/* Compute and insert migration along directed edge (may fork child) */
static MIGRATION *
create_migration(RBFNODE *from_rbf, RBFNODE *to_rbf)
{
const double end_thresh = 5e-6;
PRICEMAT pmtx;
MIGRATION *newmig;
double *src_rem, *dst_rem;
double total_rem = 1., move_amt;
int i, j;
/* check if exists already */
for (newmig = from_rbf->ejl; newmig != NULL;
newmig = nextedge(from_rbf,newmig))
if (newmig->rbfv[1] == to_rbf)
return(NULL);
/* else allocate */
#ifdef DEBUG
fprintf(stderr, "Building path from (theta,phi) (%.0f,%.0f) ",
get_theta180(from_rbf->invec),
get_phi360(from_rbf->invec));
fprintf(stderr, "to (%.0f,%.0f) with %d x %d matrix\n",
get_theta180(to_rbf->invec),
get_phi360(to_rbf->invec),
from_rbf->nrbf, to_rbf->nrbf);
#endif
newmig = new_migration(from_rbf, to_rbf);
if (run_subprocess())
return(newmig); /* child continues */
price_routes(&pmtx, from_rbf, to_rbf);
src_rem = (double *)malloc(sizeof(double)*from_rbf->nrbf);
dst_rem = (double *)malloc(sizeof(double)*to_rbf->nrbf);
if ((src_rem == NULL) | (dst_rem == NULL)) {
fprintf(stderr, "%s: Out of memory in create_migration()\n",
progname);
exit(1);
}
/* starting quantities */
memset(newmig->mtx, 0, sizeof(float)*from_rbf->nrbf*to_rbf->nrbf);
for (i = from_rbf->nrbf; i--; )
src_rem[i] = rbf_volume(&from_rbf->rbfa[i]) / from_rbf->vtotal;
for (j = to_rbf->nrbf; j--; )
dst_rem[j] = rbf_volume(&to_rbf->rbfa[j]) / to_rbf->vtotal;
do { /* move a bit at a time */
move_amt = migration_step(newmig, src_rem, dst_rem, &pmtx);
total_rem -= move_amt;
} while ((total_rem > end_thresh) & (move_amt > 0));
for (i = from_rbf->nrbf; i--; ) { /* normalize final matrix */
double nf = rbf_volume(&from_rbf->rbfa[i]);
if (nf <= FTINY) continue;
nf = from_rbf->vtotal / nf;
for (j = to_rbf->nrbf; j--; )
mtx_coef(newmig,i,j) *= nf; /* row now sums to 1.0 */
}
end_subprocess(); /* exit here if subprocess */
free_routes(&pmtx); /* free working arrays */
free(src_rem);
free(dst_rem);
return(newmig);
}
/* Take a step in migration by choosing optimal bucket to transfer */
static double
migration_step(MIGRATION *mig, double *src_rem, double *dst_rem, const PRICEMAT *pm)
{
const double maxamt = 1./(double)pm->ncols;
const double minamt = maxamt*5e-6;
double *src_cost;
struct {
int s, d; /* source and destination */
double price; /* price estimate per amount moved */
double amt; /* amount we can move */
} cur, best;
int i;
/* allocate cost array */
src_cost = (double *)malloc(sizeof(double)*pm->nrows);
if (src_cost == NULL) {
fprintf(stderr, "%s: Out of memory in migration_step()\n",
progname);
exit(1);
}
for (i = pm->nrows; i--; ) /* starting costs for diff. */
src_cost[i] = min_cost(src_rem[i], dst_rem, pm, i);
/* find best source & dest. */
best.s = best.d = -1; best.price = FHUGE; best.amt = 0;
for (cur.s = pm->nrows; cur.s--; ) {
double cost_others = 0;
if (src_rem[cur.s] <= minamt)
continue;
/* examine cheapest dest. */
for (i = 0; i < pm->ncols; i++)
if (dst_rem[ cur.d = psortrow(pm,cur.s)[i] ] > minamt)
break;
if (i >= pm->ncols)
break;
if ((cur.price = pricerow(pm,cur.s)[cur.d]) >= best.price)
continue; /* no point checking further */
cur.amt = (src_rem[cur.s] < dst_rem[cur.d]) ?
src_rem[cur.s] : dst_rem[cur.d];
if (cur.amt > maxamt) cur.amt = maxamt;
dst_rem[cur.d] -= cur.amt; /* add up differential costs */
for (i = pm->nrows; i--; )
if (i != cur.s)
cost_others += min_cost(src_rem[i], dst_rem, pm, i)
- src_cost[i];
dst_rem[cur.d] += cur.amt; /* undo trial move */
cur.price += cost_others/cur.amt; /* adjust effective price */
if (cur.price < best.price) /* are we better than best? */
best = cur;
}
free(src_cost); /* finish up */
if ((best.s < 0) | (best.d < 0)) /* nothing left to move? */
return(.0);
/* else make the actual move */
mtx_coef(mig,best.s,best.d) += best.amt;
src_rem[best.s] -= best.amt;
dst_rem[best.d] -= best.amt;
return(best.amt);
}
/* Compute and insert migration along directed edge (may fork child) */
static MIGRATION *
create_migration(RBFNODE *from_rbf, RBFNODE *to_rbf)
{
MIGRATION *newmig;
int i, j;
/* check if exists already */
for (newmig = from_rbf->ejl; newmig != NULL;
newmig = nextedge(from_rbf,newmig))
if (newmig->rbfv[1] == to_rbf)
return(NULL);
/* else allocate */
#ifdef DEBUG
fprintf(stderr, "Building path from (theta,phi) (%.1f,%.1f) ",
get_theta180(from_rbf->invec),
get_phi360(from_rbf->invec));
fprintf(stderr, "to (%.1f,%.1f) with %d x %d matrix\n",
get_theta180(to_rbf->invec),
get_phi360(to_rbf->invec),
from_rbf->nrbf, to_rbf->nrbf);
#endif
newmig = new_migration(from_rbf, to_rbf);
if (run_subprocess())
return(newmig); /* child continues */
/* compute transport plan */
compute_nDSFs(from_rbf, to_rbf);
plan_transport(newmig);
for (i = from_rbf->nrbf; i--; ) { /* normalize final matrix */
double nf = rbf_volume(&from_rbf->rbfa[i]);
if (nf <= FTINY) continue;
nf = from_rbf->vtotal / nf;
for (j = to_rbf->nrbf; j--; )
mtx_coef(newmig,i,j) *= nf; /* row now sums to 1.0 */
}
end_subprocess(); /* exit here if subprocess */
return(newmig);
}
