LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
ctpmlqt.f
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1 *> \brief \b CTPMLQT
2 *
3 * Definition:
4 * ===========
5 *
6 * SUBROUTINE CTPMLQT( SIDE, TRANS, M, N, K, L, MB, V, LDV, T, LDT,
7 * A, LDA, B, LDB, WORK, INFO )
8 *
9 * .. Scalar Arguments ..
10 * CHARACTER SIDE, TRANS
11 * INTEGER INFO, K, LDV, LDA, LDB, M, N, L, MB, LDT
12 * ..
13 * .. Array Arguments ..
14 * COMPLEX V( LDV, * ), A( LDA, * ), B( LDB, * ),
15 * $ T( LDT, * ), WORK( * )
16 * ..
17 *
18 *
19 *> \par Purpose:
20 * =============
21 *>
22 *> \verbatim
23 *>
24 *> CTPMLQT applies a complex unitary matrix Q obtained from a
25 *> "triangular-pentagonal" complex block reflector H to a general
26 *> complex matrix C, which consists of two blocks A and B.
27 *> \endverbatim
28 *
29 * Arguments:
30 * ==========
31 *
32 *> \param[in] SIDE
33 *> \verbatim
34 *> SIDE is CHARACTER*1
35 *> = 'L': apply Q or Q**H from the Left;
36 *> = 'R': apply Q or Q**H from the Right.
37 *> \endverbatim
38 *>
39 *> \param[in] TRANS
40 *> \verbatim
41 *> TRANS is CHARACTER*1
42 *> = 'N': No transpose, apply Q;
43 *> = 'C': Conjugate transpose, apply Q**H.
44 *> \endverbatim
45 *>
46 *> \param[in] M
47 *> \verbatim
48 *> M is INTEGER
49 *> The number of rows of the matrix B. M >= 0.
50 *> \endverbatim
51 *>
52 *> \param[in] N
53 *> \verbatim
54 *> N is INTEGER
55 *> The number of columns of the matrix B. N >= 0.
56 *> \endverbatim
57 *>
58 *> \param[in] K
59 *> \verbatim
60 *> K is INTEGER
61 *> The number of elementary reflectors whose product defines
62 *> the matrix Q.
63 *> \endverbatim
64 *>
65 *> \param[in] L
66 *> \verbatim
67 *> L is INTEGER
68 *> The order of the trapezoidal part of V.
69 *> K >= L >= 0. See Further Details.
70 *> \endverbatim
71 *>
72 *> \param[in] MB
73 *> \verbatim
74 *> MB is INTEGER
75 *> The block size used for the storage of T. K >= MB >= 1.
76 *> This must be the same value of MB used to generate T
77 *> in CTPLQT.
78 *> \endverbatim
79 *>
80 *> \param[in] V
81 *> \verbatim
82 *> V is COMPLEX array, dimension (LDV,K)
83 *> The i-th row must contain the vector which defines the
84 *> elementary reflector H(i), for i = 1,2,...,k, as returned by
85 *> CTPLQT in B. See Further Details.
86 *> \endverbatim
87 *>
88 *> \param[in] LDV
89 *> \verbatim
90 *> LDV is INTEGER
91 *> The leading dimension of the array V. LDV >= K.
92 *> \endverbatim
93 *>
94 *> \param[in] T
95 *> \verbatim
96 *> T is COMPLEX array, dimension (LDT,K)
97 *> The upper triangular factors of the block reflectors
98 *> as returned by CTPLQT, stored as a MB-by-K matrix.
99 *> \endverbatim
100 *>
101 *> \param[in] LDT
102 *> \verbatim
103 *> LDT is INTEGER
104 *> The leading dimension of the array T. LDT >= MB.
105 *> \endverbatim
106 *>
107 *> \param[in,out] A
108 *> \verbatim
109 *> A is COMPLEX array, dimension
110 *> (LDA,N) if SIDE = 'L' or
111 *> (LDA,K) if SIDE = 'R'
112 *> On entry, the K-by-N or M-by-K matrix A.
113 *> On exit, A is overwritten by the corresponding block of
114 *> Q*C or Q**H*C or C*Q or C*Q**H. See Further Details.
115 *> \endverbatim
116 *>
117 *> \param[in] LDA
118 *> \verbatim
119 *> LDA is INTEGER
120 *> The leading dimension of the array A.
121 *> If SIDE = 'L', LDA >= max(1,K);
122 *> If SIDE = 'R', LDA >= max(1,M).
123 *> \endverbatim
124 *>
125 *> \param[in,out] B
126 *> \verbatim
127 *> B is COMPLEX array, dimension (LDB,N)
128 *> On entry, the M-by-N matrix B.
129 *> On exit, B is overwritten by the corresponding block of
130 *> Q*C or Q**H*C or C*Q or C*Q**H. See Further Details.
131 *> \endverbatim
132 *>
133 *> \param[in] LDB
134 *> \verbatim
135 *> LDB is INTEGER
136 *> The leading dimension of the array B.
137 *> LDB >= max(1,M).
138 *> \endverbatim
139 *>
140 *> \param[out] WORK
141 *> \verbatim
142 *> WORK is COMPLEX array. The dimension of WORK is
143 *> N*MB if SIDE = 'L', or M*MB if SIDE = 'R'.
144 *> \endverbatim
145 *>
146 *> \param[out] INFO
147 *> \verbatim
148 *> INFO is INTEGER
149 *> = 0: successful exit
150 *> < 0: if INFO = -i, the i-th argument had an illegal value
151 *> \endverbatim
152 *
153 * Authors:
154 * ========
155 *
156 *> \author Univ. of Tennessee
157 *> \author Univ. of California Berkeley
158 *> \author Univ. of Colorado Denver
159 *> \author NAG Ltd.
160 *
161 *> \ingroup doubleOTHERcomputational
162 *
163 *> \par Further Details:
164 * =====================
165 *>
166 *> \verbatim
167 *>
168 *> The columns of the pentagonal matrix V contain the elementary reflectors
169 *> H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a
170 *> trapezoidal block V2:
171 *>
172 *> V = [V1] [V2].
173 *>
174 *>
175 *> The size of the trapezoidal block V2 is determined by the parameter L,
176 *> where 0 <= L <= K; V2 is lower trapezoidal, consisting of the first L
177 *> rows of a K-by-K upper triangular matrix. If L=K, V2 is lower triangular;
178 *> if L=0, there is no trapezoidal block, hence V = V1 is rectangular.
179 *>
180 *> If SIDE = 'L': C = [A] where A is K-by-N, B is M-by-N and V is K-by-M.
181 *> [B]
182 *>
183 *> If SIDE = 'R': C = [A B] where A is M-by-K, B is M-by-N and V is K-by-N.
184 *>
185 *> The complex unitary matrix Q is formed from V and T.
186 *>
187 *> If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.
188 *>
189 *> If TRANS='C' and SIDE='L', C is on exit replaced with Q**H * C.
190 *>
191 *> If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
192 *>
193 *> If TRANS='C' and SIDE='R', C is on exit replaced with C * Q**H.
194 *> \endverbatim
195 *>
196 * =====================================================================
197  SUBROUTINE ctpmlqt( SIDE, TRANS, M, N, K, L, MB, V, LDV, T, LDT,
198  $ A, LDA, B, LDB, WORK, INFO )
199 *
200 * -- LAPACK computational routine --
201 * -- LAPACK is a software package provided by Univ. of Tennessee, --
202 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
203 *
204 * .. Scalar Arguments ..
205  CHARACTER SIDE, TRANS
206  INTEGER INFO, K, LDV, LDA, LDB, M, N, L, MB, LDT
207 * ..
208 * .. Array Arguments ..
209  COMPLEX V( LDV, * ), A( LDA, * ), B( LDB, * ),
210  $ t( ldt, * ), work( * )
211 * ..
212 *
213 * =====================================================================
214 *
215 * ..
216 * .. Local Scalars ..
217  LOGICAL LEFT, RIGHT, TRAN, NOTRAN
218  INTEGER I, IB, NB, LB, KF, LDAQ
219 * ..
220 * .. External Functions ..
221  LOGICAL LSAME
222  EXTERNAL lsame
223 * ..
224 * .. External Subroutines ..
225  EXTERNAL xerbla, ctprfb
226 * ..
227 * .. Intrinsic Functions ..
228  INTRINSIC max, min
229 * ..
230 * .. Executable Statements ..
231 *
232 * .. Test the input arguments ..
233 *
234  info = 0
235  left = lsame( side, 'L' )
236  right = lsame( side, 'R' )
237  tran = lsame( trans, 'C' )
238  notran = lsame( trans, 'N' )
239 *
240  IF ( left ) THEN
241  ldaq = max( 1, k )
242  ELSE IF ( right ) THEN
243  ldaq = max( 1, m )
244  END IF
245  IF( .NOT.left .AND. .NOT.right ) THEN
246  info = -1
247  ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
248  info = -2
249  ELSE IF( m.LT.0 ) THEN
250  info = -3
251  ELSE IF( n.LT.0 ) THEN
252  info = -4
253  ELSE IF( k.LT.0 ) THEN
254  info = -5
255  ELSE IF( l.LT.0 .OR. l.GT.k ) THEN
256  info = -6
257  ELSE IF( mb.LT.1 .OR. (mb.GT.k .AND. k.GT.0) ) THEN
258  info = -7
259  ELSE IF( ldv.LT.k ) THEN
260  info = -9
261  ELSE IF( ldt.LT.mb ) THEN
262  info = -11
263  ELSE IF( lda.LT.ldaq ) THEN
264  info = -13
265  ELSE IF( ldb.LT.max( 1, m ) ) THEN
266  info = -15
267  END IF
268 *
269  IF( info.NE.0 ) THEN
270  CALL xerbla( 'CTPMLQT', -info )
271  RETURN
272  END IF
273 *
274 * .. Quick return if possible ..
275 *
276  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) RETURN
277 *
278  IF( left .AND. notran ) THEN
279 *
280  DO i = 1, k, mb
281  ib = min( mb, k-i+1 )
282  nb = min( m-l+i+ib-1, m )
283  IF( i.GE.l ) THEN
284  lb = 0
285  ELSE
286  lb = 0
287  END IF
288  CALL ctprfb( 'L', 'C', 'F', 'R', nb, n, ib, lb,
289  $ v( i, 1 ), ldv, t( 1, i ), ldt,
290  $ a( i, 1 ), lda, b, ldb, work, ib )
291  END DO
292 *
293  ELSE IF( right .AND. tran ) THEN
294 *
295  DO i = 1, k, mb
296  ib = min( mb, k-i+1 )
297  nb = min( n-l+i+ib-1, n )
298  IF( i.GE.l ) THEN
299  lb = 0
300  ELSE
301  lb = nb-n+l-i+1
302  END IF
303  CALL ctprfb( 'R', 'N', 'F', 'R', m, nb, ib, lb,
304  $ v( i, 1 ), ldv, t( 1, i ), ldt,
305  $ a( 1, i ), lda, b, ldb, work, m )
306  END DO
307 *
308  ELSE IF( left .AND. tran ) THEN
309 *
310  kf = ((k-1)/mb)*mb+1
311  DO i = kf, 1, -mb
312  ib = min( mb, k-i+1 )
313  nb = min( m-l+i+ib-1, m )
314  IF( i.GE.l ) THEN
315  lb = 0
316  ELSE
317  lb = 0
318  END IF
319  CALL ctprfb( 'L', 'N', 'F', 'R', nb, n, ib, lb,
320  $ v( i, 1 ), ldv, t( 1, i ), ldt,
321  $ a( i, 1 ), lda, b, ldb, work, ib )
322  END DO
323 *
324  ELSE IF( right .AND. notran ) THEN
325 *
326  kf = ((k-1)/mb)*mb+1
327  DO i = kf, 1, -mb
328  ib = min( mb, k-i+1 )
329  nb = min( n-l+i+ib-1, n )
330  IF( i.GE.l ) THEN
331  lb = 0
332  ELSE
333  lb = nb-n+l-i+1
334  END IF
335  CALL ctprfb( 'R', 'C', 'F', 'R', m, nb, ib, lb,
336  $ v( i, 1 ), ldv, t( 1, i ), ldt,
337  $ a( 1, i ), lda, b, ldb, work, m )
338  END DO
339 *
340  END IF
341 *
342  RETURN
343 *
344 * End of CTPMLQT
345 *
346  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ctprfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK)
CTPRFB applies a real or complex "triangular-pentagonal" blocked reflector to a real or complex matri...
Definition: ctprfb.f:251
subroutine ctpmlqt(SIDE, TRANS, M, N, K, L, MB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO)
CTPMLQT
Definition: ctpmlqt.f:199