-
Notifications
You must be signed in to change notification settings - Fork 0
/
tridi_wktn_block.f90
373 lines (335 loc) · 10.4 KB
/
tridi_wktn_block.f90
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
! trying for the message vectorization version
program tridi_wktn_block
implicit none
include "mpif.h"
integer n, myid, numproc, ierr, stat(MPI_STATUS_SIZE)
real*8, dimension(:,:), allocatable :: a, b, c, d, x, bp, acorr, acorr2
integer indexspan, startindex, ii, ij, m
parameter (n=8)
parameter (m=2) ! message length
real*8 t0, t1, t2, avgtime
call MPI_Init(ierr)
call MPI_Comm_rank(MPI_COMM_WORLD, myid, ierr)
call MPI_Comm_size(MPI_COMM_WORLD, numproc, ierr)
indexspan = n/numproc
startindex = myid*indexspan+1
allocate(a(n,n))
allocate(b(n,n))
allocate(c(n,n))
allocate(d(n,n))
allocate(x(n,indexspan))
allocate(bp(n,n))
allocate(acorr(n,indexspan))
allocate(acorr2(n,indexspan))
! initialize things
a = 1d0
b = -2d0
c = 1d0
d = -5d-1
if (numproc .gt. 1) then
! we want to precompute bp
bp(:,1) = b(:,1)
do ii=2,n
bp(:,ii) = b(:,ii) - (a(:,ii)/bp(:,ii-1))*c(:,ii-1)
enddo
! we also want to pre-compute the correction coefs for the entire vector
acorr = 0d0
if (myid .ne. 0) then
acorr(:,1) = -a(:,startindex)/bp(:,startindex-1)
do ii=2,indexspan
acorr(:,ii) = (-a(:,startindex+ii-1)/bp(:,startindex+ii-2)) * acorr(:,ii-1)
enddo
endif
acorr2 = 0d0
if (myid .ne. numproc-1) then
acorr2(:,indexspan) = -c(:,startindex+indexspan-1)/bp(:,startindex+indexspan-1)
do ii=indexspan-1,1,-1
acorr2(:,ii) = (-c(:,startindex+ii-1)/bp(:,startindex+ii-1)) * acorr2(:,ii+1)
enddo
endif
endif
t0 = MPI_Wtime()
! for testing on 1 processor
if (numproc .eq. 1) then
do ii=1,n
call solve_tridiag(a(ii,:),b(ii,:),c(ii,:),d(ii,:),x(ii,:),n)
enddo
else
call tridi_block(a,b,c,d,x,n,myid,numproc,bp,acorr,acorr2,indexspan,startindex,m,n/m)
endif
t1 = MPI_Wtime(ierr) - t0
! output
do ii=0,numproc-1
if (myid .eq. ii) then
write(*,*), "proc", myid
do ij=1,indexspan
write(*,'(8f8.2)'), x(:,ij)
enddo
endif
call MPI_Barrier(MPI_COMM_WORLD, ierr)
enddo
call MPI_ALLREDUCE(t1, avgtime, 1, MPI_REAL8, MPI_SUM, MPI_COMM_WORLD, ierr)
if (myid .eq. 0) then
write(*,*) (avgtime/numproc)
endif
! too lazy to deallocate
call MPI_Finalize(ierr)
end program tridi_wktn_block
! the magic happens here
! acorr, acorr2, and bp can all be computed once by a subroutine on program start
! for now, assume n mod m = 0
subroutine tridi_block(a,b,c,d,x,n,myid,numproc,bp,acorr,acorr2,indexspan,startindex,m,numblocks)
implicit none
include "mpif.h"
integer n, myid, numproc, ii, ij, ierr
integer stat(MPI_STATUS_SIZE)
integer indexspan, startindex, m
integer numblocks, s, e, crow, checkrecv, flag, done, z, span
integer, dimension(numblocks) :: sendreq, recvreq
real(8), dimension(n,n) :: a,b,c,d,bp ! apparently needs the ::
real(8), dimension(n,indexspan) :: vp, x, acorr, acorr2
real(8), dimension(n) :: recvbuff
real(8) :: r, corr, sendcorr
parameter (z=1) ! number of rows to calc while waiting
sendreq = 0
recvreq = 0
! Tridi pass 1
if (myid .eq. 0) then
! all root needs to do is calc and send off
do ii=1,numblocks
s=1+(ii-1)*m
e=ii*m
! print*, "root calc from ",s," to ",e
vp(s:e,1) = d(s:e,startindex)
do ij=2,indexspan
vp(s:e,ij) = d(s:e,startindex+ij-1) - a(s:e,startindex+ij-1)*vp(s:e,ij-1)/bp(s:e,startindex+ij-2)
enddo
! print*, "root isend block ",ii," to proc 1"
call MPI_Isend(vp(s:e,indexspan), m, MPI_REAL8, myid+1, 0, MPI_COMM_WORLD, sendreq(ii), ierr)
enddo
else
! post a bunch of recvs for checking later
do ii=1,numblocks
s = 1+(ii-1)*m
e = ii*m
! print*, myid, "posting irecv of block ",ii," for later"
call MPI_Irecv(recvbuff(s:e), m, MPI_REAL8, myid-1, 0, MPI_COMM_WORLD, recvreq(ii), ierr)
enddo
! cant do anything without the first block
! print*, myid, "doing first block of guessing"
vp(1:m,1) = d(1:m,startindex)
do ij=2,indexspan
vp(1:m,ij) = d(1:m,startindex+ij-1) - a(1:m,startindex+ij-1)*vp(1:m,ij-1)/bp(1:m,startindex+ij-2)
enddo
crow = 1
checkrecv = 1
! all other procs are waiting on recvs, so work on things
! assume blocks will come in order
done = 0
do while (done .eq. 0)
! check for recv
call MPI_Test(recvreq(checkrecv), flag, stat, ierr)
! if recv'd, look for next one
if (flag .eq. 1) then
! print*, myid, "recvd block ", checkrecv
! quickly correct final row and send it off
s = 1+(checkrecv-1)*m
e = checkrecv*m
vp(s:e,indexspan) = vp(s:e,indexspan) + acorr(s:e,indexspan)*recvbuff(s:e)
if (myid .ne. numproc-1) then
! print*, myid, "propagating to next proc"
call MPI_Isend(vp(s:e,indexspan), m, MPI_REAL8, myid+1, 0, MPI_COMM_WORLD, sendreq(checkrecv), ierr)
endif
checkrecv = checkrecv + 1
! if recvd all, exit while loop
if (checkrecv .gt. numblocks) then
! print*, myid, "all blocks recvd"
done = 1
else
! still have more blocks to come
! make sure guess is prepped
s = e+1 ! next block
e = e+m
vp(s:e,1) = d(s:e,startindex)
do ij=2,indexspan
vp(s:e,ij) = d(s:e,startindex+ij-1) - a(s:e,startindex+ij-1)*vp(s:e,ij-1)/bp(s:e,startindex+ij-2)
enddo
endif
else
! correct a few rows
if (crow .le. n) then
span = z
! print*,myid,"waste time?",span,crow,n,checkrecv
if (crow+span-1 .gt. n) then
span = n-crow+1
endif
! dont correct if havent recvd a block yet
if (crow+span-1 .gt. m*(checkrecv-1)) then
span = m*(checkrecv-1)-crow+1
! print*,myid,"trunc2 to",span
endif
! correct from row (crow : crow+span-1)
if (span .gt. 0) then
s = crow
e = crow+span-1
! print*, myid, "wasting time correcting from ",s," to ",e
do ij=1,indexspan-1
vp(s:e,ij) = vp(s:e,ij) + acorr(s:e,ij)*recvbuff(s:e)
enddo
crow = crow + span
endif
endif
endif
end do
! correct remaining things
if (crow .le. n) then
s = crow
e = n
! print*, myid, "computing rest of corrections from ",s," to ",e
do ij=1,indexspan-1
vp(s:e,ij) = vp(s:e,ij) + acorr(s:e,ij)*recvbuff(s:e)
enddo
endif
endif
! reset recv req array
recvreq = 0
! wait for all sends to complete?
! not necessary if clever
do ij=1,numblocks ! mpi_waitall looks annoying
call MPI_Wait(sendreq(ij), stat, ierr)
enddo
sendreq = 0
! Start Second Phase
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
if (myid .eq. numproc-1) then
! all root needs to do is calc and send off
do ii=1,numblocks
s=1+(ii-1)*m
e=ii*m
! print*, "PHASE2 root calc from ",s," to ",e
x(s:e,indexspan) = vp(s:e,indexspan)/bp(s:e,indexspan+startindex-1)
do ij=indexspan-1,1,-1
x(s:e,ij) = vp(s:e,ij)/bp(s:e,startindex+ij-1) - (c(s:e,startindex+ij-1)/bp(s:e,startindex+ij-1))*x(s:e,ij+1)
enddo
! print*, "PHASE2 root isend block ",ii," to proc 1"
call MPI_Isend(x(s:e,1), m, MPI_REAL8, myid-1, 0, MPI_COMM_WORLD, sendreq(ii), ierr)
enddo
else
! post a bunch of recvs for checking later
do ii=1,numblocks
s = 1+(ii-1)*m
e = ii*m
! print*, myid, "PHASE2 posting irecv of block ",ii," for later"
call MPI_Irecv(recvbuff(s:e), m, MPI_REAL8, myid+1, 0, MPI_COMM_WORLD, recvreq(ii), ierr)
enddo
! cant do anything without the first block
! print*, myid, "PHASE 2doing first block of guessing"
x(1:m,indexspan) = vp(1:m,indexspan)/bp(1:m,indexspan+startindex-1)
do ij=indexspan-1,1,-1
x(1:m,ij) = vp(1:m,ij)/bp(1:m,startindex+ij-1) - (c(1:m,startindex+ij-1)/bp(1:m,startindex+ij-1))*x(1:m,ij+1)
! x(1:m,ij) = x(1:)
enddo
crow = 1
checkrecv = 1
! all other procs are waiting on recvs, so work on things
! assume blocks will come in order
done = 0
do while (done .eq. 0)
! check for recv
call MPI_Test(recvreq(checkrecv), flag, stat, ierr)
! if recv'd, look for next one
if (flag .eq. 1) then
! print*, myid, "PHASE2 recvd block ", checkrecv
! quickly correct final row and send it off
s = 1+(checkrecv-1)*m
e = checkrecv*m
x(s:e,1) = x(s:e,1) + acorr2(s:e,1)*recvbuff(s:e)
if (myid .ne. 0) then
! print*, myid, "PHASE2 propagating to next proc"
call MPI_Isend(x(s:e,1), m, MPI_REAL8, myid-1, 0, MPI_COMM_WORLD, sendreq(checkrecv), ierr)
endif
checkrecv = checkrecv + 1
! if recvd all, exit while loop
if (checkrecv .gt. numblocks) then
! print*, myid, "PHASE2 all blocks recvd"
done = 1
else
! still have more blocks to come
! make sure guess is prepped
s = e+1 ! next block
e = e+m
x(s:e,indexspan) = vp(s:e,indexspan)/bp(s:e,indexspan+startindex-1)
do ij=indexspan-1,1,-1
x(s:e,ij) = vp(s:e,ij)/bp(s:e,startindex+ij-1) - (c(s:e,startindex+ij-1)/bp(s:e,startindex+ij-1))*x(s:e,ij+1)
! x(s:e,ij) = x(s:e,ij+1)
enddo
endif
else
! correct a few rows
if (crow .le. n) then
span = z
! print*,myid,"waste time?",span,crow,n,checkrecv
if (crow+span-1 .gt. n) then
span = n-crow+1
endif
! dont correct if havent recvd a block yet
if (crow+span-1 .gt. m*(checkrecv-1)) then
span = m*(checkrecv-1)-crow+1
! print*,myid,"trunc2 to",span
endif
! correct from row (crow : crow+span-1)
if (span .gt. 0) then
s = crow
e = crow+span-1
! print*, myid, "PHASE2 wasting time correcting from ",s," to ",e
do ij=2,indexspan
x(s:e,ij) = x(s:e,ij) + acorr2(s:e,ij)*recvbuff(s:e)
enddo
crow = crow + span
endif
endif
endif
end do
! correct remaining things
if (crow .le. n) then
s = crow
e = n
! print*, myid, "PHASE2 computing rest of corrections from ",s," to ",e
do ij=2,indexspan
x(s:e,ij) = x(s:e,ij) + acorr2(s:e,ij)*recvbuff(s:e)
enddo
endif
endif
! reset recv req array
recvreq = 0
! wait for all sends to complete?
! not necessary if clever
do ij=1,numblocks ! mpi_waitall looks annoying
call MPI_Wait(sendreq(ij), stat, ierr)
enddo
! DOOONE
end subroutine tridi_block
! for reference
subroutine solve_tridiag(a,b,c,v,x,n)
implicit none
integer,intent(in) :: n
real(8),dimension(n),intent(in) :: a,b,c,v
real(8),dimension(n),intent(out) :: x
real(8),dimension(n) :: bp,vp
real(8) :: m
integer i
! Make copies of the b and v variables so that they are unaltered by this sub
bp(1) = b(1)
vp(1) = v(1)
!The first pass (setting coefficients):
firstpass: do i = 2,n
m = a(i)/bp(i-1)
bp(i) = b(i) - m*c(i-1)
vp(i) = v(i) - m*vp(i-1)
end do firstpass
x(n) = vp(n)/bp(n)
!The second pass (back-substition)
backsub:do i = n-1, 1, -1
x(i) = (vp(i) - c(i)*x(i+1))/bp(i)
end do backsub
end subroutine solve_tridiag