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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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* Purpose |
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* ======= |
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* |
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* GMRES solves the linear system A*x=b using the |
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* truncated and restered GMRES method with preconditioning. |
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* |
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* Convergence test: norm( b - A*x )< TOL. |
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* |
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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 |
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* |
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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. |
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* |
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* tolerance (input/output) DOUBLE PRECISION |
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* On input, the allowable convergence measure for |
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* 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 |
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* |
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* ============================================================== |
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*/ |
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|
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#include "Common.h" |
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#include "SystemMatrix.h" |
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#include "Solver.h" |
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#ifdef _OPENMP |
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#include <omp.h> |
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#endif |
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|
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err_t Paso_Solver_GMRES( |
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Paso_SystemMatrix * A, |
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double * r, |
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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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Paso_Performance* pp) { |
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|
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/* Local variables */ |
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|
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#ifdef _OPENMP |
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const int num_threads=omp_get_max_threads(); |
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#else |
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const int num_threads=1; |
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#endif |
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double *AP,**X_PRES,**R_PRES,**P_PRES, *dots, *loc_dots; |
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double *P_PRES_dot_AP,*R_PRES_dot_P_PRES,*BREAKF,*ALPHA; |
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double R_PRES_dot_AP0,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,breakf0; |
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double tol,Factor,sum_BREAKF,gamma,SC1,SC2,norm_of_residual=0,diff,L2_R,Norm_of_residual_global=0; |
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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=0,num_iter_restart=0,num_iter; |
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dim_t i,z,order,n, Length_of_mem, th, local_n , rest, n_start ,n_end; |
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bool_t breakFlag=FALSE, maxIterFlag=FALSE, convergeFlag=FALSE,restartFlag=FALSE; |
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err_t Status=SOLVER_NO_ERROR; |
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|
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|
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/* adapt original routine parameters */ |
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n = Paso_SystemMatrix_getTotalNumRows(A); |
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Length_of_mem=MAX(Length_of_recursion,0)+1; |
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|
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/* Test the input parameters. */ |
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if (restart>0) restart=MAX(Length_of_recursion,restart); |
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if (n < 0 || Length_of_recursion<=0) { |
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return SOLVER_INPUT_ERROR; |
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} |
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|
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/* allocate memory: */ |
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X_PRES=TMPMEMALLOC(Length_of_mem,double*); |
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R_PRES=TMPMEMALLOC(Length_of_mem,double*); |
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P_PRES=TMPMEMALLOC(Length_of_mem,double*); |
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loc_dots=TMPMEMALLOC(MAX(Length_of_mem+1,3),double); |
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dots=TMPMEMALLOC(MAX(Length_of_mem+1,3),double); |
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P_PRES_dot_AP=TMPMEMALLOC(Length_of_mem,double); |
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R_PRES_dot_P_PRES=TMPMEMALLOC(Length_of_mem,double); |
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BREAKF=TMPMEMALLOC(Length_of_mem,double); |
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ALPHA=TMPMEMALLOC(Length_of_mem,double); |
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AP=TMPMEMALLOC(n,double); |
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if (AP==NULL || X_PRES ==NULL || R_PRES == NULL || P_PRES == NULL || |
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P_PRES_dot_AP == NULL || R_PRES_dot_P_PRES ==NULL || BREAKF == NULL || ALPHA == NULL || dots==NULL || loc_dots==NULL) { |
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Status=SOLVER_MEMORY_ERROR; |
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} else { |
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for (i=0;i<Length_of_mem;i++) { |
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X_PRES[i]=TMPMEMALLOC(n,double); |
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R_PRES[i]=TMPMEMALLOC(n,double); |
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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; |
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} |
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} |
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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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/* initialization */ |
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|
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restartFlag=TRUE; |
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num_iter=0; |
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|
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#pragma omp parallel for private(th,z,i,local_n, rest, n_start, n_end) |
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for (th=0;th<num_threads;++th) { |
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local_n=n/num_threads; |
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rest=n-local_n*num_threads; |
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n_start=local_n*th+MIN(th,rest); |
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n_end=local_n*(th+1)+MIN(th+1,rest); |
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memset(&AP[n_start],0,sizeof(double)*(n_end-n_start)); |
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for(i=0;i<Length_of_mem;++i) { |
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memset(&P_PRES[i][n_start],0,sizeof(double)*(n_end-n_start)); |
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memset(&R_PRES[i][n_start],0,sizeof(double)*(n_end-n_start)); |
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memset(&X_PRES[i][n_start],0,sizeof(double)*(n_end-n_start)); |
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} |
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} |
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|
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while (! (convergeFlag || maxIterFlag || breakFlag)) { |
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if (restartFlag) { |
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BREAKF[0]=PASO_ONE; |
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#pragma omp parallel for private(th,z, local_n, rest, n_start, n_end) |
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for (th=0;th<num_threads;++th) { |
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local_n=n/num_threads; |
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rest=n-local_n*num_threads; |
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n_start=local_n*th+MIN(th,rest); |
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n_end=local_n*(th+1)+MIN(th+1,rest); |
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memcpy(&R_PRES[0][n_start],&r[n_start],sizeof(double)*(n_end-n_start)); |
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memcpy(&X_PRES[0][n_start],&x[n_start],sizeof(double)*(n_end-n_start)); |
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} |
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num_iter_restart=0; |
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restartFlag=FALSE; |
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} |
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++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: */ |
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order=MIN(num_iter_restart,Length_of_recursion); |
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/*** |
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*** calculate new search direction P from R_PRES |
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***/ |
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Paso_Solver_solvePreconditioner(A,&P_PRES[0][0], &R_PRES[0][0]); |
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/*** |
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*** apply A to P to get AP |
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***/ |
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Paso_SystemMatrix_MatrixVector_CSR_OFFSET0(PASO_ONE, A, &P_PRES[0][0],PASO_ZERO, &AP[0]); |
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/*** |
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***** calculation of the norm of R and the scalar products of |
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*** the residuals and A*P: |
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***/ |
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memset(loc_dots,0,sizeof(double)*(order+1)); |
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#pragma omp parallel for private(th,z,i,local_n, rest, n_start, n_end, 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) |
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for (th=0;th<num_threads;++th) { |
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local_n=n/num_threads; |
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rest=n-local_n*num_threads; |
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n_start=local_n*th+MIN(th,rest); |
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n_end=local_n*(th+1)+MIN(th+1,rest); |
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if (order==0) { |
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R_PRES_dot_P=PASO_ZERO; |
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#pragma ivdep |
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for (z=n_start; z < n_end; ++z) { |
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R_PRES_dot_P+=R_PRES[0][z]*P_PRES[0][z]; |
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} |
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#pragma omp critical |
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{ |
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loc_dots[0]+=R_PRES_dot_P; |
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} |
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} else if (order==1) { |
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R_PRES_dot_P=PASO_ZERO; |
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P_PRES_dot_AP0=PASO_ZERO; |
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#pragma ivdep |
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for (z=n_start; z < n_end; ++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 critical |
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{ |
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loc_dots[0]+=R_PRES_dot_P; |
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loc_dots[1]+=P_PRES_dot_AP0; |
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} |
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} else if (order==2) { |
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R_PRES_dot_P=PASO_ZERO; |
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P_PRES_dot_AP0=PASO_ZERO; |
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P_PRES_dot_AP1=PASO_ZERO; |
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#pragma ivdep |
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for (z=n_start; z < n_end; ++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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} |
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#pragma omp critical |
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{ |
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loc_dots[0]+=R_PRES_dot_P; |
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loc_dots[1]+=P_PRES_dot_AP0; |
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loc_dots[2]+=P_PRES_dot_AP1; |
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} |
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} else if (order==3) { |
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R_PRES_dot_P=PASO_ZERO; |
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P_PRES_dot_AP0=PASO_ZERO; |
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P_PRES_dot_AP1=PASO_ZERO; |
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P_PRES_dot_AP2=PASO_ZERO; |
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#pragma ivdep |
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for (z=n_start; z < n_end; ++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 critical |
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{ |
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loc_dots[0]+=R_PRES_dot_P; |
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loc_dots[1]+=P_PRES_dot_AP0; |
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loc_dots[2]+=P_PRES_dot_AP1; |
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loc_dots[3]+=P_PRES_dot_AP2; |
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} |
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} else if (order==4) { |
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R_PRES_dot_P=PASO_ZERO; |
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P_PRES_dot_AP0=PASO_ZERO; |
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P_PRES_dot_AP1=PASO_ZERO; |
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P_PRES_dot_AP2=PASO_ZERO; |
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P_PRES_dot_AP3=PASO_ZERO; |
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#pragma ivdep |
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for (z=n_start; z < n_end; ++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]; |
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} |
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#pragma omp critical |
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{ |
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loc_dots[0]+=R_PRES_dot_P; |
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loc_dots[1]+=P_PRES_dot_AP0; |
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loc_dots[2]+=P_PRES_dot_AP1; |
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loc_dots[3]+=P_PRES_dot_AP2; |
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loc_dots[4]+=P_PRES_dot_AP3; |
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} |
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} else if (order==5) { |
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R_PRES_dot_P=PASO_ZERO; |
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P_PRES_dot_AP0=PASO_ZERO; |
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P_PRES_dot_AP1=PASO_ZERO; |
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P_PRES_dot_AP2=PASO_ZERO; |
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P_PRES_dot_AP3=PASO_ZERO; |
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P_PRES_dot_AP4=PASO_ZERO; |
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#pragma ivdep |
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for (z=n_start; z < n_end; ++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]; |
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P_PRES_dot_AP4+=P_PRES[4][z]*AP[z]; |
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} |
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#pragma omp critical |
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{ |
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loc_dots[0]+=R_PRES_dot_P; |
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loc_dots[1]+=P_PRES_dot_AP0; |
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loc_dots[2]+=P_PRES_dot_AP1; |
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loc_dots[3]+=P_PRES_dot_AP2; |
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loc_dots[4]+=P_PRES_dot_AP3; |
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loc_dots[5]+=P_PRES_dot_AP4; |
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} |
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} else if (order==6) { |
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R_PRES_dot_P=PASO_ZERO; |
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P_PRES_dot_AP0=PASO_ZERO; |
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P_PRES_dot_AP1=PASO_ZERO; |
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P_PRES_dot_AP2=PASO_ZERO; |
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P_PRES_dot_AP3=PASO_ZERO; |
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P_PRES_dot_AP4=PASO_ZERO; |
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P_PRES_dot_AP5=PASO_ZERO; |
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#pragma ivdep |
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for (z=n_start; z < n_end; ++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]; |
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P_PRES_dot_AP4+=P_PRES[4][z]*AP[z]; |
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P_PRES_dot_AP5+=P_PRES[5][z]*AP[z]; |
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} |
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#pragma omp critical |
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{ |
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loc_dots[0]+=R_PRES_dot_P; |
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loc_dots[1]+=P_PRES_dot_AP0; |
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loc_dots[2]+=P_PRES_dot_AP1; |
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loc_dots[3]+=P_PRES_dot_AP2; |
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loc_dots[4]+=P_PRES_dot_AP3; |
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loc_dots[5]+=P_PRES_dot_AP4; |
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loc_dots[6]+=P_PRES_dot_AP5; |
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} |
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} else { |
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R_PRES_dot_P=PASO_ZERO; |
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P_PRES_dot_AP0=PASO_ZERO; |
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P_PRES_dot_AP1=PASO_ZERO; |
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P_PRES_dot_AP2=PASO_ZERO; |
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P_PRES_dot_AP3=PASO_ZERO; |
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P_PRES_dot_AP4=PASO_ZERO; |
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P_PRES_dot_AP5=PASO_ZERO; |
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P_PRES_dot_AP6=PASO_ZERO; |
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#pragma ivdep |
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for (z=n_start; z < n_end; ++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]; |
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P_PRES_dot_AP4+=P_PRES[4][z]*AP[z]; |
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P_PRES_dot_AP5+=P_PRES[5][z]*AP[z]; |
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P_PRES_dot_AP6+=P_PRES[6][z]*AP[z]; |
| 339 |
} |
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#pragma omp critical |
| 341 |
{ |
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loc_dots[0]+=R_PRES_dot_P; |
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loc_dots[1]+=P_PRES_dot_AP0; |
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loc_dots[2]+=P_PRES_dot_AP1; |
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loc_dots[3]+=P_PRES_dot_AP2; |
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loc_dots[4]+=P_PRES_dot_AP3; |
| 347 |
loc_dots[5]+=P_PRES_dot_AP4; |
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loc_dots[6]+=P_PRES_dot_AP5; |
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loc_dots[7]+=P_PRES_dot_AP6; |
| 350 |
} |
| 351 |
for (i=7;i<order;++i) { |
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P_PRES_dot_AP0=PASO_ZERO; |
| 353 |
#pragma ivdep |
| 354 |
for (z=n_start; z < n_end; ++z) { |
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P_PRES_dot_AP0+=P_PRES[i][z]*AP[z]; |
| 356 |
} |
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#pragma omp critical |
| 358 |
{ |
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loc_dots[i+1]+=P_PRES_dot_AP0; |
| 360 |
} |
| 361 |
} |
| 362 |
} |
| 363 |
} |
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#ifdef PASO_MPI |
| 365 |
MPI_Allreduce(loc_dots, dots, order+1, MPI_DOUBLE, MPI_SUM, A->mpi_info->comm); |
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R_PRES_dot_P_PRES[0]=dots[0]; |
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memcpy(P_PRES_dot_AP,&dots[1],sizeof(double)*order); |
| 368 |
#else |
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R_PRES_dot_P_PRES[0]=loc_dots[0]; |
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memcpy(P_PRES_dot_AP,&loc_dots[1],sizeof(double)*order); |
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#endif |
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R_PRES_dot_AP0=R_PRES_dot_P_PRES[0]; |
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/*** if sum_BREAKF is equal to zero a breakdown occurs. |
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*** iteration procedure can be continued but R_PRES is not the |
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*** residual of X_PRES approximation. |
| 376 |
***/ |
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sum_BREAKF=0.; |
| 378 |
#pragma ivdep |
| 379 |
for (i=0;i<order;++i) sum_BREAKF +=BREAKF[i]; |
| 380 |
breakFlag=!((ABS(R_PRES_dot_AP0) > PASO_ZERO) && (sum_BREAKF >PASO_ZERO)); |
| 381 |
if (!breakFlag) { |
| 382 |
breakFlag=FALSE; |
| 383 |
/*** |
| 384 |
***** X_PRES and R_PRES are moved to memory: |
| 385 |
***/ |
| 386 |
Factor=0.; |
| 387 |
#pragma ivdep |
| 388 |
for (i=0;i<order;++i) { |
| 389 |
ALPHA[i]=-P_PRES_dot_AP[i]/R_PRES_dot_P_PRES[i]; |
| 390 |
Factor+=BREAKF[i]*ALPHA[i]; |
| 391 |
} |
| 392 |
|
| 393 |
save_R_PRES_dot_P_PRES=R_PRES_dot_P_PRES[Length_of_mem-1]; |
| 394 |
save_R_PRES=R_PRES[Length_of_mem-1]; |
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save_XPRES=X_PRES[Length_of_mem-1]; |
| 396 |
save_P_PRES=P_PRES[Length_of_mem-1]; |
| 397 |
#pragma ivdep |
| 398 |
for (i=Length_of_mem-1;i>0;--i) { |
| 399 |
BREAKF[i]=BREAKF[i-1]; |
| 400 |
R_PRES_dot_P_PRES[i]=R_PRES_dot_P_PRES[i-1]; |
| 401 |
R_PRES[i]=R_PRES[i-1]; |
| 402 |
X_PRES[i]=X_PRES[i-1]; |
| 403 |
P_PRES[i]=P_PRES[i-1]; |
| 404 |
} |
| 405 |
R_PRES_dot_P_PRES[0]=save_R_PRES_dot_P_PRES; |
| 406 |
R_PRES[0]=save_R_PRES; |
| 407 |
X_PRES[0]=save_XPRES; |
| 408 |
P_PRES[0]=save_P_PRES; |
| 409 |
|
| 410 |
if (ABS(Factor)<=PASO_ZERO) { |
| 411 |
Factor=1.; |
| 412 |
BREAKF[0]=PASO_ZERO; |
| 413 |
} else { |
| 414 |
Factor=1./Factor; |
| 415 |
BREAKF[0]=PASO_ONE; |
| 416 |
} |
| 417 |
for (i=0;i<order;++i) ALPHA[i]*=Factor; |
| 418 |
/* |
| 419 |
***** update of solution X_PRES and its residual R_PRES: |
| 420 |
*** |
| 421 |
*** P is used to accumulate X and AP to accumulate R. X and R |
| 422 |
*** are still needed until they are put into the X and R memory |
| 423 |
*** R_PRES and X_PRES |
| 424 |
*** |
| 425 |
**/ |
| 426 |
breakf0=BREAKF[0]; |
| 427 |
#pragma omp parallel for private(th,z,i,local_n, rest, n_start, n_end) |
| 428 |
for (th=0;th<num_threads;++th) { |
| 429 |
local_n=n/num_threads; |
| 430 |
rest=n-local_n*num_threads; |
| 431 |
n_start=local_n*th+MIN(th,rest); |
| 432 |
n_end=local_n*(th+1)+MIN(th+1,rest); |
| 433 |
if (order==0) { |
| 434 |
#pragma ivdep |
| 435 |
for (z=n_start; z < n_end; ++z) { |
| 436 |
R_PRES[0][z]= Factor* AP[z]; |
| 437 |
X_PRES[0][z]=-Factor*P_PRES[1][z]; |
| 438 |
} |
| 439 |
} else if (order==1) { |
| 440 |
#pragma ivdep |
| 441 |
for (z=n_start; z < n_end; ++z) { |
| 442 |
R_PRES[0][z]= Factor* AP[z]+ALPHA[0]*R_PRES[1][z]; |
| 443 |
X_PRES[0][z]=-Factor*P_PRES[1][z]+ALPHA[0]*X_PRES[1][z]; |
| 444 |
} |
| 445 |
} else if (order==2) { |
| 446 |
#pragma ivdep |
| 447 |
for (z=n_start; z < n_end; ++z) { |
| 448 |
R_PRES[0][z]= Factor* AP[z]+ALPHA[0]*R_PRES[1][z] |
| 449 |
+ALPHA[1]*R_PRES[2][z]; |
| 450 |
X_PRES[0][z]=-Factor*P_PRES[1][z]+ALPHA[0]*X_PRES[1][z] |
| 451 |
+ALPHA[1]*X_PRES[2][z]; |
| 452 |
} |
| 453 |
} else if (order==3) { |
| 454 |
#pragma ivdep |
| 455 |
for (z=n_start; z < n_end; ++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 |
X_PRES[0][z]=-Factor*P_PRES[1][z]+ALPHA[0]*X_PRES[1][z] |
| 460 |
+ALPHA[1]*X_PRES[2][z] |
| 461 |
+ALPHA[2]*X_PRES[3][z]; |
| 462 |
} |
| 463 |
} else if (order==4) { |
| 464 |
#pragma ivdep |
| 465 |
for (z=n_start; z < n_end; ++z) { |
| 466 |
R_PRES[0][z]= Factor*AP[z]+ALPHA[0]*R_PRES[1][z] |
| 467 |
+ALPHA[1]*R_PRES[2][z] |
| 468 |
+ALPHA[2]*R_PRES[3][z] |
| 469 |
+ALPHA[3]*R_PRES[4][z]; |
| 470 |
X_PRES[0][z]=-Factor*P_PRES[1][z]+ALPHA[0]*X_PRES[1][z] |
| 471 |
+ALPHA[1]*X_PRES[2][z] |
| 472 |
+ALPHA[2]*X_PRES[3][z] |
| 473 |
+ALPHA[3]*X_PRES[4][z]; |
| 474 |
} |
| 475 |
} else if (order==5) { |
| 476 |
#pragma ivdep |
| 477 |
for (z=n_start; z < n_end; ++z) { |
| 478 |
R_PRES[0][z]=Factor*AP[z]+ALPHA[0]*R_PRES[1][z] |
| 479 |
+ALPHA[1]*R_PRES[2][z] |
| 480 |
+ALPHA[2]*R_PRES[3][z] |
| 481 |
+ALPHA[3]*R_PRES[4][z] |
| 482 |
+ALPHA[4]*R_PRES[5][z]; |
| 483 |
X_PRES[0][z]=-Factor*P_PRES[1][z]+ALPHA[0]*X_PRES[1][z] |
| 484 |
+ALPHA[1]*X_PRES[2][z] |
| 485 |
+ALPHA[2]*X_PRES[3][z] |
| 486 |
+ALPHA[3]*X_PRES[4][z] |
| 487 |
+ALPHA[4]*X_PRES[5][z]; |
| 488 |
} |
| 489 |
} else if (order==6) { |
| 490 |
#pragma ivdep |
| 491 |
for (z=n_start; z < n_end; ++z) { |
| 492 |
R_PRES[0][z]=Factor*AP[z]+ALPHA[0]*R_PRES[1][z] |
| 493 |
+ALPHA[1]*R_PRES[2][z] |
| 494 |
+ALPHA[2]*R_PRES[3][z] |
| 495 |
+ALPHA[3]*R_PRES[4][z] |
| 496 |
+ALPHA[4]*R_PRES[5][z] |
| 497 |
+ALPHA[5]*R_PRES[6][z]; |
| 498 |
X_PRES[0][z]=-Factor*P_PRES[1][z]+ALPHA[0]*X_PRES[1][z] |
| 499 |
+ALPHA[1]*X_PRES[2][z] |
| 500 |
+ALPHA[2]*X_PRES[3][z] |
| 501 |
+ALPHA[3]*X_PRES[4][z] |
| 502 |
+ALPHA[4]*X_PRES[5][z] |
| 503 |
+ALPHA[5]*X_PRES[6][z]; |
| 504 |
} |
| 505 |
} else { |
| 506 |
#pragma ivdep |
| 507 |
for (z=n_start; z < n_end; ++z) { |
| 508 |
R_PRES[0][z]=Factor*AP[z]+ALPHA[0]*R_PRES[1][z] |
| 509 |
+ALPHA[1]*R_PRES[2][z] |
| 510 |
+ALPHA[2]*R_PRES[3][z] |
| 511 |
+ALPHA[3]*R_PRES[4][z] |
| 512 |
+ALPHA[4]*R_PRES[5][z] |
| 513 |
+ALPHA[5]*R_PRES[6][z] |
| 514 |
+ALPHA[6]*R_PRES[7][z]; |
| 515 |
X_PRES[0][z]=-Factor*P_PRES[1][z]+ALPHA[0]*X_PRES[1][z] |
| 516 |
+ALPHA[1]*X_PRES[2][z] |
| 517 |
+ALPHA[2]*X_PRES[3][z] |
| 518 |
+ALPHA[3]*X_PRES[4][z] |
| 519 |
+ALPHA[4]*X_PRES[5][z] |
| 520 |
+ALPHA[5]*X_PRES[6][z] |
| 521 |
+ALPHA[6]*X_PRES[7][z]; |
| 522 |
} |
| 523 |
for (i=7;i<order;++i) { |
| 524 |
#pragma ivdep |
| 525 |
for (z=n_start; z < n_end; ++z) { |
| 526 |
R_PRES[0][z]+=ALPHA[i]*R_PRES[i+1][z]; |
| 527 |
X_PRES[0][z]+=ALPHA[i]*X_PRES[i+1][z]; |
| 528 |
} |
| 529 |
} |
| 530 |
} |
| 531 |
} |
| 532 |
if (breakf0>0.) { |
| 533 |
/*** |
| 534 |
***** calculate gamma from min_(gamma){|R+gamma*(R_PRES-R)|_2}: |
| 535 |
***/ |
| 536 |
memset(loc_dots,0,sizeof(double)*3); |
| 537 |
#pragma omp parallel for private(th,z,i,local_n, rest, n_start, n_end,diff,SC1,SC2) |
| 538 |
for (th=0;th<num_threads;++th) { |
| 539 |
local_n=n/num_threads; |
| 540 |
rest=n-local_n*num_threads; |
| 541 |
n_start=local_n*th+MIN(th,rest); |
| 542 |
n_end=local_n*(th+1)+MIN(th+1,rest); |
| 543 |
SC1=PASO_ZERO; |
| 544 |
SC2=PASO_ZERO; |
| 545 |
#pragma ivdep |
| 546 |
for (z=n_start; z < n_end; ++z) { |
| 547 |
diff=R_PRES[0][z]-r[z]; |
| 548 |
SC1+=diff*diff; |
| 549 |
SC2+=diff*r[z]; |
| 550 |
} |
| 551 |
#pragma omp critical |
| 552 |
{ |
| 553 |
loc_dots[0]+=SC1; |
| 554 |
loc_dots[1]+=SC2; |
| 555 |
} |
| 556 |
} |
| 557 |
#ifdef PASO_MPI |
| 558 |
MPI_Allreduce(loc_dots, dots, 2, MPI_DOUBLE, MPI_SUM, A->mpi_info->comm); |
| 559 |
SC1=dots[0]; |
| 560 |
SC2=dots[1]; |
| 561 |
#else |
| 562 |
SC1=loc_dots[0]; |
| 563 |
SC2=loc_dots[1]; |
| 564 |
#endif |
| 565 |
gamma=(SC1<=PASO_ZERO) ? PASO_ZERO : -SC2/SC1; |
| 566 |
#pragma omp parallel for private(th,z,local_n, rest, n_start, n_end,diff,L2_R) |
| 567 |
for (th=0;th<num_threads;++th) { |
| 568 |
local_n=n/num_threads; |
| 569 |
rest=n-local_n*num_threads; |
| 570 |
n_start=local_n*th+MIN(th,rest); |
| 571 |
n_end=local_n*(th+1)+MIN(th+1,rest); |
| 572 |
L2_R=PASO_ZERO; |
| 573 |
#pragma ivdep |
| 574 |
for (z=n_start; z < n_end; ++z) { |
| 575 |
x[z]+=gamma*(X_PRES[0][z]-x[z]); |
| 576 |
r[z]+=gamma*(R_PRES[0][z]-r[z]); |
| 577 |
L2_R+=r[z]*r[z]; |
| 578 |
} |
| 579 |
#pragma omp critical |
| 580 |
{ |
| 581 |
loc_dots[2]+=L2_R; |
| 582 |
} |
| 583 |
} |
| 584 |
#ifdef PASO_MPI |
| 585 |
MPI_Allreduce(&loc_dots[2], &dots[2], 1, MPI_DOUBLE, MPI_SUM, A->mpi_info->comm); |
| 586 |
L2_R=dots[2]; |
| 587 |
#else |
| 588 |
L2_R=loc_dots[2]; |
| 589 |
#endif |
| 590 |
norm_of_residual=sqrt(L2_R); |
| 591 |
convergeFlag = (norm_of_residual <= tol); |
| 592 |
if (restart>0) restartFlag=(num_iter_restart >= restart); |
| 593 |
} else { |
| 594 |
convergeFlag=FALSE; |
| 595 |
restartFlag=FALSE; |
| 596 |
} |
| 597 |
maxIterFlag = (num_iter >= maxit); |
| 598 |
} |
| 599 |
} |
| 600 |
/* end of iteration */ |
| 601 |
Norm_of_residual_global=norm_of_residual; |
| 602 |
Num_iter_global=num_iter; |
| 603 |
if (maxIterFlag) { |
| 604 |
Status = SOLVER_MAXITER_REACHED; |
| 605 |
} else if (breakFlag) { |
| 606 |
Status = SOLVER_BREAKDOWN; |
| 607 |
} |
| 608 |
} |
| 609 |
for (i=0;i<Length_of_recursion;i++) { |
| 610 |
TMPMEMFREE(X_PRES[i]); |
| 611 |
TMPMEMFREE(R_PRES[i]); |
| 612 |
TMPMEMFREE(P_PRES[i]); |
| 613 |
} |
| 614 |
TMPMEMFREE(AP); |
| 615 |
TMPMEMFREE(X_PRES); |
| 616 |
TMPMEMFREE(R_PRES); |
| 617 |
TMPMEMFREE(P_PRES); |
| 618 |
TMPMEMFREE(P_PRES_dot_AP); |
| 619 |
TMPMEMFREE(R_PRES_dot_P_PRES); |
| 620 |
TMPMEMFREE(BREAKF); |
| 621 |
TMPMEMFREE(ALPHA); |
| 622 |
TMPMEMFREE(dots); |
| 623 |
TMPMEMFREE(loc_dots); |
| 624 |
*iter=Num_iter_global; |
| 625 |
*tolerance=Norm_of_residual_global; |
| 626 |
return Status; |
| 627 |
} |
| 628 |
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