void print_global_element(int element,int update[],int data_org[],
int update_index[], int rpntr[], double vector[],int proc_config[])
{
/*
* Print out the vector element corresponding to the global numbering
* 'element'. Note: if the VBR format is used, this routine will print
* out all the vector elements corresponding to this block.
*
* Author: Ray Tuminaro, Div 1422, SNL
* Date: 6/15/96
*
* Parameters
*
* element == On input, global number of vector element that
* will be printed.
* update == On input, list of pts updated on this node
* data_org == On input, indicates how the data is set out on
* this node. For example, data_org[] contains
* information on how many unknowns are internal,
* external, and border unknowns as well as which
* points need to be communicated. See User's Guide
* for more details.
* update_index == On input, ordering of update locally on this
* processor. For example, 'update_index[i]' gives
* the index location of the block which has the
* global index 'update[i]'.
* rpntr == On input, rpntr[i+1]-rpntr[i] gives the block
* size of the ith local block.
* vector == On input, vector to be printed (just one element).
* proc_config == On input, processor information:
* proc_config[AZ_node] = name of this processor
* proc_config[AZ_N_procs] = # of processors used
*/
int i,k;
/* synchronize things */
fflush(stdout);
i = AZ_gsum_int(1,proc_config);
i = AZ_find_index(element,update,
data_org[AZ_N_int_blk]+data_org[AZ_N_bord_blk]);
if (i !=-1) {
i = update_index[i];
if (data_org[AZ_matrix_type] == AZ_MSR_MATRIX)
fprintf(stdout,"(%d) = %e\n",element,vector[i]);
else if (data_org[AZ_matrix_type] == AZ_VBR_MATRIX) {
for (k = rpntr[i]; k < rpntr[i+1]; k++ )
fprintf(stdout,"(%d,%d) = %e\n",element,k-rpntr[i],vector[k]);
}
fflush(stdout);
}
/* synchronize things */
i = AZ_gsum_int(i,proc_config);
}
void init_guess_and_rhs(int update_index[], int update[], double *x[],double
*ax[],int data_org[], double val[], int indx[], int
bindx[], int rpntr[], int cpntr[], int bpntr[], int
proc_config[])
/*
* Set the initial guess and the right hand side where the right hand side
* is obtained by doing a matrix-vector multiplication.
*
* Author: Ray Tuminaro, Div 1422, SNL
* Date : 3/15/95
*
* Parameters
*
* update_index == On input, ordering of update and external
* locally on this processor. For example
* 'update_index[i]' gives the index location
* of the block which has the global index
* 'update[i]'.
* update == On input, list of pts to be updated on this node
* data_org == On input, indicates how data is set on this node.
* For example, data_org[] contains information on
* how many unknowns are internal, external and
* border unknowns as well as which points need
* to be communicated. See User's Guide for more
* details.
* val, indx, == On input, holds matrix nonzeros. See User's Guide
* bindx, rpntr, for more details.
* cpntr, bpntr
* x == On output, 'x' is allocated and set to all zeros.
* ax == On output, 'ax' is allocated and is set to the
* result of a matrix-vector product.
*/
{
int i,j;
int temp,num;
double sum = 0.0;
AZ_MATRIX *Amat;
temp = data_org[AZ_N_int_blk] + data_org[AZ_N_bord_blk];
num = data_org[AZ_N_internal] + data_org[AZ_N_border];
/* allocate vectors */
i = num + data_org[AZ_N_external];
*x = (double *) AZ_allocate((i+1)*sizeof(double));
*ax = (double *) AZ_allocate((i+1)*sizeof(double));
if (*ax == NULL) {
(void) fprintf(stderr, "Not enough space in init_guess_and_rhs() for ax\n");
exit(1);
}
for (j = 0 ; j < i ; j++ ) (*x)[j] = 0.0;
for (j = 0 ; j < i ; j++ ) (*ax)[j] = 0.0;
/* initialize 'x' to a function which will be used in matrix-vector product */
if (data_org[AZ_matrix_type] == AZ_VBR_MATRIX) {
for (i = 0; i < temp; i++) {
for (j = rpntr[i]; j < rpntr[i+1]; j++) {
(*x)[j] = (double) (update[i]) + (double)(j-rpntr[i]) /
(double)(num_PDE_eqns);
}
}
}
else {
for (i = 0; i < temp; i++) {
(*x)[i] = (double) (update[i]) / (double) (num_PDE_eqns);
}
}
/* Reorder 'x' so that it conforms to the transformed matrix */
AZ_reorder_vec(*x,data_org,update_index,rpntr);
if (application == 2) {
/* take out the constant vector. Used for the */
/* finite element problem because it is singular */
sum = AZ_gsum_double(sum, proc_config);
i = AZ_gsum_int(num, proc_config);
if (i != 0) sum = sum / ((double) i);
for (i = 0; i < num; i++) (*x)[i] -= sum;
}
Amat = AZ_matrix_create(num);
if (data_org[AZ_matrix_type] == AZ_MSR_MATRIX)
AZ_set_MSR(Amat, bindx, val, data_org, 0, NULL, AZ_LOCAL);
else if (data_org[AZ_matrix_type] == AZ_VBR_MATRIX)
AZ_set_VBR(Amat, rpntr,cpntr, bpntr, indx,bindx, val, data_org, 0, NULL,AZ_LOCAL);
Amat->matvec(*x, *ax, Amat, proc_config);
AZ_matrix_destroy( &Amat );
for (i = 0; i < num; i++) (*x)[i] = 0.0;
} /* init_guess_and_rhs */
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=3, N_levels=3, nsmooth=1;
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 */
int *data_org = NULL, *update = NULL, *external = NULL;
int *update_index = NULL, *extern_index = NULL;
int *cpntr = NULL;
int *bindx = NULL, N_update, iii;
double *val = NULL;
double *xxx, *rhs;
AZ_MATRIX *Amat;
AZ_PRECOND *Pmat = NULL;
ML *ml;
FILE *fp;
int ch,i,j, Nrigid, *garbage;
struct AZ_SCALING *scaling;
double solve_time, setup_time, start_time, *mode, *rigid;
ML_Aggregate *ag;
int nblocks, *blocks;
char filename[80];
double alpha;
int one = 1;
#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);
#else
AZ_set_proc_config(proc_config, AZ_NOT_MPI);
#endif
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. */
AZ_read_update(&N_update, &update, proc_config, N_grid_pts, num_PDE_eqns,
AZ_linear);
AZ_read_msr_matrix(update, &val, &bindx, N_update, proc_config);
AZ_transform(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();
AZ_defaults(options, params);
/*
scaling = AZ_scaling_create();
xxx = (double *) calloc( leng,sizeof(double));
rhs=(double *)calloc(leng,sizeof(double));
options[AZ_scaling] = AZ_sym_diag;
options[AZ_precond] = AZ_none;
options[AZ_max_iter] = 30;
options[AZ_keep_info] = 1;
AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, NULL, scaling);
don't forget vector rescaling ...
free(xxx);
free(rhs);
*/
options[AZ_scaling] = AZ_none;
ML_Create(&ml, N_levels);
/* set up discretization matrix and matrix vector function */
AZ_ML_Set_Amat(ml, N_levels-1, N_update, N_update, Amat, proc_config);
ML_Aggregate_Create( &ag );
Nrigid = 0;
if (proc_config[AZ_node] == 0) {
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));
AZ_random_vector(rhs, data_org, proc_config);
for (i = 0; i < Nrigid; i++) {
sprintf(filename,"rigid_body_mode%d",i+1);
AZ_input_msr_matrix(filename, update, &mode, &garbage,
N_update, proc_config);
/*
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]);
*/
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);
printf("alpha1 is %e\n",alpha);
}
alpha = -AZ_gdot(N_update, mode, rhs, proc_config)/AZ_gdot(N_update, mode, mode, proc_config);
printf("alpha2 is %e\n",alpha);
daxpy_(&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_(&N_update, &alpha, &(rigid[j*N_update]), &one, rhs, &one);
printf("alpha4 is %e\n",alpha);
}
for (i = 0; i < Nrigid; i++) {
alpha = -AZ_gdot(N_update, &(rigid[i*N_update]), rhs, proc_config);
printf("alpha is %e\n",alpha);
}
if (Nrigid != 0) {
ML_Aggregate_Set_NullSpace(ag, num_PDE_eqns, Nrigid, rigid, N_update);
/*
free(rigid);
*/
}
coarsest_level = ML_Gen_MGHierarchy_UsingAggregation(ml, N_levels-1, ML_DECREASING, ag);
coarsest_level = N_levels - coarsest_level;
/*
ML_Operator_Print(&(ml->Pmat[N_levels-2]), "Pmat");
exit(1);
*/
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--) {
j = 10;
if (level == N_levels-1) j = 10;
options[AZ_solver] = AZ_cg;
options[AZ_precond]=AZ_sym_GS; options[AZ_subdomain_solve]=AZ_icc;
/*
options[AZ_precond] = AZ_none;
*/
options[AZ_poly_ord] = 5;
ML_Gen_SmootherAztec(ml, level, options, params, proc_config, status,
j, ML_PRESMOOTHER,NULL);
ML_Gen_SmootherAztec(ml, level, options, params, proc_config, status,
j, ML_POSTSMOOTHER,NULL);
/*
ML_Gen_Smoother_SymGaussSeidel(ml , level, ML_PRESMOOTHER, nsmooth,1.0);
ML_Gen_Smoother_SymGaussSeidel(ml , level, ML_POSTSMOOTHER, nsmooth,1.0);
*/
/*
nblocks = ML_Aggregate_Get_AggrCount( ag, level );
ML_Aggregate_Get_AggrMap( ag, level, &blocks);
ML_Gen_Smoother_VBlockSymGaussSeidel( ml , level, ML_BOTH, nsmooth, 1.0,
nblocks, blocks);
ML_Gen_Smoother_VBlockSymGaussSeidel( ml , level, ML_POSTSMOOTHER, nsmooth, 1.0,
nblocks, blocks);
*/
/*
ML_Gen_Smoother_VBlockJacobi( ml , level, ML_PRESMOOTHER, nsmooth, .5,
nblocks, blocks);
ML_Gen_Smoother_VBlockJacobi( ml , level, ML_POSTSMOOTHER, nsmooth,.5,
nblocks, blocks);
*/
/*
ML_Gen_Smoother_GaussSeidel(ml , level, ML_PRESMOOTHER, nsmooth);
ML_Gen_Smoother_GaussSeidel(ml , level, ML_POSTSMOOTHER, nsmooth);
*/
/*
need to change this when num_pdes is different on different levels
*/
/*
if (level == N_levels-1) {
ML_Gen_Smoother_BlockGaussSeidel(ml , level, ML_PRESMOOTHER, nsmooth, 0.5, num_PDE_eqns);
ML_Gen_Smoother_BlockGaussSeidel(ml , level, ML_POSTSMOOTHER, nsmooth, 0.5, num_PDE_eqns);
}
else {
ML_Gen_Smoother_BlockGaussSeidel(ml , level, ML_PRESMOOTHER, nsmooth, 0.5, 2*num_PDE_eqns);
ML_Gen_Smoother_BlockGaussSeidel(ml , level, ML_POSTSMOOTHER, nsmooth, 0.5, 2*num_PDE_eqns);
}
*/
/*
*/
/*
ML_Gen_SmootherJacobi(ml , level, ML_PRESMOOTHER, nsmooth, .67);
ML_Gen_SmootherJacobi(ml , level, ML_POSTSMOOTHER, nsmooth, .67 );
*/
}
/*
ML_Gen_CoarseSolverSuperLU( ml, coarsest_level);
*/
/*
ML_Gen_SmootherSymGaussSeidel(ml , coarsest_level, ML_PRESMOOTHER, 2*nsmooth,1.);
*/
/*
ML_Gen_SmootherBlockGaussSeidel(ml , level, ML_PRESMOOTHER, 50*nsmooth, 1.0, 2*num_PDE_eqns);
*/
ML_Gen_Smoother_BlockGaussSeidel(ml , level, ML_PRESMOOTHER, 2*nsmooth, 1.0, num_PDE_eqns);
ML_Gen_Solver(ml, ML_MGV, N_levels-1, coarsest_level);
AZ_defaults(options, params);
options[AZ_solver] = AZ_GMRESR;
options[AZ_scaling] = AZ_none;
options[AZ_precond] = AZ_user_precond;
options[AZ_conv] = AZ_rhs;
options[AZ_output] = 1;
options[AZ_max_iter] = 1500;
options[AZ_poly_ord] = 5;
options[AZ_kspace] = 130;
params[AZ_tol] = 1.0e-8;
AZ_set_ML_preconditioner(&Pmat, Amat, ml, options);
setup_time = AZ_second() - start_time;
xxx = (double *) malloc( leng*sizeof(double));
/* Set rhs */
fp = fopen("AZ_capture_rhs.dat","r");
if (fp == NULL) {
if (proc_config[AZ_node] == 0) printf("taking random vector for rhs\n");
/*
AZ_random_vector(rhs, data_org, proc_config);
AZ_reorder_vec(rhs, data_org, update_index, NULL);
AZ_random_vector(xxx, data_org, proc_config);
AZ_reorder_vec(xxx, data_org, update_index, NULL);
Amat->matvec(xxx, rhs, Amat, proc_config);
*/
}
else {
ch = getc(fp);
if (ch == 'S') {
while ( (ch = getc(fp)) != '\n') ;
}
else ungetc(ch,fp);
for (i = 0; i < data_org[AZ_N_internal]+data_org[AZ_N_border]; i++)
fscanf(fp,"%lf",&(rhs[i]));
fclose(fp);
}
for (iii = 0; iii < leng; iii++) xxx[iii] = 0.0;
/* Set x */
fp = fopen("AZ_capture_init_guess.dat","r");
if (fp != NULL) {
ch = getc(fp);
if (ch == 'S') {
while ( (ch = getc(fp)) != '\n') ;
}
else ungetc(ch,fp);
for (i = 0; i < data_org[AZ_N_internal]+data_org[AZ_N_border]; i++)
fscanf(fp,"%lf",&(xxx[i]));
fclose(fp);
options[AZ_conv] = AZ_expected_values;
}
/* 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_max_iter] = 40;
*/
AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, Pmat, scaling);
for (j = 0; j < Nrigid; j++) {
alpha = -AZ_gdot(N_update, xxx, &(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, xxx, &one);
printf("alpha5 is %e\n",alpha);
}
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);
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);
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;
}
void AZ_domain_decomp(double x[], AZ_MATRIX *Amat, int options[],
int proc_config[], double params[],
struct context *context)
/*******************************************************************************
Precondition 'x' using an overlapping domain decomposition method where a
solver specified by options[AZ_subdomain_solve] is used on the subdomains.
Note: if a factorization needs to be computed on the first iteration, this
will be done and stored for future iterations.
Author: Lydie Prevost, SNL, 9222
======= Revised by R. Tuminaro (4/97), SNL, 9222
Return code: void
============
Parameter list:
===============
N_unpadded: On input, number of rows in linear system (unpadded matrix)
that will be factored (after adding values for overlapping).
Nb_unpadded: On input, number of block rows in linear system (unpadded)
that will be factored (after adding values for overlapping).
N_nz_unpadded: On input, number of nonzeros in linear system (unpadded)
that will be factored (after adding values for overlapping).
x: On output, x[] is preconditioned by performing the subdomain
solve indicated by options[AZ_subdomain_solve].
val indx
bindx rpntr: On input, arrays containing matrix nonzeros (see manual).
cpntr bpntr
options: Determines specific solution method and other parameters. In
this routine, we are concerned with options[AZ_overlap]:
== AZ_none: nonoverlapping domain decomposition
== AZ_diag: use rows corresponding to external variables
but only keep the diagonal for these rows.
== k : Obtain rows that are a distance k away from
rows owned by this processor.
data_org: Contains information on matrix data distribution and
communication parameters (see manual).
*******************************************************************************/
{
int N_unpadded, Nb_unpadded, N_nz_unpadded;
double *x_pad = NULL, *x_reord = NULL, *ext_vals = NULL;
int N_nz, N_nz_padded, nz_used;
int mem_orig, mem_overlapped, mem_factor;
int name, i, bandwidth;
int *ordering = NULL;
double condest;
/*
double start_t;
*/
int estimated_requirements;
char str[80];
int *garbage;
int N;
int *padded_data_org = NULL, *bindx, *data_org;
double *val;
int *inv_ordering = NULL;
int *map = NULL;
AZ_MATRIX *A_overlapped = NULL;
struct aztec_choices aztec_choices;
/**************************** execution begins ******************************/
data_org = Amat->data_org;
bindx = Amat->bindx;
val = Amat->val;
N_unpadded = data_org[AZ_N_internal] + data_org[AZ_N_border];
Nb_unpadded = data_org[AZ_N_int_blk]+data_org[AZ_N_bord_blk];
if (data_org[AZ_matrix_type] == AZ_MSR_MATRIX)
N_nz_unpadded = bindx[N_unpadded];
else if (data_org[AZ_matrix_type] == AZ_VBR_MATRIX)
N_nz_unpadded = (Amat->indx)[(Amat->bpntr)[Nb_unpadded]];
else {
if (Amat->N_nz < 0)
AZ_matfree_Nnzs(Amat);
N_nz_unpadded = Amat->N_nz;
}
aztec_choices.options = options;
aztec_choices.params = params;
context->aztec_choices = &aztec_choices;
context->proc_config = proc_config;
name = data_org[AZ_name];
if ((options[AZ_pre_calc] >= AZ_reuse) && (context->Pmat_computed)) {
N = context->N;
N_nz = context->N_nz;
A_overlapped = context->A_overlapped;
A_overlapped->data_org = data_org;
A_overlapped->matvec = Amat->matvec;
}
else {
sprintf(str,"A_over %s",context->tag);
A_overlapped = (AZ_MATRIX *) AZ_manage_memory(sizeof(AZ_MATRIX),
AZ_ALLOC, name, str, &i);
AZ_matrix_init(A_overlapped, 0);
context->A_overlapped = A_overlapped;
A_overlapped->data_org = data_org;
A_overlapped->matvec = Amat->matvec;
A_overlapped->matrix_type = AZ_MSR_MATRIX;
AZ_init_subdomain_solver(context);
AZ_compute_matrix_size(Amat, options, N_nz_unpadded, N_unpadded,
&N_nz_padded, data_org[AZ_N_external],
&(context->max_row), &N, &N_nz, params[AZ_ilut_fill],
&(context->extra_fact_nz_per_row),
Nb_unpadded,&bandwidth);
estimated_requirements = N_nz;
if (N_nz*2 > N_nz) N_nz = N_nz*2; /* check for overflow */
/* Add extra memory to N_nz. */
/* This extra memory is used */
/* as temporary space during */
/* overlapping calculation */
/* Readjust N_nz by allocating auxilliary arrays and allocate */
/* the MSR matrix to check that there is enough space. */
/* block off some space for map and padded_data_org in dd_overlap */
garbage = (int *) AZ_allocate((AZ_send_list + 2*(N-N_unpadded) +10)*
sizeof(int));
AZ_hold_space(context, N);
if (N_nz*((int) sizeof(double)) < N_nz) N_nz=N_nz/2; /* check for overflow */
if (N_nz*((int) sizeof(double)) < N_nz) N_nz=N_nz/2; /* check for overflow */
if (N_nz*((int) sizeof(double)) < N_nz) N_nz=N_nz/2; /* check for overflow */
if (N_nz*((int) sizeof(double)) < N_nz) N_nz=N_nz/2; /* check for overflow */
if (N_nz*((int) sizeof(double)) < N_nz) N_nz=N_nz/2; /* check for overflow */
N_nz = AZ_adjust_N_nz_to_fit_memory(N_nz,
context->N_large_int_arrays,
context->N_large_dbl_arrays);
context->N_nz_factors = N_nz;
if (N_nz <= N_nz_unpadded) {
AZ_printf_out("Error: Not enough space for domain decomposition\n");
AZ_exit(1);
}
if (estimated_requirements > N_nz ) estimated_requirements = N_nz;
/* allocate matrix via AZ_manage_memory() */
sprintf(str,"bindx %s",context->tag);
A_overlapped->bindx =(int *) AZ_manage_memory(N_nz*sizeof(int),
AZ_ALLOC, name, str, &i);
sprintf(str,"val %s",context->tag);
A_overlapped->val =(double *) AZ_manage_memory(N_nz*sizeof(double),
AZ_ALLOC, name, str, &i);
context->N_nz_allocated = N_nz;
AZ_free_space_holder(context);
AZ_free(garbage);
/* convert to MSR if necessary */
if (data_org[AZ_matrix_type] == AZ_VBR_MATRIX)
AZ_vb2msr(Nb_unpadded,val,Amat->indx,bindx,Amat->rpntr,Amat->cpntr,
Amat->bpntr, A_overlapped->val, A_overlapped->bindx);
else if (data_org[AZ_matrix_type] == AZ_MSR_MATRIX) {
for (i = 0 ; i < N_nz_unpadded; i++ ) {
A_overlapped->bindx[i] = bindx[i];
A_overlapped->val[i] = val[i];
}
}
else AZ_matfree_2_msr(Amat,A_overlapped->val,A_overlapped->bindx,N_nz);
mem_orig = AZ_gsum_int(A_overlapped->bindx[N_unpadded],proc_config);
/*
start_t = AZ_second();
*/
AZ_pad_matrix(context, proc_config, N_unpadded, &N,
&(context->map), &(context->padded_data_org), &N_nz,
estimated_requirements);
/*
if (proc_config[AZ_node] == 0)
AZ_printf_out("matrix padding took %e seconds\n",AZ_second()-start_t);
*/
mem_overlapped = AZ_gsum_int(A_overlapped->bindx[N],proc_config);
if (options[AZ_reorder]) {
/*
start_t = AZ_second();
*/
AZ_find_MSR_ordering(A_overlapped->bindx,
&(context->ordering),N,
&(context->inv_ordering),name,context);
/*
if (proc_config[AZ_node] == 0)
AZ_printf_out("took %e seconds to find ordering\n", AZ_second()-start_t);
*/
/*
start_t = AZ_second();
*/
AZ_mat_reorder(N,A_overlapped->bindx,A_overlapped->val,
context->ordering, context->inv_ordering);
/*
if (proc_config[AZ_node] == 0)
AZ_printf_out("took %e seconds to reorder\n", AZ_second()-start_t);
*/
/* NOTE: ordering is freed inside AZ_mat_reorder */
#ifdef AZ_COL_REORDER
if (options[AZ_reorder]==2) {
AZ_mat_colperm(N,A_overlapped->bindx,A_overlapped->val,
&(context->ordering), name, context );
}
#endif
}
/* Do a factorization if needed. */
/*
start_t = AZ_second();
*/
AZ_factor_subdomain(context, N, N_nz, &nz_used);
if (options[AZ_output] > 0 && options[AZ_diagnostics]!=AZ_none) {
AZ_printf_out("\n*********************************************************************\n");
condest = AZ_condest(N, context);
AZ_printf_out("***** Condition number estimate for subdomain preconditioner on PE %d = %.4e\n",
proc_config[AZ_node], condest);
AZ_printf_out("*********************************************************************\n");
}
/*
start_t = AZ_second()-start_t;
max_time = AZ_gmax_double(start_t,proc_config);
min_time = AZ_gmin_double(start_t,proc_config);
if (proc_config[AZ_node] == 0)
AZ_printf_out("time for subdomain solvers ranges from %e to %e\n",
min_time,max_time);
*/
if ( A_overlapped->matrix_type == AZ_MSR_MATRIX)
AZ_compress_msr(&(A_overlapped->bindx), &(A_overlapped->val),
context->N_nz_allocated, nz_used, name, context);
context->N_nz = nz_used;
context->N = N;
context->N_nz_allocated = nz_used;
mem_factor = AZ_gsum_int(nz_used,proc_config);
if (proc_config[AZ_node] == 0)
AZ_print_header(options,mem_overlapped,mem_orig,mem_factor);
if (options[AZ_overlap] >= 1) {
sprintf(str,"x_pad %s",context->tag);
context->x_pad = (double *) AZ_manage_memory(N*sizeof(double),
AZ_ALLOC, name, str, &i);
sprintf(str,"ext_vals %s",context->tag);
context->ext_vals = (double *) AZ_manage_memory((N-N_unpadded)*
sizeof(double), AZ_ALLOC, name,
str, &i);
}
if (options[AZ_reorder]) {
sprintf(str,"x_reord %s",context->tag);
context->x_reord = (double *) AZ_manage_memory(N*sizeof(double),
AZ_ALLOC, name, str, &i);
}
}
/* Solve L u = x where the solution u overwrites x */
x_reord = context->x_reord;
inv_ordering = context->inv_ordering;
ordering = context->ordering;
x_pad = context->x_pad;
ext_vals = context->ext_vals;
padded_data_org = context->padded_data_org;
map = context->map;
if (x_pad == NULL) x_pad = x;
if (options[AZ_overlap] >= 1) {
for (i = 0 ; i < N_unpadded ; i++) x_pad[i] = x[i];
AZ_exchange_bdry(x_pad,padded_data_org, proc_config);
for (i = 0 ; i < N-N_unpadded ; i++ )
ext_vals[map[i]-N_unpadded] = x_pad[i+N_unpadded];
for (i = 0 ; i < N-N_unpadded ; i++ ) x_pad[i + N_unpadded] = ext_vals[i];
}
else if (options[AZ_overlap] == AZ_diag)
AZ_exchange_bdry(x_pad,data_org, proc_config);
if (x_reord == NULL) x_reord = x_pad;
if (options[AZ_reorder]) {
/* Apply row permutation to the right hand side */
/* ((P'A P)Pi') Pi P'x = P'rhs, b= P'rhs */
for (i = 0 ; i < N ; i++ ) x_reord[inv_ordering[i]] = x_pad[i];
}
AZ_solve_subdomain(x_reord,N, context);
#ifdef AZ_COL_REORDER
/* Apply column permutation to the solution */
if (options[AZ_reorder]==1){
/* ((P'A P) P'sol = P'rhs sol = P( P'sol) */
for (i = 0; i < N; i++) x_pad[i] = x_reord[inv_ordering[i]];
}
if (options[AZ_reorder]==2){
/*
* ((P'A P)Pi') Pi P'sol = P'rhs sol = P Pi'( Pi P'sol)
* Version 1:
* for (i = 0; i < N; i++) pi_sol[i] = x_reord[ordering[i]];
* for (j = 0; j < N; j++) x_pad[j] = pi_sol[inv_ordering[j]];
* Version 2:
*/
for (i = 0; i < N; i++) x_pad[i] = x_reord[ ordering[inv_ordering[i]] ];
}
#else
if (options[AZ_reorder])
for (i = 0; i < N; i++) x_pad[i] = x_reord[inv_ordering[i]];
#endif
AZ_combine_overlapped_values(options[AZ_type_overlap],padded_data_org,
options, x_pad, map,ext_vals,name,proc_config);
if (x_pad != x)
for (i = 0 ; i < N_unpadded ; i++ ) x[i] = x_pad[i];
} /* subdomain driver*/
