LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
cungbr.f
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1 *> \brief \b CUNGBR
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CUNGBR( 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 * COMPLEX A( LDA, * ), TAU( * ), WORK( * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> CUNGBR generates one of the complex unitary matrices Q or P**H
38 *> determined by CGEBRD when reducing a complex matrix A to bidiagonal
39 *> form: A = Q * B * P**H. Q and P**H 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 CUNGBR 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 CUNGBR 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**H
50 *> is of order N:
51 *> if k < n, P**H = G(k) . . . G(2) G(1) and CUNGBR returns the first m
52 *> rows of P**H, where n >= m >= k;
53 *> if k >= n, P**H = G(n-1) . . . G(2) G(1) and CUNGBR returns P**H 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**H is
64 *> required, as defined in the transformation applied by CGEBRD:
65 *> = 'Q': generate Q;
66 *> = 'P': generate P**H.
67 *> \endverbatim
68 *>
69 *> \param[in] M
70 *> \verbatim
71 *> M is INTEGER
72 *> The number of rows of the matrix Q or P**H 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**H 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 CGEBRD.
90 *> If VECT = 'P', the number of rows in the original K-by-N
91 *> matrix reduced by CGEBRD.
92 *> K >= 0.
93 *> \endverbatim
94 *>
95 *> \param[in,out] A
96 *> \verbatim
97 *> A is COMPLEX array, dimension (LDA,N)
98 *> On entry, the vectors which define the elementary reflectors,
99 *> as returned by CGEBRD.
100 *> On exit, the M-by-N matrix Q or P**H.
101 *> \endverbatim
102 *>
103 *> \param[in] LDA
104 *> \verbatim
105 *> LDA is INTEGER
106 *> The leading dimension of the array A. LDA >= M.
107 *> \endverbatim
108 *>
109 *> \param[in] TAU
110 *> \verbatim
111 *> TAU is COMPLEX 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**H, as
116 *> returned by CGEBRD in its array argument TAUQ or TAUP.
117 *> \endverbatim
118 *>
119 *> \param[out] WORK
120 *> \verbatim
121 *> WORK is COMPLEX 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 complexGBcomputational
156 *
157 * =====================================================================
158  SUBROUTINE cungbr( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
159 *
160 * -- LAPACK computational routine (version 3.4.1) --
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  COMPLEX a( lda, * ), tau( * ), work( * )
171 * ..
172 *
173 * =====================================================================
174 *
175 * .. Parameters ..
176  COMPLEX zero, one
177  parameter( zero = ( 0.0e+0, 0.0e+0 ),
178  \$ one = ( 1.0e+0, 0.0e+0 ) )
179 * ..
180 * .. Local Scalars ..
181  LOGICAL lquery, wantq
182  INTEGER i, iinfo, j, lwkopt, mn
183 * ..
184 * .. External Functions ..
185  LOGICAL lsame
186  INTEGER ilaenv
187  EXTERNAL ilaenv, lsame
188 * ..
189 * .. External Subroutines ..
190  EXTERNAL cunglq, cungqr, xerbla
191 * ..
192 * .. Intrinsic Functions ..
193  INTRINSIC max, min
194 * ..
195 * .. Executable Statements ..
196 *
197 * Test the input arguments
198 *
199  info = 0
200  wantq = lsame( vect, 'Q' )
201  mn = min( m, n )
202  lquery = ( lwork.EQ.-1 )
203  IF( .NOT.wantq .AND. .NOT.lsame( vect, 'P' ) ) THEN
204  info = -1
205  ELSE IF( m.LT.0 ) THEN
206  info = -2
207  ELSE IF( n.LT.0 .OR. ( wantq .AND. ( n.GT.m .OR. n.LT.min( m,
208  \$ k ) ) ) .OR. ( .NOT.wantq .AND. ( m.GT.n .OR. m.LT.
209  \$ min( n, k ) ) ) ) THEN
210  info = -3
211  ELSE IF( k.LT.0 ) THEN
212  info = -4
213  ELSE IF( lda.LT.max( 1, m ) ) THEN
214  info = -6
215  ELSE IF( lwork.LT.max( 1, mn ) .AND. .NOT.lquery ) THEN
216  info = -9
217  END IF
218 *
219  IF( info.EQ.0 ) THEN
220  work( 1 ) = 1
221  IF( wantq ) THEN
222  IF( m.GE.k ) THEN
223  CALL cungqr( m, n, k, a, lda, tau, work, -1, iinfo )
224  ELSE
225  IF( m.GT.1 ) THEN
226  CALL cungqr( m-1, m-1, m-1, a( 2, 2 ), lda, tau, work,
227  \$ -1, iinfo )
228  END IF
229  END IF
230  ELSE
231  IF( k.LT.n ) THEN
232  CALL cunglq( m, n, k, a, lda, tau, work, -1, iinfo )
233  ELSE
234  IF( n.GT.1 ) THEN
235  CALL cunglq( n-1, n-1, n-1, a( 2, 2 ), lda, tau, work,
236  \$ -1, iinfo )
237  END IF
238  END IF
239  END IF
240  lwkopt = work( 1 )
241  lwkopt = max(lwkopt, mn)
242  END IF
243 *
244  IF( info.NE.0 ) THEN
245  CALL xerbla( 'CUNGBR', -info )
246  return
247  ELSE IF( lquery ) THEN
248  work( 1 ) = lwkopt
249  return
250  END IF
251 *
252 * Quick return if possible
253 *
254  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
255  work( 1 ) = 1
256  return
257  END IF
258 *
259  IF( wantq ) THEN
260 *
261 * Form Q, determined by a call to CGEBRD to reduce an m-by-k
262 * matrix
263 *
264  IF( m.GE.k ) THEN
265 *
266 * If m >= k, assume m >= n >= k
267 *
268  CALL cungqr( m, n, k, a, lda, tau, work, lwork, iinfo )
269 *
270  ELSE
271 *
272 * If m < k, assume m = n
273 *
274 * Shift the vectors which define the elementary reflectors one
275 * column to the right, and set the first row and column of Q
276 * to those of the unit matrix
277 *
278  DO 20 j = m, 2, -1
279  a( 1, j ) = zero
280  DO 10 i = j + 1, m
281  a( i, j ) = a( i, j-1 )
282  10 continue
283  20 continue
284  a( 1, 1 ) = one
285  DO 30 i = 2, m
286  a( i, 1 ) = zero
287  30 continue
288  IF( m.GT.1 ) THEN
289 *
290 * Form Q(2:m,2:m)
291 *
292  CALL cungqr( m-1, m-1, m-1, a( 2, 2 ), lda, tau, work,
293  \$ lwork, iinfo )
294  END IF
295  END IF
296  ELSE
297 *
298 * Form P**H, determined by a call to CGEBRD to reduce a k-by-n
299 * matrix
300 *
301  IF( k.LT.n ) THEN
302 *
303 * If k < n, assume k <= m <= n
304 *
305  CALL cunglq( m, n, k, a, lda, tau, work, lwork, iinfo )
306 *
307  ELSE
308 *
309 * If k >= n, assume m = n
310 *
311 * Shift the vectors which define the elementary reflectors one
312 * row downward, and set the first row and column of P**H to
313 * those of the unit matrix
314 *
315  a( 1, 1 ) = one
316  DO 40 i = 2, n
317  a( i, 1 ) = zero
318  40 continue
319  DO 60 j = 2, n
320  DO 50 i = j - 1, 2, -1
321  a( i, j ) = a( i-1, j )
322  50 continue
323  a( 1, j ) = zero
324  60 continue
325  IF( n.GT.1 ) THEN
326 *
327 * Form P**H(2:n,2:n)
328 *
329  CALL cunglq( n-1, n-1, n-1, a( 2, 2 ), lda, tau, work,
330  \$ lwork, iinfo )
331  END IF
332  END IF
333  END IF
334  work( 1 ) = lwkopt
335  return
336 *
337 * End of CUNGBR
338 *
339  END