/* TODO: Refactor this routine */
static inline
int create_subtasks
(cluster_t *cl, int tid, proc_t *procinfo,
rrr_t *RRR, val_t *Wstruct, vec_t *Zstruct,
workQ_t *workQ, counter_t *num_left)
{
/* From inputs */
int cl_begin = cl->begin;
int cl_end = cl->end;
int depth = cl->depth;
int bl_begin = cl->bl_begin;
int bl_end = cl->bl_end;
int bl_size = bl_end - bl_begin + 1;
double bl_spdiam = cl->bl_spdiam;
double lgap;
int pid = procinfo->pid;
int nproc = procinfo->nproc;
int nthreads = procinfo->nthreads;
bool proc_involved=true;
double *restrict Wgap = Wstruct->Wgap;
double *restrict Wshifted = Wstruct->Wshifted;
int *restrict iproc = Wstruct->iproc;
int ldz = Zstruct->ldz;
double *restrict Z = Zstruct->Z;
int *restrict Zindex = Zstruct->Zindex;
/* others */
int i, l, k;
int max_size;
task_t *task;
bool task_inserted;
int new_first, new_last, new_size, new_ftt1, new_ftt2;
int sn_first, sn_last, sn_size;
rrr_t *RRR_parent;
int new_lpid, new_rpid;
double *restrict D_parent;
double *restrict L_parent;
int my_first, my_last;
bool copy_parent_rrr;
max_size = fmax(1, PMR_get_counter_value(num_left) /
(fmin(depth+1,4)*nthreads) );
task_inserted = true;
new_first = cl_begin;
for (i=cl_begin; i<=cl_end; i++) {
if ( i == cl_end )
new_last = i;
else if ( Wgap[i] >= MIN_RELGAP*fabs(Wshifted[i]) )
new_last = i;
else
continue;
new_size = new_last - new_first + 1;
if (new_size == 1) {
/* singleton was found */
if (new_first==cl_begin || task_inserted==true) {
/* initialize new singleton task */
sn_first = new_first;
sn_last = new_first;
sn_size = 1;
} else {
/* extend singleton task by one */
sn_last++;
sn_size++;
}
/* insert task if ... */
if (i==cl_end || sn_size>=max_size ||
Wgap[i+1] < MIN_RELGAP*fabs(Wshifted[i+1])) {
/* Check if process involved in s-task */
proc_involved = false;
for (k=sn_first; k<=sn_last; k++) {
if (iproc[k] == pid) {
proc_involved = true;
break;
}
}
if (proc_involved == false) {
task_inserted = true;
new_first = i + 1;
continue;
}
/* Insert task as process is involved */
if (sn_first == cl_begin) {
lgap = cl->lgap;
} else {
lgap = Wgap[sn_first-1];
}
PMR_increment_rrr_dependencies(RRR);
task = PMR_create_s_task(sn_first, sn_last, depth+1, bl_begin,
bl_end, bl_spdiam, lgap, RRR);
PMR_insert_task_at_back(workQ->s_queue, task);
task_inserted = true;
} else {
task_inserted = false;
}
} else {
/* cluster was found */
/* check if process involved in processing the new cluster */
new_lpid = nproc-1;
new_rpid = -1;
for (l=new_first; l<=new_last; l++) {
if (iproc[l] != -1) {
new_lpid = imin(new_lpid, iproc[l]);
new_rpid = imax(new_rpid, iproc[l]);
}
}
if (new_lpid > pid || new_rpid < pid) {
task_inserted = true;
new_first = i + 1;
continue;
}
/* find gap to the left */
if (new_first == cl_begin) {
lgap = cl->lgap;
} else {
lgap = Wgap[new_first - 1];
}
/* determine where to store the parent rrr needed by the
* cluster to find its new rrr */
my_first = imax(new_first, cl->proc_W_begin);
my_last = imin(new_last, cl->proc_W_end);
if ( my_first == my_last ) {
/* only one eigenvalue of cluster belongs to process */
copy_parent_rrr = true;
} else {
/* store parent rrr in Z at column new_ftt */
copy_parent_rrr = false;
}
new_ftt1 = Zindex[my_first ];
new_ftt2 = Zindex[my_first + 1];
if (copy_parent_rrr == true) {
/* Copy parent RRR into alloceted arrays and mark them
* for freeing later */
D_parent = (double *) malloc(bl_size * sizeof(double));
assert(D_parent != NULL);
L_parent = (double *) malloc(bl_size * sizeof(double));
assert(L_parent != NULL);
memcpy(D_parent, RRR->D, bl_size*sizeof(double));
memcpy(L_parent, RRR->L, bl_size*sizeof(double));
RRR_parent = PMR_create_rrr(D_parent, L_parent, NULL,
NULL, bl_size, depth);
PMR_set_copied_parent_rrr_flag(RRR_parent, true);
} else {
/* copy parent RRR into Z to make cluster task independent */
memcpy(&Z[new_ftt1*ldz+bl_begin], RRR->D,
bl_size*sizeof(double));
memcpy(&Z[new_ftt2*ldz+bl_begin], RRR->L,
bl_size*sizeof(double));
RRR_parent = PMR_create_rrr(&Z[new_ftt1*ldz + bl_begin],
&Z[new_ftt2*ldz + bl_begin],
NULL, NULL, bl_size, depth);
}
/* Create the task for the cluster and put it in the queue */
task = PMR_create_c_task(new_first, new_last, depth+1,
bl_begin, bl_end, bl_spdiam, lgap,
cl->proc_W_begin, cl->proc_W_end,
new_lpid, new_rpid, RRR_parent);
if (new_lpid != new_rpid)
PMR_insert_task_at_back(workQ->r_queue, task);
else
PMR_insert_task_at_back(workQ->c_queue, task);
task_inserted = true;
} /* if singleton or cluster found */
new_first = i + 1;
} /* end i */
/* set flag in RRR that last singleton is created */
PMR_set_parent_processed_flag(RRR);
/* clean up */
PMR_try_destroy_rrr(RRR);
free(cl);
return 0;
} /* end create_subtasks */
/*
* Initialize work queue by putting all tasks for the process
* into the work queue.
*/
static
int init_workQ
(proc_t *procinfo, in_t *Dstruct, val_t *Wstruct, int *nzp, workQ_t *workQ)
{
int pid = procinfo->pid;
int nproc = procinfo->nproc;
int nthreads = procinfo->nthreads;
double *restrict D = Dstruct->D;
double *restrict L = Dstruct->E;
int nsplit = Dstruct->nsplit;
int *restrict isplit = Dstruct->isplit;
double *restrict W = Wstruct->W;
double *restrict Werr = Wstruct->Werr;
double *restrict Wgap = Wstruct->Wgap;
int *restrict iproc = Wstruct->iproc;
double *restrict Wshifted = Wstruct->Wshifted;
double *restrict gersch = Wstruct->gersch;
int nz = *nzp;
/* Loop over blocks */
int i, j, k, l;
int ibegin = 0;
for ( j=0; j<nsplit; j++ ) {
int iend = isplit[j] - 1;
int isize = iend - ibegin + 1;
double sigma = L[iend];
/* Use Gerschgorin disks to find spectral diameter */
double gl = gersch[2*ibegin ];
double gu = gersch[2*ibegin + 1];
for (i=ibegin+1; i<iend; i++) {
gl = fmin(gl, gersch[2*i ]);
gu = fmax(gu, gersch[2*i + 1]);
}
double spdiam = gu - gl;
double avggap = spdiam / (isize-1);
/* Find eigenvalues in block */
int nbl = 0;
int iWbegin = iend + 1;
int iWend = ibegin - 1;
for (i=ibegin; i<=iend; i++) {
if (nbl == 0 && iproc[i] == pid) {
iWbegin = i;
iWend = i;
nbl++;
k = i+1;
while (k <=iend && iproc[k] == pid) {
iWend++;
nbl++;
k++;
}
/* iWend = iWbegin + nbl - 1; instead of incrementing in loop */
}
}
/* If no eigenvalues for process in block continue */
if (nbl == 0) {
ibegin = iend + 1;
continue;
}
/* Compute DL and DLL for later computation of singletons
* (freed when all singletons of root are computed) */
double *DL = (double*)malloc(isize*sizeof(double));
assert(DL != NULL);
double *DLL = (double*)malloc(isize*sizeof(double));
assert(DLL != NULL);
for (i=0; i<isize-1; i++) {
double tmp = D[i+ibegin]*L[i+ibegin];
DL[i] = tmp;
DLL[i] = tmp*L[i+ibegin];
}
rrr_t *RRR = PMR_create_rrr(&D[ibegin], &L[ibegin], DL, DLL, isize, 0);
PMR_increment_rrr_dependencies(RRR);
/* In W apply shift of current block to eigenvalues
* to get unshifted values w.r.t. T */
for (i=ibegin; i<=iend; i++)
W[i] += sigma;
/* Split eigenvalues of block into singletons and clusters
* and add them to process work queue */
int max_size = imax(1, nz/nthreads);
bool task_inserted = false;
int new_first=ibegin, new_last;
int sn_first, sn_last, sn_size;
for (i=ibegin; i<=iend; i++) {
if (i == iend)
new_last = i;
else if (Wgap[i] >= MIN_RELGAP*fabs(Wshifted[i]))
new_last = i;
else
continue;
/* Skip rest if no eigenvalues of process */
if (new_first > iWend || new_last < iWbegin) {
new_first = i + 1;
continue;
}
int new_size = new_last - new_first + 1;
if (new_size == 1) {
/* Singleton was found */
if (new_first < iWbegin || new_first > iWend) {
new_first = i + 1;
continue;
} else {
if (new_first==iWbegin || task_inserted==true) {
/* Initialize new singleton task */
sn_first = new_first;
sn_last = new_first;
sn_size = 1;
} else {
/* Extend singleton task by one */
sn_last++;
sn_size++;
}
}
/* Insert task if ... */
if (i==iWend || sn_size>=max_size ||
Wgap[i+1] < MIN_RELGAP*fabs(Wshifted[i+1])) {
double lgap;
if (sn_first == ibegin) {
lgap = fmax(0.0, W[ibegin] - Werr[ibegin] - gl );
} else {
lgap = Wgap[sn_first-1];
}
PMR_increment_rrr_dependencies(RRR);
task_t *task =
PMR_create_s_task
(sn_first, sn_last, 1, ibegin, iend, spdiam, lgap, RRR);
PMR_insert_task_at_back(workQ->s_queue, task);
task_inserted = true;
} else {
task_inserted = false;
}
} else {
/* Cluster was found */
int cl_first = new_first;
int cl_last = new_last;
int cl_size = new_size;
/* Split cluster into clusters by absolut criterion */
if (cl_size > 3) {
/* Split cluster to smaller clusters [cl_first:cl_last] */
for (k=new_first+1; k<new_last; k++) {
if (k == new_last-1)
cl_last = new_last;
else if (k != cl_first && Wgap[k] > 0.8*avggap)
cl_last = k;
else
continue;
/* Skip cluster if no eigenvalues of process in it */
if (cl_last < iWbegin || cl_first > iWend) {
cl_first = k + 1;
continue;
}
/* Record left gap of cluster */
double lgap;
if (cl_first == ibegin) {
lgap = fmax(0.0, W[ibegin] - Werr[ibegin] - gl);
} else {
lgap = Wgap[cl_first-1];
}
/* Determine processes involved in processing the cluster */
int left_pid = nproc-1;
int right_pid = 0;
for (l=cl_first; l<=cl_last; l++) {
if (iproc[l] != -1) {
left_pid = imin(left_pid, iproc[l]);
right_pid = imax(right_pid, iproc[l]);
}
}
rrr_t *RRR_parent =
PMR_create_rrr(&D[ibegin], &L[ibegin], NULL, NULL, isize, 0);
task_t *task =
PMR_create_c_task
(cl_first, cl_last, 1, ibegin, iend, spdiam, lgap, iWbegin,
iWend, left_pid, right_pid, RRR_parent);
/* Insert task into queue, depending if cluster need
* communication with other processes */
if (left_pid != right_pid)
PMR_insert_task_at_back(workQ->r_queue, task);
else
PMR_insert_task_at_back(workQ->c_queue, task);
cl_first = k + 1;
} /* end k */
} else {
/* Cluster is too small to split, so insert it to queue */
/* Record left gap of cluster */
double lgap;
if (cl_first == ibegin) {
lgap = fmax(0.0, W[ibegin] - Werr[ibegin] - gl );
} else {
lgap = Wgap[cl_first-1];
}
/* Determine processes involved */
int left_pid = nproc-1;
int right_pid = 0;
for (l=cl_first; l<=cl_last; l++) {
if (iproc[l] != -1) {
left_pid = imin(left_pid, iproc[l]);
right_pid = imax(right_pid, iproc[l]);
}
}
rrr_t *RRR_parent =
PMR_create_rrr
(&D[ibegin], &L[ibegin], NULL, NULL, isize, 0);
task_t *task =
PMR_create_c_task
(cl_first, cl_last, 1, ibegin,
iend, spdiam, lgap, iWbegin, iWend,
left_pid, right_pid, RRR_parent);
/* Insert task into queue, depending if cluster need
* communication with other processes */
if (left_pid != right_pid)
PMR_insert_task_at_back(workQ->r_queue, task);
else
PMR_insert_task_at_back(workQ->c_queue, task);
}
task_inserted = true;
} /* end new_size */
new_first = i + 1;
} /* end of splitting eigenvalues into tasks */
/* Set flag in RRR that last singleton is created */
PMR_set_parent_processed_flag(RRR);
PMR_try_destroy_rrr(RRR);
ibegin = iend + 1;
} /* end loop over blocks */
return 0;
}
static inline
rrr_t* compute_new_rrr
(cluster_t *cl, int tid, proc_t *procinfo,
val_t *Wstruct, vec_t *Zstruct,
tol_t *tolstruct, double *work, int *iwork)
{
int cl_begin = cl->begin;
int cl_end = cl->end;
int cl_size = cl_end - cl_begin + 1;
int depth = cl->depth;
int bl_begin = cl->bl_begin;
int bl_end = cl->bl_end;
int bl_size = bl_end - bl_begin + 1;
double bl_spdiam = cl->bl_spdiam;
rrr_t *RRR_parent = cl->RRR;
double *restrict Werr = Wstruct->Werr;
double *restrict Wgap = Wstruct->Wgap;
int *restrict Windex = Wstruct->Windex;
double *restrict Wshifted = Wstruct->Wshifted;
/* Allocate memory for new representation for cluster */
double *D = (double*)malloc(bl_size*sizeof(double));
double *L = (double*)malloc(bl_size*sizeof(double));
double *DL = (double*)malloc(bl_size*sizeof(double));
double *DLL = (double*)malloc(bl_size*sizeof(double));
assert(D!=NULL);
assert(L!=NULL);
assert(DL!=NULL);
assert(DLL!=NULL);
/* Recompute DL and DLL */
int i;
double tmp;
double *D_parent = RRR_parent->D;
double *L_parent = RRR_parent->L;
for (i=0; i<bl_size-1; i++) {
tmp = D_parent[i]*L_parent[i];
DL[i] = tmp;
DLL[i] = tmp*L_parent[i];
}
double *DL_parent = DL;
double *DLL_parent = DLL;
double RQtol = 2*DBL_EPSILON;
double pivmin = tolstruct->pivmin;
/* to shift as close as possible refine extremal eigenvalues */
int k, p;
double savegap;
for (k=0; k<2; k++) {
if (k == 0) {
p = Windex[cl_begin];
savegap = Wgap[cl_begin];
Wgap[cl_begin] = 0.0;
} else {
p = Windex[cl_end ];
savegap = Wgap[cl_end];
Wgap[cl_end] = 0.0;
}
int info;
int offset = Windex[cl_begin] - 1;
odrrb
(&bl_size, D_parent, DLL_parent, &p, &p, &RQtol,
&RQtol, &offset, &Wshifted[cl_begin], &Wgap[cl_begin],
&Werr[cl_begin], work, iwork, &pivmin, &bl_spdiam, &bl_size, &info);
assert( info == 0 );
if (k == 0) {
Wgap[cl_begin] = fmax(0, (Wshifted[cl_begin+1]-Werr[cl_begin+1])
- (Wshifted[cl_begin]+Werr[cl_begin]) );
} else {
Wgap[cl_end] = savegap;
}
} /* end k */
double left_gap = cl->lgap;
double right_gap = Wgap[cl_end];
/* Compute new RRR and store it in D and L */
int info;
int IONE=1;
double tau;
odrrf
(&bl_size, D_parent, L_parent, DL_parent,
&IONE, &cl_size, &Wshifted[cl_begin], &Wgap[cl_begin],
&Werr[cl_begin], &bl_spdiam, &left_gap, &right_gap,
&pivmin, &tau, D, L, work, &info);
assert(info == 0);
/* Update shift and store it */
tmp = L_parent[bl_size-1] + tau;
L[bl_size-1] = tmp;
/* Compute D*L and D*L*L */
for (i=0; i<bl_size-1; i++) {
tmp = D[i]*L[i];
DL[i] = tmp;
DLL[i] = tmp*L[i];
}
/* New RRR of cluster is usually created at the parent level and
* initialized to parent RRR, now reset to contain new RRR */
if (RRR_parent->copied_parent_rrr == true) {
free(RRR_parent->D);
free(RRR_parent->L);
}
rrr_t *RRR = PMR_reset_rrr(RRR_parent, D, L, DL, DLL, bl_size, depth+1);
/* Update shifted eigenvalues */
for (k=cl_begin; k<=cl_end; k++) {
double fudge = THREE*DBL_EPSILON*fabs(Wshifted[k]);
Wshifted[k] -= tau;
fudge += FOUR*DBL_EPSILON*fabs(Wshifted[k]);
Werr[k] += fudge;
}
/* Assure that structure is not freed while it is processed */
PMR_increment_rrr_dependencies(RRR);
return RRR;
} /* end compute_new_rrr */
static inline void init_workQ(workQ_t *workQ, in_t *Dstruct,
val_t *Wstruct)
{
double *restrict D = Dstruct->D;
double *restrict L = Dstruct->E;
int *restrict isplit = Dstruct->isplit;
int m = Wstruct->m;
double *vlp = Wstruct->vlp;
double *restrict W = Wstruct->W;
double *restrict Werr = Wstruct->Werr;
int *restrict iblock = Wstruct->iblock;
int j;
int begin , end;
int Wbegin, Wend;
int nbl;
double sigma;
rrr_t *RRR;
double lgap;
task_t *task;
/* For every unreducible block of the matrix create a task
* and put it in the queue */
begin = 0;
Wbegin = 0;
for (j=0; j<Dstruct->nsplit; j++) {
end = isplit[j] - 1;
sigma = L[end];
Wend = Wbegin-1;
while (Wend < m-1 && iblock[Wend + 1] == j+1) {
Wend++;
}
if (Wend < Wbegin) {
begin = end + 1;
continue;
}
nbl = end - begin + 1;
RRR = PMR_create_rrr(&D[begin], &L[begin], NULL, NULL, nbl, -1);
if (nbl == 1) {
/* To make sure that RRR is freed when s-task is processed */
PMR_increment_rrr_dependencies(RRR);
PMR_set_parent_processed_flag(RRR);
task = PMR_create_s_task(Wbegin, Wbegin, 1, begin, end, Wbegin,
Wend, 0, 0, RRR);
PMR_insert_task_at_back(workQ->s_queue, task);
begin = end + 1;
Wbegin = Wend + 1;
continue;
}
lgap = fmax(0.0, (W[Wbegin]+sigma) - Werr[Wbegin] - (*vlp) );
task = PMR_create_c_task(Wbegin, Wend, 0, begin, end, Wbegin,
Wend, 0, lgap, RRR);
PMR_insert_task_at_back(workQ->c_queue, task);
begin = end + 1;
Wbegin = Wend + 1;
}
/* end of loop over block */
}