| 1 |
|
| 2 |
/* $Id$ */ |
| 3 |
|
| 4 |
/******************************************************* |
| 5 |
* |
| 6 |
* Copyright 2003-2007 by ACceSS MNRF |
| 7 |
* Copyright 2007 by University of Queensland |
| 8 |
* |
| 9 |
* http://esscc.uq.edu.au |
| 10 |
* Primary Business: Queensland, Australia |
| 11 |
* Licensed under the Open Software License version 3.0 |
| 12 |
* http://www.opensource.org/licenses/osl-3.0.php |
| 13 |
* |
| 14 |
*******************************************************/ |
| 15 |
|
| 16 |
/* PCG iterations */ |
| 17 |
|
| 18 |
#include "SystemMatrix.h" |
| 19 |
#include "Paso.h" |
| 20 |
#include "Solver.h" |
| 21 |
|
| 22 |
#ifdef _OPENMP |
| 23 |
#include <omp.h> |
| 24 |
#endif |
| 25 |
|
| 26 |
#ifdef PASO_MPI |
| 27 |
#include <mpi.h> |
| 28 |
#endif |
| 29 |
|
| 30 |
/* |
| 31 |
* |
| 32 |
* Purpose |
| 33 |
* ======= |
| 34 |
* |
| 35 |
* PCG solves the linear system A*x = b using the |
| 36 |
* preconditioned conjugate gradient method plus a smoother |
| 37 |
* A has to be symmetric. |
| 38 |
* |
| 39 |
* Convergence test: norm( b - A*x )< TOL. |
| 40 |
* For other measures, see the above reference. |
| 41 |
* |
| 42 |
* Arguments |
| 43 |
* ========= |
| 44 |
* |
| 45 |
* r (input) DOUBLE PRECISION array, dimension N. |
| 46 |
* On entry, residual of inital guess x |
| 47 |
* |
| 48 |
* x (input/output) DOUBLE PRECISION array, dimension N. |
| 49 |
* On input, the initial guess. |
| 50 |
* |
| 51 |
* ITER (input/output) INT |
| 52 |
* On input, the maximum iterations to be performed. |
| 53 |
* On output, actual number of iterations performed. |
| 54 |
* |
| 55 |
* INFO (output) INT |
| 56 |
* |
| 57 |
* = SOLVER_NO_ERROR: Successful exit. Iterated approximate solution returned. |
| 58 |
* = SOLVEr_MAXITER_REACHED |
| 59 |
* = SOLVER_INPUT_ERROR Illegal parameter: |
| 60 |
* = SOLVEr_BREAKDOWN: If parameters rHO or OMEGA become smaller |
| 61 |
* = SOLVER_MEMORY_ERROR : If parameters rHO or OMEGA become smaller |
| 62 |
* |
| 63 |
* ============================================================== |
| 64 |
*/ |
| 65 |
|
| 66 |
err_t Paso_Solver_PCG( |
| 67 |
Paso_SystemMatrix * A, |
| 68 |
double * r, |
| 69 |
double * x, |
| 70 |
dim_t *iter, |
| 71 |
double * tolerance, |
| 72 |
Paso_Performance* pp) { |
| 73 |
|
| 74 |
|
| 75 |
/* Local variables */ |
| 76 |
dim_t num_iter=0,maxit,num_iter_global; |
| 77 |
dim_t i0; |
| 78 |
bool_t breakFlag=FALSE, maxIterFlag=FALSE, convergeFlag=FALSE; |
| 79 |
err_t status = SOLVER_NO_ERROR; |
| 80 |
dim_t n = Paso_SystemMatrix_getTotalNumRows(A); |
| 81 |
double *resid = tolerance, *rs=NULL, *p=NULL, *v=NULL, *x2=NULL ; |
| 82 |
double tau_old,tau,beta,delta,gamma_1,gamma_2,alpha,sum_1,sum_2,sum_3,sum_4,sum_5,tol; |
| 83 |
#ifdef PASO_MPI |
| 84 |
double loc_sum[2], sum[2]; |
| 85 |
#endif |
| 86 |
double norm_of_residual,norm_of_residual_global; |
| 87 |
register double d; |
| 88 |
|
| 89 |
/* */ |
| 90 |
/*-----------------------------------------------------------------*/ |
| 91 |
/* */ |
| 92 |
/* Start of Calculation : */ |
| 93 |
/* --------------------- */ |
| 94 |
/* */ |
| 95 |
/* */ |
| 96 |
rs=TMPMEMALLOC(n,double); |
| 97 |
p=TMPMEMALLOC(n,double); |
| 98 |
v=TMPMEMALLOC(n,double); |
| 99 |
x2=TMPMEMALLOC(n,double); |
| 100 |
|
| 101 |
/* Test the input parameters. */ |
| 102 |
|
| 103 |
if (n < 0) { |
| 104 |
status = SOLVER_INPUT_ERROR; |
| 105 |
} else if (rs==NULL || p==NULL || v==NULL || x2==NULL) { |
| 106 |
status = SOLVER_MEMORY_ERROR; |
| 107 |
} else { |
| 108 |
maxit = *iter; |
| 109 |
tol = *resid; |
| 110 |
#pragma omp parallel firstprivate(maxit,tol,convergeFlag,maxIterFlag,breakFlag) \ |
| 111 |
private(tau_old,tau,beta,delta,gamma_1,gamma_2,alpha,norm_of_residual,num_iter) |
| 112 |
{ |
| 113 |
Performance_startMonitor(pp,PERFORMANCE_SOLVER); |
| 114 |
/* initialize data */ |
| 115 |
#pragma omp for private(i0) schedule(static) |
| 116 |
for (i0=0;i0<n;i0++) { |
| 117 |
rs[i0]=r[i0]; |
| 118 |
x2[i0]=x[i0]; |
| 119 |
} |
| 120 |
#pragma omp for private(i0) schedule(static) |
| 121 |
for (i0=0;i0<n;i0++) { |
| 122 |
p[i0]=0; |
| 123 |
v[i0]=0; |
| 124 |
} |
| 125 |
num_iter=0; |
| 126 |
tau = 0; |
| 127 |
/* start of iteration */ |
| 128 |
while (!(convergeFlag || maxIterFlag || breakFlag)) { |
| 129 |
++(num_iter); |
| 130 |
#pragma omp barrier |
| 131 |
#pragma omp master |
| 132 |
{ |
| 133 |
sum_1 = 0; |
| 134 |
sum_2 = 0; |
| 135 |
sum_3 = 0; |
| 136 |
sum_4 = 0; |
| 137 |
sum_5 = 0; |
| 138 |
} |
| 139 |
/* v=prec(r) */ |
| 140 |
Performance_stopMonitor(pp,PERFORMANCE_SOLVER); |
| 141 |
Performance_startMonitor(pp,PERFORMANCE_PRECONDITIONER); |
| 142 |
Paso_Solver_solvePreconditioner(A,v,r); |
| 143 |
Performance_stopMonitor(pp,PERFORMANCE_PRECONDITIONER); |
| 144 |
Performance_startMonitor(pp,PERFORMANCE_SOLVER); |
| 145 |
/* tau=v*r */ |
| 146 |
#pragma omp for private(i0) reduction(+:sum_1) schedule(static) |
| 147 |
for (i0=0;i0<n;i0++) sum_1+=v[i0]*r[i0]; /* Limit to local values of v[] and r[] */ |
| 148 |
#ifdef PASO_MPI |
| 149 |
/* In case we have many MPI processes, each of which may have several OMP threads: |
| 150 |
OMP master participates in an MPI reduction to get global sum_1 */ |
| 151 |
#pragma omp master |
| 152 |
{ |
| 153 |
loc_sum[0] = sum_1; |
| 154 |
MPI_Allreduce(loc_sum, &sum_1, 1, MPI_DOUBLE, MPI_SUM, A->mpi_info->comm); |
| 155 |
} |
| 156 |
#endif |
| 157 |
tau_old=tau; |
| 158 |
tau=sum_1; |
| 159 |
/* p=v+beta*p */ |
| 160 |
if (num_iter==1) { |
| 161 |
#pragma omp for private(i0) schedule(static) |
| 162 |
for (i0=0;i0<n;i0++) p[i0]=v[i0]; |
| 163 |
} else { |
| 164 |
beta=tau/tau_old; |
| 165 |
#pragma omp for private(i0) schedule(static) |
| 166 |
for (i0=0;i0<n;i0++) p[i0]=v[i0]+beta*p[i0]; |
| 167 |
} |
| 168 |
/* v=A*p */ |
| 169 |
Performance_stopMonitor(pp,PERFORMANCE_SOLVER); |
| 170 |
Performance_startMonitor(pp,PERFORMANCE_MVM); |
| 171 |
Paso_SystemMatrix_MatrixVector_CSR_OFFSET0(ONE, A, p,ZERO,v); |
| 172 |
Paso_SystemMatrix_MatrixVector_CSR_OFFSET0(ONE, A, p,ZERO,v); |
| 173 |
Performance_stopMonitor(pp,PERFORMANCE_MVM); |
| 174 |
Performance_startMonitor(pp,PERFORMANCE_SOLVER); |
| 175 |
/* delta=p*v */ |
| 176 |
#pragma omp for private(i0) reduction(+:sum_2) schedule(static) |
| 177 |
for (i0=0;i0<n;i0++) sum_2+=v[i0]*p[i0]; |
| 178 |
#ifdef PASO_MPI |
| 179 |
#pragma omp master |
| 180 |
{ |
| 181 |
loc_sum[0] = sum_2; |
| 182 |
MPI_Allreduce(loc_sum, &sum_2, 1, MPI_DOUBLE, MPI_SUM, A->mpi_info->comm); |
| 183 |
} |
| 184 |
#endif |
| 185 |
delta=sum_2; |
| 186 |
|
| 187 |
|
| 188 |
if (! (breakFlag = (ABS(delta) <= TOLERANCE_FOR_SCALARS))) { |
| 189 |
alpha=tau/delta; |
| 190 |
/* smoother */ |
| 191 |
#pragma omp for private(i0) schedule(static) |
| 192 |
for (i0=0;i0<n;i0++) r[i0]-=alpha*v[i0]; |
| 193 |
#pragma omp for private(i0,d) reduction(+:sum_3,sum_4) schedule(static) |
| 194 |
for (i0=0;i0<n;i0++) { |
| 195 |
d=r[i0]-rs[i0]; |
| 196 |
sum_3+=d*d; |
| 197 |
sum_4+=d*rs[i0]; |
| 198 |
} |
| 199 |
#ifdef PASO_MPI |
| 200 |
#pragma omp master |
| 201 |
{ |
| 202 |
loc_sum[0] = sum_3; |
| 203 |
loc_sum[1] = sum_4; |
| 204 |
MPI_Allreduce(loc_sum, sum, 2, MPI_DOUBLE, MPI_SUM, A->mpi_info->comm); |
| 205 |
sum_3=sum[0]; |
| 206 |
sum_4=sum[1]; |
| 207 |
} |
| 208 |
#endif |
| 209 |
gamma_1= ( (ABS(sum_3)<= ZERO) ? 0 : -sum_4/sum_3) ; |
| 210 |
gamma_2= ONE-gamma_1; |
| 211 |
#pragma omp for private(i0) schedule(static) |
| 212 |
for (i0=0;i0<n;++i0) { |
| 213 |
rs[i0]=gamma_2*rs[i0]+gamma_1*r[i0]; |
| 214 |
x2[i0]+=alpha*p[i0]; |
| 215 |
x[i0]=gamma_2*x[i0]+gamma_1*x2[i0]; |
| 216 |
} |
| 217 |
#pragma omp for private(i0) reduction(+:sum_5) schedule(static) |
| 218 |
for (i0=0;i0<n;++i0) sum_5+=rs[i0]*rs[i0]; |
| 219 |
#ifdef PASO_MPI |
| 220 |
#pragma omp master |
| 221 |
{ |
| 222 |
loc_sum[0] = sum_5; |
| 223 |
MPI_Allreduce(loc_sum, &sum_5, 1, MPI_DOUBLE, MPI_SUM, A->mpi_info->comm); |
| 224 |
} |
| 225 |
#endif |
| 226 |
norm_of_residual=sqrt(sum_5); |
| 227 |
convergeFlag = norm_of_residual <= tol; |
| 228 |
maxIterFlag = num_iter == maxit; |
| 229 |
breakFlag = (ABS(tau) <= TOLERANCE_FOR_SCALARS); |
| 230 |
} |
| 231 |
} |
| 232 |
/* end of iteration */ |
| 233 |
#pragma omp master |
| 234 |
{ |
| 235 |
num_iter_global=num_iter; |
| 236 |
norm_of_residual_global=norm_of_residual; |
| 237 |
if (maxIterFlag) { |
| 238 |
status = SOLVER_MAXITER_REACHED; |
| 239 |
} else if (breakFlag) { |
| 240 |
status = SOLVER_BREAKDOWN; |
| 241 |
} |
| 242 |
} |
| 243 |
Performance_stopMonitor(pp,PERFORMANCE_SOLVER); |
| 244 |
} /* end of parallel region */ |
| 245 |
TMPMEMFREE(rs); |
| 246 |
TMPMEMFREE(x2); |
| 247 |
TMPMEMFREE(v); |
| 248 |
TMPMEMFREE(p); |
| 249 |
*iter=num_iter_global; |
| 250 |
*resid=norm_of_residual_global; |
| 251 |
} |
| 252 |
/* End of PCG */ |
| 253 |
return status; |
| 254 |
} |
Parent Directory
| 
Revision Log