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/******************************************************* |
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* |
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* Copyright (c) 2003-2008 by University of Queensland |
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* Earth Systems Science Computational Center (ESSCC) |
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* http://www.uq.edu.au/esscc |
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* |
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* Primary Business: Queensland, Australia |
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* Licensed under the Open Software License version 3.0 |
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* http://www.opensource.org/licenses/osl-3.0.php |
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* |
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*******************************************************/ |
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|
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|
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/**************************************************************/ |
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|
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/* Paso: AMG preconditioner with reordering */ |
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|
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/**************************************************************/ |
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|
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/* Author: artak@access.edu.au */ |
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|
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/**************************************************************/ |
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|
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#include "Paso.h" |
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#include "Solver.h" |
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#include "PasoUtil.h" |
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#include "UMFPACK.h" |
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#include "Pattern_coupling.h" |
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|
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/**************************************************************/ |
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|
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/* free all memory used by AMG */ |
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|
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void Paso_Solver_AMG_free(Paso_Solver_AMG * in) { |
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if (in!=NULL) { |
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Paso_Solver_AMG_free(in->AMG_of_Schur); |
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Paso_Solver_Jacobi_free(in->GS); |
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MEMFREE(in->inv_A_FF); |
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MEMFREE(in->A_FF_pivot); |
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Paso_SparseMatrix_free(in->A_FC); |
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Paso_SparseMatrix_free(in->A_CF); |
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MEMFREE(in->rows_in_F); |
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MEMFREE(in->rows_in_C); |
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MEMFREE(in->mask_F); |
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MEMFREE(in->mask_C); |
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MEMFREE(in->x_F); |
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MEMFREE(in->b_F); |
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MEMFREE(in->x_C); |
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MEMFREE(in->b_C); |
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MEMFREE(in); |
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} |
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} |
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|
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/**************************************************************/ |
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|
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/* constructs the block-block factorization of |
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|
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[ A_FF A_FC ] |
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A_p= |
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[ A_CF A_FF ] |
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|
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to |
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|
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[ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ] |
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[ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] |
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|
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|
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where S=A_FF-ACF*invA_FF*A_FC within the shape of S |
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|
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then AMG is applied to S again until S becomes empty |
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|
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*/ |
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Paso_Solver_AMG* Paso_Solver_getAMG(Paso_SparseMatrix *A_p,bool_t verbose,dim_t level, double couplingParam) { |
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Paso_Solver_AMG* out=NULL; |
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dim_t n=A_p->numRows; |
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dim_t n_block=A_p->row_block_size; |
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index_t* mis_marker=NULL; |
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index_t* counter=NULL; |
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index_t iPtr,*index, *where_p, iPtr_s; |
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dim_t i,k,j; |
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Paso_SparseMatrix * schur=NULL; |
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Paso_SparseMatrix * schur_withFillIn=NULL; |
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double time0=0,time1=0,time2=0,S=0; |
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/*Paso_Pattern* test;*/ |
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|
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/* identify independend set of rows/columns */ |
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mis_marker=TMPMEMALLOC(n,index_t); |
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counter=TMPMEMALLOC(n,index_t); |
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out=MEMALLOC(1,Paso_Solver_AMG); |
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out->AMG_of_Schur=NULL; |
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out->inv_A_FF=NULL; |
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out->A_FF_pivot=NULL; |
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out->A_FC=NULL; |
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out->A_CF=NULL; |
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out->rows_in_F=NULL; |
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out->rows_in_C=NULL; |
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out->mask_F=NULL; |
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out->mask_C=NULL; |
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out->x_F=NULL; |
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out->b_F=NULL; |
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out->x_C=NULL; |
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out->b_C=NULL; |
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out->GS=NULL; |
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out->A=Paso_SparseMatrix_getReference(A_p); |
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/*out->GS=Paso_Solver_getGS(A_p,verbose);*/ |
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out->GS=Paso_Solver_getJacobi(A_p); |
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/*out->GS->sweeps=2;*/ |
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out->level=level; |
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|
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if ( !(Paso_checkPtr(mis_marker) || Paso_checkPtr(out) || Paso_checkPtr(counter) ) ) { |
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/* identify independend set of rows/columns */ |
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#pragma omp parallel for private(i) schedule(static) |
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for (i=0;i<n;++i) mis_marker[i]=-1; |
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Paso_Pattern_coup(A_p,mis_marker,couplingParam); |
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if (Paso_noError()) { |
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#pragma omp parallel for private(i) schedule(static) |
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for (i = 0; i < n; ++i) counter[i]=mis_marker[i]; |
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out->n=n; |
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out->n_block=n_block; |
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out->n_F=Paso_Util_cumsum(n,counter); |
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out->mask_F=MEMALLOC(n,index_t); |
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out->rows_in_F=MEMALLOC(out->n_F,index_t); |
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out->inv_A_FF=MEMALLOC(n_block*n_block*out->n_F,double); |
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out->A_FF_pivot=NULL; /* later use for block size>3 */ |
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if (! (Paso_checkPtr(out->mask_F) || Paso_checkPtr(out->inv_A_FF) || Paso_checkPtr(out->rows_in_F) ) ) { |
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/* creates an index for F from mask */ |
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#pragma omp parallel for private(i) schedule(static) |
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for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1; |
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#pragma omp parallel for private(i) schedule(static) |
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for (i = 0; i < n; ++i) { |
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if (mis_marker[i]) { |
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out->rows_in_F[counter[i]]=i; |
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out->mask_F[i]=counter[i]; |
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} else { |
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out->mask_F[i]=-1; |
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} |
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} |
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|
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/* Compute row-sum for getting rs(A_FF)^-1*/ |
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#pragma omp parallel for private(i,iPtr,j,S) schedule(static) |
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for (i = 0; i < out->n_F; ++i) { |
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S=0; |
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for (iPtr=A_p->pattern->ptr[out->rows_in_F[i]];iPtr<A_p->pattern->ptr[out->rows_in_F[i] + 1]; ++iPtr) { |
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j=A_p->pattern->index[iPtr]; |
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if (mis_marker[j]) |
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S+=A_p->val[iPtr]; |
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} |
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out->inv_A_FF[i]=1./S; |
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} |
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|
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if( Paso_noError()) { |
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/* if there are no nodes in the coarse level there is no more work to do */ |
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out->n_C=n-out->n_F; |
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if (level>0 && out->n_F>500) { |
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/*if (out->n_F>500) {*/ |
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out->rows_in_C=MEMALLOC(out->n_C,index_t); |
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out->mask_C=MEMALLOC(n,index_t); |
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if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) { |
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/* creates an index for C from mask */ |
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#pragma omp parallel for private(i) schedule(static) |
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for (i = 0; i < n; ++i) counter[i]=! mis_marker[i]; |
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Paso_Util_cumsum(n,counter); |
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#pragma omp parallel for private(i) schedule(static) |
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for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1; |
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#pragma omp parallel for private(i) schedule(static) |
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for (i = 0; i < n; ++i) { |
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if (! mis_marker[i]) { |
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out->rows_in_C[counter[i]]=i; |
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out->mask_C[i]=counter[i]; |
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} else { |
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out->mask_C[i]=-1; |
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} |
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} |
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/* get A_CF block: */ |
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out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F); |
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if (Paso_noError()) { |
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/* get A_FC block: */ |
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out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C); |
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/* get A_CC block: */ |
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if (Paso_noError()) { |
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schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C); |
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/*find the pattern of the schur complement with fill in*/ |
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|
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schur_withFillIn=Paso_SparseMatrix_alloc(A_p->type,Paso_Pattern_binop(PATTERN_FORMAT_DEFAULT, schur->pattern, Paso_Pattern_multiply(PATTERN_FORMAT_DEFAULT,out->A_CF->pattern,out->A_FC->pattern)),1,1); |
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|
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/*fprintf(stderr,"Sparsity of Schure: %dx%d LEN %d Percentage %f\n",schur_withFillIn->pattern->numOutput,schur_withFillIn->pattern->numInput,schur_withFillIn->len,schur_withFillIn->len/(1.*schur_withFillIn->pattern->numOutput*schur_withFillIn->pattern->numInput));*/ |
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|
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/* copy values over*/ |
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#pragma omp parallel for private(i,iPtr,j,iPtr_s,index,where_p) schedule(static) |
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for (i = 0; i < schur_withFillIn->numRows; ++i) { |
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for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) { |
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j=schur_withFillIn->pattern->index[iPtr]; |
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iPtr_s=schur->pattern->ptr[i]; |
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schur_withFillIn->val[iPtr]=0.; |
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index=&(schur->pattern->index[iPtr_s]); |
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where_p=(index_t*)bsearch(&j, |
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index, |
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schur->pattern->ptr[i + 1]-schur->pattern->ptr[i], |
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sizeof(index_t), |
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Paso_comparIndex); |
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if (where_p!=NULL) { |
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schur_withFillIn->val[iPtr]=schur->val[iPtr_s+(index_t)(where_p-index)]; |
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} |
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} |
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} |
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|
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if (Paso_noError()) { |
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Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC); |
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out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,verbose,level-1,couplingParam); |
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Paso_SparseMatrix_free(schur); |
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} |
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/* allocate work arrays for AMG application */ |
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if (Paso_noError()) { |
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out->x_F=MEMALLOC(n_block*out->n_F,double); |
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out->b_F=MEMALLOC(n_block*out->n_F,double); |
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out->x_C=MEMALLOC(n_block*out->n_C,double); |
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out->b_C=MEMALLOC(n_block*out->n_C,double); |
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|
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if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) { |
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#pragma omp parallel for private(i,k) schedule(static) |
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for (i = 0; i < out->n_F; ++i) { |
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for (k=0; k<n_block;++k) { |
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out->x_F[i*n_block+k]=0.; |
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out->b_F[i*n_block+k]=0.; |
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} |
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} |
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#pragma omp parallel for private(i,k) schedule(static) |
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for (i = 0; i < out->n_C; ++i) { |
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for (k=0; k<n_block;++k) { |
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out->x_C[i*n_block+k]=0.; |
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out->b_C[i*n_block+k]=0.; |
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} |
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} |
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} |
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} |
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} |
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} |
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} |
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} |
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} |
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} |
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} |
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} |
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TMPMEMFREE(mis_marker); |
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TMPMEMFREE(counter); |
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if (Paso_noError()) { |
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if (verbose) { |
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printf("AMG: %d unknowns eliminated. %d left.\n",out->n_F,n-out->n_F); |
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if (level>0 && out->n_F>500) { |
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/* if (out->n_F<500) {*/ |
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printf("timing: AMG: MIS/reordering/elemination : %e/%e/%e\n",time2,time0,time1); |
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} else { |
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printf("timing: AMG: MIS: %e\n",time2); |
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} |
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} |
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return out; |
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} else { |
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Paso_Solver_AMG_free(out); |
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return NULL; |
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} |
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} |
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|
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/**************************************************************/ |
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|
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/* apply AMG precondition b-> x |
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|
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in fact it solves |
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|
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[ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ] [ x_F ] = [b_F] |
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[ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C] |
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|
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in the form |
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|
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b->[b_F,b_C] |
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x_F=invA_FF*b_F |
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b_C=b_C-A_CF*x_F |
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x_C=AMG(b_C) |
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b_F=b_F-A_FC*x_C |
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x_F=invA_FF*b_F |
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x<-[x_F,x_C] |
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|
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should be called within a parallel region |
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barrier synconization should be performed to make sure that the input vector available |
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|
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*/ |
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|
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void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) { |
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dim_t i; |
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double *r=MEMALLOC(amg->n,double); |
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/*Paso_Solver_GS* GS=NULL;*/ |
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double *x0=MEMALLOC(amg->n,double); |
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double time0=0; |
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|
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if (amg->level==0 || amg->n_F<=500) { |
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/*if (amg->n_F<=500) {*/ |
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time0=Paso_timer(); |
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|
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Paso_Solver_solveJacobi(amg->GS,x,b); |
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|
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/* #pragma omp parallel for private(i) schedule(static) |
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for (i=0;i<amg->n;++i) r[i]=b[i]; |
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Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r); |
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Paso_Solver_solveGS(amg->GS,x0,r); |
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#pragma omp parallel for private(i) schedule(static) |
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for (i=0;i<amg->n;++i) { |
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x[i]+=x0[i]; |
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} |
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*/ |
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/*Paso_UMFPACK1(amg->A,x,b,0);*/ |
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|
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time0=Paso_timer()-time0; |
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/*fprintf(stderr,"timing: DIRECT SOLVER: %e/\n",time0);*/ |
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} else { |
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|
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/* presmoothing */ |
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Paso_Solver_solveJacobi(amg->GS,x,b); |
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/* |
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#pragma omp parallel for private(i) schedule(static) |
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for (i=0;i<amg->n;++i) r[i]=b[i]; |
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|
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Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r); |
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Paso_Solver_solveGS(amg->GS,x0,r); |
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|
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#pragma omp parallel for private(i) schedule(static) |
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for (i=0;i<amg->n;++i) { |
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x[i]+=x0[i]; |
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} |
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*/ |
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/* end of presmoothing */ |
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|
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#pragma omp parallel for private(i) schedule(static) |
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for (i=0;i<amg->n;++i) r[i]=b[i]; |
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|
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/*r=b-Ax*/ |
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Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r); |
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|
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/* b->[b_F,b_C] */ |
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#pragma omp parallel for private(i) schedule(static) |
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for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]]; |
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|
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#pragma omp parallel for private(i) schedule(static) |
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for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]]; |
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|
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/* x_F=invA_FF*b_F */ |
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Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F); |
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|
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/* b_C=b_C-A_CF*x_F */ |
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Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C); |
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|
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/* x_C=AMG(b_C) */ |
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Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C); |
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|
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/* b_F=b_F-A_FC*x_C */ |
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Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F); |
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/* x_F=invA_FF*b_F */ |
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Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F); |
| 358 |
/* x<-[x_F,x_C] */ |
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|
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#pragma omp parallel for private(i) schedule(static) |
| 361 |
for (i=0;i<amg->n;++i) { |
| 362 |
if (amg->mask_C[i]>-1) { |
| 363 |
x[i]=amg->x_C[amg->mask_C[i]]; |
| 364 |
} else { |
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x[i]=amg->x_F[amg->mask_F[i]]; |
| 366 |
} |
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} |
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|
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/*postsmoothing*/ |
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|
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#pragma omp parallel for private(i) schedule(static) |
| 372 |
for (i=0;i<amg->n;++i) r[i]=b[i]; |
| 373 |
|
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/*r=b-Ax*/ |
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Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r); |
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Paso_Solver_solveJacobi(amg->GS,x0,r); |
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|
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#pragma omp parallel for private(i) schedule(static) |
| 379 |
for (i=0;i<amg->n;++i) x[i]+=x0[i]; |
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|
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|
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/*#pragma omp parallel for private(i) schedule(static) |
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for (i=0;i<amg->n;++i) r[i]=b[i]; |
| 384 |
|
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Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r); |
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Paso_Solver_solveGS(amg->GS,x0,r); |
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|
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#pragma omp parallel for private(i) schedule(static) |
| 389 |
for (i=0;i<amg->n;++i) { |
| 390 |
x[i]+=x0[i]; |
| 391 |
} |
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*/ |
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/*end of postsmoothing*/ |
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|
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} |
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MEMFREE(r); |
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MEMFREE(x0); |
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return; |
| 399 |
} |
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|
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/* |
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* $Log$ |
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* |
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*/ |
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