1: *
2: * Definition:
3: * ===========
4: *
5: * SUBROUTINE DLAMTSQR( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T,
6: * $ LDT, C, LDC, WORK, LWORK, INFO )
7: *
8: *
9: * .. Scalar Arguments ..
10: * CHARACTER SIDE, TRANS
11: * INTEGER INFO, LDA, M, N, K, MB, NB, LDT, LWORK, LDC
12: * ..
13: * .. Array Arguments ..
14: * DOUBLE A( LDA, * ), WORK( * ), C(LDC, * ),
15: * $ T( LDT, * )
16: *> \par Purpose:
17: * =============
18: *>
19: *> \verbatim
20: *>
21: *> DLAMTSQR overwrites the general real M-by-N matrix C with
22: *>
23: *>
24: *> SIDE = 'L' SIDE = 'R'
25: *> TRANS = 'N': Q * C C * Q
26: *> TRANS = 'T': Q**T * C C * Q**T
27: *> where Q is a real orthogonal matrix defined as the product
28: *> of blocked elementary reflectors computed by tall skinny
29: *> QR factorization (DLATSQR)
30: *> \endverbatim
31: *
32: * Arguments:
33: * ==========
34: *
35: *> \param[in] SIDE
36: *> \verbatim
37: *> SIDE is CHARACTER*1
38: *> = 'L': apply Q or Q**T from the Left;
39: *> = 'R': apply Q or Q**T from the Right.
40: *> \endverbatim
41: *>
42: *> \param[in] TRANS
43: *> \verbatim
44: *> TRANS is CHARACTER*1
45: *> = 'N': No transpose, apply Q;
46: *> = 'T': Transpose, apply Q**T.
47: *> \endverbatim
48: *>
49: *> \param[in] M
50: *> \verbatim
51: *> M is INTEGER
52: *> The number of rows of the matrix A. M >=0.
53: *> \endverbatim
54: *>
55: *> \param[in] N
56: *> \verbatim
57: *> N is INTEGER
58: *> The number of columns of the matrix C. M >= N >= 0.
59: *> \endverbatim
60: *>
61: *> \param[in] K
62: *> \verbatim
63: *> K is INTEGER
64: *> The number of elementary reflectors whose product defines
65: *> the matrix Q.
66: *> N >= K >= 0;
67: *>
68: *> \endverbatim
69: *>
70: *> \param[in] MB
71: *> \verbatim
72: *> MB is INTEGER
73: *> The block size to be used in the blocked QR.
74: *> MB > N. (must be the same as DLATSQR)
75: *> \endverbatim
76: *>
77: *> \param[in] NB
78: *> \verbatim
79: *> NB is INTEGER
80: *> The column block size to be used in the blocked QR.
81: *> N >= NB >= 1.
82: *> \endverbatim
83: *>
84: *> \param[in] A
85: *> \verbatim
86: *> A is DOUBLE PRECISION array, dimension (LDA,K)
87: *> The i-th column must contain the vector which defines the
88: *> blockedelementary reflector H(i), for i = 1,2,...,k, as
89: *> returned by DLATSQR in the first k columns of
90: *> its array argument A.
91: *> \endverbatim
92: *>
93: *> \param[in] LDA
94: *> \verbatim
95: *> LDA is INTEGER
96: *> The leading dimension of the array A.
97: *> If SIDE = 'L', LDA >= max(1,M);
98: *> if SIDE = 'R', LDA >= max(1,N).
99: *> \endverbatim
100: *>
101: *> \param[in] T
102: *> \verbatim
103: *> T is DOUBLE PRECISION array, dimension
104: *> ( N * Number of blocks(CEIL(M-K/MB-K)),
105: *> The blocked upper triangular block reflectors stored in compact form
106: *> as a sequence of upper triangular blocks. See below
107: *> for further details.
108: *> \endverbatim
109: *>
110: *> \param[in] LDT
111: *> \verbatim
112: *> LDT is INTEGER
113: *> The leading dimension of the array T. LDT >= NB.
114: *> \endverbatim
115: *>
116: *> \param[in,out] C
117: *> \verbatim
118: *> C is DOUBLE PRECISION array, dimension (LDC,N)
119: *> On entry, the M-by-N matrix C.
120: *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
121: *> \endverbatim
122: *>
123: *> \param[in] LDC
124: *> \verbatim
125: *> LDC is INTEGER
126: *> The leading dimension of the array C. LDC >= max(1,M).
127: *> \endverbatim
128: *>
129: *> \param[out] WORK
130: *> \verbatim
131: *> (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
132: *>
133: *> \endverbatim
134: *> \param[in] LWORK
135: *> \verbatim
136: *> LWORK is INTEGER
137: *> The dimension of the array WORK.
138: *>
139: *> If SIDE = 'L', LWORK >= max(1,N)*NB;
140: *> if SIDE = 'R', LWORK >= max(1,MB)*NB.
141: *> If LWORK = -1, then a workspace query is assumed; the routine
142: *> only calculates the optimal size of the WORK array, returns
143: *> this value as the first entry of the WORK array, and no error
144: *> message related to LWORK is issued by XERBLA.
145: *>
146: *> \endverbatim
147: *> \param[out] INFO
148: *> \verbatim
149: *> INFO is INTEGER
150: *> = 0: successful exit
151: *> < 0: if INFO = -i, the i-th argument had an illegal value
152: *> \endverbatim
153: *
154: * Authors:
155: * ========
156: *
157: *> \author Univ. of Tennessee
158: *> \author Univ. of California Berkeley
159: *> \author Univ. of Colorado Denver
160: *> \author NAG Ltd.
161: *
162: *> \par Further Details:
163: * =====================
164: *>
165: *> \verbatim
166: *> Tall-Skinny QR (TSQR) performs QR by a sequence of orthogonal transformations,
167: *> representing Q as a product of other orthogonal matrices
168: *> Q = Q(1) * Q(2) * . . . * Q(k)
169: *> where each Q(i) zeros out subdiagonal entries of a block of MB rows of A:
170: *> Q(1) zeros out the subdiagonal entries of rows 1:MB of A
171: *> Q(2) zeros out the bottom MB-N rows of rows [1:N,MB+1:2*MB-N] of A
172: *> Q(3) zeros out the bottom MB-N rows of rows [1:N,2*MB-N+1:3*MB-2*N] of A
173: *> . . .
174: *>
175: *> Q(1) is computed by GEQRT, which represents Q(1) by Householder vectors
176: *> stored under the diagonal of rows 1:MB of A, and by upper triangular
177: *> block reflectors, stored in array T(1:LDT,1:N).
178: *> For more information see Further Details in GEQRT.
179: *>
180: *> Q(i) for i>1 is computed by TPQRT, which represents Q(i) by Householder vectors
181: *> stored in rows [(i-1)*(MB-N)+N+1:i*(MB-N)+N] of A, and by upper triangular
182: *> block reflectors, stored in array T(1:LDT,(i-1)*N+1:i*N).
183: *> The last Q(k) may use fewer rows.
184: *> For more information see Further Details in TPQRT.
185: *>
186: *> For more details of the overall algorithm, see the description of
187: *> Sequential TSQR in Section 2.2 of [1].
188: *>
189: *> [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,”
190: *> J. Demmel, L. Grigori, M. Hoemmen, J. Langou,
191: *> SIAM J. Sci. Comput, vol. 34, no. 1, 2012
192: *> \endverbatim
193: *>
194: * =====================================================================
195: SUBROUTINE DLAMTSQR( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T,
196: $ LDT, C, LDC, WORK, LWORK, INFO )
197: *
198: * -- LAPACK computational routine (version 3.7.1) --
199: * -- LAPACK is a software package provided by Univ. of Tennessee, --
200: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
201: * June 2017
202: *
203: * .. Scalar Arguments ..
204: CHARACTER SIDE, TRANS
205: INTEGER INFO, LDA, M, N, K, MB, NB, LDT, LWORK, LDC
206: * ..
207: * .. Array Arguments ..
208: DOUBLE PRECISION A( LDA, * ), WORK( * ), C(LDC, * ),
209: $ T( LDT, * )
210: * ..
211: *
212: * =====================================================================
213: *
214: * ..
215: * .. Local Scalars ..
216: LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
217: INTEGER I, II, KK, LW, CTR
218: * ..
219: * .. External Functions ..
220: LOGICAL LSAME
221: EXTERNAL LSAME
222: * .. External Subroutines ..
223: EXTERNAL DGEMQRT, DTPMQRT, XERBLA
224: * ..
225: * .. Executable Statements ..
226: *
227: * Test the input arguments
228: *
229: LQUERY = LWORK.LT.0
230: NOTRAN = LSAME( TRANS, 'N' )
231: TRAN = LSAME( TRANS, 'T' )
232: LEFT = LSAME( SIDE, 'L' )
233: RIGHT = LSAME( SIDE, 'R' )
234: IF (LEFT) THEN
235: LW = N * NB
236: ELSE
237: LW = MB * NB
238: END IF
239: *
240: INFO = 0
241: IF( .NOT.LEFT .AND. .NOT.RIGHT ) THEN
242: INFO = -1
243: ELSE IF( .NOT.TRAN .AND. .NOT.NOTRAN ) THEN
244: INFO = -2
245: ELSE IF( M.LT.0 ) THEN
246: INFO = -3
247: ELSE IF( N.LT.0 ) THEN
248: INFO = -4
249: ELSE IF( K.LT.0 ) THEN
250: INFO = -5
251: ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
252: INFO = -9
253: ELSE IF( LDT.LT.MAX( 1, NB) ) THEN
254: INFO = -11
255: ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
256: INFO = -13
257: ELSE IF(( LWORK.LT.MAX(1,LW)).AND.(.NOT.LQUERY)) THEN
258: INFO = -15
259: END IF
260: *
261: * Determine the block size if it is tall skinny or short and wide
262: *
263: IF( INFO.EQ.0) THEN
264: WORK(1) = LW
265: END IF
266: *
267: IF( INFO.NE.0 ) THEN
268: CALL XERBLA( 'DLAMTSQR', -INFO )
269: RETURN
270: ELSE IF (LQUERY) THEN
271: RETURN
272: END IF
273: *
274: * Quick return if possible
275: *
276: IF( MIN(M,N,K).EQ.0 ) THEN
277: RETURN
278: END IF
279: *
280: IF((MB.LE.K).OR.(MB.GE.MAX(M,N,K))) THEN
281: CALL DGEMQRT( SIDE, TRANS, M, N, K, NB, A, LDA,
282: $ T, LDT, C, LDC, WORK, INFO)
283: RETURN
284: END IF
285: *
286: IF(LEFT.AND.NOTRAN) THEN
287: *
288: * Multiply Q to the last block of C
289: *
290: KK = MOD((M-K),(MB-K))
291: CTR = (M-K)/(MB-K)
292: IF (KK.GT.0) THEN
293: II=M-KK+1
294: CALL DTPMQRT('L','N',KK , N, K, 0, NB, A(II,1), LDA,
295: $ T(1,CTR*K+1),LDT , C(1,1), LDC,
296: $ C(II,1), LDC, WORK, INFO )
297: ELSE
298: II=M+1
299: END IF
300: *
301: DO I=II-(MB-K),MB+1,-(MB-K)
302: *
303: * Multiply Q to the current block of C (I:I+MB,1:N)
304: *
305: CTR = CTR - 1
306: CALL DTPMQRT('L','N',MB-K , N, K, 0,NB, A(I,1), LDA,
307: $ T(1,CTR*K+1),LDT, C(1,1), LDC,
308: $ C(I,1), LDC, WORK, INFO )
309: *
310: END DO
311: *
312: * Multiply Q to the first block of C (1:MB,1:N)
313: *
314: CALL DGEMQRT('L','N',MB , N, K, NB, A(1,1), LDA, T
315: $ ,LDT ,C(1,1), LDC, WORK, INFO )
316: *
317: ELSE IF (LEFT.AND.TRAN) THEN
318: *
319: * Multiply Q to the first block of C
320: *
321: KK = MOD((M-K),(MB-K))
322: II=M-KK+1
323: CTR = 1
324: CALL DGEMQRT('L','T',MB , N, K, NB, A(1,1), LDA, T
325: $ ,LDT ,C(1,1), LDC, WORK, INFO )
326: *
327: DO I=MB+1,II-MB+K,(MB-K)
328: *
329: * Multiply Q to the current block of C (I:I+MB,1:N)
330: *
331: CALL DTPMQRT('L','T',MB-K , N, K, 0,NB, A(I,1), LDA,
332: $ T(1,CTR * K + 1),LDT, C(1,1), LDC,
333: $ C(I,1), LDC, WORK, INFO )
334: CTR = CTR + 1
335: *
336: END DO
337: IF(II.LE.M) THEN
338: *
339: * Multiply Q to the last block of C
340: *
341: CALL DTPMQRT('L','T',KK , N, K, 0,NB, A(II,1), LDA,
342: $ T(1,CTR * K + 1), LDT, C(1,1), LDC,
343: $ C(II,1), LDC, WORK, INFO )
344: *
345: END IF
346: *
347: ELSE IF(RIGHT.AND.TRAN) THEN
348: *
349: * Multiply Q to the last block of C
350: *
351: KK = MOD((N-K),(MB-K))
352: CTR = (N-K)/(MB-K)
353: IF (KK.GT.0) THEN
354: II=N-KK+1
355: CALL DTPMQRT('R','T',M , KK, K, 0, NB, A(II,1), LDA,
356: $ T(1,CTR*K+1), LDT, C(1,1), LDC,
357: $ C(1,II), LDC, WORK, INFO )
358: ELSE
359: II=N+1
360: END IF
361: *
362: DO I=II-(MB-K),MB+1,-(MB-K)
363: *
364: * Multiply Q to the current block of C (1:M,I:I+MB)
365: *
366: CTR = CTR - 1
367: CALL DTPMQRT('R','T',M , MB-K, K, 0,NB, A(I,1), LDA,
368: $ T(1,CTR*K+1), LDT, C(1,1), LDC,
369: $ C(1,I), LDC, WORK, INFO )
370: *
371: END DO
372: *
373: * Multiply Q to the first block of C (1:M,1:MB)
374: *
375: CALL DGEMQRT('R','T',M , MB, K, NB, A(1,1), LDA, T
376: $ ,LDT ,C(1,1), LDC, WORK, INFO )
377: *
378: ELSE IF (RIGHT.AND.NOTRAN) THEN
379: *
380: * Multiply Q to the first block of C
381: *
382: KK = MOD((N-K),(MB-K))
383: II=N-KK+1
384: CTR = 1
385: CALL DGEMQRT('R','N', M, MB , K, NB, A(1,1), LDA, T
386: $ ,LDT ,C(1,1), LDC, WORK, INFO )
387: *
388: DO I=MB+1,II-MB+K,(MB-K)
389: *
390: * Multiply Q to the current block of C (1:M,I:I+MB)
391: *
392: CALL DTPMQRT('R','N', M, MB-K, K, 0,NB, A(I,1), LDA,
393: $ T(1, CTR * K + 1),LDT, C(1,1), LDC,
394: $ C(1,I), LDC, WORK, INFO )
395: CTR = CTR + 1
396: *
397: END DO
398: IF(II.LE.N) THEN
399: *
400: * Multiply Q to the last block of C
401: *
402: CALL DTPMQRT('R','N', M, KK , K, 0,NB, A(II,1), LDA,
403: $ T(1, CTR * K + 1),LDT, C(1,1), LDC,
404: $ C(1,II), LDC, WORK, INFO )
405: *
406: END IF
407: *
408: END IF
409: *
410: WORK(1) = LW
411: RETURN
412: *
413: * End of DLAMTSQR
414: *
415: END
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