LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
ztpmlqt.f
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1 *> \brief \b ZTPMLQT
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download ZTPMLQT + dependencies
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11 *> [TGZ]</a>
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13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztpmlqt.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZTPMLQT( SIDE, TRANS, M, N, K, L, MB, V, LDV, T, LDT,
22 * A, LDA, B, LDB, WORK, INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER SIDE, TRANS
26 * INTEGER INFO, K, LDV, LDA, LDB, M, N, L, MB, LDT
27 * ..
28 * .. Array Arguments ..
29 * COMPLEX*16 V( LDV, * ), A( LDA, * ), B( LDB, * ),
30 * $ T( LDT, * ), WORK( * )
31 * ..
32 *
33 *
34 *> \par Purpose:
35 * =============
36 *>
37 *> \verbatim
38 *>
39 *> ZTPMLQT applies a complex unitary matrix Q obtained from a
40 *> "triangular-pentagonal" complex block reflector H to a general
41 *> complex matrix C, which consists of two blocks A and B.
42 *> \endverbatim
43 *
44 * Arguments:
45 * ==========
46 *
47 *> \param[in] SIDE
48 *> \verbatim
49 *> SIDE is CHARACTER*1
50 *> = 'L': apply Q or Q**H from the Left;
51 *> = 'R': apply Q or Q**H from the Right.
52 *> \endverbatim
53 *>
54 *> \param[in] TRANS
55 *> \verbatim
56 *> TRANS is CHARACTER*1
57 *> = 'N': No transpose, apply Q;
58 *> = 'C': Conjugate transpose, apply Q**H.
59 *> \endverbatim
60 *>
61 *> \param[in] M
62 *> \verbatim
63 *> M is INTEGER
64 *> The number of rows of the matrix B. M >= 0.
65 *> \endverbatim
66 *>
67 *> \param[in] N
68 *> \verbatim
69 *> N is INTEGER
70 *> The number of columns of the matrix B. N >= 0.
71 *> \endverbatim
72 *>
73 *> \param[in] K
74 *> \verbatim
75 *> K is INTEGER
76 *> The number of elementary reflectors whose product defines
77 *> the matrix Q.
78 *> \endverbatim
79 *>
80 *> \param[in] L
81 *> \verbatim
82 *> L is INTEGER
83 *> The order of the trapezoidal part of V.
84 *> K >= L >= 0. See Further Details.
85 *> \endverbatim
86 *>
87 *> \param[in] MB
88 *> \verbatim
89 *> MB is INTEGER
90 *> The block size used for the storage of T. K >= MB >= 1.
91 *> This must be the same value of MB used to generate T
92 *> in ZTPLQT.
93 *> \endverbatim
94 *>
95 *> \param[in] V
96 *> \verbatim
97 *> V is COMPLEX*16 array, dimension (LDV,K)
98 *> The i-th row must contain the vector which defines the
99 *> elementary reflector H(i), for i = 1,2,...,k, as returned by
100 *> ZTPLQT in B. See Further Details.
101 *> \endverbatim
102 *>
103 *> \param[in] LDV
104 *> \verbatim
105 *> LDV is INTEGER
106 *> The leading dimension of the array V. LDV >= K.
107 *> \endverbatim
108 *>
109 *> \param[in] T
110 *> \verbatim
111 *> T is COMPLEX*16 array, dimension (LDT,K)
112 *> The upper triangular factors of the block reflectors
113 *> as returned by ZTPLQT, stored as a MB-by-K matrix.
114 *> \endverbatim
115 *>
116 *> \param[in] LDT
117 *> \verbatim
118 *> LDT is INTEGER
119 *> The leading dimension of the array T. LDT >= MB.
120 *> \endverbatim
121 *>
122 *> \param[in,out] A
123 *> \verbatim
124 *> A is COMPLEX*16 array, dimension
125 *> (LDA,N) if SIDE = 'L' or
126 *> (LDA,K) if SIDE = 'R'
127 *> On entry, the K-by-N or M-by-K matrix A.
128 *> On exit, A is overwritten by the corresponding block of
129 *> Q*C or Q**H*C or C*Q or C*Q**H. See Further Details.
130 *> \endverbatim
131 *>
132 *> \param[in] LDA
133 *> \verbatim
134 *> LDA is INTEGER
135 *> The leading dimension of the array A.
136 *> If SIDE = 'L', LDA >= max(1,K);
137 *> If SIDE = 'R', LDA >= max(1,M).
138 *> \endverbatim
139 *>
140 *> \param[in,out] B
141 *> \verbatim
142 *> B is COMPLEX*16 array, dimension (LDB,N)
143 *> On entry, the M-by-N matrix B.
144 *> On exit, B is overwritten by the corresponding block of
145 *> Q*C or Q**H*C or C*Q or C*Q**H. See Further Details.
146 *> \endverbatim
147 *>
148 *> \param[in] LDB
149 *> \verbatim
150 *> LDB is INTEGER
151 *> The leading dimension of the array B.
152 *> LDB >= max(1,M).
153 *> \endverbatim
154 *>
155 *> \param[out] WORK
156 *> \verbatim
157 *> WORK is COMPLEX*16 array. The dimension of WORK is
158 *> N*MB if SIDE = 'L', or M*MB if SIDE = 'R'.
159 *> \endverbatim
160 *>
161 *> \param[out] INFO
162 *> \verbatim
163 *> INFO is INTEGER
164 *> = 0: successful exit
165 *> < 0: if INFO = -i, the i-th argument had an illegal value
166 *> \endverbatim
167 *
168 * Authors:
169 * ========
170 *
171 *> \author Univ. of Tennessee
172 *> \author Univ. of California Berkeley
173 *> \author Univ. of Colorado Denver
174 *> \author NAG Ltd.
175 *
176 *> \ingroup doubleOTHERcomputational
177 *
178 *> \par Further Details:
179 * =====================
180 *>
181 *> \verbatim
182 *>
183 *> The columns of the pentagonal matrix V contain the elementary reflectors
184 *> H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a
185 *> trapezoidal block V2:
186 *>
187 *> V = [V1] [V2].
188 *>
189 *>
190 *> The size of the trapezoidal block V2 is determined by the parameter L,
191 *> where 0 <= L <= K; V2 is lower trapezoidal, consisting of the first L
192 *> rows of a K-by-K upper triangular matrix. If L=K, V2 is lower triangular;
193 *> if L=0, there is no trapezoidal block, hence V = V1 is rectangular.
194 *>
195 *> If SIDE = 'L': C = [A] where A is K-by-N, B is M-by-N and V is K-by-M.
196 *> [B]
197 *>
198 *> If SIDE = 'R': C = [A B] where A is M-by-K, B is M-by-N and V is K-by-N.
199 *>
200 *> The complex unitary matrix Q is formed from V and T.
201 *>
202 *> If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.
203 *>
204 *> If TRANS='C' and SIDE='L', C is on exit replaced with Q**H * C.
205 *>
206 *> If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
207 *>
208 *> If TRANS='C' and SIDE='R', C is on exit replaced with C * Q**H.
209 *> \endverbatim
210 *>
211 * =====================================================================
212  SUBROUTINE ztpmlqt( SIDE, TRANS, M, N, K, L, MB, V, LDV, T, LDT,
213  $ A, LDA, B, LDB, WORK, INFO )
214 *
215 * -- LAPACK computational routine --
216 * -- LAPACK is a software package provided by Univ. of Tennessee, --
217 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
218 *
219 * .. Scalar Arguments ..
220  CHARACTER SIDE, TRANS
221  INTEGER INFO, K, LDV, LDA, LDB, M, N, L, MB, LDT
222 * ..
223 * .. Array Arguments ..
224  COMPLEX*16 V( LDV, * ), A( LDA, * ), B( LDB, * ),
225  $ t( ldt, * ), work( * )
226 * ..
227 *
228 * =====================================================================
229 *
230 * ..
231 * .. Local Scalars ..
232  LOGICAL LEFT, RIGHT, TRAN, NOTRAN
233  INTEGER I, IB, NB, LB, KF, LDAQ
234 * ..
235 * .. External Functions ..
236  LOGICAL LSAME
237  EXTERNAL lsame
238 * ..
239 * .. External Subroutines ..
240  EXTERNAL xerbla, ztprfb
241 * ..
242 * .. Intrinsic Functions ..
243  INTRINSIC max, min
244 * ..
245 * .. Executable Statements ..
246 *
247 * .. Test the input arguments ..
248 *
249  info = 0
250  left = lsame( side, 'L' )
251  right = lsame( side, 'R' )
252  tran = lsame( trans, 'C' )
253  notran = lsame( trans, 'N' )
254 *
255  IF ( left ) THEN
256  ldaq = max( 1, k )
257  ELSE IF ( right ) THEN
258  ldaq = max( 1, m )
259  END IF
260  IF( .NOT.left .AND. .NOT.right ) THEN
261  info = -1
262  ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
263  info = -2
264  ELSE IF( m.LT.0 ) THEN
265  info = -3
266  ELSE IF( n.LT.0 ) THEN
267  info = -4
268  ELSE IF( k.LT.0 ) THEN
269  info = -5
270  ELSE IF( l.LT.0 .OR. l.GT.k ) THEN
271  info = -6
272  ELSE IF( mb.LT.1 .OR. (mb.GT.k .AND. k.GT.0) ) THEN
273  info = -7
274  ELSE IF( ldv.LT.k ) THEN
275  info = -9
276  ELSE IF( ldt.LT.mb ) THEN
277  info = -11
278  ELSE IF( lda.LT.ldaq ) THEN
279  info = -13
280  ELSE IF( ldb.LT.max( 1, m ) ) THEN
281  info = -15
282  END IF
283 *
284  IF( info.NE.0 ) THEN
285  CALL xerbla( 'ZTPMLQT', -info )
286  RETURN
287  END IF
288 *
289 * .. Quick return if possible ..
290 *
291  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) RETURN
292 *
293  IF( left .AND. notran ) THEN
294 *
295  DO i = 1, k, mb
296  ib = min( mb, k-i+1 )
297  nb = min( m-l+i+ib-1, m )
298  IF( i.GE.l ) THEN
299  lb = 0
300  ELSE
301  lb = 0
302  END IF
303  CALL ztprfb( 'L', 'C', 'F', 'R', nb, n, ib, lb,
304  $ v( i, 1 ), ldv, t( 1, i ), ldt,
305  $ a( i, 1 ), lda, b, ldb, work, ib )
306  END DO
307 *
308  ELSE IF( right .AND. tran ) THEN
309 *
310  DO i = 1, k, mb
311  ib = min( mb, k-i+1 )
312  nb = min( n-l+i+ib-1, n )
313  IF( i.GE.l ) THEN
314  lb = 0
315  ELSE
316  lb = nb-n+l-i+1
317  END IF
318  CALL ztprfb( 'R', 'N', 'F', 'R', m, nb, ib, lb,
319  $ v( i, 1 ), ldv, t( 1, i ), ldt,
320  $ a( 1, i ), lda, b, ldb, work, m )
321  END DO
322 *
323  ELSE IF( left .AND. tran ) THEN
324 *
325  kf = ((k-1)/mb)*mb+1
326  DO i = kf, 1, -mb
327  ib = min( mb, k-i+1 )
328  nb = min( m-l+i+ib-1, m )
329  IF( i.GE.l ) THEN
330  lb = 0
331  ELSE
332  lb = 0
333  END IF
334  CALL ztprfb( 'L', 'N', 'F', 'R', nb, n, ib, lb,
335  $ v( i, 1 ), ldv, t( 1, i ), ldt,
336  $ a( i, 1 ), lda, b, ldb, work, ib )
337  END DO
338 *
339  ELSE IF( right .AND. notran ) THEN
340 *
341  kf = ((k-1)/mb)*mb+1
342  DO i = kf, 1, -mb
343  ib = min( mb, k-i+1 )
344  nb = min( n-l+i+ib-1, n )
345  IF( i.GE.l ) THEN
346  lb = 0
347  ELSE
348  lb = nb-n+l-i+1
349  END IF
350  CALL ztprfb( 'R', 'C', 'F', 'R', m, nb, ib, lb,
351  $ v( i, 1 ), ldv, t( 1, i ), ldt,
352  $ a( 1, i ), lda, b, ldb, work, m )
353  END DO
354 *
355  END IF
356 *
357  RETURN
358 *
359 * End of ZTPMLQT
360 *
361  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ztprfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK)
ZTPRFB applies a real or complex "triangular-pentagonal" blocked reflector to a real or complex matri...
Definition: ztprfb.f:251
subroutine ztpmlqt(SIDE, TRANS, M, N, K, L, MB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO)
ZTPMLQT
Definition: ztpmlqt.f:214