1: *> \brief \b DORGTSQR_ROW
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DORGTSQR_ROW + dependencies
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11: *> [TGZ]</a>
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13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorgtsqr_row.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DORGTSQR_ROW( M, N, MB, NB, A, LDA, T, LDT, WORK,
22: * $ LWORK, INFO )
23: * IMPLICIT NONE
24: *
25: * .. Scalar Arguments ..
26: * INTEGER INFO, LDA, LDT, LWORK, M, N, MB, NB
27: * ..
28: * .. Array Arguments ..
29: * DOUBLE PRECISION A( LDA, * ), T( LDT, * ), WORK( * )
30: * ..
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DORGTSQR_ROW generates an M-by-N real matrix Q_out with
38: *> orthonormal columns from the output of DLATSQR. These N orthonormal
39: *> columns are the first N columns of a product of complex unitary
40: *> matrices Q(k)_in of order M, which are returned by DLATSQR in
41: *> a special format.
42: *>
43: *> Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).
44: *>
45: *> The input matrices Q(k)_in are stored in row and column blocks in A.
46: *> See the documentation of DLATSQR for more details on the format of
47: *> Q(k)_in, where each Q(k)_in is represented by block Householder
48: *> transformations. This routine calls an auxiliary routine DLARFB_GETT,
49: *> where the computation is performed on each individual block. The
50: *> algorithm first sweeps NB-sized column blocks from the right to left
51: *> starting in the bottom row block and continues to the top row block
52: *> (hence _ROW in the routine name). This sweep is in reverse order of
53: *> the order in which DLATSQR generates the output blocks.
54: *> \endverbatim
55: *
56: * Arguments:
57: * ==========
58: *
59: *> \param[in] M
60: *> \verbatim
61: *> M is INTEGER
62: *> The number of rows of the matrix A. M >= 0.
63: *> \endverbatim
64: *>
65: *> \param[in] N
66: *> \verbatim
67: *> N is INTEGER
68: *> The number of columns of the matrix A. M >= N >= 0.
69: *> \endverbatim
70: *>
71: *> \param[in] MB
72: *> \verbatim
73: *> MB is INTEGER
74: *> The row block size used by DLATSQR to return
75: *> arrays A and T. MB > N.
76: *> (Note that if MB > M, then M is used instead of MB
77: *> as the row block size).
78: *> \endverbatim
79: *>
80: *> \param[in] NB
81: *> \verbatim
82: *> NB is INTEGER
83: *> The column block size used by DLATSQR to return
84: *> arrays A and T. NB >= 1.
85: *> (Note that if NB > N, then N is used instead of NB
86: *> as the column block size).
87: *> \endverbatim
88: *>
89: *> \param[in,out] A
90: *> \verbatim
91: *> A is DOUBLE PRECISION array, dimension (LDA,N)
92: *>
93: *> On entry:
94: *>
95: *> The elements on and above the diagonal are not used as
96: *> input. The elements below the diagonal represent the unit
97: *> lower-trapezoidal blocked matrix V computed by DLATSQR
98: *> that defines the input matrices Q_in(k) (ones on the
99: *> diagonal are not stored). See DLATSQR for more details.
100: *>
101: *> On exit:
102: *>
103: *> The array A contains an M-by-N orthonormal matrix Q_out,
104: *> i.e the columns of A are orthogonal unit vectors.
105: *> \endverbatim
106: *>
107: *> \param[in] LDA
108: *> \verbatim
109: *> LDA is INTEGER
110: *> The leading dimension of the array A. LDA >= max(1,M).
111: *> \endverbatim
112: *>
113: *> \param[in] T
114: *> \verbatim
115: *> T is DOUBLE PRECISION array,
116: *> dimension (LDT, N * NIRB)
117: *> where NIRB = Number_of_input_row_blocks
118: *> = MAX( 1, CEIL((M-N)/(MB-N)) )
119: *> Let NICB = Number_of_input_col_blocks
120: *> = CEIL(N/NB)
121: *>
122: *> The upper-triangular block reflectors used to define the
123: *> input matrices Q_in(k), k=(1:NIRB*NICB). The block
124: *> reflectors are stored in compact form in NIRB block
125: *> reflector sequences. Each of the NIRB block reflector
126: *> sequences is stored in a larger NB-by-N column block of T
127: *> and consists of NICB smaller NB-by-NB upper-triangular
128: *> column blocks. See DLATSQR for more details on the format
129: *> of T.
130: *> \endverbatim
131: *>
132: *> \param[in] LDT
133: *> \verbatim
134: *> LDT is INTEGER
135: *> The leading dimension of the array T.
136: *> LDT >= max(1,min(NB,N)).
137: *> \endverbatim
138: *>
139: *> \param[out] WORK
140: *> \verbatim
141: *> (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
142: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
143: *> \endverbatim
144: *>
145: *> \param[in] LWORK
146: *> \verbatim
147: *> The dimension of the array WORK.
148: *> LWORK >= NBLOCAL * MAX(NBLOCAL,(N-NBLOCAL)),
149: *> where NBLOCAL=MIN(NB,N).
150: *> If LWORK = -1, then a workspace query is assumed.
151: *> The routine only calculates the optimal size of the WORK
152: *> array, returns this value as the first entry of the WORK
153: *> array, and no error message related to LWORK is issued
154: *> by XERBLA.
155: *> \endverbatim
156: *>
157: *> \param[out] INFO
158: *> \verbatim
159: *> INFO is INTEGER
160: *> = 0: successful exit
161: *> < 0: if INFO = -i, the i-th argument had an illegal value
162: *> \endverbatim
163: *>
164: * Authors:
165: * ========
166: *
167: *> \author Univ. of Tennessee
168: *> \author Univ. of California Berkeley
169: *> \author Univ. of Colorado Denver
170: *> \author NAG Ltd.
171: *
172: *> \ingroup doubleOTHERcomputational
173: *
174: *> \par Contributors:
175: * ==================
176: *>
177: *> \verbatim
178: *>
179: *> November 2020, Igor Kozachenko,
180: *> Computer Science Division,
181: *> University of California, Berkeley
182: *>
183: *> \endverbatim
184: *>
185: * =====================================================================
186: SUBROUTINE DORGTSQR_ROW( M, N, MB, NB, A, LDA, T, LDT, WORK,
187: $ LWORK, INFO )
188: IMPLICIT NONE
189: *
190: * -- LAPACK computational routine --
191: * -- LAPACK is a software package provided by Univ. of Tennessee, --
192: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
193: *
194: * .. Scalar Arguments ..
195: INTEGER INFO, LDA, LDT, LWORK, M, N, MB, NB
196: * ..
197: * .. Array Arguments ..
198: DOUBLE PRECISION A( LDA, * ), T( LDT, * ), WORK( * )
199: * ..
200: *
201: * =====================================================================
202: *
203: * .. Parameters ..
204: DOUBLE PRECISION ONE, ZERO
205: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
206: * ..
207: * .. Local Scalars ..
208: LOGICAL LQUERY
209: INTEGER NBLOCAL, MB2, M_PLUS_ONE, ITMP, IB_BOTTOM,
210: $ LWORKOPT, NUM_ALL_ROW_BLOCKS, JB_T, IB, IMB,
211: $ KB, KB_LAST, KNB, MB1
212: * ..
213: * .. Local Arrays ..
214: DOUBLE PRECISION DUMMY( 1, 1 )
215: * ..
216: * .. External Subroutines ..
217: EXTERNAL DLARFB_GETT, DLASET, XERBLA
218: * ..
219: * .. Intrinsic Functions ..
220: INTRINSIC DBLE, MAX, MIN
221: * ..
222: * .. Executable Statements ..
223: *
224: * Test the input parameters
225: *
226: INFO = 0
227: LQUERY = LWORK.EQ.-1
228: IF( M.LT.0 ) THEN
229: INFO = -1
230: ELSE IF( N.LT.0 .OR. M.LT.N ) THEN
231: INFO = -2
232: ELSE IF( MB.LE.N ) THEN
233: INFO = -3
234: ELSE IF( NB.LT.1 ) THEN
235: INFO = -4
236: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
237: INFO = -6
238: ELSE IF( LDT.LT.MAX( 1, MIN( NB, N ) ) ) THEN
239: INFO = -8
240: ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
241: INFO = -10
242: END IF
243: *
244: NBLOCAL = MIN( NB, N )
245: *
246: * Determine the workspace size.
247: *
248: IF( INFO.EQ.0 ) THEN
249: LWORKOPT = NBLOCAL * MAX( NBLOCAL, ( N - NBLOCAL ) )
250: END IF
251: *
252: * Handle error in the input parameters and handle the workspace query.
253: *
254: IF( INFO.NE.0 ) THEN
255: CALL XERBLA( 'DORGTSQR_ROW', -INFO )
256: RETURN
257: ELSE IF ( LQUERY ) THEN
258: WORK( 1 ) = DBLE( LWORKOPT )
259: RETURN
260: END IF
261: *
262: * Quick return if possible
263: *
264: IF( MIN( M, N ).EQ.0 ) THEN
265: WORK( 1 ) = DBLE( LWORKOPT )
266: RETURN
267: END IF
268: *
269: * (0) Set the upper-triangular part of the matrix A to zero and
270: * its diagonal elements to one.
271: *
272: CALL DLASET('U', M, N, ZERO, ONE, A, LDA )
273: *
274: * KB_LAST is the column index of the last column block reflector
275: * in the matrices T and V.
276: *
277: KB_LAST = ( ( N-1 ) / NBLOCAL ) * NBLOCAL + 1
278: *
279: *
280: * (1) Bottom-up loop over row blocks of A, except the top row block.
281: * NOTE: If MB>=M, then the loop is never executed.
282: *
283: IF ( MB.LT.M ) THEN
284: *
285: * MB2 is the row blocking size for the row blocks before the
286: * first top row block in the matrix A. IB is the row index for
287: * the row blocks in the matrix A before the first top row block.
288: * IB_BOTTOM is the row index for the last bottom row block
289: * in the matrix A. JB_T is the column index of the corresponding
290: * column block in the matrix T.
291: *
292: * Initialize variables.
293: *
294: * NUM_ALL_ROW_BLOCKS is the number of row blocks in the matrix A
295: * including the first row block.
296: *
297: MB2 = MB - N
298: M_PLUS_ONE = M + 1
299: ITMP = ( M - MB - 1 ) / MB2
300: IB_BOTTOM = ITMP * MB2 + MB + 1
301: NUM_ALL_ROW_BLOCKS = ITMP + 2
302: JB_T = NUM_ALL_ROW_BLOCKS * N + 1
303: *
304: DO IB = IB_BOTTOM, MB+1, -MB2
305: *
306: * Determine the block size IMB for the current row block
307: * in the matrix A.
308: *
309: IMB = MIN( M_PLUS_ONE - IB, MB2 )
310: *
311: * Determine the column index JB_T for the current column block
312: * in the matrix T.
313: *
314: JB_T = JB_T - N
315: *
316: * Apply column blocks of H in the row block from right to left.
317: *
318: * KB is the column index of the current column block reflector
319: * in the matrices T and V.
320: *
321: DO KB = KB_LAST, 1, -NBLOCAL
322: *
323: * Determine the size of the current column block KNB in
324: * the matrices T and V.
325: *
326: KNB = MIN( NBLOCAL, N - KB + 1 )
327: *
328: CALL DLARFB_GETT( 'I', IMB, N-KB+1, KNB,
329: $ T( 1, JB_T+KB-1 ), LDT, A( KB, KB ), LDA,
330: $ A( IB, KB ), LDA, WORK, KNB )
331: *
332: END DO
333: *
334: END DO
335: *
336: END IF
337: *
338: * (2) Top row block of A.
339: * NOTE: If MB>=M, then we have only one row block of A of size M
340: * and we work on the entire matrix A.
341: *
342: MB1 = MIN( MB, M )
343: *
344: * Apply column blocks of H in the top row block from right to left.
345: *
346: * KB is the column index of the current block reflector in
347: * the matrices T and V.
348: *
349: DO KB = KB_LAST, 1, -NBLOCAL
350: *
351: * Determine the size of the current column block KNB in
352: * the matrices T and V.
353: *
354: KNB = MIN( NBLOCAL, N - KB + 1 )
355: *
356: IF( MB1-KB-KNB+1.EQ.0 ) THEN
357: *
358: * In SLARFB_GETT parameters, when M=0, then the matrix B
359: * does not exist, hence we need to pass a dummy array
360: * reference DUMMY(1,1) to B with LDDUMMY=1.
361: *
362: CALL DLARFB_GETT( 'N', 0, N-KB+1, KNB,
363: $ T( 1, KB ), LDT, A( KB, KB ), LDA,
364: $ DUMMY( 1, 1 ), 1, WORK, KNB )
365: ELSE
366: CALL DLARFB_GETT( 'N', MB1-KB-KNB+1, N-KB+1, KNB,
367: $ T( 1, KB ), LDT, A( KB, KB ), LDA,
368: $ A( KB+KNB, KB), LDA, WORK, KNB )
369:
370: END IF
371: *
372: END DO
373: *
374: WORK( 1 ) = DBLE( LWORKOPT )
375: RETURN
376: *
377: * End of DORGTSQR_ROW
378: *
379: END
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