ScaLAPACK 2.1  2.1
ScaLAPACK: Scalable Linear Algebra PACKage
pzpbtrs.f
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1  SUBROUTINE pzpbtrs( UPLO, N, BW, NRHS, A, JA, DESCA, B, IB, DESCB,
2  $ 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 UPLO
13  INTEGER BW, IB, INFO, JA, LAF, LWORK, N, NRHS
14 * ..
15 * .. Array Arguments ..
16  INTEGER DESCA( * ), DESCB( * )
17  COMPLEX*16 A( * ), AF( * ), B( * ), WORK( * )
18 * ..
19 *
20 *
21 * Purpose
22 * =======
23 *
24 * PZPBTRS solves a system of linear equations
25 *
26 * A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS)
27 *
28 * where A(1:N, JA:JA+N-1) is the matrix used to produce the factors
29 * stored in A(1:N,JA:JA+N-1) and AF by PZPBTRF.
30 * A(1:N, JA:JA+N-1) is an N-by-N complex
31 * banded symmetric positive definite distributed
32 * matrix with bandwidth BW.
33 * Depending on the value of UPLO, A stores either U or L in the equn
34 * A(1:N, JA:JA+N-1) = U'*U or L*L' as computed by PZPBTRF.
35 *
36 * Routine PZPBTRF MUST be called first.
37 *
38 * =====================================================================
39 *
40 * Arguments
41 * =========
42 *
43 * UPLO (global input) CHARACTER
44 * = 'U': Upper triangle of A(1:N, JA:JA+N-1) is stored;
45 * = 'L': Lower triangle of A(1:N, JA:JA+N-1) is stored.
46 *
47 * N (global input) INTEGER
48 * The number of rows and columns to be operated on, i.e. the
49 * order of the distributed submatrix A(1:N, JA:JA+N-1). N >= 0.
50 *
51 * BW (global input) INTEGER
52 * Number of subdiagonals in L or U. 0 <= BW <= N-1
53 *
54 * NRHS (global input) INTEGER
55 * The number of right hand sides, i.e., the number of columns
56 * of the distributed submatrix B(IB:IB+N-1, 1:NRHS).
57 * NRHS >= 0.
58 *
59 * A (local input/local output) COMPLEX*16 pointer into
60 * local memory to an array with first dimension
61 * LLD_A >=(bw+1) (stored in DESCA).
62 * On entry, this array contains the local pieces of the
63 * N-by-N symmetric banded distributed Cholesky factor L or
64 * L^T A(1:N, JA:JA+N-1).
65 * This local portion is stored in the packed banded format
66 * used in LAPACK. Please see the Notes below and the
67 * ScaLAPACK manual for more detail on the format of
68 * distributed matrices.
69 *
70 * JA (global input) INTEGER
71 * The index in the global array A that points to the start of
72 * the matrix to be operated on (which may be either all of A
73 * or a submatrix of A).
74 *
75 * DESCA (global and local input) INTEGER array of dimension DLEN.
76 * if 1D type (DTYPE_A=501), DLEN >= 7;
77 * if 2D type (DTYPE_A=1), DLEN >= 9 .
78 * The array descriptor for the distributed matrix A.
79 * Contains information of mapping of A to memory. Please
80 * see NOTES below for full description and options.
81 *
82 * B (local input/local output) COMPLEX*16 pointer into
83 * local memory to an array of local lead dimension lld_b>=NB.
84 * On entry, this array contains the
85 * the local pieces of the right hand sides
86 * B(IB:IB+N-1, 1:NRHS).
87 * On exit, this contains the local piece of the solutions
88 * distributed matrix X.
89 *
90 * IB (global input) INTEGER
91 * The row index in the global array B that points to the first
92 * row of the matrix to be operated on (which may be either
93 * all of B or a submatrix of B).
94 *
95 * DESCB (global and local input) INTEGER array of dimension DLEN.
96 * if 1D type (DTYPE_B=502), DLEN >=7;
97 * if 2D type (DTYPE_B=1), DLEN >= 9.
98 * The array descriptor for the distributed matrix B.
99 * Contains information of mapping of B to memory. Please
100 * see NOTES below for full description and options.
101 *
102 * AF (local output) COMPLEX*16 array, dimension LAF.
103 * Auxiliary Fillin Space.
104 * Fillin is created during the factorization routine
105 * PZPBTRF and this is stored in AF. If a linear system
106 * is to be solved using PZPBTRS after the factorization
107 * routine, AF *must not be altered* after the factorization.
108 *
109 * LAF (local input) INTEGER
110 * Size of user-input Auxiliary Fillin space AF. Must be >=
111 * (NB+2*bw)*bw
112 * If LAF is not large enough, an error code will be returned
113 * and the minimum acceptable size will be returned in AF( 1 )
114 *
115 * WORK (local workspace/local output)
116 * COMPLEX*16 temporary workspace. This space may
117 * be overwritten in between calls to routines. WORK must be
118 * the size given in LWORK.
119 * On exit, WORK( 1 ) contains the minimal LWORK.
120 *
121 * LWORK (local input or global input) INTEGER
122 * Size of user-input workspace WORK.
123 * If LWORK is too small, the minimal acceptable size will be
124 * returned in WORK(1) and an error code is returned. LWORK>=
125 * (bw*NRHS)
126 *
127 * INFO (global output) INTEGER
128 * = 0: successful exit
129 * < 0: If the i-th argument is an array and the j-entry had
130 * an illegal value, then INFO = -(i*100+j), if the i-th
131 * argument is a scalar and had an illegal value, then
132 * INFO = -i.
133 *
134 * =====================================================================
135 *
136 *
137 * Restrictions
138 * ============
139 *
140 * The following are restrictions on the input parameters. Some of these
141 * are temporary and will be removed in future releases, while others
142 * may reflect fundamental technical limitations.
143 *
144 * Non-cyclic restriction: VERY IMPORTANT!
145 * P*NB>= mod(JA-1,NB)+N.
146 * The mapping for matrices must be blocked, reflecting the nature
147 * of the divide and conquer algorithm as a task-parallel algorithm.
148 * This formula in words is: no processor may have more than one
149 * chunk of the matrix.
150 *
151 * Blocksize cannot be too small:
152 * If the matrix spans more than one processor, the following
153 * restriction on NB, the size of each block on each processor,
154 * must hold:
155 * NB >= 2*BW
156 * The bulk of parallel computation is done on the matrix of size
157 * O(NB) on each processor. If this is too small, divide and conquer
158 * is a poor choice of algorithm.
159 *
160 * Submatrix reference:
161 * JA = IB
162 * Alignment restriction that prevents unnecessary communication.
163 *
164 *
165 * =====================================================================
166 *
167 *
168 * Notes
169 * =====
170 *
171 * If the factorization routine and the solve routine are to be called
172 * separately (to solve various sets of righthand sides using the same
173 * coefficient matrix), the auxiliary space AF *must not be altered*
174 * between calls to the factorization routine and the solve routine.
175 *
176 * The best algorithm for solving banded and tridiagonal linear systems
177 * depends on a variety of parameters, especially the bandwidth.
178 * Currently, only algorithms designed for the case N/P >> bw are
179 * implemented. These go by many names, including Divide and Conquer,
180 * Partitioning, domain decomposition-type, etc.
181 *
182 * Algorithm description: Divide and Conquer
183 *
184 * The Divide and Conqer algorithm assumes the matrix is narrowly
185 * banded compared with the number of equations. In this situation,
186 * it is best to distribute the input matrix A one-dimensionally,
187 * with columns atomic and rows divided amongst the processes.
188 * The basic algorithm divides the banded matrix up into
189 * P pieces with one stored on each processor,
190 * and then proceeds in 2 phases for the factorization or 3 for the
191 * solution of a linear system.
192 * 1) Local Phase:
193 * The individual pieces are factored independently and in
194 * parallel. These factors are applied to the matrix creating
195 * fillin, which is stored in a non-inspectable way in auxiliary
196 * space AF. Mathematically, this is equivalent to reordering
197 * the matrix A as P A P^T and then factoring the principal
198 * leading submatrix of size equal to the sum of the sizes of
199 * the matrices factored on each processor. The factors of
200 * these submatrices overwrite the corresponding parts of A
201 * in memory.
202 * 2) Reduced System Phase:
203 * A small (BW* (P-1)) system is formed representing
204 * interaction of the larger blocks, and is stored (as are its
205 * factors) in the space AF. A parallel Block Cyclic Reduction
206 * algorithm is used. For a linear system, a parallel front solve
207 * followed by an analagous backsolve, both using the structure
208 * of the factored matrix, are performed.
209 * 3) Backsubsitution Phase:
210 * For a linear system, a local backsubstitution is performed on
211 * each processor in parallel.
212 *
213 *
214 * Descriptors
215 * ===========
216 *
217 * Descriptors now have *types* and differ from ScaLAPACK 1.0.
218 *
219 * Note: banded codes can use either the old two dimensional
220 * or new one-dimensional descriptors, though the processor grid in
221 * both cases *must be one-dimensional*. We describe both types below.
222 *
223 * Each global data object is described by an associated description
224 * vector. This vector stores the information required to establish
225 * the mapping between an object element and its corresponding process
226 * and memory location.
227 *
228 * Let A be a generic term for any 2D block cyclicly distributed array.
229 * Such a global array has an associated description vector DESCA.
230 * In the following comments, the character _ should be read as
231 * "of the global array".
232 *
233 * NOTATION STORED IN EXPLANATION
234 * --------------- -------------- --------------------------------------
235 * DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
236 * DTYPE_A = 1.
237 * CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
238 * the BLACS process grid A is distribu-
239 * ted over. The context itself is glo-
240 * bal, but the handle (the integer
241 * value) may vary.
242 * M_A (global) DESCA( M_ ) The number of rows in the global
243 * array A.
244 * N_A (global) DESCA( N_ ) The number of columns in the global
245 * array A.
246 * MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
247 * the rows of the array.
248 * NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
249 * the columns of the array.
250 * RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
251 * row of the array A is distributed.
252 * CSRC_A (global) DESCA( CSRC_ ) The process column over which the
253 * first column of the array A is
254 * distributed.
255 * LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
256 * array. LLD_A >= MAX(1,LOCr(M_A)).
257 *
258 * Let K be the number of rows or columns of a distributed matrix,
259 * and assume that its process grid has dimension p x q.
260 * LOCr( K ) denotes the number of elements of K that a process
261 * would receive if K were distributed over the p processes of its
262 * process column.
263 * Similarly, LOCc( K ) denotes the number of elements of K that a
264 * process would receive if K were distributed over the q processes of
265 * its process row.
266 * The values of LOCr() and LOCc() may be determined via a call to the
267 * ScaLAPACK tool function, NUMROC:
268 * LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
269 * LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
270 * An upper bound for these quantities may be computed by:
271 * LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
272 * LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
273 *
274 *
275 * One-dimensional descriptors:
276 *
277 * One-dimensional descriptors are a new addition to ScaLAPACK since
278 * version 1.0. They simplify and shorten the descriptor for 1D
279 * arrays.
280 *
281 * Since ScaLAPACK supports two-dimensional arrays as the fundamental
282 * object, we allow 1D arrays to be distributed either over the
283 * first dimension of the array (as if the grid were P-by-1) or the
284 * 2nd dimension (as if the grid were 1-by-P). This choice is
285 * indicated by the descriptor type (501 or 502)
286 * as described below.
287 *
288 * IMPORTANT NOTE: the actual BLACS grid represented by the
289 * CTXT entry in the descriptor may be *either* P-by-1 or 1-by-P
290 * irrespective of which one-dimensional descriptor type
291 * (501 or 502) is input.
292 * This routine will interpret the grid properly either way.
293 * ScaLAPACK routines *do not support intercontext operations* so that
294 * the grid passed to a single ScaLAPACK routine *must be the same*
295 * for all array descriptors passed to that routine.
296 *
297 * NOTE: In all cases where 1D descriptors are used, 2D descriptors
298 * may also be used, since a one-dimensional array is a special case
299 * of a two-dimensional array with one dimension of size unity.
300 * The two-dimensional array used in this case *must* be of the
301 * proper orientation:
302 * If the appropriate one-dimensional descriptor is DTYPEA=501
303 * (1 by P type), then the two dimensional descriptor must
304 * have a CTXT value that refers to a 1 by P BLACS grid;
305 * If the appropriate one-dimensional descriptor is DTYPEA=502
306 * (P by 1 type), then the two dimensional descriptor must
307 * have a CTXT value that refers to a P by 1 BLACS grid.
308 *
309 *
310 * Summary of allowed descriptors, types, and BLACS grids:
311 * DTYPE 501 502 1 1
312 * BLACS grid 1xP or Px1 1xP or Px1 1xP Px1
313 * -----------------------------------------------------
314 * A OK NO OK NO
315 * B NO OK NO OK
316 *
317 * Note that a consequence of this chart is that it is not possible
318 * for *both* DTYPE_A and DTYPE_B to be 2D_type(1), as these lead
319 * to opposite requirements for the orientation of the BLACS grid,
320 * and as noted before, the *same* BLACS context must be used in
321 * all descriptors in a single ScaLAPACK subroutine call.
322 *
323 * Let A be a generic term for any 1D block cyclicly distributed array.
324 * Such a global array has an associated description vector DESCA.
325 * In the following comments, the character _ should be read as
326 * "of the global array".
327 *
328 * NOTATION STORED IN EXPLANATION
329 * --------------- ---------- ------------------------------------------
330 * DTYPE_A(global) DESCA( 1 ) The descriptor type. For 1D grids,
331 * TYPE_A = 501: 1-by-P grid.
332 * TYPE_A = 502: P-by-1 grid.
333 * CTXT_A (global) DESCA( 2 ) The BLACS context handle, indicating
334 * the BLACS process grid A is distribu-
335 * ted over. The context itself is glo-
336 * bal, but the handle (the integer
337 * value) may vary.
338 * N_A (global) DESCA( 3 ) The size of the array dimension being
339 * distributed.
340 * NB_A (global) DESCA( 4 ) The blocking factor used to distribute
341 * the distributed dimension of the array.
342 * SRC_A (global) DESCA( 5 ) The process row or column over which the
343 * first row or column of the array
344 * is distributed.
345 * LLD_A (local) DESCA( 6 ) The leading dimension of the local array
346 * storing the local blocks of the distri-
347 * buted array A. Minimum value of LLD_A
348 * depends on TYPE_A.
349 * TYPE_A = 501: LLD_A >=
350 * size of undistributed dimension, 1.
351 * TYPE_A = 502: LLD_A >=NB_A, 1.
352 * Reserved DESCA( 7 ) Reserved for future use.
353 *
354 *
355 *
356 * =====================================================================
357 *
358 * Code Developer: Andrew J. Cleary, University of Tennessee.
359 * Current address: Lawrence Livermore National Labs.
360 * This version released: August, 2001.
361 *
362 * =====================================================================
363 *
364 * ..
365 * .. Parameters ..
366  DOUBLE PRECISION ONE, ZERO
367  parameter( one = 1.0d+0 )
368  parameter( zero = 0.0d+0 )
369  COMPLEX*16 CONE, CZERO
370  parameter( cone = ( 1.0d+0, 0.0d+0 ) )
371  parameter( czero = ( 0.0d+0, 0.0d+0 ) )
372  INTEGER INT_ONE
373  parameter( int_one = 1 )
374  INTEGER DESCMULT, BIGNUM
375  parameter(descmult = 100, bignum = descmult * descmult)
376  INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
377  $ lld_, mb_, m_, nb_, n_, rsrc_
378  parameter( block_cyclic_2d = 1, dlen_ = 9, dtype_ = 1,
379  $ ctxt_ = 2, m_ = 3, n_ = 4, mb_ = 5, nb_ = 6,
380  $ rsrc_ = 7, csrc_ = 8, lld_ = 9 )
381 * ..
382 * .. Local Scalars ..
383  INTEGER CSRC, FIRST_PROC, ICTXT, ICTXT_NEW, ICTXT_SAVE,
384  $ idum1, idum3, ja_new, llda, lldb, mycol, myrow,
385  $ nb, np, npcol, nprow, np_save, part_offset,
386  $ return_code, store_m_b, store_n_a,
387  $ work_size_min
388 * ..
389 * .. Local Arrays ..
390  INTEGER DESCA_1XP( 7 ), DESCB_PX1( 7 ),
391  $ param_check( 16, 3 )
392 * ..
393 * .. External Subroutines ..
394  EXTERNAL blacs_gridinfo, desc_convert, globchk, pxerbla,
395  $ pzpbtrsv, reshape
396 * ..
397 * .. External Functions ..
398  LOGICAL LSAME
399  INTEGER NUMROC
400  EXTERNAL lsame, numroc
401 * ..
402 * .. Intrinsic Functions ..
403  INTRINSIC ichar, min, mod
404 * ..
405 * .. Executable Statements ..
406 *
407 * Test the input parameters
408 *
409  info = 0
410 *
411 * Convert descriptor into standard form for easy access to
412 * parameters, check that grid is of right shape.
413 *
414  desca_1xp( 1 ) = 501
415  descb_px1( 1 ) = 502
416 *
417  CALL desc_convert( desca, desca_1xp, return_code )
418 *
419  IF( return_code .NE. 0) THEN
420  info = -( 7*100 + 2 )
421  ENDIF
422 *
423  CALL desc_convert( descb, descb_px1, return_code )
424 *
425  IF( return_code .NE. 0) THEN
426  info = -( 10*100 + 2 )
427  ENDIF
428 *
429 * Consistency checks for DESCA and DESCB.
430 *
431 * Context must be the same
432  IF( desca_1xp( 2 ) .NE. descb_px1( 2 ) ) THEN
433  info = -( 10*100 + 2 )
434  ENDIF
435 *
436 * These are alignment restrictions that may or may not be removed
437 * in future releases. -Andy Cleary, April 14, 1996.
438 *
439 * Block sizes must be the same
440  IF( desca_1xp( 4 ) .NE. descb_px1( 4 ) ) THEN
441  info = -( 10*100 + 4 )
442  ENDIF
443 *
444 * Source processor must be the same
445 *
446  IF( desca_1xp( 5 ) .NE. descb_px1( 5 ) ) THEN
447  info = -( 10*100 + 5 )
448  ENDIF
449 *
450 * Get values out of descriptor for use in code.
451 *
452  ictxt = desca_1xp( 2 )
453  csrc = desca_1xp( 5 )
454  nb = desca_1xp( 4 )
455  llda = desca_1xp( 6 )
456  store_n_a = desca_1xp( 3 )
457  lldb = descb_px1( 6 )
458  store_m_b = descb_px1( 3 )
459 *
460 * Get grid parameters
461 *
462 *
463  CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
464  np = nprow * npcol
465 *
466 *
467 *
468  IF( lsame( uplo, 'U' ) ) THEN
469  idum1 = ichar( 'U' )
470  ELSE IF ( lsame( uplo, 'L' ) ) THEN
471  idum1 = ichar( 'L' )
472  ELSE
473  info = -1
474  END IF
475 *
476  IF( lwork .LT. -1) THEN
477  info = -14
478  ELSE IF ( lwork .EQ. -1 ) THEN
479  idum3 = -1
480  ELSE
481  idum3 = 1
482  ENDIF
483 *
484  IF( n .LT. 0 ) THEN
485  info = -2
486  ENDIF
487 *
488  IF( n+ja-1 .GT. store_n_a ) THEN
489  info = -( 7*100 + 6 )
490  ENDIF
491 *
492  IF(( bw .GT. n-1 ) .OR.
493  $ ( bw .LT. 0 ) ) THEN
494  info = -3
495  ENDIF
496 *
497  IF( llda .LT. (bw+1) ) THEN
498  info = -( 7*100 + 6 )
499  ENDIF
500 *
501  IF( nb .LE. 0 ) THEN
502  info = -( 7*100 + 4 )
503  ENDIF
504 *
505  IF( n+ib-1 .GT. store_m_b ) THEN
506  info = -( 10*100 + 3 )
507  ENDIF
508 *
509  IF( lldb .LT. nb ) THEN
510  info = -( 10*100 + 6 )
511  ENDIF
512 *
513  IF( nrhs .LT. 0 ) THEN
514  info = -3
515  ENDIF
516 *
517 * Current alignment restriction
518 *
519  IF( ja .NE. ib) THEN
520  info = -6
521  ENDIF
522 *
523 * Argument checking that is specific to Divide & Conquer routine
524 *
525  IF( nprow .NE. 1 ) THEN
526  info = -( 7*100+2 )
527  ENDIF
528 *
529  IF( n .GT. np*nb-mod( ja-1, nb )) THEN
530  info = -( 2 )
531  CALL pxerbla( ictxt,
532  $ 'PZPBTRS, D&C alg.: only 1 block per proc',
533  $ -info )
534  RETURN
535  ENDIF
536 *
537  IF((ja+n-1.GT.nb) .AND. ( nb.LT.2*bw )) THEN
538  info = -( 7*100+4 )
539  CALL pxerbla( ictxt,
540  $ 'PZPBTRS, D&C alg.: NB too small',
541  $ -info )
542  RETURN
543  ENDIF
544 *
545 *
546  work_size_min =
547  $ (bw*nrhs)
548 *
549  work( 1 ) = work_size_min
550 *
551  IF( lwork .LT. work_size_min ) THEN
552  IF( lwork .NE. -1 ) THEN
553  info = -14
554  CALL pxerbla( ictxt,
555  $ 'PZPBTRS: worksize error',
556  $ -info )
557  ENDIF
558  RETURN
559  ENDIF
560 *
561 * Pack params and positions into arrays for global consistency check
562 *
563  param_check( 16, 1 ) = descb(5)
564  param_check( 15, 1 ) = descb(4)
565  param_check( 14, 1 ) = descb(3)
566  param_check( 13, 1 ) = descb(2)
567  param_check( 12, 1 ) = descb(1)
568  param_check( 11, 1 ) = ib
569  param_check( 10, 1 ) = desca(5)
570  param_check( 9, 1 ) = desca(4)
571  param_check( 8, 1 ) = desca(3)
572  param_check( 7, 1 ) = desca(1)
573  param_check( 6, 1 ) = ja
574  param_check( 5, 1 ) = nrhs
575  param_check( 4, 1 ) = bw
576  param_check( 3, 1 ) = n
577  param_check( 2, 1 ) = idum3
578  param_check( 1, 1 ) = idum1
579 *
580  param_check( 16, 2 ) = 1005
581  param_check( 15, 2 ) = 1004
582  param_check( 14, 2 ) = 1003
583  param_check( 13, 2 ) = 1002
584  param_check( 12, 2 ) = 1001
585  param_check( 11, 2 ) = 9
586  param_check( 10, 2 ) = 705
587  param_check( 9, 2 ) = 704
588  param_check( 8, 2 ) = 703
589  param_check( 7, 2 ) = 701
590  param_check( 6, 2 ) = 6
591  param_check( 5, 2 ) = 4
592  param_check( 4, 2 ) = 3
593  param_check( 3, 2 ) = 2
594  param_check( 2, 2 ) = 14
595  param_check( 1, 2 ) = 1
596 *
597 * Want to find errors with MIN( ), so if no error, set it to a big
598 * number. If there already is an error, multiply by the the
599 * descriptor multiplier.
600 *
601  IF( info.GE.0 ) THEN
602  info = bignum
603  ELSE IF( info.LT.-descmult ) THEN
604  info = -info
605  ELSE
606  info = -info * descmult
607  END IF
608 *
609 * Check consistency across processors
610 *
611  CALL globchk( ictxt, 16, param_check, 16,
612  $ param_check( 1, 3 ), info )
613 *
614 * Prepare output: set info = 0 if no error, and divide by DESCMULT
615 * if error is not in a descriptor entry.
616 *
617  IF( info.EQ.bignum ) THEN
618  info = 0
619  ELSE IF( mod( info, descmult ) .EQ. 0 ) THEN
620  info = -info / descmult
621  ELSE
622  info = -info
623  END IF
624 *
625  IF( info.LT.0 ) THEN
626  CALL pxerbla( ictxt, 'PZPBTRS', -info )
627  RETURN
628  END IF
629 *
630 * Quick return if possible
631 *
632  IF( n.EQ.0 )
633  $ RETURN
634 *
635  IF( nrhs.EQ.0 )
636  $ RETURN
637 *
638 *
639 * Adjust addressing into matrix space to properly get into
640 * the beginning part of the relevant data
641 *
642  part_offset = nb*( (ja-1)/(npcol*nb) )
643 *
644  IF ( (mycol-csrc) .LT. (ja-part_offset-1)/nb ) THEN
645  part_offset = part_offset + nb
646  ENDIF
647 *
648  IF ( mycol .LT. csrc ) THEN
649  part_offset = part_offset - nb
650  ENDIF
651 *
652 * Form a new BLACS grid (the "standard form" grid) with only procs
653 * holding part of the matrix, of size 1xNP where NP is adjusted,
654 * starting at csrc=0, with JA modified to reflect dropped procs.
655 *
656 * First processor to hold part of the matrix:
657 *
658  first_proc = mod( ( ja-1 )/nb+csrc, npcol )
659 *
660 * Calculate new JA one while dropping off unused processors.
661 *
662  ja_new = mod( ja-1, nb ) + 1
663 *
664 * Save and compute new value of NP
665 *
666  np_save = np
667  np = ( ja_new+n-2 )/nb + 1
668 *
669 * Call utility routine that forms "standard-form" grid
670 *
671  CALL reshape( ictxt, int_one, ictxt_new, int_one,
672  $ first_proc, int_one, np )
673 *
674 * Use new context from standard grid as context.
675 *
676  ictxt_save = ictxt
677  ictxt = ictxt_new
678  desca_1xp( 2 ) = ictxt_new
679  descb_px1( 2 ) = ictxt_new
680 *
681 * Get information about new grid.
682 *
683  CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
684 *
685 * Drop out processors that do not have part of the matrix.
686 *
687  IF( myrow .LT. 0 ) THEN
688  GOTO 1234
689  ENDIF
690 *
691 *
692 *
693 * Begin main code
694 *
695  info = 0
696 *
697 * Call frontsolve routine
698 *
699  IF( lsame( uplo, 'L' ) ) THEN
700 *
701  CALL pzpbtrsv( 'L', 'N', n, bw, nrhs, a( part_offset+1 ),
702  $ ja_new, desca_1xp, b, ib, descb_px1, af, laf,
703  $ work, lwork, info )
704 *
705  ELSE
706 *
707  CALL pzpbtrsv( 'U', 'C', n, bw, nrhs, a( part_offset+1 ),
708  $ ja_new, desca_1xp, b, ib, descb_px1, af, laf,
709  $ work, lwork, info )
710 *
711  ENDIF
712 *
713 * Call backsolve routine
714 *
715  IF( lsame( uplo, 'L' ) ) THEN
716 *
717  CALL pzpbtrsv( 'L', 'C', n, bw, nrhs, a( part_offset+1 ),
718  $ ja_new, desca_1xp, b, ib, descb_px1, af, laf,
719  $ work, lwork, info )
720 *
721  ELSE
722 *
723  CALL pzpbtrsv( 'U', 'N', n, bw, nrhs, a( part_offset+1 ),
724  $ ja_new, desca_1xp, b, ib, descb_px1, af, laf,
725  $ work, lwork, info )
726 *
727  ENDIF
728  1000 CONTINUE
729 *
730 *
731 * Free BLACS space used to hold standard-form grid.
732 *
733  IF( ictxt_save .NE. ictxt_new ) THEN
734  CALL blacs_gridexit( ictxt_new )
735  ENDIF
736 *
737  1234 CONTINUE
738 *
739 * Restore saved input parameters
740 *
741  ictxt = ictxt_save
742  np = np_save
743 *
744 * Output minimum worksize
745 *
746  work( 1 ) = work_size_min
747 *
748 *
749  RETURN
750 *
751 * End of PZPBTRS
752 *
753  END
globchk
subroutine globchk(ICTXT, N, X, LDX, IWORK, INFO)
Definition: pchkxmat.f:403
pzpbtrsv
subroutine pzpbtrsv(UPLO, TRANS, N, BW, NRHS, A, JA, DESCA, B, IB, DESCB, AF, LAF, WORK, LWORK, INFO)
Definition: pzpbtrsv.f:3
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
desc_convert
subroutine desc_convert(DESC_IN, DESC_OUT, INFO)
Definition: desc_convert.f:2
pzpbtrs
subroutine pzpbtrs(UPLO, N, BW, NRHS, A, JA, DESCA, B, IB, DESCB, AF, LAF, WORK, LWORK, INFO)
Definition: pzpbtrs.f:3
pxerbla
subroutine pxerbla(ICTXT, SRNAME, INFO)
Definition: pxerbla.f:2
min
#define min(A, B)
Definition: pcgemr.c:181