1: *> \brief \b DLAMSWLQ
2: *
3: * Definition:
4: * ===========
5: *
6: * SUBROUTINE DLAMSWLQ( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T,
7: * $ LDT, C, LDC, WORK, LWORK, INFO )
8: *
9: *
10: * .. Scalar Arguments ..
11: * CHARACTER SIDE, TRANS
12: * INTEGER INFO, LDA, M, N, K, MB, NB, LDT, LWORK, LDC
13: * ..
14: * .. Array Arguments ..
15: * DOUBLE A( LDA, * ), WORK( * ), C(LDC, * ),
16: * $ T( LDT, * )
17: *> \par Purpose:
18: * =============
19: *>
20: *> \verbatim
21: *>
22: *> DLAMSWLQ overwrites the general real M-by-N matrix C with
23: *>
24: *>
25: *> SIDE = 'L' SIDE = 'R'
26: *> TRANS = 'N': Q * C C * Q
27: *> TRANS = 'T': Q**T * C C * Q**T
28: *> where Q is a real orthogonal matrix defined as the product of blocked
29: *> elementary reflectors computed by short wide LQ
30: *> factorization (DLASWLQ)
31: *> \endverbatim
32: *
33: * Arguments:
34: * ==========
35: *
36: *> \param[in] SIDE
37: *> \verbatim
38: *> SIDE is CHARACTER*1
39: *> = 'L': apply Q or Q**T from the Left;
40: *> = 'R': apply Q or Q**T from the Right.
41: *> \endverbatim
42: *>
43: *> \param[in] TRANS
44: *> \verbatim
45: *> TRANS is CHARACTER*1
46: *> = 'N': No transpose, apply Q;
47: *> = 'T': Transpose, apply Q**T.
48: *> \endverbatim
49: *>
50: *> \param[in] M
51: *> \verbatim
52: *> M is INTEGER
53: *> The number of rows of the matrix C. M >=0.
54: *> \endverbatim
55: *>
56: *> \param[in] N
57: *> \verbatim
58: *> N is INTEGER
59: *> The number of columns of the matrix C. N >= 0.
60: *> \endverbatim
61: *>
62: *> \param[in] K
63: *> \verbatim
64: *> K is INTEGER
65: *> The number of elementary reflectors whose product defines
66: *> the matrix Q.
67: *> M >= K >= 0;
68: *>
69: *> \endverbatim
70: *> \param[in] MB
71: *> \verbatim
72: *> MB is INTEGER
73: *> The row block size to be used in the blocked LQ.
74: *> M >= MB >= 1
75: *> \endverbatim
76: *>
77: *> \param[in] NB
78: *> \verbatim
79: *> NB is INTEGER
80: *> The column block size to be used in the blocked LQ.
81: *> NB > M.
82: *> \endverbatim
83: *>
84: *> \param[in] A
85: *> \verbatim
86: *> A is DOUBLE PRECISION array, dimension
87: *> (LDA,M) if SIDE = 'L',
88: *> (LDA,N) if SIDE = 'R'
89: *> The i-th row must contain the vector which defines the blocked
90: *> elementary reflector H(i), for i = 1,2,...,k, as returned by
91: *> DLASWLQ in the first k rows of its array argument A.
92: *> \endverbatim
93: *>
94: *> \param[in] LDA
95: *> \verbatim
96: *> LDA is INTEGER
97: *> The leading dimension of the array A. LDA >= max(1,K).
98: *> \endverbatim
99: *>
100: *> \param[in] T
101: *> \verbatim
102: *> T is DOUBLE PRECISION array, dimension
103: *> ( M * Number of blocks(CEIL(N-K/NB-K)),
104: *> The blocked upper triangular block reflectors stored in compact form
105: *> as a sequence of upper triangular blocks. See below
106: *> for further details.
107: *> \endverbatim
108: *>
109: *> \param[in] LDT
110: *> \verbatim
111: *> LDT is INTEGER
112: *> The leading dimension of the array T. LDT >= MB.
113: *> \endverbatim
114: *>
115: *> \param[in,out] C
116: *> \verbatim
117: *> C is DOUBLE PRECISION array, dimension (LDC,N)
118: *> On entry, the M-by-N matrix C.
119: *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
120: *> \endverbatim
121: *>
122: *> \param[in] LDC
123: *> \verbatim
124: *> LDC is INTEGER
125: *> The leading dimension of the array C. LDC >= max(1,M).
126: *> \endverbatim
127: *>
128: *> \param[out] WORK
129: *> \verbatim
130: *> (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
131: *> \endverbatim
132: *>
133: *> \param[in] LWORK
134: *> \verbatim
135: *> LWORK is INTEGER
136: *> The dimension of the array WORK.
137: *> If SIDE = 'L', LWORK >= max(1,NB) * MB;
138: *> if SIDE = 'R', LWORK >= max(1,M) * MB.
139: *> If LWORK = -1, then a workspace query is assumed; the routine
140: *> only calculates the optimal size of the WORK array, returns
141: *> this value as the first entry of the WORK array, and no error
142: *> message related to LWORK is issued by XERBLA.
143: *> \endverbatim
144: *>
145: *> \param[out] INFO
146: *> \verbatim
147: *> INFO is INTEGER
148: *> = 0: successful exit
149: *> < 0: if INFO = -i, the i-th argument had an illegal value
150: *> \endverbatim
151: *
152: * Authors:
153: * ========
154: *
155: *> \author Univ. of Tennessee
156: *> \author Univ. of California Berkeley
157: *> \author Univ. of Colorado Denver
158: *> \author NAG Ltd.
159: *
160: *> \par Further Details:
161: * =====================
162: *>
163: *> \verbatim
164: *> Short-Wide LQ (SWLQ) performs LQ by a sequence of orthogonal transformations,
165: *> representing Q as a product of other orthogonal matrices
166: *> Q = Q(1) * Q(2) * . . . * Q(k)
167: *> where each Q(i) zeros out upper diagonal entries of a block of NB rows of A:
168: *> Q(1) zeros out the upper diagonal entries of rows 1:NB of A
169: *> Q(2) zeros out the bottom MB-N rows of rows [1:M,NB+1:2*NB-M] of A
170: *> Q(3) zeros out the bottom MB-N rows of rows [1:M,2*NB-M+1:3*NB-2*M] of A
171: *> . . .
172: *>
173: *> Q(1) is computed by GELQT, which represents Q(1) by Householder vectors
174: *> stored under the diagonal of rows 1:MB of A, and by upper triangular
175: *> block reflectors, stored in array T(1:LDT,1:N).
176: *> For more information see Further Details in GELQT.
177: *>
178: *> Q(i) for i>1 is computed by TPLQT, which represents Q(i) by Householder vectors
179: *> stored in columns [(i-1)*(NB-M)+M+1:i*(NB-M)+M] of A, and by upper triangular
180: *> block reflectors, stored in array T(1:LDT,(i-1)*M+1:i*M).
181: *> The last Q(k) may use fewer rows.
182: *> For more information see Further Details in TPLQT.
183: *>
184: *> For more details of the overall algorithm, see the description of
185: *> Sequential TSQR in Section 2.2 of [1].
186: *>
187: *> [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,”
188: *> J. Demmel, L. Grigori, M. Hoemmen, J. Langou,
189: *> SIAM J. Sci. Comput, vol. 34, no. 1, 2012
190: *> \endverbatim
191: *>
192: * =====================================================================
193: SUBROUTINE DLAMSWLQ( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T,
194: $ LDT, C, LDC, WORK, LWORK, INFO )
195: *
196: * -- LAPACK computational routine --
197: * -- LAPACK is a software package provided by Univ. of Tennessee, --
198: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
199: *
200: * .. Scalar Arguments ..
201: CHARACTER SIDE, TRANS
202: INTEGER INFO, LDA, M, N, K, MB, NB, LDT, LWORK, LDC
203: * ..
204: * .. Array Arguments ..
205: DOUBLE PRECISION A( LDA, * ), WORK( * ), C(LDC, * ),
206: $ T( LDT, * )
207: * ..
208: *
209: * =====================================================================
210: *
211: * ..
212: * .. Local Scalars ..
213: LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
214: INTEGER I, II, KK, CTR, LW
215: * ..
216: * .. External Functions ..
217: LOGICAL LSAME
218: EXTERNAL LSAME
219: * .. External Subroutines ..
220: EXTERNAL DTPMLQT, DGEMLQT, XERBLA
221: * ..
222: * .. Executable Statements ..
223: *
224: * Test the input arguments
225: *
226: LQUERY = LWORK.LT.0
227: NOTRAN = LSAME( TRANS, 'N' )
228: TRAN = LSAME( TRANS, 'T' )
229: LEFT = LSAME( SIDE, 'L' )
230: RIGHT = LSAME( SIDE, 'R' )
231: IF (LEFT) THEN
232: LW = N * MB
233: ELSE
234: LW = M * MB
235: END IF
236: *
237: INFO = 0
238: IF( .NOT.LEFT .AND. .NOT.RIGHT ) THEN
239: INFO = -1
240: ELSE IF( .NOT.TRAN .AND. .NOT.NOTRAN ) THEN
241: INFO = -2
242: ELSE IF( K.LT.0 ) THEN
243: INFO = -5
244: ELSE IF( M.LT.K ) THEN
245: INFO = -3
246: ELSE IF( N.LT.0 ) THEN
247: INFO = -4
248: ELSE IF( K.LT.MB .OR. MB.LT.1) THEN
249: INFO = -6
250: ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
251: INFO = -9
252: ELSE IF( LDT.LT.MAX( 1, MB) ) THEN
253: INFO = -11
254: ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
255: INFO = -13
256: ELSE IF(( LWORK.LT.MAX(1,LW)).AND.(.NOT.LQUERY)) THEN
257: INFO = -15
258: END IF
259: *
260: IF( INFO.NE.0 ) THEN
261: CALL XERBLA( 'DLAMSWLQ', -INFO )
262: WORK(1) = LW
263: RETURN
264: ELSE IF (LQUERY) THEN
265: WORK(1) = LW
266: RETURN
267: END IF
268: *
269: * Quick return if possible
270: *
271: IF( MIN(M,N,K).EQ.0 ) THEN
272: RETURN
273: END IF
274: *
275: IF((NB.LE.K).OR.(NB.GE.MAX(M,N,K))) THEN
276: CALL DGEMLQT( SIDE, TRANS, M, N, K, MB, A, LDA,
277: $ T, LDT, C, LDC, WORK, INFO)
278: RETURN
279: END IF
280: *
281: IF(LEFT.AND.TRAN) THEN
282: *
283: * Multiply Q to the last block of C
284: *
285: KK = MOD((M-K),(NB-K))
286: CTR = (M-K)/(NB-K)
287: IF (KK.GT.0) THEN
288: II=M-KK+1
289: CALL DTPMLQT('L','T',KK , N, K, 0, MB, A(1,II), LDA,
290: $ T(1,CTR*K+1), LDT, C(1,1), LDC,
291: $ C(II,1), LDC, WORK, INFO )
292: ELSE
293: II=M+1
294: END IF
295: *
296: DO I=II-(NB-K),NB+1,-(NB-K)
297: *
298: * Multiply Q to the current block of C (1:M,I:I+NB)
299: *
300: CTR = CTR - 1
301: CALL DTPMLQT('L','T',NB-K , N, K, 0,MB, A(1,I), LDA,
302: $ T(1, CTR*K+1),LDT, C(1,1), LDC,
303: $ C(I,1), LDC, WORK, INFO )
304:
305: END DO
306: *
307: * Multiply Q to the first block of C (1:M,1:NB)
308: *
309: CALL DGEMLQT('L','T',NB , N, K, MB, A(1,1), LDA, T
310: $ ,LDT ,C(1,1), LDC, WORK, INFO )
311: *
312: ELSE IF (LEFT.AND.NOTRAN) THEN
313: *
314: * Multiply Q to the first block of C
315: *
316: KK = MOD((M-K),(NB-K))
317: II=M-KK+1
318: CTR = 1
319: CALL DGEMLQT('L','N',NB , N, K, MB, A(1,1), LDA, T
320: $ ,LDT ,C(1,1), LDC, WORK, INFO )
321: *
322: DO I=NB+1,II-NB+K,(NB-K)
323: *
324: * Multiply Q to the current block of C (I:I+NB,1:N)
325: *
326: CALL DTPMLQT('L','N',NB-K , N, K, 0,MB, A(1,I), LDA,
327: $ T(1,CTR*K+1), LDT, C(1,1), LDC,
328: $ C(I,1), LDC, WORK, INFO )
329: CTR = CTR + 1
330: *
331: END DO
332: IF(II.LE.M) THEN
333: *
334: * Multiply Q to the last block of C
335: *
336: CALL DTPMLQT('L','N',KK , N, K, 0, MB, A(1,II), LDA,
337: $ T(1,CTR*K+1), LDT, C(1,1), LDC,
338: $ C(II,1), LDC, WORK, INFO )
339: *
340: END IF
341: *
342: ELSE IF(RIGHT.AND.NOTRAN) THEN
343: *
344: * Multiply Q to the last block of C
345: *
346: KK = MOD((N-K),(NB-K))
347: CTR = (N-K)/(NB-K)
348: IF (KK.GT.0) THEN
349: II=N-KK+1
350: CALL DTPMLQT('R','N',M , KK, K, 0, MB, A(1, II), LDA,
351: $ T(1,CTR *K+1), LDT, C(1,1), LDC,
352: $ C(1,II), LDC, WORK, INFO )
353: ELSE
354: II=N+1
355: END IF
356: *
357: DO I=II-(NB-K),NB+1,-(NB-K)
358: *
359: * Multiply Q to the current block of C (1:M,I:I+MB)
360: *
361: CTR = CTR - 1
362: CALL DTPMLQT('R','N', M, NB-K, K, 0, MB, A(1, I), LDA,
363: $ T(1,CTR*K+1), LDT, C(1,1), LDC,
364: $ C(1,I), LDC, WORK, INFO )
365: *
366: END DO
367: *
368: * Multiply Q to the first block of C (1:M,1:MB)
369: *
370: CALL DGEMLQT('R','N',M , NB, K, MB, A(1,1), LDA, T
371: $ ,LDT ,C(1,1), LDC, WORK, INFO )
372: *
373: ELSE IF (RIGHT.AND.TRAN) THEN
374: *
375: * Multiply Q to the first block of C
376: *
377: KK = MOD((N-K),(NB-K))
378: CTR = 1
379: II=N-KK+1
380: CALL DGEMLQT('R','T',M , NB, K, MB, A(1,1), LDA, T
381: $ ,LDT ,C(1,1), LDC, WORK, INFO )
382: *
383: DO I=NB+1,II-NB+K,(NB-K)
384: *
385: * Multiply Q to the current block of C (1:M,I:I+MB)
386: *
387: CALL DTPMLQT('R','T',M , NB-K, K, 0,MB, A(1,I), LDA,
388: $ T(1,CTR*K+1), LDT, C(1,1), LDC,
389: $ C(1,I), LDC, WORK, INFO )
390: CTR = CTR + 1
391: *
392: END DO
393: IF(II.LE.N) THEN
394: *
395: * Multiply Q to the last block of C
396: *
397: CALL DTPMLQT('R','T',M , KK, K, 0,MB, A(1,II), LDA,
398: $ T(1,CTR*K+1),LDT, C(1,1), LDC,
399: $ C(1,II), LDC, WORK, INFO )
400: *
401: END IF
402: *
403: END IF
404: *
405: WORK(1) = LW
406: RETURN
407: *
408: * End of DLAMSWLQ
409: *
410: END
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