Annotation of rpl/lapack/lapack/dlatsqr.f, revision 1.3
1.1 bertrand 1: *
2: * Definition:
3: * ===========
4: *
5: * SUBROUTINE DLATSQR( 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: * DOUBLE PRECISION A( LDA, * ), T( LDT, * ), WORK( * )
13: * ..
14: *
15: *
16: *> \par Purpose:
17: * =============
18: *>
19: *> \verbatim
20: *>
21: *> DLATSQR 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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) DOUBLE PRECISION 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).
132: *> For more information see Further Details in GEQRT.
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.
138: *> For more information see Further Details in TPQRT.
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 DLATSQR( 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: DOUBLE PRECISION 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 DGEQRT, DTPQRT, 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( 'DLATSQR', -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 DGEQRT( M, N, NB, A, LDA, T, LDT, WORK, INFO)
222: RETURN
223: END IF
224: *
225: KK = MOD((M-N),(MB-N))
226: II=M-KK+1
227: *
228: * Compute the QR factorization of the first block A(1:MB,1:N)
229: *
230: CALL DGEQRT( MB, N, NB, A(1,1), LDA, T, LDT, WORK, INFO )
231: *
232: CTR = 1
233: DO I = MB+1, II-MB+N , (MB-N)
234: *
235: * Compute the QR factorization of the current block A(I:I+MB-N,1:N)
236: *
237: CALL DTPQRT( MB-N, N, 0, NB, A(1,1), LDA, A( I, 1 ), LDA,
238: $ T(1, CTR * N + 1),
239: $ LDT, WORK, INFO )
240: CTR = CTR + 1
241: END DO
242: *
243: * Compute the QR factorization of the last block A(II:M,1:N)
244: *
245: IF (II.LE.M) THEN
246: CALL DTPQRT( KK, N, 0, NB, A(1,1), LDA, A( II, 1 ), LDA,
247: $ T(1, CTR * N + 1), LDT,
248: $ WORK, INFO )
249: END IF
250: *
251: WORK( 1 ) = N*NB
252: RETURN
253: *
254: * End of DLATSQR
255: *
256: END
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