ScaLAPACK 2.1  2.1
ScaLAPACK: Scalable Linear Algebra PACKage
pcdttrs.f
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1  SUBROUTINE pcdttrs( TRANS, N, NRHS, DL, D, DU, JA, DESCA, B, IB,
2  $ DESCB, AF, LAF, WORK, LWORK, INFO )
3 *
4 *
5 *
6 * -- ScaLAPACK routine (version 1.7) --
7 * University of Tennessee, Knoxville, Oak Ridge National Laboratory,
8 * and University of California, Berkeley.
9 * August 7, 2001
10 *
11 * .. Scalar Arguments ..
12  CHARACTER TRANS
13  INTEGER IB, INFO, JA, LAF, LWORK, N, NRHS
14 * ..
15 * .. Array Arguments ..
16  INTEGER DESCA( * ), DESCB( * )
17  COMPLEX AF( * ), B( * ), D( * ), DL( * ), DU( * ),
18  $ work( * )
19 * ..
20 *
21 *
22 * Purpose
23 * =======
24 *
25 * PCDTTRS solves a system of linear equations
26 *
27 * A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS)
28 * or
29 * A(1:N, JA:JA+N-1)' * X = B(IB:IB+N-1, 1:NRHS)
30 *
31 * where A(1:N, JA:JA+N-1) is the matrix used to produce the factors
32 * stored in A(1:N,JA:JA+N-1) and AF by PCDTTRF.
33 * A(1:N, JA:JA+N-1) is an N-by-N complex
34 * tridiagonal diagonally dominant-like distributed
35 * matrix.
36 *
37 * Routine PCDTTRF MUST be called first.
38 *
39 * =====================================================================
40 *
41 * Arguments
42 * =========
43 *
44 *
45 * TRANS (global input) CHARACTER
46 * = 'N': Solve with A(1:N, JA:JA+N-1);
47 * = 'C': Solve with conjugate_transpose( A(1:N, JA:JA+N-1) );
48 *
49 * N (global input) INTEGER
50 * The number of rows and columns to be operated on, i.e. the
51 * order of the distributed submatrix A(1:N, JA:JA+N-1). N >= 0.
52 *
53 * NRHS (global input) INTEGER
54 * The number of right hand sides, i.e., the number of columns
55 * of the distributed submatrix B(IB:IB+N-1, 1:NRHS).
56 * NRHS >= 0.
57 *
58 * DL (local input/local output) COMPLEX pointer to local
59 * part of global vector storing the lower diagonal of the
60 * matrix. Globally, DL(1) is not referenced, and DL must be
61 * aligned with D.
62 * Must be of size >= DESCA( NB_ ).
63 * On exit, this array contains information containing the
64 * factors of the matrix.
65 *
66 * D (local input/local output) COMPLEX pointer to local
67 * part of global vector storing the main diagonal of the
68 * matrix.
69 * On exit, this array contains information containing the
70 * factors of the matrix.
71 * Must be of size >= DESCA( NB_ ).
72 *
73 * DU (local input/local output) COMPLEX pointer to local
74 * part of global vector storing the upper diagonal of the
75 * matrix. Globally, DU(n) is not referenced, and DU must be
76 * aligned with D.
77 * On exit, this array contains information containing the
78 * factors of the matrix.
79 * Must be of size >= DESCA( NB_ ).
80 *
81 * JA (global input) INTEGER
82 * The index in the global array A that points to the start of
83 * the matrix to be operated on (which may be either all of A
84 * or a submatrix of A).
85 *
86 * DESCA (global and local input) INTEGER array of dimension DLEN.
87 * if 1D type (DTYPE_A=501 or 502), DLEN >= 7;
88 * if 2D type (DTYPE_A=1), DLEN >= 9.
89 * The array descriptor for the distributed matrix A.
90 * Contains information of mapping of A to memory. Please
91 * see NOTES below for full description and options.
92 *
93 * B (local input/local output) COMPLEX pointer into
94 * local memory to an array of local lead dimension lld_b>=NB.
95 * On entry, this array contains the
96 * the local pieces of the right hand sides
97 * B(IB:IB+N-1, 1:NRHS).
98 * On exit, this contains the local piece of the solutions
99 * distributed matrix X.
100 *
101 * IB (global input) INTEGER
102 * The row index in the global array B that points to the first
103 * row of the matrix to be operated on (which may be either
104 * all of B or a submatrix of B).
105 *
106 * DESCB (global and local input) INTEGER array of dimension DLEN.
107 * if 1D type (DTYPE_B=502), DLEN >=7;
108 * if 2D type (DTYPE_B=1), DLEN >= 9.
109 * The array descriptor for the distributed matrix B.
110 * Contains information of mapping of B to memory. Please
111 * see NOTES below for full description and options.
112 *
113 * AF (local output) COMPLEX array, dimension LAF.
114 * Auxiliary Fillin Space.
115 * Fillin is created during the factorization routine
116 * PCDTTRF and this is stored in AF. If a linear system
117 * is to be solved using PCDTTRS after the factorization
118 * routine, AF *must not be altered* after the factorization.
119 *
120 * LAF (local input) INTEGER
121 * Size of user-input Auxiliary Fillin space AF. Must be >=
122 * 2*(NB+2)
123 * If LAF is not large enough, an error code will be returned
124 * and the minimum acceptable size will be returned in AF( 1 )
125 *
126 * WORK (local workspace/local output)
127 * COMPLEX temporary workspace. This space may
128 * be overwritten in between calls to routines. WORK must be
129 * the size given in LWORK.
130 * On exit, WORK( 1 ) contains the minimal LWORK.
131 *
132 * LWORK (local input or global input) INTEGER
133 * Size of user-input workspace WORK.
134 * If LWORK is too small, the minimal acceptable size will be
135 * returned in WORK(1) and an error code is returned. LWORK>=
136 * 10*NPCOL+4*NRHS
137 *
138 * INFO (local output) INTEGER
139 * = 0: successful exit
140 * < 0: If the i-th argument is an array and the j-entry had
141 * an illegal value, then INFO = -(i*100+j), if the i-th
142 * argument is a scalar and had an illegal value, then
143 * INFO = -i.
144 *
145 * =====================================================================
146 *
147 *
148 * Restrictions
149 * ============
150 *
151 * The following are restrictions on the input parameters. Some of these
152 * are temporary and will be removed in future releases, while others
153 * may reflect fundamental technical limitations.
154 *
155 * Non-cyclic restriction: VERY IMPORTANT!
156 * P*NB>= mod(JA-1,NB)+N.
157 * The mapping for matrices must be blocked, reflecting the nature
158 * of the divide and conquer algorithm as a task-parallel algorithm.
159 * This formula in words is: no processor may have more than one
160 * chunk of the matrix.
161 *
162 * Blocksize cannot be too small:
163 * If the matrix spans more than one processor, the following
164 * restriction on NB, the size of each block on each processor,
165 * must hold:
166 * NB >= 2
167 * The bulk of parallel computation is done on the matrix of size
168 * O(NB) on each processor. If this is too small, divide and conquer
169 * is a poor choice of algorithm.
170 *
171 * Submatrix reference:
172 * JA = IB
173 * Alignment restriction that prevents unnecessary communication.
174 *
175 *
176 * =====================================================================
177 *
178 *
179 * Notes
180 * =====
181 *
182 * If the factorization routine and the solve routine are to be called
183 * separately (to solve various sets of righthand sides using the same
184 * coefficient matrix), the auxiliary space AF *must not be altered*
185 * between calls to the factorization routine and the solve routine.
186 *
187 * The best algorithm for solving banded and tridiagonal linear systems
188 * depends on a variety of parameters, especially the bandwidth.
189 * Currently, only algorithms designed for the case N/P >> bw are
190 * implemented. These go by many names, including Divide and Conquer,
191 * Partitioning, domain decomposition-type, etc.
192 * For tridiagonal matrices, it is obvious: N/P >> bw(=1), and so D&C
193 * algorithms are the appropriate choice.
194 *
195 * Algorithm description: Divide and Conquer
196 *
197 * The Divide and Conqer algorithm assumes the matrix is narrowly
198 * banded compared with the number of equations. In this situation,
199 * it is best to distribute the input matrix A one-dimensionally,
200 * with columns atomic and rows divided amongst the processes.
201 * The basic algorithm divides the tridiagonal matrix up into
202 * P pieces with one stored on each processor,
203 * and then proceeds in 2 phases for the factorization or 3 for the
204 * solution of a linear system.
205 * 1) Local Phase:
206 * The individual pieces are factored independently and in
207 * parallel. These factors are applied to the matrix creating
208 * fillin, which is stored in a non-inspectable way in auxiliary
209 * space AF. Mathematically, this is equivalent to reordering
210 * the matrix A as P A P^T and then factoring the principal
211 * leading submatrix of size equal to the sum of the sizes of
212 * the matrices factored on each processor. The factors of
213 * these submatrices overwrite the corresponding parts of A
214 * in memory.
215 * 2) Reduced System Phase:
216 * A small ((P-1)) system is formed representing
217 * interaction of the larger blocks, and is stored (as are its
218 * factors) in the space AF. A parallel Block Cyclic Reduction
219 * algorithm is used. For a linear system, a parallel front solve
220 * followed by an analagous backsolve, both using the structure
221 * of the factored matrix, are performed.
222 * 3) Backsubsitution Phase:
223 * For a linear system, a local backsubstitution is performed on
224 * each processor in parallel.
225 *
226 *
227 * Descriptors
228 * ===========
229 *
230 * Descriptors now have *types* and differ from ScaLAPACK 1.0.
231 *
232 * Note: tridiagonal codes can use either the old two dimensional
233 * or new one-dimensional descriptors, though the processor grid in
234 * both cases *must be one-dimensional*. We describe both types below.
235 *
236 * Each global data object is described by an associated description
237 * vector. This vector stores the information required to establish
238 * the mapping between an object element and its corresponding process
239 * and memory location.
240 *
241 * Let A be a generic term for any 2D block cyclicly distributed array.
242 * Such a global array has an associated description vector DESCA.
243 * In the following comments, the character _ should be read as
244 * "of the global array".
245 *
246 * NOTATION STORED IN EXPLANATION
247 * --------------- -------------- --------------------------------------
248 * DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
249 * DTYPE_A = 1.
250 * CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
251 * the BLACS process grid A is distribu-
252 * ted over. The context itself is glo-
253 * bal, but the handle (the integer
254 * value) may vary.
255 * M_A (global) DESCA( M_ ) The number of rows in the global
256 * array A.
257 * N_A (global) DESCA( N_ ) The number of columns in the global
258 * array A.
259 * MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
260 * the rows of the array.
261 * NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
262 * the columns of the array.
263 * RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
264 * row of the array A is distributed.
265 * CSRC_A (global) DESCA( CSRC_ ) The process column over which the
266 * first column of the array A is
267 * distributed.
268 * LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
269 * array. LLD_A >= MAX(1,LOCr(M_A)).
270 *
271 * Let K be the number of rows or columns of a distributed matrix,
272 * and assume that its process grid has dimension p x q.
273 * LOCr( K ) denotes the number of elements of K that a process
274 * would receive if K were distributed over the p processes of its
275 * process column.
276 * Similarly, LOCc( K ) denotes the number of elements of K that a
277 * process would receive if K were distributed over the q processes of
278 * its process row.
279 * The values of LOCr() and LOCc() may be determined via a call to the
280 * ScaLAPACK tool function, NUMROC:
281 * LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
282 * LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
283 * An upper bound for these quantities may be computed by:
284 * LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
285 * LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
286 *
287 *
288 * One-dimensional descriptors:
289 *
290 * One-dimensional descriptors are a new addition to ScaLAPACK since
291 * version 1.0. They simplify and shorten the descriptor for 1D
292 * arrays.
293 *
294 * Since ScaLAPACK supports two-dimensional arrays as the fundamental
295 * object, we allow 1D arrays to be distributed either over the
296 * first dimension of the array (as if the grid were P-by-1) or the
297 * 2nd dimension (as if the grid were 1-by-P). This choice is
298 * indicated by the descriptor type (501 or 502)
299 * as described below.
300 * However, for tridiagonal matrices, since the objects being
301 * distributed are the individual vectors storing the diagonals, we
302 * have adopted the convention that both the P-by-1 descriptor and
303 * the 1-by-P descriptor are allowed and are equivalent for
304 * tridiagonal matrices. Thus, for tridiagonal matrices,
305 * DTYPE_A = 501 or 502 can be used interchangeably
306 * without any other change.
307 * We require that the distributed vectors storing the diagonals of a
308 * tridiagonal matrix be aligned with each other. Because of this, a
309 * single descriptor, DESCA, serves to describe the distribution of
310 * of all diagonals simultaneously.
311 *
312 * IMPORTANT NOTE: the actual BLACS grid represented by the
313 * CTXT entry in the descriptor may be *either* P-by-1 or 1-by-P
314 * irrespective of which one-dimensional descriptor type
315 * (501 or 502) is input.
316 * This routine will interpret the grid properly either way.
317 * ScaLAPACK routines *do not support intercontext operations* so that
318 * the grid passed to a single ScaLAPACK routine *must be the same*
319 * for all array descriptors passed to that routine.
320 *
321 * NOTE: In all cases where 1D descriptors are used, 2D descriptors
322 * may also be used, since a one-dimensional array is a special case
323 * of a two-dimensional array with one dimension of size unity.
324 * The two-dimensional array used in this case *must* be of the
325 * proper orientation:
326 * If the appropriate one-dimensional descriptor is DTYPEA=501
327 * (1 by P type), then the two dimensional descriptor must
328 * have a CTXT value that refers to a 1 by P BLACS grid;
329 * If the appropriate one-dimensional descriptor is DTYPEA=502
330 * (P by 1 type), then the two dimensional descriptor must
331 * have a CTXT value that refers to a P by 1 BLACS grid.
332 *
333 *
334 * Summary of allowed descriptors, types, and BLACS grids:
335 * DTYPE 501 502 1 1
336 * BLACS grid 1xP or Px1 1xP or Px1 1xP Px1
337 * -----------------------------------------------------
338 * A OK OK OK NO
339 * B NO OK NO OK
340 *
341 * Note that a consequence of this chart is that it is not possible
342 * for *both* DTYPE_A and DTYPE_B to be 2D_type(1), as these lead
343 * to opposite requirements for the orientation of the BLACS grid,
344 * and as noted before, the *same* BLACS context must be used in
345 * all descriptors in a single ScaLAPACK subroutine call.
346 *
347 * Let A be a generic term for any 1D block cyclicly distributed array.
348 * Such a global array has an associated description vector DESCA.
349 * In the following comments, the character _ should be read as
350 * "of the global array".
351 *
352 * NOTATION STORED IN EXPLANATION
353 * --------------- ---------- ------------------------------------------
354 * DTYPE_A(global) DESCA( 1 ) The descriptor type. For 1D grids,
355 * TYPE_A = 501: 1-by-P grid.
356 * TYPE_A = 502: P-by-1 grid.
357 * CTXT_A (global) DESCA( 2 ) The BLACS context handle, indicating
358 * the BLACS process grid A is distribu-
359 * ted over. The context itself is glo-
360 * bal, but the handle (the integer
361 * value) may vary.
362 * N_A (global) DESCA( 3 ) The size of the array dimension being
363 * distributed.
364 * NB_A (global) DESCA( 4 ) The blocking factor used to distribute
365 * the distributed dimension of the array.
366 * SRC_A (global) DESCA( 5 ) The process row or column over which the
367 * first row or column of the array
368 * is distributed.
369 * Ignored DESCA( 6 ) Ignored for tridiagonal matrices.
370 * Reserved DESCA( 7 ) Reserved for future use.
371 *
372 *
373 *
374 * =====================================================================
375 *
376 * Code Developer: Andrew J. Cleary, University of Tennessee.
377 * Current address: Lawrence Livermore National Labs.
378 * This version released: August, 2001.
379 *
380 * =====================================================================
381 *
382 * ..
383 * .. Parameters ..
384  REAL ONE, ZERO
385  parameter( one = 1.0e+0 )
386  parameter( zero = 0.0e+0 )
387  COMPLEX CONE, CZERO
388  parameter( cone = ( 1.0e+0, 0.0e+0 ) )
389  parameter( czero = ( 0.0e+0, 0.0e+0 ) )
390  INTEGER INT_ONE
391  parameter( int_one = 1 )
392  INTEGER DESCMULT, BIGNUM
393  parameter(descmult = 100, bignum = descmult * descmult)
394  INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
395  $ lld_, mb_, m_, nb_, n_, rsrc_
396  parameter( block_cyclic_2d = 1, dlen_ = 9, dtype_ = 1,
397  $ ctxt_ = 2, m_ = 3, n_ = 4, mb_ = 5, nb_ = 6,
398  $ rsrc_ = 7, csrc_ = 8, lld_ = 9 )
399 * ..
400 * .. Local Scalars ..
401  INTEGER CSRC, FIRST_PROC, ICTXT, ICTXT_NEW, ICTXT_SAVE,
402  $ idum2, idum3, ja_new, llda, lldb, mycol, myrow,
403  $ my_num_cols, nb, np, npcol, nprow, np_save,
404  $ odd_size, part_offset, part_size,
405  $ return_code, store_m_b, store_n_a, temp,
406  $ work_size_min
407 * ..
408 * .. Local Arrays ..
409  INTEGER DESCA_1XP( 7 ), DESCB_PX1( 7 ),
410  $ param_check( 15, 3 )
411 * ..
412 * .. External Subroutines ..
413  EXTERNAL blacs_gridinfo, desc_convert, globchk,
414  $ pcdttrsv, pxerbla, reshape
415 * ..
416 * .. External Functions ..
417  LOGICAL LSAME
418  INTEGER NUMROC
419  COMPLEX CDOTC
420  EXTERNAL cdotc, lsame, numroc
421 * ..
422 * .. Intrinsic Functions ..
423  INTRINSIC ichar, min, mod
424 * ..
425 * .. Executable Statements ..
426 *
427 * Test the input parameters
428 *
429  info = 0
430 *
431 * Convert descriptor into standard form for easy access to
432 * parameters, check that grid is of right shape.
433 *
434  desca_1xp( 1 ) = 501
435  descb_px1( 1 ) = 502
436 *
437  temp = desca( dtype_ )
438  IF( temp .EQ. 502 ) THEN
439 * Temporarily set the descriptor type to 1xP type
440  desca( dtype_ ) = 501
441  ENDIF
442 *
443  CALL desc_convert( desca, desca_1xp, return_code )
444 *
445  desca( dtype_ ) = temp
446 *
447  IF( return_code .NE. 0) THEN
448  info = -( 8*100 + 2 )
449  ENDIF
450 *
451  CALL desc_convert( descb, descb_px1, return_code )
452 *
453  IF( return_code .NE. 0) THEN
454  info = -( 11*100 + 2 )
455  ENDIF
456 *
457 * Consistency checks for DESCA and DESCB.
458 *
459 * Context must be the same
460  IF( desca_1xp( 2 ) .NE. descb_px1( 2 ) ) THEN
461  info = -( 11*100 + 2 )
462  ENDIF
463 *
464 * These are alignment restrictions that may or may not be removed
465 * in future releases. -Andy Cleary, April 14, 1996.
466 *
467 * Block sizes must be the same
468  IF( desca_1xp( 4 ) .NE. descb_px1( 4 ) ) THEN
469  info = -( 11*100 + 4 )
470  ENDIF
471 *
472 * Source processor must be the same
473 *
474  IF( desca_1xp( 5 ) .NE. descb_px1( 5 ) ) THEN
475  info = -( 11*100 + 5 )
476  ENDIF
477 *
478 * Get values out of descriptor for use in code.
479 *
480  ictxt = desca_1xp( 2 )
481  csrc = desca_1xp( 5 )
482  nb = desca_1xp( 4 )
483  llda = desca_1xp( 6 )
484  store_n_a = desca_1xp( 3 )
485  lldb = descb_px1( 6 )
486  store_m_b = descb_px1( 3 )
487 *
488 * Get grid parameters
489 *
490 *
491  CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
492  np = nprow * npcol
493 *
494 *
495 *
496  IF( lsame( trans, 'N' ) ) THEN
497  idum2 = ichar( 'N' )
498  ELSE IF ( lsame( trans, 'C' ) ) THEN
499  idum2 = ichar( 'C' )
500  ELSE
501  info = -1
502  END IF
503 *
504  IF( lwork .LT. -1) THEN
505  info = -15
506  ELSE IF ( lwork .EQ. -1 ) THEN
507  idum3 = -1
508  ELSE
509  idum3 = 1
510  ENDIF
511 *
512  IF( n .LT. 0 ) THEN
513  info = -2
514  ENDIF
515 *
516  IF( n+ja-1 .GT. store_n_a ) THEN
517  info = -( 8*100 + 6 )
518  ENDIF
519 *
520  IF( n+ib-1 .GT. store_m_b ) THEN
521  info = -( 11*100 + 3 )
522  ENDIF
523 *
524  IF( lldb .LT. nb ) THEN
525  info = -( 11*100 + 6 )
526  ENDIF
527 *
528  IF( nrhs .LT. 0 ) THEN
529  info = -3
530  ENDIF
531 *
532 * Current alignment restriction
533 *
534  IF( ja .NE. ib) THEN
535  info = -7
536  ENDIF
537 *
538 * Argument checking that is specific to Divide & Conquer routine
539 *
540  IF( nprow .NE. 1 ) THEN
541  info = -( 8*100+2 )
542  ENDIF
543 *
544  IF( n .GT. np*nb-mod( ja-1, nb )) THEN
545  info = -( 2 )
546  CALL pxerbla( ictxt,
547  $ 'PCDTTRS, D&C alg.: only 1 block per proc',
548  $ -info )
549  RETURN
550  ENDIF
551 *
552  IF((ja+n-1.GT.nb) .AND. ( nb.LT.2*int_one )) THEN
553  info = -( 8*100+4 )
554  CALL pxerbla( ictxt,
555  $ 'PCDTTRS, D&C alg.: NB too small',
556  $ -info )
557  RETURN
558  ENDIF
559 *
560 *
561  work_size_min =
562  $ 10*npcol+4*nrhs
563 *
564  work( 1 ) = work_size_min
565 *
566  IF( lwork .LT. work_size_min ) THEN
567  IF( lwork .NE. -1 ) THEN
568  info = -15
569  CALL pxerbla( ictxt,
570  $ 'PCDTTRS: worksize error',
571  $ -info )
572  ENDIF
573  RETURN
574  ENDIF
575 *
576 * Pack params and positions into arrays for global consistency check
577 *
578  param_check( 15, 1 ) = descb(5)
579  param_check( 14, 1 ) = descb(4)
580  param_check( 13, 1 ) = descb(3)
581  param_check( 12, 1 ) = descb(2)
582  param_check( 11, 1 ) = descb(1)
583  param_check( 10, 1 ) = ib
584  param_check( 9, 1 ) = desca(5)
585  param_check( 8, 1 ) = desca(4)
586  param_check( 7, 1 ) = desca(3)
587  param_check( 6, 1 ) = desca(1)
588  param_check( 5, 1 ) = ja
589  param_check( 4, 1 ) = nrhs
590  param_check( 3, 1 ) = n
591  param_check( 2, 1 ) = idum3
592  param_check( 1, 1 ) = idum2
593 *
594  param_check( 15, 2 ) = 1105
595  param_check( 14, 2 ) = 1104
596  param_check( 13, 2 ) = 1103
597  param_check( 12, 2 ) = 1102
598  param_check( 11, 2 ) = 1101
599  param_check( 10, 2 ) = 10
600  param_check( 9, 2 ) = 805
601  param_check( 8, 2 ) = 804
602  param_check( 7, 2 ) = 803
603  param_check( 6, 2 ) = 801
604  param_check( 5, 2 ) = 7
605  param_check( 4, 2 ) = 3
606  param_check( 3, 2 ) = 2
607  param_check( 2, 2 ) = 15
608  param_check( 1, 2 ) = 1
609 *
610 * Want to find errors with MIN( ), so if no error, set it to a big
611 * number. If there already is an error, multiply by the the
612 * descriptor multiplier.
613 *
614  IF( info.GE.0 ) THEN
615  info = bignum
616  ELSE IF( info.LT.-descmult ) THEN
617  info = -info
618  ELSE
619  info = -info * descmult
620  END IF
621 *
622 * Check consistency across processors
623 *
624  CALL globchk( ictxt, 15, param_check, 15,
625  $ param_check( 1, 3 ), info )
626 *
627 * Prepare output: set info = 0 if no error, and divide by DESCMULT
628 * if error is not in a descriptor entry.
629 *
630  IF( info.EQ.bignum ) THEN
631  info = 0
632  ELSE IF( mod( info, descmult ) .EQ. 0 ) THEN
633  info = -info / descmult
634  ELSE
635  info = -info
636  END IF
637 *
638  IF( info.LT.0 ) THEN
639  CALL pxerbla( ictxt, 'PCDTTRS', -info )
640  RETURN
641  END IF
642 *
643 * Quick return if possible
644 *
645  IF( n.EQ.0 )
646  $ RETURN
647 *
648  IF( nrhs.EQ.0 )
649  $ RETURN
650 *
651 *
652 * Adjust addressing into matrix space to properly get into
653 * the beginning part of the relevant data
654 *
655  part_offset = nb*( (ja-1)/(npcol*nb) )
656 *
657  IF ( (mycol-csrc) .LT. (ja-part_offset-1)/nb ) THEN
658  part_offset = part_offset + nb
659  ENDIF
660 *
661  IF ( mycol .LT. csrc ) THEN
662  part_offset = part_offset - nb
663  ENDIF
664 *
665 * Form a new BLACS grid (the "standard form" grid) with only procs
666 * holding part of the matrix, of size 1xNP where NP is adjusted,
667 * starting at csrc=0, with JA modified to reflect dropped procs.
668 *
669 * First processor to hold part of the matrix:
670 *
671  first_proc = mod( ( ja-1 )/nb+csrc, npcol )
672 *
673 * Calculate new JA one while dropping off unused processors.
674 *
675  ja_new = mod( ja-1, nb ) + 1
676 *
677 * Save and compute new value of NP
678 *
679  np_save = np
680  np = ( ja_new+n-2 )/nb + 1
681 *
682 * Call utility routine that forms "standard-form" grid
683 *
684  CALL reshape( ictxt, int_one, ictxt_new, int_one,
685  $ first_proc, int_one, np )
686 *
687 * Use new context from standard grid as context.
688 *
689  ictxt_save = ictxt
690  ictxt = ictxt_new
691  desca_1xp( 2 ) = ictxt_new
692  descb_px1( 2 ) = ictxt_new
693 *
694 * Get information about new grid.
695 *
696  CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
697 *
698 * Drop out processors that do not have part of the matrix.
699 *
700  IF( myrow .LT. 0 ) THEN
701  GOTO 1234
702  ENDIF
703 *
704 * ********************************
705 * Values reused throughout routine
706 *
707 * User-input value of partition size
708 *
709  part_size = nb
710 *
711 * Number of columns in each processor
712 *
713  my_num_cols = numroc( n, part_size, mycol, 0, npcol )
714 *
715 * Offset in columns to beginning of main partition in each proc
716 *
717  IF ( mycol .EQ. 0 ) THEN
718  part_offset = part_offset+mod( ja_new-1, part_size )
719  my_num_cols = my_num_cols - mod(ja_new-1, part_size )
720  ENDIF
721 *
722 * Size of main (or odd) partition in each processor
723 *
724  odd_size = my_num_cols
725  IF ( mycol .LT. np-1 ) THEN
726  odd_size = odd_size - int_one
727  ENDIF
728 *
729 *
730 *
731 * Begin main code
732 *
733  info = 0
734 *
735 * Call frontsolve routine
736 *
737  IF( lsame( trans, 'N' ) ) THEN
738 *
739  CALL pcdttrsv( 'L', 'N', n, nrhs, dl( part_offset+1 ),
740  $ d( part_offset+1 ), du( part_offset+1 ), ja_new,
741  $ desca_1xp, b, ib, descb_px1, af, laf, work,
742  $ lwork, info )
743 *
744  ELSE
745 *
746  CALL pcdttrsv( 'U', 'C', n, nrhs, dl( part_offset+1 ),
747  $ d( part_offset+1 ), du( part_offset+1 ), ja_new,
748  $ desca_1xp, b, ib, descb_px1, af, laf, work,
749  $ lwork, info )
750 *
751  ENDIF
752 *
753 * Call backsolve routine
754 *
755  IF( lsame( trans, 'C' ) ) THEN
756 *
757  CALL pcdttrsv( 'L', 'C', n, nrhs, dl( part_offset+1 ),
758  $ d( part_offset+1 ), du( part_offset+1 ), ja_new,
759  $ desca_1xp, b, ib, descb_px1, af, laf, work,
760  $ lwork, info )
761 *
762  ELSE
763 *
764  CALL pcdttrsv( 'U', 'N', n, nrhs, dl( part_offset+1 ),
765  $ d( part_offset+1 ), du( part_offset+1 ), ja_new,
766  $ desca_1xp, b, ib, descb_px1, af, laf, work,
767  $ lwork, info )
768 *
769  ENDIF
770  1000 CONTINUE
771 *
772 *
773 * Free BLACS space used to hold standard-form grid.
774 *
775  IF( ictxt_save .NE. ictxt_new ) THEN
776  CALL blacs_gridexit( ictxt_new )
777  ENDIF
778 *
779  1234 CONTINUE
780 *
781 * Restore saved input parameters
782 *
783  ictxt = ictxt_save
784  np = np_save
785 *
786 * Output minimum worksize
787 *
788  work( 1 ) = work_size_min
789 *
790 *
791  RETURN
792 *
793 * End of PCDTTRS
794 *
795  END
globchk
subroutine globchk(ICTXT, N, X, LDX, IWORK, INFO)
Definition: pchkxmat.f:403
reshape
void reshape(int *context_in, int *major_in, int *context_out, int *major_out, int *first_proc, int *nprow_new, int *npcol_new)
Definition: reshape.c:77
pcdttrsv
subroutine pcdttrsv(UPLO, TRANS, N, NRHS, DL, D, DU, JA, DESCA, B, IB, DESCB, AF, LAF, WORK, LWORK, INFO)
Definition: pcdttrsv.f:3
desc_convert
subroutine desc_convert(DESC_IN, DESC_OUT, INFO)
Definition: desc_convert.f:2
pcdttrs
subroutine pcdttrs(TRANS, N, NRHS, DL, D, DU, JA, DESCA, B, IB, DESCB, AF, LAF, WORK, LWORK, INFO)
Definition: pcdttrs.f:3
pxerbla
subroutine pxerbla(ICTXT, SRNAME, INFO)
Definition: pxerbla.f:2
min
#define min(A, B)
Definition: pcgemr.c:181