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