LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
zunmtr.f
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1 *> \brief \b ZUNMTR
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZUNMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC,
22 * WORK, LWORK, INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER SIDE, TRANS, UPLO
26 * INTEGER INFO, LDA, LDC, LWORK, M, N
27 * ..
28 * .. Array Arguments ..
29 * COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> ZUNMTR overwrites the general complex M-by-N matrix C with
39 *>
40 *> SIDE = 'L' SIDE = 'R'
41 *> TRANS = 'N': Q * C C * Q
42 *> TRANS = 'C': Q**H * C C * Q**H
43 *>
44 *> where Q is a complex unitary matrix of order nq, with nq = m if
45 *> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
46 *> nq-1 elementary reflectors, as returned by ZHETRD:
47 *>
48 *> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
49 *>
50 *> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
51 *> \endverbatim
52 *
53 * Arguments:
54 * ==========
55 *
56 *> \param[in] SIDE
57 *> \verbatim
58 *> SIDE is CHARACTER*1
59 *> = 'L': apply Q or Q**H from the Left;
60 *> = 'R': apply Q or Q**H from the Right.
61 *> \endverbatim
62 *>
63 *> \param[in] UPLO
64 *> \verbatim
65 *> UPLO is CHARACTER*1
66 *> = 'U': Upper triangle of A contains elementary reflectors
67 *> from ZHETRD;
68 *> = 'L': Lower triangle of A contains elementary reflectors
69 *> from ZHETRD.
70 *> \endverbatim
71 *>
72 *> \param[in] TRANS
73 *> \verbatim
74 *> TRANS is CHARACTER*1
75 *> = 'N': No transpose, apply Q;
76 *> = 'C': Conjugate transpose, apply Q**H.
77 *> \endverbatim
78 *>
79 *> \param[in] M
80 *> \verbatim
81 *> M is INTEGER
82 *> The number of rows of the matrix C. M >= 0.
83 *> \endverbatim
84 *>
85 *> \param[in] N
86 *> \verbatim
87 *> N is INTEGER
88 *> The number of columns of the matrix C. N >= 0.
89 *> \endverbatim
90 *>
91 *> \param[in] A
92 *> \verbatim
93 *> A is COMPLEX*16 array, dimension
94 *> (LDA,M) if SIDE = 'L'
95 *> (LDA,N) if SIDE = 'R'
96 *> The vectors which define the elementary reflectors, as
97 *> returned by ZHETRD.
98 *> \endverbatim
99 *>
100 *> \param[in] LDA
101 *> \verbatim
102 *> LDA is INTEGER
103 *> The leading dimension of the array A.
104 *> LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
105 *> \endverbatim
106 *>
107 *> \param[in] TAU
108 *> \verbatim
109 *> TAU is COMPLEX*16 array, dimension
110 *> (M-1) if SIDE = 'L'
111 *> (N-1) if SIDE = 'R'
112 *> TAU(i) must contain the scalar factor of the elementary
113 *> reflector H(i), as returned by ZHETRD.
114 *> \endverbatim
115 *>
116 *> \param[in,out] C
117 *> \verbatim
118 *> C is COMPLEX*16 array, dimension (LDC,N)
119 *> On entry, the M-by-N matrix C.
120 *> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
121 *> \endverbatim
122 *>
123 *> \param[in] LDC
124 *> \verbatim
125 *> LDC is INTEGER
126 *> The leading dimension of the array C. LDC >= max(1,M).
127 *> \endverbatim
128 *>
129 *> \param[out] WORK
130 *> \verbatim
131 *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
132 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
133 *> \endverbatim
134 *>
135 *> \param[in] LWORK
136 *> \verbatim
137 *> LWORK is INTEGER
138 *> The dimension of the array WORK.
139 *> If SIDE = 'L', LWORK >= max(1,N);
140 *> if SIDE = 'R', LWORK >= max(1,M).
141 *> For optimum performance LWORK >= N*NB if SIDE = 'L', and
142 *> LWORK >=M*NB if SIDE = 'R', where NB is the optimal
143 *> blocksize.
144 *>
145 *> If LWORK = -1, then a workspace query is assumed; the routine
146 *> only calculates the optimal size of the WORK array, returns
147 *> this value as the first entry of the WORK array, and no error
148 *> message related to LWORK is issued by XERBLA.
149 *> \endverbatim
150 *>
151 *> \param[out] INFO
152 *> \verbatim
153 *> INFO is INTEGER
154 *> = 0: successful exit
155 *> < 0: if INFO = -i, the i-th argument had an illegal value
156 *> \endverbatim
157 *
158 * Authors:
159 * ========
160 *
161 *> \author Univ. of Tennessee
162 *> \author Univ. of California Berkeley
163 *> \author Univ. of Colorado Denver
164 *> \author NAG Ltd.
165 *
166 *> \ingroup complex16OTHERcomputational
167 *
168 * =====================================================================
169  SUBROUTINE zunmtr( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC,
170  $ WORK, LWORK, INFO )
171 *
172 * -- LAPACK computational routine --
173 * -- LAPACK is a software package provided by Univ. of Tennessee, --
174 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
175 *
176 * .. Scalar Arguments ..
177  CHARACTER SIDE, TRANS, UPLO
178  INTEGER INFO, LDA, LDC, LWORK, M, N
179 * ..
180 * .. Array Arguments ..
181  COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
182 * ..
183 *
184 * =====================================================================
185 *
186 * .. Local Scalars ..
187  LOGICAL LEFT, LQUERY, UPPER
188  INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
189 * ..
190 * .. External Functions ..
191  LOGICAL LSAME
192  INTEGER ILAENV
193  EXTERNAL lsame, ilaenv
194 * ..
195 * .. External Subroutines ..
196  EXTERNAL xerbla, zunmql, zunmqr
197 * ..
198 * .. Intrinsic Functions ..
199  INTRINSIC max
200 * ..
201 * .. Executable Statements ..
202 *
203 * Test the input arguments
204 *
205  info = 0
206  left = lsame( side, 'L' )
207  upper = lsame( uplo, 'U' )
208  lquery = ( lwork.EQ.-1 )
209 *
210 * NQ is the order of Q and NW is the minimum dimension of WORK
211 *
212  IF( left ) THEN
213  nq = m
214  nw = max( 1, n )
215  ELSE
216  nq = n
217  nw = max( 1, m )
218  END IF
219  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
220  info = -1
221  ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
222  info = -2
223  ELSE IF( .NOT.lsame( trans, 'N' ) .AND. .NOT.lsame( trans, 'C' ) )
224  $ THEN
225  info = -3
226  ELSE IF( m.LT.0 ) THEN
227  info = -4
228  ELSE IF( n.LT.0 ) THEN
229  info = -5
230  ELSE IF( lda.LT.max( 1, nq ) ) THEN
231  info = -7
232  ELSE IF( ldc.LT.max( 1, m ) ) THEN
233  info = -10
234  ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
235  info = -12
236  END IF
237 *
238  IF( info.EQ.0 ) THEN
239  IF( upper ) THEN
240  IF( left ) THEN
241  nb = ilaenv( 1, 'ZUNMQL', side // trans, m-1, n, m-1,
242  $ -1 )
243  ELSE
244  nb = ilaenv( 1, 'ZUNMQL', side // trans, m, n-1, n-1,
245  $ -1 )
246  END IF
247  ELSE
248  IF( left ) THEN
249  nb = ilaenv( 1, 'ZUNMQR', side // trans, m-1, n, m-1,
250  $ -1 )
251  ELSE
252  nb = ilaenv( 1, 'ZUNMQR', side // trans, m, n-1, n-1,
253  $ -1 )
254  END IF
255  END IF
256  lwkopt = nw*nb
257  work( 1 ) = lwkopt
258  END IF
259 *
260  IF( info.NE.0 ) THEN
261  CALL xerbla( 'ZUNMTR', -info )
262  RETURN
263  ELSE IF( lquery ) THEN
264  RETURN
265  END IF
266 *
267 * Quick return if possible
268 *
269  IF( m.EQ.0 .OR. n.EQ.0 .OR. nq.EQ.1 ) THEN
270  work( 1 ) = 1
271  RETURN
272  END IF
273 *
274  IF( left ) THEN
275  mi = m - 1
276  ni = n
277  ELSE
278  mi = m
279  ni = n - 1
280  END IF
281 *
282  IF( upper ) THEN
283 *
284 * Q was determined by a call to ZHETRD with UPLO = 'U'
285 *
286  CALL zunmql( side, trans, mi, ni, nq-1, a( 1, 2 ), lda, tau, c,
287  $ ldc, work, lwork, iinfo )
288  ELSE
289 *
290 * Q was determined by a call to ZHETRD with UPLO = 'L'
291 *
292  IF( left ) THEN
293  i1 = 2
294  i2 = 1
295  ELSE
296  i1 = 1
297  i2 = 2
298  END IF
299  CALL zunmqr( side, trans, mi, ni, nq-1, a( 2, 1 ), lda, tau,
300  $ c( i1, i2 ), ldc, work, lwork, iinfo )
301  END IF
302  work( 1 ) = lwkopt
303  RETURN
304 *
305 * End of ZUNMTR
306 *
307  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zunmtr(SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMTR
Definition: zunmtr.f:171
subroutine zunmql(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMQL
Definition: zunmql.f:167
subroutine zunmqr(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMQR
Definition: zunmqr.f:167