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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: GS preconditioner with reordering */ |
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|
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/**************************************************************/ |
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|
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/* Copyrights by ACcESS Australia 2003,2004,2005,2006,2007,2008 */ |
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/* Author: artak@uq.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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#include <stdio.h> |
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|
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/**************************************************************/ |
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|
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/* free all memory used by GS */ |
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|
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void Paso_Solver_GS_free(Paso_Solver_GS * in) { |
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if (in!=NULL) { |
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MEMFREE(in->colorOf); |
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Paso_SparseMatrix_free(in->factors); |
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MEMFREE(in->diag); |
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MEMFREE(in->main_iptr); |
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Paso_Pattern_free(in->pattern); |
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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 incomplete block factorization of |
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|
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*/ |
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Paso_Solver_GS* Paso_Solver_getGS(Paso_SparseMatrix * A,bool_t verbose) { |
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dim_t n=A->numRows; |
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dim_t n_block=A->row_block_size; |
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dim_t block_size=A->block_size; |
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index_t num_colors=0, *mis_marker=NULL; |
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register index_t i,iptr_main,iPtr,iptr_ik,k,iptr_kj,j,iptr_ij,color,color2; |
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double time0,time_color,time_fac; |
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/* allocations: */ |
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Paso_Solver_GS* out=MEMALLOC(1,Paso_Solver_GS); |
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if (Paso_checkPtr(out)) return NULL; |
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out->colorOf=MEMALLOC(n,index_t); |
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out->diag=MEMALLOC( ((size_t) n) * ((size_t) block_size),double); |
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/*out->diag=MEMALLOC(A->len,double);*/ |
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out->main_iptr=MEMALLOC(n,index_t); |
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out->pattern=Paso_Pattern_getReference(A->pattern); |
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out->factors=Paso_SparseMatrix_getReference(A); |
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out->n_block=n_block; |
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out->n=n; |
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|
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if ( !(Paso_checkPtr(out->colorOf) || Paso_checkPtr(out->main_iptr) || Paso_checkPtr(out->factors)) ) { |
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time0=Paso_timer(); |
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Paso_Pattern_color(A->pattern,&out->num_colors,out->colorOf); |
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time_color=Paso_timer()-time0; |
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|
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if (Paso_noError()) { |
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time0=Paso_timer(); |
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|
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if (! (Paso_checkPtr(out->diag))) { |
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if (n_block==1) { |
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#pragma omp parallel for private(i, iPtr) schedule(static) |
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for (i = 0; i < A->pattern->numOutput; i++) { |
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out->diag[i]=1.; |
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/* find main diagonal */ |
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for (iPtr = A->pattern->ptr[i]; iPtr < A->pattern->ptr[i + 1]; iPtr++) { |
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if (A->pattern->index[iPtr]==i) { |
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iptr_main=iPtr; |
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out->diag[i]=A->val[iPtr]; |
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break; |
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} |
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} |
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out->main_iptr[i]=iptr_main; |
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} |
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} else if (n_block==2) { |
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#pragma omp parallel for private(i, iPtr) schedule(static) |
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for (i = 0; i < A->pattern->numOutput; i++) { |
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out->diag[i*4+0]= 1.; |
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out->diag[i*4+1]= 0.; |
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out->diag[i*4+2]= 0.; |
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out->diag[i*4+3]= 1.; |
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/* find main diagonal */ |
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for (iPtr = A->pattern->ptr[i]; iPtr < A->pattern->ptr[i + 1]; iPtr++) { |
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if (A->pattern->index[iPtr]==i) { |
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iptr_main=iPtr; |
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out->diag[i*4]= A->val[iPtr*4]; |
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out->diag[i*4+1]=A->val[iPtr*4+1]; |
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out->diag[i*4+2]=A->val[iPtr*4+2]; |
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out->diag[i*4+3]= A->val[iPtr*4+3]; |
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break; |
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} |
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} |
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out->main_iptr[i]=iptr_main; |
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} |
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} else if (n_block==3) { |
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#pragma omp parallel for private(i, iPtr) schedule(static) |
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for (i = 0; i < A->pattern->numOutput; i++) { |
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out->diag[i*9 ]=1.; |
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out->diag[i*9+1]=0.; |
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out->diag[i*9+2]=0.; |
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out->diag[i*9+3]=0.; |
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out->diag[i*9+4]=1.; |
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out->diag[i*9+5]=0.; |
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out->diag[i*9+6]=0.; |
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out->diag[i*9+7]=0.; |
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out->diag[i*9+8]=1.; |
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/* find main diagonal */ |
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for (iPtr = A->pattern->ptr[i]; iPtr < A->pattern->ptr[i + 1]; iPtr++) { |
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if (A->pattern->index[iPtr]==i) { |
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iptr_main=iPtr; |
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out->diag[i*9 ]=A->val[iPtr*9 ]; |
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out->diag[i*9+1]=A->val[iPtr*9+1]; |
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out->diag[i*9+2]=A->val[iPtr*9+2]; |
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out->diag[i*9+3]=A->val[iPtr*9+3]; |
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out->diag[i*9+4]=A->val[iPtr*9+4]; |
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out->diag[i*9+5]=A->val[iPtr*9+5]; |
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out->diag[i*9+6]=A->val[iPtr*9+6]; |
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out->diag[i*9+7]=A->val[iPtr*9+7]; |
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out->diag[i*9+8]=A->val[iPtr*9+8]; |
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break; |
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} |
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} |
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out->main_iptr[i]=iptr_main; |
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} |
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} |
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} |
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|
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time_fac=Paso_timer()-time0; |
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} |
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} |
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if (Paso_noError()) { |
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if (verbose) { |
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printf("GS: %d color used \n",out->num_colors); |
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printf("timing: GS: coloring/elemination : %e/%e\n",time_color,time_fac); |
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} |
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return out; |
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} else { |
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Paso_Solver_GS_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 GS precondition b-> x |
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|
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in fact it solves LD^{-1}Ux=b in the form x= U^{-1} D L^{-1}b |
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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_solveGS(Paso_Solver_GS * gs, double * x, double * b) { |
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register dim_t i,k; |
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register index_t color,iptr_ik,iptr_main; |
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register double A11,A12,A21,A22,A13,A23,A33,A32,A31,S1,S2,S3,R1,R2,R3,D,S21,S22,S12,S11,S13,S23,S33,S32,S31; |
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dim_t n_block=gs->n_block; |
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dim_t n=gs->n; |
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index_t* pivot=NULL; |
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|
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/* copy x into b*/ |
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#pragma omp parallel for private(i) schedule(static) |
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for (i=0;i<n*n_block;++i) x[i]=b[i]; |
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/* forward substitution */ |
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for (color=0;color<gs->num_colors;++color) { |
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if (n_block==1) { |
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#pragma omp parallel for schedule(static) private(i,iptr_ik,k,S1,R1,iptr_main) |
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for (i = 0; i < n; ++i) { |
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if (gs->colorOf[i]==color) { |
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/* x_i=x_i-a_ik*x_k */ |
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S1=x[i]; |
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for (iptr_ik=gs->pattern->ptr[i];iptr_ik<gs->pattern->ptr[i+1]; ++iptr_ik) { |
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k=gs->pattern->index[iptr_ik]; |
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if (gs->colorOf[k]<color) { |
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R1=x[k]; |
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S1-=gs->factors->val[iptr_ik]*R1; |
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} |
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} |
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iptr_main=gs->main_iptr[i]; |
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x[i]=(1/gs->factors->val[iptr_main])*S1; |
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} |
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} |
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} else if (n_block==2) { |
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#pragma omp parallel for schedule(static) private(i,iptr_ik,k,iptr_main,S1,S2,R1,R2) |
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for (i = 0; i < n; ++i) { |
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if (gs->colorOf[i]==color) { |
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/* x_i=x_i-a_ik*x_k */ |
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S1=x[2*i]; |
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S2=x[2*i+1]; |
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for (iptr_ik=gs->pattern->ptr[i];iptr_ik<gs->pattern->ptr[i+1]; ++iptr_ik) { |
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k=gs->pattern->index[iptr_ik]; |
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if (gs->colorOf[k]<color) { |
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R1=x[2*k]; |
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R2=x[2*k+1]; |
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S1-=gs->factors->val[4*iptr_ik ]*R1+gs->factors->val[4*iptr_ik+2]*R2; |
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S2-=gs->factors->val[4*iptr_ik+1]*R1+gs->factors->val[4*iptr_ik+3]*R2; |
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} |
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} |
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iptr_main=gs->main_iptr[i]; |
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A11=gs->factors->val[iptr_main*4]; |
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A21=gs->factors->val[iptr_main*4+1]; |
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A12=gs->factors->val[iptr_main*4+2]; |
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A22=gs->factors->val[iptr_main*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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S11= A22*D; |
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S21=-A21*D; |
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S12=-A12*D; |
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S22= A11*D; |
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x[2*i ]=S11*S1+S12*S2; |
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x[2*i+1]=S21*S1+S22*S2; |
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} else { |
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Paso_setError(ZERO_DIVISION_ERROR, "Paso_Solver_getGS: 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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} else if (n_block==3) { |
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#pragma omp parallel for schedule(static) private(i,iptr_ik,iptr_main,k,S1,S2,S3,R1,R2,R3) |
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for (i = 0; i < n; ++i) { |
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if (gs->colorOf[i]==color) { |
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/* x_i=x_i-a_ik*x_k */ |
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S1=x[3*i]; |
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S2=x[3*i+1]; |
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S3=x[3*i+2]; |
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for (iptr_ik=gs->pattern->ptr[i];iptr_ik<gs->pattern->ptr[i+1]; ++iptr_ik) { |
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k=gs->pattern->index[iptr_ik]; |
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if (gs->colorOf[k]<color) { |
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R1=x[3*k]; |
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R2=x[3*k+1]; |
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R3=x[3*k+2]; |
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S1-=gs->factors->val[9*iptr_ik ]*R1+gs->factors->val[9*iptr_ik+3]*R2+gs->factors->val[9*iptr_ik+6]*R3; |
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S2-=gs->factors->val[9*iptr_ik+1]*R1+gs->factors->val[9*iptr_ik+4]*R2+gs->factors->val[9*iptr_ik+7]*R3; |
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S3-=gs->factors->val[9*iptr_ik+2]*R1+gs->factors->val[9*iptr_ik+5]*R2+gs->factors->val[9*iptr_ik+8]*R3; |
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} |
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} |
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iptr_main=gs->main_iptr[i]; |
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A11=gs->factors->val[iptr_main*9 ]; |
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A21=gs->factors->val[iptr_main*9+1]; |
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A31=gs->factors->val[iptr_main*9+2]; |
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A12=gs->factors->val[iptr_main*9+3]; |
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A22=gs->factors->val[iptr_main*9+4]; |
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A32=gs->factors->val[iptr_main*9+5]; |
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A13=gs->factors->val[iptr_main*9+6]; |
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A23=gs->factors->val[iptr_main*9+7]; |
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A33=gs->factors->val[iptr_main*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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S11=(A22*A33-A23*A32)*D; |
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S21=(A31*A23-A21*A33)*D; |
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S31=(A21*A32-A31*A22)*D; |
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S12=(A13*A32-A12*A33)*D; |
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S22=(A11*A33-A31*A13)*D; |
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S32=(A12*A31-A11*A32)*D; |
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S13=(A12*A23-A13*A22)*D; |
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S23=(A13*A21-A11*A23)*D; |
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S33=(A11*A22-A12*A21)*D; |
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/* a_ik=a_ii^{-1}*a_ik */ |
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x[3*i ]=S11*S1+S12*S2+S13*S3; |
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x[3*i+1]=S21*S1+S22*S2+S23*S3; |
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x[3*i+2]=S31*S1+S32*S2+S33*S3; |
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} else { |
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Paso_setError(ZERO_DIVISION_ERROR, "Paso_Solver_getGS: 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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} |
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|
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/* Multipling with diag(A) */ |
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Paso_Solver_applyBlockDiagonalMatrix(gs->n_block,gs->n,gs->diag,pivot,x,x); |
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|
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/* backward substitution */ |
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for (color=(gs->num_colors)-1;color>-1;--color) { |
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if (n_block==1) { |
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#pragma omp parallel for schedule(static) private(i,iptr_ik,k,S1,R1) |
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for (i = 0; i < n; ++i) { |
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if (gs->colorOf[i]==color) { |
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/* x_i=x_i-a_ik*x_k */ |
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S1=x[i]; |
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for (iptr_ik=gs->pattern->ptr[i];iptr_ik<gs->pattern->ptr[i+1]; ++iptr_ik) { |
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k=gs->pattern->index[iptr_ik]; |
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if (gs->colorOf[k]>color) { |
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R1=x[k]; |
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S1-=gs->factors->val[iptr_ik]*R1; |
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} |
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} |
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/*x[i]=S1;*/ |
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iptr_main=gs->main_iptr[i]; |
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x[i]=(1/gs->factors->val[iptr_main])*S1; |
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} |
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} |
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} else if (n_block==2) { |
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#pragma omp parallel for schedule(static) private(i,iptr_ik,k,S1,S2,R1,R2) |
| 317 |
for (i = 0; i < n; ++i) { |
| 318 |
if (gs->colorOf[i]==color) { |
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/* x_i=x_i-a_ik*x_k */ |
| 320 |
S1=x[2*i]; |
| 321 |
S2=x[2*i+1]; |
| 322 |
for (iptr_ik=gs->pattern->ptr[i];iptr_ik<gs->pattern->ptr[i+1]; ++iptr_ik) { |
| 323 |
k=gs->pattern->index[iptr_ik]; |
| 324 |
if (gs->colorOf[k]>color) { |
| 325 |
R1=x[2*k]; |
| 326 |
R2=x[2*k+1]; |
| 327 |
S1-=gs->factors->val[4*iptr_ik ]*R1+gs->factors->val[4*iptr_ik+2]*R2; |
| 328 |
S2-=gs->factors->val[4*iptr_ik+1]*R1+gs->factors->val[4*iptr_ik+3]*R2; |
| 329 |
} |
| 330 |
} |
| 331 |
/*x[2*i]=S1; |
| 332 |
x[2*i+1]=S2;*/ |
| 333 |
iptr_main=gs->main_iptr[i]; |
| 334 |
A11=gs->factors->val[iptr_main*4]; |
| 335 |
A21=gs->factors->val[iptr_main*4+1]; |
| 336 |
A12=gs->factors->val[iptr_main*4+2]; |
| 337 |
A22=gs->factors->val[iptr_main*4+3]; |
| 338 |
D = A11*A22-A12*A21; |
| 339 |
if (ABS(D)>0.) { |
| 340 |
D=1./D; |
| 341 |
S11= A22*D; |
| 342 |
S21=-A21*D; |
| 343 |
S12=-A12*D; |
| 344 |
S22= A11*D; |
| 345 |
x[2*i ]=S11*S1+S12*S2; |
| 346 |
x[2*i+1]=S21*S1+S22*S2; |
| 347 |
} else { |
| 348 |
Paso_setError(ZERO_DIVISION_ERROR, "Paso_Solver_getGS: non-regular main diagonal block."); |
| 349 |
} |
| 350 |
|
| 351 |
} |
| 352 |
} |
| 353 |
} else if (n_block==3) { |
| 354 |
#pragma omp parallel for schedule(static) private(i,iptr_ik,k,S1,S2,S3,R1,R2,R3) |
| 355 |
for (i = 0; i < n; ++i) { |
| 356 |
if (gs->colorOf[i]==color) { |
| 357 |
/* x_i=x_i-a_ik*x_k */ |
| 358 |
S1=x[3*i ]; |
| 359 |
S2=x[3*i+1]; |
| 360 |
S3=x[3*i+2]; |
| 361 |
for (iptr_ik=gs->pattern->ptr[i];iptr_ik<gs->pattern->ptr[i+1]; ++iptr_ik) { |
| 362 |
k=gs->pattern->index[iptr_ik]; |
| 363 |
if (gs->colorOf[k]>color) { |
| 364 |
R1=x[3*k]; |
| 365 |
R2=x[3*k+1]; |
| 366 |
R3=x[3*k+2]; |
| 367 |
S1-=gs->factors->val[9*iptr_ik ]*R1+gs->factors->val[9*iptr_ik+3]*R2+gs->factors->val[9*iptr_ik+6]*R3; |
| 368 |
S2-=gs->factors->val[9*iptr_ik+1]*R1+gs->factors->val[9*iptr_ik+4]*R2+gs->factors->val[9*iptr_ik+7]*R3; |
| 369 |
S3-=gs->factors->val[9*iptr_ik+2]*R1+gs->factors->val[9*iptr_ik+5]*R2+gs->factors->val[9*iptr_ik+8]*R3; |
| 370 |
} |
| 371 |
} |
| 372 |
/* x[3*i]=S1; |
| 373 |
x[3*i+1]=S2; |
| 374 |
x[3*i+2]=S3; |
| 375 |
*/ iptr_main=gs->main_iptr[i]; |
| 376 |
A11=gs->factors->val[iptr_main*9 ]; |
| 377 |
A21=gs->factors->val[iptr_main*9+1]; |
| 378 |
A31=gs->factors->val[iptr_main*9+2]; |
| 379 |
A12=gs->factors->val[iptr_main*9+3]; |
| 380 |
A22=gs->factors->val[iptr_main*9+4]; |
| 381 |
A32=gs->factors->val[iptr_main*9+5]; |
| 382 |
A13=gs->factors->val[iptr_main*9+6]; |
| 383 |
A23=gs->factors->val[iptr_main*9+7]; |
| 384 |
A33=gs->factors->val[iptr_main*9+8]; |
| 385 |
D = A11*(A22*A33-A23*A32)+ A12*(A31*A23-A21*A33)+A13*(A21*A32-A31*A22); |
| 386 |
if (ABS(D)>0.) { |
| 387 |
D=1./D; |
| 388 |
S11=(A22*A33-A23*A32)*D; |
| 389 |
S21=(A31*A23-A21*A33)*D; |
| 390 |
S31=(A21*A32-A31*A22)*D; |
| 391 |
S12=(A13*A32-A12*A33)*D; |
| 392 |
S22=(A11*A33-A31*A13)*D; |
| 393 |
S32=(A12*A31-A11*A32)*D; |
| 394 |
S13=(A12*A23-A13*A22)*D; |
| 395 |
S23=(A13*A21-A11*A23)*D; |
| 396 |
S33=(A11*A22-A12*A21)*D; |
| 397 |
x[3*i ]=S11*S1+S12*S2+S13*S3; |
| 398 |
x[3*i+1]=S21*S1+S22*S2+S23*S3; |
| 399 |
x[3*i+2]=S31*S1+S32*S2+S33*S3; |
| 400 |
} else { |
| 401 |
Paso_setError(ZERO_DIVISION_ERROR, "Paso_Solver_getGS: non-regular main diagonal block."); |
| 402 |
} |
| 403 |
} |
| 404 |
} |
| 405 |
} |
| 406 |
} |
| 407 |
|
| 408 |
if (gs->sweeps>1) { |
| 409 |
/* Compute the residual b=b-Ax*/ |
| 410 |
Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(DBLE(-1), gs->factors, x, DBLE(2), b); |
| 411 |
/* Go round again*/ |
| 412 |
gs->sweeps=gs->sweeps-1; |
| 413 |
Paso_Solver_solveGS(gs,x,b); |
| 414 |
} |
| 415 |
|
| 416 |
return; |
| 417 |
} |
| 418 |
|
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