int Zoltan_RIB_inertial2d(
int Tflops_Special, /* Use Tflops_Special communication;
should be 0 if called from serial_rib */
struct Dot_Struct *dotpt, /* graph data structure for weights */
int *dindx, /* index array into dotpt; if NULL, access dotpt
directly */
int dotnum, /* number of vtxs in graph */
int wgtflag, /* are vertex weights being used? */
double cm[3], /* center of mass in each direction */
double evec[3], /* eigenvector */
double *value, /* array for value to sort on */
MPI_Comm comm, /* communicator for partition */
int proc, /* global proc number (Tflops_Special) */
int nproc, /* Number of procs in partition (Tflops_Special) */
int proclower /* Lowest numbered proc in partition (Tflops_Special)*/
)
{
double tensor[2][2]; /* inertial tensor */
double xcm, ycm; /* center of mass in each direction */
double tmp1[3], tmp2[3]; /* temporary variables for MPI_Allreduces */
double xx, yy, xy; /* elements of inertial tensor */
double xdif, ydif; /* deviation from center of mass */
double eval, res; /* eigenvalue and error in eval calculation */
double wgt_sum; /* sum of all the vertex weights */
int i, j; /* loop counter */
double xcmt, ycmt, wgtt; /* temp for center of mass */
double xxt, yyt, xyt; /* temp for tensor */
int rank = 0; /* rank in partition (Tflops_Special) */
/* Compute center of mass and total mass. */
xcm = ycm = 0.0;
if (wgtflag) {
wgt_sum = 0.0;
for (j = 0; j < dotnum; j++) {
i = (dindx ? dindx[j] : j);
wgt_sum += dotpt[i].Weight[0];
xcm += dotpt[i].Weight[0]*dotpt[i].X[0];
ycm += dotpt[i].Weight[0]*dotpt[i].X[1];
}
}
else {
wgt_sum = dotnum;
for (j = 0; j < dotnum; j++) {
i = (dindx ? dindx[j] : j);
xcm += dotpt[i].X[0];
ycm += dotpt[i].X[1];
}
}
/* Sum weights across processors */
if (Tflops_Special) {
rank = proc - proclower;
tmp1[0] = xcm; tmp1[1] = ycm; tmp1[2] = wgt_sum;
Zoltan_RIB_reduce_double(tmp1, tmp2, 3, comm, nproc, rank, proc, 1);
xcmt = tmp2[0]; ycmt = tmp2[1]; wgtt = tmp2[2];
}
else {
tmp1[0] = xcm; tmp1[1] = ycm; tmp1[2] = wgt_sum;
MPI_Allreduce(tmp1, tmp2, 3, MPI_DOUBLE, MPI_SUM, comm);
xcmt = tmp2[0]; ycmt = tmp2[1]; wgtt = tmp2[2];
}
xcm = xcmt/wgtt;
ycm = ycmt/wgtt;
/* Generate 3 elements of Inertial tensor. */
xx = yy = xy = 0.0;
if (wgtflag)
for (j = 0; j < dotnum; j++) {
i = (dindx ? dindx[j] : j);
xdif = dotpt[i].X[0] - xcm;
ydif = dotpt[i].X[1] - ycm;
xx += dotpt[i].Weight[0]*xdif*xdif;
yy += dotpt[i].Weight[0]*ydif*ydif;
xy += dotpt[i].Weight[0]*xdif*ydif;
}
else
for (j = 0; j < dotnum; j++) {
i = (dindx ? dindx[j] : j);
xdif = dotpt[i].X[0] - xcm;
ydif = dotpt[i].X[1] - ycm;
xx += xdif*xdif;
yy += ydif*ydif;
xy += xdif*ydif;
}
/* Sum tensor across processors */
if (Tflops_Special) {
tmp1[0] = xx; tmp1[1] = yy; tmp1[2] = xy;
Zoltan_RIB_reduce_double(tmp1, tmp2, 3, comm, nproc, rank, proc, 1);
xxt = tmp2[0]; yyt = tmp2[1]; xyt = tmp2[2];
}
else {
tmp1[0] = xx; tmp1[1] = yy; tmp1[2] = xy;
MPI_Allreduce(tmp1, tmp2, 3, MPI_DOUBLE, MPI_SUM, comm);
xxt = tmp2[0]; yyt = tmp2[1]; xyt = tmp2[2];
}
/* Compute eigenvector with maximum eigenvalue. */
tensor[0][0] = xxt;
tensor[1][1] = yyt;
tensor[1][0] = tensor[0][1] = xyt;
evals2(tensor, &res, &eval);
eigenvec2(tensor, eval, evec, &res);
/* Calculate value to sort/split on for each cell. */
/* This is inner product with eigenvector. */
for (j = 0; j < dotnum; j++) {
i = (dindx ? dindx[j] : j);
value[j] = (dotpt[i].X[0] - xcm)*evec[0] +
(dotpt[i].X[1] - ycm)*evec[1];
}
cm[0] = xcm;
cm[1] = ycm;
/* zero unused third dimension */
cm[2] = evec[2] = 0.0;
return(ZOLTAN_OK);
}
void
inertial2d (
struct vtx_data **graph, /* graph data structure for weights */
int nvtxs, /* number of vtxs in graph */
int cube_or_mesh, /* 0 => hypercube, d => d-dimensional mesh */
int nsets, /* number of sets to divide into */
float *x,
float *y, /* x and y coordinates of vertices */
int *sets, /* set each vertex gets assigned to */
double *goal, /* desired set sizes */
int using_vwgts /* are vertex weights being used? */
)
{
extern int DEBUG_INERTIAL; /* debug flag for inertial method */
extern double inertial_axis_time; /* time spent finding inertial axis */
extern double median_time; /* time spent computing medians */
double tensor[2][2]; /* inertial tensor */
double evec[2]; /* eigenvector of tensor */
double *value; /* values along selected direction to sort */
double xcm, ycm; /* center of mass in each direction */
double xx, yy, xy; /* elements of inertial tensor */
double xdif, ydif; /* deviation from center of mass */
double eval, res; /* eigenvalue and error in eval calculation */
double vwgt_sum; /* sum of all the vertex weights */
double time; /* timing parameters */
int *space; /* space required by median routine */
int i; /* loop counter */
double seconds();
void evals2(), eigenvec2(), rec_median_1();
/* Compute center of mass and total mass. */
time = seconds();
xcm = ycm = 0.0;
if (using_vwgts) {
vwgt_sum = 0.0;
for (i = 1; i <= nvtxs; i++) {
vwgt_sum += graph[i]->vwgt;
xcm += graph[i]->vwgt * x[i];
ycm += graph[i]->vwgt * y[i];
}
}
else {
vwgt_sum = nvtxs;
for (i = 1; i <= nvtxs; i++) {
xcm += x[i];
ycm += y[i];
}
}
xcm /= vwgt_sum;
ycm /= vwgt_sum;
/* Generate 3 elements of Inertial tensor. */
xx = yy = xy = 0.0;
if (using_vwgts) {
for (i = 1; i <= nvtxs; i++) {
xdif = x[i] - xcm;
ydif = y[i] - ycm;
xx += graph[i]->vwgt * xdif * xdif;
yy += graph[i]->vwgt * ydif * ydif;
xy += graph[i]->vwgt * xdif * ydif;
}
}
else {
for (i = 1; i <= nvtxs; i++) {
xdif = x[i] - xcm;
ydif = y[i] - ycm;
xx += xdif * xdif;
yy += ydif * ydif;
xy += xdif * ydif;
}
}
/* Compute eigenvector with maximum eigenvalue. */
tensor[0][0] = xx;
tensor[1][1] = yy;
tensor[1][0] = tensor[0][1] = xy;
evals2(tensor, &res, &eval);
eigenvec2(tensor, eval, evec, &res);
inertial_axis_time += seconds() - time;
if (DEBUG_INERTIAL > 0) {
printf("Principle Axis = (%g, %g), Eval=%g, Residual=%e\n",
evec[0], evec[1], eval, res);
}
/* Allocate space for value array. */
value = smalloc((nvtxs + 1) * sizeof(double));
/* Calculate value to sort/split on for each cell. */
/* This is inner product with eigenvector. */
for (i = 1; i <= nvtxs; i++) {
value[i] = (x[i] - xcm) * evec[0] + (y[i] - ycm) * evec[1];
}
/* Now find the median value and partition based upon it. */
space = smalloc(nvtxs * sizeof(int));
time = seconds();
rec_median_1(graph, value, nvtxs, space, cube_or_mesh, nsets, goal,
using_vwgts, sets, TRUE);
median_time += seconds() - time;
sfree(space);
sfree(value);
}
