ScaLAPACK 2.1  2.1 ScaLAPACK: Scalable Linear Algebra PACKage
pdgeequ.f
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1  SUBROUTINE pdgeequ( M, N, A, IA, JA, DESCA, R, C, ROWCND, COLCND,
2  \$ AMAX, 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 1, 1997
8 *
9 * .. Scalar Arguments ..
10  INTEGER IA, INFO, JA, M, N
11  DOUBLE PRECISION AMAX, COLCND, ROWCND
12 * ..
13 * .. Array Arguments ..
14  INTEGER DESCA( * )
15  DOUBLE PRECISION A( * ), C( * ), R( * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * PDGEEQU computes row and column scalings intended to equilibrate an
22 * M-by-N distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA:JA+N-1) and
23 * reduce its condition number. R returns the row scale factors and C
24 * the column scale factors, chosen to try to make the largest entry in
25 * each row and column of the distributed matrix B with elements
26 * B(i,j) = R(i) * A(i,j) * C(j) have absolute value 1.
27 *
28 * R(i) and C(j) are restricted to be between SMLNUM = smallest safe
29 * number and BIGNUM = largest safe number. Use of these scaling
30 * factors is not guaranteed to reduce the condition number of
31 * sub( A ) but works well in practice.
32 *
33 * Notes
34 * =====
35 *
36 * Each global data object is described by an associated description
37 * vector. This vector stores the information required to establish
38 * the mapping between an object element and its corresponding process
39 * and memory location.
40 *
41 * Let A be a generic term for any 2D block cyclicly distributed array.
42 * Such a global array has an associated description vector DESCA.
43 * In the following comments, the character _ should be read as
44 * "of the global array".
45 *
46 * NOTATION STORED IN EXPLANATION
47 * --------------- -------------- --------------------------------------
48 * DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
49 * DTYPE_A = 1.
50 * CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
51 * the BLACS process grid A is distribu-
52 * ted over. The context itself is glo-
53 * bal, but the handle (the integer
54 * value) may vary.
55 * M_A (global) DESCA( M_ ) The number of rows in the global
56 * array A.
57 * N_A (global) DESCA( N_ ) The number of columns in the global
58 * array A.
59 * MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
60 * the rows of the array.
61 * NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
62 * the columns of the array.
63 * RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
64 * row of the array A is distributed.
65 * CSRC_A (global) DESCA( CSRC_ ) The process column over which the
66 * first column of the array A is
67 * distributed.
68 * LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
69 * array. LLD_A >= MAX(1,LOCr(M_A)).
70 *
71 * Let K be the number of rows or columns of a distributed matrix,
72 * and assume that its process grid has dimension p x q.
73 * LOCr( K ) denotes the number of elements of K that a process
74 * would receive if K were distributed over the p processes of its
75 * process column.
76 * Similarly, LOCc( K ) denotes the number of elements of K that a
77 * process would receive if K were distributed over the q processes of
78 * its process row.
79 * The values of LOCr() and LOCc() may be determined via a call to the
80 * ScaLAPACK tool function, NUMROC:
81 * LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
82 * LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
83 * An upper bound for these quantities may be computed by:
84 * LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
85 * LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*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) DOUBLE PRECISION pointer into the local memory
99 * to an array of dimension ( LLD_A, LOCc(JA+N-1) ), the
100 * local pieces of the M-by-N distributed matrix whose
101 * equilibration factors are to be computed.
102 *
103 * IA (global input) INTEGER
104 * The row index in the global array A indicating the first
105 * row of sub( A ).
106 *
107 * JA (global input) INTEGER
108 * The column index in the global array A indicating the
109 * first column of sub( A ).
110 *
111 * DESCA (global and local input) INTEGER array of dimension DLEN_.
112 * The array descriptor for the distributed matrix A.
113 *
114 * R (local output) DOUBLE PRECISION array, dimension LOCr(M_A)
115 * If INFO = 0 or INFO > IA+M-1, R(IA:IA+M-1) contains the row
116 * scale factors for sub( A ). R is aligned with the distributed
117 * matrix A, and replicated across every process column. R is
118 * tied to the distributed matrix A.
119 *
120 * C (local output) DOUBLE PRECISION array, dimension LOCc(N_A)
121 * If INFO = 0, C(JA:JA+N-1) contains the column scale factors
122 * for sub( A ). C is aligned with the distributed matrix A, and
123 * replicated down every process row. C is tied to the distri-
124 * buted matrix A.
125 *
126 * ROWCND (global output) DOUBLE PRECISION
127 * If INFO = 0 or INFO > IA+M-1, ROWCND contains the ratio of
128 * the smallest R(i) to the largest R(i) (IA <= i <= IA+M-1).
129 * If ROWCND >= 0.1 and AMAX is neither too large nor too small,
130 * it is not worth scaling by R(IA:IA+M-1).
131 *
132 * COLCND (global output) DOUBLE PRECISION
133 * If INFO = 0, COLCND contains the ratio of the smallest C(j)
134 * to the largest C(j) (JA <= j <= JA+N-1). If COLCND >= 0.1, it
135 * is not worth scaling by C(JA:JA+N-1).
136 *
137 * AMAX (global output) DOUBLE PRECISION
138 * Absolute value of largest distributed matrix element. If
139 * AMAX is very close to overflow or very close to underflow,
140 * the matrix should be scaled.
141 *
142 * INFO (global output) INTEGER
143 * = 0: successful exit
144 * < 0: If the i-th argument is an array and the j-entry had
145 * an illegal value, then INFO = -(i*100+j), if the i-th
146 * argument is a scalar and had an illegal value, then
147 * INFO = -i.
148 * > 0: If INFO = i, and i is
149 * <= M: the i-th row of the distributed matrix sub( A )
150 * is exactly zero,
151 * > M: the (i-M)-th column of the distributed
152 * matrix sub( A ) is exactly zero.
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  DOUBLE PRECISION ONE, ZERO
163  parameter( one = 1.0d+0, zero = 0.0d+0 )
164 * ..
165 * .. Local Scalars ..
166  CHARACTER COLCTOP, ROWCTOP
167  INTEGER I, IACOL, IAROW, ICOFF, ICTXT, IDUMM, IIA,
168  \$ ioffa, iroff, j, jja, lda, mp, mycol, myrow,
169  \$ npcol, nprow, nq
170  DOUBLE PRECISION BIGNUM, RCMAX, RCMIN, SMLNUM
171 * ..
172 * .. Local Arrays ..
173  INTEGER DESCC( DLEN_ ), DESCR( DLEN_ )
174 * ..
175 * .. External Subroutines ..
176  EXTERNAL blacs_gridinfo, chk1mat, descset, dgamn2d,
177  \$ dgamx2d, igamx2d, infog2l, pchk1mat, pb_topget,
178  \$ pxerbla
179 * ..
180 * .. External Functions ..
181  INTEGER INDXL2G, NUMROC
182  DOUBLE PRECISION PDLAMCH
183  EXTERNAL indxl2g, numroc, pdlamch
184 * ..
185 * .. Intrinsic Functions ..
186  INTRINSIC abs, max, min, mod
187 * ..
188 * .. Executable Statements ..
189 *
190 * Get grid parameters
191 *
192  ictxt = desca( ctxt_ )
193  CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
194 *
195 * Test the input parameters.
196 *
197  info = 0
198  IF( nprow.EQ.-1 ) THEN
199  info = -(600+ctxt_)
200  ELSE
201  CALL chk1mat( m, 1, n, 2, ia, ja, desca, 6, info )
202  CALL pchk1mat( m, 1, n, 2, ia, ja, desca, 6, 0, idumm, idumm,
203  \$ info )
204  END IF
205 *
206  IF( info.NE.0 ) THEN
207  CALL pxerbla( ictxt, 'PDGEEQU', -info )
208  RETURN
209  END IF
210 *
211 * Quick return if possible
212 *
213  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
214  rowcnd = one
215  colcnd = one
216  amax = zero
217  RETURN
218  END IF
219 *
220  CALL pb_topget( ictxt, 'Combine', 'Rowwise', rowctop )
221  CALL pb_topget( ictxt, 'Combine', 'Columnwise', colctop )
222 *
223 * Get machine constants and local indexes.
224 *
225  smlnum = pdlamch( ictxt, 'S' )
226  bignum = one / smlnum
227  CALL infog2l( ia, ja, desca, nprow, npcol, myrow, mycol, iia, jja,
228  \$ iarow, iacol )
229  iroff = mod( ia-1, desca( mb_ ) )
230  icoff = mod( ja-1, desca( nb_ ) )
231  mp = numroc( m+iroff, desca( mb_ ), myrow, iarow, nprow )
232  nq = numroc( n+icoff, desca( nb_ ), mycol, iacol, npcol )
233  IF( myrow.EQ.iarow )
234  \$ mp = mp - iroff
235  IF( mycol.EQ.iacol )
236  \$ nq = nq - icoff
237  lda = desca( lld_ )
238 *
239 * Assign descriptors for R and C arrays
240 *
241  CALL descset( descr, m, 1, desca( mb_ ), 1, 0, 0, ictxt,
242  \$ max( 1, mp ) )
243  CALL descset( descc, 1, n, 1, desca( nb_ ), 0, 0, ictxt, 1 )
244 *
245 * Compute row scale factors.
246 *
247  DO 10 i = iia, iia+mp-1
248  r( i ) = zero
249  10 CONTINUE
250 *
251 * Find the maximum element in each row.
252 *
253  ioffa = (jja-1)*lda
254  DO 30 j = jja, jja+nq-1
255  DO 20 i = iia, iia+mp-1
256  r( i ) = max( r( i ), abs( a( ioffa + i ) ) )
257  20 CONTINUE
258  ioffa = ioffa + lda
259  30 CONTINUE
260  CALL dgamx2d( ictxt, 'Rowwise', rowctop, mp, 1, r( iia ),
261  \$ max( 1, mp ), idumm, idumm, -1, -1, mycol )
262 *
263 * Find the maximum and minimum scale factors.
264 *
265  rcmin = bignum
266  rcmax = zero
267  DO 40 i = iia, iia+mp-1
268  rcmax = max( rcmax, r( i ) )
269  rcmin = min( rcmin, r( i ) )
270  40 CONTINUE
271  CALL dgamx2d( ictxt, 'Columnwise', colctop, 1, 1, rcmax, 1, idumm,
272  \$ idumm, -1, -1, mycol )
273  CALL dgamn2d( ictxt, 'Columnwise', colctop, 1, 1, rcmin, 1, idumm,
274  \$ idumm, -1, -1, mycol )
275  amax = rcmax
276 *
277  IF( rcmin.EQ.zero ) THEN
278 *
279 * Find the first zero scale factor and return an error code.
280 *
281  DO 50 i = iia, iia+mp-1
282  IF( r( i ).EQ.zero .AND. info.EQ.0 )
283  \$ info = indxl2g( i, desca( mb_ ), myrow, desca( rsrc_ ),
284  \$ nprow ) - ia + 1
285  50 CONTINUE
286  CALL igamx2d( ictxt, 'Columnwise', colctop, 1, 1, info, 1,
287  \$ idumm, idumm, -1, -1, mycol )
288  IF( info.NE.0 )
289  \$ RETURN
290  ELSE
291 *
292 * Invert the scale factors.
293 *
294  DO 60 i = iia, iia+mp-1
295  r( i ) = one / min( max( r( i ), smlnum ), bignum )
296  60 CONTINUE
297 *
298 * Compute ROWCND = min(R(I)) / max(R(I))
299 *
300  rowcnd = max( rcmin, smlnum ) / min( rcmax, bignum )
301 *
302  END IF
303 *
304 * Compute column scale factors
305 *
306  DO 70 j = jja, jja+nq-1
307  c( j ) = zero
308  70 CONTINUE
309 *
310 * Find the maximum element in each column,
311 * assuming the row scaling computed above.
312 *
313  ioffa = (jja-1)*lda
314  DO 90 j = jja, jja+nq-1
315  DO 80 i = iia, iia+mp-1
316  c( j ) = max( c( j ), abs( a( ioffa + i ) )*r( i ) )
317  80 CONTINUE
318  ioffa = ioffa + lda
319  90 CONTINUE
320  CALL dgamx2d( ictxt, 'Columnwise', colctop, 1, nq, c( jja ),
321  \$ 1, idumm, idumm, -1, -1, mycol )
322 *
323 * Find the maximum and minimum scale factors.
324 *
325  rcmin = bignum
326  rcmax = zero
327  DO 100 j = jja, jja+nq-1
328  rcmin = min( rcmin, c( j ) )
329  rcmax = max( rcmax, c( j ) )
330  100 CONTINUE
331  CALL dgamx2d( ictxt, 'Columnwise', colctop, 1, 1, rcmax, 1, idumm,
332  \$ idumm, -1, -1, mycol )
333  CALL dgamn2d( ictxt, 'Columnwise', colctop, 1, 1, rcmin, 1, idumm,
334  \$ idumm, -1, -1, mycol )
335 *
336  IF( rcmin.EQ.zero ) THEN
337 *
338 * Find the first zero scale factor and return an error code.
339 *
340  DO 110 j = jja, jja+nq-1
341  IF( c( j ).EQ.zero .AND. info.EQ.0 )
342  \$ info = m + indxl2g( j, desca( nb_ ), mycol,
343  \$ desca( csrc_ ), npcol ) - ja + 1
344  110 CONTINUE
345  CALL igamx2d( ictxt, 'Columnwise', colctop, 1, 1, info, 1,
346  \$ idumm, idumm, -1, -1, mycol )
347  IF( info.NE.0 )
348  \$ RETURN
349  ELSE
350 *
351 * Invert the scale factors.
352 *
353  DO 120 j = jja, jja+nq-1
354  c( j ) = one / min( max( c( j ), smlnum ), bignum )
355  120 CONTINUE
356 *
357 * Compute COLCND = min(C(J)) / max(C(J))
358 *
359  colcnd = max( rcmin, smlnum ) / min( rcmax, bignum )
360 *
361  END IF
362 *
363  RETURN
364 *
365 * End of PDGEEQU
366 *
367  END
max
#define max(A, B)
Definition: pcgemr.c:180
infog2l
subroutine infog2l(GRINDX, GCINDX, DESC, NPROW, NPCOL, MYROW, MYCOL, LRINDX, LCINDX, RSRC, CSRC)
Definition: infog2l.f:3
pdgeequ
subroutine pdgeequ(M, N, A, IA, JA, DESCA, R, C, ROWCND, COLCND, AMAX, INFO)
Definition: pdgeequ.f:3
pchk1mat
subroutine pchk1mat(MA, MAPOS0, NA, NAPOS0, IA, JA, DESCA, DESCAPOS0, NEXTRA, EX, EXPOS, INFO)
Definition: pchkxmat.f:3
descset
subroutine descset(DESC, M, N, MB, NB, IRSRC, ICSRC, ICTXT, LLD)
Definition: descset.f:3
chk1mat
subroutine chk1mat(MA, MAPOS0, NA, NAPOS0, IA, JA, DESCA, DESCAPOS0, INFO)
Definition: chk1mat.f:3
pxerbla
subroutine pxerbla(ICTXT, SRNAME, INFO)
Definition: pxerbla.f:2
min
#define min(A, B)
Definition: pcgemr.c:181