LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
clatsqr.f
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1 *
2 * Definition:
3 * ===========
4 *
5 * SUBROUTINE CLATSQR( M, N, MB, NB, A, LDA, T, LDT, WORK,
6 * LWORK, INFO)
7 *
8 * .. Scalar Arguments ..
9 * INTEGER INFO, LDA, M, N, MB, NB, LDT, LWORK
10 * ..
11 * .. Array Arguments ..
12 * COMPLEX A( LDA, * ), T( LDT, * ), WORK( * )
13 * ..
14 *
15 *
16 *> \par Purpose:
17 * =============
18 *>
19 *> \verbatim
20 *>
21 *> SLATSQR computes a blocked Tall-Skinny QR factorization of
22 *> an M-by-N matrix A, where M >= N:
23 *> A = Q * R .
24 *> \endverbatim
25 *
26 * Arguments:
27 * ==========
28 *
29 *> \param[in] M
30 *> \verbatim
31 *> M is INTEGER
32 *> The number of rows of the matrix A. M >= 0.
33 *> \endverbatim
34 *>
35 *> \param[in] N
36 *> \verbatim
37 *> N is INTEGER
38 *> The number of columns of the matrix A. M >= N >= 0.
39 *> \endverbatim
40 *>
41 *> \param[in] MB
42 *> \verbatim
43 *> MB is INTEGER
44 *> The row block size to be used in the blocked QR.
45 *> MB > N.
46 *> \endverbatim
47 *>
48 *> \param[in] NB
49 *> \verbatim
50 *> NB is INTEGER
51 *> The column block size to be used in the blocked QR.
52 *> N >= NB >= 1.
53 *> \endverbatim
54 *>
55 *> \param[in,out] A
56 *> \verbatim
57 *> A is COMPLEX array, dimension (LDA,N)
58 *> On entry, the M-by-N matrix A.
59 *> On exit, the elements on and above the diagonal
60 *> of the array contain the N-by-N upper triangular matrix R;
61 *> the elements below the diagonal represent Q by the columns
62 *> of blocked V (see Further Details).
63 *> \endverbatim
64 *>
65 *> \param[in] LDA
66 *> \verbatim
67 *> LDA is INTEGER
68 *> The leading dimension of the array A. LDA >= max(1,M).
69 *> \endverbatim
70 *>
71 *> \param[out] T
72 *> \verbatim
73 *> T is COMPLEX array,
74 *> dimension (LDT, N * Number_of_row_blocks)
75 *> where Number_of_row_blocks = CEIL((M-N)/(MB-N))
76 *> The blocked upper triangular block reflectors stored in compact form
77 *> as a sequence of upper triangular blocks.
78 *> See Further Details below.
79 *> \endverbatim
80 *>
81 *> \param[in] LDT
82 *> \verbatim
83 *> LDT is INTEGER
84 *> The leading dimension of the array T. LDT >= NB.
85 *> \endverbatim
86 *>
87 *> \param[out] WORK
88 *> \verbatim
89 *> (workspace) COMPLEX array, dimension (MAX(1,LWORK))
90 *> \endverbatim
91 *>
92 *> \param[in] LWORK
93 *> \verbatim
94 *> The dimension of the array WORK. LWORK >= NB*N.
95 *> If LWORK = -1, then a workspace query is assumed; the routine
96 *> only calculates the optimal size of the WORK array, returns
97 *> this value as the first entry of the WORK array, and no error
98 *> message related to LWORK is issued by XERBLA.
99 *> \endverbatim
100 *>
101 *> \param[out] INFO
102 *> \verbatim
103 *> INFO is INTEGER
104 *> = 0: successful exit
105 *> < 0: if INFO = -i, the i-th argument had an illegal value
106 *> \endverbatim
107 *
108 * Authors:
109 * ========
110 *
111 *> \author Univ. of Tennessee
112 *> \author Univ. of California Berkeley
113 *> \author Univ. of Colorado Denver
114 *> \author NAG Ltd.
115 *
116 *> \par Further Details:
117 * =====================
118 *>
119 *> \verbatim
120 *> Tall-Skinny QR (TSQR) performs QR by a sequence of orthogonal transformations,
121 *> representing Q as a product of other orthogonal matrices
122 *> Q = Q(1) * Q(2) * . . . * Q(k)
123 *> where each Q(i) zeros out subdiagonal entries of a block of MB rows of A:
124 *> Q(1) zeros out the subdiagonal entries of rows 1:MB of A
125 *> Q(2) zeros out the bottom MB-N rows of rows [1:N,MB+1:2*MB-N] of A
126 *> Q(3) zeros out the bottom MB-N rows of rows [1:N,2*MB-N+1:3*MB-2*N] of A
127 *> . . .
128 *>
129 *> Q(1) is computed by GEQRT, which represents Q(1) by Householder vectors
130 *> stored under the diagonal of rows 1:MB of A, and by upper triangular
131 *> block reflectors, stored in array T(1:LDT,1:N).
133 *>
134 *> Q(i) for i>1 is computed by TPQRT, which represents Q(i) by Householder vectors
135 *> stored in rows [(i-1)*(MB-N)+N+1:i*(MB-N)+N] of A, and by upper triangular
136 *> block reflectors, stored in array T(1:LDT,(i-1)*N+1:i*N).
137 *> The last Q(k) may use fewer rows.
139 *>
140 *> For more details of the overall algorithm, see the description of
141 *> Sequential TSQR in Section 2.2 of [1].
142 *>
143 *> [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,”
144 *> J. Demmel, L. Grigori, M. Hoemmen, J. Langou,
145 *> SIAM J. Sci. Comput, vol. 34, no. 1, 2012
146 *> \endverbatim
147 *>
148 * =====================================================================
149  SUBROUTINE clatsqr( M, N, MB, NB, A, LDA, T, LDT, WORK,
150  \$ LWORK, INFO)
151 *
152 * -- LAPACK computational routine (version 3.7.0) --
153 * -- LAPACK is a software package provided by Univ. of Tennessee, --
154 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd. --
155 * December 2016
156 *
157 * .. Scalar Arguments ..
158  INTEGER INFO, LDA, M, N, MB, NB, LDT, LWORK
159 * ..
160 * .. Array Arguments ..
161  COMPLEX A( lda, * ), WORK( * ), T(ldt, *)
162 * ..
163 *
164 * =====================================================================
165 *
166 * ..
167 * .. Local Scalars ..
168  LOGICAL LQUERY
169  INTEGER I, II, KK, CTR
170 * ..
171 * .. EXTERNAL FUNCTIONS ..
172  LOGICAL LSAME
173  EXTERNAL lsame
174 * .. EXTERNAL SUBROUTINES ..
175  EXTERNAL cgeqrt, ctpqrt, xerbla
176 * .. INTRINSIC FUNCTIONS ..
177  INTRINSIC max, min, mod
178 * ..
179 * .. EXECUTABLE STATEMENTS ..
180 *
181 * TEST THE INPUT ARGUMENTS
182 *
183  info = 0
184 *
185  lquery = ( lwork.EQ.-1 )
186 *
187  IF( m.LT.0 ) THEN
188  info = -1
189  ELSE IF( n.LT.0 .OR. m.LT.n ) THEN
190  info = -2
191  ELSE IF( mb.LE.n ) THEN
192  info = -3
193  ELSE IF( nb.LT.1 .OR. ( nb.GT.n .AND. n.GT.0 )) THEN
194  info = -4
195  ELSE IF( lda.LT.max( 1, m ) ) THEN
196  info = -5
197  ELSE IF( ldt.LT.nb ) THEN
198  info = -8
199  ELSE IF( lwork.LT.(n*nb) .AND. (.NOT.lquery) ) THEN
200  info = -10
201  END IF
202  IF( info.EQ.0) THEN
203  work(1) = nb*n
204  END IF
205  IF( info.NE.0 ) THEN
206  CALL xerbla( 'CLATSQR', -info )
207  RETURN
208  ELSE IF (lquery) THEN
209  RETURN
210  END IF
211 *
212 * Quick return if possible
213 *
214  IF( min(m,n).EQ.0 ) THEN
215  RETURN
216  END IF
217 *
218 * The QR Decomposition
219 *
220  IF ((mb.LE.n).OR.(mb.GE.m)) THEN
221  CALL cgeqrt( m, n, nb, a, lda, t, ldt, work, info)
222  RETURN
223  END IF
224  kk = mod((m-n),(mb-n))
225  ii=m-kk+1
226 *
227 * Compute the QR factorization of the first block A(1:MB,1:N)
228 *
229  CALL cgeqrt( mb, n, nb, a(1,1), lda, t, ldt, work, info )
230  ctr = 1
231 *
232  DO i = mb+1, ii-mb+n , (mb-n)
233 *
234 * Compute the QR factorization of the current block A(I:I+MB-N,1:N)
235 *
236  CALL ctpqrt( mb-n, n, 0, nb, a(1,1), lda, a( i, 1 ), lda,
237  \$ t(1,ctr * n + 1),
238  \$ ldt, work, info )
239  ctr = ctr + 1
240  END DO
241 *
242 * Compute the QR factorization of the last block A(II:M,1:N)
243 *
244  IF (ii.LE.m) THEN
245  CALL ctpqrt( kk, n, 0, nb, a(1,1), lda, a( ii, 1 ), lda,
246  \$ t(1, ctr * n + 1), ldt,
247  \$ work, info )
248  END IF
249 *
250  work( 1 ) = n*nb
251  RETURN
252 *
253 * End of CLATSQR
254 *
255  END
subroutine ctpqrt(M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO)
CTPQRT
Definition: ctpqrt.f:191
subroutine clatsqr(M, N, MB, NB, A, LDA, T, LDT, WORK, LWORK, INFO)
Definition: clatsqr.f:151
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine cgeqrt(M, N, NB, A, LDA, T, LDT, WORK, INFO)
CGEQRT
Definition: cgeqrt.f:143