ScaLAPACK 2.1  2.1
ScaLAPACK: Scalable Linear Algebra PACKage
pzgetrf.f
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1  SUBROUTINE pzgetrf( M, N, A, IA, JA, DESCA, IPIV, INFO )
2 *
3 * -- ScaLAPACK routine (version 1.7) --
4 * University of Tennessee, Knoxville, Oak Ridge National Laboratory,
5 * and University of California, Berkeley.
6 * May 25, 2001
7 *
8 * .. Scalar Arguments ..
9  INTEGER IA, INFO, JA, M, N
10 * ..
11 * .. Array Arguments ..
12  INTEGER DESCA( * ), IPIV( * )
13  COMPLEX*16 A( * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * PZGETRF computes an LU factorization of a general M-by-N distributed
20 * matrix sub( A ) = (IA:IA+M-1,JA:JA+N-1) using partial pivoting with
21 * row interchanges.
22 *
23 * The factorization has the form sub( A ) = P * L * U, where P is a
24 * permutation matrix, L is lower triangular with unit diagonal ele-
25 * ments (lower trapezoidal if m > n), and U is upper triangular
26 * (upper trapezoidal if m < n). L and U are stored in sub( A ).
27 *
28 * This is the right-looking Parallel Level 3 BLAS version of the
29 * algorithm.
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 * This routine requires square block decomposition ( MB_A = NB_A ).
86 *
87 * Arguments
88 * =========
89 *
90 * M (global input) INTEGER
91 * The number of rows to be operated on, i.e. the number of rows
92 * of the distributed submatrix sub( A ). M >= 0.
93 *
94 * N (global input) INTEGER
95 * The number of columns to be operated on, i.e. the number of
96 * columns of the distributed submatrix sub( A ). N >= 0.
97 *
98 * A (local input/local output) COMPLEX*16 pointer into the
99 * local memory to an array of dimension (LLD_A, LOCc(JA+N-1)).
100 * On entry, this array contains the local pieces of the M-by-N
101 * distributed matrix sub( A ) to be factored. On exit, this
102 * array contains the local pieces of the factors L and U from
103 * the factorization sub( A ) = P*L*U; the unit diagonal ele-
104 * ments of L are not stored.
105 *
106 * IA (global input) INTEGER
107 * The row index in the global array A indicating the first
108 * row of sub( A ).
109 *
110 * JA (global input) INTEGER
111 * The column index in the global array A indicating the
112 * first column of sub( A ).
113 *
114 * DESCA (global and local input) INTEGER array of dimension DLEN_.
115 * The array descriptor for the distributed matrix A.
116 *
117 * IPIV (local output) INTEGER array, dimension ( LOCr(M_A)+MB_A )
118 * This array contains the pivoting information.
119 * IPIV(i) -> The global row local row i was swapped with.
120 * This array is tied to the distributed matrix A.
121 *
122 * INFO (global output) INTEGER
123 * = 0: successful exit
124 * < 0: If the i-th argument is an array and the j-entry had
125 * an illegal value, then INFO = -(i*100+j), if the i-th
126 * argument is a scalar and had an illegal value, then
127 * INFO = -i.
128 * > 0: If INFO = K, U(IA+K-1,JA+K-1) is exactly zero.
129 * The factorization has been completed, but the factor U
130 * is exactly singular, and division by zero will occur if
131 * it is used to solve a system of equations.
132 *
133 * =====================================================================
134 *
135 * .. Parameters ..
136  INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
137  $ LLD_, MB_, M_, NB_, N_, RSRC_
138  parameter( block_cyclic_2d = 1, dlen_ = 9, dtype_ = 1,
139  $ ctxt_ = 2, m_ = 3, n_ = 4, mb_ = 5, nb_ = 6,
140  $ rsrc_ = 7, csrc_ = 8, lld_ = 9 )
141  COMPLEX*16 ONE
142  parameter( one = 1.0d+0 )
143 * ..
144 * .. Local Scalars ..
145  CHARACTER COLBTOP, COLCTOP, ROWBTOP
146  INTEGER I, ICOFF, ICTXT, IINFO, IN, IROFF, J, JB, JN,
147  $ MN, MYCOL, MYROW, NPCOL, NPROW
148 * ..
149 * .. Local Arrays ..
150  INTEGER IDUM1( 1 ), IDUM2( 1 )
151 * ..
152 * .. External Subroutines ..
153  EXTERNAL blacs_gridinfo, chk1mat, igamn2d, pchk1mat,
154  $ pb_topget, pb_topset, pxerbla, pzgemm, pzgetf2,
155  $ pzlaswp, pztrsm
156 * ..
157 * .. External Functions ..
158  INTEGER ICEIL
159  EXTERNAL iceil
160 * ..
161 * .. Intrinsic Functions ..
162  INTRINSIC min, mod
163 * ..
164 * .. Executable Statements ..
165 *
166 * Get grid parameters
167 *
168  ictxt = desca( ctxt_ )
169  CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
170 *
171 * Test the input parameters
172 *
173  info = 0
174  IF( nprow.EQ.-1 ) THEN
175  info = -(600+ctxt_)
176  ELSE
177  CALL chk1mat( m, 1, n, 2, ia, ja, desca, 6, info )
178  IF( info.EQ.0 ) THEN
179  iroff = mod( ia-1, desca( mb_ ) )
180  icoff = mod( ja-1, desca( nb_ ) )
181  IF( iroff.NE.0 ) THEN
182  info = -4
183  ELSE IF( icoff.NE.0 ) THEN
184  info = -5
185  ELSE IF( desca( mb_ ).NE.desca( nb_ ) ) THEN
186  info = -(600+nb_)
187  END IF
188  END IF
189  CALL pchk1mat( m, 1, n, 2, ia, ja, desca, 6, 0, idum1,
190  $ idum2, info )
191  END IF
192 *
193  IF( info.NE.0 ) THEN
194  CALL pxerbla( ictxt, 'PZGETRF', -info )
195  RETURN
196  END IF
197 *
198 * Quick return if possible
199 *
200  IF( desca( m_ ).EQ.1 ) THEN
201  ipiv( 1 ) = 1
202  RETURN
203  ELSE IF( m.EQ.0 .OR. n.EQ.0 ) THEN
204  RETURN
205  END IF
206 *
207 * Split-ring topology for the communication along process rows
208 *
209  CALL pb_topget( ictxt, 'Broadcast', 'Rowwise', rowbtop )
210  CALL pb_topget( ictxt, 'Broadcast', 'Columnwise', colbtop )
211  CALL pb_topget( ictxt, 'Combine', 'Columnwise', colctop )
212  CALL pb_topset( ictxt, 'Broadcast', 'Rowwise', 'S-ring' )
213  CALL pb_topset( ictxt, 'Broadcast', 'Columnwise', ' ' )
214  CALL pb_topset( ictxt, 'Combine', 'Columnwise', ' ' )
215 *
216 * Handle the first block of columns separately
217 *
218  mn = min( m, n )
219  in = min( iceil( ia, desca( mb_ ) )*desca( mb_ ), ia+m-1 )
220  jn = min( iceil( ja, desca( nb_ ) )*desca( nb_ ), ja+mn-1 )
221  jb = jn - ja + 1
222 *
223 * Factor diagonal and subdiagonal blocks and test for exact
224 * singularity.
225 *
226  CALL pzgetf2( m, jb, a, ia, ja, desca, ipiv, info )
227 *
228  IF( jb+1.LE.n ) THEN
229 *
230 * Apply interchanges to columns JN+1:JA+N-1.
231 *
232  CALL pzlaswp( 'Forward', 'Rows', n-jb, a, ia, jn+1, desca,
233  $ ia, in, ipiv )
234 *
235 * Compute block row of U.
236 *
237  CALL pztrsm( 'Left', 'Lower', 'No transpose', 'Unit', jb,
238  $ n-jb, one, a, ia, ja, desca, a, ia, jn+1, desca )
239 *
240  IF( jb+1.LE.m ) THEN
241 *
242 * Update trailing submatrix.
243 *
244  CALL pzgemm( 'No transpose', 'No transpose', m-jb, n-jb, jb,
245  $ -one, a, in+1, ja, desca, a, ia, jn+1, desca,
246  $ one, a, in+1, jn+1, desca )
247 *
248  END IF
249  END IF
250 *
251 * Loop over the remaining blocks of columns.
252 *
253  DO 10 j = jn+1, ja+mn-1, desca( nb_ )
254  jb = min( mn-j+ja, desca( nb_ ) )
255  i = ia + j - ja
256 *
257 * Factor diagonal and subdiagonal blocks and test for exact
258 * singularity.
259 *
260  CALL pzgetf2( m-j+ja, jb, a, i, j, desca, ipiv, iinfo )
261 *
262  IF( info.EQ.0 .AND. iinfo.GT.0 )
263  $ info = iinfo + j - ja
264 *
265 * Apply interchanges to columns JA:J-JA.
266 *
267  CALL pzlaswp( 'Forward', 'Rowwise', j-ja, a, ia, ja, desca,
268  $ i, i+jb-1, ipiv )
269 *
270  IF( j-ja+jb+1.LE.n ) THEN
271 *
272 * Apply interchanges to columns J+JB:JA+N-1.
273 *
274  CALL pzlaswp( 'Forward', 'Rowwise', n-j-jb+ja, a, ia, j+jb,
275  $ desca, i, i+jb-1, ipiv )
276 *
277 * Compute block row of U.
278 *
279  CALL pztrsm( 'Left', 'Lower', 'No transpose', 'Unit', jb,
280  $ n-j-jb+ja, one, a, i, j, desca, a, i, j+jb,
281  $ desca )
282 *
283  IF( j-ja+jb+1.LE.m ) THEN
284 *
285 * Update trailing submatrix.
286 *
287  CALL pzgemm( 'No transpose', 'No transpose', m-j-jb+ja,
288  $ n-j-jb+ja, jb, -one, a, i+jb, j, desca, a,
289  $ i, j+jb, desca, one, a, i+jb, j+jb, desca )
290 *
291  END IF
292  END IF
293 *
294  10 CONTINUE
295 *
296  IF( info.EQ.0 )
297  $ info = mn + 1
298  CALL igamn2d( ictxt, 'Rowwise', ' ', 1, 1, info, 1, idum1, idum2,
299  $ -1, -1, mycol )
300  IF( info.EQ.mn+1 )
301  $ info = 0
302 *
303  CALL pb_topset( ictxt, 'Broadcast', 'Rowwise', rowbtop )
304  CALL pb_topset( ictxt, 'Broadcast', 'Columnwise', colbtop )
305  CALL pb_topset( ictxt, 'Combine', 'Columnwise', colctop )
306 *
307  RETURN
308 *
309 * End of PZGETRF
310 *
311  END
pzlaswp
subroutine pzlaswp(DIREC, ROWCOL, N, A, IA, JA, DESCA, K1, K2, IPIV)
Definition: pzlaswp.f:3
pzgetf2
subroutine pzgetf2(M, N, A, IA, JA, DESCA, IPIV, INFO)
Definition: pzgetf2.f:2
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
pzgetrf
subroutine pzgetrf(M, N, A, IA, JA, DESCA, IPIV, INFO)
Definition: pzgetrf.f:2
pxerbla
subroutine pxerbla(ICTXT, SRNAME, INFO)
Definition: pxerbla.f:2
min
#define min(A, B)
Definition: pcgemr.c:181