| 1 |
/* $Id$ */ |
| 2 |
|
| 3 |
/* |
| 4 |
* Purpose |
| 5 |
* ======= |
| 6 |
* |
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* GMRES solves the linear system A*x=b using the |
| 8 |
* truncated and restered GMRES method with preconditioning. |
| 9 |
* |
| 10 |
* Convergence test: norm( b - A*x )< TOL. |
| 11 |
* |
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* |
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* |
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* Arguments |
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* ========= |
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* |
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* r (input/output) double array, dimension n. |
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* On entry, residual of inital guess X |
| 19 |
* |
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* x (input/output) double array, dimension n. |
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* On input, the initial guess. |
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* |
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* iter (input/output) int |
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* On input, the maximum num_iterations to be performed. |
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* On output, actual number of num_iterations performed. |
| 26 |
* |
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* tolerance (input/output) DOUBLE PRECISION |
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* On input, the allowable convergence measure for |
| 29 |
* norm( b - A*x ) |
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* On output, the final value of this measure. |
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* |
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* Length_of_recursion (input) gives the number of residual to be kept in orthogonalization process |
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* |
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* restart (input) If restart>0, iteration is resterted a after restart steps. |
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* |
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* INFO (output) int |
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* |
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* =SOLVER_NO_ERROR: Successful exit. num_iterated approximate solution returned. |
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* =SOLVER_MAXNUM_ITER_REACHED |
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* =SOLVER_INPUT_ERROR Illegal parameter: |
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* =SOLVER_BREAKDOWN: bad luck! |
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* =SOLVER_MEMORY_ERROR : no memory available |
| 43 |
* |
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* ============================================================== |
| 45 |
*/ |
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|
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#include "Common.h" |
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#include "SystemMatrix.h" |
| 49 |
#include "Solver.h" |
| 50 |
#ifdef _OPENMP |
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#include <omp.h> |
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#endif |
| 53 |
|
| 54 |
err_t Paso_Solver_GMRES( |
| 55 |
Paso_SystemMatrix * A, |
| 56 |
double * r, |
| 57 |
double * x, |
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dim_t *iter, |
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double * tolerance,dim_t Length_of_recursion,dim_t restart) { |
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|
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/* Local variables */ |
| 62 |
|
| 63 |
double *AP,*X_PRES[MAX(Length_of_recursion,0)+1],*R_PRES[MAX(Length_of_recursion,0)+1],*P_PRES[MAX(Length_of_recursion,0)+1]; |
| 64 |
double P_PRES_dot_AP[MAX(Length_of_recursion,0)],R_PRES_dot_P_PRES[MAX(Length_of_recursion,0)+1],BREAKF[MAX(Length_of_recursion,0)+1],ALPHA[MAX(Length_of_recursion,0)]; |
| 65 |
double P_PRES_dot_AP0,P_PRES_dot_AP1,P_PRES_dot_AP2,P_PRES_dot_AP3,P_PRES_dot_AP4,P_PRES_dot_AP5,P_PRES_dot_AP6,R_PRES_dot_P,abs_RP,breakf0; |
| 66 |
double tol,Factor,sum_BREAKF,gamma,SC1,SC2,norm_of_residual,diff,L2_R,Norm_of_residual_global; |
| 67 |
double *save_XPRES, *save_P_PRES, *save_R_PRES,save_R_PRES_dot_P_PRES; |
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dim_t maxit,Num_iter_global,num_iter_restart,num_iter; |
| 69 |
dim_t i,z,order; |
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bool_t breakFlag=FALSE, maxIterFlag=FALSE, convergeFlag=FALSE,restartFlag=FALSE; |
| 71 |
err_t Status=SOLVER_NO_ERROR; |
| 72 |
|
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/* adapt original routine parameters */ |
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|
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dim_t n=A->num_cols * A-> col_block_size; |
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dim_t Length_of_mem=MAX(Length_of_recursion,0)+1; |
| 77 |
|
| 78 |
/* Test the input parameters. */ |
| 79 |
if (restart>0) restart=MAX(Length_of_recursion,restart); |
| 80 |
if (n < 0 || Length_of_recursion<=0) { |
| 81 |
return SOLVER_INPUT_ERROR; |
| 82 |
} |
| 83 |
|
| 84 |
/* allocate memory: */ |
| 85 |
|
| 86 |
AP=TMPMEMALLOC(n,double); |
| 87 |
if (AP==NULL) Status=SOLVER_MEMORY_ERROR; |
| 88 |
for (i=0;i<Length_of_mem;i++) { |
| 89 |
X_PRES[i]=TMPMEMALLOC(n,double); |
| 90 |
R_PRES[i]=TMPMEMALLOC(n,double); |
| 91 |
P_PRES[i]=TMPMEMALLOC(n,double); |
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if (X_PRES[i]==NULL || R_PRES[i]==NULL || P_PRES[i]==NULL) Status=SOLVER_MEMORY_ERROR; |
| 93 |
} |
| 94 |
if ( Status ==SOLVER_NO_ERROR ) { |
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|
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/* now PRES starts : */ |
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maxit=*iter; |
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tol=*tolerance; |
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|
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#pragma omp parallel firstprivate(maxit,tol,convergeFlag,maxIterFlag,breakFlag) \ |
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private(num_iter,i,num_iter_restart,order,sum_BREAKF,gamma,restartFlag,norm_of_residual,abs_RP,breakf0,\ |
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save_XPRES,save_P_PRES,save_R_PRES,save_R_PRES_dot_P_PRES) |
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{ |
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/* initialization */ |
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|
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restartFlag=TRUE; |
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num_iter=0; |
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#pragma omp for private(z) schedule(static) nowait |
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for (z=0; z < n; ++z) AP[z]=0; |
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for(i=0;i<Length_of_mem;++i) { |
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#pragma omp for private(z) schedule(static) nowait |
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for (z=0; z < n; ++z) { |
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P_PRES[i][z]=0; |
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R_PRES[i][z]=0; |
| 115 |
X_PRES[i][z]=0; |
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} |
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} |
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|
| 119 |
while (! (convergeFlag || maxIterFlag || breakFlag)) { |
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#pragma omp barrier |
| 121 |
if (restartFlag) { |
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#pragma omp master |
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BREAKF[0]=ONE; |
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#pragma omp for private(z) schedule(static) nowait |
| 125 |
for (z=0; z < n; ++z) { |
| 126 |
R_PRES[0][z]=r[z]; |
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X_PRES[0][z]=x[z]; |
| 128 |
} |
| 129 |
num_iter_restart=0; |
| 130 |
restartFlag=FALSE; |
| 131 |
} |
| 132 |
++num_iter; |
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++num_iter_restart; |
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/* order is the dimension of the space on which the residual is minimized: */ |
| 135 |
order=MIN(num_iter_restart,Length_of_recursion); |
| 136 |
/*** |
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*** calculate new search direction P from R_PRES |
| 138 |
***/ |
| 139 |
Paso_Solver_solvePreconditioner(A,&P_PRES[0][0], &R_PRES[0][0]); |
| 140 |
/*** |
| 141 |
*** apply A to P to get AP |
| 142 |
***/ |
| 143 |
Paso_SystemMatrix_MatrixVector_CSR_OFFSET0(ONE, A, &P_PRES[0][0],ZERO, &AP[0]); |
| 144 |
/*** |
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***** calculation of the norm of R and the scalar products of |
| 146 |
*** the residuals and A*P: |
| 147 |
***/ |
| 148 |
if (order==0) { |
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#pragma omp master |
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R_PRES_dot_P=ZERO; |
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#pragma omp barrier |
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#pragma omp for private(z) reduction(+:R_PRES_dot_P) schedule(static) |
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for (z=0;z<n;++z) |
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R_PRES_dot_P+=R_PRES[0][z]*P_PRES[0][z]; |
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#pragma omp master |
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R_PRES_dot_P_PRES[0]=R_PRES_dot_P; |
| 157 |
} else if (order==1) { |
| 158 |
#pragma omp master |
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{ |
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R_PRES_dot_P=ZERO; |
| 161 |
P_PRES_dot_AP0=ZERO; |
| 162 |
} |
| 163 |
#pragma omp barrier |
| 164 |
#pragma omp for private(z) reduction(+:R_PRES_dot_P,P_PRES_dot_AP0) schedule(static) |
| 165 |
for (z=0;z<n;++z) { |
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R_PRES_dot_P+=R_PRES[0][z]*P_PRES[0][z]; |
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P_PRES_dot_AP0+=P_PRES[0][z]*AP[z]; |
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} |
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#pragma omp master |
| 170 |
{ |
| 171 |
P_PRES_dot_AP[0]=P_PRES_dot_AP0; |
| 172 |
R_PRES_dot_P_PRES[0]=R_PRES_dot_P; |
| 173 |
} |
| 174 |
} else if (order==2) { |
| 175 |
#pragma omp master |
| 176 |
{ |
| 177 |
R_PRES_dot_P=ZERO; |
| 178 |
P_PRES_dot_AP0=ZERO; |
| 179 |
P_PRES_dot_AP1=ZERO; |
| 180 |
} |
| 181 |
#pragma omp barrier |
| 182 |
#pragma omp for private(z) reduction(+:R_PRES_dot_P,P_PRES_dot_AP0,P_PRES_dot_AP1) schedule(static) |
| 183 |
for (z=0;z<n;++z) { |
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R_PRES_dot_P+=R_PRES[0][z]*P_PRES[0][z]; |
| 185 |
P_PRES_dot_AP0+=P_PRES[0][z]*AP[z]; |
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P_PRES_dot_AP1+=P_PRES[1][z]*AP[z]; |
| 187 |
} |
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#pragma omp master |
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{ |
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P_PRES_dot_AP[0]=P_PRES_dot_AP0; |
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P_PRES_dot_AP[1]=P_PRES_dot_AP1; |
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R_PRES_dot_P_PRES[0]=R_PRES_dot_P; |
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} |
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} else if (order==3) { |
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#pragma omp master |
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{ |
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R_PRES_dot_P=ZERO; |
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P_PRES_dot_AP0=ZERO; |
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P_PRES_dot_AP1=ZERO; |
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P_PRES_dot_AP2=ZERO; |
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} |
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#pragma omp barrier |
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#pragma omp for private(z) reduction(+:R_PRES_dot_P,P_PRES_dot_AP0,P_PRES_dot_AP1,P_PRES_dot_AP2) schedule(static) |
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for (z=0;z<n;++z) { |
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R_PRES_dot_P+=R_PRES[0][z]*P_PRES[0][z]; |
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P_PRES_dot_AP0+=P_PRES[0][z]*AP[z]; |
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P_PRES_dot_AP1+=P_PRES[1][z]*AP[z]; |
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P_PRES_dot_AP2+=P_PRES[2][z]*AP[z]; |
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} |
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#pragma omp master |
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{ |
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P_PRES_dot_AP[0]=P_PRES_dot_AP0; |
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P_PRES_dot_AP[1]=P_PRES_dot_AP1; |
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P_PRES_dot_AP[2]=P_PRES_dot_AP2; |
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R_PRES_dot_P_PRES[0]=R_PRES_dot_P; |
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} |
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} else if (order==4) { |
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#pragma omp master |
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{ |
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R_PRES_dot_P=ZERO; |
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P_PRES_dot_AP0=ZERO; |
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P_PRES_dot_AP1=ZERO; |
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P_PRES_dot_AP2=ZERO; |
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P_PRES_dot_AP3=ZERO; |
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} |
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#pragma omp barrier |
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#pragma omp for private(z) reduction(+:R_PRES_dot_P,P_PRES_dot_AP0,P_PRES_dot_AP1,P_PRES_dot_AP2,P_PRES_dot_AP3) schedule(static) |
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for (z=0;z<n;++z) { |
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R_PRES_dot_P+=R_PRES[0][z]*P_PRES[0][z]; |
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P_PRES_dot_AP0+=P_PRES[0][z]*AP[z]; |
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P_PRES_dot_AP1+=P_PRES[1][z]*AP[z]; |
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P_PRES_dot_AP2+=P_PRES[2][z]*AP[z]; |
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P_PRES_dot_AP3+=P_PRES[3][z]*AP[z]; |
| 234 |
} |
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#pragma omp master |
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{ |
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P_PRES_dot_AP[0]=P_PRES_dot_AP0; |
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P_PRES_dot_AP[1]=P_PRES_dot_AP1; |
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P_PRES_dot_AP[2]=P_PRES_dot_AP2; |
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P_PRES_dot_AP[3]=P_PRES_dot_AP3; |
| 241 |
R_PRES_dot_P_PRES[0]=R_PRES_dot_P; |
| 242 |
} |
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} else if (order==5) { |
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#pragma omp master |
| 245 |
{ |
| 246 |
R_PRES_dot_P=ZERO; |
| 247 |
P_PRES_dot_AP0=ZERO; |
| 248 |
P_PRES_dot_AP1=ZERO; |
| 249 |
P_PRES_dot_AP2=ZERO; |
| 250 |
P_PRES_dot_AP3=ZERO; |
| 251 |
P_PRES_dot_AP4=ZERO; |
| 252 |
} |
| 253 |
#pragma omp barrier |
| 254 |
#pragma omp for private(z) reduction(+:R_PRES_dot_P,P_PRES_dot_AP0,P_PRES_dot_AP1,P_PRES_dot_AP2,P_PRES_dot_AP3,P_PRES_dot_AP4) schedule(static) |
| 255 |
for (z=0;z<n;++z) { |
| 256 |
R_PRES_dot_P+=R_PRES[0][z]*P_PRES[0][z]; |
| 257 |
P_PRES_dot_AP0+=P_PRES[0][z]*AP[z]; |
| 258 |
P_PRES_dot_AP1+=P_PRES[1][z]*AP[z]; |
| 259 |
P_PRES_dot_AP2+=P_PRES[2][z]*AP[z]; |
| 260 |
P_PRES_dot_AP3+=P_PRES[3][z]*AP[z]; |
| 261 |
P_PRES_dot_AP4+=P_PRES[4][z]*AP[z]; |
| 262 |
} |
| 263 |
#pragma omp master |
| 264 |
{ |
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P_PRES_dot_AP[0]=P_PRES_dot_AP0; |
| 266 |
P_PRES_dot_AP[1]=P_PRES_dot_AP1; |
| 267 |
P_PRES_dot_AP[2]=P_PRES_dot_AP2; |
| 268 |
P_PRES_dot_AP[3]=P_PRES_dot_AP3; |
| 269 |
P_PRES_dot_AP[4]=P_PRES_dot_AP4; |
| 270 |
R_PRES_dot_P_PRES[0]=R_PRES_dot_P; |
| 271 |
} |
| 272 |
} else if (order==6) { |
| 273 |
#pragma omp master |
| 274 |
{ |
| 275 |
R_PRES_dot_P=ZERO; |
| 276 |
P_PRES_dot_AP0=ZERO; |
| 277 |
P_PRES_dot_AP1=ZERO; |
| 278 |
P_PRES_dot_AP2=ZERO; |
| 279 |
P_PRES_dot_AP3=ZERO; |
| 280 |
P_PRES_dot_AP4=ZERO; |
| 281 |
P_PRES_dot_AP5=ZERO; |
| 282 |
} |
| 283 |
#pragma omp barrier |
| 284 |
#pragma omp for private(z) reduction(+:R_PRES_dot_P,P_PRES_dot_AP0,P_PRES_dot_AP1,P_PRES_dot_AP2,P_PRES_dot_AP3,P_PRES_dot_AP4,P_PRES_dot_AP5) schedule(static) |
| 285 |
for (z=0;z<n;++z) { |
| 286 |
R_PRES_dot_P+=R_PRES[0][z]*P_PRES[0][z]; |
| 287 |
P_PRES_dot_AP0+=P_PRES[0][z]*AP[z]; |
| 288 |
P_PRES_dot_AP1+=P_PRES[1][z]*AP[z]; |
| 289 |
P_PRES_dot_AP2+=P_PRES[2][z]*AP[z]; |
| 290 |
P_PRES_dot_AP3+=P_PRES[3][z]*AP[z]; |
| 291 |
P_PRES_dot_AP4+=P_PRES[4][z]*AP[z]; |
| 292 |
P_PRES_dot_AP5+=P_PRES[5][z]*AP[z]; |
| 293 |
} |
| 294 |
#pragma omp master |
| 295 |
{ |
| 296 |
P_PRES_dot_AP[0]=P_PRES_dot_AP0; |
| 297 |
P_PRES_dot_AP[1]=P_PRES_dot_AP1; |
| 298 |
P_PRES_dot_AP[2]=P_PRES_dot_AP2; |
| 299 |
P_PRES_dot_AP[3]=P_PRES_dot_AP3; |
| 300 |
P_PRES_dot_AP[4]=P_PRES_dot_AP4; |
| 301 |
P_PRES_dot_AP[5]=P_PRES_dot_AP5; |
| 302 |
R_PRES_dot_P_PRES[0]=R_PRES_dot_P; |
| 303 |
} |
| 304 |
} else if (order>6) { |
| 305 |
#pragma omp master |
| 306 |
{ |
| 307 |
R_PRES_dot_P=ZERO; |
| 308 |
P_PRES_dot_AP0=ZERO; |
| 309 |
P_PRES_dot_AP1=ZERO; |
| 310 |
P_PRES_dot_AP2=ZERO; |
| 311 |
P_PRES_dot_AP3=ZERO; |
| 312 |
P_PRES_dot_AP4=ZERO; |
| 313 |
P_PRES_dot_AP5=ZERO; |
| 314 |
P_PRES_dot_AP6=ZERO; |
| 315 |
} |
| 316 |
#pragma omp barrier |
| 317 |
#pragma omp for private(z) reduction(+:R_PRES_dot_P,P_PRES_dot_AP0,P_PRES_dot_AP1,P_PRES_dot_AP2,P_PRES_dot_AP3,P_PRES_dot_AP4,P_PRES_dot_AP5,P_PRES_dot_AP6) schedule(static) |
| 318 |
for (z=0;z<n;++z) { |
| 319 |
R_PRES_dot_P+=R_PRES[0][z]*P_PRES[0][z]; |
| 320 |
P_PRES_dot_AP0+=P_PRES[0][z]*AP[z]; |
| 321 |
P_PRES_dot_AP1+=P_PRES[1][z]*AP[z]; |
| 322 |
P_PRES_dot_AP2+=P_PRES[2][z]*AP[z]; |
| 323 |
P_PRES_dot_AP3+=P_PRES[3][z]*AP[z]; |
| 324 |
P_PRES_dot_AP4+=P_PRES[4][z]*AP[z]; |
| 325 |
P_PRES_dot_AP5+=P_PRES[5][z]*AP[z]; |
| 326 |
P_PRES_dot_AP6+=P_PRES[6][z]*AP[z]; |
| 327 |
} |
| 328 |
#pragma omp master |
| 329 |
{ |
| 330 |
P_PRES_dot_AP[0]=P_PRES_dot_AP0; |
| 331 |
P_PRES_dot_AP[1]=P_PRES_dot_AP1; |
| 332 |
P_PRES_dot_AP[2]=P_PRES_dot_AP2; |
| 333 |
P_PRES_dot_AP[3]=P_PRES_dot_AP3; |
| 334 |
P_PRES_dot_AP[4]=P_PRES_dot_AP4; |
| 335 |
P_PRES_dot_AP[5]=P_PRES_dot_AP5; |
| 336 |
P_PRES_dot_AP[6]=P_PRES_dot_AP6; |
| 337 |
R_PRES_dot_P_PRES[0]=R_PRES_dot_P; |
| 338 |
|
| 339 |
P_PRES_dot_AP0=ZERO; |
| 340 |
} |
| 341 |
for (i=7;i<order;++i) { |
| 342 |
#pragma omp barrier |
| 343 |
#pragma omp for private(z) reduction(+:P_PRES_dot_AP0) schedule(static) |
| 344 |
for (z=0;z<n;++z) P_PRES_dot_AP0+=P_PRES[i][z]*AP[z]; |
| 345 |
#pragma omp master |
| 346 |
{ |
| 347 |
P_PRES_dot_AP[i]=P_PRES_dot_AP0; |
| 348 |
P_PRES_dot_AP0=ZERO; |
| 349 |
} |
| 350 |
} |
| 351 |
} |
| 352 |
/* this fixes a problem with the intel compiler */ |
| 353 |
#pragma omp master |
| 354 |
P_PRES_dot_AP0=R_PRES_dot_P_PRES[0]; |
| 355 |
#pragma omp barrier |
| 356 |
/*** if sum_BREAKF is equal to zero a breakdown occurs. |
| 357 |
*** iteration procedure can be continued but R_PRES is not the |
| 358 |
*** residual of X_PRES approximation. |
| 359 |
***/ |
| 360 |
sum_BREAKF=0.; |
| 361 |
for (i=0;i<order;++i) sum_BREAKF +=BREAKF[i]; |
| 362 |
breakFlag=!((ABS(P_PRES_dot_AP0) > ZERO) && (sum_BREAKF >ZERO)); |
| 363 |
if (!breakFlag) { |
| 364 |
breakFlag=FALSE; |
| 365 |
/*** |
| 366 |
***** X_PRES and R_PRES are moved to memory: |
| 367 |
***/ |
| 368 |
#pragma omp master |
| 369 |
{ |
| 370 |
Factor=0.; |
| 371 |
for (i=0;i<order;++i) { |
| 372 |
ALPHA[i]=-P_PRES_dot_AP[i]/R_PRES_dot_P_PRES[i]; |
| 373 |
Factor+=BREAKF[i]*ALPHA[i]; |
| 374 |
} |
| 375 |
|
| 376 |
save_R_PRES_dot_P_PRES=R_PRES_dot_P_PRES[Length_of_mem-1]; |
| 377 |
save_R_PRES=R_PRES[Length_of_mem-1]; |
| 378 |
save_XPRES=X_PRES[Length_of_mem-1]; |
| 379 |
save_P_PRES=P_PRES[Length_of_mem-1]; |
| 380 |
for (i=Length_of_mem-1;i>0;--i) { |
| 381 |
BREAKF[i]=BREAKF[i-1]; |
| 382 |
R_PRES_dot_P_PRES[i]=R_PRES_dot_P_PRES[i-1]; |
| 383 |
R_PRES[i]=R_PRES[i-1]; |
| 384 |
X_PRES[i]=X_PRES[i-1]; |
| 385 |
P_PRES[i]=P_PRES[i-1]; |
| 386 |
} |
| 387 |
R_PRES_dot_P_PRES[0]=save_R_PRES_dot_P_PRES; |
| 388 |
R_PRES[0]=save_R_PRES; |
| 389 |
X_PRES[0]=save_XPRES; |
| 390 |
P_PRES[0]=save_P_PRES; |
| 391 |
|
| 392 |
if (ABS(Factor)<=ZERO) { |
| 393 |
Factor=1.; |
| 394 |
BREAKF[0]=ZERO; |
| 395 |
} else { |
| 396 |
Factor=1./Factor; |
| 397 |
BREAKF[0]=ONE; |
| 398 |
} |
| 399 |
for (i=0;i<order;++i) ALPHA[i]*=Factor; |
| 400 |
} |
| 401 |
/* |
| 402 |
***** update of solution X_PRES and its residual R_PRES: |
| 403 |
*** |
| 404 |
*** P is used to accumulate X and AP to accumulate R. X and R |
| 405 |
*** are still needed until they are put into the X and R memory |
| 406 |
*** R_PRES and X_PRES |
| 407 |
*** |
| 408 |
**/ |
| 409 |
#pragma omp barrier |
| 410 |
breakf0=BREAKF[0]; |
| 411 |
if (order==0) { |
| 412 |
#pragma omp for private(z) schedule(static) |
| 413 |
for (z=0;z<n;++z) { |
| 414 |
R_PRES[0][z]= Factor* AP[z]; |
| 415 |
X_PRES[0][z]=-Factor*P_PRES[1][z]; |
| 416 |
} |
| 417 |
} else if (order==1) { |
| 418 |
#pragma omp for private(z) schedule(static) |
| 419 |
for (z=0;z<n;++z) { |
| 420 |
R_PRES[0][z]= Factor* AP[z]+ALPHA[0]*R_PRES[1][z]; |
| 421 |
X_PRES[0][z]=-Factor*P_PRES[1][z]+ALPHA[0]*X_PRES[1][z]; |
| 422 |
} |
| 423 |
} else if (order==2) { |
| 424 |
#pragma omp for private(z) schedule(static) |
| 425 |
for (z=0;z<n;++z) { |
| 426 |
R_PRES[0][z]= Factor* AP[z]+ALPHA[0]*R_PRES[1][z] |
| 427 |
+ALPHA[1]*R_PRES[2][z]; |
| 428 |
X_PRES[0][z]=-Factor*P_PRES[1][z]+ALPHA[0]*X_PRES[1][z] |
| 429 |
+ALPHA[1]*X_PRES[2][z]; |
| 430 |
} |
| 431 |
} else if (order==3) { |
| 432 |
#pragma omp for private(z) schedule(static) |
| 433 |
for (z=0;z<n;++z) { |
| 434 |
R_PRES[0][z]= Factor*AP[z]+ALPHA[0]*R_PRES[1][z] |
| 435 |
+ALPHA[1]*R_PRES[2][z] |
| 436 |
+ALPHA[2]*R_PRES[3][z]; |
| 437 |
X_PRES[0][z]=-Factor*P_PRES[1][z]+ALPHA[0]*X_PRES[1][z] |
| 438 |
+ALPHA[1]*X_PRES[2][z] |
| 439 |
+ALPHA[2]*X_PRES[3][z]; |
| 440 |
} |
| 441 |
} else if (order==4) { |
| 442 |
#pragma omp for private(z) schedule(static) |
| 443 |
for (z=0;z<n;++z) { |
| 444 |
R_PRES[0][z]= Factor*AP[z]+ALPHA[0]*R_PRES[1][z] |
| 445 |
+ALPHA[1]*R_PRES[2][z] |
| 446 |
+ALPHA[2]*R_PRES[3][z] |
| 447 |
+ALPHA[3]*R_PRES[4][z]; |
| 448 |
X_PRES[0][z]=-Factor*P_PRES[1][z]+ALPHA[0]*X_PRES[1][z] |
| 449 |
+ALPHA[1]*X_PRES[2][z] |
| 450 |
+ALPHA[2]*X_PRES[3][z] |
| 451 |
+ALPHA[3]*X_PRES[4][z]; |
| 452 |
} |
| 453 |
} else if (order==5) { |
| 454 |
#pragma omp for private(z) schedule(static) |
| 455 |
for (z=0;z<n;++z) { |
| 456 |
R_PRES[0][z]=Factor*AP[z]+ALPHA[0]*R_PRES[1][z] |
| 457 |
+ALPHA[1]*R_PRES[2][z] |
| 458 |
+ALPHA[2]*R_PRES[3][z] |
| 459 |
+ALPHA[3]*R_PRES[4][z] |
| 460 |
+ALPHA[4]*R_PRES[5][z]; |
| 461 |
X_PRES[0][z]=-Factor*P_PRES[1][z]+ALPHA[0]*X_PRES[1][z] |
| 462 |
+ALPHA[1]*X_PRES[2][z] |
| 463 |
+ALPHA[2]*X_PRES[3][z] |
| 464 |
+ALPHA[3]*X_PRES[4][z] |
| 465 |
+ALPHA[4]*X_PRES[5][z]; |
| 466 |
} |
| 467 |
} else if (order==6) { |
| 468 |
#pragma omp for private(z) schedule(static) |
| 469 |
for (z=0;z<n;++z) { |
| 470 |
R_PRES[0][z]=Factor*AP[z]+ALPHA[0]*R_PRES[1][z] |
| 471 |
+ALPHA[1]*R_PRES[2][z] |
| 472 |
+ALPHA[2]*R_PRES[3][z] |
| 473 |
+ALPHA[3]*R_PRES[4][z] |
| 474 |
+ALPHA[4]*R_PRES[5][z] |
| 475 |
+ALPHA[5]*R_PRES[6][z]; |
| 476 |
X_PRES[0][z]=-Factor*P_PRES[1][z]+ALPHA[0]*X_PRES[1][z] |
| 477 |
+ALPHA[1]*X_PRES[2][z] |
| 478 |
+ALPHA[2]*X_PRES[3][z] |
| 479 |
+ALPHA[3]*X_PRES[4][z] |
| 480 |
+ALPHA[4]*X_PRES[5][z] |
| 481 |
+ALPHA[5]*X_PRES[6][z]; |
| 482 |
} |
| 483 |
} else if (order>6) { |
| 484 |
#pragma omp for private(z) schedule(static) |
| 485 |
for (z=0;z<n;++z) { |
| 486 |
R_PRES[0][z]=Factor*AP[z]+ALPHA[0]*R_PRES[1][z] |
| 487 |
+ALPHA[1]*R_PRES[2][z] |
| 488 |
+ALPHA[2]*R_PRES[3][z] |
| 489 |
+ALPHA[3]*R_PRES[4][z] |
| 490 |
+ALPHA[4]*R_PRES[5][z] |
| 491 |
+ALPHA[5]*R_PRES[6][z] |
| 492 |
+ALPHA[6]*R_PRES[7][z]; |
| 493 |
X_PRES[0][z]=-Factor*P_PRES[1][z]+ALPHA[0]*X_PRES[1][z] |
| 494 |
+ALPHA[1]*X_PRES[2][z] |
| 495 |
+ALPHA[2]*X_PRES[3][z] |
| 496 |
+ALPHA[3]*X_PRES[4][z] |
| 497 |
+ALPHA[4]*X_PRES[5][z] |
| 498 |
+ALPHA[5]*X_PRES[6][z] |
| 499 |
+ALPHA[6]*X_PRES[7][z]; |
| 500 |
} |
| 501 |
for (i=7;i<order;++i) { |
| 502 |
#pragma omp for private(z) schedule(static) |
| 503 |
for (z=0;z<n;++z) { |
| 504 |
R_PRES[0][z]+=ALPHA[i]*R_PRES[i+1][z]; |
| 505 |
X_PRES[0][z]+=ALPHA[i]*X_PRES[i+1][z]; |
| 506 |
} |
| 507 |
} |
| 508 |
} |
| 509 |
if (breakf0>0.) { |
| 510 |
/*** |
| 511 |
***** calculate gamma from min_(gamma){|R+gamma*(R_PRES-R)|_2}: |
| 512 |
***/ |
| 513 |
#pragma omp master |
| 514 |
{ |
| 515 |
SC1=ZERO; |
| 516 |
SC2=ZERO; |
| 517 |
L2_R=ZERO; |
| 518 |
} |
| 519 |
#pragma omp barrier |
| 520 |
#pragma omp for private(z,diff) reduction(+:SC1,SC2) schedule(static) |
| 521 |
for (z=0;z<n;++z) { |
| 522 |
diff=R_PRES[0][z]-r[z]; |
| 523 |
SC1+=diff*diff; |
| 524 |
SC2+=diff*r[z]; |
| 525 |
} |
| 526 |
gamma=(SC1<=ZERO) ? ZERO : -SC2/SC1; |
| 527 |
#pragma omp for private(z) reduction(+:L2_R) schedule(static) |
| 528 |
for (z=0;z<n;++z) { |
| 529 |
x[z]+=gamma*(X_PRES[0][z]-x[z]); |
| 530 |
r[z]+=gamma*(R_PRES[0][z]-r[z]); |
| 531 |
L2_R+=r[z]*r[z]; |
| 532 |
} |
| 533 |
norm_of_residual=sqrt(L2_R); |
| 534 |
convergeFlag = (norm_of_residual <= tol); |
| 535 |
if (restart>0) restartFlag=(num_iter_restart >= restart); |
| 536 |
} else { |
| 537 |
convergeFlag=FALSE; |
| 538 |
restartFlag=FALSE; |
| 539 |
} |
| 540 |
maxIterFlag = (num_iter >= maxit); |
| 541 |
} |
| 542 |
} |
| 543 |
/* end of iteration */ |
| 544 |
#pragma omp master |
| 545 |
{ |
| 546 |
Norm_of_residual_global=norm_of_residual; |
| 547 |
Num_iter_global=num_iter; |
| 548 |
if (maxIterFlag) { |
| 549 |
Status = SOLVER_MAXITER_REACHED; |
| 550 |
} else if (breakFlag) { |
| 551 |
Status = SOLVER_BREAKDOWN; |
| 552 |
} |
| 553 |
} |
| 554 |
} /* end of parallel region */ |
| 555 |
TMPMEMFREE(AP); |
| 556 |
for (i=0;i<Length_of_recursion;i++) { |
| 557 |
TMPMEMFREE(X_PRES[i]); |
| 558 |
TMPMEMFREE(R_PRES[i]); |
| 559 |
TMPMEMFREE(P_PRES[i]); |
| 560 |
} |
| 561 |
*iter=Num_iter_global; |
| 562 |
*tolerance=Norm_of_residual_global; |
| 563 |
} |
| 564 |
return Status; |
| 565 |
} |
| 566 |
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