int main(int argc, char *argv[])
{
int num_PDE_eqns=1, N_levels=3, nsmooth=2;
int leng, level, N_grid_pts, coarsest_level;
int leng1,leng2;
/* See Aztec User's Guide for more information on the */
/* variables that follow. */
int proc_config[AZ_PROC_SIZE], options[AZ_OPTIONS_SIZE];
double params[AZ_PARAMS_SIZE], status[AZ_STATUS_SIZE];
/* data structure for matrix corresponding to the fine grid */
double *val = NULL, *xxx, *rhs, solve_time, setup_time, start_time;
AZ_MATRIX *Amat;
AZ_PRECOND *Pmat = NULL;
ML *ml;
FILE *fp;
int i, j, Nrigid, *garbage, nblocks=0, *blocks = NULL, *block_pde=NULL;
struct AZ_SCALING *scaling;
ML_Aggregate *ag;
double *mode, *rigid=NULL, alpha;
char filename[80];
int one = 1;
int proc,nprocs;
char pathfilename[100];
#ifdef ML_MPI
MPI_Init(&argc,&argv);
/* get number of processors and the name of this processor */
AZ_set_proc_config(proc_config, MPI_COMM_WORLD);
proc = proc_config[AZ_node];
nprocs = proc_config[AZ_N_procs];
#else
AZ_set_proc_config(proc_config, AZ_NOT_MPI);
proc = 0;
nprocs = 1;
#endif
if (proc_config[AZ_node] == 0) {
sprintf(pathfilename,"%s/inputfile",argv[1]);
ML_Reader_ReadInput(pathfilename, &context);
}
else context = (struct reader_context *) ML_allocate(sizeof(struct reader_context));
AZ_broadcast((char *) context, sizeof(struct reader_context), proc_config,
AZ_PACK);
AZ_broadcast((char *) NULL , 0 , proc_config, AZ_SEND);
N_levels = context->N_levels;
printf("N_levels %d\n",N_levels);
nsmooth = context->nsmooth;
num_PDE_eqns = context->N_dofPerNode;
printf("num_PDE_eqns %d\n",num_PDE_eqns);
ML_Set_PrintLevel(context->output_level);
/* read in the number of matrix equations */
leng = 0;
if (proc_config[AZ_node] == 0) {
sprintf(pathfilename,"%s/data_matrix.txt",argv[1]);
fp=fopen(pathfilename,"r");
if (fp==NULL) {
printf("**ERR** couldn't open file data_matrix.txt\n");
exit(1);
}
fscanf(fp,"%d",&leng);
fclose(fp);
}
leng = AZ_gsum_int(leng, proc_config);
N_grid_pts=leng/num_PDE_eqns;
/* initialize the list of global indices. NOTE: the list of global */
/* indices must be in ascending order so that subsequent calls to */
/* AZ_find_index() will function properly. */
#if 0
if (proc_config[AZ_N_procs] == 1) i = AZ_linear;
else i = AZ_file;
#endif
i = AZ_linear;
/* cannot use AZ_input_update for variable blocks (forgot why, but debugged through it)*/
/* make a linear distribution of the matrix */
/* if the linear distribution does not align with the blocks, */
/* this is corrected in ML_AZ_Reader_ReadVariableBlocks */
leng1 = leng/nprocs;
leng2 = leng-leng1*nprocs;
if (proc >= leng2)
{
leng2 += (proc*leng1);
}
else
{
leng1++;
leng2 = proc*leng1;
}
N_update = leng1;
update = (int*)AZ_allocate((N_update+1)*sizeof(int));
if (update==NULL)
{
(void) fprintf (stderr, "Not enough space to allocate 'update'\n");
fflush(stderr); exit(EXIT_FAILURE);
}
for (i=0; i<N_update; i++) update[i] = i+leng2;
#if 0 /* debug */
printf("proc %d N_update %d\n",proc_config[AZ_node],N_update);
fflush(stdout);
#endif
sprintf(pathfilename,"%s/data_vblocks.txt",argv[1]);
ML_AZ_Reader_ReadVariableBlocks(pathfilename,&nblocks,&blocks,&block_pde,
&N_update,&update,proc_config);
#if 0 /* debug */
printf("proc %d N_update %d\n",proc_config[AZ_node],N_update);
fflush(stdout);
#endif
sprintf(pathfilename,"%s/data_matrix.txt",argv[1]);
AZ_input_msr_matrix(pathfilename,update, &val, &bindx, N_update, proc_config);
/* This code is to fix things up so that we are sure we have */
/* all blocks (including the ghost nodes) the same size. */
/* not sure, whether this is a good idea with variable blocks */
/* the examples inpufiles (see top of this file) don't need it */
/* anyway */
/*
AZ_block_MSR(&bindx, &val, N_update, num_PDE_eqns, update);
*/
AZ_transform_norowreordering(proc_config, &external, bindx, val, update, &update_index,
&extern_index, &data_org, N_update, 0, 0, 0, &cpntr,
AZ_MSR_MATRIX);
Amat = AZ_matrix_create( leng );
AZ_set_MSR(Amat, bindx, val, data_org, 0, NULL, AZ_LOCAL);
Amat->matrix_type = data_org[AZ_matrix_type];
data_org[AZ_N_rows] = data_org[AZ_N_internal] + data_org[AZ_N_border];
start_time = AZ_second();
options[AZ_scaling] = AZ_none;
ML_Create(&ml, N_levels);
/* set up discretization matrix and matrix vector function */
AZ_ML_Set_Amat(ml, 0, N_update, N_update, Amat, proc_config);
ML_Set_ResidualOutputFrequency(ml, context->output);
ML_Set_Tolerance(ml, context->tol);
ML_Aggregate_Create( &ag );
if (ML_strcmp(context->agg_coarsen_scheme,"Mis") == 0) {
ML_Aggregate_Set_CoarsenScheme_MIS(ag);
}
else if (ML_strcmp(context->agg_coarsen_scheme,"Uncoupled") == 0) {
ML_Aggregate_Set_CoarsenScheme_Uncoupled(ag);
}
else if (ML_strcmp(context->agg_coarsen_scheme,"Coupled") == 0) {
ML_Aggregate_Set_CoarsenScheme_Coupled(ag);
}
else if (ML_strcmp(context->agg_coarsen_scheme,"Metis") == 0) {
ML_Aggregate_Set_CoarsenScheme_METIS(ag);
for (i=0; i<N_levels; i++)
ML_Aggregate_Set_NodesPerAggr(ml,ag,i,9);
}
else if (ML_strcmp(context->agg_coarsen_scheme,"VBMetis") == 0) {
/* when no blocks read, use standard metis assuming constant block sizes */
if (!blocks)
ML_Aggregate_Set_CoarsenScheme_METIS(ag);
else {
ML_Aggregate_Set_CoarsenScheme_VBMETIS(ag);
ML_Aggregate_Set_Vblocks_CoarsenScheme_VBMETIS(ag,0,N_levels,nblocks,
blocks,block_pde,N_update);
}
for (i=0; i<N_levels; i++)
ML_Aggregate_Set_NodesPerAggr(ml,ag,i,9);
}
else {
printf("**ERR** ML: Unknown aggregation scheme %s\n",context->agg_coarsen_scheme);
exit(-1);
}
ML_Aggregate_Set_DampingFactor(ag, context->agg_damping);
ML_Aggregate_Set_MaxCoarseSize( ag, context->maxcoarsesize);
ML_Aggregate_Set_Threshold(ag, context->agg_thresh);
if (ML_strcmp(context->agg_spectral_norm,"Calc") == 0) {
ML_Set_SpectralNormScheme_Calc(ml);
}
else if (ML_strcmp(context->agg_spectral_norm,"Anorm") == 0) {
ML_Set_SpectralNormScheme_Anorm(ml);
}
else {
printf("**WRN** ML: Unknown spectral norm scheme %s\n",context->agg_spectral_norm);
}
/* read in the rigid body modes */
Nrigid = 0;
if (proc_config[AZ_node] == 0) {
sprintf(filename,"data_nullsp%d.txt",Nrigid);
sprintf(pathfilename,"%s/%s",argv[1],filename);
while( (fp = fopen(pathfilename,"r")) != NULL) {
fclose(fp);
Nrigid++;
sprintf(filename,"data_nullsp%d.txt",Nrigid);
sprintf(pathfilename,"%s/%s",argv[1],filename);
}
}
Nrigid = AZ_gsum_int(Nrigid,proc_config);
if (Nrigid != 0) {
rigid = (double *) ML_allocate( sizeof(double)*Nrigid*(N_update+1) );
if (rigid == NULL) {
printf("Error: Not enough space for rigid body modes\n");
}
}
/* Set rhs */
sprintf(pathfilename,"%s/data_rhs.txt",argv[1]);
fp = fopen(pathfilename,"r");
if (fp == NULL) {
rhs=(double *)ML_allocate(leng*sizeof(double));
if (proc_config[AZ_node] == 0) printf("taking linear vector for rhs\n");
for (i = 0; i < N_update; i++) rhs[i] = (double) update[i];
}
else {
fclose(fp);
if (proc_config[AZ_node] == 0) printf("reading rhs from a file\n");
AZ_input_msr_matrix(pathfilename, update, &rhs, &garbage, N_update,
proc_config);
}
AZ_reorder_vec(rhs, data_org, update_index, NULL);
for (i = 0; i < Nrigid; i++) {
sprintf(filename,"data_nullsp%d.txt",i);
sprintf(pathfilename,"%s/%s",argv[1],filename);
AZ_input_msr_matrix(pathfilename, update, &mode, &garbage, N_update,
proc_config);
AZ_reorder_vec(mode, data_org, update_index, NULL);
#if 0 /* test the given rigid body mode, output-vector should be ~0 */
Amat->matvec(mode, rigid, Amat, proc_config);
for (j = 0; j < N_update; j++) printf("this is %d %e\n",j,rigid[j]);
#endif
for (j = 0; j < i; j++) {
alpha = -AZ_gdot(N_update, mode, &(rigid[j*N_update]), proc_config)/
AZ_gdot(N_update, &(rigid[j*N_update]), &(rigid[j*N_update]),
proc_config);
DAXPY_F77(&N_update, &alpha, &(rigid[j*N_update]), &one, mode, &one);
}
/* rhs orthogonalization */
alpha = -AZ_gdot(N_update, mode, rhs, proc_config)/
AZ_gdot(N_update, mode, mode, proc_config);
DAXPY_F77(&N_update, &alpha, mode, &one, rhs, &one);
for (j = 0; j < N_update; j++) rigid[i*N_update+j] = mode[j];
free(mode);
free(garbage);
}
for (j = 0; j < Nrigid; j++) {
alpha = -AZ_gdot(N_update, rhs, &(rigid[j*N_update]), proc_config)/
AZ_gdot(N_update, &(rigid[j*N_update]), &(rigid[j*N_update]),
proc_config);
DAXPY_F77(&N_update, &alpha, &(rigid[j*N_update]), &one, rhs, &one);
}
#if 0 /* for testing the default nullsp */
ML_Aggregate_Set_NullSpace(ag, num_PDE_eqns, 6, NULL, N_update);
#else
if (Nrigid != 0) {
ML_Aggregate_Set_NullSpace(ag, num_PDE_eqns, Nrigid, rigid, N_update);
}
#endif
if (rigid) ML_free(rigid);
ag->keep_agg_information = 1;
coarsest_level = ML_Gen_MGHierarchy_UsingAggregation(ml, 0,
ML_INCREASING, ag);
coarsest_level--;
if ( proc_config[AZ_node] == 0 )
printf("Coarse level = %d \n", coarsest_level);
#if 0
/* set up smoothers */
if (!blocks)
blocks = (int *) ML_allocate(sizeof(int)*N_update);
#endif
for (level = 0; level < coarsest_level; level++) {
num_PDE_eqns = ml->Amat[level].num_PDEs;
/* Sparse approximate inverse smoother that acutally does both */
/* pre and post smoothing. */
if (ML_strcmp(context->smoother,"Parasails") == 0) {
ML_Gen_Smoother_ParaSails(ml , level, ML_PRESMOOTHER, nsmooth,
parasails_sym, parasails_thresh,
parasails_nlevels, parasails_filter,
(int) parasails_loadbal, parasails_factorized);
}
/* This is the symmetric Gauss-Seidel smoothing that we usually use. */
/* In parallel, it is not a true Gauss-Seidel in that each processor */
/* does a Gauss-Seidel on its local submatrix independent of the */
/* other processors. */
else if (ML_strcmp(context->smoother,"GaussSeidel") == 0) {
ML_Gen_Smoother_GaussSeidel(ml , level, ML_BOTH, nsmooth,1.);
}
else if (ML_strcmp(context->smoother,"SymGaussSeidel") == 0) {
ML_Gen_Smoother_SymGaussSeidel(ml , level, ML_BOTH, nsmooth,1.);
}
else if (ML_strcmp(context->smoother,"Poly") == 0) {
ML_Gen_Smoother_Cheby(ml, level, ML_BOTH, 30., nsmooth);
}
else if (ML_strcmp(context->smoother,"BlockGaussSeidel") == 0) {
ML_Gen_Smoother_BlockGaussSeidel(ml , level, ML_BOTH, nsmooth,1.,
num_PDE_eqns);
}
else if (ML_strcmp(context->smoother,"VBSymGaussSeidel") == 0) {
if (blocks) ML_free(blocks);
if (block_pde) ML_free(block_pde);
blocks = NULL;
block_pde = NULL;
nblocks = 0;
ML_Aggregate_Get_Vblocks_CoarsenScheme_VBMETIS(ag,level,N_levels,&nblocks,
&blocks,&block_pde);
if (blocks==NULL) ML_Gen_Blocks_Aggregates(ag, level, &nblocks, &blocks);
ML_Gen_Smoother_VBlockSymGaussSeidel(ml , level, ML_BOTH, nsmooth,1.,
nblocks, blocks);
}
/* This is a true Gauss Seidel in parallel. This seems to work for */
/* elasticity problems. However, I don't believe that this is very */
/* efficient in parallel. */
/*
nblocks = ml->Amat[level].invec_leng;
for (i =0; i < nblocks; i++) blocks[i] = i;
ML_Gen_Smoother_VBlockSymGaussSeidelSequential(ml , level, ML_PRESMOOTHER,
nsmooth, 1., nblocks, blocks);
ML_Gen_Smoother_VBlockSymGaussSeidelSequential(ml, level, ML_POSTSMOOTHER,
nsmooth, 1., nblocks, blocks);
*/
/* Jacobi Smoothing */
else if (ML_strcmp(context->smoother,"Jacobi") == 0) {
ML_Gen_Smoother_Jacobi(ml , level, ML_PRESMOOTHER, nsmooth,.4);
ML_Gen_Smoother_Jacobi(ml , level, ML_POSTSMOOTHER, nsmooth,.4);
}
/* This does a block Gauss-Seidel (not true GS in parallel) */
/* where each processor has 'nblocks' blocks. */
/* */
else if (ML_strcmp(context->smoother,"Metis") == 0) {
if (blocks) ML_free(blocks);
if (block_pde) ML_free(block_pde);
nblocks = 250;
ML_Gen_Blocks_Metis(ml, level, &nblocks, &blocks);
ML_Gen_Smoother_VBlockSymGaussSeidel(ml , level, ML_BOTH, nsmooth,1.,
nblocks, blocks);
}
else {
printf("unknown smoother %s\n",context->smoother);
exit(1);
}
}
/* set coarse level solver */
nsmooth = context->coarse_its;
/* Sparse approximate inverse smoother that acutally does both */
/* pre and post smoothing. */
if (ML_strcmp(context->coarse_solve,"Parasails") == 0) {
ML_Gen_Smoother_ParaSails(ml , coarsest_level, ML_PRESMOOTHER, nsmooth,
parasails_sym, parasails_thresh,
parasails_nlevels, parasails_filter,
(int) parasails_loadbal, parasails_factorized);
}
else if (ML_strcmp(context->coarse_solve,"GaussSeidel") == 0) {
ML_Gen_Smoother_GaussSeidel(ml , coarsest_level, ML_BOTH, nsmooth,1.);
}
else if (ML_strcmp(context->coarse_solve,"Poly") == 0) {
ML_Gen_Smoother_Cheby(ml, coarsest_level, ML_BOTH, 30., nsmooth);
}
else if (ML_strcmp(context->coarse_solve,"SymGaussSeidel") == 0) {
ML_Gen_Smoother_SymGaussSeidel(ml , coarsest_level, ML_BOTH, nsmooth,1.);
}
else if (ML_strcmp(context->coarse_solve,"BlockGaussSeidel") == 0) {
ML_Gen_Smoother_BlockGaussSeidel(ml, coarsest_level, ML_BOTH, nsmooth,1.,
num_PDE_eqns);
}
else if (ML_strcmp(context->coarse_solve,"Aggregate") == 0) {
if (blocks) ML_free(blocks);
if (block_pde) ML_free(block_pde);
ML_Gen_Blocks_Aggregates(ag, coarsest_level, &nblocks, &blocks);
ML_Gen_Smoother_VBlockSymGaussSeidel(ml , coarsest_level, ML_BOTH,
nsmooth,1., nblocks, blocks);
}
else if (ML_strcmp(context->coarse_solve,"Jacobi") == 0) {
ML_Gen_Smoother_Jacobi(ml , coarsest_level, ML_BOTH, nsmooth,.5);
}
else if (ML_strcmp(context->coarse_solve,"Metis") == 0) {
if (blocks) ML_free(blocks);
if (block_pde) ML_free(block_pde);
nblocks = 250;
ML_Gen_Blocks_Metis(ml, coarsest_level, &nblocks, &blocks);
ML_Gen_Smoother_VBlockSymGaussSeidel(ml , coarsest_level, ML_BOTH,
nsmooth,1., nblocks, blocks);
}
else if (ML_strcmp(context->coarse_solve,"SuperLU") == 0) {
ML_Gen_CoarseSolverSuperLU( ml, coarsest_level);
}
else if (ML_strcmp(context->coarse_solve,"Amesos") == 0) {
ML_Gen_Smoother_Amesos(ml,coarsest_level,ML_AMESOS_KLU,-1, 0.0);
}
else {
printf("unknown coarse grid solver %s\n",context->coarse_solve);
exit(1);
}
ML_Gen_Solver(ml, ML_MGV, 0, coarsest_level);
AZ_defaults(options, params);
if (ML_strcmp(context->krylov,"Cg") == 0) {
options[AZ_solver] = AZ_cg;
}
else if (ML_strcmp(context->krylov,"Bicgstab") == 0) {
options[AZ_solver] = AZ_bicgstab;
}
else if (ML_strcmp(context->krylov,"Tfqmr") == 0) {
options[AZ_solver] = AZ_tfqmr;
}
else if (ML_strcmp(context->krylov,"Gmres") == 0) {
options[AZ_solver] = AZ_gmres;
}
else {
printf("unknown krylov method %s\n",context->krylov);
}
if (blocks) ML_free(blocks);
if (block_pde) ML_free(block_pde);
options[AZ_scaling] = AZ_none;
options[AZ_precond] = AZ_user_precond;
options[AZ_conv] = AZ_r0;
options[AZ_output] = 1;
options[AZ_max_iter] = context->max_outer_its;
options[AZ_poly_ord] = 5;
options[AZ_kspace] = 130;
params[AZ_tol] = context->tol;
options[AZ_output] = context->output;
ML_free(context);
AZ_set_ML_preconditioner(&Pmat, Amat, ml, options);
setup_time = AZ_second() - start_time;
xxx = (double *) malloc( leng*sizeof(double));
for (iii = 0; iii < leng; iii++) xxx[iii] = 0.0;
/* Set x */
/*
there is no initguess supplied with these examples for the moment....
*/
fp = fopen("initguessfile","r");
if (fp != NULL) {
fclose(fp);
if (proc_config[AZ_node]== 0) printf("reading initial guess from file\n");
AZ_input_msr_matrix("data_initguess.txt", update, &xxx, &garbage, N_update,
proc_config);
options[AZ_conv] = AZ_expected_values;
}
else if (proc_config[AZ_node]== 0) printf("taking 0 initial guess \n");
AZ_reorder_vec(xxx, data_org, update_index, NULL);
/* if Dirichlet BC ... put the answer in */
for (i = 0; i < data_org[AZ_N_internal]+data_org[AZ_N_border]; i++) {
if ( (val[i] > .99999999) && (val[i] < 1.0000001))
xxx[i] = rhs[i];
}
fp = fopen("AZ_no_multilevel.dat","r");
scaling = AZ_scaling_create();
start_time = AZ_second();
if (fp != NULL) {
fclose(fp);
options[AZ_precond] = AZ_none;
options[AZ_scaling] = AZ_sym_diag;
options[AZ_ignore_scaling] = AZ_TRUE;
options[AZ_keep_info] = 1;
AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, NULL, scaling);
/*
options[AZ_pre_calc] = AZ_reuse;
options[AZ_conv] = AZ_expected_values;
if (proc_config[AZ_node] == 0)
printf("\n-------- Second solve with improved convergence test -----\n");
AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, NULL, scaling);
if (proc_config[AZ_node] == 0)
printf("\n-------- Third solve with improved convergence test -----\n");
AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, NULL, scaling);
*/
}
else {
options[AZ_keep_info] = 1;
AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, Pmat, scaling);
options[AZ_pre_calc] = AZ_reuse;
options[AZ_conv] = AZ_expected_values;
/*
if (proc_config[AZ_node] == 0)
printf("\n-------- Second solve with improved convergence test -----\n");
AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, Pmat, scaling);
if (proc_config[AZ_node] == 0)
printf("\n-------- Third solve with improved convergence test -----\n");
AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, Pmat, scaling);
*/
}
solve_time = AZ_second() - start_time;
if (proc_config[AZ_node] == 0)
printf("Solve time = %e, MG Setup time = %e\n", solve_time, setup_time);
if (proc_config[AZ_node] == 0)
printf("Printing out a few entries of the solution ...\n");
for (j=0;j<Amat->data_org[AZ_N_internal]+ Amat->data_org[AZ_N_border];j++)
if (update[j] == 7) {printf("solution(gid = %d) = %10.4e\n",
update[j],xxx[update_index[j]]); fflush(stdout);}
j = AZ_gsum_int(7, proc_config); /* sync processors */
for (j=0;j<Amat->data_org[AZ_N_internal]+ Amat->data_org[AZ_N_border];j++)
if (update[j] == 23) {printf("solution(gid = %d) = %10.4e\n",
update[j],xxx[update_index[j]]); fflush(stdout);}
j = AZ_gsum_int(7, proc_config); /* sync processors */
for (j=0;j<Amat->data_org[AZ_N_internal]+ Amat->data_org[AZ_N_border];j++)
if (update[j] == 47) {printf("solution(gid = %d) = %10.4e\n",
update[j],xxx[update_index[j]]); fflush(stdout);}
j = AZ_gsum_int(7, proc_config); /* sync processors */
for (j=0;j<Amat->data_org[AZ_N_internal]+ Amat->data_org[AZ_N_border];j++)
if (update[j] == 101) {printf("solution(gid = %d) = %10.4e\n",
update[j],xxx[update_index[j]]); fflush(stdout);}
j = AZ_gsum_int(7, proc_config); /* sync processors */
for (j=0;j<Amat->data_org[AZ_N_internal]+ Amat->data_org[AZ_N_border];j++)
if (update[j] == 171) {printf("solution(gid = %d) = %10.4e\n",
update[j],xxx[update_index[j]]); fflush(stdout);}
ML_Aggregate_Destroy(&ag);
ML_Destroy(&ml);
AZ_free((void *) Amat->data_org);
AZ_free((void *) Amat->val);
AZ_free((void *) Amat->bindx);
AZ_free((void *) update);
AZ_free((void *) external);
AZ_free((void *) extern_index);
AZ_free((void *) update_index);
AZ_scaling_destroy(&scaling);
if (Amat != NULL) AZ_matrix_destroy(&Amat);
if (Pmat != NULL) AZ_precond_destroy(&Pmat);
free(xxx);
free(rhs);
#ifdef ML_MPI
MPI_Finalize();
#endif
return 0;
}
int main(int argc, char *argv[])
{
int num_PDE_eqns=6, N_levels=4, nsmooth=2;
int leng, level, N_grid_pts, coarsest_level;
/* See Aztec User's Guide for more information on the */
/* variables that follow. */
int proc_config[AZ_PROC_SIZE], options[AZ_OPTIONS_SIZE];
double params[AZ_PARAMS_SIZE], status[AZ_STATUS_SIZE];
/* data structure for matrix corresponding to the fine grid */
double *val = NULL, *xxx, *rhs, solve_time, setup_time, start_time;
AZ_MATRIX *Amat;
AZ_PRECOND *Pmat = NULL;
ML *ml;
FILE *fp;
int i, j, Nrigid, *garbage = NULL;
#ifdef ML_partition
int nblocks;
int *block_list = NULL;
int k;
#endif
struct AZ_SCALING *scaling;
ML_Aggregate *ag;
double *mode, *rigid;
char filename[80];
double alpha;
int allocated = 0;
int old_prec, old_sol;
double old_tol;
/*
double *Amode, beta, biggest;
int big_ind = -1, ii;
*/
ML_Operator *Amatrix;
int *rowi_col = NULL, rowi_N, count2, ccc;
double *rowi_val = NULL;
double max_diag, min_diag, max_sum, sum;
int nBlocks, *blockIndices, Ndof;
#ifdef ML_partition
FILE *fp2;
int count;
if (argc != 2) {
printf("Usage: ml_read_elas num_processors\n");
exit(1);
}
else sscanf(argv[1],"%d",&nblocks);
#endif
#ifdef HAVE_MPI
MPI_Init(&argc,&argv);
/* get number of processors and the name of this processor */
AZ_set_proc_config(proc_config, MPI_COMM_WORLD);
#else
AZ_set_proc_config(proc_config, AZ_NOT_MPI);
#endif
/* read in the number of matrix equations */
leng = 0;
if (proc_config[AZ_node] == 0) {
# ifdef binary
fp=fopen(".data","rb");
# else
fp=fopen(".data","r");
# endif
if (fp==NULL) {
printf("couldn't open file .data\n");
exit(1);
}
# ifdef binary
fread(&leng, sizeof(int), 1, fp);
# else
fscanf(fp,"%d",&leng);
# endif
fclose(fp);
}
leng = AZ_gsum_int(leng, proc_config);
N_grid_pts=leng/num_PDE_eqns;
/* initialize the list of global indices. NOTE: the list of global */
/* indices must be in ascending order so that subsequent calls to */
/* AZ_find_index() will function properly. */
if (proc_config[AZ_N_procs] == 1) i = AZ_linear;
else i = AZ_file;
AZ_read_update(&N_update, &update, proc_config, N_grid_pts, num_PDE_eqns,i);
AZ_read_msr_matrix(update, &val, &bindx, N_update, proc_config);
/* This code is to fix things up so that we are sure we have */
/* all block (including the ghost nodes the same size. */
AZ_block_MSR(&bindx, &val, N_update, num_PDE_eqns, update);
AZ_transform_norowreordering(proc_config, &external, bindx, val, update, &update_index,
&extern_index, &data_org, N_update, 0, 0, 0, &cpntr,
AZ_MSR_MATRIX);
Amat = AZ_matrix_create( leng );
AZ_set_MSR(Amat, bindx, val, data_org, 0, NULL, AZ_LOCAL);
Amat->matrix_type = data_org[AZ_matrix_type];
data_org[AZ_N_rows] = data_org[AZ_N_internal] + data_org[AZ_N_border];
#ifdef SCALE_ME
ML_MSR_sym_diagonal_scaling(Amat, proc_config, &scaling_vect);
#endif
start_time = AZ_second();
options[AZ_scaling] = AZ_none;
ML_Create(&ml, N_levels);
ML_Set_PrintLevel(10);
/* set up discretization matrix and matrix vector function */
AZ_ML_Set_Amat(ml, N_levels-1, N_update, N_update, Amat, proc_config);
#ifdef ML_partition
/* this code is meant to partition the matrices so that things can be */
/* run in parallel later. */
/* It is meant to be run on only one processor. */
#ifdef MB_MODIF
fp2 = fopen(".update","w");
#else
fp2 = fopen("partition_file","w");
#endif
ML_Operator_AmalgamateAndDropWeak(&(ml->Amat[N_levels-1]), num_PDE_eqns, 0.0);
ML_Gen_Blocks_Metis(ml, N_levels-1, &nblocks, &block_list);
for (i = 0; i < nblocks; i++) {
count = 0;
for (j = 0; j < ml->Amat[N_levels-1].outvec_leng; j++) {
if (block_list[j] == i) count++;
}
fprintf(fp2," %d\n",count*num_PDE_eqns);
for (j = 0; j < ml->Amat[N_levels-1].outvec_leng; j++) {
if (block_list[j] == i) {
for (k = 0; k < num_PDE_eqns; k++) fprintf(fp2,"%d\n",j*num_PDE_eqns+k);
}
}
}
fclose(fp2);
ML_Operator_UnAmalgamateAndDropWeak(&(ml->Amat[N_levels-1]),num_PDE_eqns,0.0);
#ifdef MB_MODIF
printf(" partition file dumped in .update\n");
#endif
exit(1);
#endif
ML_Aggregate_Create( &ag );
/*
ML_Aggregate_Set_CoarsenScheme_MIS(ag);
*/
#ifdef MB_MODIF
ML_Aggregate_Set_DampingFactor(ag,1.50);
#else
ML_Aggregate_Set_DampingFactor(ag,1.5);
#endif
ML_Aggregate_Set_CoarsenScheme_METIS(ag);
ML_Aggregate_Set_NodesPerAggr( ml, ag, -1, 35);
/*
ML_Aggregate_Set_Phase3AggregateCreationAggressiveness(ag, 10.001);
*/
ML_Aggregate_Set_Threshold(ag, 0.0);
ML_Aggregate_Set_MaxCoarseSize( ag, 300);
/* read in the rigid body modes */
Nrigid = 0;
/* to ensure compatibility with RBM dumping software */
if (proc_config[AZ_node] == 0) {
sprintf(filename,"rigid_body_mode%02d",Nrigid+1);
while( (fp = fopen(filename,"r")) != NULL) {
which_filename = 1;
fclose(fp);
Nrigid++;
sprintf(filename,"rigid_body_mode%02d",Nrigid+1);
}
sprintf(filename,"rigid_body_mode%d",Nrigid+1);
while( (fp = fopen(filename,"r")) != NULL) {
fclose(fp);
Nrigid++;
sprintf(filename,"rigid_body_mode%d",Nrigid+1);
}
}
Nrigid = AZ_gsum_int(Nrigid,proc_config);
if (Nrigid != 0) {
rigid = (double *) ML_allocate( sizeof(double)*Nrigid*(N_update+1) );
if (rigid == NULL) {
printf("Error: Not enough space for rigid body modes\n");
}
}
rhs = (double *) malloc(leng*sizeof(double));
xxx = (double *) malloc(leng*sizeof(double));
for (iii = 0; iii < leng; iii++) xxx[iii] = 0.0;
for (i = 0; i < Nrigid; i++) {
if (which_filename == 1) sprintf(filename,"rigid_body_mode%02d",i+1);
else sprintf(filename,"rigid_body_mode%d",i+1);
AZ_input_msr_matrix(filename,update,&mode,&garbage,N_update,proc_config);
AZ_reorder_vec(mode, data_org, update_index, NULL);
/* here is something to stick a rigid body mode as the initial */
/* The idea is to solve A x = 0 without smoothing with a two */
/* level method. If everything is done properly, we should */
/* converge in 2 iterations. */
/* Note: we must also zero out components of the rigid body */
/* mode that correspond to Dirichlet bcs. */
if (i == -4) {
for (iii = 0; iii < leng; iii++) xxx[iii] = mode[iii];
ccc = 0;
Amatrix = &(ml->Amat[N_levels-1]);
for (iii = 0; iii < Amatrix->outvec_leng; iii++) {
ML_get_matrix_row(Amatrix,1,&iii,&allocated,&rowi_col,&rowi_val,
&rowi_N, 0);
count2 = 0;
for (j = 0; j < rowi_N; j++) if (rowi_val[j] != 0.) count2++;
if (count2 <= 1) { xxx[iii] = 0.; ccc++; }
}
free(rowi_col); free(rowi_val);
allocated = 0; rowi_col = NULL; rowi_val = NULL;
}
/*
* Rescale matrix/rigid body modes and checking
*
AZ_sym_rescale_sl(mode, Amat->data_org, options, proc_config, scaling);
Amat->matvec(mode, rigid, Amat, proc_config);
for (j = 0; j < N_update; j++) printf("this is %d %e\n",j,rigid[j]);
*/
/* Here is some code to check that the rigid body modes are */
/* really rigid body modes. The idea is to multiply by A and */
/* then to zero out things that we "think" are boundaries. */
/* In this hardwired example, things near boundaries */
/* correspond to matrix rows that do not have 81 nonzeros. */
/*
Amode = (double *) malloc(leng*sizeof(double));
Amat->matvec(mode, Amode, Amat, proc_config);
j = 0;
biggest = 0.0;
for (ii = 0; ii < N_update; ii++) {
if ( Amat->bindx[ii+1] - Amat->bindx[ii] != 80) {
Amode[ii] = 0.; j++;
}
else {
if ( fabs(Amode[ii]) > biggest) {
biggest=fabs(Amode[ii]); big_ind = ii;
}
}
}
printf("%d entries zeroed out of %d elements\n",j,N_update);
alpha = AZ_gdot(N_update, Amode, Amode, proc_config);
beta = AZ_gdot(N_update, mode, mode, proc_config);
printf("||A r||^2 =%e, ||r||^2 = %e, ratio = %e\n",
alpha,beta,alpha/beta);
printf("the biggest is %e at row %d\n",biggest,big_ind);
free(Amode);
*/
/* orthogonalize mode with respect to previous modes. */
for (j = 0; j < i; j++) {
alpha = -AZ_gdot(N_update, mode, &(rigid[j*N_update]), proc_config)/
AZ_gdot(N_update, &(rigid[j*N_update]),
&(rigid[j*N_update]), proc_config);
/* daxpy_(&N_update,&alpha,&(rigid[j*N_update]), &one, mode, &one); */
}
#ifndef MB_MODIF
printf(" after mb %e %e %e\n",mode[0],mode[1],mode[2]);
#endif
for (j = 0; j < N_update; j++) rigid[i*N_update+j] = mode[j];
free(mode);
free(garbage); garbage = NULL;
}
if (Nrigid != 0) {
ML_Aggregate_Set_BlockDiagScaling(ag);
ML_Aggregate_Set_NullSpace(ag, num_PDE_eqns, Nrigid, rigid, N_update);
free(rigid);
}
#ifdef SCALE_ME
ML_Aggregate_Scale_NullSpace(ag, scaling_vect, N_update);
#endif
coarsest_level = ML_Gen_MGHierarchy_UsingAggregation(ml, N_levels-1,
ML_DECREASING, ag);
AZ_defaults(options, params);
coarsest_level = N_levels - coarsest_level;
if ( proc_config[AZ_node] == 0 )
printf("Coarse level = %d \n", coarsest_level);
/* set up smoothers */
for (level = N_levels-1; level > coarsest_level; level--) {
/*
ML_Gen_Smoother_BlockGaussSeidel(ml, level,ML_BOTH, 1, 1., num_PDE_eqns);
*/
/* Sparse approximate inverse smoother that acutally does both */
/* pre and post smoothing. */
/*
ML_Gen_Smoother_ParaSails(ml , level, ML_PRESMOOTHER, nsmooth,
parasails_sym, parasails_thresh,
parasails_nlevels, parasails_filter,
parasails_loadbal, parasails_factorized);
*/
/* This is the symmetric Gauss-Seidel smoothing that we usually use. */
/* In parallel, it is not a true Gauss-Seidel in that each processor */
/* does a Gauss-Seidel on its local submatrix independent of the */
/* other processors. */
/* ML_Gen_Smoother_Cheby(ml, level, ML_BOTH, 30., nsmooth); */
Ndof = ml->Amat[level].invec_leng;
ML_Gen_Blocks_Aggregates(ag, level, &nBlocks, &blockIndices);
ML_Gen_Smoother_BlockDiagScaledCheby(ml, level, ML_BOTH, 30.,nsmooth,
nBlocks, blockIndices);
/*
ML_Gen_Smoother_SymGaussSeidel(ml , level, ML_BOTH, nsmooth,1.);
*/
/* This is a true Gauss Seidel in parallel. This seems to work for */
/* elasticity problems. However, I don't believe that this is very */
/* efficient in parallel. */
/*
nblocks = ml->Amat[level].invec_leng/num_PDE_eqns;
blocks = (int *) ML_allocate(sizeof(int)*N_update);
for (i =0; i < ml->Amat[level].invec_leng; i++)
blocks[i] = i/num_PDE_eqns;
ML_Gen_Smoother_VBlockSymGaussSeidelSequential(ml , level, ML_PRESMOOTHER,
nsmooth, 1., nblocks, blocks);
ML_Gen_Smoother_VBlockSymGaussSeidelSequential(ml, level, ML_POSTSMOOTHER,
nsmooth, 1., nblocks, blocks);
free(blocks);
*/
/* Block Jacobi Smoothing */
/*
nblocks = ml->Amat[level].invec_leng/num_PDE_eqns;
blocks = (int *) ML_allocate(sizeof(int)*N_update);
for (i =0; i < ml->Amat[level].invec_leng; i++)
blocks[i] = i/num_PDE_eqns;
ML_Gen_Smoother_VBlockJacobi(ml , level, ML_BOTH, nsmooth,
ML_ONE_STEP_CG, nblocks, blocks);
free(blocks);
*/
/* Jacobi Smoothing */
/*
ML_Gen_Smoother_Jacobi(ml , level, ML_PRESMOOTHER, nsmooth, ML_ONE_STEP_CG);
ML_Gen_Smoother_Jacobi(ml , level, ML_POSTSMOOTHER, nsmooth,ML_ONE_STEP_CG);
*/
/* This does a block Gauss-Seidel (not true GS in parallel) */
/* where each processor has 'nblocks' blocks. */
/*
nblocks = 250;
ML_Gen_Blocks_Metis(ml, level, &nblocks, &blocks);
ML_Gen_Smoother_VBlockJacobi(ml , level, ML_BOTH, nsmooth,ML_ONE_STEP_CG,
nblocks, blocks);
free(blocks);
*/
num_PDE_eqns = 6;
}
/* Choose coarse grid solver: mls, superlu, symGS, or Aztec */
/*
ML_Gen_Smoother_Cheby(ml, coarsest_level, ML_BOTH, 30., nsmooth);
ML_Gen_CoarseSolverSuperLU( ml, coarsest_level);
*/
/*
ML_Gen_Smoother_SymGaussSeidel(ml , coarsest_level, ML_BOTH, nsmooth,1.);
*/
old_prec = options[AZ_precond];
old_sol = options[AZ_solver];
old_tol = params[AZ_tol];
params[AZ_tol] = 1.0e-9;
params[AZ_tol] = 1.0e-5;
options[AZ_precond] = AZ_Jacobi;
options[AZ_solver] = AZ_cg;
options[AZ_poly_ord] = 1;
options[AZ_conv] = AZ_r0;
options[AZ_orth_kvecs] = AZ_TRUE;
j = AZ_gsum_int(ml->Amat[coarsest_level].outvec_leng, proc_config);
options[AZ_keep_kvecs] = j - 6;
options[AZ_max_iter] = options[AZ_keep_kvecs];
ML_Gen_SmootherAztec(ml, coarsest_level, options, params,
proc_config, status, options[AZ_keep_kvecs], ML_PRESMOOTHER, NULL);
options[AZ_conv] = AZ_noscaled;
options[AZ_keep_kvecs] = 0;
options[AZ_orth_kvecs] = 0;
options[AZ_precond] = old_prec;
options[AZ_solver] = old_sol;
params[AZ_tol] = old_tol;
/* */
#ifdef RST_MODIF
ML_Gen_Solver(ml, ML_MGV, N_levels-1, coarsest_level);
#else
#ifdef MB_MODIF
ML_Gen_Solver(ml, ML_SAAMG, N_levels-1, coarsest_level);
#else
ML_Gen_Solver(ml, ML_MGFULLV, N_levels-1, coarsest_level);
#endif
#endif
options[AZ_solver] = AZ_GMRESR;
options[AZ_solver] = AZ_cg;
options[AZ_scaling] = AZ_none;
options[AZ_precond] = AZ_user_precond;
options[AZ_conv] = AZ_r0;
options[AZ_conv] = AZ_noscaled;
options[AZ_output] = 1;
options[AZ_max_iter] = 500;
options[AZ_poly_ord] = 5;
options[AZ_kspace] = 40;
params[AZ_tol] = 4.8e-6;
AZ_set_ML_preconditioner(&Pmat, Amat, ml, options);
setup_time = AZ_second() - start_time;
/* Set rhs */
fp = fopen("AZ_capture_rhs.dat","r");
if (fp == NULL) {
AZ_random_vector(rhs, data_org, proc_config);
if (proc_config[AZ_node] == 0) printf("taking random vector for rhs\n");
for (i = 0; i < -N_update; i++) {
rhs[i] = (double) update[i]; rhs[i] = 7.;
}
}
else {
if (proc_config[AZ_node]== 0) printf("reading rhs guess from file\n");
AZ_input_msr_matrix("AZ_capture_rhs.dat", update, &rhs, &garbage,
N_update, proc_config);
free(garbage);
}
AZ_reorder_vec(rhs, data_org, update_index, NULL);
printf("changing rhs by multiplying with A\n");
Amat->matvec(rhs, xxx, Amat, proc_config);
for (i = 0; i < N_update; i++) rhs[i] = xxx[i];
fp = fopen("AZ_capture_init_guess.dat","r");
if (fp != NULL) {
fclose(fp);
if (proc_config[AZ_node]== 0) printf("reading initial guess from file\n");
AZ_input_msr_matrix("AZ_capture_init_guess.dat", update, &xxx, &garbage,
N_update, proc_config);
free(garbage);
xxx = (double *) realloc(xxx, sizeof(double)*(
Amat->data_org[AZ_N_internal]+
Amat->data_org[AZ_N_border] +
Amat->data_org[AZ_N_external]));
}
AZ_reorder_vec(xxx, data_org, update_index, NULL);
/* if Dirichlet BC ... put the answer in */
/*
for (i = 0; i < data_org[AZ_N_internal]+data_org[AZ_N_border]; i++) {
if ( (val[i] > .99999999) && (val[i] < 1.0000001))
xxx[i] = rhs[i];
}
*/
fp = fopen("AZ_no_multilevel.dat","r");
scaling = AZ_scaling_create();
start_time = AZ_second();
if (fp != NULL) {
fclose(fp);
options[AZ_precond] = AZ_none;
options[AZ_scaling] = AZ_sym_diag;
options[AZ_ignore_scaling] = AZ_TRUE;
options[AZ_keep_info] = 1;
AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, NULL, scaling);
/*
options[AZ_pre_calc] = AZ_reuse;
options[AZ_conv] = AZ_expected_values;
if (proc_config[AZ_node] == 0)
printf("\n-------- Second solve with improved convergence test -----\n");
AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, NULL, scaling);
if (proc_config[AZ_node] == 0)
printf("\n-------- Third solve with improved convergence test -----\n");
AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, NULL, scaling);
*/
}
else {
options[AZ_keep_info] = 1;
options[AZ_conv] = AZ_noscaled;
options[AZ_conv] = AZ_r0;
params[AZ_tol] = 1.0e-7;
/* ML_Iterate(ml, xxx, rhs); */
alpha = sqrt(AZ_gdot(N_update, xxx, xxx, proc_config));
printf("init guess = %e\n",alpha);
alpha = sqrt(AZ_gdot(N_update, rhs, rhs, proc_config));
printf("rhs = %e\n",alpha);
#ifdef SCALE_ME
ML_MSR_scalerhs(rhs, scaling_vect, data_org[AZ_N_internal] +
data_org[AZ_N_border]);
ML_MSR_scalesol(xxx, scaling_vect, data_org[AZ_N_internal] +
data_org[AZ_N_border]);
#endif
max_diag = 0.;
min_diag = 1.e30;
max_sum = 0.;
for (i = 0; i < N_update; i++) {
if (Amat->val[i] < 0.) printf("woops negative diagonal A(%d,%d) = %e\n",
i,i,Amat->val[i]);
if (Amat->val[i] > max_diag) max_diag = Amat->val[i];
if (Amat->val[i] < min_diag) min_diag = Amat->val[i];
sum = fabs(Amat->val[i]);
for (j = Amat->bindx[i]; j < Amat->bindx[i+1]; j++) {
sum += fabs(Amat->val[j]);
}
if (sum > max_sum) max_sum = sum;
}
printf("Largest diagonal = %e, min diag = %e large abs row sum = %e\n",
max_diag, min_diag, max_sum);
AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, Pmat, scaling);
options[AZ_pre_calc] = AZ_reuse;
options[AZ_conv] = AZ_expected_values;
/*
if (proc_config[AZ_node] == 0)
printf("\n-------- Second solve with improved convergence test -----\n");
AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, Pmat, scaling);
if (proc_config[AZ_node] == 0)
printf("\n-------- Third solve with improved convergence test -----\n");
AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, Pmat, scaling);
*/
}
solve_time = AZ_second() - start_time;
if (proc_config[AZ_node] == 0)
printf("Solve time = %e, MG Setup time = %e\n", solve_time, setup_time);
if (proc_config[AZ_node] == 0)
printf("Printing out a few entries of the solution ...\n");
for (j=0;j<Amat->data_org[AZ_N_internal]+ Amat->data_org[AZ_N_border];j++)
if (update[j] == 7) {printf("solution(gid = %d) = %10.4e\n",
update[j],xxx[update_index[j]]); fflush(stdout);}
j = AZ_gsum_int(7, proc_config); /* sync processors */
for (j=0;j<Amat->data_org[AZ_N_internal]+ Amat->data_org[AZ_N_border];j++)
if (update[j] == 23) {printf("solution(gid = %d) = %10.4e\n",
update[j],xxx[update_index[j]]); fflush(stdout);}
j = AZ_gsum_int(7, proc_config); /* sync processors */
for (j=0;j<Amat->data_org[AZ_N_internal]+ Amat->data_org[AZ_N_border];j++)
if (update[j] == 47) {printf("solution(gid = %d) = %10.4e\n",
update[j],xxx[update_index[j]]); fflush(stdout);}
j = AZ_gsum_int(7, proc_config); /* sync processors */
for (j=0;j<Amat->data_org[AZ_N_internal]+ Amat->data_org[AZ_N_border];j++)
if (update[j] == 101) {printf("solution(gid = %d) = %10.4e\n",
update[j],xxx[update_index[j]]); fflush(stdout);}
j = AZ_gsum_int(7, proc_config); /* sync processors */
for (j=0;j<Amat->data_org[AZ_N_internal]+ Amat->data_org[AZ_N_border];j++)
if (update[j] == 171) {printf("solution(gid = %d) = %10.4e\n",
update[j],xxx[update_index[j]]); fflush(stdout);}
ML_Aggregate_Destroy(&ag);
ML_Destroy(&ml);
AZ_free((void *) Amat->data_org);
AZ_free((void *) Amat->val);
AZ_free((void *) Amat->bindx);
AZ_free((void *) update);
AZ_free((void *) external);
AZ_free((void *) extern_index);
AZ_free((void *) update_index);
AZ_scaling_destroy(&scaling);
if (Amat != NULL) AZ_matrix_destroy(&Amat);
if (Pmat != NULL) AZ_precond_destroy(&Pmat);
free(xxx);
free(rhs);
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return 0;
}