ScaLAPACK 2.1  2.1
ScaLAPACK: Scalable Linear Algebra PACKage
pctzrzf.f
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1  SUBROUTINE pctzrzf( M, N, 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, LWORK, M, N
11 * ..
12 * .. Array Arguments ..
13  INTEGER DESCA( * )
14  COMPLEX A( * ), TAU( * ), WORK( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * PCTZRZF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix
21 * sub( A ) = A(IA:IA+M-1,JA:JA+N-1) to upper triangular form by means
22 * of unitary transformations.
23 *
24 * The upper trapezoidal matrix sub( A ) is factored as
25 *
26 * sub( A ) = ( R 0 ) * Z,
27 *
28 * where Z is an N-by-N unitary matrix and R is an M-by-M upper
29 * triangular matrix.
30 *
31 * Notes
32 * =====
33 *
34 * Each global data object is described by an associated description
35 * vector. This vector stores the information required to establish
36 * the mapping between an object element and its corresponding process
37 * and memory location.
38 *
39 * Let A be a generic term for any 2D block cyclicly distributed array.
40 * Such a global array has an associated description vector DESCA.
41 * In the following comments, the character _ should be read as
42 * "of the global array".
43 *
44 * NOTATION STORED IN EXPLANATION
45 * --------------- -------------- --------------------------------------
46 * DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
47 * DTYPE_A = 1.
48 * CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
49 * the BLACS process grid A is distribu-
50 * ted over. The context itself is glo-
51 * bal, but the handle (the integer
52 * value) may vary.
53 * M_A (global) DESCA( M_ ) The number of rows in the global
54 * array A.
55 * N_A (global) DESCA( N_ ) The number of columns in the global
56 * array A.
57 * MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
58 * the rows of the array.
59 * NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
60 * the columns of the array.
61 * RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
62 * row of the array A is distributed.
63 * CSRC_A (global) DESCA( CSRC_ ) The process column over which the
64 * first column of the array A is
65 * distributed.
66 * LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
67 * array. LLD_A >= MAX(1,LOCr(M_A)).
68 *
69 * Let K be the number of rows or columns of a distributed matrix,
70 * and assume that its process grid has dimension p x q.
71 * LOCr( K ) denotes the number of elements of K that a process
72 * would receive if K were distributed over the p processes of its
73 * process column.
74 * Similarly, LOCc( K ) denotes the number of elements of K that a
75 * process would receive if K were distributed over the q processes of
76 * its process row.
77 * The values of LOCr() and LOCc() may be determined via a call to the
78 * ScaLAPACK tool function, NUMROC:
79 * LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
80 * LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
81 * An upper bound for these quantities may be computed by:
82 * LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
83 * LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
84 *
85 * Arguments
86 * =========
87 *
88 * M (global input) INTEGER
89 * The number of rows to be operated on, i.e. the number of rows
90 * of the distributed submatrix sub( A ). M >= 0.
91 *
92 * N (global input) INTEGER
93 * The number of columns to be operated on, i.e. the number of
94 * columns of the distributed submatrix sub( A ). N >= 0.
95 *
96 * A (local input/local output) COMPLEX pointer into the
97 * local memory to an array of dimension (LLD_A, LOCc(JA+N-1)).
98 * On entry, the local pieces of the M-by-N distributed matrix
99 * sub( A ) which is to be factored. On exit, the leading M-by-M
100 * upper triangular part of sub( A ) contains the upper trian-
101 * gular matrix R, and elements M+1 to N of the first M rows of
102 * sub( A ), with the array TAU, represent the unitary matrix Z
103 * as a product of M elementary reflectors.
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 output) COMPLEX, array, dimension LOCr(IA+M-1)
117 * This array contains the scalar factors of the elementary
118 * reflectors. TAU is tied to the distributed matrix A.
119 *
120 * WORK (local workspace/local output) COMPLEX array,
121 * dimension (LWORK)
122 * On exit, WORK(1) returns the minimal and optimal LWORK.
123 *
124 * LWORK (local or global input) INTEGER
125 * The dimension of the array WORK.
126 * LWORK is local input and must be at least
127 * LWORK >= MB_A * ( Mp0 + Nq0 + MB_A ), where
128 *
129 * IROFF = MOD( IA-1, MB_A ), ICOFF = MOD( JA-1, NB_A ),
130 * IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ),
131 * IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ),
132 * Mp0 = NUMROC( M+IROFF, MB_A, MYROW, IAROW, NPROW ),
133 * Nq0 = NUMROC( N+ICOFF, NB_A, MYCOL, IACOL, NPCOL ),
134 *
135 * and NUMROC, INDXG2P are ScaLAPACK tool functions;
136 * MYROW, MYCOL, NPROW and NPCOL can be determined by calling
137 * the subroutine BLACS_GRIDINFO.
138 *
139 * If LWORK = -1, then LWORK is global input and a workspace
140 * query is assumed; the routine only calculates the minimum
141 * and optimal size for all work arrays. Each of these
142 * values is returned in the first entry of the corresponding
143 * work array, and no error message is issued by PXERBLA.
144 *
145 * INFO (global output) INTEGER
146 * = 0: successful exit
147 * < 0: If the i-th argument is an array and the j-entry had
148 * an illegal value, then INFO = -(i*100+j), if the i-th
149 * argument is a scalar and had an illegal value, then
150 * INFO = -i.
151 *
152 * Further Details
153 * ===============
154 *
155 * The factorization is obtained by Householder's method. The kth
156 * transformation matrix, Z( k ), whose conjugate transpose is used to
157 * introduce zeros into the (m - k + 1)th row of sub( A ), is given in
158 * the form
159 *
160 * Z( k ) = ( I 0 ),
161 * ( 0 T( k ) )
162 *
163 * where
164 *
165 * T( k ) = I - tau*u( k )*u( k )', u( k ) = ( 1 ),
166 * ( 0 )
167 * ( z( k ) )
168 *
169 * tau is a scalar and z( k ) is an ( n - m ) element vector.
170 * tau and z( k ) are chosen to annihilate the elements of the kth row
171 * of sub( A ).
172 *
173 * The scalar tau is returned in the kth element of TAU and the vector
174 * u( k ) in the kth row of sub( A ), such that the elements of z( k )
175 * are in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned
176 * in the upper triangular part of sub( A ).
177 *
178 * Z is given by
179 *
180 * Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
181 *
182 * =====================================================================
183 *
184 * .. Parameters ..
185  INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
186  $ lld_, mb_, m_, nb_, n_, rsrc_
187  parameter( block_cyclic_2d = 1, dlen_ = 9, dtype_ = 1,
188  $ ctxt_ = 2, m_ = 3, n_ = 4, mb_ = 5, nb_ = 6,
189  $ rsrc_ = 7, csrc_ = 8, lld_ = 9 )
190  COMPLEX ZERO
191  parameter( zero = ( 0.0e+0, 0.0e+0 ) )
192 * ..
193 * .. Local Scalars ..
194  LOGICAL LQUERY
195  CHARACTER COLBTOP, ROWBTOP
196  INTEGER I, IACOL, IAROW, IB, ICTXT, IIA, IL, IN, IPW,
197  $ iroffa, j, jm1, l, lwmin, mp0, mycol, myrow,
198  $ npcol, nprow, nq0
199 * ..
200 * .. Local Arrays ..
201  INTEGER IDUM1( 1 ), IDUM2( 1 )
202 * ..
203 * .. External Subroutines ..
204  EXTERNAL blacs_gridinfo, chk1mat, infog1l, pchk1mat,
205  $ pclatrz, pclarzb, pclarzt, pb_topget,
206  $ pb_topset, pxerbla
207 * ..
208 * .. External Functions ..
209  INTEGER ICEIL, INDXG2P, NUMROC
210  EXTERNAL iceil, indxg2p, numroc
211 * ..
212 * .. Intrinsic Functions ..
213  INTRINSIC cmplx, max, min, mod, real
214 * ..
215 * .. Executable Statements ..
216 *
217 * Get grid parameters
218 *
219  ictxt = desca( ctxt_ )
220  CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
221 *
222 * Test the input parameters
223 *
224  info = 0
225  IF( nprow.EQ.-1 ) THEN
226  info = -(600+ctxt_)
227  ELSE
228  CALL chk1mat( m, 1, n, 2, ia, ja, desca, 6, info )
229  IF( info.EQ.0 ) THEN
230  iroffa = mod( ia-1, desca( mb_ ) )
231  iarow = indxg2p( ia, desca( mb_ ), myrow, desca( rsrc_ ),
232  $ nprow )
233  iacol = indxg2p( ja, desca( nb_ ), mycol, desca( csrc_ ),
234  $ npcol )
235  mp0 = numroc( m+iroffa, desca( mb_ ), myrow, iarow, nprow )
236  nq0 = numroc( n+mod( ja-1, desca( nb_ ) ), desca( nb_ ),
237  $ mycol, iacol, npcol )
238  lwmin = desca( mb_ ) * ( mp0 + nq0 + desca( mb_ ) )
239 *
240  work( 1 ) = cmplx( real( lwmin ) )
241  lquery = ( lwork.EQ.-1 )
242  IF( n.LT.m ) THEN
243  info = -2
244  ELSE IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
245  info = -9
246  END IF
247  END IF
248  IF( lquery ) THEN
249  idum1( 1 ) = -1
250  ELSE
251  idum1( 1 ) = 1
252  END IF
253  idum2( 1 ) = 9
254  CALL pchk1mat( m, 1, n, 2, ia, ja, desca, 6, 1, idum1, idum2,
255  $ info )
256  END IF
257 *
258  IF( info.NE.0 ) THEN
259  CALL pxerbla( ictxt, 'PCTZRZF', -info )
260  RETURN
261  ELSE IF( lquery ) THEN
262  RETURN
263  END IF
264 *
265 * Quick return if possible
266 *
267  IF( m.EQ.0 .OR. n.EQ.0 )
268  $ RETURN
269 *
270  IF( m.EQ.n ) THEN
271 *
272  CALL infog1l( ia, desca( mb_ ), nprow, myrow, desca( rsrc_ ),
273  $ iia, iarow )
274  IF( myrow.EQ.iarow )
275  $ mp0 = mp0 - iroffa
276  DO 10 i = iia, iia+mp0-1
277  tau( i ) = zero
278  10 CONTINUE
279 *
280  ELSE
281 *
282  l = n-m
283  jm1 = ja + min( m+1, n ) - 1
284  ipw = desca( mb_ ) * desca( mb_ ) + 1
285  in = min( iceil( ia, desca( mb_ ) ) * desca( mb_ ), ia+m-1 )
286  il = max( ( (ia+m-2) / desca( mb_ ) ) * desca( mb_ ) + 1, ia )
287  CALL pb_topget( ictxt, 'Broadcast', 'Rowwise', rowbtop )
288  CALL pb_topget( ictxt, 'Broadcast', 'Columnwise', colbtop )
289  CALL pb_topset( ictxt, 'Broadcast', 'Rowwise', ' ' )
290  CALL pb_topset( ictxt, 'Broadcast', 'Columnwise', 'D-ring' )
291 *
292 * Use blocked code initially
293 *
294  DO 20 i = il, in+1, -desca( mb_ )
295  ib = min( ia+m-i, desca( mb_ ) )
296  j = ja + i - ia
297 *
298 * Compute the complete orthogonal factorization of the current
299 * block A(i:i+ib-1,j:ja+n-1)
300 *
301  CALL pclatrz( ib, ja+n-j, l, a, i, j, desca, tau, work )
302 *
303  IF( i.GT.ia ) THEN
304 *
305 * Form the triangular factor of the block reflector
306 * H = H(i+ib-1) . . . H(i+1) H(i)
307 *
308  CALL pclarzt( 'Backward', 'Rowwise', l, ib, a, i, jm1,
309  $ desca, tau, work, work( ipw ) )
310 *
311 * Apply H to A(ia:i-1,j:ja+n-1) from the right
312 *
313  CALL pclarzb( 'Right', 'No transpose', 'Backward',
314  $ 'Rowwise', i-ia, ja+n-j, ib, l, a, i, jm1,
315  $ desca, work, a, ia, j, desca, work( ipw ) )
316  END IF
317 *
318  20 CONTINUE
319 *
320 * Use unblocked code to factor the last or only block
321 *
322  CALL pclatrz( in-ia+1, n, n-m, a, ia, ja, desca, tau, work )
323 *
324  CALL pb_topset( ictxt, 'Broadcast', 'Rowwise', rowbtop )
325  CALL pb_topset( ictxt, 'Broadcast', 'Columnwise', colbtop )
326 *
327  END IF
328 *
329  work( 1 ) = cmplx( real( lwmin ) )
330 *
331  RETURN
332 *
333 * End of PCTZRZF
334 *
335  END
cmplx
float cmplx[2]
Definition: pblas.h:132
max
#define max(A, B)
Definition: pcgemr.c:180
infog1l
subroutine infog1l(GINDX, NB, NPROCS, MYROC, ISRCPROC, LINDX, ROCSRC)
Definition: infog1l.f:3
pclarzb
subroutine pclarzb(SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, IV, JV, DESCV, T, C, IC, JC, DESCC, WORK)
Definition: pclarzb.f:3
pclarzt
subroutine pclarzt(DIRECT, STOREV, N, K, V, IV, JV, DESCV, TAU, T, WORK)
Definition: pclarzt.f:3
pchk1mat
subroutine pchk1mat(MA, MAPOS0, NA, NAPOS0, IA, JA, DESCA, DESCAPOS0, NEXTRA, EX, EXPOS, INFO)
Definition: pchkxmat.f:3
pclatrz
subroutine pclatrz(M, N, L, A, IA, JA, DESCA, TAU, WORK)
Definition: pclatrz.f:2
chk1mat
subroutine chk1mat(MA, MAPOS0, NA, NAPOS0, IA, JA, DESCA, DESCAPOS0, INFO)
Definition: chk1mat.f:3
pctzrzf
subroutine pctzrzf(M, N, A, IA, JA, DESCA, TAU, WORK, LWORK, INFO)
Definition: pctzrzf.f:3
pxerbla
subroutine pxerbla(ICTXT, SRNAME, INFO)
Definition: pxerbla.f:2
min
#define min(A, B)
Definition: pcgemr.c:181