ScaLAPACK 2.1  2.1
ScaLAPACK: Scalable Linear Algebra PACKage
pdgeqlf.f
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1  SUBROUTINE pdgeqlf( 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  DOUBLE PRECISION A( * ), TAU( * ), WORK( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * PDGEQLF computes a QL factorization of a real distributed M-by-N
21 * matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = Q * L.
22 *
23 * Notes
24 * =====
25 *
26 * Each global data object is described by an associated description
27 * vector. This vector stores the information required to establish
28 * the mapping between an object element and its corresponding process
29 * and memory location.
30 *
31 * Let A be a generic term for any 2D block cyclicly distributed array.
32 * Such a global array has an associated description vector DESCA.
33 * In the following comments, the character _ should be read as
34 * "of the global array".
35 *
36 * NOTATION STORED IN EXPLANATION
37 * --------------- -------------- --------------------------------------
38 * DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
39 * DTYPE_A = 1.
40 * CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
41 * the BLACS process grid A is distribu-
42 * ted over. The context itself is glo-
43 * bal, but the handle (the integer
44 * value) may vary.
45 * M_A (global) DESCA( M_ ) The number of rows in the global
46 * array A.
47 * N_A (global) DESCA( N_ ) The number of columns in the global
48 * array A.
49 * MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
50 * the rows of the array.
51 * NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
52 * the columns of the array.
53 * RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
54 * row of the array A is distributed.
55 * CSRC_A (global) DESCA( CSRC_ ) The process column over which the
56 * first column of the array A is
57 * distributed.
58 * LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
59 * array. LLD_A >= MAX(1,LOCr(M_A)).
60 *
61 * Let K be the number of rows or columns of a distributed matrix,
62 * and assume that its process grid has dimension p x q.
63 * LOCr( K ) denotes the number of elements of K that a process
64 * would receive if K were distributed over the p processes of its
65 * process column.
66 * Similarly, LOCc( K ) denotes the number of elements of K that a
67 * process would receive if K were distributed over the q processes of
68 * its process row.
69 * The values of LOCr() and LOCc() may be determined via a call to the
70 * ScaLAPACK tool function, NUMROC:
71 * LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
72 * LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
73 * An upper bound for these quantities may be computed by:
74 * LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
75 * LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
76 *
77 * Arguments
78 * =========
79 *
80 * M (global input) INTEGER
81 * The number of rows to be operated on, i.e. the number of rows
82 * of the distributed submatrix sub( A ). M >= 0.
83 *
84 * N (global input) INTEGER
85 * The number of columns to be operated on, i.e. the number of
86 * columns of the distributed submatrix sub( A ). N >= 0.
87 *
88 * A (local input/local output) DOUBLE PRECISION pointer into the
89 * local memory to an array of dimension (LLD_A, LOCc(JA+N-1)).
90 * On entry, the local pieces of the M-by-N distributed matrix
91 * sub( A ) which is to be factored. On exit, if M >= N, the
92 * lower triangle of the distributed submatrix
93 * A( IA+M-N:IA+M-1, JA:JA+N-1 ) contains the N-by-N lower
94 * triangular matrix L; if M <= N, the elements on and below
95 * the (N-M)-th superdiagonal contain the M by N lower
96 * trapezoidal matrix L; the remaining elements, with the
97 * array TAU, represent the orthogonal matrix Q as a product of
98 * elementary reflectors (see Further Details).
99 *
100 * IA (global input) INTEGER
101 * The row index in the global array A indicating the first
102 * row of sub( A ).
103 *
104 * JA (global input) INTEGER
105 * The column index in the global array A indicating the
106 * first column of sub( A ).
107 *
108 * DESCA (global and local input) INTEGER array of dimension DLEN_.
109 * The array descriptor for the distributed matrix A.
110 *
111 * TAU (local output) DOUBLE PRECISION array, dimension LOCc(JA+N-1)
112 * This array contains the scalar factors of the elementary
113 * reflectors. TAU is tied to the distributed matrix A.
114 *
115 * WORK (local workspace/local output) DOUBLE PRECISION array,
116 * dimension (LWORK)
117 * On exit, WORK(1) returns the minimal and optimal LWORK.
118 *
119 * LWORK (local or global input) INTEGER
120 * The dimension of the array WORK.
121 * LWORK is local input and must be at least
122 * LWORK >= NB_A * ( Mp0 + Nq0 + NB_A ), where
123 *
124 * IROFF = MOD( IA-1, MB_A ), ICOFF = MOD( JA-1, NB_A ),
125 * IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ),
126 * IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ),
127 * Mp0 = NUMROC( M+IROFF, MB_A, MYROW, IAROW, NPROW ),
128 * Nq0 = NUMROC( N+ICOFF, NB_A, MYCOL, IACOL, NPCOL ),
129 *
130 * and NUMROC, INDXG2P are ScaLAPACK tool functions;
131 * MYROW, MYCOL, NPROW and NPCOL can be determined by calling
132 * the subroutine BLACS_GRIDINFO.
133 *
134 * If LWORK = -1, then LWORK is global input and a workspace
135 * query is assumed; the routine only calculates the minimum
136 * and optimal size for all work arrays. Each of these
137 * values is returned in the first entry of the corresponding
138 * work array, and no error message is issued by PXERBLA.
139 *
140 * INFO (global output) INTEGER
141 * = 0: successful exit
142 * < 0: If the i-th argument is an array and the j-entry had
143 * an illegal value, then INFO = -(i*100+j), if the i-th
144 * argument is a scalar and had an illegal value, then
145 * INFO = -i.
146 *
147 * Further Details
148 * ===============
149 *
150 * The matrix Q is represented as a product of elementary reflectors
151 *
152 * Q = H(ja+k-1) . . . H(ja+1) H(ja), where k = min(m,n).
153 *
154 * Each H(i) has the form
155 *
156 * H(i) = I - tau * v * v'
157 *
158 * where tau is a real scalar, and v is a real vector with
159 * v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
160 * A(ia:ia+m-k+i-2,ja+n-k+i-1), and tau in TAU(ja+n-k+i-1).
161 *
162 * =====================================================================
163 *
164 * .. Parameters ..
165  INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
166  $ lld_, mb_, m_, nb_, n_, rsrc_
167  parameter( block_cyclic_2d = 1, dlen_ = 9, dtype_ = 1,
168  $ ctxt_ = 2, m_ = 3, n_ = 4, mb_ = 5, nb_ = 6,
169  $ rsrc_ = 7, csrc_ = 8, lld_ = 9 )
170 * ..
171 * .. Local Scalars ..
172  LOGICAL LQUERY
173  CHARACTER COLBTOP, ROWBTOP
174  INTEGER IACOL, IAROW, IINFO, ICTXT, IPW, J, JB, JL, JN,
175  $ k, lwmin, mp0, mu, mycol, myrow, npcol, nprow,
176  $ nq0, nu
177 * ..
178 * .. Local Arrays ..
179  INTEGER IDUM1( 1 ), IDUM2( 1 )
180 * ..
181 * .. External Subroutines ..
182  EXTERNAL blacs_gridinfo, chk1mat, pchk1mat, pdgeql2,
183  $ pdlarfb, pdlarft, pb_topget, pb_topset,
184  $ pxerbla
185 * ..
186 * .. External Functions ..
187  INTEGER ICEIL, INDXG2P, NUMROC
188  EXTERNAL iceil, indxg2p, numroc
189 * ..
190 * .. Intrinsic Functions ..
191  INTRINSIC dble, min, mod
192 * ..
193 * .. Executable Statements ..
194 *
195 * Get grid parameters
196 *
197  ictxt = desca( ctxt_ )
198  CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
199 *
200 * Test the input parameters
201 *
202  info = 0
203  IF( nprow.EQ.-1 ) THEN
204  info = -(600+ctxt_)
205  ELSE
206  CALL chk1mat( m, 1, n, 2, ia, ja, desca, 6, info )
207  IF( info.EQ.0 ) THEN
208  iarow = indxg2p( ia, desca( mb_ ), myrow, desca( rsrc_ ),
209  $ nprow )
210  iacol = indxg2p( ja, desca( nb_ ), mycol, desca( csrc_ ),
211  $ npcol )
212  mp0 = numroc( m+mod( ia-1, desca( mb_ ) ), desca( mb_ ),
213  $ myrow, iarow, nprow )
214  nq0 = numroc( n+mod( ja-1, desca( nb_ ) ), desca( nb_ ),
215  $ mycol, iacol, npcol )
216  lwmin = desca( nb_ ) * ( mp0 + nq0 + desca( nb_ ) )
217 *
218  work( 1 ) = dble( lwmin )
219  lquery = ( lwork.EQ.-1 )
220  IF( lwork.LT.lwmin .AND. .NOT.lquery )
221  $ info = -9
222  END IF
223  IF( lwork.EQ.-1 ) THEN
224  idum1( 1 ) = -1
225  ELSE
226  idum1( 1 ) = 1
227  END IF
228  idum2( 1 ) = 9
229  CALL pchk1mat( m, 1, n, 2, ia, ja, desca, 6, 1, idum1, idum2,
230  $ info )
231  END IF
232 *
233  IF( info.NE.0 ) THEN
234  CALL pxerbla( ictxt, 'PDGEQLF', -info )
235  RETURN
236  ELSE IF( lquery ) THEN
237  RETURN
238  END IF
239 *
240 * Quick return if possible
241 *
242  IF( m.EQ.0 .OR. n.EQ.0 )
243  $ RETURN
244 *
245  k = min( m, n )
246  ipw = desca( nb_ ) * desca( nb_ ) + 1
247  jn = min( iceil( ja+n-k, desca( nb_ ) ) * desca( nb_ ), ja+n-1 )
248  jl = max( ( (ja+n-2) / desca( nb_ ) ) * desca( nb_ ) + 1, ja )
249  CALL pb_topget( ictxt, 'Broadcast', 'Rowwise', rowbtop )
250  CALL pb_topget( ictxt, 'Broadcast', 'Columnwise', colbtop )
251  CALL pb_topset( ictxt, 'Broadcast', 'Rowwise', 'D-ring' )
252  CALL pb_topset( ictxt, 'Broadcast', 'Columnwise', ' ' )
253 *
254  IF( jl.GE.jn+1 ) THEN
255 *
256 * Use blocked code initially
257 *
258  DO 10 j = jl, jn+1, -desca( nb_ )
259  jb = min( ja+n-j, desca( nb_ ) )
260 *
261 * Compute the QL factorization of the current block
262 * A(ia:ia+m-n+j+jb-ja-1,j:j+jb-1)
263 *
264  CALL pdgeql2( m-n+j+jb-ja, jb, a, ia, j, desca, tau, work,
265  $ lwork, iinfo )
266 *
267  IF( j.GT.ja ) THEN
268 *
269 * Form the triangular factor of the block reflector
270 * H = H(j+jb-1) . . . H(j+1) H(j)
271 *
272  CALL pdlarft( 'Backward', 'Columnwise', m-n+j+jb-ja, jb,
273  $ a, ia, j, desca, tau, work, work( ipw ) )
274 *
275 * Apply H' to A(ia:ia+m-n+j+jb-ja-1,ja:j-1) from the
276 * left
277 *
278  CALL pdlarfb( 'Left', 'Transpose', 'Backward',
279  $ 'Columnwise', m-n+j+jb-ja, j-ja, jb, a, ia,
280  $ j, desca, work, a, ia, ja, desca,
281  $ work( ipw ) )
282  END IF
283 *
284  10 CONTINUE
285 *
286  mu = m - n + jn - ja + 1
287  nu = jn - ja + 1
288 *
289  ELSE
290 *
291  mu = m
292  nu = n
293 *
294  END IF
295 *
296 * Use unblocked code to factor the last or only block
297 *
298  IF( mu.GT.0 .AND. nu.GT.0 )
299  $ CALL pdgeql2( mu, nu, a, ia, ja, desca, tau, work, lwork,
300  $ iinfo )
301 *
302  CALL pb_topset( ictxt, 'Broadcast', 'Rowwise', rowbtop )
303  CALL pb_topset( ictxt, 'Broadcast', 'Columnwise', colbtop )
304 *
305  work( 1 ) = dble( lwmin )
306 *
307  RETURN
308 *
309 * End of PDGEQLF
310 *
311  END
max
#define max(A, B)
Definition: pcgemr.c:180
pdgeql2
subroutine pdgeql2(M, N, A, IA, JA, DESCA, TAU, WORK, LWORK, INFO)
Definition: pdgeql2.f:3
pdlarft
subroutine pdlarft(DIRECT, STOREV, N, K, V, IV, JV, DESCV, TAU, T, WORK)
Definition: pdlarft.f:3
pdgeqlf
subroutine pdgeqlf(M, N, A, IA, JA, DESCA, TAU, WORK, LWORK, INFO)
Definition: pdgeqlf.f:3
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
pdlarfb
subroutine pdlarfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, IV, JV, DESCV, T, C, IC, JC, DESCC, WORK)
Definition: pdlarfb.f:3
pxerbla
subroutine pxerbla(ICTXT, SRNAME, INFO)
Definition: pxerbla.f:2
min
#define min(A, B)
Definition: pcgemr.c:181