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pcg.F90 @ 13bb187

Revision 13bb187, 32.8 KB checked in by Oleg Batrashev <ogbash@…>, 2 years ago (diff)
Remove coarse preliminary factorisation, move coarse solve into levels>1.
Property mode set to `100644`

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1	! DOUG - Domain decomposition On Unstructured Grids
2	! Copyright (C) 1998-2006 Faculty of Computer Science, University of Tartu and
3	! Department of Mathematics, University of Bath
4	!
5	! This library is free software; you can redistribute it and/or
6	! modify it under the terms of the GNU Lesser General Public
7	! License as published by the Free Software Foundation; either
8	! version 2.1 of the License, or (at your option) any later version.
9	!
10	! This library is distributed in the hope that it will be useful,
11	! but WITHOUT ANY WARRANTY; without even the implied warranty of
12	! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13	! Lesser General Public License for more details.
14	!
15	! You should have received a copy of the GNU Lesser General Public
16	! License along with this library; if not, write to the Free Software
17	! Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
18	! or contact the authors (University of Tartu, Faculty of Computer Science, Chair
19	! of Distributed Systems, Liivi 2, 50409 Tartu, Estonia, http://dougdevel.org,
20	! mailto:info(at)dougdevel.org)
21
22	!!----------------------------------
23	!! Preconditioned Conjugate Gradient
24	!!----------------------------------
25	module pcg_mod
26
27	use ConvInf_mod
28	use SpMtx_mods
29	use Mesh_class
30	use globals
31
32	implicit none
33
34	#include<doug_config.h>
35
36	#ifdef D_COMPLEX
37	#define float complex
38	#else
39	#define float real
40	#endif
41
42	integer,save :: coarseid=0
43	private :: &
44	preconditioner, &
45	msolve
46
47	! profiling
48	real(kind=rk), private, save :: time_preconditioner = 0
49
50	contains
51
52	!--------------------------------------------
53	! Preconditioned conjugate gradient method
54	!--------------------------------------------
55	subroutine pcg (A, b, x, Msh, tol_, maxit_, &
56	x0_, solinf, resvects_, CoarseMtx_)
57	implicit none
58
59	type(SpMtx),intent(in out) :: A ! System matrix (sparse)
60	float(kind=rk),dimension(:),pointer :: b ! RHS
61	float(kind=rk),dimension(:),pointer :: x ! Solution
62	! Mesh - aux data for Ax operation
63	type(Mesh), intent(in) :: Msh
64
65	! Optional arguments
66	! Tolerance of the method
67	real(kind=rk), intent(in), optional :: tol_
68	! Max number of iterations
69	integer, intent(in), optional :: maxit_
70	! Initial guess
71	float(kind=rk), dimension(:), intent(in), optional :: x0_
72	! Solution statistics
73	type(ConvInf), intent(in out), optional :: solinf
74	! Fill in the 'resvect' or not
75	logical, intent(in), optional :: resvects_
76	type(SpMtx),optional :: CoarseMtx_ ! Coarse matrix
77
78	real(kind=rk) :: tol ! Tolerance
79	integer :: maxit ! Max number of iterations
80	logical :: resvects=.false.
81
82	!real(kind=rk), dimension(size(b)) :: r, p, q, m, z, b_k
83	real(kind=rk),dimension(:),pointer :: r, p, q, m, z, b_k
84	real(kind=rk) :: rho_curr, rho_prev, init_norm, res_norm
85	real(kind=rk) :: alpha, beta, tmp, ratio_norm
86	integer :: iter,nfreds
87	integer :: ierr
88	! + test
89	float(kind=rk), dimension(:), pointer :: arr_copy, gv_tmp
90
91	!!$ real(kind=rk) :: r_max
92
93	write(stream,'(/a)') 'Preconditioned conjugate gradient:'
94
95	if (size(b) /= size(x)) &
96	call DOUG_abort('[pcg] : SEVERE : size(b) /= size(x)',-1)
97
98	!!$ if (present(x0_))
99	!!$ ! use method with initial guess
100
101
102	nfreds=size(b)
103	allocate(r(nfreds))
104	allocate(p(nfreds))
105	allocate(q(nfreds))
106	allocate(m(nfreds))
107	allocate(z(nfreds))
108	allocate(b_k(nfreds))
109
110
111	tol = sctls%solve_tolerance
112	if (present(tol_)) &
113	tol = tol_
114
115	maxit = sctls%solve_maxiters
116	if (maxit==-1) maxit=100000
117	if (present(maxit_)) &
118	maxit = maxit_
119
120	if (present(resvects_).and.(.not.present(solinf))) &
121	call DOUG_abort('[pcg] : SEVERE : "resvects_" must be given along'//&
122	' with "solinf".',-1)
123
124	! Allocate convergence info structure
125	if (present(solinf).and.(.not.present(resvects_))) then
126	call ConvInf_Init(solinf)
127	else if (present(solinf)) then
128	if (present(resvects_).and.(resvects_.eqv.(.true.))) then
129	call ConvInf_Init(solinf, maxit)
130	resvects = .true.
131	end if
132	end if
133
134	! Initialise auxiliary data structures
135	! to assist with pmvm
136	call pmvmCommStructs_init(A, Msh)
137
138	! + test
139	if (ismaster()) &
140	allocate(gv_tmp(Msh%ngf))
141	allocate(arr_copy(Msh%nlf))
142
143	! Build preconditioner
144	! call preconditioner(A, m, CoarseMtx_)
145	!!$ ! + test
146	!!$ arr_copy = m
147	!!$ call Vect_newToOldPerm(arr_copy)
148	!!$ gv_tmp = 0.0_rk
149	!!$ call Vect_Gather(arr_copy, gv_tmp, Msh)
150	!!$ if (ismaster()) &
151	!!$ call Vect_Print(gv_tmp, 'm ::')
152
153	!!$ ! + test
154	!!$ !b = 1.0_rk
155	!!$ arr_copy = b
156	!!$ call Vect_newToOldPerm(arr_copy)
157	!!$ call Vect_Print(arr_copy, 'b local (original ordering) ::')
158	!!$ gv_tmp = 0.0_rk
159	!!$ call Vect_Gather(arr_copy, gv_tmp, Msh)
160	!!$ if (ismaster()) &
161	!!$ call Vect_Print(gv_tmp, 'b global (original ordering) ::')
162
163	!!$ ! + test
164	!!$ arr_copy = x
165	!!$ call Vect_newToOldPerm(arr_copy)
166	!!$ call Vect_Print(arr_copy, 'x local (original ordering) ::')
167	!!$ gv_tmp = 0.0_rk
168	!!$ call Vect_Gather(arr_copy, gv_tmp, Msh)
169	!!$ if (ismaster()) &
170	!!$ call Vect_Print(gv_tmp, 'x global (original ordering) ::')
171
172	!r = b - SpMtx_pmvm(A, x, Msh)
173	call SpMtx_pmvm(r,A,x,Msh)
174	r = b - r
175	!call Vect_Print(r,'initial residual')
176
177	! + test
178	!!$ arr_copy = r
179	!!$ call Vect_newToOldPerm(arr_copy)
180	!!$ gv_tmp = 0.0_rk
181	!!$ call Vect_Gather(arr_copy, gv_tmp, Msh)
182	!!$ if (ismaster()) &
183	!!$ call Vect_Print(gv_tmp, 'r ::')
184
185	init_norm = Vect_dot_product(r,r)
186	if (init_norm == 0.0) &
187	init_norm = 1.0
188
189	write(stream,'(a,i6,a,e8.2)') 'maxit = ',maxit,', tol = ',tol
190	write(stream,'(a,e22.15)') 'init_norm = ', dsqrt(init_norm)
191
192	iter = 1
193	ratio_norm = 1.0_rk
194	do while((ratio_norm > tol*tol).and.(iter <= maxit))
195	call msolve(m,r,z)
196	!if (present(CoarseMtx_)) then
197	! call preconditioner(z,A,r,CoarseMtx_)
198	! !z=r
199	!else
200	! call preconditioner(z,A,r)
201	!endif
202
203	!call Vect_Print(z,'preconditioner')
204
205	! compute current rho
206	rho_curr = Vect_dot_product(r,z)
207	if (iter == 1) then
208	p = z
209	else
210	beta = rho_curr / rho_prev
211	p = z + beta * p
212	end if
213	!q = SpMtx_pmvm(A, p, Msh)
214	call SpMtx_pmvm(q,A,p,Msh)
215	! compute alpha
216	alpha = rho_curr / Vect_dot_product(p,q)
217	x = x + alpha * p
218	r = r - alpha * q
219	rho_prev = rho_curr
220	! check
221	res_norm = Vect_dot_product(r,r)
222	ratio_norm = dsqrt(res_norm) / dsqrt(init_norm)
223	!!$ ratio_norm = res_norm / init_norm
224	if (ismaster()) &
225	write(stream, '(i5,a,e22.15)') iter,': res_norm=',dsqrt(res_norm)
226	!write(stream, '(i5,a,e22.15,e22.15)') iter,': dsqrt(ratio_norm)=',&
227	!dsqrt(ratio_norm), dsqrt(res_norm)
228	iter = iter + 1
229	end do
230
231	! Deallocate auxiliary data structures
232	! helped to assist with pmvm
233	call pmvmCommStructs_destroy()
234
235	deallocate(b_k)
236	deallocate(z)
237	deallocate(m)
238	deallocate(q)
239	deallocate(p)
240	deallocate(r)
241	if (associated(gv_tmp)) deallocate(gv_tmp)
242	if (associated(arr_copy)) deallocate(arr_copy)
243	end subroutine pcg
244
245	subroutine preconditioner_1level(sol,A,rhs,M,res,A_interf_,refactor_)
246	use subsolvers
247	implicit none
248	real(kind=rk),dimension(:),pointer :: sol !< solution
249	type(SpMtx) :: A !< sparse system matrix
250	real(kind=rk),dimension(:),pointer :: rhs !< right hand side
251	type(Mesh),intent(in) :: M !< Mesh
252	real(kind=rk),dimension(:),pointer :: res !< residual vector, allocated
253	!! here for multiplicative Schwarz
254	type(SpMtx),optional :: A_interf_ !< matr@interf.
255	logical,intent(inout),optional :: refactor_
256
257	type(SpMtx) :: A_tmp
258
259	if (refactor_.and.present(A_interf_)) then!{
260	if (sctls%verbose>9) then
261	!call SpMtx_printMat(A)
262	call SpMtx_printRaw(A)
263	!call SpMtx_printMat(A_interf_)
264	call SpMtx_printRaw(A_interf_)
265	!stop
266	endif
267	if (sctls%input_type==DCTL_INPUT_TYPE_ASSEMBLED) then
268	! we need the fully sorted entries but A has block struct...
269	! keep the original values...
270	if (associated(A%M_bound)) then
271	A_tmp=SpMtx_newInit(nnz=A%nnz,nblocks=A%nblocks,&
272	nrows=A%nrows,ncols=A%ncols,&
273	indi=A%indi,indj=A%indj,val=A%val,&
274	arrange_type=A%arrange_type,M_bound=A%M_bound)
275	else
276	A_tmp=SpMtx_newInit(nnz=A%nnz,nblocks=A%nblocks,&
277	nrows=A%nrows,ncols=A%ncols,&
278	indi=A%indi,indj=A%indj,val=A%val,&
279	arrange_type=A%arrange_type)
280	endif
281	A%arrange_type=D_SpMtx_ARRNG_NO
282	!A%nrows=max(A%nrows,A_interf_%nrows)
283	!A%ncols=max(A%nrows,A_interf_%ncols)
284	!if (associated(A%M_bound)) then
285	! deallocate(A%M_bound)
286	!endif
287	call SpMtx_arrange(A,D_SpMtx_ARRNG_ROWS,sort=.true.)
288	call sparse_multisolve(sol=sol,A=A,M=M,rhs=rhs,res=res, &
289	A_interf_=A_interf_, &
290	refactor=refactor_) !fine solves
291	if (sctls%method>1) then ! For multiplicative Schwarz method...:
292	refactor_=.false.
293	call sparse_multisolve(sol=sol,A=A,M=M,rhs=rhs,res=res, &
294	A_interf_=A_interf_, &
295	refactor=refactor_) !fine solves
296	endif
297	! put the original structure and orders back:
298	A%indi=A_tmp%indi
299	A%indj=A_tmp%indj
300	A%val=A_tmp%val
301	if (associated(A_tmp%M_bound)) A%M_bound=A_tmp%M_bound
302	A%nrows=A_tmp%nrows
303	A%ncols=A_tmp%ncols
304	A%arrange_type=A_tmp%arrange_type
305	call SpMtx_Destroy(A_tmp)
306	else
307	call sparse_multisolve(sol=sol,A=A,M=M,rhs=rhs,res=res, &
308	A_interf_=A_interf_, &
309	refactor=refactor_) !fine solves
310	if (sctls%method>1) then ! For multiplicative Schwarz method...:
311	refactor_=.false.
312	call sparse_multisolve(sol=sol,A=A,M=M,rhs=rhs,res=res, &
313	A_interf_=A_interf_, &
314	refactor=refactor_) !fine solves
315	endif
316	endif
317	elseif (refactor_.and.sctls%input_type==DCTL_INPUT_TYPE_ASSEMBLED) then!}{
318	if (associated(A%M_bound)) then
319	A_tmp=SpMtx_newInit(nnz=size(A%indi),nblocks=A%nblocks,&
320	nrows=A%nrows,ncols=A%ncols,&
321	indi=A%indi,indj=A%indj,val=A%val,&
322	arrange_type=A%arrange_type,M_bound=A%M_bound)
323	else
324	A_tmp=SpMtx_newInit(nnz=size(A%indi),nblocks=A%nblocks,&
325	nrows=A%nrows,ncols=A%ncols,&
326	indi=A%indi,indj=A%indj,val=A%val,&
327	arrange_type=A%arrange_type)
328	endif
329	A_tmp%nnz=A%nnz
330	A%arrange_type=D_SpMtx_ARRNG_NO
331	call SpMtx_arrange(A,D_SpMtx_ARRNG_ROWS,sort=.true.)
332	call sparse_multisolve(sol=sol,A=A,M=M,rhs=rhs,res=res, &
333	refactor=refactor_) !fine solves
334	if (sctls%method>1) then ! For multiplicative Schwarz method...:
335	refactor_=.false.
336	call sparse_multisolve(sol=sol,A=A,M=M,rhs=rhs,res=res, &
337	refactor=refactor_) !fine solves
338	endif
339	! put the original structure and orders back:
340	A%indi=A_tmp%indi
341	A%indj=A_tmp%indj
342	A%val=A_tmp%val
343	if (associated(A_tmp%M_bound)) A%M_bound=A_tmp%M_bound
344	A%nrows=A_tmp%nrows
345	A%ncols=A_tmp%ncols
346	A%arrange_type=A_tmp%arrange_type
347	call SpMtx_Destroy(A_tmp)
348	else!}{
349	call sparse_multisolve(sol=sol,A=A,M=M,rhs=rhs,res=res, &
350	A_interf_=A_interf_, &
351	refactor=refactor_) !fine solves
352	if (sctls%method>1) then ! For multiplicative Schwarz method...:
353	refactor_=.false.
354	call sparse_multisolve(sol=sol,A=A,M=M,rhs=rhs,res=res, &
355	A_interf_=A_interf_, &
356	refactor=refactor_) !fine solves
357	endif
358	endif!}
359	end subroutine preconditioner_1level
360
361	subroutine prec2Level_exchangeMatrix(CoarseMtx_)
362	use CoarseAllgathers
363	type(SpMtx) :: CoarseMtx_ !< Coarse matrix
364	integer :: ol
365	logical :: add
366
367	ol=max(sctls%overlap,sctls%smoothers)
368	if (ol==0) then
369	add=.false.
370	else
371	add=.true.
372	endif
373
374	call AllSendCoarseMtx(cdat%LAC,CoarseMtx_,cdat%lg_cfmap,&
375	cdat%ngfc,cdat%nprocs,cdat%send)
376	call AllRecvCoarseMtx(CoarseMtx_,cdat%send,add=add) ! Recieve it
377
378	end subroutine prec2Level_exchangeMatrix
379
380	!-------------------------------
381	!> Make preconditioner
382	!-------------------------------
383	subroutine preconditioner(sol,A,rhs,M, &
384	A_interf_,CoarseMtx_,Restrict,refactor_,bugtrack_)
385	use subsolvers
386	use CoarseMtx_mod
387	use CoarseAllgathers
388	use Vect_mod
389	implicit none
390	real(kind=rk),dimension(:),pointer :: sol !< solution
391	type(SpMtx) :: A !< sparse system matrix
392	real(kind=rk),dimension(:),pointer :: rhs !< right hand side
393	type(Mesh),intent(in) :: M !< Mesh
394	real(kind=rk),dimension(:),pointer :: res !< residual vector, allocated
395	!! here for multiplicative Schwarz
396	type(SpMtx),optional :: A_interf_ !< matr@interf.
397	type(SpMtx),optional :: CoarseMtx_ !< Coarse matrix
398	type(SpMtx),optional :: Restrict !< Restriction matrix
399	logical,intent(inout),optional :: refactor_
400	logical,optional :: bugtrack_
401	! ----- local: ------
402	real(kind=rk),dimension(:),pointer,save :: csol,crhs,tmpsol,tmpsol2,clrhs
403	integer :: i,ol
404	logical :: add,bugtrack
405	real(kind=rk) :: t1
406	logical :: isFirstIter
407
408	t1 = MPI_WTime()
409
410	if (present(bugtrack_)) then
411	bugtrack=bugtrack_
412	else
413	bugtrack=.false.
414	endif
415	! ----------------------------
416	isFirstIter = present(refactor_).and.refactor_
417	if (sctls%method==0) then
418	sol=rhs
419	return
420	endif
421	sol=0.0_rk
422	if (sctls%method>1) then ! For multiplicative Schwarz method...:
423	allocate(res(size(rhs)))
424	endif
425	if (present(CoarseMtx_)) then !{
426	if (.not.present(Restrict)) call DOUG_abort("Restriction matrix needs to be passed along with the coarse matrix!")
427
428	if (isFirstIter.and.cdat%active) then
429	! First iteration - send matrix
430	call prec2Level_exchangeMatrix(CoarseMtx_)
431	end if
432
433	! after coarse matrix is received allocate coarse vectors
434	if (isFirstIter.and.sctls%levels>1) then
435	if (associated(crhs)) then
436	if (size(crhs)/=CoarseMtx_%ncols) then
437	deallocate(csol)
438	deallocate(crhs)
439	allocate(crhs(CoarseMtx_%ncols))
440	allocate(csol(CoarseMtx_%nrows))
441	endif
442	else
443	allocate(crhs(CoarseMtx_%ncols))
444	allocate(csol(CoarseMtx_%nrows))
445	endif
446	allocate(clrhs(Restrict%nrows)) ! allocate memory for vector
447	end if
448	if (.not.associated(tmpsol)) then
449	!allocate(tmpsol(A%nrows))
450	allocate(tmpsol(size(rhs)))
451	endif
452
453	if (cdat%active) then
454	! Send coarse vector
455	call SpMtx_Ax(clrhs,Restrict,rhs,dozero=.true.) ! restrict <RA>
456	if (cdat_vec%active) then
457	call AllSendCoarseVector(clrhs,cdat_vec%nprocs,cdat_vec%cdisps,&
458	cdat_vec%send,useprev=.not.isFirstIter)
459	else
460	call AllSendCoarseVector(clrhs,cdat%nprocs,cdat%cdisps,&
461	cdat%send,useprev=.not.isFirstIter)
462	endif
463	end if ! cdat%active
464
465	! first level prec
466	if (sctls%input_type==DCTL_INPUT_TYPE_ELEMENTAL.or.numprocs>1) then
467	call sparse_multisolve(sol=sol,A=A,M=M,rhs=rhs,res=res, &
468	A_interf_=A_interf_, &
469	refactor=refactor_) !fine solves
470	else
471	call sparse_multisolve(sol=sol,A=A,M=M,rhs=rhs,res=res, &
472	A_interf_=A_interf_,AC=CoarseMtx_, &
473	refactor=refactor_,Restrict=Restrict) !fine solves
474	endif
475
476	if (sctls%levels>1) then
477	ol=max(sctls%overlap,sctls%smoothers)
478	if (isFirstIter.and..not.cdat%active) then ! 1 processor case
479	if (sctls%smoothers==-1) then
480	allocate(tmpsol2(A%nrows))
481	tmpsol2=0.0_rk
482	call exact_sparse_multismoother(tmpsol2,A,rhs)
483	call SpMtx_Ax(crhs,Restrict,tmpsol2,dozero=.true.) ! restriction
484	else
485	if (sctls%method>1.and.sctls%method/=5) then ! multiplicative Schwarz
486	call SpMtx_Ax(crhs,Restrict,res,dozero=.true.) ! restriction
487	else
488	call SpMtx_Ax(crhs,Restrict,rhs,dozero=.true.) ! restriction
489	endif
490	endif
491	endif
492	end if
493
494	!csol=0.0_rk
495	if (cdat%active) then
496	! Recieve the vector for solve
497	if (cdat_vec%active) then
498	call AllRecvCoarseVector(crhs,cdat_vec%nprocs,&
499	cdat_vec%cdisps,cdat_vec%glg_cfmap,cdat_vec%send)
500	else
501	call AllRecvCoarseVector(crhs,cdat%nprocs,&
502	cdat%cdisps,cdat%glg_cfmap,cdat%send)
503	endif
504	!write(stream,*) "Got coarse vector!"
505	!call MPI_BARRIER(MPI_COMM_WORLD,i)
506	end if
507
508	if (sctls%levels>1) then
509	if (isFirstIter) then
510	write (stream,*) &
511	'factorising coarse matrix of size',CoarseMtx_%nrows, &
512	' and nnz:',CoarseMtx_%nnz
513	call free_spmtx_subsolves(CoarseMtx_)
514	allocate(CoarseMtx_%subsolve_ids(1))
515	CoarseMtx_%subsolve_ids=0
516	CoarseMtx_%nsubsolves=1
517	end if
518
519	! Coarse solve
520	call sparse_singlesolve(CoarseMtx_%subsolve_ids(1),csol,crhs,&
521	nfreds=CoarseMtx_%nrows, &
522	nnz=CoarseMtx_%nnz, &
523	indi=CoarseMtx_%indi, &
524	indj=CoarseMtx_%indj, &
525	val=CoarseMtx_%val)
526	if (bugtrack)write(stream,*) "(f) Coarse SOL is:",csol
527
528	if (cdat_vec%active) then
529	call Vect_remap(csol,clrhs,cdat_vec%gl_cfmap,dozero=.true.)
530	call SpMtx_Ax(tmpsol,Restrict,clrhs,dozero=.true.,transp=.true.)
531	elseif (cdat%active) then
532	call Vect_remap(csol,clrhs,cdat%gl_cfmap,dozero=.true.)
533	call SpMtx_Ax(tmpsol,Restrict,clrhs,dozero=.true.,transp=.true.)
534	else
535	if (sctls%smoothers==-1) then
536	call SpMtx_Ax(tmpsol2,Restrict,csol,dozero=.true.,transp=.true.) ! interpolation
537	tmpsol=0.0_rk
538	call exact_sparse_multismoother(tmpsol,A,tmpsol2)
539	else
540	call SpMtx_Ax(tmpsol,Restrict,csol,dozero=.true.,transp=.true.) ! interpolation
541	endif
542	endif
543
544	if (.not.(cdat_vec%active)) then
545	if (sctls%smoothers==-1) then
546	tmpsol2=0.0_rk
547	call exact_sparse_multismoother(tmpsol2,A,rhs)
548	call SpMtx_Ax(crhs,Restrict,tmpsol2,dozero=.true.) ! restriction
549	else
550	call SpMtx_Ax(crhs,Restrict,rhs,dozero=.true.) ! restriction
551	endif
552	endif
553	endif !}
554	if (sctls%method==1) then
555	!call Print_Glob_Vect(sol,M,'sol===',chk_endind=M%ninner)
556	sol(1:A%nrows)=sol(1:A%nrows)+tmpsol(1:A%nrows)
557	elseif (sctls%method==3) then ! fully multiplicative Schwarz
558	sol(1:A%nrows)=sol(1:A%nrows)+tmpsol(1:A%nrows)
559	! calculate the residual:
560	call SpMtx_Ax(res,A,sol,dozero=.true.) !
561	res=rhs-res
562	elseif (sctls%method==2.and.ol>0) then ! fully multiplicative Schwarz
563	sol(1:A%nrows)=tmpsol(1:A%nrows)
564	! calculate the residual:
565	call SpMtx_Ax(res,A,sol,dozero=.true.) !
566	res=rhs-res
567	endif
568	if (sctls%method>1) then ! For multiplicative Schwarz method...:
569	refactor_=.false.
570	if (sctls%input_type==DCTL_INPUT_TYPE_ELEMENTAL) then
571	call sparse_multisolve(sol=sol,A=A,M=M,rhs=rhs,res=res, &
572	A_interf_=A_interf_, &
573	refactor=refactor_) !fine solves
574	else
575	call sparse_multisolve(sol=sol,A=A,M=M,rhs=rhs,res=res, &
576	A_interf_=A_interf_,AC=CoarseMtx_, &
577	refactor=refactor_,Restrict=Restrict) !fine solves
578	endif
579	endif
580	if (((ol==0.and.sctls%method==2).or.sctls%method==5).and.sctls%levels>1) then
581	! multiplicative on fine level, additive with coarse level:
582	sol(1:A%nrows)=sol(1:A%nrows)+tmpsol(1:A%nrows)
583	endif
584	else !}{
585	call preconditioner_1level(sol,A,rhs,M,res,A_interf_,refactor_)
586	endif !}
587	if (sctls%method>1) then ! For multiplicative Schwarz method...:
588	if (associated(res)) deallocate(res)
589	endif
590
591	time_preconditioner = time_preconditioner + MPI_WTime()-t1
592
593	end subroutine preconditioner
594
595	!--------------------------
596	! Solve
597	!--------------------------
598	subroutine msolve (m, r, z)
599	implicit none
600	real(kind=rk), dimension(:), intent(in) :: m, r
601	real(kind=rk), dimension(:), intent(in out) :: z
602	integer :: i
603
604	do i = 1, size(r)
605	z(i) = r(i) !/ m(i)
606	end do
607	end subroutine msolve
608
609	!--------------------------
610	!> Preconditioned conjugent gradient method with eigenvalues
611	!--------------------------
612	subroutine pcg_weigs (A,b,x,Msh,it,cond_num,A_interf_,tol_,maxit_, &
613	x0_,solinf,resvects_,CoarseMtx_,Restrict,refactor_)
614	use CoarseAllgathers
615
616	implicit none
617
618	type(SpMtx),intent(in out) :: A !< System matrix (sparse)
619	float(kind=rk),dimension(:),pointer :: b !< right hand side
620	float(kind=rk),dimension(:),pointer :: x !< Solution
621	type(Mesh),intent(in) :: Msh !< Mesh - aux data for Ax operation
622
623	integer,intent(out) :: it
624	real(kind=rk),intent(out) :: cond_num
625
626	! Optional arguments
627	type(SpMtx),intent(in out),optional :: A_interf_ !< matr@interf.
628	real(kind=rk), intent(in), optional :: tol_ !< Tolerance of the method
629	integer, intent(in), optional :: maxit_ !< Max number of iterations
630	float(kind=rk), dimension(:), intent(in), optional :: x0_ !< Initial guess
631	type(ConvInf), intent(in out), optional :: solinf !< Solution statistics
632	logical, intent(in), optional :: resvects_ !< Fill in the 'resvect' or not
633	type(SpMtx),optional :: CoarseMtx_ !< Coarse matrix
634	type(SpMtx),optional :: Restrict !< Restriction mtx
635	logical,intent(in),optional :: refactor_
636
637	! Local variables
638	logical :: refactor
639
640	real(kind=rk) :: tol ! Tolerance
641	integer :: maxit ! Max number of iterations
642	logical :: resvects=.false.
643
644	real(kind=rk),dimension(:),pointer,save :: r, p, q, m, z, b_k
645	real(kind=rk),dimension(:),pointer,save :: ztmp !TODO remove me
646	real(kind=rk) :: rho_curr, rho_prev, init_norm, res_norm
647	real(kind=rk) :: tmp,ratio_norm
648	integer :: nfreds
649	integer :: ierr
650	real(kind=rk),dimension(:),pointer,save :: dd,ee,alpha,beta
651	!logical,parameter :: bugtrack=.true.
652	logical,parameter :: bugtrack=.false.
653	! profiling
654	real(8) :: time_iterations, t1
655
656	write(stream,'(/a)') 'Preconditioned conjugate gradient:'
657	if (present(refactor_).and.refactor_) then
658	refactor=.true.
659	else
660	refactor=.false.
661	endif
662
663	if (size(b) /= size(x)) &
664	call DOUG_abort('[pcg] : SEVERE : size(b) /= size(x)',-1)
665
666	nfreds=size(b)
667	if (.not.associated(r)) then
668	allocate(r(nfreds))
669	allocate(p(nfreds))
670	allocate(q(nfreds))
671	allocate(m(nfreds))
672	allocate(z(nfreds))
673	allocate(b_k(nfreds))
674	endif
675
676	tol = sctls%solve_tolerance
677	if (present(tol_)) &
678	tol = tol_
679
680	maxit = sctls%solve_maxiters
681	if (maxit==-1) maxit=100000
682	if (present(maxit_)) &
683	maxit = maxit_
684
685	if (present(resvects_).and.(.not.present(solinf))) &
686	call DOUG_abort('[pcg] : SEVERE : "resvects_" must be given along'//&
687	' with "solinf".',-1)
688
689	! Allocate convergence info structure
690	if (present(solinf).and.(.not.present(resvects_))) then
691	call ConvInf_Init(solinf)
692	else if (present(solinf).and.&
693	(present(resvects_).and.(resvects_.eqv.(.true.)))) then
694	call ConvInf_Init(solinf, maxit)
695	resvects = .true.
696	end if
697
698
699	! Initialise auxiliary data structures
700	! to assist with pmvm
701	call pmvmCommStructs_init(A, Msh)
702
703
704	if (bugtrack)call Print_Glob_Vect(x,Msh,'global x===')
705	call SpMtx_pmvm(r,A,x,Msh)
706
707	r = b - r
708	init_norm = Vect_dot_product(r,r)
709	if (init_norm == 0.0) &
710	init_norm = 1.0
711
712
713	write(stream,'(a,i6,a,e8.2)') 'maxit = ',maxit,', tol = ',tol
714	write(stream,'(a,e22.15)') 'init_norm = ', dsqrt(init_norm)
715
716	it = 0
717	ratio_norm = 1.0_rk
718	! arrays for eigenvalue calculation:
719	if (.not.associated(dd)) then
720	allocate(dd(maxit))
721	allocate(ee(maxit))
722	allocate(alpha(maxit))
723	allocate(beta(maxit))
724	endif
725
726	time_iterations = 0.
727	! iterations
728	do while((ratio_norm > tol*tol).and.(it < maxit))
729	it = it + 1
730	t1 = MPI_WTime()
731
732	if (bugtrack)call Print_Glob_Vect(r,Msh,'global r===',chk_endind=Msh%ninner)
733	call preconditioner(sol=z, &
734	A=A, &
735	rhs=r, &
736	M=Msh, &
737	A_interf_=A_interf_, &
738	CoarseMtx_=CoarseMtx_, &
739	Restrict=Restrict, &
740	refactor_=refactor, &
741	bugtrack_=bugtrack)
742
743	refactor=.false.
744	if (bugtrack)call Print_Glob_Vect(z,Msh,'global bef comm z===',chk_endind=Msh%ninner)
745	if (sctls%method/=0) then
746	call Add_common_interf(z,A,Msh)
747	endif
748	!call Print_Glob_Vect(z,Msh,'global aft comm z===',chk_endind=Msh%ninner)
749	!call Print_Glob_Vect(z,Msh,'global z===')
750	! compute current rho
751	rho_curr = Vect_dot_product(r,z)
752
753	if (it == 1) then
754	p = z
755	else
756	beta(it) = rho_curr / rho_prev
757	p = z + beta(it) * p
758	end if
759	call SpMtx_pmvm(q,A, p, Msh)
760	if (bugtrack)call Print_Glob_Vect(q,Msh,'global q===')
761	! compute alpha
762	alpha(it) = rho_curr / Vect_dot_product(p,q)
763	x = x + alpha(it) * p
764	if (bugtrack)call Print_Glob_Vect(x,Msh,'global x===')
765	r = r - alpha(it) * q
766	if (bugtrack)call Print_Glob_Vect(r,Msh,'global r===')
767	rho_prev = rho_curr
768	! check
769	res_norm = Vect_dot_product(r,r)
770	!write (stream,*) "Norm is", res_norm
771	ratio_norm = res_norm / init_norm
772
773	time_iterations = time_iterations + MPI_WTime()-t1
774
775	if (ismaster()) &
776	write(stream, '(i5,a,e22.15)') it,': res_norm=',dsqrt(res_norm)
777	end do
778
779	if(pstream/=0) then
780	write(pstream, "(I0,':pcg iterations:',I0)") myrank, it
781	write(pstream, "(I0,':iterations time:',F0.3)") myrank, time_iterations
782	write(pstream, "(I0,':preconditioner time:',F0.3)") myrank, time_preconditioner
783	end if
784
785	if (ismaster()) then
786	call CalculateEigenvalues(it,dd,ee,alpha,beta,maxit)
787	cond_num=dd(it)/dd(1)
788	write(stream,'(a,i3,a,e10.4)') '#it:',it,' Cond#: ',cond_num
789	endif
790	!deallocate(beta)
791	!deallocate(alpha)
792	!deallocate(ee)
793	!deallocate(dd)
794	! Deallocate auxiliary data structures
795	! helped to assist with pmvm
796	! call pmvmCommStructs_destroy()
797
798	!deallocate(b_k)
799	!deallocate(z)
800	!deallocate(m)
801	!deallocate(q)
802	!deallocate(p)
803	!deallocate(r)
804	end subroutine pcg_weigs
805
806
807	subroutine CalculateEigenvalues(it,dd,ee,alpha,beta,MaxIt)
808	! Finds eigenvalues using Lanczos connection
809	implicit none
810	integer :: it,MaxIt
811	real(kind=rk),dimension(:),pointer :: dd,ee,alpha,beta
812	integer :: i,j,ierr
813
814	dd(1) = 1.0_rk/alpha(1)
815	ee(1) = 0.0_rk
816	do i=2,it
817	if (alpha(i)==0.or.beta(i)<0) then
818	print *,'Unable to compute eigenvalue number',i,' and '
819	do j=1,i
820	print *,j,' alpha:',alpha(j),' beta:',beta
821	enddo
822	return
823	else
824	dd(i) = 1.0_rk/alpha(i) + beta(i)/alpha(i-1)
825	ee(i) = -dsqrt(beta(i))/alpha(i-1)
826	endif
827	enddo
828	!call tql1(it,dd,ee,MaxIt,ierr)
829	call tql1(it,dd,ee,ierr)
830	if (ierr > 0) then
831	print *,'Cancelled after EigMaxIt while calculating eig',ierr
832	endif
833	end subroutine CalculateEigenvalues
834
835	subroutine tql1(n,d,e,ierr)
836	implicit none
837	integer :: i,j,l,m,n,ii,l1,l2,mml,ierr
838	real(kind=rk) :: d(n),e(n)
839	real(kind=rk) :: c,c2,c3,dl1,el1,f,g,h,p,r,s,s2,tst1,tst2 !,pythag
840	!
841	! this subroutine is a translation of the algol procedure tql1,
842	! num. math. 11, 293-306(1968) by bowdler, martin, reinsch, and
843	! wilkinson.
844	! handbook for auto. comp., vol.ii-linear algebra, 227-240(1971).
845	!
846	! this subroutine finds the eigenvalues of a symmetric
847	! tridiagonal matrix by the ql method.
848	!
849	! on input
850	! n is the order of the matrix.
851	! d contains the diagonal elements of the input matrix.
852	! e contains the subdiagonal elements of the input matrix
853	! in its last n-1 positions. e(1) is arbitrary.
854	!
855	! on output
856	! d contains the eigenvalues in ascending order. if an
857	! error exit is made, the eigenvalues are correct and
858	! ordered for indices 1,2,...ierr-1, but may not be
859	! the smallest eigenvalues.
860	! e has been destroyed.
861	! ierr is set to
862	! zero for normal return,
863	! j if the j-th eigenvalue has not been
864	! determined after 30 iterations.
865	! calls pythag for sqrt(aa + bb) .
866	!
867	! questions and comments should be directed to burton s. garbow,
868	! mathematics and computer science div, argonne national laboratory
869	!
870	! this version dated august 1983.
871	!
872	! ------------------------------------------------------------------
873	!
874	ierr = 0
875	if (n .eq. 1) go to 1001
876	!
877	do 100 i = 2, n
878	100 e(i-1) = e(i)
879	!
880	f = 0.0e0
881	tst1 = 0.0e0
882	e(n) = 0.0e0
883
884	do 290 l = 1, n
885	j = 0
886	h = abs(d(l)) + abs(e(l))
887	if (tst1 .lt. h) tst1 = h
888	! .......... look for small sub-diagonal element ..........
889	do 110 m = l, n
890	tst2 = tst1 + abs(e(m))
891	if (tst2 .eq. tst1) go to 120
892	! .......... e(n) is always zero, so there is no exit
893	! throu gh the bottom of the loop ..........
894	110 continue
895
896	120 if (m .eq. l) go to 210
897	130 if (j .eq. 30 ) go to 1000
898	j = j + 1
899	! .......... form shift ..........
900	l1 = l + 1
901	l2 = l1 + 1
902	g = d(l)
903	p = (d(l1) - g) / (2.0e0 * e(l))
904	r = pythag(p,1.0e0_rk)
905	d(l) = e(l) / (p + sign(r,p))
906	d(l1) = e(l) * (p + sign(r,p))
907	dl1 = d(l1)
908	h = g - d(l)
909	if (l2 .gt. n) go to 145
910
911	do 140 i = l2, n
912	140 d(i) = d(i) - h
913
914	145 f = f + h
915	! .......... ql transformation ..........
916	p = d(m)
917	c = 1.0e0
918	c2 = c
919	el1 = e(l1)
920	s = 0.0e0
921	mml = m - l
922	! .......... for i=m-1 step -1 until l do -- ..........
923	do 200 ii = 1, mml
924	c3 = c2
925	c2 = c
926	s2 = s
927	i = m - ii
928	g = c * e(i)
929	h = c * p
930	r = pythag(p,e(i))
931	e(i+1) = s * r
932	s = e(i) / r
933	c = p / r
934	p = c * d(i) - s * g
935	d(i+1) = h + s * (c * g + s * d(i))
936	200 continue
937
938	p = -s * s2 * c3 * el1 * e(l) / dl1
939	e(l) = s * p
940	d(l) = c * p
941	tst2 = tst1 + abs(e(l))
942	if (tst2 .gt. tst1) go to 130
943	210 p = d(l) + f
944	! .......... order eigenvalues ..........
945	if (l .eq. 1) go to 250
946	! .......... for i=l step -1 until 2 do -- ..........
947	do 230 ii = 2, l
948	i = l + 2 - ii
949	if (p .ge. d(i-1)) go to 270
950	d(i) = d(i-1)
951	230 continue
952
953	250 i = 1
954	270 d(i) = p
955	290 continue
956
957	go to 1001
958	! .......... set error -- no convergence to an
959	! eigenvalue after 30 iterations ..........
960	1000 ierr = l
961	1001 return
962	end subroutine tql1
963
964	function pythag(a,b) result(pyt)
965	! finds dsqrt(a2+b2) without overflow or destructive underflow
966	implicit none
967	real(kind=rk) :: a,b,pyt
968	real(kind=rk) :: p,r,s,t,u
969
970	p = dmax1(dabs(a),dabs(b))
971	if (p .eq. 0.0d0) go to 20
972	r = (dmin1(dabs(a),dabs(b))/p)**2
973	10 continue
974	t = 4.0d0 + r
975	if (t .eq. 4.0d0) go to 20
976	s = r/t
977	u = 1.0d0 + 2.0d0*s
978	p = u*p
979	r = (s/u)*2 r
980	go to 10
981	20 pyt = p
982	return
983	end function pythag
984
985
986	end module pcg_mod
987
988

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