ScaLAPACK 2.1  2.1
ScaLAPACK: Scalable Linear Algebra PACKage
pzunglq.f
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1  SUBROUTINE pzunglq( M, N, K, A, IA, JA, DESCA, TAU, WORK, LWORK,
2  $ INFO )
3 *
4 * -- ScaLAPACK routine (version 1.7) --
5 * University of Tennessee, Knoxville, Oak Ridge National Laboratory,
6 * and University of California, Berkeley.
7 * May 25, 2001
8 *
9 * .. Scalar Arguments ..
10  INTEGER IA, INFO, JA, K, LWORK, M, N
11 * ..
12 * .. Array Arguments ..
13  INTEGER DESCA( * )
14  COMPLEX*16 A( * ), TAU( * ), WORK( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * PZUNGLQ generates an M-by-N complex distributed matrix Q denoting
21 * A(IA:IA+M-1,JA:JA+N-1) with orthonormal rows, which is defined as
22 * the first M rows of a product of K elementary reflectors of order N
23 *
24 * Q = H(k)' . . . H(2)' H(1)'
25 *
26 * as returned by PZGELQF.
27 *
28 * Notes
29 * =====
30 *
31 * Each global data object is described by an associated description
32 * vector. This vector stores the information required to establish
33 * the mapping between an object element and its corresponding process
34 * and memory location.
35 *
36 * Let A be a generic term for any 2D block cyclicly distributed array.
37 * Such a global array has an associated description vector DESCA.
38 * In the following comments, the character _ should be read as
39 * "of the global array".
40 *
41 * NOTATION STORED IN EXPLANATION
42 * --------------- -------------- --------------------------------------
43 * DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
44 * DTYPE_A = 1.
45 * CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
46 * the BLACS process grid A is distribu-
47 * ted over. The context itself is glo-
48 * bal, but the handle (the integer
49 * value) may vary.
50 * M_A (global) DESCA( M_ ) The number of rows in the global
51 * array A.
52 * N_A (global) DESCA( N_ ) The number of columns in the global
53 * array A.
54 * MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
55 * the rows of the array.
56 * NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
57 * the columns of the array.
58 * RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
59 * row of the array A is distributed.
60 * CSRC_A (global) DESCA( CSRC_ ) The process column over which the
61 * first column of the array A is
62 * distributed.
63 * LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
64 * array. LLD_A >= MAX(1,LOCr(M_A)).
65 *
66 * Let K be the number of rows or columns of a distributed matrix,
67 * and assume that its process grid has dimension p x q.
68 * LOCr( K ) denotes the number of elements of K that a process
69 * would receive if K were distributed over the p processes of its
70 * process column.
71 * Similarly, LOCc( K ) denotes the number of elements of K that a
72 * process would receive if K were distributed over the q processes of
73 * its process row.
74 * The values of LOCr() and LOCc() may be determined via a call to the
75 * ScaLAPACK tool function, NUMROC:
76 * LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
77 * LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
78 * An upper bound for these quantities may be computed by:
79 * LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
80 * LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
81 *
82 * Arguments
83 * =========
84 *
85 * M (global input) INTEGER
86 * The number of rows to be operated on i.e the number of rows
87 * of the distributed submatrix Q. M >= 0.
88 *
89 * N (global input) INTEGER
90 * The number of columns to be operated on i.e the number of
91 * columns of the distributed submatrix Q. N >= M >= 0.
92 *
93 * K (global input) INTEGER
94 * The number of elementary reflectors whose product defines the
95 * matrix Q. M >= K >= 0.
96 *
97 * A (local input/local output) COMPLEX*16 pointer into the
98 * local memory to an array of dimension (LLD_A,LOCc(JA+N-1)).
99 * On entry, the i-th row must contain the vector which defines
100 * the elementary reflector H(i), IA <= i <= IA+K-1, as
101 * returned by PZGELQF in the K rows of its distributed matrix
102 * argument A(IA:IA+K-1,JA:*). On exit, this array contains the
103 * local pieces of the M-by-N distributed matrix Q.
104 *
105 * IA (global input) INTEGER
106 * The row index in the global array A indicating the first
107 * row of sub( A ).
108 *
109 * JA (global input) INTEGER
110 * The column index in the global array A indicating the
111 * first column of sub( A ).
112 *
113 * DESCA (global and local input) INTEGER array of dimension DLEN_.
114 * The array descriptor for the distributed matrix A.
115 *
116 * TAU (local input) COMPLEX*16, array, dimension LOCr(IA+K-1).
117 * This array contains the scalar factors TAU(i) of the
118 * elementary reflectors H(i) as returned by PZGELQF.
119 * TAU is tied to the distributed matrix A.
120 *
121 * WORK (local workspace/local output) COMPLEX*16 array,
122 * dimension (LWORK)
123 * On exit, WORK(1) returns the minimal and optimal LWORK.
124 *
125 * LWORK (local or global input) INTEGER
126 * The dimension of the array WORK.
127 * LWORK is local input and must be at least
128 * LWORK >= MB_A * ( MpA0 + NqA0 + MB_A ), where
129 *
130 * IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ),
131 * IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ),
132 * IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ),
133 * MpA0 = NUMROC( M+IROFFA, MB_A, MYROW, IAROW, NPROW ),
134 * NqA0 = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ),
135 *
136 * INDXG2P and NUMROC are ScaLAPACK tool functions;
137 * MYROW, MYCOL, NPROW and NPCOL can be determined by calling
138 * the subroutine BLACS_GRIDINFO.
139 *
140 * If LWORK = -1, then LWORK is global input and a workspace
141 * query is assumed; the routine only calculates the minimum
142 * and optimal size for all work arrays. Each of these
143 * values is returned in the first entry of the corresponding
144 * work array, and no error message is issued by PXERBLA.
145 *
146 *
147 * INFO (global output) INTEGER
148 * = 0: successful exit
149 * < 0: If the i-th argument is an array and the j-entry had
150 * an illegal value, then INFO = -(i*100+j), if the i-th
151 * argument is a scalar and had an illegal value, then
152 * INFO = -i.
153 *
154 * =====================================================================
155 *
156 * .. Parameters ..
157  INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
158  $ lld_, mb_, m_, nb_, n_, rsrc_
159  parameter( block_cyclic_2d = 1, dlen_ = 9, dtype_ = 1,
160  $ ctxt_ = 2, m_ = 3, n_ = 4, mb_ = 5, nb_ = 6,
161  $ rsrc_ = 7, csrc_ = 8, lld_ = 9 )
162  COMPLEX*16 ZERO
163  parameter( zero = ( 0.0d+0, 0.0d+0 ) )
164 * ..
165 * .. Local Scalars ..
166  LOGICAL LQUERY
167  CHARACTER COLBTOP, ROWBTOP
168  INTEGER I, IACOL, IAROW, IB, ICTXT, IINFO, IL, IN, IPW,
169  $ j, lwmin, mpa0, mycol, myrow, npcol, nprow,
170  $ nqa0
171 * ..
172 * .. Local Arrays ..
173  INTEGER IDUM1( 2 ), IDUM2( 2 )
174 * ..
175 * .. External Subroutines ..
176  EXTERNAL blacs_gridinfo, chk1mat, pchk1mat, pb_topget,
177  $ pb_topset, pxerbla, pzlarfb, pzlarft,
178  $ pzlaset, pzungl2
179 * ..
180 * .. External Functions ..
181  INTEGER ICEIL, INDXG2P, NUMROC
182  EXTERNAL iceil, indxg2p, numroc
183 * ..
184 * .. Intrinsic Functions ..
185  INTRINSIC dble, dcmplx, max, min, mod
186 * ..
187 * .. Executable Statements ..
188 *
189 * Get grid parameters
190 *
191  ictxt = desca( ctxt_ )
192  CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
193 *
194 * Test the input parameters
195 *
196  info = 0
197  IF( nprow.EQ.-1 ) THEN
198  info = -(700+ctxt_)
199  ELSE
200  CALL chk1mat( m, 1, n, 2, ia, ja, desca, 7, info )
201  IF( info.EQ.0 ) THEN
202  iarow = indxg2p( ia, desca( mb_ ), myrow, desca( rsrc_ ),
203  $ nprow )
204  iacol = indxg2p( ja, desca( nb_ ), mycol, desca( csrc_ ),
205  $ npcol )
206  mpa0 = numroc( m+mod( ia-1, desca( mb_ ) ), desca( mb_ ),
207  $ myrow, iarow, nprow )
208  nqa0 = numroc( n+mod( ja-1, desca( nb_ ) ), desca( nb_ ),
209  $ mycol, iacol, npcol )
210  lwmin = desca( mb_ ) * ( mpa0 + nqa0 + desca( mb_ ) )
211 *
212  work( 1 ) = dcmplx( dble( lwmin ) )
213  lquery = ( lwork.EQ.-1 )
214  IF( n.LT.m ) THEN
215  info = -2
216  ELSE IF( k.LT.0 .OR. k.GT.m ) THEN
217  info = -3
218  ELSE IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
219  info = -10
220  END IF
221  END IF
222  idum1( 1 ) = k
223  idum2( 1 ) = 3
224  IF( lwork.EQ.-1 ) THEN
225  idum1( 2 ) = -1
226  ELSE
227  idum1( 2 ) = 1
228  END IF
229  idum2( 2 ) = 10
230  CALL pchk1mat( m, 1, n, 2, ia, ja, desca, 7, 2, idum1, idum2,
231  $ info )
232  END IF
233 *
234  IF( info.NE.0 ) THEN
235  CALL pxerbla( ictxt, 'PZUNGLQ', -info )
236  RETURN
237  ELSE IF( lquery ) THEN
238  RETURN
239  END IF
240 *
241 * Quick return if possible
242 *
243  IF( m.LE.0 )
244  $ RETURN
245 *
246  ipw = desca( mb_ ) * desca( mb_ ) + 1
247  in = min( iceil( ia, desca( mb_ ) ) * desca( mb_ ), ia+k-1 )
248  il = max( ( (ia+k-2) / desca( mb_ ) ) * desca( mb_ ) + 1, ia )
249  CALL pb_topget( ictxt, 'Broadcast', 'Rowwise', rowbtop )
250  CALL pb_topget( ictxt, 'Broadcast', 'Columnwise', colbtop )
251  CALL pb_topset( ictxt, 'Broadcast', 'Rowwise', ' ' )
252  CALL pb_topset( ictxt, 'Broadcast', 'Columnwise', 'D-ring' )
253 *
254  CALL pzlaset( 'All', ia+m-il, il-ia, zero, zero, a, il, ja,
255  $ desca )
256 *
257 * Use unblocked code for the last or only block.
258 *
259  CALL pzungl2( ia+m-il, n-il+ia, ia+k-il, a, il, ja+il-ia, desca,
260  $ tau, work, lwork, iinfo )
261 *
262 * Is there at least one block of rows to loop over ?
263 *
264  IF( il.GT.in+1 ) THEN
265 *
266 * Use blocked code
267 *
268  DO 10 i = il-desca( mb_ ), in+1, -desca( mb_ )
269  ib = min( desca( mb_ ), ia+m-i )
270  j = ja + i - ia
271 *
272  IF( i+ib.LE.ia+m-1 ) THEN
273 *
274 * Form the triangular factor of the block reflector
275 * H = H(i) H(i+1) . . . H(i+ib-1)
276 *
277  CALL pzlarft( 'Forward', 'Rowwise', n-i+ia, ib, a, i, j,
278  $ desca, tau, work, work( ipw ) )
279 *
280 * Apply H' to A(i+ib:ia+m-1,j:ja+n-1) from the right
281 *
282  CALL pzlarfb( 'Right', 'Conjugate transpose', 'Forward',
283  $ 'Rowwise', m-i-ib+ia, n-i+ia, ib, a, i, j,
284  $ desca, work, a, i+ib, j, desca,
285  $ work( ipw ) )
286  END IF
287 *
288 * Apply H' to columns j:ja+n-1 of current block
289 *
290  CALL pzungl2( ib, n-i+ia, ib, a, i, j, desca, tau, work,
291  $ lwork, iinfo )
292 *
293 * Set columns ia:i-1 of current block to zero
294 *
295  CALL pzlaset( 'All', ib, i-ia, zero, zero, a, i, ja, desca )
296  10 CONTINUE
297 *
298  END IF
299 *
300 * Handle first block separately
301 *
302  IF( il.GT.ia ) THEN
303 *
304  ib = in - ia + 1
305 *
306 * Form the triangular factor of the block reflector
307 * H = H(i) H(i+1) . . . H(i+ib-1)
308 *
309  CALL pzlarft( 'Forward', 'Rowwise', n, ib, a, ia, ja, desca,
310  $ tau, work, work( ipw ) )
311 *
312 * Apply H' to A(ia+ib:ia+m-1,ja:ja+n-1) from the right
313 *
314  CALL pzlarfb( 'Right', 'Conjugate transpose', 'Forward',
315  $ 'Rowwise', m-ib, n, ib, a, ia, ja, desca, work,
316  $ a, ia+ib, ja, desca, work( ipw ) )
317 *
318 * Apply H' to columns ja:ja+n-1 of current block
319 *
320  CALL pzungl2( ib, n, ib, a, ia, ja, desca, tau, work, lwork,
321  $ iinfo )
322 *
323  END IF
324 *
325  CALL pb_topset( ictxt, 'Broadcast', 'Rowwise', rowbtop )
326  CALL pb_topset( ictxt, 'Broadcast', 'Columnwise', colbtop )
327 *
328  work( 1 ) = dcmplx( dble( lwmin ) )
329 *
330  RETURN
331 *
332 * End of PZUNGLQ
333 *
334  END
pzlarfb
subroutine pzlarfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, IV, JV, DESCV, T, C, IC, JC, DESCC, WORK)
Definition: pzlarfb.f:3
max
#define max(A, B)
Definition: pcgemr.c:180
pzunglq
subroutine pzunglq(M, N, K, A, IA, JA, DESCA, TAU, WORK, LWORK, INFO)
Definition: pzunglq.f:3
pzlaset
subroutine pzlaset(UPLO, M, N, ALPHA, BETA, A, IA, JA, DESCA)
Definition: pzblastst.f:7509
pchk1mat
subroutine pchk1mat(MA, MAPOS0, NA, NAPOS0, IA, JA, DESCA, DESCAPOS0, NEXTRA, EX, EXPOS, INFO)
Definition: pchkxmat.f:3
chk1mat
subroutine chk1mat(MA, MAPOS0, NA, NAPOS0, IA, JA, DESCA, DESCAPOS0, INFO)
Definition: chk1mat.f:3
pzlarft
subroutine pzlarft(DIRECT, STOREV, N, K, V, IV, JV, DESCV, TAU, T, WORK)
Definition: pzlarft.f:3
pzungl2
subroutine pzungl2(M, N, K, A, IA, JA, DESCA, TAU, WORK, LWORK, INFO)
Definition: pzungl2.f:3
pxerbla
subroutine pxerbla(ICTXT, SRNAME, INFO)
Definition: pxerbla.f:2
min
#define min(A, B)
Definition: pcgemr.c:181