LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
cunmrq.f
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1 *> \brief \b CUNMRQ
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CUNMRQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
22 * WORK, LWORK, INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER SIDE, TRANS
26 * INTEGER INFO, K, LDA, LDC, LWORK, M, N
27 * ..
28 * .. Array Arguments ..
29 * COMPLEX A( LDA, * ), C( LDC, * ), TAU( * ),
30 * \$ WORK( * )
31 * ..
32 *
33 *
34 *> \par Purpose:
35 * =============
36 *>
37 *> \verbatim
38 *>
39 *> CUNMRQ overwrites the general complex M-by-N matrix C with
40 *>
41 *> SIDE = 'L' SIDE = 'R'
42 *> TRANS = 'N': Q * C C * Q
43 *> TRANS = 'C': Q**H * C C * Q**H
44 *>
45 *> where Q is a complex unitary matrix defined as the product of k
46 *> elementary reflectors
47 *>
48 *> Q = H(1)**H H(2)**H . . . H(k)**H
49 *>
50 *> as returned by CGERQF. Q is of order M if SIDE = 'L' and of order N
51 *> if SIDE = 'R'.
52 *> \endverbatim
53 *
54 * Arguments:
55 * ==========
56 *
57 *> \param[in] SIDE
58 *> \verbatim
59 *> SIDE is CHARACTER*1
60 *> = 'L': apply Q or Q**H from the Left;
61 *> = 'R': apply Q or Q**H from the Right.
62 *> \endverbatim
63 *>
64 *> \param[in] TRANS
65 *> \verbatim
66 *> TRANS is CHARACTER*1
67 *> = 'N': No transpose, apply Q;
68 *> = 'C': Transpose, apply Q**H.
69 *> \endverbatim
70 *>
71 *> \param[in] M
72 *> \verbatim
73 *> M is INTEGER
74 *> The number of rows of the matrix C. M >= 0.
75 *> \endverbatim
76 *>
77 *> \param[in] N
78 *> \verbatim
79 *> N is INTEGER
80 *> The number of columns of the matrix C. N >= 0.
81 *> \endverbatim
82 *>
83 *> \param[in] K
84 *> \verbatim
85 *> K is INTEGER
86 *> The number of elementary reflectors whose product defines
87 *> the matrix Q.
88 *> If SIDE = 'L', M >= K >= 0;
89 *> if SIDE = 'R', N >= K >= 0.
90 *> \endverbatim
91 *>
92 *> \param[in] A
93 *> \verbatim
94 *> A is COMPLEX array, dimension
95 *> (LDA,M) if SIDE = 'L',
96 *> (LDA,N) if SIDE = 'R'
97 *> The i-th row must contain the vector which defines the
98 *> elementary reflector H(i), for i = 1,2,...,k, as returned by
99 *> CGERQF in the last k rows of its array argument A.
100 *> \endverbatim
101 *>
102 *> \param[in] LDA
103 *> \verbatim
104 *> LDA is INTEGER
105 *> The leading dimension of the array A. LDA >= max(1,K).
106 *> \endverbatim
107 *>
108 *> \param[in] TAU
109 *> \verbatim
110 *> TAU is COMPLEX array, dimension (K)
111 *> TAU(i) must contain the scalar factor of the elementary
112 *> reflector H(i), as returned by CGERQF.
113 *> \endverbatim
114 *>
115 *> \param[in,out] C
116 *> \verbatim
117 *> C is COMPLEX array, dimension (LDC,N)
118 *> On entry, the M-by-N matrix C.
119 *> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
120 *> \endverbatim
121 *>
122 *> \param[in] LDC
123 *> \verbatim
124 *> LDC is INTEGER
125 *> The leading dimension of the array C. LDC >= max(1,M).
126 *> \endverbatim
127 *>
128 *> \param[out] WORK
129 *> \verbatim
130 *> WORK is COMPLEX array, dimension (MAX(1,LWORK))
131 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
132 *> \endverbatim
133 *>
134 *> \param[in] LWORK
135 *> \verbatim
136 *> LWORK is INTEGER
137 *> The dimension of the array WORK.
138 *> If SIDE = 'L', LWORK >= max(1,N);
139 *> if SIDE = 'R', LWORK >= max(1,M).
140 *> For good performance, LWORK should generally be larger.
141 *>
142 *> If LWORK = -1, then a workspace query is assumed; the routine
143 *> only calculates the optimal size of the WORK array, returns
144 *> this value as the first entry of the WORK array, and no error
145 *> message related to LWORK is issued by XERBLA.
146 *> \endverbatim
147 *>
148 *> \param[out] INFO
149 *> \verbatim
150 *> INFO is INTEGER
151 *> = 0: successful exit
152 *> < 0: if INFO = -i, the i-th argument had an illegal value
153 *> \endverbatim
154 *
155 * Authors:
156 * ========
157 *
158 *> \author Univ. of Tennessee
159 *> \author Univ. of California Berkeley
160 *> \author Univ. of Colorado Denver
161 *> \author NAG Ltd.
162 *
163 *> \date November 2015
164 *
165 *> \ingroup complexOTHERcomputational
166 *
167 * =====================================================================
168  SUBROUTINE cunmrq( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
169  \$ work, lwork, info )
170 *
171 * -- LAPACK computational routine (version 3.6.0) --
172 * -- LAPACK is a software package provided by Univ. of Tennessee, --
173 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
174 * November 2015
175 *
176 * .. Scalar Arguments ..
177  CHARACTER SIDE, TRANS
178  INTEGER INFO, K, LDA, LDC, LWORK, M, N
179 * ..
180 * .. Array Arguments ..
181  COMPLEX A( lda, * ), C( ldc, * ), TAU( * ),
182  \$ work( * )
183 * ..
184 *
185 * =====================================================================
186 *
187 * .. Parameters ..
188  INTEGER NBMAX, LDT, TSIZE
189  parameter ( nbmax = 64, ldt = nbmax+1,
190  \$ tsize = ldt*nbmax )
191 * ..
192 * .. Local Scalars ..
193  LOGICAL LEFT, LQUERY, NOTRAN
194  CHARACTER TRANST
195  INTEGER I, I1, I2, I3, IB, IINFO, IWT, LDWORK, LWKOPT,
196  \$ mi, nb, nbmin, ni, nq, nw
197 * ..
198 * .. External Functions ..
199  LOGICAL LSAME
200  INTEGER ILAENV
201  EXTERNAL lsame, ilaenv
202 * ..
203 * .. External Subroutines ..
204  EXTERNAL clarfb, clarft, cunmr2, xerbla
205 * ..
206 * .. Intrinsic Functions ..
207  INTRINSIC max, min
208 * ..
209 * .. Executable Statements ..
210 *
211 * Test the input arguments
212 *
213  info = 0
214  left = lsame( side, 'L' )
215  notran = lsame( trans, 'N' )
216  lquery = ( lwork.EQ.-1 )
217 *
218 * NQ is the order of Q and NW is the minimum dimension of WORK
219 *
220  IF( left ) THEN
221  nq = m
222  nw = max( 1, n )
223  ELSE
224  nq = n
225  nw = max( 1, m )
226  END IF
227  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
228  info = -1
229  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'C' ) ) THEN
230  info = -2
231  ELSE IF( m.LT.0 ) THEN
232  info = -3
233  ELSE IF( n.LT.0 ) THEN
234  info = -4
235  ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
236  info = -5
237  ELSE IF( lda.LT.max( 1, k ) ) THEN
238  info = -7
239  ELSE IF( ldc.LT.max( 1, m ) ) THEN
240  info = -10
241  ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
242  info = -12
243  END IF
244 *
245  IF( info.EQ.0 ) THEN
246 *
247 * Compute the workspace requirements
248 *
249  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
250  lwkopt = 1
251  ELSE
252  nb = min( nbmax, ilaenv( 1, 'CUNMRQ', side // trans, m, n,
253  \$ k, -1 ) )
254  lwkopt = nw*nb + tsize
255  END IF
256  work( 1 ) = lwkopt
257  END IF
258 *
259  IF( info.NE.0 ) THEN
260  CALL xerbla( 'CUNMRQ', -info )
261  RETURN
262  ELSE IF( lquery ) THEN
263  RETURN
264  END IF
265 *
266 * Quick return if possible
267 *
268  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
269  RETURN
270  END IF
271 *
272  nbmin = 2
273  ldwork = nw
274  IF( nb.GT.1 .AND. nb.LT.k ) THEN
275  IF( lwork.LT.nw*nb+tsize ) THEN
276  nb = (lwork-tsize) / ldwork
277  nbmin = max( 2, ilaenv( 2, 'CUNMRQ', side // trans, m, n, k,
278  \$ -1 ) )
279  END IF
280  END IF
281 *
282  IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
283 *
284 * Use unblocked code
285 *
286  CALL cunmr2( side, trans, m, n, k, a, lda, tau, c, ldc, work,
287  \$ iinfo )
288  ELSE
289 *
290 * Use blocked code
291 *
292  iwt = 1 + nw*nb
293  IF( ( left .AND. .NOT.notran ) .OR.
294  \$ ( .NOT.left .AND. notran ) ) THEN
295  i1 = 1
296  i2 = k
297  i3 = nb
298  ELSE
299  i1 = ( ( k-1 ) / nb )*nb + 1
300  i2 = 1
301  i3 = -nb
302  END IF
303 *
304  IF( left ) THEN
305  ni = n
306  ELSE
307  mi = m
308  END IF
309 *
310  IF( notran ) THEN
311  transt = 'C'
312  ELSE
313  transt = 'N'
314  END IF
315 *
316  DO 10 i = i1, i2, i3
317  ib = min( nb, k-i+1 )
318 *
319 * Form the triangular factor of the block reflector
320 * H = H(i+ib-1) . . . H(i+1) H(i)
321 *
322  CALL clarft( 'Backward', 'Rowwise', nq-k+i+ib-1, ib,
323  \$ a( i, 1 ), lda, tau( i ), work( iwt ), ldt )
324  IF( left ) THEN
325 *
326 * H or H**H is applied to C(1:m-k+i+ib-1,1:n)
327 *
328  mi = m - k + i + ib - 1
329  ELSE
330 *
331 * H or H**H is applied to C(1:m,1:n-k+i+ib-1)
332 *
333  ni = n - k + i + ib - 1
334  END IF
335 *
336 * Apply H or H**H
337 *
338  CALL clarfb( side, transt, 'Backward', 'Rowwise', mi, ni,
339  \$ ib, a( i, 1 ), lda, work( iwt ), ldt, c, ldc,
340  \$ work, ldwork )
341  10 CONTINUE
342  END IF
343  work( 1 ) = lwkopt
344  RETURN
345 *
346 * End of CUNMRQ
347 *
348  END
subroutine clarft(DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
CLARFT forms the triangular factor T of a block reflector H = I - vtvH
Definition: clarft.f:165
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine cunmrq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
CUNMRQ
Definition: cunmrq.f:170
subroutine cunmr2(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
CUNMR2 multiplies a general matrix by the unitary matrix from a RQ factorization determined by cgerqf...
Definition: cunmr2.f:161
subroutine clarfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
CLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix...
Definition: clarfb.f:197