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pdpbtrf.f
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1 SUBROUTINE pdpbtrf( 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 DOUBLE PRECISION A( * ), AF( * ), WORK( * )
15* ..
16*
17*
18* Purpose
19* =======
20*
21* PDPBTRF computes a Cholesky factorization
22* of an N-by-N real 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 PDPBTRS 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension LAF.
85* Auxiliary Fillin Space.
86* Fillin is created during the factorization routine
87* PDPBTRF and this is stored in AF. If a linear system
88* is to be solved using PDPBTRS 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* DOUBLE PRECISION 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*
346* =====================================================================
347*
348* .. Parameters ..
349 DOUBLE PRECISION ONE
350 parameter( one = 1.0d+0 )
351 DOUBLE PRECISION ZERO
352 PARAMETER ( zero = 0.0d+0 )
353 INTEGER INT_ONE
354 parameter( int_one = 1 )
355 INTEGER DESCMULT, BIGNUM
356 parameter( descmult = 100, bignum = descmult*descmult )
357 INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
358 $ lld_, mb_, m_, nb_, n_, rsrc_
359 parameter( block_cyclic_2d = 1, dlen_ = 9, dtype_ = 1,
360 $ ctxt_ = 2, m_ = 3, n_ = 4, mb_ = 5, nb_ = 6,
361 $ rsrc_ = 7, csrc_ = 8, lld_ = 9 )
362* ..
363* .. Local Scalars ..
364 INTEGER COMM_PROC, CSRC, FIRST_PROC, I, ICTXT,
365 $ ictxt_new, ictxt_save, idum1, idum3, ja_new,
366 $ laf_min, level_dist, llda, mbw2, mycol, myrow,
367 $ my_num_cols, nb, next_tri_size_m,
368 $ next_tri_size_n, np, npcol, nprow, np_save,
369 $ odd_size, ofst, part_offset, part_size,
370 $ prev_tri_size_m, prev_tri_size_n, return_code,
371 $ store_n_a, work_size_min
372* ..
373* .. Local Arrays ..
374 INTEGER DESCA_1XP( 7 ), PARAM_CHECK( 9, 3 )
375* ..
376* .. External Subroutines ..
377 EXTERNAL blacs_gridexit, blacs_gridinfo, daxpy,
378 $ desc_convert, dgemm, dgerv2d, dgesd2d, dlamov,
379 $ dlatcpy, dpbtrf, dpotrf, dsyrk, dtbtrs, dtrmm,
380 $ dtrrv2d, dtrsd2d, dtrsm, dtrtrs, globchk,
381 $ igamx2d, igebr2d, igebs2d, pxerbla, reshape
382* ..
383* .. External Functions ..
384 LOGICAL LSAME
385 INTEGER NUMROC
386 EXTERNAL lsame, numroc
387* ..
388* .. Intrinsic Functions ..
389 INTRINSIC ichar, min, mod
390* ..
391* .. Executable Statements ..
392*
393* Test the input parameters
394*
395 info = 0
396*
397* Convert descriptor into standard form for easy access to
398* parameters, check that grid is of right shape.
399*
400 desca_1xp( 1 ) = 501
401*
402 CALL desc_convert( desca, desca_1xp, return_code )
403*
404 IF( return_code.NE.0 ) THEN
405 info = -( 6*100+2 )
406 END IF
407*
408* Get values out of descriptor for use in code.
409*
410 ictxt = desca_1xp( 2 )
411 csrc = desca_1xp( 5 )
412 nb = desca_1xp( 4 )
413 llda = desca_1xp( 6 )
414 store_n_a = desca_1xp( 3 )
415*
416* Get grid parameters
417*
418*
419* Pre-calculate bw^2
420*
421 mbw2 = bw*bw
422*
423 CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
424 np = nprow*npcol
425*
426*
427*
428 IF( lsame( uplo, 'U' ) ) THEN
429 idum1 = ichar( 'U' )
430 ELSE IF( lsame( uplo, 'L' ) ) THEN
431 idum1 = ichar( 'L' )
432 ELSE
433 info = -1
434 END IF
435*
436 IF( lwork.LT.-1 ) THEN
437 info = -10
438 ELSE IF( lwork.EQ.-1 ) THEN
439 idum3 = -1
440 ELSE
441 idum3 = 1
442 END IF
443*
444 IF( n.LT.0 ) THEN
445 info = -2
446 END IF
447*
448 IF( n+ja-1.GT.store_n_a ) THEN
449 info = -( 6*100+6 )
450 END IF
451*
452 IF( ( bw.GT.n-1 ) .OR. ( bw.LT.0 ) ) THEN
453 info = -3
454 END IF
455*
456 IF( llda.LT.( bw+1 ) ) THEN
457 info = -( 6*100+6 )
458 END IF
459*
460 IF( nb.LE.0 ) THEN
461 info = -( 6*100+4 )
462 END IF
463*
464* Argument checking that is specific to Divide & Conquer routine
465*
466 IF( nprow.NE.1 ) THEN
467 info = -( 6*100+2 )
468 END IF
469*
470 IF( n.GT.np*nb-mod( ja-1, nb ) ) THEN
471 info = -( 2 )
472 CALL pxerbla( ictxt, 'PDPBTRF, D&C alg.: only 1 block per proc'
473 $ , -info )
474 RETURN
475 END IF
476*
477 IF( ( ja+n-1.GT.nb ) .AND. ( nb.LT.2*bw ) ) THEN
478 info = -( 6*100+4 )
479 CALL pxerbla( ictxt, 'PDPBTRF, D&C alg.: NB too small', -info )
480 RETURN
481 END IF
482*
483*
484* Check auxiliary storage size
485*
486 laf_min = ( nb+2*bw )*bw
487*
488 IF( laf.LT.laf_min ) THEN
489 info = -8
490* put minimum value of laf into AF( 1 )
491 af( 1 ) = laf_min
492 CALL pxerbla( ictxt, 'PDPBTRF: auxiliary storage error ',
493 $ -info )
494 RETURN
495 END IF
496*
497* Check worksize
498*
499 work_size_min = bw*bw
500*
501 work( 1 ) = work_size_min
502*
503 IF( lwork.LT.work_size_min ) THEN
504 IF( lwork.NE.-1 ) THEN
505 info = -10
506 CALL pxerbla( ictxt, 'PDPBTRF: worksize error ', -info )
507 END IF
508 RETURN
509 END IF
510*
511* Pack params and positions into arrays for global consistency check
512*
513 param_check( 9, 1 ) = desca( 5 )
514 param_check( 8, 1 ) = desca( 4 )
515 param_check( 7, 1 ) = desca( 3 )
516 param_check( 6, 1 ) = desca( 1 )
517 param_check( 5, 1 ) = ja
518 param_check( 4, 1 ) = bw
519 param_check( 3, 1 ) = n
520 param_check( 2, 1 ) = idum3
521 param_check( 1, 1 ) = idum1
522*
523 param_check( 9, 2 ) = 605
524 param_check( 8, 2 ) = 604
525 param_check( 7, 2 ) = 603
526 param_check( 6, 2 ) = 601
527 param_check( 5, 2 ) = 5
528 param_check( 4, 2 ) = 3
529 param_check( 3, 2 ) = 2
530 param_check( 2, 2 ) = 10
531 param_check( 1, 2 ) = 1
532*
533* Want to find errors with MIN( ), so if no error, set it to a big
534* number. If there already is an error, multiply by the the
535* descriptor multiplier.
536*
537 IF( info.GE.0 ) THEN
538 info = bignum
539 ELSE IF( info.LT.-descmult ) THEN
540 info = -info
541 ELSE
542 info = -info*descmult
543 END IF
544*
545* Check consistency across processors
546*
547 CALL globchk( ictxt, 9, param_check, 9, param_check( 1, 3 ),
548 $ info )
549*
550* Prepare output: set info = 0 if no error, and divide by DESCMULT
551* if error is not in a descriptor entry.
552*
553 IF( info.EQ.bignum ) THEN
554 info = 0
555 ELSE IF( mod( info, descmult ).EQ.0 ) THEN
556 info = -info / descmult
557 ELSE
558 info = -info
559 END IF
560*
561 IF( info.LT.0 ) THEN
562 CALL pxerbla( ictxt, 'pdpbtrf', -INFO )
563 RETURN
564 END IF
565*
566* Quick return if possible
567*
568.EQ. IF( N0 )
569 $ RETURN
570*
571*
572* Adjust addressing into matrix space to properly get into
573* the beginning part of the relevant data
574*
575 PART_OFFSET = NB*( ( JA-1 ) / ( NPCOL*NB ) )
576*
577.LT. IF( ( MYCOL-CSRC )( JA-PART_OFFSET-1 ) / NB ) THEN
578 PART_OFFSET = PART_OFFSET + NB
579 END IF
580*
581.LT. IF( MYCOLCSRC ) THEN
582 PART_OFFSET = PART_OFFSET - NB
583 END IF
584*
585* Form a new BLACS grid (the "standard form" grid) with only procs
586* holding part of the matrix, of size 1xNP where NP is adjusted,
587* starting at csrc=0, with JA modified to reflect dropped procs.
588*
589* First processor to hold part of the matrix:
590*
591 FIRST_PROC = MOD( ( JA-1 ) / NB+CSRC, NPCOL )
592*
593* Calculate new JA one while dropping off unused processors.
594*
595 JA_NEW = MOD( JA-1, NB ) + 1
596*
597* Save and compute new value of NP
598*
599 NP_SAVE = NP
600 NP = ( JA_NEW+N-2 ) / NB + 1
601*
602* Call utility routine that forms "standard-form" grid
603*
604 CALL RESHAPE( ICTXT, INT_ONE, ICTXT_NEW, INT_ONE, FIRST_PROC,
605 $ INT_ONE, NP )
606*
607* Use new context from standard grid as context.
608*
609 ICTXT_SAVE = ICTXT
610 ICTXT = ICTXT_NEW
611 DESCA_1XP( 2 ) = ICTXT_NEW
612*
613* Get information about new grid.
614*
615 CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
616*
617* Drop out processors that do not have part of the matrix.
618*
619.LT. IF( MYROW0 ) THEN
620 GO TO 120
621 END IF
622*
623* ********************************
624* Values reused throughout routine
625*
626* User-input value of partition size
627*
628 PART_SIZE = NB
629*
630* Number of columns in each processor
631*
632 MY_NUM_COLS = NUMROC( N, PART_SIZE, MYCOL, 0, NPCOL )
633*
634* Offset in columns to beginning of main partition in each proc
635*
636.EQ. IF( MYCOL0 ) THEN
637 PART_OFFSET = PART_OFFSET + MOD( JA_NEW-1, PART_SIZE )
638 MY_NUM_COLS = MY_NUM_COLS - MOD( JA_NEW-1, PART_SIZE )
639 END IF
640*
641* Offset in elements
642*
643 OFST = PART_OFFSET*LLDA
644*
645* Size of main (or odd) partition in each processor
646*
647 ODD_SIZE = MY_NUM_COLS
648.LT. IF( MYCOLNP-1 ) THEN
649 ODD_SIZE = ODD_SIZE - BW
650 END IF
651*
652*
653* Zero out space for fillin
654*
655 DO 10 I = 1, LAF_MIN
656 AF( I ) = ZERO
657 10 CONTINUE
658*
659* Zero out space for work
660*
661 DO 20 I = 1, WORK_SIZE_MIN
662 WORK( I ) = ZERO
663 20 CONTINUE
664*
665* Begin main code
666*
667 IF( LSAME( UPLO, 'l' ) ) THEN
668*
669********************************************************************
670* PHASE 1: Local computation phase.
671********************************************************************
672*
673*
674* Sizes of the extra triangles communicated bewtween processors
675*
676.GT. IF( MYCOL0 ) THEN
677 PREV_TRI_SIZE_M = MIN( BW, NUMROC( N, PART_SIZE, MYCOL, 0,
678 $ NPCOL ) )
679 PREV_TRI_SIZE_N = MIN( BW, NUMROC( N, PART_SIZE, MYCOL-1, 0,
680 $ NPCOL ) )
681 END IF
682*
683.LT. IF( MYCOLNPCOL-1 ) THEN
684 NEXT_TRI_SIZE_M = MIN( BW, NUMROC( N, PART_SIZE, MYCOL+1, 0,
685 $ NPCOL ) )
686 NEXT_TRI_SIZE_N = MIN( BW, NUMROC( N, PART_SIZE, MYCOL, 0,
687 $ NPCOL ) )
688 END IF
689*
690.LT. IF( MYCOLNP-1 ) THEN
691* Transfer last triangle D_i of local matrix to next processor
692* which needs it to calculate fillin due to factorization of
693* its main (odd) block A_i.
694* Overlap the send with the factorization of A_i.
695*
696 CALL DTRSD2D( ICTXT, 'u', 'n', NEXT_TRI_SIZE_M,
697 $ NEXT_TRI_SIZE_N, A( OFST+ODD_SIZE*LLDA+( BW+
698 $ 1 ) ), LLDA-1, 0, MYCOL+1 )
699*
700 END IF
701*
702*
703* Factor main partition A_i = L_i {L_i}^T in each processor
704*
705 CALL DPBTRF( UPLO, ODD_SIZE, BW, A( OFST+1 ), LLDA, INFO )
706*
707.NE. IF( INFO0 ) THEN
708 INFO = MYCOL + 1
709 GO TO 30
710 END IF
711*
712*
713.LT. IF( MYCOLNP-1 ) THEN
714* Apply factorization to odd-even connection block B_i
715*
716* transpose the connection block in preparation.
717*
718 CALL DLATCPY( 'u', BW, BW, A( ( OFST+( BW+1 )+( ODD_SIZE-
719 $ BW )*LLDA ) ), LLDA-1,
720 $ AF( ODD_SIZE*BW+2*MBW2+1+BW-BW ), BW )
721*
722* Perform the triangular system solve {L_i}{{B'}_i}^T = {B_i}^T
723*
724 CALL DTRTRS( 'l', 'n', 'n', BW, BW,
725 $ A( OFST+1+( ODD_SIZE-BW )*LLDA ), LLDA-1,
726 $ AF( ODD_SIZE*BW+2*MBW2+1 ), BW, INFO )
727*
728*
729* transpose resulting block to its location
730* in main storage.
731*
732 CALL DLATCPY( 'l', BW, BW, AF( ODD_SIZE*BW+2*MBW2+1+BW-BW ),
733 $ BW, A( ( OFST+( BW+1 )+( ODD_SIZE-BW )*
734 $ LLDA ) ), LLDA-1 )
735*
736*
737* Compute contribution to diagonal block(s) of reduced system.
738* {C'}_i = {C_i}-{{B'}_i}{{B'}_i}^T
739*
740* The following method uses more flops than necessary but
741* does not necessitate the writing of a new BLAS routine.
742*
743*
744 CALL DSYRK( UPLO, 't', BW, BW, -ONE,
745 $ AF( ODD_SIZE*BW+2*MBW2+1 ), BW, ONE,
746 $ A( OFST+1+ODD_SIZE*LLDA ), LLDA-1 )
747*
748 END IF
749* End of "if ( MYCOL .lt. NP-1 )..." loop
750*
751*
752 30 CONTINUE
753* If the processor could not locally factor, it jumps here.
754*
755.NE. IF( MYCOL0 ) THEN
756* Discard temporary matrix stored beginning in
757* AF( (odd_size+2*bw)*bw+1 ) and use for
758* off_diagonal block of reduced system.
759*
760* Receive previously transmitted matrix section, which forms
761* the right-hand-side for the triangular solve that calculates
762* the "spike" fillin.
763*
764*
765 CALL DTRRV2D( ICTXT, 'u', 'n', PREV_TRI_SIZE_M,
766 $ PREV_TRI_SIZE_N, AF( 1 ), ODD_SIZE, 0,
767 $ MYCOL-1 )
768*
769.EQ. IF( INFO0 ) THEN
770*
771* Calculate the "spike" fillin, ${L_i} {{G}_i}^T = {D_i}$ .
772*
773 CALL DTBTRS( 'l', 'n', 'n', ODD_SIZE, BW, BW,
774 $ A( OFST+1 ), LLDA, AF( 1 ), ODD_SIZE, INFO )
775*
776*
777* Calculate the update block for previous proc, E_i = G_i{G_i}^T
778*
779 CALL DSYRK( 'l', 't', BW, ODD_SIZE, -ONE, AF( 1 ),
780 $ ODD_SIZE, ZERO, AF( 1+( ODD_SIZE+2*BW )*BW ),
781 $ BW )
782*
783*
784* Initiate send of E_i to previous processor to overlap
785* with next computation.
786*
787 CALL DGESD2D( ICTXT, BW, BW, AF( ODD_SIZE*BW+2*MBW2+1 ),
788 $ BW, 0, MYCOL-1 )
789*
790*
791.LT. IF( MYCOLNP-1 ) THEN
792*
793* Calculate off-diagonal block(s) of reduced system.
794* Note: for ease of use in solution of reduced system, store
795* L's off-diagonal block in transpose form.
796* {F_i}^T = {H_i}{{B'}_i}^T
797*
798* Copy matrix H_i (the last bw cols of G_i) to AF storage
799* as per requirements of BLAS routine DTRMM.
800* Since we have G_i^T stored, transpose
801* H_i^T to H_i.
802*
803 CALL DLATCPY( 'n', BW, BW, AF( ODD_SIZE-BW+1 ),
804 $ ODD_SIZE, AF( ( ODD_SIZE )*BW+1 ), BW )
805*
806 CALL DTRMM( 'r', 'u', 't', 'n', BW, BW, -ONE,
807 $ A( ( OFST+( BW+1 )+( ODD_SIZE-BW )*
808 $ LLDA ) ), LLDA-1, AF( ( ODD_SIZE )*BW+1 ),
809 $ BW )
810*
811*
812 END IF
813*
814 END IF
815* End of "if ( MYCOL .ne. 0 )..."
816*
817 END IF
818* End of "if (info.eq.0) then"
819*
820*
821* Check to make sure no processors have found errors
822*
823 CALL IGAMX2D( ICTXT, 'a', ' ', 1, 1, INFO, 1, INFO, INFO, -1,
824 $ 0, 0 )
825*
826.EQ. IF( MYCOL0 ) THEN
827 CALL IGEBS2D( ICTXT, 'a', ' ', 1, 1, INFO, 1 )
828 ELSE
829 CALL IGEBR2D( ICTXT, 'a', ' ', 1, 1, INFO, 1, 0, 0 )
830 END IF
831*
832.NE. IF( INFO0 ) THEN
833 GO TO 110
834 END IF
835* No errors found, continue
836*
837*
838********************************************************************
839* PHASE 2: Formation and factorization of Reduced System.
840********************************************************************
841*
842* Gather up local sections of reduced system
843*
844*
845* The last processor does not participate in the factorization of
846* the reduced system, having sent its E_i already.
847.EQ. IF( MYCOLNPCOL-1 ) THEN
848 GO TO 60
849 END IF
850*
851* Initiate send of off-diag block(s) to overlap with next part.
852* Off-diagonal block needed on neighboring processor to start
853* algorithm.
854*
855.EQ..AND..GT. IF( ( MOD( MYCOL+1, 2 )0 ) ( MYCOL0 ) ) THEN
856*
857 CALL DGESD2D( ICTXT, BW, BW, AF( ODD_SIZE*BW+1 ), BW, 0,
858 $ MYCOL-1 )
859*
860 END IF
861*
862* Copy last diagonal block into AF storage for subsequent
863* operations.
864*
865 CALL DLAMOV( 'n', BW, BW, A( OFST+ODD_SIZE*LLDA+1 ), LLDA-1,
866 $ AF( ODD_SIZE*BW+MBW2+1 ), BW )
867*
868* Receive cont. to diagonal block that is stored on this proc.
869*
870.LT. IF( MYCOLNPCOL-1 ) THEN
871*
872 CALL DGERV2D( ICTXT, BW, BW, AF( ODD_SIZE*BW+2*MBW2+1 ), BW,
873 $ 0, MYCOL+1 )
874*
875* Add contribution to diagonal block
876*
877 CALL DAXPY( MBW2, ONE, AF( ODD_SIZE*BW+2*MBW2+1 ), 1,
878 $ AF( ODD_SIZE*BW+MBW2+1 ), 1 )
879*
880 END IF
881*
882*
883* *************************************
884* Modification Loop
885*
886* The distance for sending and receiving for each level starts
887* at 1 for the first level.
888 LEVEL_DIST = 1
889*
890* Do until this proc is needed to modify other procs' equations
891*
892 40 CONTINUE
893.NE. IF( MOD( ( MYCOL+1 ) / LEVEL_DIST, 2 )0 )
894 $ GO TO 50
895*
896* Receive and add contribution to diagonal block from the left
897*
898.GE. IF( MYCOL-LEVEL_DIST0 ) THEN
899 CALL DGERV2D( ICTXT, BW, BW, WORK( 1 ), BW, 0,
900 $ MYCOL-LEVEL_DIST )
901*
902 CALL DAXPY( MBW2, ONE, WORK( 1 ), 1,
903 $ AF( ODD_SIZE*BW+MBW2+1 ), 1 )
904*
905 END IF
906*
907* Receive and add contribution to diagonal block from the right
908*
909.LT. IF( MYCOL+LEVEL_DISTNPCOL-1 ) THEN
910 CALL DGERV2D( ICTXT, BW, BW, WORK( 1 ), BW, 0,
911 $ MYCOL+LEVEL_DIST )
912*
913 CALL DAXPY( MBW2, ONE, WORK( 1 ), 1,
914 $ AF( ODD_SIZE*BW+MBW2+1 ), 1 )
915*
916 END IF
917*
918 LEVEL_DIST = LEVEL_DIST*2
919*
920 GO TO 40
921 50 CONTINUE
922* [End of GOTO Loop]
923*
924*
925* *********************************
926* Calculate and use this proc's blocks to modify other procs'...
927*
928* Factor diagonal block
929*
930 CALL DPOTRF( 'l', BW, AF( ODD_SIZE*BW+MBW2+1 ), BW, INFO )
931*
932.NE. IF( INFO0 ) THEN
933 INFO = NPCOL + MYCOL
934 END IF
935*
936* ****************************************************************
937* Receive offdiagonal block from processor to right.
938* If this is the first group of processors, the receive comes
939* from a different processor than otherwise.
940*
941.EQ. IF( LEVEL_DIST1 ) THEN
942 COMM_PROC = MYCOL + 1
943*
944* Move block into place that it will be expected to be for
945* calcs.
946*
947 CALL DLAMOV( 'n', BW, BW, AF( ODD_SIZE*BW+1 ), BW,
948 $ AF( ODD_SIZE*BW+2*MBW2+1 ), BW )
949*
950 ELSE
951 COMM_PROC = MYCOL + LEVEL_DIST / 2
952 END IF
953*
954.LE. IF( MYCOL / LEVEL_DIST( NPCOL-1 ) / LEVEL_DIST-2 ) THEN
955*
956 CALL DGERV2D( ICTXT, BW, BW, AF( ODD_SIZE*BW+1 ), BW, 0,
957 $ COMM_PROC )
958*
959.EQ. IF( INFO0 ) THEN
960*
961*
962* Modify upper off_diagonal block with diagonal block
963*
964*
965 CALL DTRSM( 'l', 'l', 'n', 'n', BW, BW, ONE,
966 $ AF( ODD_SIZE*BW+MBW2+1 ), BW,
967 $ AF( ODD_SIZE*BW+1 ), BW )
968*
969 END IF
970* End of "if ( info.eq.0 ) then"
971*
972* Calculate contribution from this block to next diagonal block
973*
974 CALL DSYRK( 'l', 't', BW, BW, -ONE, AF( ( ODD_SIZE )*BW+1 ),
975 $ BW, ZERO, WORK( 1 ), BW )
976*
977* Send contribution to diagonal block's owning processor.
978*
979 CALL DGESD2D( ICTXT, BW, BW, WORK( 1 ), BW, 0,
980 $ MYCOL+LEVEL_DIST )
981*
982 END IF
983* End of "if( mycol/level_dist .le. (npcol-1)/level_dist-2 )..."
984*
985*
986* ****************************************************************
987* Receive off_diagonal block from left and use to finish with this
988* processor.
989*
990.GT..AND. IF( ( MYCOL / LEVEL_DIST0 )
991.LE. $ ( MYCOL / LEVEL_DIST( NPCOL-1 ) / LEVEL_DIST-1 ) ) THEN
992*
993.GT. IF( LEVEL_DIST1 ) THEN
994*
995* Receive offdiagonal block(s) from proc level_dist/2 to the
996* left
997*
998 CALL DGERV2D( ICTXT, BW, BW, AF( ODD_SIZE*BW+2*MBW2+1 ),
999 $ BW, 0, MYCOL-LEVEL_DIST / 2 )
1000*
1001 END IF
1002*
1003*
1004.EQ. IF( INFO0 ) THEN
1005*
1006* Use diagonal block(s) to modify this offdiagonal block
1007*
1008 CALL DTRSM( 'r', 'l', 't', 'N', bw, bw, one,
1009 $ af( odd_size*bw+mbw2+1 ), bw,
1010 $ af( odd_size*bw+2*mbw2+1 ), bw )
1011*
1012 END IF
1013* End of "if( info.eq.0 ) then"
1014*
1015* Use offdiag block(s) to calculate modification to diag block
1016* of processor to the left
1017*
1018 CALL dsyrk( 'L', 'N', bw, bw, -one,
1019 $ af( ( odd_size+2*bw )*bw+1 ), bw, zero,
1020 $ work( 1 ), bw )
1021*
1022* Send contribution to diagonal block's owning processor.
1023*
1024 CALL dgesd2d( ictxt, bw, bw, work( 1 ), bw, 0,
1025 $ mycol-level_dist )
1026*
1027* *******************************************************
1028*
1029 IF( mycol / level_dist.LE.( npcol-1 ) / level_dist-2 ) THEN
1030*
1031* Decide which processor offdiagonal block(s) goes to
1032*
1033 IF( ( mod( mycol / ( 2*level_dist ), 2 ) ).EQ.0 ) THEN
1034 comm_proc = mycol + level_dist
1035 ELSE
1036 comm_proc = mycol - level_dist
1037 END IF
1038*
1039* Use offdiagonal blocks to calculate offdiag
1040* block to send to neighboring processor. Depending
1041* on circumstances, may need to transpose the matrix.
1042*
1043 CALL dgemm( 'N', 'N', bw, bw, bw, -one,
1044 $ af( odd_size*bw+2*mbw2+1 ), bw,
1045 $ af( odd_size*bw+1 ), bw, zero, work( 1 ),
1046 $ bw )
1047*
1048* Send contribution to offdiagonal block's owning processor.
1049*
1050 CALL dgesd2d( ictxt, bw, bw, work( 1 ), bw, 0,
1051 $ comm_proc )
1052*
1053 END IF
1054*
1055 END IF
1056* End of "if( mycol/level_dist.le. (npcol-1)/level_dist -1 )..."
1057*
1058 60 CONTINUE
1059*
1060 ELSE
1061*
1062* CASE UPLO = 'U'
1063*
1064********************************************************************
1065* PHASE 1: Local computation phase.
1066********************************************************************
1067*
1068*
1069* Sizes of the extra triangles communicated bewtween processors
1070*
1071 IF( mycol.GT.0 ) THEN
1072 prev_tri_size_m = min( bw, numroc( n, part_size, mycol, 0,
1073 $ npcol ) )
1074 prev_tri_size_n = min( bw, numroc( n, part_size, mycol-1, 0,
1075 $ npcol ) )
1076 END IF
1077*
1078 IF( mycol.LT.npcol-1 ) THEN
1079 next_tri_size_m = min( bw, numroc( n, part_size, mycol+1, 0,
1080 $ npcol ) )
1081 next_tri_size_n = min( bw, numroc( n, part_size, mycol, 0,
1082 $ npcol ) )
1083 END IF
1084*
1085*
1086*
1087* Factor main partition A_i^T = U_i {U_i}^T in each processor
1088*
1089 CALL dpbtrf( uplo, odd_size, bw, a( ofst+1 ), llda, info )
1090*
1091 IF( info.NE.0 ) THEN
1092 info = mycol + 1
1093 GO TO 70
1094 END IF
1095*
1096*
1097 IF( mycol.LT.np-1 ) THEN
1098* Apply factorization to odd-even connection block B_i
1099*
1100* Move the connection block in preparation.
1101*
1102 CALL dlamov( 'L', bw, bw, a( ( ofst+1+odd_size*llda ) ),
1103 $ llda-1, af( odd_size*bw+2*mbw2+1+bw-bw ), bw )
1104*
1105*
1106* Perform the triangular solve {L_i}{{B'}_i}^T = {B_i}^T
1107*
1108 CALL dtrtrs( 'U', 'T', 'N', bw, bw,
1109 $ a( ofst+bw+1+( odd_size-bw )*llda ), llda-1,
1110 $ af( odd_size*bw+2*mbw2+1 ), bw, info )
1111*
1112* Move the resulting block back to its location in main storage.
1113*
1114 CALL dlamov( 'L', bw, bw, af( odd_size*bw+2*mbw2+1+bw-bw ),
1115 $ bw, a( ( ofst+1+odd_size*llda ) ), llda-1 )
1116*
1117*
1118* Compute contribution to diagonal block(s) of reduced system.
1119* {C'}_i^T = {C_i}^T-{{B'}_i}^T{{B'}_i}
1120*
1121* The following method uses more flops than necessary but
1122* does not necessitate the writing of a new BLAS routine.
1123*
1124*
1125 CALL dsyrk( uplo, 'T', bw, bw, -one,
1126 $ af( odd_size*bw+2*mbw2+1 ), bw, one,
1127 $ a( ofst+bw+1+odd_size*llda ), llda-1 )
1128*
1129 END IF
1130* End of "if ( MYCOL .lt. NP-1 )..." loop
1131*
1132*
1133 70 CONTINUE
1134* If the processor could not locally factor, it jumps here.
1135*
1136 IF( mycol.NE.0 ) THEN
1137* Discard temporary matrix stored beginning in
1138* AF( (odd_size+2*bw)*bw+1 ) and use for
1139* off_diagonal block of reduced system.
1140*
1141* Calculate the "spike" fillin, ${L_i} {{G}_i}^T = {D_i}$ .
1142*
1143*
1144* Copy D block into AF storage for solve.
1145*
1146 CALL dlatcpy( 'L', prev_tri_size_n, prev_tri_size_m,
1147 $ a( ofst+1 ), llda-1, af( 1 ), odd_size )
1148*
1149 IF( info.EQ.0 ) THEN
1150*
1151 CALL dtbtrs( 'U', 'T', 'n', ODD_SIZE, BW, BW,
1152 $ A( OFST+1 ), LLDA, AF( 1 ), ODD_SIZE, INFO )
1153*
1154*
1155* Calculate the update block for previous proc, E_i = G_i{G_i}^T
1156*
1157 CALL DSYRK( 'l', 't', BW, ODD_SIZE, -ONE, AF( 1 ),
1158 $ ODD_SIZE, ZERO, AF( 1+( ODD_SIZE+2*BW )*BW ),
1159 $ BW )
1160*
1161*
1162* Initiate send of E_i to previous processor to overlap
1163* with next computation.
1164*
1165 CALL DGESD2D( ICTXT, BW, BW, AF( ODD_SIZE*BW+2*MBW2+1 ),
1166 $ BW, 0, MYCOL-1 )
1167*
1168*
1169.LT. IF( MYCOLNP-1 ) THEN
1170*
1171* Calculate off-diagonal block(s) of reduced system.
1172* Note: for ease of use in solution of reduced system, store
1173* L's off-diagonal block in transpose form.
1174* {F_i}^T = {H_i}{{B'}_i}^T
1175*
1176* Copy matrix H_i (the last bw cols of G_i) to AF storage
1177* as per requirements of BLAS routine DTRMM.
1178* Since we have G_i^T stored, transpose
1179* H_i^T to H_i.
1180*
1181 CALL DLATCPY( 'n', BW, BW, AF( ODD_SIZE-BW+1 ),
1182 $ ODD_SIZE, AF( ( ODD_SIZE )*BW+1 ), BW )
1183*
1184 CALL DTRMM( 'r', 'l', 'n', 'n', BW, BW, -ONE,
1185 $ A( ( OFST+1+ODD_SIZE*LLDA ) ), LLDA-1,
1186 $ AF( ( ODD_SIZE )*BW+1 ), BW )
1187*
1188 END IF
1189*
1190 END IF
1191* End of "if ( MYCOL .ne. 0 )..."
1192*
1193 END IF
1194* End of "if (info.eq.0) then"
1195*
1196*
1197* Check to make sure no processors have found errors
1198*
1199 CALL IGAMX2D( ICTXT, 'a', ' ', 1, 1, INFO, 1, INFO, INFO, -1,
1200 $ 0, 0 )
1201*
1202.EQ. IF( MYCOL0 ) THEN
1203 CALL IGEBS2D( ICTXT, 'a', ' ', 1, 1, INFO, 1 )
1204 ELSE
1205 CALL IGEBR2D( ICTXT, 'a', ' ', 1, 1, INFO, 1, 0, 0 )
1206 END IF
1207*
1208.NE. IF( INFO0 ) THEN
1209 GO TO 110
1210 END IF
1211* No errors found, continue
1212*
1213*
1214********************************************************************
1215* PHASE 2: Formation and factorization of Reduced System.
1216********************************************************************
1217*
1218* Gather up local sections of reduced system
1219*
1220*
1221* The last processor does not participate in the factorization of
1222* the reduced system, having sent its E_i already.
1223.EQ. IF( MYCOLNPCOL-1 ) THEN
1224 GO TO 100
1225 END IF
1226*
1227* Initiate send of off-diag block(s) to overlap with next part.
1228* Off-diagonal block needed on neighboring processor to start
1229* algorithm.
1230*
1231.EQ..AND..GT. IF( ( MOD( MYCOL+1, 2 )0 ) ( MYCOL0 ) ) THEN
1232*
1233 CALL DGESD2D( ICTXT, BW, BW, AF( ODD_SIZE*BW+1 ), BW, 0,
1234 $ MYCOL-1 )
1235*
1236 END IF
1237*
1238* Transpose last diagonal block into AF storage for subsequent
1239* operations.
1240*
1241 CALL DLATCPY( 'u', BW, BW, A( OFST+ODD_SIZE*LLDA+1+BW ),
1242 $ LLDA-1, AF( ODD_SIZE*BW+MBW2+1 ), BW )
1243*
1244* Receive cont. to diagonal block that is stored on this proc.
1245*
1246.LT. IF( MYCOLNPCOL-1 ) THEN
1247*
1248 CALL DGERV2D( ICTXT, BW, BW, AF( ODD_SIZE*BW+2*MBW2+1 ), BW,
1249 $ 0, MYCOL+1 )
1250*
1251* Add contribution to diagonal block
1252*
1253 CALL DAXPY( MBW2, ONE, AF( ODD_SIZE*BW+2*MBW2+1 ), 1,
1254 $ AF( ODD_SIZE*BW+MBW2+1 ), 1 )
1255*
1256 END IF
1257*
1258*
1259* *************************************
1260* Modification Loop
1261*
1262* The distance for sending and receiving for each level starts
1263* at 1 for the first level.
1264 LEVEL_DIST = 1
1265*
1266* Do until this proc is needed to modify other procs' equations
1267*
1268 80 CONTINUE
1269.NE. IF( MOD( ( MYCOL+1 ) / LEVEL_DIST, 2 )0 )
1270 $ GO TO 90
1271*
1272* Receive and add contribution to diagonal block from the left
1273*
1274.GE. IF( MYCOL-LEVEL_DIST0 ) THEN
1275 CALL DGERV2D( ICTXT, BW, BW, WORK( 1 ), BW, 0,
1276 $ MYCOL-LEVEL_DIST )
1277*
1278 CALL DAXPY( MBW2, ONE, WORK( 1 ), 1,
1279 $ AF( ODD_SIZE*BW+MBW2+1 ), 1 )
1280*
1281 END IF
1282*
1283* Receive and add contribution to diagonal block from the right
1284*
1285.LT. IF( MYCOL+LEVEL_DISTNPCOL-1 ) THEN
1286 CALL DGERV2D( ICTXT, BW, BW, WORK( 1 ), BW, 0,
1287 $ MYCOL+LEVEL_DIST )
1288*
1289 CALL DAXPY( MBW2, ONE, WORK( 1 ), 1,
1290 $ AF( ODD_SIZE*BW+MBW2+1 ), 1 )
1291*
1292 END IF
1293*
1294 LEVEL_DIST = LEVEL_DIST*2
1295*
1296 GO TO 80
1297 90 CONTINUE
1298* [End of GOTO Loop]
1299*
1300*
1301* *********************************
1302* Calculate and use this proc's blocks to modify other procs'...
1303*
1304* Factor diagonal block
1305*
1306 CALL DPOTRF( 'l', BW, AF( ODD_SIZE*BW+MBW2+1 ), BW, INFO )
1307*
1308.NE. IF( INFO0 ) THEN
1309 INFO = NPCOL + MYCOL
1310 END IF
1311*
1312* ****************************************************************
1313* Receive offdiagonal block from processor to right.
1314* If this is the first group of processors, the receive comes
1315* from a different processor than otherwise.
1316*
1317.EQ. IF( LEVEL_DIST1 ) THEN
1318 COMM_PROC = MYCOL + 1
1319*
1320* Move block into place that it will be expected to be for
1321* calcs.
1322*
1323 CALL DLAMOV( 'n', BW, BW, AF( ODD_SIZE*BW+1 ), BW,
1324 $ AF( ODD_SIZE*BW+2*MBW2+1 ), BW )
1325*
1326 ELSE
1327 COMM_PROC = MYCOL + LEVEL_DIST / 2
1328 END IF
1329*
1330.LE. IF( MYCOL / LEVEL_DIST( NPCOL-1 ) / LEVEL_DIST-2 ) THEN
1331*
1332 CALL DGERV2D( ICTXT, BW, BW, AF( ODD_SIZE*BW+1 ), BW, 0,
1333 $ COMM_PROC )
1334*
1335.EQ. IF( INFO0 ) THEN
1336*
1337*
1338* Modify upper off_diagonal block with diagonal block
1339*
1340*
1341 CALL DTRSM( 'l', 'l', 'n', 'n', BW, BW, ONE,
1342 $ AF( ODD_SIZE*BW+MBW2+1 ), BW,
1343 $ AF( ODD_SIZE*BW+1 ), BW )
1344*
1345 END IF
1346* End of "if ( info.eq.0 ) then"
1347*
1348* Calculate contribution from this block to next diagonal block
1349*
1350 CALL DSYRK( 'l', 't', BW, BW, -ONE, AF( ( ODD_SIZE )*BW+1 ),
1351 $ BW, ZERO, WORK( 1 ), BW )
1352*
1353* Send contribution to diagonal block's owning processor.
1354*
1355 CALL DGESD2D( ICTXT, BW, BW, WORK( 1 ), BW, 0,
1356 $ MYCOL+LEVEL_DIST )
1357*
1358 END IF
1359* End of "if( mycol/level_dist .le. (npcol-1)/level_dist-2 )..."
1360*
1361*
1362* ****************************************************************
1363* Receive off_diagonal block from left and use to finish with this
1364* processor.
1365*
1366.GT..AND. IF( ( MYCOL / LEVEL_DIST0 )
1367.LE. $ ( MYCOL / LEVEL_DIST( NPCOL-1 ) / LEVEL_DIST-1 ) ) THEN
1368*
1369.GT. IF( LEVEL_DIST1 ) THEN
1370*
1371* Receive offdiagonal block(s) from proc level_dist/2 to the
1372* left
1373*
1374 CALL DGERV2D( ICTXT, BW, BW, AF( ODD_SIZE*BW+2*MBW2+1 ),
1375 $ BW, 0, MYCOL-LEVEL_DIST / 2 )
1376*
1377 END IF
1378*
1379*
1380.EQ. IF( INFO0 ) THEN
1381*
1382* Use diagonal block(s) to modify this offdiagonal block
1383*
1384 CALL DTRSM( 'r', 'l', 't', 'n', BW, BW, ONE,
1385 $ AF( ODD_SIZE*BW+MBW2+1 ), BW,
1386 $ AF( ODD_SIZE*BW+2*MBW2+1 ), BW )
1387*
1388 END IF
1389* End of "if( info.eq.0 ) then"
1390*
1391* Use offdiag block(s) to calculate modification to diag block
1392* of processor to the left
1393*
1394 CALL DSYRK( 'l', 'n', BW, BW, -ONE,
1395 $ AF( ( ODD_SIZE+2*BW )*BW+1 ), BW, ZERO,
1396 $ WORK( 1 ), BW )
1397*
1398* Send contribution to diagonal block's owning processor.
1399*
1400 CALL DGESD2D( ICTXT, BW, BW, WORK( 1 ), BW, 0,
1401 $ MYCOL-LEVEL_DIST )
1402*
1403* *******************************************************
1404*
1405.LE. IF( MYCOL / LEVEL_DIST( NPCOL-1 ) / LEVEL_DIST-2 ) THEN
1406*
1407* Decide which processor offdiagonal block(s) goes to
1408*
1409.EQ. IF( ( MOD( MYCOL / ( 2*LEVEL_DIST ), 2 ) )0 ) THEN
1410 COMM_PROC = MYCOL + LEVEL_DIST
1411 ELSE
1412 COMM_PROC = MYCOL - LEVEL_DIST
1413 END IF
1414*
1415* Use offdiagonal blocks to calculate offdiag
1416* block to send to neighboring processor. Depending
1417* on circumstances, may need to transpose the matrix.
1418*
1419 CALL DGEMM( 'n', 'n', BW, BW, BW, -ONE,
1420 $ AF( ODD_SIZE*BW+2*MBW2+1 ), BW,
1421 $ AF( ODD_SIZE*BW+1 ), BW, ZERO, WORK( 1 ),
1422 $ BW )
1423*
1424* Send contribution to offdiagonal block's owning processor.
1425*
1426 CALL DGESD2D( ICTXT, BW, BW, WORK( 1 ), BW, 0,
1427 $ COMM_PROC )
1428*
1429 END IF
1430*
1431 END IF
1432* End of "if( mycol/level_dist.le. (npcol-1)/level_dist -1 )..."
1433*
1434 100 CONTINUE
1435*
1436 END IF
1437*
1438 110 CONTINUE
1439*
1440*
1441* Free BLACS space used to hold standard-form grid.
1442*
1443.NE. IF( ICTXT_SAVEICTXT_NEW ) THEN
1444 CALL BLACS_GRIDEXIT( ICTXT_NEW )
1445 END IF
1446*
1447 120 CONTINUE
1448*
1449* Restore saved input parameters
1450*
1451 ICTXT = ICTXT_SAVE
1452 NP = NP_SAVE
1453*
1454* Output minimum worksize
1455*
1456 WORK( 1 ) = WORK_SIZE_MIN
1457*
1458* Make INFO consistent across processors
1459*
1460 CALL IGAMX2D( ICTXT, 'a', ' ', 1, 1, INFO, 1, INFO, INFO, -1, 0,
1461 $ 0 )
1462*
1463.EQ. IF( MYCOL0 ) THEN
1464 CALL IGEBS2D( ICTXT, 'a', ' ', 1, 1, INFO, 1 )
1465 ELSE
1466 CALL IGEBR2D( ICTXT, 'a', ' ', 1, 1, INFO, 1, 0, 0 )
1467 END IF
1468*
1469*
1470 RETURN
1471*
1472* End of PDPBTRF
1473*
1474 END
desc_convert
subroutine desc_convert(desc_in, desc_out, info)
Definition desc_convert.f:2
dlatcpy
subroutine dlatcpy(uplo, m, n, a, lda, b, ldb)
Definition dlatcpy.f:2
dtbtrs
subroutine dtbtrs(uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, info)
DTBTRS
Definition dtbtrs.f:146
dtrtrs
subroutine dtrtrs(uplo, trans, diag, n, nrhs, a, lda, b, ldb, info)
DTRTRS
Definition dtrtrs.f:140
dpbtrf
subroutine dpbtrf(uplo, n, kd, ab, ldab, info)
DPBTRF
Definition dpbtrf.f:142
dpotrf
subroutine dpotrf(uplo, n, a, lda, info)
DPOTRF
Definition dpotrf.f:107
daxpy
subroutine daxpy(n, da, dx, incx, dy, incy)
DAXPY
Definition daxpy.f:89
dsyrk
subroutine dsyrk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
DSYRK
Definition dsyrk.f:169
dgemm
subroutine dgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
DGEMM
Definition dgemm.f:187
dtrmm
subroutine dtrmm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
DTRMM
Definition dtrmm.f:177
dtrsm
subroutine dtrsm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
DTRSM
Definition dtrsm.f:181
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
pdpbtrf
subroutine pdpbtrf(uplo, n, bw, a, ja, desca, af, laf, work, lwork, info)
Definition pdpbtrf.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