1 c---------------------------------------------------------------------
2 c---------------------------------------------------------------------
6 c---------------------------------------------------------------------
7 c---------------------------------------------------------------------
9 c---------------------------------------------------------------------
10 c Performs line solves in Z direction by first factoring
11 c the block-tridiagonal matrix into an upper triangular matrix,
12 c and then performing back substitution to solve for the unknow
13 c vectors of each line.
15 c Make sure we treat elements zero to cell_size in the direction
17 c---------------------------------------------------------------------
22 integer c, kstart, stage,
23 > first, last, recv_id, error, r_status(MPI_STATUS_SIZE),
24 > isize,jsize,ksize,send_id
28 c---------------------------------------------------------------------
29 c in our terminology stage is the number of the cell in the y-direction
30 c i.e. stage = 1 means the start of the line stage=ncells means end
31 c---------------------------------------------------------------------
34 isize = cell_size(1,c) - 1
35 jsize = cell_size(2,c) - 1
36 ksize = cell_size(3,c) - 1
37 c---------------------------------------------------------------------
39 c---------------------------------------------------------------------
40 if (stage .eq. ncells) then
46 if (stage .eq. 1) then
47 c---------------------------------------------------------------------
48 c This is the first cell, so solve without receiving data
49 c---------------------------------------------------------------------
52 call z_solve_cell(first,last,c)
54 c---------------------------------------------------------------------
55 c Not the first cell of this line, so receive info from
56 c processor working on preceeding cell
57 c---------------------------------------------------------------------
59 call z_receive_solve_info(recv_id,c)
60 c---------------------------------------------------------------------
61 c overlap computations and communications
62 c---------------------------------------------------------------------
64 c---------------------------------------------------------------------
66 c---------------------------------------------------------------------
67 call mpi_wait(send_id,r_status,error)
68 call mpi_wait(recv_id,r_status,error)
69 c---------------------------------------------------------------------
70 c install C'(kstart+1) and rhs'(kstart+1) to be used in this cell
71 c---------------------------------------------------------------------
72 call z_unpack_solve_info(c)
73 call z_solve_cell(first,last,c)
76 if (last .eq. 0) call z_send_solve_info(send_id,c)
79 c---------------------------------------------------------------------
80 c now perform backsubstitution in reverse direction
81 c---------------------------------------------------------------------
82 do stage = ncells, 1, -1
86 if (stage .eq. 1) first = 1
87 if (stage .eq. ncells) then
89 c---------------------------------------------------------------------
90 c last cell, so perform back substitute without waiting
91 c---------------------------------------------------------------------
92 call z_backsubstitute(first, last,c)
94 call z_receive_backsub_info(recv_id,c)
95 call mpi_wait(send_id,r_status,error)
96 call mpi_wait(recv_id,r_status,error)
97 call z_unpack_backsub_info(c)
98 call z_backsubstitute(first,last,c)
100 if (first .eq. 0) call z_send_backsub_info(send_id,c)
107 c---------------------------------------------------------------------
108 c---------------------------------------------------------------------
110 subroutine z_unpack_solve_info(c)
111 c---------------------------------------------------------------------
112 c---------------------------------------------------------------------
114 c---------------------------------------------------------------------
115 c unpack C'(-1) and rhs'(-1) for
117 c---------------------------------------------------------------------
121 integer i,j,m,n,ptr,c,kstart
129 lhsc(m,n,i,j,kstart-1,c) = out_buffer(ptr+n)
134 rhs(n,i,j,kstart-1,c) = out_buffer(ptr+n)
143 c---------------------------------------------------------------------
144 c---------------------------------------------------------------------
146 subroutine z_send_solve_info(send_id,c)
148 c---------------------------------------------------------------------
149 c---------------------------------------------------------------------
151 c---------------------------------------------------------------------
152 c pack up and send C'(kend) and rhs'(kend) for
154 c---------------------------------------------------------------------
159 integer i,j,m,n,ksize,ptr,c,ip,jp
160 integer error,send_id,buffer_size
162 ksize = cell_size(3,c)-1
163 ip = cell_coord(1,c) - 1
164 jp = cell_coord(2,c) - 1
165 buffer_size=MAX_CELL_DIM*MAX_CELL_DIM*
166 > (BLOCK_SIZE*BLOCK_SIZE + BLOCK_SIZE)
168 c---------------------------------------------------------------------
170 c---------------------------------------------------------------------
176 in_buffer(ptr+n) = lhsc(m,n,i,j,ksize,c)
181 in_buffer(ptr+n) = rhs(n,i,j,ksize,c)
187 c---------------------------------------------------------------------
189 c---------------------------------------------------------------------
190 call mpi_isend(in_buffer, buffer_size,
191 > dp_type, successor(3),
192 > BOTTOM+ip+jp*NCELLS, comm_solve,
198 c---------------------------------------------------------------------
199 c---------------------------------------------------------------------
201 subroutine z_send_backsub_info(send_id,c)
203 c---------------------------------------------------------------------
204 c---------------------------------------------------------------------
206 c---------------------------------------------------------------------
207 c pack up and send U(jstart) for all i and j
208 c---------------------------------------------------------------------
213 integer i,j,n,ptr,c,kstart,ip,jp
214 integer error,send_id,buffer_size
216 c---------------------------------------------------------------------
217 c Send element 0 to previous processor
218 c---------------------------------------------------------------------
220 ip = cell_coord(1,c)-1
221 jp = cell_coord(2,c)-1
222 buffer_size=MAX_CELL_DIM*MAX_CELL_DIM*BLOCK_SIZE
227 in_buffer(ptr+n) = rhs(n,i,j,kstart,c)
233 call mpi_isend(in_buffer, buffer_size,
234 > dp_type, predecessor(3),
235 > TOP+ip+jp*NCELLS, comm_solve,
241 c---------------------------------------------------------------------
242 c---------------------------------------------------------------------
244 subroutine z_unpack_backsub_info(c)
246 c---------------------------------------------------------------------
247 c---------------------------------------------------------------------
249 c---------------------------------------------------------------------
250 c unpack U(ksize) for all i and j
251 c---------------------------------------------------------------------
261 backsub_info(n,i,j,c) = out_buffer(ptr+n)
271 c---------------------------------------------------------------------
272 c---------------------------------------------------------------------
274 subroutine z_receive_backsub_info(recv_id,c)
276 c---------------------------------------------------------------------
277 c---------------------------------------------------------------------
279 c---------------------------------------------------------------------
281 c---------------------------------------------------------------------
286 integer error,recv_id,ip,jp,c,buffer_size
287 ip = cell_coord(1,c) - 1
288 jp = cell_coord(2,c) - 1
289 buffer_size=MAX_CELL_DIM*MAX_CELL_DIM*BLOCK_SIZE
290 call mpi_irecv(out_buffer, buffer_size,
291 > dp_type, successor(3),
292 > TOP+ip+jp*NCELLS, comm_solve,
298 c---------------------------------------------------------------------
299 c---------------------------------------------------------------------
301 subroutine z_receive_solve_info(recv_id,c)
303 c---------------------------------------------------------------------
304 c---------------------------------------------------------------------
306 c---------------------------------------------------------------------
308 c---------------------------------------------------------------------
313 integer ip,jp,recv_id,error,c,buffer_size
314 ip = cell_coord(1,c) - 1
315 jp = cell_coord(2,c) - 1
316 buffer_size=MAX_CELL_DIM*MAX_CELL_DIM*
317 > (BLOCK_SIZE*BLOCK_SIZE + BLOCK_SIZE)
318 call mpi_irecv(out_buffer, buffer_size,
319 > dp_type, predecessor(3),
320 > BOTTOM+ip+jp*NCELLS, comm_solve,
326 c---------------------------------------------------------------------
327 c---------------------------------------------------------------------
329 subroutine z_backsubstitute(first, last, c)
331 c---------------------------------------------------------------------
332 c---------------------------------------------------------------------
334 c---------------------------------------------------------------------
335 c back solve: if last cell, then generate U(ksize)=rhs(ksize)
336 c else assume U(ksize) is loaded in un pack backsub_info
338 c after call u(kstart) will be sent to next cell
339 c---------------------------------------------------------------------
343 integer first, last, c, i, k
344 integer m,n,j,jsize,isize,ksize,kstart
347 isize = cell_size(1,c)-end(1,c)-1
348 jsize = cell_size(2,c)-end(2,c)-1
349 ksize = cell_size(3,c)-1
350 if (last .eq. 0) then
351 do j=start(2,c),jsize
352 do i=start(1,c),isize
353 c---------------------------------------------------------------------
354 c U(jsize) uses info from previous cell if not last cell
355 c---------------------------------------------------------------------
358 rhs(m,i,j,ksize,c) = rhs(m,i,j,ksize,c)
359 > - lhsc(m,n,i,j,ksize,c)*
360 > backsub_info(n,i,j,c)
366 do k=ksize-1,kstart,-1
367 do j=start(2,c),jsize
368 do i=start(1,c),isize
371 rhs(m,i,j,k,c) = rhs(m,i,j,k,c)
372 > - lhsc(m,n,i,j,k,c)*rhs(n,i,j,k+1,c)
382 c---------------------------------------------------------------------
383 c---------------------------------------------------------------------
385 subroutine z_solve_cell(first,last,c)
387 c---------------------------------------------------------------------
388 c---------------------------------------------------------------------
390 c---------------------------------------------------------------------
391 c performs guaussian elimination on this cell.
393 c assumes that unpacking routines for non-first cells
394 c preload C' and rhs' from previous cell.
396 c assumed send happens outside this routine, but that
397 c c'(KMAX) and rhs'(KMAX) will be sent to next cell.
398 c---------------------------------------------------------------------
404 integer i,j,k,isize,ksize,jsize,kstart
405 double precision utmp(6,-2:KMAX+1)
408 isize = cell_size(1,c)-end(1,c)-1
409 jsize = cell_size(2,c)-end(2,c)-1
410 ksize = cell_size(3,c)-1
412 call lhsabinit(lhsa, lhsb, ksize)
414 do j=start(2,c),jsize
415 do i=start(1,c),isize
417 c---------------------------------------------------------------------
418 c This function computes the left hand side for the three z-factors
419 c---------------------------------------------------------------------
421 c---------------------------------------------------------------------
422 c Compute the indices for storing the block-diagonal matrix;
423 c determine c (labeled f) and s jacobians for cell c
424 c---------------------------------------------------------------------
425 do k = start(3,c)-1, cell_size(3,c)-end(3,c)
426 utmp(1,k) = 1.0d0 / u(1,i,j,k,c)
427 utmp(2,k) = u(2,i,j,k,c)
428 utmp(3,k) = u(3,i,j,k,c)
429 utmp(4,k) = u(4,i,j,k,c)
430 utmp(5,k) = u(5,i,j,k,c)
431 utmp(6,k) = qs(i,j,k,c)
434 do k = start(3,c)-1, cell_size(3,c)-end(3,c)
440 fjac(1,1,k) = 0.0d+00
441 fjac(1,2,k) = 0.0d+00
442 fjac(1,3,k) = 0.0d+00
443 fjac(1,4,k) = 1.0d+00
444 fjac(1,5,k) = 0.0d+00
446 fjac(2,1,k) = - ( utmp(2,k)*utmp(4,k) )
448 fjac(2,2,k) = utmp(4,k) * tmp1
449 fjac(2,3,k) = 0.0d+00
450 fjac(2,4,k) = utmp(2,k) * tmp1
451 fjac(2,5,k) = 0.0d+00
453 fjac(3,1,k) = - ( utmp(3,k)*utmp(4,k) )
455 fjac(3,2,k) = 0.0d+00
456 fjac(3,3,k) = utmp(4,k) * tmp1
457 fjac(3,4,k) = utmp(3,k) * tmp1
458 fjac(3,5,k) = 0.0d+00
460 fjac(4,1,k) = - (utmp(4,k)*utmp(4,k) * tmp2 )
462 fjac(4,2,k) = - c2 * utmp(2,k) * tmp1
463 fjac(4,3,k) = - c2 * utmp(3,k) * tmp1
464 fjac(4,4,k) = ( 2.0d+00 - c2 )
468 fjac(5,1,k) = ( c2 * 2.0d0 * utmp(6,k)
469 > - c1 * ( utmp(5,k) * tmp1 ) )
470 > * ( utmp(4,k) * tmp1 )
471 fjac(5,2,k) = - c2 * ( utmp(2,k)*utmp(4,k) )
473 fjac(5,3,k) = - c2 * ( utmp(3,k)*utmp(4,k) )
475 fjac(5,4,k) = c1 * ( utmp(5,k) * tmp1 )
477 > + utmp(4,k)*utmp(4,k) * tmp2 )
478 fjac(5,5,k) = c1 * utmp(4,k) * tmp1
480 njac(1,1,k) = 0.0d+00
481 njac(1,2,k) = 0.0d+00
482 njac(1,3,k) = 0.0d+00
483 njac(1,4,k) = 0.0d+00
484 njac(1,5,k) = 0.0d+00
486 njac(2,1,k) = - c3c4 * tmp2 * utmp(2,k)
487 njac(2,2,k) = c3c4 * tmp1
488 njac(2,3,k) = 0.0d+00
489 njac(2,4,k) = 0.0d+00
490 njac(2,5,k) = 0.0d+00
492 njac(3,1,k) = - c3c4 * tmp2 * utmp(3,k)
493 njac(3,2,k) = 0.0d+00
494 njac(3,3,k) = c3c4 * tmp1
495 njac(3,4,k) = 0.0d+00
496 njac(3,5,k) = 0.0d+00
498 njac(4,1,k) = - con43 * c3c4 * tmp2 * utmp(4,k)
499 njac(4,2,k) = 0.0d+00
500 njac(4,3,k) = 0.0d+00
501 njac(4,4,k) = con43 * c3 * c4 * tmp1
502 njac(4,5,k) = 0.0d+00
504 njac(5,1,k) = - ( c3c4
505 > - c1345 ) * tmp3 * (utmp(2,k)**2)
506 > - ( c3c4 - c1345 ) * tmp3 * (utmp(3,k)**2)
508 > - c1345 ) * tmp3 * (utmp(4,k)**2)
509 > - c1345 * tmp2 * utmp(5,k)
511 njac(5,2,k) = ( c3c4 - c1345 ) * tmp2 * utmp(2,k)
512 njac(5,3,k) = ( c3c4 - c1345 ) * tmp2 * utmp(3,k)
513 njac(5,4,k) = ( con43 * c3c4
514 > - c1345 ) * tmp2 * utmp(4,k)
515 njac(5,5,k) = ( c1345 )* tmp1
520 c---------------------------------------------------------------------
521 c now joacobians set, so form left hand side in z direction
522 c---------------------------------------------------------------------
523 do k = start(3,c), ksize-end(3,c)
528 lhsa(1,1,k) = - tmp2 * fjac(1,1,k-1)
529 > - tmp1 * njac(1,1,k-1)
531 lhsa(1,2,k) = - tmp2 * fjac(1,2,k-1)
532 > - tmp1 * njac(1,2,k-1)
533 lhsa(1,3,k) = - tmp2 * fjac(1,3,k-1)
534 > - tmp1 * njac(1,3,k-1)
535 lhsa(1,4,k) = - tmp2 * fjac(1,4,k-1)
536 > - tmp1 * njac(1,4,k-1)
537 lhsa(1,5,k) = - tmp2 * fjac(1,5,k-1)
538 > - tmp1 * njac(1,5,k-1)
540 lhsa(2,1,k) = - tmp2 * fjac(2,1,k-1)
541 > - tmp1 * njac(2,1,k-1)
542 lhsa(2,2,k) = - tmp2 * fjac(2,2,k-1)
543 > - tmp1 * njac(2,2,k-1)
545 lhsa(2,3,k) = - tmp2 * fjac(2,3,k-1)
546 > - tmp1 * njac(2,3,k-1)
547 lhsa(2,4,k) = - tmp2 * fjac(2,4,k-1)
548 > - tmp1 * njac(2,4,k-1)
549 lhsa(2,5,k) = - tmp2 * fjac(2,5,k-1)
550 > - tmp1 * njac(2,5,k-1)
552 lhsa(3,1,k) = - tmp2 * fjac(3,1,k-1)
553 > - tmp1 * njac(3,1,k-1)
554 lhsa(3,2,k) = - tmp2 * fjac(3,2,k-1)
555 > - tmp1 * njac(3,2,k-1)
556 lhsa(3,3,k) = - tmp2 * fjac(3,3,k-1)
557 > - tmp1 * njac(3,3,k-1)
559 lhsa(3,4,k) = - tmp2 * fjac(3,4,k-1)
560 > - tmp1 * njac(3,4,k-1)
561 lhsa(3,5,k) = - tmp2 * fjac(3,5,k-1)
562 > - tmp1 * njac(3,5,k-1)
564 lhsa(4,1,k) = - tmp2 * fjac(4,1,k-1)
565 > - tmp1 * njac(4,1,k-1)
566 lhsa(4,2,k) = - tmp2 * fjac(4,2,k-1)
567 > - tmp1 * njac(4,2,k-1)
568 lhsa(4,3,k) = - tmp2 * fjac(4,3,k-1)
569 > - tmp1 * njac(4,3,k-1)
570 lhsa(4,4,k) = - tmp2 * fjac(4,4,k-1)
571 > - tmp1 * njac(4,4,k-1)
573 lhsa(4,5,k) = - tmp2 * fjac(4,5,k-1)
574 > - tmp1 * njac(4,5,k-1)
576 lhsa(5,1,k) = - tmp2 * fjac(5,1,k-1)
577 > - tmp1 * njac(5,1,k-1)
578 lhsa(5,2,k) = - tmp2 * fjac(5,2,k-1)
579 > - tmp1 * njac(5,2,k-1)
580 lhsa(5,3,k) = - tmp2 * fjac(5,3,k-1)
581 > - tmp1 * njac(5,3,k-1)
582 lhsa(5,4,k) = - tmp2 * fjac(5,4,k-1)
583 > - tmp1 * njac(5,4,k-1)
584 lhsa(5,5,k) = - tmp2 * fjac(5,5,k-1)
585 > - tmp1 * njac(5,5,k-1)
588 lhsb(1,1,k) = 1.0d+00
589 > + tmp1 * 2.0d+00 * njac(1,1,k)
590 > + tmp1 * 2.0d+00 * dz1
591 lhsb(1,2,k) = tmp1 * 2.0d+00 * njac(1,2,k)
592 lhsb(1,3,k) = tmp1 * 2.0d+00 * njac(1,3,k)
593 lhsb(1,4,k) = tmp1 * 2.0d+00 * njac(1,4,k)
594 lhsb(1,5,k) = tmp1 * 2.0d+00 * njac(1,5,k)
596 lhsb(2,1,k) = tmp1 * 2.0d+00 * njac(2,1,k)
597 lhsb(2,2,k) = 1.0d+00
598 > + tmp1 * 2.0d+00 * njac(2,2,k)
599 > + tmp1 * 2.0d+00 * dz2
600 lhsb(2,3,k) = tmp1 * 2.0d+00 * njac(2,3,k)
601 lhsb(2,4,k) = tmp1 * 2.0d+00 * njac(2,4,k)
602 lhsb(2,5,k) = tmp1 * 2.0d+00 * njac(2,5,k)
604 lhsb(3,1,k) = tmp1 * 2.0d+00 * njac(3,1,k)
605 lhsb(3,2,k) = tmp1 * 2.0d+00 * njac(3,2,k)
606 lhsb(3,3,k) = 1.0d+00
607 > + tmp1 * 2.0d+00 * njac(3,3,k)
608 > + tmp1 * 2.0d+00 * dz3
609 lhsb(3,4,k) = tmp1 * 2.0d+00 * njac(3,4,k)
610 lhsb(3,5,k) = tmp1 * 2.0d+00 * njac(3,5,k)
612 lhsb(4,1,k) = tmp1 * 2.0d+00 * njac(4,1,k)
613 lhsb(4,2,k) = tmp1 * 2.0d+00 * njac(4,2,k)
614 lhsb(4,3,k) = tmp1 * 2.0d+00 * njac(4,3,k)
615 lhsb(4,4,k) = 1.0d+00
616 > + tmp1 * 2.0d+00 * njac(4,4,k)
617 > + tmp1 * 2.0d+00 * dz4
618 lhsb(4,5,k) = tmp1 * 2.0d+00 * njac(4,5,k)
620 lhsb(5,1,k) = tmp1 * 2.0d+00 * njac(5,1,k)
621 lhsb(5,2,k) = tmp1 * 2.0d+00 * njac(5,2,k)
622 lhsb(5,3,k) = tmp1 * 2.0d+00 * njac(5,3,k)
623 lhsb(5,4,k) = tmp1 * 2.0d+00 * njac(5,4,k)
624 lhsb(5,5,k) = 1.0d+00
625 > + tmp1 * 2.0d+00 * njac(5,5,k)
626 > + tmp1 * 2.0d+00 * dz5
628 lhsc(1,1,i,j,k,c) = tmp2 * fjac(1,1,k+1)
629 > - tmp1 * njac(1,1,k+1)
631 lhsc(1,2,i,j,k,c) = tmp2 * fjac(1,2,k+1)
632 > - tmp1 * njac(1,2,k+1)
633 lhsc(1,3,i,j,k,c) = tmp2 * fjac(1,3,k+1)
634 > - tmp1 * njac(1,3,k+1)
635 lhsc(1,4,i,j,k,c) = tmp2 * fjac(1,4,k+1)
636 > - tmp1 * njac(1,4,k+1)
637 lhsc(1,5,i,j,k,c) = tmp2 * fjac(1,5,k+1)
638 > - tmp1 * njac(1,5,k+1)
640 lhsc(2,1,i,j,k,c) = tmp2 * fjac(2,1,k+1)
641 > - tmp1 * njac(2,1,k+1)
642 lhsc(2,2,i,j,k,c) = tmp2 * fjac(2,2,k+1)
643 > - tmp1 * njac(2,2,k+1)
645 lhsc(2,3,i,j,k,c) = tmp2 * fjac(2,3,k+1)
646 > - tmp1 * njac(2,3,k+1)
647 lhsc(2,4,i,j,k,c) = tmp2 * fjac(2,4,k+1)
648 > - tmp1 * njac(2,4,k+1)
649 lhsc(2,5,i,j,k,c) = tmp2 * fjac(2,5,k+1)
650 > - tmp1 * njac(2,5,k+1)
652 lhsc(3,1,i,j,k,c) = tmp2 * fjac(3,1,k+1)
653 > - tmp1 * njac(3,1,k+1)
654 lhsc(3,2,i,j,k,c) = tmp2 * fjac(3,2,k+1)
655 > - tmp1 * njac(3,2,k+1)
656 lhsc(3,3,i,j,k,c) = tmp2 * fjac(3,3,k+1)
657 > - tmp1 * njac(3,3,k+1)
659 lhsc(3,4,i,j,k,c) = tmp2 * fjac(3,4,k+1)
660 > - tmp1 * njac(3,4,k+1)
661 lhsc(3,5,i,j,k,c) = tmp2 * fjac(3,5,k+1)
662 > - tmp1 * njac(3,5,k+1)
664 lhsc(4,1,i,j,k,c) = tmp2 * fjac(4,1,k+1)
665 > - tmp1 * njac(4,1,k+1)
666 lhsc(4,2,i,j,k,c) = tmp2 * fjac(4,2,k+1)
667 > - tmp1 * njac(4,2,k+1)
668 lhsc(4,3,i,j,k,c) = tmp2 * fjac(4,3,k+1)
669 > - tmp1 * njac(4,3,k+1)
670 lhsc(4,4,i,j,k,c) = tmp2 * fjac(4,4,k+1)
671 > - tmp1 * njac(4,4,k+1)
673 lhsc(4,5,i,j,k,c) = tmp2 * fjac(4,5,k+1)
674 > - tmp1 * njac(4,5,k+1)
676 lhsc(5,1,i,j,k,c) = tmp2 * fjac(5,1,k+1)
677 > - tmp1 * njac(5,1,k+1)
678 lhsc(5,2,i,j,k,c) = tmp2 * fjac(5,2,k+1)
679 > - tmp1 * njac(5,2,k+1)
680 lhsc(5,3,i,j,k,c) = tmp2 * fjac(5,3,k+1)
681 > - tmp1 * njac(5,3,k+1)
682 lhsc(5,4,i,j,k,c) = tmp2 * fjac(5,4,k+1)
683 > - tmp1 * njac(5,4,k+1)
684 lhsc(5,5,i,j,k,c) = tmp2 * fjac(5,5,k+1)
685 > - tmp1 * njac(5,5,k+1)
691 c---------------------------------------------------------------------
692 c outer most do loops - sweeping in i direction
693 c---------------------------------------------------------------------
694 if (first .eq. 1) then
696 c---------------------------------------------------------------------
697 c multiply c(i,j,kstart) by b_inverse and copy back to c
698 c multiply rhs(kstart) by b_inverse(kstart) and copy to rhs
699 c---------------------------------------------------------------------
700 call binvcrhs( lhsb(1,1,kstart),
701 > lhsc(1,1,i,j,kstart,c),
702 > rhs(1,i,j,kstart,c) )
706 c---------------------------------------------------------------------
707 c begin inner most do loop
708 c do all the elements of the cell unless last
709 c---------------------------------------------------------------------
710 do k=kstart+first,ksize-last
712 c---------------------------------------------------------------------
713 c subtract A*lhs_vector(k-1) from lhs_vector(k)
715 c rhs(k) = rhs(k) - A*rhs(k-1)
716 c---------------------------------------------------------------------
717 call matvec_sub(lhsa(1,1,k),
718 > rhs(1,i,j,k-1,c),rhs(1,i,j,k,c))
720 c---------------------------------------------------------------------
721 c B(k) = B(k) - C(k-1)*A(k)
722 c call matmul_sub(aa,i,j,k,c,cc,i,j,k-1,c,bb,i,j,k,c)
723 c---------------------------------------------------------------------
724 call matmul_sub(lhsa(1,1,k),
725 > lhsc(1,1,i,j,k-1,c),
728 c---------------------------------------------------------------------
729 c multiply c(i,j,k) by b_inverse and copy back to c
730 c multiply rhs(i,j,1) by b_inverse(i,j,1) and copy to rhs
731 c---------------------------------------------------------------------
732 call binvcrhs( lhsb(1,1,k),
738 c---------------------------------------------------------------------
739 c Now finish up special cases for last cell
740 c---------------------------------------------------------------------
741 if (last .eq. 1) then
743 c---------------------------------------------------------------------
744 c rhs(ksize) = rhs(ksize) - A*rhs(ksize-1)
745 c---------------------------------------------------------------------
746 call matvec_sub(lhsa(1,1,ksize),
747 > rhs(1,i,j,ksize-1,c),rhs(1,i,j,ksize,c))
749 c---------------------------------------------------------------------
750 c B(ksize) = B(ksize) - C(ksize-1)*A(ksize)
751 c call matmul_sub(aa,i,j,ksize,c,
752 c $ cc,i,j,ksize-1,c,bb,i,j,ksize,c)
753 c---------------------------------------------------------------------
754 call matmul_sub(lhsa(1,1,ksize),
755 > lhsc(1,1,i,j,ksize-1,c),
758 c---------------------------------------------------------------------
759 c multiply rhs(ksize) by b_inverse(ksize) and copy to rhs
760 c---------------------------------------------------------------------
761 call binvrhs( lhsb(1,1,ksize),
762 > rhs(1,i,j,ksize,c) )