1 c---------------------------------------------------------------------
2 c---------------------------------------------------------------------
6 c---------------------------------------------------------------------
7 c---------------------------------------------------------------------
9 c---------------------------------------------------------------------
10 c Performs line solves in Y 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---------------------------------------------------------------------
24 > first, last, recv_id, error, r_status(MPI_STATUS_SIZE),
25 > isize,jsize,ksize,send_id
29 c---------------------------------------------------------------------
30 c in our terminology stage is the number of the cell in the y-direction
31 c i.e. stage = 1 means the start of the line stage=ncells means end
32 c---------------------------------------------------------------------
35 isize = cell_size(1,c) - 1
36 jsize = cell_size(2,c) - 1
37 ksize = cell_size(3,c) - 1
39 c---------------------------------------------------------------------
41 c---------------------------------------------------------------------
42 if (stage .eq. ncells) then
48 if (stage .eq. 1) then
49 c---------------------------------------------------------------------
50 c This is the first cell, so solve without receiving data
51 c---------------------------------------------------------------------
54 call y_solve_cell(first,last,c)
56 c---------------------------------------------------------------------
57 c Not the first cell of this line, so receive info from
58 c processor working on preceeding cell
59 c---------------------------------------------------------------------
61 call y_receive_solve_info(recv_id,c)
62 c---------------------------------------------------------------------
63 c overlap computations and communications
64 c---------------------------------------------------------------------
66 c---------------------------------------------------------------------
68 c---------------------------------------------------------------------
69 call mpi_wait(send_id,r_status,error)
70 call mpi_wait(recv_id,r_status,error)
71 c---------------------------------------------------------------------
72 c install C'(jstart+1) and rhs'(jstart+1) to be used in this cell
73 c---------------------------------------------------------------------
74 call y_unpack_solve_info(c)
75 call y_solve_cell(first,last,c)
78 if (last .eq. 0) call y_send_solve_info(send_id,c)
81 c---------------------------------------------------------------------
82 c now perform backsubstitution in reverse direction
83 c---------------------------------------------------------------------
84 do stage = ncells, 1, -1
88 if (stage .eq. 1) first = 1
89 if (stage .eq. ncells) then
91 c---------------------------------------------------------------------
92 c last cell, so perform back substitute without waiting
93 c---------------------------------------------------------------------
94 call y_backsubstitute(first, last,c)
96 call y_receive_backsub_info(recv_id,c)
97 call mpi_wait(send_id,r_status,error)
98 call mpi_wait(recv_id,r_status,error)
99 call y_unpack_backsub_info(c)
100 call y_backsubstitute(first,last,c)
102 if (first .eq. 0) call y_send_backsub_info(send_id,c)
109 c---------------------------------------------------------------------
110 c---------------------------------------------------------------------
112 subroutine y_unpack_solve_info(c)
114 c---------------------------------------------------------------------
115 c---------------------------------------------------------------------
117 c---------------------------------------------------------------------
118 c unpack C'(-1) and rhs'(-1) for
120 c---------------------------------------------------------------------
124 integer i,k,m,n,ptr,c,jstart
132 lhsc(m,n,i,jstart-1,k,c) = out_buffer(ptr+n)
137 rhs(n,i,jstart-1,k,c) = out_buffer(ptr+n)
146 c---------------------------------------------------------------------
147 c---------------------------------------------------------------------
149 subroutine y_send_solve_info(send_id,c)
151 c---------------------------------------------------------------------
152 c---------------------------------------------------------------------
154 c---------------------------------------------------------------------
155 c pack up and send C'(jend) and rhs'(jend) for
157 c---------------------------------------------------------------------
162 integer i,k,m,n,jsize,ptr,c,ip,kp
163 integer error,send_id,buffer_size
165 jsize = cell_size(2,c)-1
166 ip = cell_coord(1,c) - 1
167 kp = cell_coord(3,c) - 1
168 buffer_size=MAX_CELL_DIM*MAX_CELL_DIM*
169 > (BLOCK_SIZE*BLOCK_SIZE + BLOCK_SIZE)
171 c---------------------------------------------------------------------
173 c---------------------------------------------------------------------
179 in_buffer(ptr+n) = lhsc(m,n,i,jsize,k,c)
184 in_buffer(ptr+n) = rhs(n,i,jsize,k,c)
190 c---------------------------------------------------------------------
192 c---------------------------------------------------------------------
193 call mpi_isend(in_buffer, buffer_size,
194 > dp_type, successor(2),
195 > SOUTH+ip+kp*NCELLS, comm_solve,
201 c---------------------------------------------------------------------
202 c---------------------------------------------------------------------
204 subroutine y_send_backsub_info(send_id,c)
206 c---------------------------------------------------------------------
207 c---------------------------------------------------------------------
209 c---------------------------------------------------------------------
210 c pack up and send U(jstart) for all i and k
211 c---------------------------------------------------------------------
216 integer i,k,n,ptr,c,jstart,ip,kp
217 integer error,send_id,buffer_size
219 c---------------------------------------------------------------------
220 c Send element 0 to previous processor
221 c---------------------------------------------------------------------
223 ip = cell_coord(1,c)-1
224 kp = cell_coord(3,c)-1
225 buffer_size=MAX_CELL_DIM*MAX_CELL_DIM*BLOCK_SIZE
230 in_buffer(ptr+n) = rhs(n,i,jstart,k,c)
235 call mpi_isend(in_buffer, buffer_size,
236 > dp_type, predecessor(2),
237 > NORTH+ip+kp*NCELLS, comm_solve,
243 c---------------------------------------------------------------------
244 c---------------------------------------------------------------------
246 subroutine y_unpack_backsub_info(c)
248 c---------------------------------------------------------------------
249 c---------------------------------------------------------------------
251 c---------------------------------------------------------------------
252 c unpack U(jsize) for all i and k
253 c---------------------------------------------------------------------
263 backsub_info(n,i,k,c) = out_buffer(ptr+n)
272 c---------------------------------------------------------------------
273 c---------------------------------------------------------------------
275 subroutine y_receive_backsub_info(recv_id,c)
277 c---------------------------------------------------------------------
278 c---------------------------------------------------------------------
280 c---------------------------------------------------------------------
282 c---------------------------------------------------------------------
287 integer error,recv_id,ip,kp,c,buffer_size
288 ip = cell_coord(1,c) - 1
289 kp = cell_coord(3,c) - 1
290 buffer_size=MAX_CELL_DIM*MAX_CELL_DIM*BLOCK_SIZE
291 call mpi_irecv(out_buffer, buffer_size,
292 > dp_type, successor(2),
293 > NORTH+ip+kp*NCELLS, comm_solve,
298 c---------------------------------------------------------------------
299 c---------------------------------------------------------------------
301 subroutine y_receive_solve_info(recv_id,c)
303 c---------------------------------------------------------------------
304 c---------------------------------------------------------------------
306 c---------------------------------------------------------------------
308 c---------------------------------------------------------------------
313 integer ip,kp,recv_id,error,c,buffer_size
314 ip = cell_coord(1,c) - 1
315 kp = cell_coord(3,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(2),
320 > SOUTH+ip+kp*NCELLS, comm_solve,
326 c---------------------------------------------------------------------
327 c---------------------------------------------------------------------
329 subroutine y_backsubstitute(first, last, c)
331 c---------------------------------------------------------------------
332 c---------------------------------------------------------------------
334 c---------------------------------------------------------------------
335 c back solve: if last cell, then generate U(jsize)=rhs(jsize)
336 c else assume U(jsize) is loaded in un pack backsub_info
338 c after call u(jstart) will be sent to next cell
339 c---------------------------------------------------------------------
343 integer first, last, c, i, k
344 integer m,n,j,jsize,isize,ksize,jstart
347 isize = cell_size(1,c)-end(1,c)-1
348 jsize = cell_size(2,c)-1
349 ksize = cell_size(3,c)-end(3,c)-1
350 if (last .eq. 0) then
351 do k=start(3,c),ksize
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,jsize,k,c) = rhs(m,i,jsize,k,c)
359 > - lhsc(m,n,i,jsize,k,c)*
360 > backsub_info(n,i,k,c)
366 do k=start(3,c),ksize
367 do j=jsize-1,jstart,-1
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+1,k,c)
382 c---------------------------------------------------------------------
383 c---------------------------------------------------------------------
385 subroutine y_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'(JMAX) and rhs'(JMAX) will be sent to next cell
398 c---------------------------------------------------------------------
404 integer i,j,k,isize,ksize,jsize,jstart
405 double precision utmp(6,-2:JMAX+1)
408 isize = cell_size(1,c)-end(1,c)-1
409 jsize = cell_size(2,c)-1
410 ksize = cell_size(3,c)-end(3,c)-1
412 call lhsabinit(lhsa, lhsb, jsize)
414 do k=start(3,c),ksize
415 do i=start(1,c),isize
417 c---------------------------------------------------------------------
418 c This function computes the left hand side for the three y-factors
419 c---------------------------------------------------------------------
421 c---------------------------------------------------------------------
422 c Compute the indices for storing the tri-diagonal matrix;
423 c determine a (labeled f) and n jacobians for cell c
424 c---------------------------------------------------------------------
425 do j = start(2,c)-1, cell_size(2,c)-end(2,c)
426 utmp(1,j) = 1.0d0 / u(1,i,j,k,c)
427 utmp(2,j) = u(2,i,j,k,c)
428 utmp(3,j) = u(3,i,j,k,c)
429 utmp(4,j) = u(4,i,j,k,c)
430 utmp(5,j) = u(5,i,j,k,c)
431 utmp(6,j) = qs(i,j,k,c)
434 do j = start(2,c)-1, cell_size(2,c)-end(2,c)
440 fjac(1,1,j) = 0.0d+00
441 fjac(1,2,j) = 0.0d+00
442 fjac(1,3,j) = 1.0d+00
443 fjac(1,4,j) = 0.0d+00
444 fjac(1,5,j) = 0.0d+00
446 fjac(2,1,j) = - ( utmp(2,j)*utmp(3,j) )
448 fjac(2,2,j) = utmp(3,j) * tmp1
449 fjac(2,3,j) = utmp(2,j) * tmp1
450 fjac(2,4,j) = 0.0d+00
451 fjac(2,5,j) = 0.0d+00
453 fjac(3,1,j) = - ( utmp(3,j)*utmp(3,j)*tmp2)
455 fjac(3,2,j) = - c2 * utmp(2,j) * tmp1
456 fjac(3,3,j) = ( 2.0d+00 - c2 )
458 fjac(3,4,j) = - c2 * utmp(4,j) * tmp1
461 fjac(4,1,j) = - ( utmp(3,j)*utmp(4,j) )
463 fjac(4,2,j) = 0.0d+00
464 fjac(4,3,j) = utmp(4,j) * tmp1
465 fjac(4,4,j) = utmp(3,j) * tmp1
466 fjac(4,5,j) = 0.0d+00
468 fjac(5,1,j) = ( c2 * 2.0d0 * utmp(6,j)
469 > - c1 * utmp(5,j) * tmp1 )
471 fjac(5,2,j) = - c2 * utmp(2,j)*utmp(3,j)
473 fjac(5,3,j) = c1 * utmp(5,j) * tmp1
475 > + utmp(3,j)*utmp(3,j) * tmp2 )
476 fjac(5,4,j) = - c2 * ( utmp(3,j)*utmp(4,j) )
478 fjac(5,5,j) = c1 * utmp(3,j) * tmp1
480 njac(1,1,j) = 0.0d+00
481 njac(1,2,j) = 0.0d+00
482 njac(1,3,j) = 0.0d+00
483 njac(1,4,j) = 0.0d+00
484 njac(1,5,j) = 0.0d+00
486 njac(2,1,j) = - c3c4 * tmp2 * utmp(2,j)
487 njac(2,2,j) = c3c4 * tmp1
488 njac(2,3,j) = 0.0d+00
489 njac(2,4,j) = 0.0d+00
490 njac(2,5,j) = 0.0d+00
492 njac(3,1,j) = - con43 * c3c4 * tmp2 * utmp(3,j)
493 njac(3,2,j) = 0.0d+00
494 njac(3,3,j) = con43 * c3c4 * tmp1
495 njac(3,4,j) = 0.0d+00
496 njac(3,5,j) = 0.0d+00
498 njac(4,1,j) = - c3c4 * tmp2 * utmp(4,j)
499 njac(4,2,j) = 0.0d+00
500 njac(4,3,j) = 0.0d+00
501 njac(4,4,j) = c3c4 * tmp1
502 njac(4,5,j) = 0.0d+00
504 njac(5,1,j) = - ( c3c4
505 > - c1345 ) * tmp3 * (utmp(2,j)**2)
507 > - c1345 ) * tmp3 * (utmp(3,j)**2)
508 > - ( c3c4 - c1345 ) * tmp3 * (utmp(4,j)**2)
509 > - c1345 * tmp2 * utmp(5,j)
511 njac(5,2,j) = ( c3c4 - c1345 ) * tmp2 * utmp(2,j)
512 njac(5,3,j) = ( con43 * c3c4
513 > - c1345 ) * tmp2 * utmp(3,j)
514 njac(5,4,j) = ( c3c4 - c1345 ) * tmp2 * utmp(4,j)
515 njac(5,5,j) = ( c1345 ) * tmp1
519 c---------------------------------------------------------------------
520 c now joacobians set, so form left hand side in y direction
521 c---------------------------------------------------------------------
522 do j = start(2,c), jsize-end(2,c)
527 lhsa(1,1,j) = - tmp2 * fjac(1,1,j-1)
528 > - tmp1 * njac(1,1,j-1)
530 lhsa(1,2,j) = - tmp2 * fjac(1,2,j-1)
531 > - tmp1 * njac(1,2,j-1)
532 lhsa(1,3,j) = - tmp2 * fjac(1,3,j-1)
533 > - tmp1 * njac(1,3,j-1)
534 lhsa(1,4,j) = - tmp2 * fjac(1,4,j-1)
535 > - tmp1 * njac(1,4,j-1)
536 lhsa(1,5,j) = - tmp2 * fjac(1,5,j-1)
537 > - tmp1 * njac(1,5,j-1)
539 lhsa(2,1,j) = - tmp2 * fjac(2,1,j-1)
540 > - tmp1 * njac(2,1,j-1)
541 lhsa(2,2,j) = - tmp2 * fjac(2,2,j-1)
542 > - tmp1 * njac(2,2,j-1)
544 lhsa(2,3,j) = - tmp2 * fjac(2,3,j-1)
545 > - tmp1 * njac(2,3,j-1)
546 lhsa(2,4,j) = - tmp2 * fjac(2,4,j-1)
547 > - tmp1 * njac(2,4,j-1)
548 lhsa(2,5,j) = - tmp2 * fjac(2,5,j-1)
549 > - tmp1 * njac(2,5,j-1)
551 lhsa(3,1,j) = - tmp2 * fjac(3,1,j-1)
552 > - tmp1 * njac(3,1,j-1)
553 lhsa(3,2,j) = - tmp2 * fjac(3,2,j-1)
554 > - tmp1 * njac(3,2,j-1)
555 lhsa(3,3,j) = - tmp2 * fjac(3,3,j-1)
556 > - tmp1 * njac(3,3,j-1)
558 lhsa(3,4,j) = - tmp2 * fjac(3,4,j-1)
559 > - tmp1 * njac(3,4,j-1)
560 lhsa(3,5,j) = - tmp2 * fjac(3,5,j-1)
561 > - tmp1 * njac(3,5,j-1)
563 lhsa(4,1,j) = - tmp2 * fjac(4,1,j-1)
564 > - tmp1 * njac(4,1,j-1)
565 lhsa(4,2,j) = - tmp2 * fjac(4,2,j-1)
566 > - tmp1 * njac(4,2,j-1)
567 lhsa(4,3,j) = - tmp2 * fjac(4,3,j-1)
568 > - tmp1 * njac(4,3,j-1)
569 lhsa(4,4,j) = - tmp2 * fjac(4,4,j-1)
570 > - tmp1 * njac(4,4,j-1)
572 lhsa(4,5,j) = - tmp2 * fjac(4,5,j-1)
573 > - tmp1 * njac(4,5,j-1)
575 lhsa(5,1,j) = - tmp2 * fjac(5,1,j-1)
576 > - tmp1 * njac(5,1,j-1)
577 lhsa(5,2,j) = - tmp2 * fjac(5,2,j-1)
578 > - tmp1 * njac(5,2,j-1)
579 lhsa(5,3,j) = - tmp2 * fjac(5,3,j-1)
580 > - tmp1 * njac(5,3,j-1)
581 lhsa(5,4,j) = - tmp2 * fjac(5,4,j-1)
582 > - tmp1 * njac(5,4,j-1)
583 lhsa(5,5,j) = - tmp2 * fjac(5,5,j-1)
584 > - tmp1 * njac(5,5,j-1)
587 lhsb(1,1,j) = 1.0d+00
588 > + tmp1 * 2.0d+00 * njac(1,1,j)
589 > + tmp1 * 2.0d+00 * dy1
590 lhsb(1,2,j) = tmp1 * 2.0d+00 * njac(1,2,j)
591 lhsb(1,3,j) = tmp1 * 2.0d+00 * njac(1,3,j)
592 lhsb(1,4,j) = tmp1 * 2.0d+00 * njac(1,4,j)
593 lhsb(1,5,j) = tmp1 * 2.0d+00 * njac(1,5,j)
595 lhsb(2,1,j) = tmp1 * 2.0d+00 * njac(2,1,j)
596 lhsb(2,2,j) = 1.0d+00
597 > + tmp1 * 2.0d+00 * njac(2,2,j)
598 > + tmp1 * 2.0d+00 * dy2
599 lhsb(2,3,j) = tmp1 * 2.0d+00 * njac(2,3,j)
600 lhsb(2,4,j) = tmp1 * 2.0d+00 * njac(2,4,j)
601 lhsb(2,5,j) = tmp1 * 2.0d+00 * njac(2,5,j)
603 lhsb(3,1,j) = tmp1 * 2.0d+00 * njac(3,1,j)
604 lhsb(3,2,j) = tmp1 * 2.0d+00 * njac(3,2,j)
605 lhsb(3,3,j) = 1.0d+00
606 > + tmp1 * 2.0d+00 * njac(3,3,j)
607 > + tmp1 * 2.0d+00 * dy3
608 lhsb(3,4,j) = tmp1 * 2.0d+00 * njac(3,4,j)
609 lhsb(3,5,j) = tmp1 * 2.0d+00 * njac(3,5,j)
611 lhsb(4,1,j) = tmp1 * 2.0d+00 * njac(4,1,j)
612 lhsb(4,2,j) = tmp1 * 2.0d+00 * njac(4,2,j)
613 lhsb(4,3,j) = tmp1 * 2.0d+00 * njac(4,3,j)
614 lhsb(4,4,j) = 1.0d+00
615 > + tmp1 * 2.0d+00 * njac(4,4,j)
616 > + tmp1 * 2.0d+00 * dy4
617 lhsb(4,5,j) = tmp1 * 2.0d+00 * njac(4,5,j)
619 lhsb(5,1,j) = tmp1 * 2.0d+00 * njac(5,1,j)
620 lhsb(5,2,j) = tmp1 * 2.0d+00 * njac(5,2,j)
621 lhsb(5,3,j) = tmp1 * 2.0d+00 * njac(5,3,j)
622 lhsb(5,4,j) = tmp1 * 2.0d+00 * njac(5,4,j)
623 lhsb(5,5,j) = 1.0d+00
624 > + tmp1 * 2.0d+00 * njac(5,5,j)
625 > + tmp1 * 2.0d+00 * dy5
627 lhsc(1,1,i,j,k,c) = tmp2 * fjac(1,1,j+1)
628 > - tmp1 * njac(1,1,j+1)
630 lhsc(1,2,i,j,k,c) = tmp2 * fjac(1,2,j+1)
631 > - tmp1 * njac(1,2,j+1)
632 lhsc(1,3,i,j,k,c) = tmp2 * fjac(1,3,j+1)
633 > - tmp1 * njac(1,3,j+1)
634 lhsc(1,4,i,j,k,c) = tmp2 * fjac(1,4,j+1)
635 > - tmp1 * njac(1,4,j+1)
636 lhsc(1,5,i,j,k,c) = tmp2 * fjac(1,5,j+1)
637 > - tmp1 * njac(1,5,j+1)
639 lhsc(2,1,i,j,k,c) = tmp2 * fjac(2,1,j+1)
640 > - tmp1 * njac(2,1,j+1)
641 lhsc(2,2,i,j,k,c) = tmp2 * fjac(2,2,j+1)
642 > - tmp1 * njac(2,2,j+1)
644 lhsc(2,3,i,j,k,c) = tmp2 * fjac(2,3,j+1)
645 > - tmp1 * njac(2,3,j+1)
646 lhsc(2,4,i,j,k,c) = tmp2 * fjac(2,4,j+1)
647 > - tmp1 * njac(2,4,j+1)
648 lhsc(2,5,i,j,k,c) = tmp2 * fjac(2,5,j+1)
649 > - tmp1 * njac(2,5,j+1)
651 lhsc(3,1,i,j,k,c) = tmp2 * fjac(3,1,j+1)
652 > - tmp1 * njac(3,1,j+1)
653 lhsc(3,2,i,j,k,c) = tmp2 * fjac(3,2,j+1)
654 > - tmp1 * njac(3,2,j+1)
655 lhsc(3,3,i,j,k,c) = tmp2 * fjac(3,3,j+1)
656 > - tmp1 * njac(3,3,j+1)
658 lhsc(3,4,i,j,k,c) = tmp2 * fjac(3,4,j+1)
659 > - tmp1 * njac(3,4,j+1)
660 lhsc(3,5,i,j,k,c) = tmp2 * fjac(3,5,j+1)
661 > - tmp1 * njac(3,5,j+1)
663 lhsc(4,1,i,j,k,c) = tmp2 * fjac(4,1,j+1)
664 > - tmp1 * njac(4,1,j+1)
665 lhsc(4,2,i,j,k,c) = tmp2 * fjac(4,2,j+1)
666 > - tmp1 * njac(4,2,j+1)
667 lhsc(4,3,i,j,k,c) = tmp2 * fjac(4,3,j+1)
668 > - tmp1 * njac(4,3,j+1)
669 lhsc(4,4,i,j,k,c) = tmp2 * fjac(4,4,j+1)
670 > - tmp1 * njac(4,4,j+1)
672 lhsc(4,5,i,j,k,c) = tmp2 * fjac(4,5,j+1)
673 > - tmp1 * njac(4,5,j+1)
675 lhsc(5,1,i,j,k,c) = tmp2 * fjac(5,1,j+1)
676 > - tmp1 * njac(5,1,j+1)
677 lhsc(5,2,i,j,k,c) = tmp2 * fjac(5,2,j+1)
678 > - tmp1 * njac(5,2,j+1)
679 lhsc(5,3,i,j,k,c) = tmp2 * fjac(5,3,j+1)
680 > - tmp1 * njac(5,3,j+1)
681 lhsc(5,4,i,j,k,c) = tmp2 * fjac(5,4,j+1)
682 > - tmp1 * njac(5,4,j+1)
683 lhsc(5,5,i,j,k,c) = tmp2 * fjac(5,5,j+1)
684 > - tmp1 * njac(5,5,j+1)
690 c---------------------------------------------------------------------
691 c outer most do loops - sweeping in i direction
692 c---------------------------------------------------------------------
693 if (first .eq. 1) then
695 c---------------------------------------------------------------------
696 c multiply c(i,jstart,k) by b_inverse and copy back to c
697 c multiply rhs(jstart) by b_inverse(jstart) and copy to rhs
698 c---------------------------------------------------------------------
699 call binvcrhs( lhsb(1,1,jstart),
700 > lhsc(1,1,i,jstart,k,c),
701 > rhs(1,i,jstart,k,c) )
705 c---------------------------------------------------------------------
706 c begin inner most do loop
707 c do all the elements of the cell unless last
708 c---------------------------------------------------------------------
709 do j=jstart+first,jsize-last
711 c---------------------------------------------------------------------
712 c subtract A*lhs_vector(j-1) from lhs_vector(j)
714 c rhs(j) = rhs(j) - A*rhs(j-1)
715 c---------------------------------------------------------------------
716 call matvec_sub(lhsa(1,1,j),
717 > rhs(1,i,j-1,k,c),rhs(1,i,j,k,c))
719 c---------------------------------------------------------------------
720 c B(j) = B(j) - C(j-1)*A(j)
721 c---------------------------------------------------------------------
722 call matmul_sub(lhsa(1,1,j),
723 > lhsc(1,1,i,j-1,k,c),
726 c---------------------------------------------------------------------
727 c multiply c(i,j,k) by b_inverse and copy back to c
728 c multiply rhs(i,1,k) by b_inverse(i,1,k) and copy to rhs
729 c---------------------------------------------------------------------
730 call binvcrhs( lhsb(1,1,j),
736 c---------------------------------------------------------------------
737 c Now finish up special cases for last cell
738 c---------------------------------------------------------------------
739 if (last .eq. 1) then
741 c---------------------------------------------------------------------
742 c rhs(jsize) = rhs(jsize) - A*rhs(jsize-1)
743 c---------------------------------------------------------------------
744 call matvec_sub(lhsa(1,1,jsize),
745 > rhs(1,i,jsize-1,k,c),rhs(1,i,jsize,k,c))
747 c---------------------------------------------------------------------
748 c B(jsize) = B(jsize) - C(jsize-1)*A(jsize)
749 c call matmul_sub(aa,i,jsize,k,c,
750 c $ cc,i,jsize-1,k,c,bb,i,jsize,k,c)
751 c---------------------------------------------------------------------
752 call matmul_sub(lhsa(1,1,jsize),
753 > lhsc(1,1,i,jsize-1,k,c),
756 c---------------------------------------------------------------------
757 c multiply rhs(jsize) by b_inverse(jsize) and copy to rhs
758 c---------------------------------------------------------------------
759 call binvrhs( lhsb(1,1,jsize),
760 > rhs(1,i,jsize,k,c) )