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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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/* 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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|
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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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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) { |
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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; |
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dim_t i,k; |
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Paso_SparseMatrix * schur=NULL; |
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double A11,A12,A13,A21,A22,A23,A31,A32,A33,D,time0,time1,time2; |
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|
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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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|
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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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time0=Paso_timer(); |
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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_mis(A_p->pattern,mis_marker); |
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time2=Paso_timer()-time0; |
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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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#pragma omp parallel |
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{ |
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/* creates an index for F from mask */ |
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#pragma omp 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 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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#pragma omp for private(i, where_p,iPtr,A11,A12,A13,A21,A22,A23,A31,A32,A33,D,index) schedule(static) |
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for (i = 0; i < out->n_F; i++) { |
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/* find main diagonal */ |
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iPtr=A_p->pattern->ptr[out->rows_in_F[i]]; |
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index=&(A_p->pattern->index[iPtr]); |
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where_p=(index_t*)bsearch(&out->rows_in_F[i], |
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index, |
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A_p->pattern->ptr[out->rows_in_F[i] + 1]-A_p->pattern->ptr[out->rows_in_F[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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Paso_setError(VALUE_ERROR, "Paso_Solver_getAMG: main diagonal element missing."); |
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} else { |
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iPtr+=(index_t)(where_p-index); |
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/* get inverse of A_FF block: */ |
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if (n_block==1) { |
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if (ABS(A_p->val[iPtr])>0.) { |
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out->inv_A_FF[i]=1./A_p->val[iPtr]; |
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} else { |
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Paso_setError(ZERO_DIVISION_ERROR, "Paso_Solver_getAMG: Break-down in AMG decomposition: non-regular main diagonal block."); |
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} |
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} else if (n_block==2) { |
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A11=A_p->val[iPtr*4]; |
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A21=A_p->val[iPtr*4+1]; |
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A12=A_p->val[iPtr*4+2]; |
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A22=A_p->val[iPtr*4+3]; |
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D = A11*A22-A12*A21; |
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if (ABS(D) > 0 ){ |
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D=1./D; |
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out->inv_A_FF[i*4]= A22*D; |
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out->inv_A_FF[i*4+1]=-A21*D; |
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out->inv_A_FF[i*4+2]=-A12*D; |
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out->inv_A_FF[i*4+3]= A11*D; |
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} else { |
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Paso_setError(ZERO_DIVISION_ERROR, "Paso_Solver_getAMG:Break-down in AMG decomposition: non-regular main diagonal block."); |
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} |
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} else if (n_block==3) { |
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A11=A_p->val[iPtr*9 ]; |
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A21=A_p->val[iPtr*9+1]; |
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A31=A_p->val[iPtr*9+2]; |
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A12=A_p->val[iPtr*9+3]; |
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A22=A_p->val[iPtr*9+4]; |
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A32=A_p->val[iPtr*9+5]; |
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A13=A_p->val[iPtr*9+6]; |
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A23=A_p->val[iPtr*9+7]; |
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A33=A_p->val[iPtr*9+8]; |
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D = A11*(A22*A33-A23*A32)+ A12*(A31*A23-A21*A33)+A13*(A21*A32-A31*A22); |
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if (ABS(D) > 0 ){ |
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D=1./D; |
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out->inv_A_FF[i*9 ]=(A22*A33-A23*A32)*D; |
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out->inv_A_FF[i*9+1]=(A31*A23-A21*A33)*D; |
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out->inv_A_FF[i*9+2]=(A21*A32-A31*A22)*D; |
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out->inv_A_FF[i*9+3]=(A13*A32-A12*A33)*D; |
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out->inv_A_FF[i*9+4]=(A11*A33-A31*A13)*D; |
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out->inv_A_FF[i*9+5]=(A12*A31-A11*A32)*D; |
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out->inv_A_FF[i*9+6]=(A12*A23-A13*A22)*D; |
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out->inv_A_FF[i*9+7]=(A13*A21-A11*A23)*D; |
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out->inv_A_FF[i*9+8]=(A11*A22-A12*A21)*D; |
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} else { |
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Paso_setError(ZERO_DIVISION_ERROR, "Paso_Solver_getAMG:Break-down in AMG decomposition: non-regular main diagonal block."); |
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} |
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} |
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} |
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} |
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} /* end parallel region */ |
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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 (out->n_C>0) { |
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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 |
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{ |
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#pragma omp 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 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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} /* end parallel region */ |
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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_FF 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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time0=Paso_timer()-time0; |
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if (Paso_noError()) { |
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time1=Paso_timer(); |
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/* update A_CC block to get Schur complement and then apply AMG to it */ |
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Paso_Solver_updateIncompleteSchurComplement(schur,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC); |
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time1=Paso_timer()-time1; |
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out->AMG_of_Schur=Paso_Solver_getAMG(schur,verbose); |
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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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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 |
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{ |
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#pragma omp 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 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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} /* end parallel region */ |
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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 (out->n_C>0) { |
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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,k; |
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dim_t n_block=amg->n_block; |
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|
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if (amg->n_C==0) { |
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/* x=invA_FF*b */ |
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Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,x,b); |
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} else { |
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/* b->[b_F,b_C] */ |
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if (n_block==1) { |
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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]=b[amg->rows_in_F[i]]; |
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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]=b[amg->rows_in_C[i]]; |
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} else { |
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#pragma omp parallel for private(i,k) schedule(static) |
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for (i=0;i<amg->n_F;++i) |
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for (k=0;k<n_block;k++) amg->b_F[amg->n_block*i+k]=b[n_block*amg->rows_in_F[i]+k]; |
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#pragma omp parallel for private(i,k) schedule(static) |
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for (i=0;i<amg->n_C;++i) |
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for (k=0;k<n_block;k++) amg->b_C[amg->n_block*i+k]=b[n_block*amg->rows_in_C[i]+k]; |
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} |
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/* x_F=invA_FF*b_F */ |
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Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F); |
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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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/* 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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/* 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(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F); |
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/* x<-[x_F,x_C] */ |
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if (n_block==1) { |
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#pragma omp parallel for private(i) schedule(static) |
| 352 |
for (i=0;i<amg->n;++i) { |
| 353 |
if (amg->mask_C[i]>-1) { |
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x[i]=amg->x_C[amg->mask_C[i]]; |
| 355 |
} else { |
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x[i]=amg->x_F[amg->mask_F[i]]; |
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} |
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} |
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} else { |
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#pragma omp parallel for private(i,k) schedule(static) |
| 361 |
for (i=0;i<amg->n;++i) { |
| 362 |
if (amg->mask_C[i]>-1) { |
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for (k=0;k<n_block;k++) x[n_block*i+k]=amg->x_C[n_block*amg->mask_C[i]+k]; |
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} else { |
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for (k=0;k<n_block;k++) x[n_block*i+k]=amg->x_F[n_block*amg->mask_F[i]+k]; |
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} |
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} |
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} |
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/* all done */ |
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} |
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return; |
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} |
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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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