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pzpbtrf.f
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1 SUBROUTINE pzpbtrf( UPLO, N, BW, A, JA, DESCA, AF, LAF, WORK,
2 $ LWORK, INFO )
3*
4* -- ScaLAPACK routine (version 2.0.2) --
5* Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver
6* May 1 2012
7*
8* .. Scalar Arguments ..
9 CHARACTER UPLO
10 INTEGER BW, INFO, JA, LAF, LWORK, N
11* ..
12* .. Array Arguments ..
13 INTEGER DESCA( * )
14 COMPLEX*16 A( * ), AF( * ), WORK( * )
15* ..
16*
17*
18* Purpose
19* =======
20*
21* PZPBTRF computes a Cholesky factorization
22* of an N-by-N complex banded
23* symmetric positive definite distributed matrix
24* with bandwidth BW: A(1:N, JA:JA+N-1).
25* Reordering is used to increase parallelism in the factorization.
26* This reordering results in factors that are DIFFERENT from those
27* produced by equivalent sequential codes. These factors cannot
28* be used directly by users; however, they can be used in
29* subsequent calls to PZPBTRS to solve linear systems.
30*
31* The factorization has the form
32*
33* P A(1:N, JA:JA+N-1) P^T = U' U , if UPLO = 'U', or
34*
35* P A(1:N, JA:JA+N-1) P^T = L L', if UPLO = 'L'
36*
37* where U is a banded upper triangular matrix and L is banded
38* lower triangular, and P is a permutation matrix.
39*
40* =====================================================================
41*
42* Arguments
43* =========
44*
45* UPLO (global input) CHARACTER
46* = 'U': Upper triangle of A(1:N, JA:JA+N-1) is stored;
47* = 'L': Lower triangle of A(1:N, JA:JA+N-1) is stored.
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* BW (global input) INTEGER
54* Number of subdiagonals in L or U. 0 <= BW <= N-1
55*
56* A (local input/local output) COMPLEX*16 pointer into
57* local memory to an array with first dimension
58* LLD_A >=(bw+1) (stored in DESCA).
59* On entry, this array contains the local pieces of the
60* N-by-N symmetric banded distributed matrix
61* A(1:N, JA:JA+N-1) to be factored.
62* This local portion is stored in the packed banded format
63* used in LAPACK. Please see the Notes below and the
64* ScaLAPACK manual for more detail on the format of
65* distributed matrices.
66* On exit, this array contains information containing details
67* of the factorization.
68* Note that permutations are performed on the matrix, so that
69* the factors returned are different from those returned
70* by LAPACK.
71*
72* JA (global input) INTEGER
73* The index in the global array A that points to the start of
74* the matrix to be operated on (which may be either all of A
75* or a submatrix of A).
76*
77* DESCA (global and local input) INTEGER array of dimension DLEN.
78* if 1D type (DTYPE_A=501), DLEN >= 7;
79* if 2D type (DTYPE_A=1), DLEN >= 9 .
80* The array descriptor for the distributed matrix A.
81* Contains information of mapping of A to memory. Please
82* see NOTES below for full description and options.
83*
84* AF (local output) COMPLEX*16 array, dimension LAF.
85* Auxiliary Fillin Space.
86* Fillin is created during the factorization routine
87* PZPBTRF and this is stored in AF. If a linear system
88* is to be solved using PZPBTRS after the factorization
89* routine, AF *must not be altered* after the factorization.
90*
91* LAF (local input) INTEGER
92* Size of user-input Auxiliary Fillin space AF. Must be >=
93* (NB+2*bw)*bw
94* If LAF is not large enough, an error code will be returned
95* and the minimum acceptable size will be returned in AF( 1 )
96*
97* WORK (local workspace/local output)
98* COMPLEX*16 temporary workspace. This space may
99* be overwritten in between calls to routines. WORK must be
100* the size given in LWORK.
101* On exit, WORK( 1 ) contains the minimal LWORK.
102*
103* LWORK (local input or global input) INTEGER
104* Size of user-input workspace WORK.
105* If LWORK is too small, the minimal acceptable size will be
106* returned in WORK(1) and an error code is returned. LWORK>=
107* bw*bw
108*
109* INFO (global output) INTEGER
110* = 0: successful exit
111* < 0: If the i-th argument is an array and the j-entry had
112* an illegal value, then INFO = -(i*100+j), if the i-th
113* argument is a scalar and had an illegal value, then
114* INFO = -i.
115* > 0: If INFO = K<=NPROCS, the submatrix stored on processor
116* INFO and factored locally was not
117* positive definite, and
118* the factorization was not completed.
119* If INFO = K>NPROCS, the submatrix stored on processor
120* INFO-NPROCS representing interactions with other
121* processors was not
122* positive definite,
123* and the factorization was not completed.
124*
125* =====================================================================
126*
127*
128* Restrictions
129* ============
130*
131* The following are restrictions on the input parameters. Some of these
132* are temporary and will be removed in future releases, while others
133* may reflect fundamental technical limitations.
134*
135* Non-cyclic restriction: VERY IMPORTANT!
136* P*NB>= mod(JA-1,NB)+N.
137* The mapping for matrices must be blocked, reflecting the nature
138* of the divide and conquer algorithm as a task-parallel algorithm.
139* This formula in words is: no processor may have more than one
140* chunk of the matrix.
141*
142* Blocksize cannot be too small:
143* If the matrix spans more than one processor, the following
144* restriction on NB, the size of each block on each processor,
145* must hold:
146* NB >= 2*BW
147* The bulk of parallel computation is done on the matrix of size
148* O(NB) on each processor. If this is too small, divide and conquer
149* is a poor choice of algorithm.
150*
151* Submatrix reference:
152* JA = IB
153* Alignment restriction that prevents unnecessary communication.
154*
155*
156* =====================================================================
157*
158*
159* Notes
160* =====
161*
162* If the factorization routine and the solve routine are to be called
163* separately (to solve various sets of righthand sides using the same
164* coefficient matrix), the auxiliary space AF *must not be altered*
165* between calls to the factorization routine and the solve routine.
166*
167* The best algorithm for solving banded and tridiagonal linear systems
168* depends on a variety of parameters, especially the bandwidth.
169* Currently, only algorithms designed for the case N/P >> bw are
170* implemented. These go by many names, including Divide and Conquer,
171* Partitioning, domain decomposition-type, etc.
172*
173* Algorithm description: Divide and Conquer
174*
175* The Divide and Conqer algorithm assumes the matrix is narrowly
176* banded compared with the number of equations. In this situation,
177* it is best to distribute the input matrix A one-dimensionally,
178* with columns atomic and rows divided amongst the processes.
179* The basic algorithm divides the banded matrix up into
180* P pieces with one stored on each processor,
181* and then proceeds in 2 phases for the factorization or 3 for the
182* solution of a linear system.
183* 1) Local Phase:
184* The individual pieces are factored independently and in
185* parallel. These factors are applied to the matrix creating
186* fillin, which is stored in a non-inspectable way in auxiliary
187* space AF. Mathematically, this is equivalent to reordering
188* the matrix A as P A P^T and then factoring the principal
189* leading submatrix of size equal to the sum of the sizes of
190* the matrices factored on each processor. The factors of
191* these submatrices overwrite the corresponding parts of A
192* in memory.
193* 2) Reduced System Phase:
194* A small (BW* (P-1)) system is formed representing
195* interaction of the larger blocks, and is stored (as are its
196* factors) in the space AF. A parallel Block Cyclic Reduction
197* algorithm is used. For a linear system, a parallel front solve
198* followed by an analagous backsolve, both using the structure
199* of the factored matrix, are performed.
200* 3) Backsubsitution Phase:
201* For a linear system, a local backsubstitution is performed on
202* each processor in parallel.
203*
204*
205* Descriptors
206* ===========
207*
208* Descriptors now have *types* and differ from ScaLAPACK 1.0.
209*
210* Note: banded codes can use either the old two dimensional
211* or new one-dimensional descriptors, though the processor grid in
212* both cases *must be one-dimensional*. We describe both types below.
213*
214* Each global data object is described by an associated description
215* vector. This vector stores the information required to establish
216* the mapping between an object element and its corresponding process
217* and memory location.
218*
219* Let A be a generic term for any 2D block cyclicly distributed array.
220* Such a global array has an associated description vector DESCA.
221* In the following comments, the character _ should be read as
222* "of the global array".
223*
224* NOTATION STORED IN EXPLANATION
225* --------------- -------------- --------------------------------------
226* DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
227* DTYPE_A = 1.
228* CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
229* the BLACS process grid A is distribu-
230* ted over. The context itself is glo-
231* bal, but the handle (the integer
232* value) may vary.
233* M_A (global) DESCA( M_ ) The number of rows in the global
234* array A.
235* N_A (global) DESCA( N_ ) The number of columns in the global
236* array A.
237* MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
238* the rows of the array.
239* NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
240* the columns of the array.
241* RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
242* row of the array A is distributed.
243* CSRC_A (global) DESCA( CSRC_ ) The process column over which the
244* first column of the array A is
245* distributed.
246* LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
247* array. LLD_A >= MAX(1,LOCr(M_A)).
248*
249* Let K be the number of rows or columns of a distributed matrix,
250* and assume that its process grid has dimension p x q.
251* LOCr( K ) denotes the number of elements of K that a process
252* would receive if K were distributed over the p processes of its
253* process column.
254* Similarly, LOCc( K ) denotes the number of elements of K that a
255* process would receive if K were distributed over the q processes of
256* its process row.
257* The values of LOCr() and LOCc() may be determined via a call to the
258* ScaLAPACK tool function, NUMROC:
259* LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
260* LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
261* An upper bound for these quantities may be computed by:
262* LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
263* LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
264*
265*
266* One-dimensional descriptors:
267*
268* One-dimensional descriptors are a new addition to ScaLAPACK since
269* version 1.0. They simplify and shorten the descriptor for 1D
270* arrays.
271*
272* Since ScaLAPACK supports two-dimensional arrays as the fundamental
273* object, we allow 1D arrays to be distributed either over the
274* first dimension of the array (as if the grid were P-by-1) or the
275* 2nd dimension (as if the grid were 1-by-P). This choice is
276* indicated by the descriptor type (501 or 502)
277* as described below.
278*
279* IMPORTANT NOTE: the actual BLACS grid represented by the
280* CTXT entry in the descriptor may be *either* P-by-1 or 1-by-P
281* irrespective of which one-dimensional descriptor type
282* (501 or 502) is input.
283* This routine will interpret the grid properly either way.
284* ScaLAPACK routines *do not support intercontext operations* so that
285* the grid passed to a single ScaLAPACK routine *must be the same*
286* for all array descriptors passed to that routine.
287*
288* NOTE: In all cases where 1D descriptors are used, 2D descriptors
289* may also be used, since a one-dimensional array is a special case
290* of a two-dimensional array with one dimension of size unity.
291* The two-dimensional array used in this case *must* be of the
292* proper orientation:
293* If the appropriate one-dimensional descriptor is DTYPEA=501
294* (1 by P type), then the two dimensional descriptor must
295* have a CTXT value that refers to a 1 by P BLACS grid;
296* If the appropriate one-dimensional descriptor is DTYPEA=502
297* (P by 1 type), then the two dimensional descriptor must
298* have a CTXT value that refers to a P by 1 BLACS grid.
299*
300*
301* Summary of allowed descriptors, types, and BLACS grids:
302* DTYPE 501 502 1 1
303* BLACS grid 1xP or Px1 1xP or Px1 1xP Px1
304* -----------------------------------------------------
305* A OK NO OK NO
306* B NO OK NO OK
307*
308* Let A be a generic term for any 1D block cyclicly distributed array.
309* Such a global array has an associated description vector DESCA.
310* In the following comments, the character _ should be read as
311* "of the global array".
312*
313* NOTATION STORED IN EXPLANATION
314* --------------- ---------- ------------------------------------------
315* DTYPE_A(global) DESCA( 1 ) The descriptor type. For 1D grids,
316* TYPE_A = 501: 1-by-P grid.
317* TYPE_A = 502: P-by-1 grid.
318* CTXT_A (global) DESCA( 2 ) The BLACS context handle, indicating
319* the BLACS process grid A is distribu-
320* ted over. The context itself is glo-
321* bal, but the handle (the integer
322* value) may vary.
323* N_A (global) DESCA( 3 ) The size of the array dimension being
324* distributed.
325* NB_A (global) DESCA( 4 ) The blocking factor used to distribute
326* the distributed dimension of the array.
327* SRC_A (global) DESCA( 5 ) The process row or column over which the
328* first row or column of the array
329* is distributed.
330* LLD_A (local) DESCA( 6 ) The leading dimension of the local array
331* storing the local blocks of the distri-
332* buted array A. Minimum value of LLD_A
333* depends on TYPE_A.
334* TYPE_A = 501: LLD_A >=
335* size of undistributed dimension, 1.
336* TYPE_A = 502: LLD_A >=NB_A, 1.
337* Reserved DESCA( 7 ) Reserved for future use.
338*
339*
340*
341* =====================================================================
342*
343* Code Developer: Andrew J. Cleary, University of Tennessee.
344* Current address: Lawrence Livermore National Labs.
345* This version released: August, 2001.
346*
347* =====================================================================
348*
349* ..
350* .. Parameters ..
351 DOUBLE PRECISION ONE, ZERO
352 parameter( one = 1.0d+0 )
353 parameter( zero = 0.0d+0 )
354 COMPLEX*16 CONE, CZERO
355 parameter( cone = ( 1.0d+0, 0.0d+0 ) )
356 parameter( czero = ( 0.0d+0, 0.0d+0 ) )
357 INTEGER INT_ONE
358 parameter( int_one = 1 )
359 INTEGER DESCMULT, BIGNUM
360 parameter(descmult = 100, bignum = descmult * descmult)
361 INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
362 $ lld_, mb_, m_, nb_, n_, rsrc_
363 parameter( block_cyclic_2d = 1, dlen_ = 9, dtype_ = 1,
364 $ ctxt_ = 2, m_ = 3, n_ = 4, mb_ = 5, nb_ = 6,
365 $ rsrc_ = 7, csrc_ = 8, lld_ = 9 )
366* ..
367* .. Local Scalars ..
368 INTEGER COMM_PROC, CSRC, FIRST_PROC, I, ICTXT,
369 $ ictxt_new, ictxt_save, idum1, idum3, ja_new,
370 $ laf_min, level_dist, llda, mbw2, mycol, myrow,
371 $ my_num_cols, nb, next_tri_size_m,
372 $ next_tri_size_n, np, npcol, nprow, np_save,
373 $ odd_size, ofst, part_offset, part_size,
374 $ prev_tri_size_m, prev_tri_size_n, return_code,
375 $ store_n_a, work_size_min
376* ..
377* .. Local Arrays ..
378 INTEGER DESCA_1XP( 7 ), PARAM_CHECK( 9, 3 )
379* ..
380* .. External Subroutines ..
381 EXTERNAL blacs_get, blacs_gridexit, blacs_gridinfo,
382 $ desc_convert, globchk, pxerbla, reshape, zaxpy,
383 $ zgemm, zgerv2d, zgesd2d, zlamov, zlatcpy,
384 $ zpbtrf, zpotrf, zsyrk, ztbtrs, ztrmm, ztrrv2d,
385 $ ztrsd2d, ztrsm, ztrtrs
386* ..
387* .. External Functions ..
388 LOGICAL LSAME
389 INTEGER NUMROC
390 EXTERNAL lsame, numroc
391* ..
392* .. Intrinsic Functions ..
393 INTRINSIC ichar, min, mod
394* ..
395* .. Executable Statements ..
396*
397* Test the input parameters
398*
399 info = 0
400*
401* Convert descriptor into standard form for easy access to
402* parameters, check that grid is of right shape.
403*
404 desca_1xp( 1 ) = 501
405*
406 CALL desc_convert( desca, desca_1xp, return_code )
407*
408 IF( return_code .NE. 0) THEN
409 info = -( 6*100 + 2 )
410 ENDIF
411*
412* Get values out of descriptor for use in code.
413*
414 ictxt = desca_1xp( 2 )
415 csrc = desca_1xp( 5 )
416 nb = desca_1xp( 4 )
417 llda = desca_1xp( 6 )
418 store_n_a = desca_1xp( 3 )
419*
420* Get grid parameters
421*
422*
423* Pre-calculate bw^2
424*
425 mbw2 = bw * bw
426*
427 CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
428 np = nprow * npcol
429*
430*
431*
432 IF( lsame( uplo, 'U' ) ) THEN
433 idum1 = ichar( 'U' )
434 ELSE IF ( lsame( uplo, 'L' ) ) THEN
435 idum1 = ichar( 'L' )
436 ELSE
437 info = -1
438 END IF
439*
440 IF( lwork .LT. -1) THEN
441 info = -10
442 ELSE IF ( lwork .EQ. -1 ) THEN
443 idum3 = -1
444 ELSE
445 idum3 = 1
446 ENDIF
447*
448 IF( n .LT. 0 ) THEN
449 info = -2
450 ENDIF
451*
452 IF( n+ja-1 .GT. store_n_a ) THEN
453 info = -( 6*100 + 6 )
454 ENDIF
455*
456 IF(( bw .GT. n-1 ) .OR.
457 $ ( bw .LT. 0 ) ) THEN
458 info = -3
459 ENDIF
460*
461 IF( llda .LT. (bw+1) ) THEN
462 info = -( 6*100 + 6 )
463 ENDIF
464*
465 IF( nb .LE. 0 ) THEN
466 info = -( 6*100 + 4 )
467 ENDIF
468*
469* Argument checking that is specific to Divide & Conquer routine
470*
471 IF( nprow .NE. 1 ) THEN
472 info = -( 6*100+2 )
473 ENDIF
474*
475 IF( n .GT. np*nb-mod( ja-1, nb )) THEN
476 info = -( 2 )
477 CALL pxerbla( ictxt,
478 $ 'PZPBTRF, D&C alg.: only 1 block per proc',
479 $ -info )
480 RETURN
481 ENDIF
482*
483 IF((ja+n-1.GT.nb) .AND. ( nb.LT.2*bw )) THEN
484 info = -( 6*100+4 )
485 CALL pxerbla( ictxt,
486 $ 'PZPBTRF, D&C alg.: NB too small',
487 $ -info )
488 RETURN
489 ENDIF
490*
491*
492* Check auxiliary storage size
493*
494 laf_min = (nb+2*bw)*bw
495*
496 IF( laf .LT. laf_min ) THEN
497 info = -8
498* put minimum value of laf into AF( 1 )
499 af( 1 ) = laf_min
500 CALL pxerbla( ictxt,
501 $ 'PZPBTRF: auxiliary storage error ',
502 $ -info )
503 RETURN
504 ENDIF
505*
506* Check worksize
507*
508 work_size_min = bw*bw
509*
510 work( 1 ) = work_size_min
511*
512 IF( lwork .LT. work_size_min ) THEN
513 IF( lwork .NE. -1 ) THEN
514 info = -10
515 CALL pxerbla( ictxt,
516 $ 'PZPBTRF: worksize error ',
517 $ -info )
518 ENDIF
519 RETURN
520 ENDIF
521*
522* Pack params and positions into arrays for global consistency check
523*
524 param_check( 9, 1 ) = desca(5)
525 param_check( 8, 1 ) = desca(4)
526 param_check( 7, 1 ) = desca(3)
527 param_check( 6, 1 ) = desca(1)
528 param_check( 5, 1 ) = ja
529 param_check( 4, 1 ) = bw
530 param_check( 3, 1 ) = n
531 param_check( 2, 1 ) = idum3
532 param_check( 1, 1 ) = idum1
533*
534 param_check( 9, 2 ) = 605
535 param_check( 8, 2 ) = 604
536 param_check( 7, 2 ) = 603
537 param_check( 6, 2 ) = 601
538 param_check( 5, 2 ) = 5
539 param_check( 4, 2 ) = 3
540 param_check( 3, 2 ) = 2
541 param_check( 2, 2 ) = 10
542 param_check( 1, 2 ) = 1
543*
544* Want to find errors with MIN( ), so if no error, set it to a big
545* number. If there already is an error, multiply by the the
546* descriptor multiplier.
547*
548 IF( info.GE.0 ) THEN
549 info = bignum
550 ELSE IF( info.LT.-descmult ) THEN
551 info = -info
552 ELSE
553 info = -info * descmult
554 END IF
555*
556* Check consistency across processors
557*
558 CALL globchk( ictxt, 9, param_check, 9,
559 $ param_check( 1, 3 ), info )
560*
561* Prepare output: set info = 0 if no error, and divide by DESCMULT
562* if error is not in a descriptor entry.
563*
564 IF( info.EQ.bignum ) THEN
565 info = 0
566 ELSE IF( mod( info, descmult ) .EQ. 0 ) THEN
567 info = -info / descmult
568 ELSE
569 info = -info
570 END IF
571*
572 IF( info.LT.0 ) THEN
573 CALL pxerbla( ictxt, 'PZPBTRF', -info )
574 RETURN
575 END IF
576*
577* Quick return if possible
578*
579 IF( n.EQ.0 )
580 $ RETURN
581*
582*
583* Adjust addressing into matrix space to properly get into
584* the beginning part of the relevant data
585*
586 part_offset = nb*( (ja-1)/(npcol*nb) )
587*
588 IF ( (mycol-csrc) .LT. (ja-part_offset-1)/nb ) THEN
589 part_offset = part_offset + nb
590 ENDIF
591*
592 IF ( mycol .LT. csrc ) THEN
593 part_offset = part_offset - nb
594 ENDIF
595*
596* Form a new BLACS grid (the "standard form" grid) with only procs
597* holding part of the matrix, of size 1xNP where NP is adjusted,
598* starting at csrc=0, with JA modified to reflect dropped procs.
599*
600* First processor to hold part of the matrix:
601*
602 first_proc = mod( ( ja-1 )/nb+csrc, npcol )
603*
604* Calculate new JA one while dropping off unused processors.
605*
606 ja_new = mod( ja-1, nb ) + 1
607*
608* Save and compute new value of NP
609*
610 np_save = np
611 np = ( ja_new+n-2 )/nb + 1
612*
613* Call utility routine that forms "standard-form" grid
614*
615 CALL reshape( ictxt, int_one, ictxt_new, int_one,
616 $ first_proc, int_one, np )
617*
618* Use new context from standard grid as context.
619*
620 ictxt_save = ictxt
621 ictxt = ictxt_new
622 desca_1xp( 2 ) = ictxt_new
623*
624* Get information about new grid.
625*
626 CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
627*
628* Drop out processors that do not have part of the matrix.
629*
630 IF( myrow .LT. 0 ) THEN
631 GOTO 1234
632 ENDIF
633*
634* ********************************
635* Values reused throughout routine
636*
637* User-input value of partition size
638*
639 part_size = nb
640*
641* Number of columns in each processor
642*
643 my_num_cols = numroc( n, part_size, mycol, 0, npcol )
644*
645* Offset in columns to beginning of main partition in each proc
646*
647 IF ( mycol .EQ. 0 ) THEN
648 part_offset = part_offset+mod( ja_new-1, part_size )
649 my_num_cols = my_num_cols - mod(ja_new-1, part_size )
650 ENDIF
651*
652* Offset in elements
653*
654 ofst = part_offset*llda
655*
656* Size of main (or odd) partition in each processor
657*
658 odd_size = my_num_cols
659 IF ( mycol .LT. np-1 ) THEN
660 odd_size = odd_size - bw
661 ENDIF
662*
663*
664* Zero out space for fillin
665*
666 DO 10 i=1, laf_min
667 af( i ) = czero
668 10 CONTINUE
669*
670* Zero out space for work
671*
672 DO 20 i=1, work_size_min
673 work( i ) = czero
674 20 CONTINUE
675*
676* Begin main code
677*
678 IF ( lsame( uplo, 'L' ) ) THEN
679*
680********************************************************************
681* PHASE 1: Local computation phase.
682********************************************************************
683*
684*
685* Sizes of the extra triangles communicated bewtween processors
686*
687 IF( mycol .GT. 0 ) THEN
688 prev_tri_size_m= min( bw,
689 $ numroc( n, part_size, mycol, 0, npcol ) )
690 prev_tri_size_n=min( bw,
691 $ numroc( n, part_size, mycol-1, 0, npcol ) )
692 ENDIF
693*
694 IF( mycol .LT. npcol-1 ) THEN
695 next_tri_size_m=min( bw,
696 $ numroc( n, part_size, mycol+1, 0, npcol ) )
697 next_tri_size_n= min( bw,
698 $ numroc( n, part_size, mycol, 0, npcol ) )
699 ENDIF
700*
701 IF ( mycol .LT. np-1 ) THEN
702* Transfer last triangle D_i of local matrix to next processor
703* which needs it to calculate fillin due to factorization of
704* its main (odd) block A_i.
705* Overlap the send with the factorization of A_i.
706*
707 CALL ztrsd2d( ictxt, 'U', 'N', next_tri_size_m,
708 $ next_tri_size_n, a( ofst+odd_size*llda+(bw+1) ),
709 $ llda-1, 0, mycol+1 )
710*
711 ENDIF
712*
713*
714* Factor main partition A_i = L_i {L_i}^C in each processor
715*
716 CALL zpbtrf( uplo, odd_size, bw, a( ofst + 1),
717 $ llda, info )
718*
719 IF( info.NE.0 ) THEN
720 info = mycol+1
721 GOTO 1500
722 ENDIF
723*
724*
725 IF ( mycol .LT. np-1 ) THEN
726* Apply factorization to odd-even connection block B_i
727*
728* conjugate transpose the connection block in preparation.
729*
730 CALL zlatcpy( 'U', bw, bw,
731 $ a(( ofst+(bw+1)+(odd_size-bw)*llda )), llda-1,
732 $ af( odd_size*bw+2*mbw2+1+bw-bw ), bw )
733*
734* Perform the triangular system solve {L_i}{{B'}_i}^C = {B_i}^C
735*
736 CALL ztrtrs( 'L', 'N', 'N', bw, bw,
737 $ a( ofst+1+(odd_size-bw)*llda ), llda-1,
738 $ af( odd_size*bw+2*mbw2+1 ), bw, info )
739*
740*
741* conjugate transpose resulting block to its location
742* in main storage.
743*
744 CALL zlatcpy( 'L', bw, bw, af( odd_size*bw+2*mbw2+1+bw-bw ),
745 $ bw, a(( ofst+(bw+1)+(odd_size-bw)*llda )),
746 $ llda-1 )
747*
748*
749* Compute contribution to diagonal block(s) of reduced system.
750* {C'}_i = {C_i}-{{B'}_i}{{B'}_i}^C
751*
752* The following method uses more flops than necessary but
753* does not necessitate the writing of a new BLAS routine.
754*
755*
756 CALL zherk( uplo, 'C', bw, bw, -one,
757 $ af( odd_size*bw+2*mbw2+1 ), bw, one,
758 $ a( ofst+1+odd_size*llda ), llda-1 )
759*
760 ENDIF
761* End of "if ( MYCOL .lt. NP-1 )..." loop
762*
763*
764 1500 CONTINUE
765* If the processor could not locally factor, it jumps here.
766*
767 IF ( mycol .NE. 0 ) THEN
768* Discard temporary matrix stored beginning in
769* AF( (odd_size+2*bw)*bw+1 ) and use for
770* off_diagonal block of reduced system.
771*
772* Receive previously transmitted matrix section, which forms
773* the right-hand-side for the triangular solve that calculates
774* the "spike" fillin.
775*
776*
777 CALL ztrrv2d( ictxt, 'U', 'N', prev_tri_size_m,
778 $ prev_tri_size_n, af( 1 ), odd_size, 0,
779 $ mycol-1 )
780*
781 IF (info.EQ.0) THEN
782*
783* Calculate the "spike" fillin, ${L_i} {{G}_i}^C = {D_i}$ .
784*
785 CALL ztbtrs( 'L', 'N', 'N', odd_size, bw, bw, a( ofst + 1 ),
786 $ llda, af( 1 ), odd_size, info )
787*
788*
789* Calculate the update block for previous proc, E_i = G_i{G_i}^C
790*
791 CALL zherk( 'L', 'C', bw, odd_size,
792 $ -one, af( 1 ), odd_size, zero,
793 $ af( 1 + (odd_size+2*bw)*bw), bw )
794*
795*
796* Initiate send of E_i to previous processor to overlap
797* with next computation.
798*
799 CALL zgesd2d( ictxt, bw, bw, af( odd_size*bw+2*mbw2+1 ), bw,
800 $ 0, mycol-1 )
801*
802*
803 IF ( mycol .LT. np-1 ) THEN
804*
805* Calculate off-diagonal block(s) of reduced system.
806* Note: for ease of use in solution of reduced system, store
807* L's off-diagonal block in conjugate transpose form.
808* {F_i}^C = {H_i}{{B'}_i}^C
809*
810* Copy matrix H_i (the last bw cols of G_i) to AF storage
811* as per requirements of BLAS routine ZTRMM.
812* Since we have G_i^C stored, conjugate transpose
813* H_i^C to H_i.
814*
815 CALL zlatcpy( 'N', bw, bw,
816 $ af( odd_size-bw+1 ), odd_size,
817 $ af( (odd_size)*bw+1), bw )
818*
819 CALL ztrmm( 'R', 'U', 'C', 'N', bw, bw, -cone,
820 $ a( ( ofst+(bw+1)+(odd_size-bw)*llda ) ), llda-1,
821 $ af( (odd_size)*bw+1 ), bw )
822*
823*
824 ENDIF
825*
826 ENDIF
827* End of "if ( MYCOL .ne. 0 )..."
828*
829 ENDIF
830* End of "if (info.eq.0) then"
831*
832*
833* Check to make sure no processors have found errors
834*
835 CALL igamx2d( ictxt, 'A', ' ', 1, 1, info, 1, info, info,
836 $ -1, 0, 0 )
837*
838 IF( mycol.EQ.0 ) THEN
839 CALL igebs2d( ictxt, 'A', ' ', 1, 1, info, 1 )
840 ELSE
841 CALL igebr2d( ictxt, 'A', ' ', 1, 1, info, 1, 0, 0 )
842 ENDIF
843*
844 IF ( info.NE.0 ) THEN
845 GOTO 1000
846 ENDIF
847* No errors found, continue
848*
849*
850********************************************************************
851* PHASE 2: Formation and factorization of Reduced System.
852********************************************************************
853*
854* Gather up local sections of reduced system
855*
856*
857* The last processor does not participate in the factorization of
858* the reduced system, having sent its E_i already.
859 IF( mycol .EQ. npcol-1 ) THEN
860 GOTO 14
861 ENDIF
862*
863* Initiate send of off-diag block(s) to overlap with next part.
864* Off-diagonal block needed on neighboring processor to start
865* algorithm.
866*
867 IF( (mod( mycol+1, 2 ) .EQ. 0) .AND. ( mycol .GT. 0 ) ) THEN
868*
869 CALL zgesd2d( ictxt, bw, bw,
870 $ af( odd_size*bw+1 ),
871 $ bw, 0, mycol-1 )
872*
873 ENDIF
874*
875* Copy last diagonal block into AF storage for subsequent
876* operations.
877*
878 CALL zlamov( 'N', bw, bw,
879 $ a( ofst+odd_size*llda+1 ),
880 $ llda-1, af( odd_size*bw+mbw2+1 ),
881 $ bw )
882*
883* Receive cont. to diagonal block that is stored on this proc.
884*
885 IF( mycol.LT. npcol-1 ) THEN
886*
887 CALL zgerv2d( ictxt, bw, bw,
888 $ af( odd_size*bw+2*mbw2+1 ),
889 $ bw, 0,
890 $ mycol+1 )
891*
892* Add contribution to diagonal block
893*
894 CALL zaxpy( mbw2, cone,
895 $ af( odd_size*bw+2*mbw2+1 ),
896 $ 1, af( odd_size*bw+mbw2+1 ), 1 )
897*
898 ENDIF
899*
900*
901* *************************************
902* Modification Loop
903*
904* The distance for sending and receiving for each level starts
905* at 1 for the first level.
906 level_dist = 1
907*
908* Do until this proc is needed to modify other procs' equations
909*
910 12 CONTINUE
911 IF( mod( (mycol+1)/level_dist, 2) .NE. 0 ) GOTO 11
912*
913* Receive and add contribution to diagonal block from the left
914*
915 IF( mycol-level_dist .GE. 0 ) THEN
916 CALL zgerv2d( ictxt, bw, bw, work( 1 ),
917 $ bw, 0, mycol-level_dist )
918*
919 CALL zaxpy( mbw2, cone, work( 1 ), 1,
920 $ af( odd_size*bw+mbw2+1 ), 1 )
921*
922 ENDIF
923*
924* Receive and add contribution to diagonal block from the right
925*
926 IF( mycol+level_dist .LT. npcol-1 ) THEN
927 CALL zgerv2d( ictxt, bw, bw, work( 1 ),
928 $ bw, 0, mycol+level_dist )
929*
930 CALL zaxpy( mbw2, cone, work( 1 ), 1,
931 $ af( odd_size*bw+mbw2+1 ), 1 )
932*
933 ENDIF
934*
935 level_dist = level_dist*2
936*
937 GOTO 12
938 11 CONTINUE
939* [End of GOTO Loop]
940*
941*
942* *********************************
943* Calculate and use this proc's blocks to modify other procs'...
944*
945* Factor diagonal block
946*
947 CALL zpotrf( 'L', bw, af( odd_size*bw+mbw2+1 ),
948 $ bw, info )
949*
950 IF( info.NE.0 ) THEN
951 info = npcol + mycol
952 ENDIF
953*
954* ****************************************************************
955* Receive offdiagonal block from processor to right.
956* If this is the first group of processors, the receive comes
957* from a different processor than otherwise.
958*
959 IF( level_dist .EQ. 1 )THEN
960 comm_proc = mycol + 1
961*
962* Move block into place that it will be expected to be for
963* calcs.
964*
965 CALL zlamov( 'N', bw, bw, af( odd_size*bw+1 ), bw,
966 $ af( odd_size*bw+2*mbw2+1 ), bw )
967*
968 ELSE
969 comm_proc = mycol + level_dist/2
970 ENDIF
971*
972 IF( mycol/level_dist .LE. (npcol-1)/level_dist-2 )THEN
973*
974 CALL zgerv2d( ictxt, bw, bw,
975 $ af( odd_size*bw+1 ),
976 $ bw, 0, comm_proc )
977*
978 IF( info .EQ. 0 ) THEN
979*
980*
981* Modify upper off_diagonal block with diagonal block
982*
983*
984 CALL ztrsm( 'L', 'L', 'N', 'N', bw, bw, cone,
985 $ af( odd_size*bw+mbw2+1 ), bw,
986 $ af( odd_size*bw+1 ), bw )
987*
988 ENDIF
989* End of "if ( info.eq.0 ) then"
990*
991* Calculate contribution from this block to next diagonal block
992*
993 CALL zherk( 'L', 'C', bw, bw, -one,
994 $ af( (odd_size)*bw+1 ), bw, zero,
995 $ work( 1 ), bw )
996*
997* Send contribution to diagonal block's owning processor.
998*
999 CALL zgesd2d( ictxt, bw, bw, work( 1 ), bw,
1000 $ 0, mycol+level_dist )
1001*
1002 ENDIF
1003* End of "if( mycol/level_dist .le. (npcol-1)/level_dist-2 )..."
1004*
1005*
1006* ****************************************************************
1007* Receive off_diagonal block from left and use to finish with this
1008* processor.
1009*
1010 IF( (mycol/level_dist .GT. 0 ).AND.
1011 $ ( mycol/level_dist .LE. (npcol-1)/level_dist-1 ) ) THEN
1012*
1013 IF( level_dist .GT. 1)THEN
1014*
1015* Receive offdiagonal block(s) from proc level_dist/2 to the
1016* left
1017*
1018 CALL zgerv2d( ictxt, bw, bw,
1019 $ af( odd_size*bw+2*mbw2+1 ),
1020 $ bw, 0, mycol-level_dist/2 )
1021*
1022 ENDIF
1023*
1024*
1025 IF( info.EQ.0 ) THEN
1026*
1027* Use diagonal block(s) to modify this offdiagonal block
1028*
1029 CALL ztrsm( 'R', 'L', 'C', 'N', bw, bw, cone,
1030 $ af( odd_size*bw+mbw2+1 ), bw,
1031 $ af( odd_size*bw+2*mbw2+1 ), bw )
1032*
1033 ENDIF
1034* End of "if( info.eq.0 ) then"
1035*
1036* Use offdiag block(s) to calculate modification to diag block
1037* of processor to the left
1038*
1039 CALL zherk( 'L', 'N', bw, bw, -one,
1040 $ af( (odd_size+2*bw)*bw+1 ), bw, zero,
1041 $ work( 1 ), bw )
1042*
1043* Send contribution to diagonal block's owning processor.
1044*
1045 CALL zgesd2d( ictxt, bw, bw, work( 1 ), bw,
1046 $ 0, mycol-level_dist )
1047*
1048* *******************************************************
1049*
1050 IF( mycol/level_dist .LE. (npcol-1)/level_dist-2 ) THEN
1051*
1052* Decide which processor offdiagonal block(s) goes to
1053*
1054 IF( ( mod( mycol/( 2*level_dist ),2 )) .EQ.0 ) THEN
1055 comm_proc = mycol + level_dist
1056 ELSE
1057 comm_proc = mycol - level_dist
1058 ENDIF
1059*
1060* Use offdiagonal blocks to calculate offdiag
1061* block to send to neighboring processor. Depending
1062* on circumstances, may need to transpose the matrix.
1063*
1064 CALL zgemm( 'N', 'N', bw, bw, bw, -cone,
1065 $ af( odd_size*bw+2*mbw2+1 ), bw,
1066 $ af( odd_size*bw+1 ), bw, czero, work( 1 ),
1067 $ bw )
1068*
1069* Send contribution to offdiagonal block's owning processor.
1070*
1071 CALL zgesd2d( ictxt, bw, bw, work( 1 ), bw,
1072 $ 0, comm_proc )
1073*
1074 ENDIF
1075*
1076 ENDIF
1077* End of "if( mycol/level_dist.le. (npcol-1)/level_dist -1 )..."
1078*
1079 14 CONTINUE
1080*
1081 ELSE
1082*
1083* CASE UPLO = 'U'
1084*
1085********************************************************************
1086* PHASE 1: Local computation phase.
1087********************************************************************
1088*
1089*
1090* Sizes of the extra triangles communicated bewtween processors
1091*
1092 IF( mycol .GT. 0 ) THEN
1093 prev_tri_size_m= min( bw,
1094 $ numroc( n, part_size, mycol, 0, npcol ) )
1095 prev_tri_size_n=min( bw,
1096 $ numroc( n, part_size, mycol-1, 0, npcol ) )
1097 ENDIF
1098*
1099 IF( mycol .LT. npcol-1 ) THEN
1100 next_tri_size_m=min( bw,
1101 $ numroc( n, part_size, mycol+1, 0, npcol ) )
1102 next_tri_size_n= min( bw,
1103 $ numroc( n, part_size, mycol, 0, npcol ) )
1104 ENDIF
1105*
1106*
1107*
1108* Factor main partition A_i^C = U_i {U_i}^C in each processor
1109*
1110 CALL zpbtrf( uplo, odd_size, bw, a( ofst + 1),
1111 $ llda, info )
1112*
1113 IF( info.NE.0 ) THEN
1114 info = mycol+1
1115 GOTO 1600
1116 ENDIF
1117*
1118*
1119 IF ( mycol .LT. np-1 ) THEN
1120* Apply factorization to odd-even connection block B_i
1121*
1122* Move the connection block in preparation.
1123*
1124 CALL zlamov( 'L', bw, bw, a( ( ofst+1+odd_size*llda ) ),
1125 $ llda-1, af( odd_size*bw+2*mbw2+1+bw-bw ), bw )
1126*
1127*
1128* Perform the triangular solve {L_i}{{B'}_i}^C = {B_i}^C
1129*
1130 CALL ztrtrs( 'U', 'C', 'N', bw, bw,
1131 $ a( ofst+bw+1+(odd_size-bw)*llda ), llda-1,
1132 $ af( odd_size*bw+2*mbw2+1 ), bw, info )
1133*
1134* Move the resulting block back to its location in main storage.
1135*
1136 CALL zlamov( 'L', bw, bw, af( odd_size*bw+2*mbw2+1+bw-bw ),
1137 $ bw, a(( ofst+1+odd_size*llda )), llda-1 )
1138*
1139*
1140* Compute contribution to diagonal block(s) of reduced system.
1141* {C'}_i^C = {C_i}^C-{{B'}_i}^C{{B'}_i}
1142*
1143* The following method uses more flops than necessary but
1144* does not necessitate the writing of a new BLAS routine.
1145*
1146*
1147 CALL zherk( uplo, 'C', bw, bw, -one,
1148 $ af( odd_size*bw+2*mbw2+1 ), bw, one,
1149 $ a( ofst+bw+1+odd_size*llda ), llda-1 )
1150*
1151 ENDIF
1152* End of "if ( MYCOL .lt. NP-1 )..." loop
1153*
1154*
1155 1600 CONTINUE
1156* If the processor could not locally factor, it jumps here.
1157*
1158 IF ( mycol .NE. 0 ) THEN
1159* Discard temporary matrix stored beginning in
1160* AF( (odd_size+2*bw)*bw+1 ) and use for
1161* off_diagonal block of reduced system.
1162*
1163* Calculate the "spike" fillin, ${L_i} {{G}_i}^C = {D_i}$ .
1164*
1165*
1166* Copy D block into AF storage for solve.
1167*
1168 CALL zlatcpy( 'L', prev_tri_size_n, prev_tri_size_m,
1169 $ a( ofst+1 ), llda-1, af( 1 ), odd_size )
1170*
1171 IF ( info.EQ.0 ) THEN
1172*
1173 CALL ztbtrs( 'U', 'C', 'N', odd_size, bw, bw,
1174 $ a( ofst + 1 ), llda,
1175 $ af( 1 ), odd_size, info )
1176*
1177*
1178* Calculate the update block for previous proc, E_i = G_i{G_i}^C
1179*
1180 CALL zherk( 'L', 'C', bw, odd_size,
1181 $ -one, af( 1 ), odd_size, zero,
1182 $ af( 1 + (odd_size+2*bw)*bw), bw )
1183*
1184*
1185* Initiate send of E_i to previous processor to overlap
1186* with next computation.
1187*
1188 CALL zgesd2d( ictxt, bw, bw, af( odd_size*bw+2*mbw2+1 ), bw,
1189 $ 0, mycol-1 )
1190*
1191*
1192 IF ( mycol .LT. np-1 ) THEN
1193*
1194* Calculate off-diagonal block(s) of reduced system.
1195* Note: for ease of use in solution of reduced system, store
1196* L's off-diagonal block in conjugate transpose form.
1197* {F_i}^C = {H_i}{{B'}_i}^C
1198*
1199* Copy matrix H_i (the last bw cols of G_i) to AF storage
1200* as per requirements of BLAS routine ZTRMM.
1201* Since we have G_i^C stored, conjugate transpose
1202* H_i^C to H_i.
1203*
1204 CALL zlatcpy( 'N', bw, bw,
1205 $ af( odd_size-bw+1 ), odd_size,
1206 $ af( (odd_size)*bw+1), bw )
1207*
1208 CALL ztrmm( 'R', 'L', 'N', 'N', bw, bw, -cone,
1209 $ a( ( ofst+1+odd_size*llda ) ), llda-1,
1210 $ af( (odd_size)*bw+1 ), bw )
1211*
1212 ENDIF
1213*
1214 ENDIF
1215* End of "if ( MYCOL .ne. 0 )..."
1216*
1217 ENDIF
1218* End of "if (info.eq.0) then"
1219*
1220*
1221* Check to make sure no processors have found errors
1222*
1223 CALL igamx2d( ictxt, 'A', ' ', 1, 1, info, 1, info, info,
1224 $ -1, 0, 0 )
1225*
1226 IF( mycol.EQ.0 ) THEN
1227 CALL igebs2d( ictxt, 'A', ' ', 1, 1, info, 1 )
1228 ELSE
1229 CALL igebr2d( ictxt, 'a', ' ', 1, 1, INFO, 1, 0, 0 )
1230 ENDIF
1231*
1232.NE. IF ( INFO0 ) THEN
1233 GOTO 1000
1234 ENDIF
1235* No errors found, continue
1236*
1237*
1238********************************************************************
1239* PHASE 2: Formation and factorization of Reduced System.
1240********************************************************************
1241*
1242* Gather up local sections of reduced system
1243*
1244*
1245* The last processor does not participate in the factorization of
1246* the reduced system, having sent its E_i already.
1247.EQ. IF( MYCOL NPCOL-1 ) THEN
1248 GOTO 24
1249 ENDIF
1250*
1251* Initiate send of off-diag block(s) to overlap with next part.
1252* Off-diagonal block needed on neighboring processor to start
1253* algorithm.
1254*
1255.EQ..AND..GT. IF( (MOD( MYCOL+1, 2 ) 0) ( MYCOL 0 ) ) THEN
1256*
1257 CALL ZGESD2D( ICTXT, BW, BW,
1258 $ AF( ODD_SIZE*BW+1 ),
1259 $ BW, 0, MYCOL-1 )
1260*
1261 ENDIF
1262*
1263* Transpose last diagonal block into AF storage for subsequent
1264* operations.
1265*
1266 CALL ZLATCPY( 'u', BW, BW,
1267 $ A( OFST+ ODD_SIZE*LLDA+1+BW ),
1268 $ LLDA-1, AF( ODD_SIZE*BW+MBW2+1 ),
1269 $ BW )
1270*
1271* Receive cont. to diagonal block that is stored on this proc.
1272*
1273.LT. IF( MYCOL NPCOL-1 ) THEN
1274*
1275 CALL ZGERV2D( ICTXT, BW, BW,
1276 $ AF( ODD_SIZE*BW+2*MBW2+1 ),
1277 $ BW, 0,
1278 $ MYCOL+1 )
1279*
1280* Add contribution to diagonal block
1281*
1282 CALL ZAXPY( MBW2, CONE,
1283 $ AF( ODD_SIZE*BW+2*MBW2+1 ),
1284 $ 1, AF( ODD_SIZE*BW+MBW2+1 ), 1 )
1285*
1286 ENDIF
1287*
1288*
1289* *************************************
1290* Modification Loop
1291*
1292* The distance for sending and receiving for each level starts
1293* at 1 for the first level.
1294 LEVEL_DIST = 1
1295*
1296* Do until this proc is needed to modify other procs' equations
1297*
1298 22 CONTINUE
1299.NE. IF( MOD( (MYCOL+1)/LEVEL_DIST, 2) 0 ) GOTO 21
1300*
1301* Receive and add contribution to diagonal block from the left
1302*
1303.GE. IF( MYCOL-LEVEL_DIST 0 ) THEN
1304 CALL ZGERV2D( ICTXT, BW, BW, WORK( 1 ),
1305 $ BW, 0, MYCOL-LEVEL_DIST )
1306*
1307 CALL ZAXPY( MBW2, CONE, WORK( 1 ), 1,
1308 $ AF( ODD_SIZE*BW+MBW2+1 ), 1 )
1309*
1310 ENDIF
1311*
1312* Receive and add contribution to diagonal block from the right
1313*
1314.LT. IF( MYCOL+LEVEL_DIST NPCOL-1 ) THEN
1315 CALL ZGERV2D( ICTXT, BW, BW, WORK( 1 ),
1316 $ BW, 0, MYCOL+LEVEL_DIST )
1317*
1318 CALL ZAXPY( MBW2, CONE, WORK( 1 ), 1,
1319 $ AF( ODD_SIZE*BW+MBW2+1 ), 1 )
1320*
1321 ENDIF
1322*
1323 LEVEL_DIST = LEVEL_DIST*2
1324*
1325 GOTO 22
1326 21 CONTINUE
1327* [End of GOTO Loop]
1328*
1329*
1330* *********************************
1331* Calculate and use this proc's blocks to modify other procs'...
1332*
1333* Factor diagonal block
1334*
1335 CALL ZPOTRF( 'l', BW, AF( ODD_SIZE*BW+MBW2+1 ),
1336 $ BW, INFO )
1337*
1338.NE. IF( INFO0 ) THEN
1339 INFO = NPCOL + MYCOL
1340 ENDIF
1341*
1342* ****************************************************************
1343* Receive offdiagonal block from processor to right.
1344* If this is the first group of processors, the receive comes
1345* from a different processor than otherwise.
1346*
1347.EQ. IF( LEVEL_DIST 1 )THEN
1348 COMM_PROC = MYCOL + 1
1349*
1350* Move block into place that it will be expected to be for
1351* calcs.
1352*
1353 CALL ZLAMOV( 'n', BW, BW, AF( ODD_SIZE*BW+1 ), BW,
1354 $ AF( ODD_SIZE*BW+2*MBW2+1 ), BW )
1355*
1356 ELSE
1357 COMM_PROC = MYCOL + LEVEL_DIST/2
1358 ENDIF
1359*
1360.LE. IF( MYCOL/LEVEL_DIST (NPCOL-1)/LEVEL_DIST-2 )THEN
1361*
1362 CALL ZGERV2D( ICTXT, BW, BW,
1363 $ AF( ODD_SIZE*BW+1 ),
1364 $ BW, 0, COMM_PROC )
1365*
1366.EQ. IF( INFO 0 ) THEN
1367*
1368*
1369* Modify upper off_diagonal block with diagonal block
1370*
1371*
1372 CALL ZTRSM( 'l', 'l', 'n', 'n', BW, BW, CONE,
1373 $ AF( ODD_SIZE*BW+MBW2+1 ), BW,
1374 $ AF( ODD_SIZE*BW+1 ), BW )
1375*
1376 ENDIF
1377* End of "if ( info.eq.0 ) then"
1378*
1379* Calculate contribution from this block to next diagonal block
1380*
1381 CALL ZHERK( 'l', 'c', BW, BW, -ONE,
1382 $ AF( (ODD_SIZE)*BW+1 ), BW, ZERO,
1383 $ WORK( 1 ), BW )
1384*
1385* Send contribution to diagonal block's owning processor.
1386*
1387 CALL ZGESD2D( ICTXT, BW, BW, WORK( 1 ), BW,
1388 $ 0, MYCOL+LEVEL_DIST )
1389*
1390 ENDIF
1391* End of "if( mycol/level_dist .le. (npcol-1)/level_dist-2 )..."
1392*
1393*
1394* ****************************************************************
1395* Receive off_diagonal block from left and use to finish with this
1396* processor.
1397*
1398.GT..AND. IF( (MYCOL/LEVEL_DIST 0 )
1399.LE. $ ( MYCOL/LEVEL_DIST (NPCOL-1)/LEVEL_DIST-1 ) ) THEN
1400*
1401.GT. IF( LEVEL_DIST 1)THEN
1402*
1403* Receive offdiagonal block(s) from proc level_dist/2 to the
1404* left
1405*
1406 CALL ZGERV2D( ICTXT, BW, BW,
1407 $ AF( ODD_SIZE*BW+2*MBW2+1 ),
1408 $ BW, 0, MYCOL-LEVEL_DIST/2 )
1409*
1410 ENDIF
1411*
1412*
1413.EQ. IF( INFO0 ) THEN
1414*
1415* Use diagonal block(s) to modify this offdiagonal block
1416*
1417 CALL ZTRSM( 'r', 'l', 'c', 'n', BW, BW, CONE,
1418 $ AF( ODD_SIZE*BW+MBW2+1 ), BW,
1419 $ AF( ODD_SIZE*BW+2*MBW2+1 ), BW )
1420*
1421 ENDIF
1422* End of "if( info.eq.0 ) then"
1423*
1424* Use offdiag block(s) to calculate modification to diag block
1425* of processor to the left
1426*
1427 CALL ZHERK( 'l', 'n', BW, BW, -ONE,
1428 $ AF( (ODD_SIZE+2*BW)*BW+1 ), BW, ZERO,
1429 $ WORK( 1 ), BW )
1430*
1431* Send contribution to diagonal block's owning processor.
1432*
1433 CALL ZGESD2D( ICTXT, BW, BW, WORK( 1 ), BW,
1434 $ 0, MYCOL-LEVEL_DIST )
1435*
1436* *******************************************************
1437*
1438.LE. IF( MYCOL/LEVEL_DIST (NPCOL-1)/LEVEL_DIST-2 ) THEN
1439*
1440* Decide which processor offdiagonal block(s) goes to
1441*
1442.EQ. IF( ( MOD( MYCOL/( 2*LEVEL_DIST ),2 )) 0 ) THEN
1443 COMM_PROC = MYCOL + LEVEL_DIST
1444 ELSE
1445 COMM_PROC = MYCOL - LEVEL_DIST
1446 ENDIF
1447*
1448* Use offdiagonal blocks to calculate offdiag
1449* block to send to neighboring processor. Depending
1450* on circumstances, may need to transpose the matrix.
1451*
1452 CALL ZGEMM( 'n', 'n', BW, BW, BW, -CONE,
1453 $ AF( ODD_SIZE*BW+2*MBW2+1 ), BW,
1454 $ AF( ODD_SIZE*BW+1 ), BW, CZERO, WORK( 1 ),
1455 $ BW )
1456*
1457* Send contribution to offdiagonal block's owning processor.
1458*
1459 CALL ZGESD2D( ICTXT, BW, BW, WORK( 1 ), BW,
1460 $ 0, COMM_PROC )
1461*
1462 ENDIF
1463*
1464 ENDIF
1465* End of "if( mycol/level_dist.le. (npcol-1)/level_dist -1 )..."
1466*
1467 24 CONTINUE
1468*
1469 ENDIF
1470*
1471 1000 CONTINUE
1472*
1473*
1474* Free BLACS space used to hold standard-form grid.
1475*
1476.NE. IF( ICTXT_SAVE ICTXT_NEW ) THEN
1477 CALL BLACS_GRIDEXIT( ICTXT_NEW )
1478 ENDIF
1479*
1480 1234 CONTINUE
1481*
1482* Restore saved input parameters
1483*
1484 ICTXT = ICTXT_SAVE
1485 NP = NP_SAVE
1486*
1487* Output minimum worksize
1488*
1489 WORK( 1 ) = WORK_SIZE_MIN
1490*
1491* Make INFO consistent across processors
1492*
1493 CALL IGAMX2D( ICTXT, 'a', ' ', 1, 1, INFO, 1, INFO, INFO,
1494 $ -1, 0, 0 )
1495*
1496.EQ. IF( MYCOL0 ) THEN
1497 CALL IGEBS2D( ICTXT, 'a', ' ', 1, 1, INFO, 1 )
1498 ELSE
1499 CALL IGEBR2D( ICTXT, 'a', ' ', 1, 1, INFO, 1, 0, 0 )
1500 ENDIF
1501*
1502*
1503 RETURN
1504*
1505* End of PZPBTRF
1506*
1507 END
desc_convert
subroutine desc_convert(desc_in, desc_out, info)
Definition desc_convert.f:2
zpbtrf
subroutine zpbtrf(uplo, n, kd, ab, ldab, info)
ZPBTRF
Definition zpbtrf.f:142
ztbtrs
subroutine ztbtrs(uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, info)
ZTBTRS
Definition ztbtrs.f:146
ztrtrs
subroutine ztrtrs(uplo, trans, diag, n, nrhs, a, lda, b, ldb, info)
ZTRTRS
Definition ztrtrs.f:140
zaxpy
subroutine zaxpy(n, za, zx, incx, zy, incy)
ZAXPY
Definition zaxpy.f:88
ztrmm
subroutine ztrmm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
ZTRMM
Definition ztrmm.f:177
zherk
subroutine zherk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
ZHERK
Definition zherk.f:173
zgemm
subroutine zgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
ZGEMM
Definition zgemm.f:187
zsyrk
subroutine zsyrk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
ZSYRK
Definition zsyrk.f:167
ztrsm
subroutine ztrsm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
ZTRSM
Definition ztrsm.f:180
zpotrf
subroutine zpotrf(uplo, n, a, lda, info)
ZPOTRF VARIANT: right looking block version of the algorithm, calling Level 3 BLAS.
Definition zpotrf.f:102
min
#define min(a, b)
Definition macros.h:20
pxerbla
subroutine pxerbla(contxt, srname, info)
Definition mpi.f:1600
blacs_gridexit
subroutine blacs_gridexit(cntxt)
Definition mpi.f:762
blacs_gridinfo
subroutine blacs_gridinfo(cntxt, nprow, npcol, myrow, mycol)
Definition mpi.f:754
globchk
subroutine globchk(ictxt, n, x, ldx, iwork, info)
Definition pchkxmat.f:403
pzpbtrf
subroutine pzpbtrf(uplo, n, bw, a, ja, desca, af, laf, work, lwork, info)
Definition pzpbtrf.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:80
zlatcpy
subroutine zlatcpy(uplo, m, n, a, lda, b, ldb)
Definition zlatcpy.f:2