/*
* Set up environment and global constraints (dir-edge constraints, containment constraints
* etc).
*
* diredges: 0=no dir edge constraints
* 1=one separation constraint for each edge (in acyclic subgraph)
* 2=DiG-CoLa level constraints
*/
CMajEnvVPSC *initCMajVPSC(int n, float *packedMat, vtx_data * graph,
ipsep_options * opt, int diredges)
{
int i, j;
/* nv is the number of real nodes */
int nConCs;
/* fprintf(stderr,"Entered initCMajVPSC\n"); */
CMajEnvVPSC *e = GNEW(CMajEnvVPSC);
e->A = NULL;
e->packedMat = packedMat;
/* if we have clusters then we'll need two constraints for each var in
* a cluster */
e->nldv = 2 * opt->clusters->nclusters;
e->nv = n - e->nldv;
e->ndv = 0;
e->gcs = NULL;
e->vs = N_GNEW(n, Variable *);
for (i = 0; i < n; i++) {
e->vs[i] = newVariable(i, 1.0, 1.0);
}
e->gm = 0;
if (diredges == 1) {
if (Verbose)
fprintf(stderr, " generate edge constraints...\n");
for (i = 0; i < e->nv; i++) {
for (j = 1; j < graph[i].nedges; j++) {
/* fprintf(stderr,"edist=%f\n",graph[i].edists[j]); */
if (graph[i].edists[j] > 0.01) {
e->gm++;
}
}
}
e->gcs = newConstraints(e->gm);
e->gm = 0;
for (i = 0; i < e->nv; i++) {
for (j = 1; j < graph[i].nedges; j++) {
int u = i, v = graph[i].edges[j];
if (graph[i].edists[j] > 0) {
e->gcs[e->gm++] =
newConstraint(e->vs[u], e->vs[v], opt->edge_gap);
}
}
}
} else if (diredges == 2) {
int *ordering = NULL, *ls = NULL, cvar;
double halfgap;
DigColaLevel *levels;
Variable **vs = e->vs;
/* e->ndv is the number of dummy variables required, one for each boundary */
if (compute_hierarchy(graph, e->nv, 1e-2, 1e-1, NULL, &ordering, &ls,
&e->ndv)) return NULL;
levels = assign_digcola_levels(ordering, e->nv, ls, e->ndv);
if (Verbose)
fprintf(stderr, "Found %d DiG-CoLa boundaries\n", e->ndv);
e->gm =
get_num_digcola_constraints(levels, e->ndv + 1) + e->ndv - 1;
e->gcs = newConstraints(e->gm);
e->gm = 0;
e->vs = N_GNEW(n + e->ndv, Variable *);
for (i = 0; i < n; i++) {
e->vs[i] = vs[i];
}
free(vs);
/* create dummy vars */
for (i = 0; i < e->ndv; i++) {
/* dummy vars should have 0 weight */
cvar = n + i;
e->vs[cvar] = newVariable(cvar, 1.0, 0.000001);
}
halfgap = opt->edge_gap;
for (i = 0; i < e->ndv; i++) {
cvar = n + i;
/* outgoing constraints for each var in level below boundary */
for (j = 0; j < levels[i].num_nodes; j++) {
e->gcs[e->gm++] =
newConstraint(e->vs[levels[i].nodes[j]], e->vs[cvar],
halfgap);
}
/* incoming constraints for each var in level above boundary */
for (j = 0; j < levels[i + 1].num_nodes; j++) {
e->gcs[e->gm++] =
newConstraint(e->vs[cvar],
e->vs[levels[i + 1].nodes[j]], halfgap);
}
}
/* constraints between adjacent boundary dummy vars */
for (i = 0; i < e->ndv - 1; i++) {
e->gcs[e->gm++] =
newConstraint(e->vs[n + i], e->vs[n + i + 1], 0);
}
}
int
stress_majorization_with_hierarchy(
vtx_data* graph, /* Input graph in sparse representation */
int n, /* Number of nodes */
int nedges_graph, /* Number of edges */
double** d_coords, /* Coordinates of nodes (output layout) */
int dim, /* Dimemsionality of layout */
int smart_ini, /* smart initialization */
int model, /* difference model */
int maxi, /* max iterations */
double levels_gap
)
{
int iterations = 0; /* Output: number of iteration of the process */
/*************************************************
** Computation of full, dense, unrestricted k-D **
** stress minimization by majorization **
** This function imposes HIERARCHY CONSTRAINTS **
*************************************************/
int i,j,k;
bool directionalityExist = FALSE;
float * lap1 = NULL;
float * dist_accumulator = NULL;
float * tmp_coords = NULL;
float ** b = NULL;
#ifdef NONCORE
FILE * fp=NULL;
#endif
double * degrees = NULL;
float * lap2=NULL;
int lap_length;
float * f_storage=NULL;
float ** coords=NULL;
double conj_tol=tolerance_cg; /* tolerance of Conjugate Gradient */
float ** unpackedLap = NULL;
CMajEnv *cMajEnv = NULL;
clock_t start_time;
double y_0;
int length;
DistType diameter;
float * Dij=NULL;
/* to compensate noises, we never consider gaps smaller than 'abs_tol' */
double abs_tol=1e-2;
/* Additionally, we never consider gaps smaller than 'abs_tol'*<avg_gap> */
double relative_tol=levels_sep_tol;
int *ordering=NULL, *levels=NULL;
double hierarchy_spread;
float constant_term;
int count;
double degree;
int step;
float val;
double old_stress, new_stress;
bool converged;
int len;
int num_levels;
float *hierarchy_boundaries;
if (graph[0].edists!=NULL) {
for (i=0; i<n; i++) {
for (j=1; j<graph[i].nedges; j++) {
directionalityExist = directionalityExist || (graph[i].edists[j]!=0);
}
}
}
if (!directionalityExist) {
return stress_majorization_kD_mkernel(graph, n, nedges_graph, d_coords, dim, smart_ini, model, maxi);
}
/******************************************************************
** First, partition nodes into layers: These are our constraints **
******************************************************************/
if (smart_ini) {
double* x;
double* y;
if (dim>2) {
/* the dim==2 case is handled below */
stress_majorization_kD_mkernel(graph, n, nedges_graph, d_coords+1, dim-1, smart_ini, model, 15);
/* now copy the y-axis into the (dim-1)-axis */
for (i=0; i<n; i++) {
d_coords[dim-1][i] = d_coords[1][i];
}
}
x = d_coords[0]; y = d_coords[1];
compute_y_coords(graph, n, y, n);
hierarchy_spread = compute_hierarchy(graph, n, abs_tol, relative_tol, y, &ordering, &levels, &num_levels);
if (num_levels<=1) {
/* no hierarchy found, use faster algorithm */
return stress_majorization_kD_mkernel(graph, n, nedges_graph, d_coords, dim, smart_ini, model, maxi);
}
if (levels_gap>0) {
/* ensure that levels are separated in the initial layout */
double displacement = 0;
int stop;
for (i=0; i<num_levels; i++) {
displacement+=MAX((double)0,levels_gap-(y[ordering[levels[i]]]+displacement-y[ordering[levels[i]-1]]));
stop = i<num_levels-1 ? levels[i+1] : n;
for (j=levels[i]; j<stop; j++) {
y[ordering[j]] += displacement;
}
}
}
if (dim==2) {
IMDS_given_dim(graph, n, y, x, Epsilon);
}
}
else {
initLayout(graph, n, dim, d_coords);
hierarchy_spread = compute_hierarchy(graph, n, abs_tol, relative_tol, NULL, &ordering, &levels, &num_levels);
}
if (n == 1) return 0;
hierarchy_boundaries = N_GNEW(num_levels, float);
/****************************************************
** Compute the all-pairs-shortest-distances matrix **
****************************************************/
if (maxi==0)
return iterations;
if (model == MODEL_SUBSET) {
/* weight graph to separate high-degree nodes */
/* and perform slower Dijkstra-based computation */
if (Verbose)
fprintf(stderr, "Calculating subset model");
Dij = compute_apsp_artifical_weights_packed(graph, n);
} else if (model == MODEL_CIRCUIT) {
Dij = circuitModel(graph, n);
if (!Dij) {
agerr(AGWARN,
"graph is disconnected. Hence, the circuit model\n");
agerr(AGPREV,
"is undefined. Reverting to the shortest path model.\n");
}
}
if (!Dij) {
if (Verbose)
fprintf(stderr, "Calculating shortest paths");
Dij = compute_apsp_packed(graph, n);
}
diameter=-1;
length = n+n*(n-1)/2;
for (i=0; i<length; i++) {
if (Dij[i]>diameter) {
diameter = (int)Dij[i];
}
}
if (!smart_ini) {
/* for numerical stability, scale down layout */
/* No Jiggling, might conflict with constraints */
double max=1;
for (i=0; i<dim; i++) {
for (j=0; j<n; j++) {
if (fabs(d_coords[i][j])>max) {
max=fabs(d_coords[i][j]);
}
}
}
for (i=0; i<dim; i++) {
for (j=0; j<n; j++) {
d_coords[i][j]*=10/max;
}
}
}
if (levels_gap>0) {
int length = n+n*(n-1)/2;
double sum1, sum2, scale_ratio;
int count;
sum1=(float)(n*(n-1)/2);
sum2=0;
for (count=0, i=0; i<n-1; i++) {
count++; // skip self distance
for (j=i+1; j<n; j++,count++) {
sum2+=distance_kD(d_coords, dim, i, j)/Dij[count];
}
}
scale_ratio=sum2/sum1;
/* double scale_ratio=10; */
for (i=0; i<length; i++) {
Dij[i]*=(float)scale_ratio;
}
}
/**************************
** Layout initialization **
**************************/
for (i=0; i<dim; i++) {
orthog1(n, d_coords[i]);
}
/* for the y-coords, don't center them, but translate them so y[0]=0 */
y_0 = d_coords[1][0];
for (i=0; i<n; i++) {
d_coords[1][i] -= y_0;
}
coords = N_GNEW(dim, float*);
f_storage = N_GNEW(dim*n, float);
for (i=0; i<dim; i++) {
coords[i] = f_storage+i*n;
for (j=0; j<n; j++) {
coords[i][j] = (float)(d_coords[i][j]);
}
}
/* compute constant term in stress sum
* which is \sum_{i<j} w_{ij}d_{ij}^2
*/
constant_term=(float)(n*(n-1)/2);
/**************************
** Laplacian computation **
**************************/
lap2 = Dij;
lap_length = n+n*(n-1)/2;
square_vec(lap_length, lap2);
/* compute off-diagonal entries */
invert_vec(lap_length, lap2);
/* compute diagonal entries */
count=0;
degrees = N_GNEW(n, double);
set_vector_val(n, 0, degrees);
for (i=0; i<n-1; i++) {
degree=0;
count++; // skip main diag entry
for (j=1; j<n-i; j++,count++) {
val = lap2[count];
degree+=val; degrees[i+j]-=val;
}
degrees[i]-=degree;
}
for (step=n,count=0,i=0; i<n; i++,count+=step,step--) {
lap2[count]=(float)degrees[i];
}
#ifdef NONCORE
fpos_t pos;
if (n>max_nodes_in_mem) {
#define FILENAME "tmp_Dij$$$.bin"
fp = fopen(FILENAME, "wb");
fwrite(lap2, sizeof(float), lap_length, fp);
fclose(fp);
}
#endif
/*************************
** Layout optimization **
*************************/
b = N_GNEW (dim, float*);
b[0] = N_GNEW (dim*n, float);
for (k=1; k<dim; k++) {
b[k] = b[0]+k*n;
}
tmp_coords = N_GNEW(n, float);
dist_accumulator = N_GNEW(n, float);
#ifdef NONCORE
if (n<=max_nodes_in_mem) {
#endif
lap1 = N_GNEW(lap_length, float);
#ifdef NONCORE
}