 1 ) = 1
219  IF( wantq ) THEN
220  IF( m.GE.k ) THEN
221  CALL sorgqr( m, n, k, a, lda, tau, work, -1, iinfo )
222  ELSE
223  IF( m.GT.1 ) THEN
224  CALL sorgqr( m-1, m-1, m-1, a( 2, 2 ), lda, tau, work,
225  $ -1, iinfo )
226  END IF
227  END IF
228  ELSE
229  IF( k.LT.n ) THEN
230  CALL sorglq( m, n, k, a, lda, tau, work, -1, iinfo )
231  ELSE
232  IF( n.GT.1 ) THEN
233  CALL sorglq( n-1, n-1, n-1, a( 2, 2 ), lda, tau, work,
234  $ -1, iinfo )
235  END IF
236  END IF
237  END IF
238  lwkopt = work( 1 )
239  lwkopt = max(lwkopt, mn)
240  END IF
241 *
242  IF( info.NE.0 ) THEN
243  CALL xerbla( 'SORGBR', -info )
244  RETURN
245  ELSE IF( lquery ) THEN
246  work( 1 ) = lwkopt
247  RETURN
248  END IF
249 *
250 * Quick return if possible
251 *
252  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
253  work( 1 ) = 1
254  RETURN
255  END IF
256 *
257  IF( wantq ) THEN
258 *
259 * Form Q, determined by a call to SGEBRD to reduce an m-by-k
260 * matrix
261 *
262  IF( m.GE.k ) THEN
263 *
264 * If m >= k, assume m >= n >= k
265 *
266  CALL sorgqr( m, n, k, a, lda, tau, work, lwork, iinfo )
267 *
268  ELSE
269 *
270 * If m < k, assume m = n
271 *
272 * Shift the vectors which define the elementary reflectors one
273 * column to the right, and set the first row and column of Q
274 * to those of the unit matrix
275 *
276  DO 20 j = m, 2, -1
277  a( 1, j ) = zero
278  DO 10 i = j + 1, m
279  a( i, j ) = a( i, j-1 )
280  10 CONTINUE
281  20 CONTINUE
282  a( 1, 1 ) = one
283  DO 30 i = 2, m
284  a( i, 1 ) = zero
285  30 CONTINUE
286  IF( m.GT.1 ) THEN
287 *
288 * Form Q(2:m,2:m)
289 *
290  CALL sorgqr( m-1, m-1, m-1, a( 2, 2 ), lda, tau, work,
291  $ lwork, iinfo )
292  END IF
293  END IF
294  ELSE
295 *
296 * Form P**T, determined by a call to SGEBRD to reduce a k-by-n
297 * matrix
298 *
299  IF( k.LT.n ) THEN
300 *
301 * If k < n, assume k <= m <= n
302 *
303  CALL sorglq( m, n, k, a, lda, tau, work, lwork, iinfo )
304 *
305  ELSE
306 *
307 * If k >= n, assume m = n
308 *
309 * Shift the vectors which define the elementary reflectors one
310 * row downward, and set the first row and column of P**T to
311 * those of the unit matrix
312 *
313  a( 1, 1 ) = one
314  DO 40 i = 2, n
315  a( i, 1 ) = zero
316  40 CONTINUE
317  DO 60 j = 2, n
318  DO 50 i = j - 1, 2, -1
319  a( i, j ) = a( i-1, j )
320  50 CONTINUE
321  a( 1, j ) = zero
322  60 CONTINUE
323  IF( n.GT.1 ) THEN
324 *
325 * Form P**T(2:n,2:n)
326 *
327  CALL sorglq( n-1, n-1, n-1, a( 2, 2 ), lda, tau, work,
328  $ lwork, iinfo )
329  END IF
330  END IF
331  END IF
332  work( 1 ) = lwkopt
333  RETURN
334 *
335 * End of SORGBR
336 *
337  END
subroutine sorglq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGLQ
Definition: sorglq.f:129
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine sorgqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGQR
Definition: sorgqr.f:130
subroutine sorgbr(VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGBR
Definition: sorgbr.f:159