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pcg.F90 @ a10a43b

Revision a10a43b, 35.8 KB checked in by Oleg Batrashev <ogbash@…>, 3 years ago (diff)
First level preconditioner (if used without 2. level) is factored out and works from C.
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	!-------------------------------
362	!> Make preconditioner
363	!-------------------------------
364	subroutine preconditioner(sol,A,rhs,M, &
365	A_interf_,CoarseMtx_,Restrict,refactor_,bugtrack_)
366	use subsolvers
367	use CoarseMtx_mod
368	use CoarseAllgathers
369	use Vect_mod
370	implicit none
371	real(kind=rk),dimension(:),pointer :: sol !< solution
372	type(SpMtx) :: A !< sparse system matrix
373	real(kind=rk),dimension(:),pointer :: rhs !< right hand side
374	type(Mesh),intent(in) :: M !< Mesh
375	real(kind=rk),dimension(:),pointer :: res !< residual vector, allocated
376	!! here for multiplicative Schwarz
377	type(SpMtx),optional :: A_interf_ !< matr@interf.
378	type(SpMtx),optional :: CoarseMtx_ !< Coarse matrix
379	type(SpMtx),optional :: Restrict !< Restriction matrix
380	logical,intent(inout),optional :: refactor_
381	logical,optional :: bugtrack_
382	! ----- local: ------
383	real(kind=rk),dimension(:),pointer,save :: csol,crhs,tmpsol,tmpsol2,clrhs
384	integer :: i,ol
385	logical :: add,bugtrack
386	real(kind=rk) :: t1
387
388	t1 = MPI_WTime()
389
390	if (present(bugtrack_)) then
391	bugtrack=bugtrack_
392	else
393	bugtrack=.false.
394	endif
395	! ----------------------------
396	if (sctls%method==0) then
397	sol=rhs
398	return
399	endif
400	sol=0.0_rk
401	if (sctls%method>1) then ! For multiplicative Schwarz method...:
402	allocate(res(size(rhs)))
403	endif
404	if (present(CoarseMtx_)) then !{
405	if (.not.present(Restrict)) call DOUG_abort("Restriction matrix needs to be passed along with the coarse matrix!")
406	if (cdat%active) then
407	! Not the first iteration, so send the coarse vector here
408	if (.not.(present(refactor_).and.refactor_)) then
409	call SpMtx_Ax(clrhs,Restrict,rhs,dozero=.true.) ! restrict <RA>
410	! And send
411	if (bugtrack)write(stream,*) "local coarse RHS is:",clrhs
412	if (cdat_vec%active) then
413	call AllSendCoarseVector(clrhs,cdat_vec%nprocs,cdat_vec%cdisps,&
414	cdat_vec%send,useprev=.true.)
415	else
416	call AllSendCoarseVector(clrhs,cdat%nprocs,cdat%cdisps,&
417	cdat%send,useprev=.true.)
418	endif
419	else ! First iteration - send matrix
420	call AllSendCoarseMtx(cdat%LAC,CoarseMtx_,cdat%lg_cfmap,&
421	cdat%ngfc,cdat%nprocs,cdat%send)
422	endif
423	endif
424
425	ol=max(sctls%overlap,sctls%smoothers)
426	if (sctls%input_type==DCTL_INPUT_TYPE_ELEMENTAL.or.numprocs>1) then
427	call sparse_multisolve(sol=sol,A=A,M=M,rhs=rhs,res=res, &
428	A_interf_=A_interf_, &
429	refactor=refactor_) !fine solves
430	else
431	call sparse_multisolve(sol=sol,A=A,M=M,rhs=rhs,res=res, &
432	A_interf_=A_interf_,AC=CoarseMtx_, &
433	refactor=refactor_,Restrict=Restrict) !fine solves
434	if (bugtrack)call Print_Glob_Vect(sol,M,'global sol===')
435	endif
436
437	if (sctls%levels>1) then
438	if (ol==0) then
439	add=.false.
440	else
441	add=.true.
442	endif
443	if (present(refactor_).and.refactor_) then !{ setup coarse solve:
444	! We have a matrix send pending
445	if (cdat%active) then
446	!write(stream,*) "Waiting the Matrix!"
447	call AllRecvCoarseMtx(CoarseMtx_,cdat%send,add=add) ! Recieve it
448	!write(stream,*) "Got Matrix!"
449	allocate(clrhs(Restrict%nrows)) ! allocate memory for vector
450	call SpMtx_Ax(clrhs,Restrict,rhs,dozero=.true.) ! restrict <RA>
451	! And send
452	if (bugtrack)write(stream,*) "(f) local Coarse RHS is:",clrhs
453	if (cdat_vec%active) then
454	call AllSendCoarseVector(clrhs,cdat_vec%nprocs,&
455	cdat_vec%cdisps,cdat_vec%send)
456	else
457	call AllSendCoarseVector(clrhs,cdat%nprocs,&
458	cdat%cdisps,cdat%send)
459	endif
460	endif
461	if (associated(crhs)) then
462	if (size(crhs)/=CoarseMtx_%ncols) then
463	deallocate(csol)
464	deallocate(crhs)
465	allocate(crhs(CoarseMtx_%ncols))
466	allocate(csol(CoarseMtx_%nrows))
467	endif
468	else
469	allocate(crhs(CoarseMtx_%ncols))
470	allocate(csol(CoarseMtx_%nrows))
471	endif
472	if (.not.associated(tmpsol)) then
473	!allocate(tmpsol(A%nrows))
474	allocate(tmpsol(size(rhs)))
475	endif
476
477	if (.not.cdat%active) then
478	if (sctls%smoothers==-1) then
479	allocate(tmpsol2(A%nrows))
480	tmpsol2=0.0_rk
481	call exact_sparse_multismoother(tmpsol2,A,rhs)
482	call SpMtx_Ax(crhs,Restrict,tmpsol2,dozero=.true.) ! restriction
483	else
484	if (sctls%method>1.and.sctls%method/=5) then ! multiplicative Schwarz
485	call SpMtx_Ax(crhs,Restrict,res,dozero=.true.) ! restriction
486	else
487	call SpMtx_Ax(crhs,Restrict,rhs,dozero=.true.) ! restriction
488	endif
489	endif
490	endif
491	!csol=0.0_rk
492	write (stream,*) &
493	'factorising coarse matrix of size',CoarseMtx_%nrows, &
494	' and nnz:',CoarseMtx_%nnz
495	call free_spmtx_subsolves(CoarseMtx_)
496	allocate(CoarseMtx_%subsolve_ids(1))
497	CoarseMtx_%subsolve_ids=0
498	CoarseMtx_%nsubsolves=1
499
500	!! TODO: force it to do it AFTER factorization, but before solve
501	!if (present(cdat)) then
502	if (cdat%active) then
503	! Factorise the matrix
504	if (sctls%verbose>2) then
505	write(stream,*)'Global coarse matrix is:---------'
506	do i=1,CoarseMtx_%nnz
507	write(stream,*) CoarseMtx_%indi(i),&
508	CoarseMtx_%indj(i),CoarseMtx_%val(i)
509	enddo
510	write(stream,*)'---------------------------------'
511	endif
512	call factorise(CoarseMtx_%subsolve_ids(1), &
513	nfreds=CoarseMtx_%nrows, &
514	nnz=CoarseMtx_%nnz, &
515	indi=CoarseMtx_%indi, &
516	indj=CoarseMtx_%indj, &
517	val=CoarseMtx_%val)
518	! Recieve the vector for solve
519	if (cdat_vec%active) then
520	call AllRecvCoarseVector(crhs,cdat_vec%nprocs,&
521	cdat_vec%cdisps,cdat_vec%glg_cfmap,cdat_vec%send)
522	else
523	call AllRecvCoarseVector(crhs,cdat%nprocs,&
524	cdat%cdisps,cdat%glg_cfmap,cdat%send)
525	endif
526	!write(stream,*) "Got coarse vector!"
527	!call MPI_BARRIER(MPI_COMM_WORLD,i)
528	endif
529	if (bugtrack) then
530	if (isnan(sum(crhs))) then
531	write(stream,*) "(f) global Coarse RHS is:",crhs
532	call DOUG_abort('Got NaN receive fromAllRecvCoarseVector...',838465)
533	endif
534	!else
535	! write(stream,*) "(f) global Coarse RHS is:",crhs
536	endif
537
538
539	call sparse_singlesolve(CoarseMtx_%subsolve_ids(1),csol,crhs, &
540	nfreds=CoarseMtx_%nrows, &
541	nnz=CoarseMtx_%nnz, &
542	indi=CoarseMtx_%indi, &
543	indj=CoarseMtx_%indj, &
544	val=CoarseMtx_%val)
545	write (stream,*) 'coarse factorisation done!',CoarseMtx_%subsolve_ids(1)
546	if (bugtrack)write(stream,*) "(f) Coarse SOL is:",csol
547
548	if (cdat_vec%active) then
549	CoarseMtx_%indi=CoarseMtx_%indi+1
550	CoarseMtx_%indj=CoarseMtx_%indj+1
551	call Vect_remap(csol,clrhs,cdat_vec%gl_cfmap,dozero=.true.)
552	call SpMtx_Ax(tmpsol,Restrict,clrhs,dozero=.true.,transp=.true.)
553	elseif (cdat%active) then
554	CoarseMtx_%indi=CoarseMtx_%indi+1
555	CoarseMtx_%indj=CoarseMtx_%indj+1
556	call Vect_remap(csol,clrhs,cdat%gl_cfmap,dozero=.true.)
557	call SpMtx_Ax(tmpsol,Restrict,clrhs,dozero=.true.,transp=.true.)
558	else
559	if (sctls%smoothers==-1) then
560	call SpMtx_Ax(tmpsol2,Restrict,csol,dozero=.true.,transp=.true.) ! interpolation
561	tmpsol=0.0_rk
562	call exact_sparse_multismoother(tmpsol,A,tmpsol2)
563	else
564	call SpMtx_Ax(tmpsol,Restrict,csol,dozero=.true.,transp=.true.) ! interpolation
565	endif
566	endif
567	if (bugtrack)call Print_Glob_Vect(tmpsol,M,'tmpsol===',chk_endind=M%ninner)
568	else !}{ apply coarse solve:
569	if (cdat_vec%active) then
570	call AllRecvCoarseVector(crhs,cdat_vec%nprocs,cdat_vec%cdisps,&
571	cdat_vec%glg_cfmap,cdat_vec%send)
572	elseif (cdat%active) then
573	call AllRecvCoarseVector(crhs,cdat%nprocs,cdat%cdisps,&
574	cdat%glg_cfmap,cdat%send)
575	else
576	if (sctls%smoothers==-1) then
577	tmpsol2=0.0_rk
578	call exact_sparse_multismoother(tmpsol2,A,rhs)
579	call SpMtx_Ax(crhs,Restrict,tmpsol2,dozero=.true.) ! restriction
580	else
581	call SpMtx_Ax(crhs,Restrict,rhs,dozero=.true.) ! restriction
582	endif
583	endif
584	call sparse_singlesolve(CoarseMtx_%subsolve_ids(1),csol,crhs, &
585	nfreds=CoarseMtx_%nrows)
586	if (cdat_vec%active) then
587	call Vect_remap(csol,clrhs,cdat_vec%gl_cfmap,dozero=.true.)
588	call SpMtx_Ax(tmpsol,Restrict,clrhs,dozero=.true.,transp=.true.)
589	elseif (cdat%active) then
590	call Vect_remap(csol,clrhs,cdat%gl_cfmap,dozero=.true.)
591	call SpMtx_Ax(tmpsol,Restrict,clrhs,dozero=.true.,transp=.true.)
592	else
593	if (sctls%smoothers==-1) then
594	call SpMtx_Ax(tmpsol2,Restrict,csol,dozero=.true.,transp=.true.) ! interpolation
595	tmpsol=0.0_rk
596	call exact_sparse_multismoother(tmpsol,A,tmpsol2)
597	else
598	call SpMtx_Ax(tmpsol,Restrict,csol,dozero=.true.,transp=.true.) ! interpolation
599	! call Vect_print(tmpsol,"csol")
600	endif
601	endif
602	endif !}
603	if (sctls%method==1) then
604	!call Print_Glob_Vect(sol,M,'sol===',chk_endind=M%ninner)
605	sol(1:A%nrows)=sol(1:A%nrows)+tmpsol(1:A%nrows)
606	elseif (sctls%method==3) then ! fully multiplicative Schwarz
607	sol(1:A%nrows)=sol(1:A%nrows)+tmpsol(1:A%nrows)
608	! calculate the residual:
609	call SpMtx_Ax(res,A,sol,dozero=.true.) !
610	res=rhs-res
611	elseif (sctls%method==2.and.ol>0) then ! fully multiplicative Schwarz
612	sol(1:A%nrows)=tmpsol(1:A%nrows)
613	! calculate the residual:
614	call SpMtx_Ax(res,A,sol,dozero=.true.) !
615	res=rhs-res
616	endif
617	endif
618	if (sctls%method>1) then ! For multiplicative Schwarz method...:
619	refactor_=.false.
620	if (sctls%input_type==DCTL_INPUT_TYPE_ELEMENTAL) then
621	call sparse_multisolve(sol=sol,A=A,M=M,rhs=rhs,res=res, &
622	A_interf_=A_interf_, &
623	refactor=refactor_) !fine solves
624	else
625	call sparse_multisolve(sol=sol,A=A,M=M,rhs=rhs,res=res, &
626	A_interf_=A_interf_,AC=CoarseMtx_, &
627	refactor=refactor_,Restrict=Restrict) !fine solves
628	endif
629	endif
630	if (((ol==0.and.sctls%method==2).or.sctls%method==5).and.sctls%levels>1) then
631	! multiplicative on fine level, additive with coarse level:
632	sol(1:A%nrows)=sol(1:A%nrows)+tmpsol(1:A%nrows)
633	endif
634	else !}{
635	call preconditioner_1level(sol,A,rhs,M,res,A_interf_,refactor_)
636	endif !}
637	if (sctls%method>1) then ! For multiplicative Schwarz method...:
638	if (associated(res)) deallocate(res)
639	endif
640
641	time_preconditioner = time_preconditioner + MPI_WTime()-t1
642
643	end subroutine preconditioner
644
645	!--------------------------
646	! Solve
647	!--------------------------
648	subroutine msolve (m, r, z)
649	implicit none
650	real(kind=rk), dimension(:), intent(in) :: m, r
651	real(kind=rk), dimension(:), intent(in out) :: z
652	integer :: i
653
654	do i = 1, size(r)
655	z(i) = r(i) !/ m(i)
656	end do
657	end subroutine msolve
658
659	!--------------------------
660	!> Preconditioned conjugent gradient method with eigenvalues
661	!--------------------------
662	subroutine pcg_weigs (A,b,x,Msh,it,cond_num,A_interf_,tol_,maxit_, &
663	x0_,solinf,resvects_,CoarseMtx_,Restrict,refactor_)
664	use CoarseAllgathers
665
666	implicit none
667
668	type(SpMtx),intent(in out) :: A !< System matrix (sparse)
669	float(kind=rk),dimension(:),pointer :: b !< right hand side
670	float(kind=rk),dimension(:),pointer :: x !< Solution
671	type(Mesh),intent(in) :: Msh !< Mesh - aux data for Ax operation
672
673	integer,intent(out) :: it
674	real(kind=rk),intent(out) :: cond_num
675
676	! Optional arguments
677	type(SpMtx),intent(in out),optional :: A_interf_ !< matr@interf.
678	real(kind=rk), intent(in), optional :: tol_ !< Tolerance of the method
679	integer, intent(in), optional :: maxit_ !< Max number of iterations
680	float(kind=rk), dimension(:), intent(in), optional :: x0_ !< Initial guess
681	type(ConvInf), intent(in out), optional :: solinf !< Solution statistics
682	logical, intent(in), optional :: resvects_ !< Fill in the 'resvect' or not
683	type(SpMtx),optional :: CoarseMtx_ !< Coarse matrix
684	type(SpMtx),optional :: Restrict !< Restriction mtx
685	logical,intent(in),optional :: refactor_
686
687	! Local variables
688	logical :: refactor
689
690	real(kind=rk) :: tol ! Tolerance
691	integer :: maxit ! Max number of iterations
692	logical :: resvects=.false.
693
694	real(kind=rk),dimension(:),pointer,save :: r, p, q, m, z, b_k
695	real(kind=rk),dimension(:),pointer,save :: ztmp !TODO remove me
696	real(kind=rk) :: rho_curr, rho_prev, init_norm, res_norm
697	real(kind=rk) :: tmp,ratio_norm
698	integer :: nfreds
699	integer :: ierr
700	real(kind=rk),dimension(:),pointer,save :: dd,ee,alpha,beta
701	!logical,parameter :: bugtrack=.true.
702	logical,parameter :: bugtrack=.false.
703	! profiling
704	real(8) :: time_iterations, t1
705
706	write(stream,'(/a)') 'Preconditioned conjugate gradient:'
707	if (present(refactor_).and.refactor_) then
708	refactor=.true.
709	else
710	refactor=.false.
711	endif
712
713	if (size(b) /= size(x)) &
714	call DOUG_abort('[pcg] : SEVERE : size(b) /= size(x)',-1)
715
716	nfreds=size(b)
717	if (.not.associated(r)) then
718	allocate(r(nfreds))
719	allocate(p(nfreds))
720	allocate(q(nfreds))
721	allocate(m(nfreds))
722	allocate(z(nfreds))
723	allocate(b_k(nfreds))
724	endif
725
726	tol = sctls%solve_tolerance
727	if (present(tol_)) &
728	tol = tol_
729
730	maxit = sctls%solve_maxiters
731	if (maxit==-1) maxit=100000
732	if (present(maxit_)) &
733	maxit = maxit_
734
735	if (present(resvects_).and.(.not.present(solinf))) &
736	call DOUG_abort('[pcg] : SEVERE : "resvects_" must be given along'//&
737	' with "solinf".',-1)
738
739	! Allocate convergence info structure
740	if (present(solinf).and.(.not.present(resvects_))) then
741	call ConvInf_Init(solinf)
742	else if (present(solinf).and.&
743	(present(resvects_).and.(resvects_.eqv.(.true.)))) then
744	call ConvInf_Init(solinf, maxit)
745	resvects = .true.
746	end if
747
748
749	! Initialise auxiliary data structures
750	! to assist with pmvm
751	call pmvmCommStructs_init(A, Msh)
752
753
754	if (bugtrack)call Print_Glob_Vect(x,Msh,'global x===')
755	call SpMtx_pmvm(r,A,x,Msh)
756
757	r = b - r
758	init_norm = Vect_dot_product(r,r)
759	if (init_norm == 0.0) &
760	init_norm = 1.0
761
762
763	write(stream,'(a,i6,a,e8.2)') 'maxit = ',maxit,', tol = ',tol
764	write(stream,'(a,e22.15)') 'init_norm = ', dsqrt(init_norm)
765
766	it = 0
767	ratio_norm = 1.0_rk
768	! arrays for eigenvalue calculation:
769	if (.not.associated(dd)) then
770	allocate(dd(maxit))
771	allocate(ee(maxit))
772	allocate(alpha(maxit))
773	allocate(beta(maxit))
774	endif
775
776	time_iterations = 0.
777	! iterations
778	do while((ratio_norm > tol*tol).and.(it < maxit))
779	it = it + 1
780	t1 = MPI_WTime()
781
782	if (bugtrack)call Print_Glob_Vect(r,Msh,'global r===',chk_endind=Msh%ninner)
783	call preconditioner(sol=z, &
784	A=A, &
785	rhs=r, &
786	M=Msh, &
787	A_interf_=A_interf_, &
788	CoarseMtx_=CoarseMtx_, &
789	Restrict=Restrict, &
790	refactor_=refactor, &
791	bugtrack_=bugtrack)
792
793	refactor=.false.
794	if (bugtrack)call Print_Glob_Vect(z,Msh,'global bef comm z===',chk_endind=Msh%ninner)
795	if (sctls%method/=0) then
796	call Add_common_interf(z,A,Msh)
797	endif
798	!call Print_Glob_Vect(z,Msh,'global aft comm z===',chk_endind=Msh%ninner)
799	!call Print_Glob_Vect(z,Msh,'global z===')
800	! compute current rho
801	rho_curr = Vect_dot_product(r,z)
802
803	if (it == 1) then
804	p = z
805	else
806	beta(it) = rho_curr / rho_prev
807	p = z + beta(it) * p
808	end if
809	call SpMtx_pmvm(q,A, p, Msh)
810	if (bugtrack)call Print_Glob_Vect(q,Msh,'global q===')
811	! compute alpha
812	alpha(it) = rho_curr / Vect_dot_product(p,q)
813	x = x + alpha(it) * p
814	if (bugtrack)call Print_Glob_Vect(x,Msh,'global x===')
815	r = r - alpha(it) * q
816	if (bugtrack)call Print_Glob_Vect(r,Msh,'global r===')
817	rho_prev = rho_curr
818	! check
819	res_norm = Vect_dot_product(r,r)
820	!write (stream,*) "Norm is", res_norm
821	ratio_norm = res_norm / init_norm
822
823	time_iterations = time_iterations + MPI_WTime()-t1
824
825	if (ismaster()) &
826	write(stream, '(i5,a,e22.15)') it,': res_norm=',dsqrt(res_norm)
827	end do
828
829	if(pstream/=0) then
830	write(pstream, "(I0,':pcg iterations:',I0)") myrank, it
831	write(pstream, "(I0,':iterations time:',F0.3)") myrank, time_iterations
832	write(pstream, "(I0,':preconditioner time:',F0.3)") myrank, time_preconditioner
833	end if
834
835	if (ismaster()) then
836	call CalculateEigenvalues(it,dd,ee,alpha,beta,maxit)
837	cond_num=dd(it)/dd(1)
838	write(stream,'(a,i3,a,e10.4)') '#it:',it,' Cond#: ',cond_num
839	endif
840	!deallocate(beta)
841	!deallocate(alpha)
842	!deallocate(ee)
843	!deallocate(dd)
844	! Deallocate auxiliary data structures
845	! helped to assist with pmvm
846	! call pmvmCommStructs_destroy()
847
848	!deallocate(b_k)
849	!deallocate(z)
850	!deallocate(m)
851	!deallocate(q)
852	!deallocate(p)
853	!deallocate(r)
854	end subroutine pcg_weigs
855
856
857	subroutine CalculateEigenvalues(it,dd,ee,alpha,beta,MaxIt)
858	! Finds eigenvalues using Lanczos connection
859	implicit none
860	integer :: it,MaxIt
861	real(kind=rk),dimension(:),pointer :: dd,ee,alpha,beta
862	integer :: i,j,ierr
863
864	dd(1) = 1.0_rk/alpha(1)
865	ee(1) = 0.0_rk
866	do i=2,it
867	if (alpha(i)==0.or.beta(i)<0) then
868	print *,'Unable to compute eigenvalue number',i,' and '
869	do j=1,i
870	print *,j,' alpha:',alpha(j),' beta:',beta
871	enddo
872	return
873	else
874	dd(i) = 1.0_rk/alpha(i) + beta(i)/alpha(i-1)
875	ee(i) = -dsqrt(beta(i))/alpha(i-1)
876	endif
877	enddo
878	!call tql1(it,dd,ee,MaxIt,ierr)
879	call tql1(it,dd,ee,ierr)
880	if (ierr > 0) then
881	print *,'Cancelled after EigMaxIt while calculating eig',ierr
882	endif
883	end subroutine CalculateEigenvalues
884
885	subroutine tql1(n,d,e,ierr)
886	implicit none
887	integer :: i,j,l,m,n,ii,l1,l2,mml,ierr
888	real(kind=rk) :: d(n),e(n)
889	real(kind=rk) :: c,c2,c3,dl1,el1,f,g,h,p,r,s,s2,tst1,tst2 !,pythag
890	!
891	! this subroutine is a translation of the algol procedure tql1,
892	! num. math. 11, 293-306(1968) by bowdler, martin, reinsch, and
893	! wilkinson.
894	! handbook for auto. comp., vol.ii-linear algebra, 227-240(1971).
895	!
896	! this subroutine finds the eigenvalues of a symmetric
897	! tridiagonal matrix by the ql method.
898	!
899	! on input
900	! n is the order of the matrix.
901	! d contains the diagonal elements of the input matrix.
902	! e contains the subdiagonal elements of the input matrix
903	! in its last n-1 positions. e(1) is arbitrary.
904	!
905	! on output
906	! d contains the eigenvalues in ascending order. if an
907	! error exit is made, the eigenvalues are correct and
908	! ordered for indices 1,2,...ierr-1, but may not be
909	! the smallest eigenvalues.
910	! e has been destroyed.
911	! ierr is set to
912	! zero for normal return,
913	! j if the j-th eigenvalue has not been
914	! determined after 30 iterations.
915	! calls pythag for sqrt(aa + bb) .
916	!
917	! questions and comments should be directed to burton s. garbow,
918	! mathematics and computer science div, argonne national laboratory
919	!
920	! this version dated august 1983.
921	!
922	! ------------------------------------------------------------------
923	!
924	ierr = 0
925	if (n .eq. 1) go to 1001
926	!
927	do 100 i = 2, n
928	100 e(i-1) = e(i)
929	!
930	f = 0.0e0
931	tst1 = 0.0e0
932	e(n) = 0.0e0
933
934	do 290 l = 1, n
935	j = 0
936	h = abs(d(l)) + abs(e(l))
937	if (tst1 .lt. h) tst1 = h
938	! .......... look for small sub-diagonal element ..........
939	do 110 m = l, n
940	tst2 = tst1 + abs(e(m))
941	if (tst2 .eq. tst1) go to 120
942	! .......... e(n) is always zero, so there is no exit
943	! throu gh the bottom of the loop ..........
944	110 continue
945
946	120 if (m .eq. l) go to 210
947	130 if (j .eq. 30 ) go to 1000
948	j = j + 1
949	! .......... form shift ..........
950	l1 = l + 1
951	l2 = l1 + 1
952	g = d(l)
953	p = (d(l1) - g) / (2.0e0 * e(l))
954	r = pythag(p,1.0e0_rk)
955	d(l) = e(l) / (p + sign(r,p))
956	d(l1) = e(l) * (p + sign(r,p))
957	dl1 = d(l1)
958	h = g - d(l)
959	if (l2 .gt. n) go to 145
960
961	do 140 i = l2, n
962	140 d(i) = d(i) - h
963
964	145 f = f + h
965	! .......... ql transformation ..........
966	p = d(m)
967	c = 1.0e0
968	c2 = c
969	el1 = e(l1)
970	s = 0.0e0
971	mml = m - l
972	! .......... for i=m-1 step -1 until l do -- ..........
973	do 200 ii = 1, mml
974	c3 = c2
975	c2 = c
976	s2 = s
977	i = m - ii
978	g = c * e(i)
979	h = c * p
980	r = pythag(p,e(i))
981	e(i+1) = s * r
982	s = e(i) / r
983	c = p / r
984	p = c * d(i) - s * g
985	d(i+1) = h + s * (c * g + s * d(i))
986	200 continue
987
988	p = -s * s2 * c3 * el1 * e(l) / dl1
989	e(l) = s * p
990	d(l) = c * p
991	tst2 = tst1 + abs(e(l))
992	if (tst2 .gt. tst1) go to 130
993	210 p = d(l) + f
994	! .......... order eigenvalues ..........
995	if (l .eq. 1) go to 250
996	! .......... for i=l step -1 until 2 do -- ..........
997	do 230 ii = 2, l
998	i = l + 2 - ii
999	if (p .ge. d(i-1)) go to 270
1000	d(i) = d(i-1)
1001	230 continue
1002
1003	250 i = 1
1004	270 d(i) = p
1005	290 continue
1006
1007	go to 1001
1008	! .......... set error -- no convergence to an
1009	! eigenvalue after 30 iterations ..........
1010	1000 ierr = l
1011	1001 return
1012	end subroutine tql1
1013
1014	function pythag(a,b) result(pyt)
1015	! finds dsqrt(a2+b2) without overflow or destructive underflow
1016	implicit none
1017	real(kind=rk) :: a,b,pyt
1018	real(kind=rk) :: p,r,s,t,u
1019
1020	p = dmax1(dabs(a),dabs(b))
1021	if (p .eq. 0.0d0) go to 20
1022	r = (dmin1(dabs(a),dabs(b))/p)**2
1023	10 continue
1024	t = 4.0d0 + r
1025	if (t .eq. 4.0d0) go to 20
1026	s = r/t
1027	u = 1.0d0 + 2.0d0*s
1028	p = u*p
1029	r = (s/u)*2 r
1030	go to 10
1031	20 pyt = p
1032	return
1033	end function pythag
1034
1035
1036	end module pcg_mod
1037
1038

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