LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
cgeqrfp.f
Go to the documentation of this file.
1 *> \brief \b CGEQRFP
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download CGEQRFP + dependencies
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgeqrfp.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgeqrfp.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgeqrfp.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CGEQRFP( M, N, A, LDA, TAU, WORK, LWORK, INFO )
22 *
23 * .. Scalar Arguments ..
24 * INTEGER INFO, LDA, LWORK, M, N
25 * ..
26 * .. Array Arguments ..
27 * COMPLEX A( LDA, * ), TAU( * ), WORK( * )
28 * ..
29 *
30 *
31 *> \par Purpose:
32 * =============
33 *>
34 *> \verbatim
35 *>
36 *> CGEQR2P computes a QR factorization of a complex M-by-N matrix A:
37 *>
38 *> A = Q * ( R ),
39 *> ( 0 )
40 *>
41 *> where:
42 *>
43 *> Q is a M-by-M orthogonal matrix;
44 *> R is an upper-triangular N-by-N matrix with nonnegative diagonal
45 *> entries;
46 *> 0 is a (M-N)-by-N zero matrix, if M > N.
47 *>
48 *> \endverbatim
49 *
50 * Arguments:
51 * ==========
52 *
53 *> \param[in] M
54 *> \verbatim
55 *> M is INTEGER
56 *> The number of rows of the matrix A. M >= 0.
57 *> \endverbatim
58 *>
59 *> \param[in] N
60 *> \verbatim
61 *> N is INTEGER
62 *> The number of columns of the matrix A. N >= 0.
63 *> \endverbatim
64 *>
65 *> \param[in,out] A
66 *> \verbatim
67 *> A is COMPLEX array, dimension (LDA,N)
68 *> On entry, the M-by-N matrix A.
69 *> On exit, the elements on and above the diagonal of the array
70 *> contain the min(M,N)-by-N upper trapezoidal matrix R (R is
71 *> upper triangular if m >= n). The diagonal entries of R
72 *> are real and nonnegative; the elements below the diagonal,
73 *> with the array TAU, represent the unitary matrix Q as a
74 *> product of min(m,n) elementary reflectors (see Further
75 *> Details).
76 *> \endverbatim
77 *>
78 *> \param[in] LDA
79 *> \verbatim
80 *> LDA is INTEGER
81 *> The leading dimension of the array A. LDA >= max(1,M).
82 *> \endverbatim
83 *>
84 *> \param[out] TAU
85 *> \verbatim
86 *> TAU is COMPLEX array, dimension (min(M,N))
87 *> The scalar factors of the elementary reflectors (see Further
88 *> Details).
89 *> \endverbatim
90 *>
91 *> \param[out] WORK
92 *> \verbatim
93 *> WORK is COMPLEX array, dimension (MAX(1,LWORK))
94 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
95 *> \endverbatim
96 *>
97 *> \param[in] LWORK
98 *> \verbatim
99 *> LWORK is INTEGER
100 *> The dimension of the array WORK. LWORK >= max(1,N).
101 *> For optimum performance LWORK >= N*NB, where NB is
102 *> the optimal blocksize.
103 *>
104 *> If LWORK = -1, then a workspace query is assumed; the routine
105 *> only calculates the optimal size of the WORK array, returns
106 *> this value as the first entry of the WORK array, and no error
107 *> message related to LWORK is issued by XERBLA.
108 *> \endverbatim
109 *>
110 *> \param[out] INFO
111 *> \verbatim
112 *> INFO is INTEGER
113 *> = 0: successful exit
114 *> < 0: if INFO = -i, the i-th argument had an illegal value
115 *> \endverbatim
116 *
117 * Authors:
118 * ========
119 *
120 *> \author Univ. of Tennessee
121 *> \author Univ. of California Berkeley
122 *> \author Univ. of Colorado Denver
123 *> \author NAG Ltd.
124 *
125 *> \ingroup complexGEcomputational
126 *
127 *> \par Further Details:
128 * =====================
129 *>
130 *> \verbatim
131 *>
132 *> The matrix Q is represented as a product of elementary reflectors
133 *>
134 *> Q = H(1) H(2) . . . H(k), where k = min(m,n).
135 *>
136 *> Each H(i) has the form
137 *>
138 *> H(i) = I - tau * v * v**H
139 *>
140 *> where tau is a complex scalar, and v is a complex vector with
141 *> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
142 *> and tau in TAU(i).
143 *>
144 *> See Lapack Working Note 203 for details
145 *> \endverbatim
146 *>
147 * =====================================================================
148  SUBROUTINE cgeqrfp( M, N, A, LDA, TAU, WORK, LWORK, INFO )
149 *
150 * -- LAPACK computational routine --
151 * -- LAPACK is a software package provided by Univ. of Tennessee, --
152 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
153 *
154 * .. Scalar Arguments ..
155  INTEGER INFO, LDA, LWORK, M, N
156 * ..
157 * .. Array Arguments ..
158  COMPLEX A( LDA, * ), TAU( * ), WORK( * )
159 * ..
160 *
161 * =====================================================================
162 *
163 * .. Local Scalars ..
164  LOGICAL LQUERY
165  INTEGER I, IB, IINFO, IWS, K, LDWORK, LWKOPT, NB,
166  $ NBMIN, NX
167 * ..
168 * .. External Subroutines ..
169  EXTERNAL cgeqr2p, clarfb, clarft, xerbla
170 * ..
171 * .. Intrinsic Functions ..
172  INTRINSIC max, min
173 * ..
174 * .. External Functions ..
175  INTEGER ILAENV
176  EXTERNAL ilaenv
177 * ..
178 * .. Executable Statements ..
179 *
180 * Test the input arguments
181 *
182  info = 0
183  nb = ilaenv( 1, 'CGEQRF', ' ', m, n, -1, -1 )
184  lwkopt = n*nb
185  work( 1 ) = lwkopt
186  lquery = ( lwork.EQ.-1 )
187  IF( m.LT.0 ) THEN
188  info = -1
189  ELSE IF( n.LT.0 ) THEN
190  info = -2
191  ELSE IF( lda.LT.max( 1, m ) ) THEN
192  info = -4
193  ELSE IF( lwork.LT.max( 1, n ) .AND. .NOT.lquery ) THEN
194  info = -7
195  END IF
196  IF( info.NE.0 ) THEN
197  CALL xerbla( 'CGEQRFP', -info )
198  RETURN
199  ELSE IF( lquery ) THEN
200  RETURN
201  END IF
202 *
203 * Quick return if possible
204 *
205  k = min( m, n )
206  IF( k.EQ.0 ) THEN
207  work( 1 ) = 1
208  RETURN
209  END IF
210 *
211  nbmin = 2
212  nx = 0
213  iws = n
214  IF( nb.GT.1 .AND. nb.LT.k ) THEN
215 *
216 * Determine when to cross over from blocked to unblocked code.
217 *
218  nx = max( 0, ilaenv( 3, 'CGEQRF', ' ', m, n, -1, -1 ) )
219  IF( nx.LT.k ) THEN
220 *
221 * Determine if workspace is large enough for blocked code.
222 *
223  ldwork = n
224  iws = ldwork*nb
225  IF( lwork.LT.iws ) THEN
226 *
227 * Not enough workspace to use optimal NB: reduce NB and
228 * determine the minimum value of NB.
229 *
230  nb = lwork / ldwork
231  nbmin = max( 2, ilaenv( 2, 'CGEQRF', ' ', m, n, -1,
232  $ -1 ) )
233  END IF
234  END IF
235  END IF
236 *
237  IF( nb.GE.nbmin .AND. nb.LT.k .AND. nx.LT.k ) THEN
238 *
239 * Use blocked code initially
240 *
241  DO 10 i = 1, k - nx, nb
242  ib = min( k-i+1, nb )
243 *
244 * Compute the QR factorization of the current block
245 * A(i:m,i:i+ib-1)
246 *
247  CALL cgeqr2p( m-i+1, ib, a( i, i ), lda, tau( i ), work,
248  $ iinfo )
249  IF( i+ib.LE.n ) THEN
250 *
251 * Form the triangular factor of the block reflector
252 * H = H(i) H(i+1) . . . H(i+ib-1)
253 *
254  CALL clarft( 'Forward', 'Columnwise', m-i+1, ib,
255  $ a( i, i ), lda, tau( i ), work, ldwork )
256 *
257 * Apply H**H to A(i:m,i+ib:n) from the left
258 *
259  CALL clarfb( 'Left', 'Conjugate transpose', 'Forward',
260  $ 'Columnwise', m-i+1, n-i-ib+1, ib,
261  $ a( i, i ), lda, work, ldwork, a( i, i+ib ),
262  $ lda, work( ib+1 ), ldwork )
263  END IF
264  10 CONTINUE
265  ELSE
266  i = 1
267  END IF
268 *
269 * Use unblocked code to factor the last or only block.
270 *
271  IF( i.LE.k )
272  $ CALL cgeqr2p( m-i+1, n-i+1, a( i, i ), lda, tau( i ), work,
273  $ iinfo )
274 *
275  work( 1 ) = iws
276  RETURN
277 *
278 * End of CGEQRFP
279 *
280  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine cgeqr2p(M, N, A, LDA, TAU, WORK, INFO)
CGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elem...
Definition: cgeqr2p.f:134
subroutine cgeqrfp(M, N, A, LDA, TAU, WORK, LWORK, INFO)
CGEQRFP
Definition: cgeqrfp.f:149
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
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:163