LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
zungqr.f
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1 *> \brief \b ZUNGQR
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 ZUNGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
22 *
23 * .. Scalar Arguments ..
24 * INTEGER INFO, K, LDA, LWORK, M, N
25 * ..
26 * .. Array Arguments ..
27 * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
28 * ..
29 *
30 *
31 *> \par Purpose:
32 * =============
33 *>
34 *> \verbatim
35 *>
36 *> ZUNGQR generates an M-by-N complex matrix Q with orthonormal columns,
37 *> which is defined as the first N columns of a product of K elementary
38 *> reflectors of order M
39 *>
40 *> Q = H(1) H(2) . . . H(k)
41 *>
42 *> as returned by ZGEQRF.
43 *> \endverbatim
44 *
45 * Arguments:
46 * ==========
47 *
48 *> \param[in] M
49 *> \verbatim
50 *> M is INTEGER
51 *> The number of rows of the matrix Q. M >= 0.
52 *> \endverbatim
53 *>
54 *> \param[in] N
55 *> \verbatim
56 *> N is INTEGER
57 *> The number of columns of the matrix Q. M >= N >= 0.
58 *> \endverbatim
59 *>
60 *> \param[in] K
61 *> \verbatim
62 *> K is INTEGER
63 *> The number of elementary reflectors whose product defines the
64 *> matrix Q. N >= K >= 0.
65 *> \endverbatim
66 *>
67 *> \param[in,out] A
68 *> \verbatim
69 *> A is COMPLEX*16 array, dimension (LDA,N)
70 *> On entry, the i-th column must contain the vector which
71 *> defines the elementary reflector H(i), for i = 1,2,...,k, as
72 *> returned by ZGEQRF in the first k columns of its array
73 *> argument A.
74 *> On exit, the M-by-N matrix Q.
75 *> \endverbatim
76 *>
77 *> \param[in] LDA
78 *> \verbatim
79 *> LDA is INTEGER
80 *> The first dimension of the array A. LDA >= max(1,M).
81 *> \endverbatim
82 *>
83 *> \param[in] TAU
84 *> \verbatim
85 *> TAU is COMPLEX*16 array, dimension (K)
86 *> TAU(i) must contain the scalar factor of the elementary
87 *> reflector H(i), as returned by ZGEQRF.
88 *> \endverbatim
89 *>
90 *> \param[out] WORK
91 *> \verbatim
92 *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
93 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
94 *> \endverbatim
95 *>
96 *> \param[in] LWORK
97 *> \verbatim
98 *> LWORK is INTEGER
99 *> The dimension of the array WORK. LWORK >= max(1,N).
100 *> For optimum performance LWORK >= N*NB, where NB is the
101 *> optimal blocksize.
102 *>
103 *> If LWORK = -1, then a workspace query is assumed; the routine
104 *> only calculates the optimal size of the WORK array, returns
105 *> this value as the first entry of the WORK array, and no error
106 *> message related to LWORK is issued by XERBLA.
107 *> \endverbatim
108 *>
109 *> \param[out] INFO
110 *> \verbatim
111 *> INFO is INTEGER
112 *> = 0: successful exit
113 *> < 0: if INFO = -i, the i-th argument has an illegal value
114 *> \endverbatim
115 *
116 * Authors:
117 * ========
118 *
119 *> \author Univ. of Tennessee
120 *> \author Univ. of California Berkeley
121 *> \author Univ. of Colorado Denver
122 *> \author NAG Ltd.
123 *
124 *> \ingroup complex16OTHERcomputational
125 *
126 * =====================================================================
127  SUBROUTINE zungqr( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
128 *
129 * -- LAPACK computational routine --
130 * -- LAPACK is a software package provided by Univ. of Tennessee, --
131 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132 *
133 * .. Scalar Arguments ..
134  INTEGER INFO, K, LDA, LWORK, M, N
135 * ..
136 * .. Array Arguments ..
137  COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
138 * ..
139 *
140 * =====================================================================
141 *
142 * .. Parameters ..
143  COMPLEX*16 ZERO
144  parameter( zero = ( 0.0d+0, 0.0d+0 ) )
145 * ..
146 * .. Local Scalars ..
147  LOGICAL LQUERY
148  INTEGER I, IB, IINFO, IWS, J, KI, KK, L, LDWORK,
149  $ LWKOPT, NB, NBMIN, NX
150 * ..
151 * .. External Subroutines ..
152  EXTERNAL xerbla, zlarfb, zlarft, zung2r
153 * ..
154 * .. Intrinsic Functions ..
155  INTRINSIC max, min
156 * ..
157 * .. External Functions ..
158  INTEGER ILAENV
159  EXTERNAL ilaenv
160 * ..
161 * .. Executable Statements ..
162 *
163 * Test the input arguments
164 *
165  info = 0
166  nb = ilaenv( 1, 'ZUNGQR', ' ', m, n, k, -1 )
167  lwkopt = max( 1, n )*nb
168  work( 1 ) = lwkopt
169  lquery = ( lwork.EQ.-1 )
170  IF( m.LT.0 ) THEN
171  info = -1
172  ELSE IF( n.LT.0 .OR. n.GT.m ) THEN
173  info = -2
174  ELSE IF( k.LT.0 .OR. k.GT.n ) THEN
175  info = -3
176  ELSE IF( lda.LT.max( 1, m ) ) THEN
177  info = -5
178  ELSE IF( lwork.LT.max( 1, n ) .AND. .NOT.lquery ) THEN
179  info = -8
180  END IF
181  IF( info.NE.0 ) THEN
182  CALL xerbla( 'ZUNGQR', -info )
183  RETURN
184  ELSE IF( lquery ) THEN
185  RETURN
186  END IF
187 *
188 * Quick return if possible
189 *
190  IF( n.LE.0 ) THEN
191  work( 1 ) = 1
192  RETURN
193  END IF
194 *
195  nbmin = 2
196  nx = 0
197  iws = n
198  IF( nb.GT.1 .AND. nb.LT.k ) THEN
199 *
200 * Determine when to cross over from blocked to unblocked code.
201 *
202  nx = max( 0, ilaenv( 3, 'ZUNGQR', ' ', m, n, k, -1 ) )
203  IF( nx.LT.k ) THEN
204 *
205 * Determine if workspace is large enough for blocked code.
206 *
207  ldwork = n
208  iws = ldwork*nb
209  IF( lwork.LT.iws ) THEN
210 *
211 * Not enough workspace to use optimal NB: reduce NB and
212 * determine the minimum value of NB.
213 *
214  nb = lwork / ldwork
215  nbmin = max( 2, ilaenv( 2, 'ZUNGQR', ' ', m, n, k, -1 ) )
216  END IF
217  END IF
218  END IF
219 *
220  IF( nb.GE.nbmin .AND. nb.LT.k .AND. nx.LT.k ) THEN
221 *
222 * Use blocked code after the last block.
223 * The first kk columns are handled by the block method.
224 *
225  ki = ( ( k-nx-1 ) / nb )*nb
226  kk = min( k, ki+nb )
227 *
228 * Set A(1:kk,kk+1:n) to zero.
229 *
230  DO 20 j = kk + 1, n
231  DO 10 i = 1, kk
232  a( i, j ) = zero
233  10 CONTINUE
234  20 CONTINUE
235  ELSE
236  kk = 0
237  END IF
238 *
239 * Use unblocked code for the last or only block.
240 *
241  IF( kk.LT.n )
242  $ CALL zung2r( m-kk, n-kk, k-kk, a( kk+1, kk+1 ), lda,
243  $ tau( kk+1 ), work, iinfo )
244 *
245  IF( kk.GT.0 ) THEN
246 *
247 * Use blocked code
248 *
249  DO 50 i = ki + 1, 1, -nb
250  ib = min( nb, k-i+1 )
251  IF( i+ib.LE.n ) THEN
252 *
253 * Form the triangular factor of the block reflector
254 * H = H(i) H(i+1) . . . H(i+ib-1)
255 *
256  CALL zlarft( 'Forward', 'Columnwise', m-i+1, ib,
257  $ a( i, i ), lda, tau( i ), work, ldwork )
258 *
259 * Apply H to A(i:m,i+ib:n) from the left
260 *
261  CALL zlarfb( 'Left', 'No transpose', 'Forward',
262  $ 'Columnwise', m-i+1, n-i-ib+1, ib,
263  $ a( i, i ), lda, work, ldwork, a( i, i+ib ),
264  $ lda, work( ib+1 ), ldwork )
265  END IF
266 *
267 * Apply H to rows i:m of current block
268 *
269  CALL zung2r( m-i+1, ib, ib, a( i, i ), lda, tau( i ), work,
270  $ iinfo )
271 *
272 * Set rows 1:i-1 of current block to zero
273 *
274  DO 40 j = i, i + ib - 1
275  DO 30 l = 1, i - 1
276  a( l, j ) = zero
277  30 CONTINUE
278  40 CONTINUE
279  50 CONTINUE
280  END IF
281 *
282  work( 1 ) = iws
283  RETURN
284 *
285 * End of ZUNGQR
286 *
287  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zlarfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
ZLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.
Definition: zlarfb.f:197
subroutine zlarft(DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
ZLARFT forms the triangular factor T of a block reflector H = I - vtvH
Definition: zlarft.f:163
subroutine zung2r(M, N, K, A, LDA, TAU, WORK, INFO)
ZUNG2R
Definition: zung2r.f:114
subroutine zungqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGQR
Definition: zungqr.f:128