LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
sorgbr.f
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1 *> \brief \b SORGBR
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
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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 = 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