# Contents of /trunk/paso/src/Solver.c

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Tue Sep 30 05:58:06 2008 UTC (10 years, 6 months ago) by artak
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```Firs version of symmetric Gauss-Seidel preconditioner with coloring
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 1 2 /******************************************************* 3 * 4 * Copyright (c) 2003-2008 by University of Queensland 5 * Earth Systems Science Computational Center (ESSCC) 6 * http://www.uq.edu.au/esscc 7 * 8 * Primary Business: Queensland, Australia 9 * Licensed under the Open Software License version 3.0 10 * http://www.opensource.org/licenses/osl-3.0.php 11 * 12 *******************************************************/ 13 14 15 /**************************************************************/ 16 17 /* Paso: SystemMatrix: controls iterative linear system solvers */ 18 19 /**************************************************************/ 20 21 /* Copyrights by ACcESS Australia 2003/04 */ 22 /* Author: gross@access.edu.au */ 23 24 /**************************************************************/ 25 26 #include "Paso.h" 27 #include "SystemMatrix.h" 28 #include "Solver.h" 29 #include "escript/blocktimer.h" 30 31 /***********************************************************************************/ 32 33 /* free space */ 34 35 void Paso_Solver_free(Paso_SystemMatrix* A) { 36 Paso_Preconditioner_free(A->solver); 37 A->solver=NULL; 38 } 39 /* call the iterative solver: */ 40 41 void Paso_Solver(Paso_SystemMatrix* A,double* x,double* b, 42 Paso_Options* options,Paso_Performance* pp) { 43 44 double norm2_of_b,tol,tolerance,time_iter; 45 double *r=NULL,norm2_of_residual,last_norm2_of_residual,norm_max_of_b; 46 double norm2_of_b_local,norm_max_of_b_local,norm2_of_residual_local; 47 double norm_max_of_residual_local,norm_max_of_residual; 48 double last_norm_max_of_residual,*scaling; 49 #ifdef PASO_MPI 50 double loc_norm; 51 #endif 52 dim_t i,totIter,cntIter,method; 53 bool_t finalizeIteration; 54 err_t errorCode; 55 dim_t numSol = Paso_SystemMatrix_getTotalNumCols(A); 56 dim_t numEqua = Paso_SystemMatrix_getTotalNumRows(A); 57 double blocktimer_precond, blocktimer_start = blocktimer_time(); 58 59 tolerance=MAX(options->tolerance,EPSILON); 60 Paso_resetError(); 61 method=Paso_Options_getSolver(options->method,PASO_PASO,options->symmetric); 62 /* check matrix type */ 63 if ((A->type & MATRIX_FORMAT_CSC) || (A->type & MATRIX_FORMAT_OFFSET1) || (A->type & MATRIX_FORMAT_SYM) ) { 64 Paso_setError(TYPE_ERROR,"Iterative solver requires CSR format with unsymmetric storage scheme and index offset 0."); 65 } 66 if (A->col_block_size != A->row_block_size) { 67 Paso_setError(TYPE_ERROR,"Iterative solver requires row and column block sizes to be equal."); 68 } 69 if (Paso_SystemMatrix_getGlobalNumCols(A) != Paso_SystemMatrix_getGlobalNumRows(A)) { 70 Paso_setError(TYPE_ERROR,"Iterative solver requires a square matrix."); 71 return; 72 } 73 /* this for testing only */ 74 if (method==PASO_NONLINEAR_GMRES) { 75 Paso_Function* F=NULL; 76 F=Paso_Function_LinearSystem_alloc(A,b,options); 77 Paso_Solver_solvePreconditioner(A,x,b); 78 errorCode=Paso_Solver_NewtonGMRES(F,x,options,pp); 79 if (errorCode!=NO_ERROR) { 80 Paso_setError(SYSTEM_ERROR,"Paso_Solver_NewtonGMRES: an error has occured."); 81 } 82 Paso_Function_LinearSystem_free(F); 83 return; 84 } 85 /* ========================= */ 86 Performance_startMonitor(pp,PERFORMANCE_ALL); 87 if (Paso_noError()) { 88 /* get normalization */ 89 scaling=Paso_SystemMatrix_borrowNormalization(A); 90 if (Paso_noError()) { 91 /* get the norm of the right hand side */ 92 norm2_of_b=0.; 93 norm_max_of_b=0.; 94 #pragma omp parallel private(norm2_of_b_local,norm_max_of_b_local) 95 { 96 norm2_of_b_local=0.; 97 norm_max_of_b_local=0.; 98 #pragma omp for private(i) schedule(static) 99 for (i = 0; i < numEqua ; ++i) { 100 norm2_of_b_local += b[i] * b[i]; 101 norm_max_of_b_local = MAX(ABS(scaling[i]*b[i]),norm_max_of_b_local); 102 } 103 #pragma omp critical 104 { 105 norm2_of_b += norm2_of_b_local; 106 norm_max_of_b = MAX(norm_max_of_b_local,norm_max_of_b); 107 } 108 } 109 /* TODO: use one call */ 110 #ifdef PASO_MPI 111 { 112 loc_norm = norm2_of_b; 113 MPI_Allreduce(&loc_norm,&norm2_of_b, 1, MPI_DOUBLE, MPI_SUM, A->mpi_info->comm); 114 loc_norm = norm_max_of_b; 115 MPI_Allreduce(&loc_norm,&norm_max_of_b, 1, MPI_DOUBLE, MPI_MAX, A->mpi_info->comm); 116 } 117 #endif 118 norm2_of_b=sqrt(norm2_of_b); 119 120 /* if norm2_of_b==0 we are ready: x=0 */ 121 if (norm2_of_b <=0.) { 122 #pragma omp parallel for private(i) schedule(static) 123 for (i = 0; i < numSol; i++) x[i]=0.; 124 if (options->verbose) printf("right hand side is identical zero.\n"); 125 } else { 126 if (options->verbose) { 127 printf("l2/lmax-norm of right hand side is %e/%e.\n",norm2_of_b,norm_max_of_b); 128 printf("l2/lmax-stopping criterion is %e/%e.\n",norm2_of_b*tolerance,norm_max_of_b*tolerance); 129 switch (method) { 130 case PASO_BICGSTAB: 131 printf("Iterative method is BiCGStab.\n"); 132 break; 133 case PASO_PCG: 134 printf("Iterative method is PCG.\n"); 135 break; 136 case PASO_TFQMR: 137 printf("Iterative method is TFQMR.\n"); 138 break; 139 case PASO_MINRES: 140 printf("Iterative method is MINRES.\n"); 141 break; 142 case PASO_PRES20: 143 printf("Iterative method is PRES20.\n"); 144 break; 145 case PASO_GMRES: 146 if (options->restart>0) { 147 printf("Iterative method is GMRES(%d,%d)\n",options->truncation,options->restart); 148 } else { 149 printf("Iterative method is GMRES(%d)\n",options->truncation); 150 } 151 break; 152 } 153 } 154 /* construct the preconditioner */ 155 156 blocktimer_precond = blocktimer_time(); 157 Performance_startMonitor(pp,PERFORMANCE_PRECONDITIONER_INIT); 158 Paso_Solver_setPreconditioner(A,options); 159 Performance_stopMonitor(pp,PERFORMANCE_PRECONDITIONER_INIT); 160 blocktimer_increment("Paso_Solver_setPreconditioner()", blocktimer_precond); 161 if (! Paso_noError()) return; 162 time_iter=Paso_timer(); 163 /* get an initial guess by evaluating the preconditioner */ 164 Paso_Solver_solvePreconditioner(A,x,b); 165 /* start the iteration process :*/ 166 r=TMPMEMALLOC(numEqua,double); 167 Paso_checkPtr(r); 168 if (Paso_noError()) { 169 totIter = 0; 170 finalizeIteration = FALSE; 171 last_norm2_of_residual=norm2_of_b; 172 last_norm_max_of_residual=norm_max_of_b; 173 /* Loop */ 174 while (! finalizeIteration) { 175 cntIter = options->iter_max - totIter; 176 finalizeIteration = TRUE; 177 /* Set initial residual. */ 178 norm2_of_residual = 0; 179 norm_max_of_residual = 0; 180 #pragma omp parallel for private(i) schedule(static) 181 for (i = 0; i < numEqua; i++) r[i]=b[i]; 182 Paso_SystemMatrix_MatrixVector_CSR_OFFSET0(DBLE(-1), A, x, DBLE(1), r); 183 184 #pragma omp parallel private(norm2_of_residual_local,norm_max_of_residual_local) 185 { 186 norm2_of_residual_local = 0; 187 norm_max_of_residual_local = 0; 188 #pragma omp for private(i) schedule(static) 189 for (i = 0; i < numEqua; i++) { 190 norm2_of_residual_local+= r[i] * r[i]; 191 norm_max_of_residual_local=MAX(ABS(scaling[i]*r[i]),norm_max_of_residual_local); 192 } 193 #pragma omp critical 194 { 195 norm2_of_residual += norm2_of_residual_local; 196 norm_max_of_residual = MAX(norm_max_of_residual_local,norm_max_of_residual); 197 } 198 } 199 /* TODO: use one call */ 200 #ifdef PASO_MPI 201 loc_norm = norm2_of_residual; 202 MPI_Allreduce(&loc_norm,&norm2_of_residual, 1, MPI_DOUBLE, MPI_SUM, A->mpi_info->comm); 203 loc_norm = norm_max_of_residual; 204 MPI_Allreduce(&loc_norm,&norm_max_of_residual, 1, MPI_DOUBLE, MPI_MAX, A->mpi_info->comm); 205 #endif 206 norm2_of_residual =sqrt(norm2_of_residual); 207 208 if (options->verbose) printf("Step %5d: l2/lmax-norm of residual is %e/%e",totIter,norm2_of_residual,norm_max_of_residual); 209 if (totIter>0 && norm2_of_residual>=last_norm2_of_residual && norm_max_of_residual>=last_norm_max_of_residual) { 210 if (options->verbose) printf(" divergence!\n"); 211 Paso_setError(WARNING, "No improvement during iteration. Iterative solver gives up."); 212 } else { 213 /* */ 214 if (norm2_of_residual>tolerance*norm2_of_b || norm_max_of_residual>tolerance*norm_max_of_b ) { 215 tol=tolerance*MIN(norm2_of_b,0.1*norm2_of_residual/norm_max_of_residual*norm_max_of_b); 216 if (options->verbose) printf(" (new tolerance = %e).\n",tol); 217 last_norm2_of_residual=norm2_of_residual; 218 last_norm_max_of_residual=norm_max_of_residual; 219 /* call the solver */ 220 switch (method) { 221 case PASO_BICGSTAB: 222 errorCode = Paso_Solver_BiCGStab(A, r, x, &cntIter, &tol, pp); 223 break; 224 case PASO_PCG: 225 errorCode = Paso_Solver_PCG(A, r, x, &cntIter, &tol, pp); 226 break; 227 case PASO_TFQMR: 228 errorCode = Paso_Solver_TFQMR(A, r, x, &cntIter, &tol, pp); 229 break; 230 case PASO_MINRES: 231 errorCode = Paso_Solver_MINRES(A, r, x, &cntIter, &tolerance, &tol, pp); 232 break; 233 case PASO_PRES20: 234 errorCode = Paso_Solver_GMRES(A, r, x, &cntIter, &tol,5,20, pp); 235 break; 236 case PASO_GMRES: 237 errorCode = Paso_Solver_GMRES(A, r, x, &cntIter, &tol,options->truncation,options->restart, pp); 238 break; 239 } 240 totIter += cntIter; 241 /* error handling */ 242 if (errorCode==NO_ERROR) { 243 finalizeIteration = FALSE; 244 } else if (errorCode==SOLVER_MAXITER_REACHED) { 245 Paso_setError(WARNING,"maximum number of iteration step reached.\nReturned solution does not fulfil stopping criterion."); 246 if (options->verbose) printf("Maximum number of iterations reached.!\n"); 247 } else if (errorCode == SOLVER_INPUT_ERROR ) { 248 Paso_setError(SYSTEM_ERROR,"illegal dimension in iterative solver."); 249 if (options->verbose) printf("Internal error!\n"); 250 } else if ( errorCode == SOLVER_BREAKDOWN ) { 251 if (cntIter <= 1) { 252 Paso_setError(ZERO_DIVISION_ERROR, "fatal break down in iterative solver."); 253 if (options->verbose) printf("Uncurable break down!\n"); 254 } else { 255 if (options->verbose) printf("Breakdown at iter %d (residual = %e). Restarting ...\n", cntIter+totIter, tol); 256 finalizeIteration = FALSE; 257 } 258 } else { 259 if (options->verbose) printf(". convergence! \n"); 260 } 261 } 262 } /* while */ 263 } 264 MEMFREE(r); 265 time_iter=Paso_timer()-time_iter; 266 if (options->verbose) { 267 printf("\ntiming: solver: %.4e sec\n",time_iter); 268 if (totIter>0) printf("timing: per iteration step: %.4e sec\n",time_iter/totIter); 269 } 270 } 271 } 272 } 273 } 274 Performance_stopMonitor(pp,PERFORMANCE_ALL); 275 blocktimer_increment("Paso_Solver()", blocktimer_start); 276 }

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