SparseMatrix call_tri(int n, int dim, real * x)
{
real one = 1;
int i, ii, jj;
SparseMatrix A;
SparseMatrix B;
int* edgelist = NULL;
real* xv = N_GNEW(n, real);
real* yv = N_GNEW(n, real);
int numberofedges;
for (i = 0; i < n; i++) {
xv[i] = x[i * 2];
yv[i] = x[i * 2 + 1];
}
if (n > 2) {
edgelist = delaunay_tri (xv, yv, n, &numberofedges);
} else {
numberofedges = 0;
}
A = SparseMatrix_new(n, n, 1, MATRIX_TYPE_REAL, FORMAT_COORD);
for (i = 0; i < numberofedges; i++) {
ii = edgelist[i * 2];
jj = edgelist[i * 2 + 1];
SparseMatrix_coordinate_form_add_entries(A, 1, &(ii), &(jj), &one);
}
if (n == 2) { /* if two points, add edge i->j */
ii = 0;
jj = 1;
SparseMatrix_coordinate_form_add_entries(A, 1, &(ii), &(jj), &one);
}
for (i = 0; i < n; i++) {
SparseMatrix_coordinate_form_add_entries(A, 1, &i, &i, &one);
}
B = SparseMatrix_from_coordinate_format(A);
SparseMatrix_delete(A);
A = SparseMatrix_symmetrize(B, FALSE);
SparseMatrix_delete(B);
B = A;
free (edgelist);
free (xv);
free (yv);
return B;
}
static SparseMatrix check_compatibility(SparseMatrix A, int ne, pedge *edges, int compatibility_method, real tol){
/* go through the links and make sure edges are compatible */
SparseMatrix B, C;
int *ia, *ja, i, j, jj;
real start;
real dist;
B = SparseMatrix_new(1, 1, 1, MATRIX_TYPE_REAL, FORMAT_COORD);
ia = A->ia; ja = A->ja;
//SparseMatrix_print("A",A);
start = clock();
for (i = 0; i < ne; i++){
for (j = ia[i]; j < ia[i+1]; j++){
jj = ja[j];
if (i == jj) continue;
if (compatibility_method == COMPATIBILITY_DIST){
dist = edge_compatibility_full(edges[i], edges[jj]);
} else if (compatibility_method == COMPATIBILITY_FULL){
dist = edge_compatibility(edges[i], edges[jj]);
}
/*
fprintf(stderr,"edge %d = {",i);
pedge_print("", edges[i]);
fprintf(stderr,"edge %d = {",jj);
pedge_print("", edges[jj]);
fprintf(stderr,"compatibility=%f\n",dist);
*/
if (ABS(dist) > tol){
B = SparseMatrix_coordinate_form_add_entries(B, 1, &i, &jj, &dist);
B = SparseMatrix_coordinate_form_add_entries(B, 1, &jj, &i, &dist);
}
}
}
C = SparseMatrix_from_coordinate_format(B);
//SparseMatrix_print("C",C);
SparseMatrix_delete(B);
B = C;
if (Verbose > 1)
fprintf(stderr, "edge compatibilitu time = %f\n",((real) (clock() - start))/CLOCKS_PER_SEC);
return B;
}
SparseMatrix call_tri2(int n, int dim, real * xx)
{
real *x, *y;
v_data *delaunay;
int i, j;
SparseMatrix A;
SparseMatrix B;
real one = 1;
x = N_GNEW(n, real);
y = N_GNEW(n, real);
for (i = 0; i < n; i++) {
x[i] = xx[dim * i];
y[i] = xx[dim * i + 1];
}
delaunay = UG_graph(x, y, n, 0);
A = SparseMatrix_new(n, n, 1, MATRIX_TYPE_REAL, FORMAT_COORD);
for (i = 0; i < n; i++) {
for (j = 1; j < delaunay[i].nedges; j++) {
SparseMatrix_coordinate_form_add_entries(A, 1, &i,
&(delaunay[i].
edges[j]), &one);
}
}
for (i = 0; i < n; i++) {
SparseMatrix_coordinate_form_add_entries(A, 1, &i, &i, &one);
}
B = SparseMatrix_from_coordinate_format(A);
B = SparseMatrix_symmetrize(B, FALSE);
SparseMatrix_delete(A);
free (x);
free (y);
freeGraph (delaunay);
return B;
}
static pedge* modularity_ink_bundling(int dim, int ne, SparseMatrix B, pedge* edges, real angle_param, real angle){
int *assignment = NULL, flag, nclusters;
real modularity;
int *clusterp, *clusters;
SparseMatrix D, C;
point_t meet1, meet2;
real ink0, ink1;
pedge e;
int i, j, jj;
int use_value_for_clustering = TRUE;
//int use_value_for_clustering = FALSE;
SparseMatrix BB;
/* B may contain negative entries */
BB = SparseMatrix_copy(B);
BB = SparseMatrix_apply_fun(BB, absfun);
modularity_clustering(BB, TRUE, 0, use_value_for_clustering, &nclusters, &assignment, &modularity, &flag);
SparseMatrix_delete(BB);
#ifdef OPENGL
clusters_global = assignment;
#endif
assert(!flag);
if (Verbose > 1) fprintf(stderr, "there are %d clusters, modularity = %f\n",nclusters, modularity);
C = SparseMatrix_new(1, 1, 1, MATRIX_TYPE_PATTERN, FORMAT_COORD);
for (i = 0; i < ne; i++){
jj = assignment[i];
SparseMatrix_coordinate_form_add_entries(C, 1, &jj, &i, NULL);
}
D = SparseMatrix_from_coordinate_format(C);
SparseMatrix_delete(C);
clusterp = D->ia;
clusters = D->ja;
for (i = 0; i < nclusters; i++){
ink1 = ink(edges, clusterp[i+1] - clusterp[i], &(clusters[clusterp[i]]), &ink0, &meet1, &meet2, angle_param, angle);
if (Verbose > 1)
fprintf(stderr,"nedges = %d ink0 = %f, ink1 = %f\n",clusterp[i+1] - clusterp[i], ink0, ink1);
if (ink1 < ink0){
for (j = clusterp[i]; j < clusterp[i+1]; j++){
/* make this edge 5 points, insert two meeting points at 1 and 2, make 3 the last point */
edges[clusters[j]] = pedge_double(edges[clusters[j]]);
e = edges[clusters[j]] = pedge_double(edges[clusters[j]]);
e->x[1*dim] = meet1.x;
e->x[1*dim+1] = meet1.y;
e->x[2*dim] = meet2.x;
e->x[2*dim+1] = meet2.y;
e->x[3*dim] = e->x[4*dim];
e->x[3*dim+1] = e->x[4*dim+1];
e->npoints = 4;
}
#ifdef OPENGL
edges_global = edges;
drawScene();
#endif
}
}
SparseMatrix_delete(D);
return edges;
}
static SparseMatrix get_overlap_graph(int dim, int n, real *x, real *width, int check_overlap_only){
/* if check_overlap_only = TRUE, we only check whether there is one overlap */
scan_point *scanpointsx, *scanpointsy;
int i, k, neighbor;
SparseMatrix A = NULL, B = NULL;
rb_red_blk_node *newNode, *newNode0, *newNode2 = NULL;
rb_red_blk_tree* treey;
real one = 1;
A = SparseMatrix_new(n, n, 1, MATRIX_TYPE_REAL, FORMAT_COORD);
scanpointsx = N_GNEW(2*n,scan_point);
for (i = 0; i < n; i++){
scanpointsx[2*i].node = i;
scanpointsx[2*i].x = x[i*dim] - width[i*dim];
scanpointsx[2*i].status = INTV_OPEN;
scanpointsx[2*i+1].node = i+n;
scanpointsx[2*i+1].x = x[i*dim] + width[i*dim];
scanpointsx[2*i+1].status = INTV_CLOSE;
}
qsort(scanpointsx, 2*n, sizeof(scan_point), comp_scan_points);
scanpointsy = N_GNEW(2*n,scan_point);
for (i = 0; i < n; i++){
scanpointsy[i].node = i;
scanpointsy[i].x = x[i*dim+1] - width[i*dim+1];
scanpointsy[i].status = INTV_OPEN;
scanpointsy[i+n].node = i;
scanpointsy[i+n].x = x[i*dim+1] + width[i*dim+1];
scanpointsy[i+n].status = INTV_CLOSE;
}
treey = RBTreeCreate(NodeComp,NodeDest,InfoDest,NodePrint,InfoPrint);
for (i = 0; i < 2*n; i++){
#ifdef DEBUG_RBTREE
fprintf(stderr," k = %d node = %d x====%f\n",(scanpointsx[i].node)%n, (scanpointsx[i].node), (scanpointsx[i].x));
#endif
k = (scanpointsx[i].node)%n;
if (scanpointsx[i].status == INTV_OPEN){
#ifdef DEBUG_RBTREE
fprintf(stderr, "inserting...");
treey->PrintKey(&(scanpointsy[k]));
#endif
RBTreeInsert(treey, &(scanpointsy[k]), NULL); /* add both open and close int for y */
#ifdef DEBUG_RBTREE
fprintf(stderr, "inserting2...");
treey->PrintKey(&(scanpointsy[k+n]));
#endif
RBTreeInsert(treey, &(scanpointsy[k+n]), NULL);
} else {
real bsta, bbsta, bsto, bbsto; int ii;
assert(scanpointsx[i].node >= n);
newNode = newNode0 = RBExactQuery(treey, &(scanpointsy[k + n]));
ii = ((scan_point *)newNode->key)->node;
assert(ii < n);
bsta = scanpointsy[ii].x; bsto = scanpointsy[ii+n].x;
#ifdef DEBUG_RBTREE
fprintf(stderr, "poping..%d....yinterval={%f,%f}\n", scanpointsy[k + n].node, bsta, bsto);
treey->PrintKey(newNode->key);
#endif
assert(treey->nil != newNode);
while ((newNode) && ((newNode = TreePredecessor(treey, newNode)) != treey->nil)){
neighbor = (((scan_point *)newNode->key)->node)%n;
bbsta = scanpointsy[neighbor].x; bbsto = scanpointsy[neighbor+n].x;/* the y-interval of the node that has one end of the interval lower than the top of the leaving interval (bsto) */
#ifdef DEBUG_RBTREE
fprintf(stderr," predecessor is node %d y = %f\n", ((scan_point *)newNode->key)->node, ((scan_point *)newNode->key)->x);
#endif
if (neighbor != k){
if (ABS(0.5*(bsta+bsto) - 0.5*(bbsta+bbsto)) < 0.5*(bsto-bsta) + 0.5*(bbsto-bbsta)){/* if the distance of the centers of the interval is less than sum of width, we have overlap */
A = SparseMatrix_coordinate_form_add_entries(A, 1, &neighbor, &k, &one);
#ifdef DEBUG_RBTREE
fprintf(stderr,"====================================== %d %d\n",k,neighbor);
#endif
if (check_overlap_only) goto check_overlap_RETURN;
}
} else {
newNode2 = newNode;
}
}
#ifdef DEBUG_RBTREE
fprintf(stderr, "deleteing...");
treey->PrintKey(newNode0->key);
#endif
if (newNode0) RBDelete(treey,newNode0);
if (newNode2 && newNode2 != treey->nil && newNode2 != newNode0) {
#ifdef DEBUG_RBTREE
fprintf(stderr, "deleteing2...");
treey->PrintKey(newNode2->key);
#endif
if (newNode0) RBDelete(treey,newNode2);
}
}
}
check_overlap_RETURN:
FREE(scanpointsx);
FREE(scanpointsy);
RBTreeDestroy(treey);
B = SparseMatrix_from_coordinate_format(A);
SparseMatrix_delete(A);
A = SparseMatrix_symmetrize(B, FALSE);
SparseMatrix_delete(B);
if (Verbose) fprintf(stderr, "found %d clashes\n", A->nz);
return A;
}
StressMajorizationSmoother SparseStressMajorizationSmoother_new(SparseMatrix A, int dim, real lambda0, real *x,
int weighting_scheme, int scale_initial_coord){
/* solve a stress model to achieve the ideal distance among a sparse set of edges recorded in A.
A must be a real matrix.
*/
StressMajorizationSmoother sm;
int i, j, k, m = A->m, *ia, *ja, *iw, *jw, *id, *jd;
int nz;
real *d, *w, *lambda;
real diag_d, diag_w, *a, dist, s = 0, stop = 0, sbot = 0;
real xdot = 0;
assert(SparseMatrix_is_symmetric(A, FALSE) && A->type == MATRIX_TYPE_REAL);
/* if x is all zero, make it random */
for (i = 0; i < m*dim; i++) xdot += x[i]*x[i];
if (xdot == 0){
for (i = 0; i < m*dim; i++) x[i] = 72*drand();
}
ia = A->ia;
ja = A->ja;
a = (real*) A->a;
sm = MALLOC(sizeof(struct StressMajorizationSmoother_struct));
sm->scaling = 1.;
sm->data = NULL;
sm->scheme = SM_SCHEME_NORMAL;
sm->D = A;
sm->tol_cg = 0.01;
sm->maxit_cg = sqrt((double) A->m);
lambda = sm->lambda = MALLOC(sizeof(real)*m);
for (i = 0; i < m; i++) sm->lambda[i] = lambda0;
nz = A->nz;
sm->Lw = SparseMatrix_new(m, m, nz + m, MATRIX_TYPE_REAL, FORMAT_CSR);
sm->Lwd = SparseMatrix_new(m, m, nz + m, MATRIX_TYPE_REAL, FORMAT_CSR);
if (!(sm->Lw) || !(sm->Lwd)) {
StressMajorizationSmoother_delete(sm);
return NULL;
}
iw = sm->Lw->ia; jw = sm->Lw->ja;
id = sm->Lwd->ia; jd = sm->Lwd->ja;
w = (real*) sm->Lw->a; d = (real*) sm->Lwd->a;
iw[0] = id[0] = 0;
nz = 0;
for (i = 0; i < m; i++){
diag_d = diag_w = 0;
for (j = ia[i]; j < ia[i+1]; j++){
k = ja[j];
if (k != i){
jw[nz] = k;
dist = a[j];
switch (weighting_scheme){
case WEIGHTING_SCHEME_SQR_DIST:
if (dist*dist == 0){
w[nz] = -100000;
} else {
w[nz] = -1/(dist*dist);
}
break;
case WEIGHTING_SCHEME_INV_DIST:
if (dist*dist == 0){
w[nz] = -100000;
} else {
w[nz] = -1/(dist);
}
break;
case WEIGHTING_SCHEME_NONE:
w[nz] = -1;
break;
default:
assert(0);
return NULL;
}
diag_w += w[nz];
jd[nz] = k;
d[nz] = w[nz]*dist;
stop += d[nz]*distance(x,dim,i,k);
sbot += d[nz]*dist;
diag_d += d[nz];
nz++;
}
}
jw[nz] = i;
lambda[i] *= (-diag_w);/* alternatively don't do that then we have a constant penalty term scaled by lambda0 */
w[nz] = -diag_w + lambda[i];
jd[nz] = i;
d[nz] = -diag_d;
nz++;
iw[i+1] = nz;
id[i+1] = nz;
}
if (scale_initial_coord){
s = stop/sbot;
} else {
s = 1.;
}
if (s == 0) {
return NULL;
}
for (i = 0; i < nz; i++) d[i] *= s;
sm->scaling = s;
sm->Lw->nz = nz;
sm->Lwd->nz = nz;
return sm;
}
StressMajorizationSmoother StressMajorizationSmoother2_new(SparseMatrix A, int dim, real lambda0, real *x,
int ideal_dist_scheme){
/* use up to dist 2 neighbor */
/* use up to dist 2 neighbor. This is used in overcoming pherical effect with ideal distance of
2-neighbors equal graph distance etc.
*/
StressMajorizationSmoother sm;
int i, j, k, l, m = A->m, *ia = A->ia, *ja = A->ja, *iw, *jw, *id, *jd;
int *mask, nz;
real *d, *w, *lambda;
real *avg_dist, diag_d, diag_w, dist, s = 0, stop = 0, sbot = 0;
SparseMatrix ID;
assert(SparseMatrix_is_symmetric(A, FALSE));
ID = ideal_distance_matrix(A, dim, x);
sm = GNEW(struct StressMajorizationSmoother_struct);
sm->scaling = 1.;
sm->data = NULL;
sm->scheme = SM_SCHEME_NORMAL;
sm->tol_cg = 0.01;
sm->maxit_cg = sqrt((double) A->m);
lambda = sm->lambda = N_GNEW(m,real);
for (i = 0; i < m; i++) sm->lambda[i] = lambda0;
mask = N_GNEW(m,int);
avg_dist = N_GNEW(m,real);
for (i = 0; i < m ;i++){
avg_dist[i] = 0;
nz = 0;
for (j = ia[i]; j < ia[i+1]; j++){
if (i == ja[j]) continue;
avg_dist[i] += distance(x, dim, i, ja[j]);
nz++;
}
assert(nz > 0);
avg_dist[i] /= nz;
}
for (i = 0; i < m; i++) mask[i] = -1;
nz = 0;
for (i = 0; i < m; i++){
mask[i] = i;
for (j = ia[i]; j < ia[i+1]; j++){
k = ja[j];
if (mask[k] != i){
mask[k] = i;
nz++;
}
}
for (j = ia[i]; j < ia[i+1]; j++){
k = ja[j];
for (l = ia[k]; l < ia[k+1]; l++){
if (mask[ja[l]] != i){
mask[ja[l]] = i;
nz++;
}
}
}
}
sm->Lw = SparseMatrix_new(m, m, nz + m, MATRIX_TYPE_REAL, FORMAT_CSR);
sm->Lwd = SparseMatrix_new(m, m, nz + m, MATRIX_TYPE_REAL, FORMAT_CSR);
if (!(sm->Lw) || !(sm->Lwd)) {
StressMajorizationSmoother_delete(sm);
return NULL;
}
iw = sm->Lw->ia; jw = sm->Lw->ja;
w = (real*) sm->Lw->a; d = (real*) sm->Lwd->a;
id = sm->Lwd->ia; jd = sm->Lwd->ja;
iw[0] = id[0] = 0;
nz = 0;
for (i = 0; i < m; i++){
mask[i] = i+m;
diag_d = diag_w = 0;
for (j = ia[i]; j < ia[i+1]; j++){
k = ja[j];
if (mask[k] != i+m){
mask[k] = i+m;
jw[nz] = k;
if (ideal_dist_scheme == IDEAL_GRAPH_DIST){
dist = 1;
} else if (ideal_dist_scheme == IDEAL_AVG_DIST){
dist = (avg_dist[i] + avg_dist[k])*0.5;
} else if (ideal_dist_scheme == IDEAL_POWER_DIST){
dist = pow(distance_cropped(x,dim,i,k),.4);
} else {
fprintf(stderr,"ideal_dist_scheme value wrong");
assert(0);
exit(1);
}
/*
w[nz] = -1./(ia[i+1]-ia[i]+ia[ja[j]+1]-ia[ja[j]]);
w[nz] = -2./(avg_dist[i]+avg_dist[k]);*/
/* w[nz] = -1.;*//* use unit weight for now, later can try 1/(deg(i)+deg(k)) */
w[nz] = -1/(dist*dist);
diag_w += w[nz];
jd[nz] = k;
/*
d[nz] = w[nz]*distance(x,dim,i,k);
d[nz] = w[nz]*dd[j];
d[nz] = w[nz]*(avg_dist[i] + avg_dist[k])*0.5;
*/
d[nz] = w[nz]*dist;
stop += d[nz]*distance(x,dim,i,k);
sbot += d[nz]*dist;
diag_d += d[nz];
nz++;
}
}
/* distance 2 neighbors */
for (j = ia[i]; j < ia[i+1]; j++){
k = ja[j];
for (l = ia[k]; l < ia[k+1]; l++){
if (mask[ja[l]] != i+m){
mask[ja[l]] = i+m;
if (ideal_dist_scheme == IDEAL_GRAPH_DIST){
dist = 2;
} else if (ideal_dist_scheme == IDEAL_AVG_DIST){
dist = (avg_dist[i] + 2*avg_dist[k] + avg_dist[ja[l]])*0.5;
} else if (ideal_dist_scheme == IDEAL_POWER_DIST){
dist = pow(distance_cropped(x,dim,i,ja[l]),.4);
} else {
fprintf(stderr,"ideal_dist_scheme value wrong");
assert(0);
exit(1);
}
jw[nz] = ja[l];
/*
w[nz] = -1/(ia[i+1]-ia[i]+ia[ja[l]+1]-ia[ja[l]]);
w[nz] = -2/(avg_dist[i] + 2*avg_dist[k] + avg_dist[ja[l]]);*/
/* w[nz] = -1.;*//* use unit weight for now, later can try 1/(deg(i)+deg(k)) */
w[nz] = -1/(dist*dist);
diag_w += w[nz];
jd[nz] = ja[l];
/*
d[nz] = w[nz]*(distance(x,dim,i,k)+distance(x,dim,k,ja[l]));
d[nz] = w[nz]*(dd[j]+dd[l]);
d[nz] = w[nz]*(avg_dist[i] + 2*avg_dist[k] + avg_dist[ja[l]])*0.5;
*/
d[nz] = w[nz]*dist;
stop += d[nz]*distance(x,dim,ja[l],k);
sbot += d[nz]*dist;
diag_d += d[nz];
nz++;
}
}
}
jw[nz] = i;
lambda[i] *= (-diag_w);/* alternatively don't do that then we have a constant penalty term scaled by lambda0 */
w[nz] = -diag_w + lambda[i];
jd[nz] = i;
d[nz] = -diag_d;
nz++;
iw[i+1] = nz;
id[i+1] = nz;
}
s = stop/sbot;
for (i = 0; i < nz; i++) d[i] *= s;
sm->scaling = s;
sm->Lw->nz = nz;
sm->Lwd->nz = nz;
FREE(mask);
FREE(avg_dist);
SparseMatrix_delete(ID);
return sm;
}
/* ================================ spring and spring-electrical based smoother ================ */
SpringSmoother SpringSmoother_new(SparseMatrix A, int dim, spring_electrical_control ctrl, real *x){
SpringSmoother sm;
int i, j, k, l, m = A->m, *ia = A->ia, *ja = A->ja, *id, *jd;
int *mask, nz;
real *d, *dd;
real *avg_dist;
SparseMatrix ID = NULL;
assert(SparseMatrix_is_symmetric(A, FALSE));
ID = ideal_distance_matrix(A, dim, x);
dd = (real*) ID->a;
sm = N_GNEW(1,struct SpringSmoother_struct);
mask = N_GNEW(m,int);
avg_dist = N_GNEW(m,real);
for (i = 0; i < m ;i++){
avg_dist[i] = 0;
nz = 0;
for (j = ia[i]; j < ia[i+1]; j++){
if (i == ja[j]) continue;
avg_dist[i] += distance(x, dim, i, ja[j]);
nz++;
}
assert(nz > 0);
avg_dist[i] /= nz;
}
for (i = 0; i < m; i++) mask[i] = -1;
nz = 0;
for (i = 0; i < m; i++){
mask[i] = i;
for (j = ia[i]; j < ia[i+1]; j++){
k = ja[j];
if (mask[k] != i){
mask[k] = i;
nz++;
}
}
for (j = ia[i]; j < ia[i+1]; j++){
k = ja[j];
for (l = ia[k]; l < ia[k+1]; l++){
if (mask[ja[l]] != i){
mask[ja[l]] = i;
nz++;
}
}
}
}
sm->D = SparseMatrix_new(m, m, nz, MATRIX_TYPE_REAL, FORMAT_CSR);
if (!(sm->D)){
SpringSmoother_delete(sm);
return NULL;
}
id = sm->D->ia; jd = sm->D->ja;
d = (real*) sm->D->a;
id[0] = 0;
nz = 0;
for (i = 0; i < m; i++){
mask[i] = i+m;
for (j = ia[i]; j < ia[i+1]; j++){
k = ja[j];
if (mask[k] != i+m){
mask[k] = i+m;
jd[nz] = k;
d[nz] = (avg_dist[i] + avg_dist[k])*0.5;
d[nz] = dd[j];
nz++;
}
}
for (j = ia[i]; j < ia[i+1]; j++){
k = ja[j];
for (l = ia[k]; l < ia[k+1]; l++){
if (mask[ja[l]] != i+m){
mask[ja[l]] = i+m;
jd[nz] = ja[l];
d[nz] = (avg_dist[i] + 2*avg_dist[k] + avg_dist[ja[l]])*0.5;
d[nz] = dd[j]+dd[l];
nz++;
}
}
}
id[i+1] = nz;
}
sm->D->nz = nz;
sm->ctrl = spring_electrical_control_new();
*(sm->ctrl) = *ctrl;
sm->ctrl->random_start = FALSE;
sm->ctrl->multilevels = 1;
sm->ctrl->step /= 2;
sm->ctrl->maxiter = 20;
FREE(mask);
FREE(avg_dist);
SparseMatrix_delete(ID);
return sm;
}
void country_graph_coloring(int seed, SparseMatrix A, int **p, real *norm_1){
int n = A->m, i, j, jj;
SparseMatrix L, A2;
int *ia = A->ia, *ja = A->ja;
int a = -1.;
real nrow;
real *v = NULL;
real norm1[2], norm2[2], norm11[2], norm22[2], norm = n;
real pi, pj;
int improved = TRUE;
assert(A->m == A->n);
A2 = SparseMatrix_symmetrize(A, TRUE);
ia = A2->ia; ja = A2->ja;
/* Laplacian */
L = SparseMatrix_new(n, n, 1, MATRIX_TYPE_REAL, FORMAT_COORD);
for (i = 0; i < n; i++){
nrow = 0.;
for (j = ia[i]; j < ia[i+1]; j++){
jj = ja[j];
if (jj != i){
nrow ++;
L = SparseMatrix_coordinate_form_add_entries(L, 1, &i, &jj, &a);
}
}
L = SparseMatrix_coordinate_form_add_entries(L, 1, &i, &i, &nrow);
}
L = SparseMatrix_from_coordinate_format(L);
/* largest eigen vector */
{
int maxit = 100;
real tol = 0.00001;
power_method(L, seed, maxit, tol, &v);
}
vector_ordering(n, v, p, TRUE);
/* swapping */
while (improved){
improved = FALSE; norm = n;
for (i = 0; i < n; i++){
get_local_12_norm(n, i, ia, ja, *p, norm1);
for (j = 0; j < n; j++){
if (j == i) continue;
get_local_12_norm(n, j, ia, ja, *p, norm2);
norm = MIN(norm, norm2[0]);
pi = (*p)[i]; pj = (*p)[j];
(*p)[i] = pj;
(*p)[j] = pi;
get_local_12_norm(n, i, ia, ja, *p, norm11);
get_local_12_norm(n, j, ia, ja, *p, norm22);
if (MIN(norm11[0],norm22[0]) > MIN(norm1[0],norm2[0])){
// ||
//(MIN(norm11[0],norm22[0]) == MIN(norm1[0],norm2[0]) && norm11[1]+norm22[1] > norm1[1]+norm2[1])) {
improved = TRUE;
norm1[0] = norm11[0];
norm1[1] = norm11[1];
continue;
}
(*p)[i] = pi;
(*p)[j] = pj;
}
}
if (Verbose) {
get_12_norm(n, ia, ja, *p, norm1);
fprintf(stderr, "norm = %f", norm);
fprintf(stderr, "norm1 = %f, norm2 = %f\n", norm1[0], norm1[1]);
}
}
get_12_norm(n, ia, ja, *p, norm1);
*norm_1 = norm1[0];
if (A2 != A) SparseMatrix_delete(A2);
SparseMatrix_delete(L);
}
Multilevel_MQ_Clustering Multilevel_MQ_Clustering_establish(Multilevel_MQ_Clustering grid, int maxcluster) {
int *matching = grid->matching;
SparseMatrix A = grid->A;
int n = grid->n, level = grid->level, nc = 0, nclusters = n;
real mq = 0, mq_in = 0, mq_out = 0, mq_new, mq_in_new, mq_out_new, mq_max = 0, mq_in_max = 0, mq_out_max = 0;
int *ia = A->ia, *ja = A->ja;
real *a, amax = 0;
real *deg_intra = grid->deg_intra, *wgt = grid->wgt;
real *deg_intra_new, *wgt_new = NULL;
int i, j, k, jj, jc, jmax;
real *deg_inter, gain = 0, *dout = grid->dout, *dout_new, deg_in_i, deg_in_j, wgt_i, wgt_j, a_ij, dout_i, dout_j, dout_max = 0, wgt_jmax = 0;
int *mask;
real maxgain = 0;
real total_gain = 0;
SingleLinkedList *neighbors = NULL, lst;
neighbors = MALLOC(sizeof(SingleLinkedList)*n);
for (i = 0; i < n; i++) neighbors[i] = NULL;
mq = grid->mq;
mq_in = grid->mq_in;
mq_out = grid->mq_out;
deg_intra_new = MALLOC(sizeof(real)*n);
wgt_new = MALLOC(sizeof(real)*n);
deg_inter = MALLOC(sizeof(real)*n);
mask = MALLOC(sizeof(int)*n);
dout_new = MALLOC(sizeof(real)*n);
for (i = 0; i < n; i++) mask[i] = -1;
assert(n == A->n);
for (i = 0; i < n; i++) matching[i] = UNMATCHED;
/* gain in merging node A into cluster B is
mq_in_new = mq_in - |E(A,A)|/(V(A))^2 - |E(B,B)|/(V(B))^2 + (|E(A,A)|+|E(B,B)|+|E(A,B)|)/(|V(A)|+|V(B)|)^2
. = mq_in - deg_intra(A)/|A|^2 - deg_intra(B)/|B|^2 + (deg_intra(A)+deg_intra(B)+a(A,B))/(|A|+|B|)^2
mq_out_new = mq_out - |E(A,B)|/(|V(A)|*V(B)|)-\sum_{C and A connected, C!=B} |E(A,C)|/(|V(A)|*|V(C)|)-\sum_{C and B connected,C!=B} |E(B,C)|/(|V(B)|*|V(C)|)
. + \sum_{C connected to A or B, C!=A, C!=B} (|E(A,C)|+|E(B,C)|)/(|V(C)|*(|V(A)|+|V(B)|)
. = mq_out + a(A,B)/(|A|*|B|)-\sum_{C and A connected} a(A,C)/(|A|*|C|)-\sum_{C and B connected} a(B,C)/(|B|*|C|)
. + \sum_{C connected to A or B, C!=A, C!=B} (a(A,C)+a(B,C))/(|C|*(|A|+|B|))
Denote:
dout(i) = \sum_{j -- i} a(i,j)/|j|
then
mq_out_new = mq_out - |E(A,B)|/(|V(A)|*V(B)|)-\sum_{C and A connected, C!=B} |E(A,C)|/(|V(A)|*|V(C)|)-\sum_{C and B connected,C!=B} |E(B,C)|/(|V(B)|*|V(C)|)
. + \sum_{C connected to A or B, C!=A, C!=B} (|E(A,C)|+|E(B,C)|)/(|V(C)|*(|V(A)|+|V(B)|)
. = mq_out + a(A,B)/(|A|*|B|)-dout(A)/|A| - dout(B)/|B|
. + (dout(A)+dout(B))/(|A|+|B|) - (a(A,B)/|A|+a(A,B)/|B|)/(|A|+|B|)
. = mq_out -dout(A)/|A| - dout(B)/|B| + (dout(A)+dout(B))/(|A|+|B|)
after merging A and B into cluster AB,
dout(AB) = dout(A) + dout(B);
dout(C) := dout(C) - a(A,C)/|A| - a(B,C)/|B| + a(A,C)/(|A|+|B|) + a(B, C)/(|A|+|B|)
mq_new = mq_in_new/(k-1) - mq_out_new/((k-1)*(k-2))
gain = mq_new - mq
*/
a = (real*) A->a;
for (i = 0; i < n; i++) {
if (matching[i] != UNMATCHED) continue;
/* accumulate connections between i and clusters */
for (j = ia[i]; j < ia[i+1]; j++) {
jj = ja[j];
if (jj == i) continue;
if ((jc=matching[jj]) != UNMATCHED) {
if (mask[jc] != i) {
mask[jc] = i;
deg_inter[jc] = a[j];
} else {
deg_inter[jc] += a[j];
}
}
}
deg_in_i = deg_intra[i];
wgt_i = wgt[i];
dout_i = dout[i];
maxgain = 0;
jmax = -1;
for (j = ia[i]; j < ia[i+1]; j++) {
jj = ja[j];
if (jj == i) continue;
jc = matching[jj];
if (jc == UNMATCHED) {
a_ij = a[j];
wgt_j = wgt[jj];
deg_in_j = deg_intra[jj];
dout_j = dout[jj];
} else if (deg_inter[jc] < 0) {
continue;
} else {
a_ij = deg_inter[jc];
wgt_j = wgt_new[jc];
deg_inter[jc] = -1; /* so that we do not redo the calulation when we hit another neighbor in cluster jc */
deg_in_j = deg_intra_new[jc];
dout_j = dout_new[jc];
}
mq_in_new = mq_in - deg_in_i/pow(wgt_i, 2) - deg_in_j/pow(wgt_j,2)
+ (deg_in_i + deg_in_j + a_ij)/pow(wgt_i + wgt_j,2);
mq_out_new = mq_out - dout_i/wgt_i - dout_j/wgt_j + (dout_i + dout_j)/(wgt_i + wgt_j);
if (nclusters > 2) {
mq_new = 2*(mq_in_new/(nclusters - 1) - mq_out_new/((nclusters - 1)*(nclusters - 2)));
} else {
mq_new = 2*mq_in_new/(nclusters - 1);
}
#ifdef DEBUG
{ int ncluster;
double mq2, mq_in2, mq_out2, *dout2;
int *matching2, nc2 = nc;
matching2 = MALLOC(sizeof(int)*A->m);
matching2 = MEMCPY(matching2, matching, sizeof(real)*A->m);
if (jc != UNMATCHED) {
matching2[i] = jc;
} else {
matching2[i] = nc2;
matching2[jj] = nc2;
nc2++;
}
for (k = 0; k < n; k++) if (matching2[k] == UNMATCHED) matching2[k] =nc2++;
mq2 = get_mq(A, matching2, &ncluster, &mq_in2, &mq_out2, &dout2);
fprintf(stderr," {dout_i, dout_j}={%f,%f}, {predicted, calculated}: mq = {%f, %f}, mq_in ={%f,%f}, mq_out = {%f,%f}\n",dout_i, dout_j, mq_new, mq2, mq_in_new, mq_in2, mq_out_new, mq_out2);
mq_new = mq2;
}
#endif
gain = mq_new - mq;
if (Verbose) fprintf(stderr,"gain in merging node %d with node %d = %f-%f = %f\n", i, jj, mq, mq_new, gain);
if (j == ia[i] || gain > maxgain) {
maxgain = gain;
jmax = jj;
amax = a_ij;
dout_max = dout_j;
wgt_jmax = wgt_j;
mq_max = mq_new;
mq_in_max = mq_in_new;
mq_out_max = mq_out_new;
}
}
/* now merge i and jmax */
if (maxgain > 0 || (nc >= 1 && nc > maxcluster)) {
total_gain += maxgain;
jc = matching[jmax];
if (jc == UNMATCHED) {
fprintf(stderr, "maxgain=%f, merge %d, %d\n",maxgain, i, jmax);
neighbors[nc] = SingleLinkedList_new_int(jmax);
neighbors[nc] = SingleLinkedList_prepend_int(neighbors[nc], i);
dout_new[nc] = dout_i + dout_max;
matching[i] = matching[jmax] = nc;
wgt_new[nc] = wgt[i] + wgt[jmax];
deg_intra_new[nc] = deg_intra[i] + deg_intra[jmax] + amax;
nc++;
} else {
fprintf(stderr,"maxgain=%f, merge with existing cluster %d, %d\n",maxgain, i, jc);
neighbors[jc] = SingleLinkedList_prepend_int(neighbors[jc], i);
dout_new[jc] = dout_i + dout_max;
wgt_new[jc] += wgt[i];
matching[i] = jc;
deg_intra_new[jc] += deg_intra[i] + amax;
}
mq = mq_max;
mq_in = mq_in_max;
mq_out = mq_out_max;
nclusters--;
} else {
fprintf(stderr,"gain: %f -- no gain, skip merging node %d\n", maxgain, i);
assert(maxgain <= 0);
neighbors[nc] = SingleLinkedList_new_int(i);
matching[i] = nc;
deg_intra_new[nc] = deg_intra[i];
wgt_new[nc] = wgt[i];
nc++;
}
/* update scaled outdegree of neighbors of i and its merged node/cluster jmax */
jc = matching[i];
lst = neighbors[jc];
do {
mask[*((int*) SingleLinkedList_get_data(lst))] = n+i;
lst = SingleLinkedList_get_next(lst);
} while (lst);
lst = neighbors[jc];
do {
k = *((int*) SingleLinkedList_get_data(lst));
for (j = ia[k]; j < ia[k+1]; j++) {
jj = ja[j];
if (mask[jj] == n+i) continue;/* link to within cluster */
if ((jc = matching[jj]) == UNMATCHED) {
if (k == i) {
dout[jj] += -a[j]/wgt_i + a[j]/(wgt_i + wgt_jmax);
} else {
dout[jj] += -a[j]/wgt_jmax + a[j]/(wgt_i + wgt_jmax);
}
} else {
if (k == i) {
dout_new[jc] += -a[j]/wgt_i + a[j]/(wgt_i + wgt_jmax);
} else {
dout_new[jc] += -a[j]/wgt_jmax + a[j]/(wgt_i + wgt_jmax);
}
}
}
lst = SingleLinkedList_get_next(lst);
} while (lst);
}
fprintf(stderr,"verbose=%d\n",Verbose);
if (Verbose) fprintf(stderr,"mq = %f new mq = %f level = %d, n = %d, nc = %d, gain = %g, mq_in = %f, mq_out = %f\n", mq, mq + total_gain,
level, n, nc, total_gain, mq_in, mq_out);
#ifdef DEBUG
{ int ncluster;
mq = get_mq(A, matching, &ncluster, &mq_in, &mq_out, &dout);
fprintf(stderr," mq = %f\n",mq);
}
#endif
if (nc >= 1 && (total_gain > 0 || nc < n)) {
/* now set up restriction and prolongation operator */
SparseMatrix P, R, R0, B, cA;
real one = 1.;
Multilevel_MQ_Clustering cgrid;
R0 = SparseMatrix_new(nc, n, 1, MATRIX_TYPE_REAL, FORMAT_COORD);
for (i = 0; i < n; i++) {
jj = matching[i];
SparseMatrix_coordinate_form_add_entries(R0, 1, &jj, &i, &one);
}
R = SparseMatrix_from_coordinate_format(R0);
SparseMatrix_delete(R0);
P = SparseMatrix_transpose(R);
B = SparseMatrix_multiply(R, A);
if (!B) goto RETURN;
cA = SparseMatrix_multiply(B, P);
if (!cA) goto RETURN;
SparseMatrix_delete(B);
grid->P = P;
grid->R = R;
level++;
cgrid = Multilevel_MQ_Clustering_init(cA, level);
deg_intra_new = REALLOC(deg_intra_new, nc*sizeof(real));
wgt_new = REALLOC(wgt_new, nc*sizeof(real));
cgrid->deg_intra = deg_intra_new;
cgrid->mq = grid->mq + total_gain;
cgrid->wgt = wgt_new;
dout_new = REALLOC(dout_new, nc*sizeof(real));
cgrid->dout = dout_new;
cgrid = Multilevel_MQ_Clustering_establish(cgrid, maxcluster);
grid->next = cgrid;
cgrid->prev = grid;
} else {
/* no more improvement, stop and final clustering found */
for (i = 0; i < n; i++) matching[i] = i;
FREE(deg_intra_new);
FREE(wgt_new);
FREE(dout_new);
}
RETURN:
for (i = 0; i < n; i++) SingleLinkedList_delete(neighbors[i], free);
FREE(neighbors);
FREE(deg_inter);
FREE(mask);
return grid;
}
static SparseMatrix get_overlap_graph(int dim, int n, real *x, real *width){
scan_point *scanpointsx, *scanpointsy;
int i, k, neighbor;
SparseMatrix A = NULL, B = NULL;
rb_red_blk_node *newNode, *newNode0;
rb_red_blk_tree* treey;
real one = 1;
A = SparseMatrix_new(n, n, 1, MATRIX_TYPE_REAL, FORMAT_COORD);
scanpointsx = N_GNEW(2*n,scan_point);
for (i = 0; i < n; i++){
scanpointsx[2*i].node = i;
scanpointsx[2*i].x = x[i*dim] - width[i*dim];
scanpointsx[2*i].status = INTV_OPEN;
scanpointsx[2*i+1].node = i+n;
scanpointsx[2*i+1].x = x[i*dim] + width[i*dim];
scanpointsx[2*i+1].status = INTV_CLOSE;
}
qsort(scanpointsx, 2*n, sizeof(scan_point), comp_scan_points);
scanpointsy = N_GNEW(2*n,scan_point);
for (i = 0; i < n; i++){
scanpointsy[i].node = i;
scanpointsy[i].x = x[i*dim+1] - width[i*dim+1];
scanpointsy[i].status = INTV_OPEN;
scanpointsy[i+n].node = i;
scanpointsy[i+n].x = x[i*dim+1] + width[i*dim+1];
scanpointsy[i+n].status = INTV_CLOSE;
}
treey = RBTreeCreate(NodeComp,NodeDest,InfoDest,NodePrint,InfoPrint);
for (i = 0; i < 2*n; i++){
#ifdef DEBUG_RBTREE
fprintf(stderr," k = %d node = %d x====%f\n",(scanpointsx[i].node)%n, (scanpointsx[i].node), (scanpointsx[i].x));
#endif
k = (scanpointsx[i].node)%n;
if (scanpointsx[i].status == INTV_OPEN){
#ifdef DEBUG_RBTREE
fprintf(stderr, "inserting...");
treey->PrintKey(&(scanpointsy[k]));
#endif
RBTreeInsert(treey, &(scanpointsy[k]), NULL); /* add both open and close int for y */
#ifdef DEBUG_RBTREE
fprintf(stderr, "inserting2...");
treey->PrintKey(&(scanpointsy[k+n]));
#endif
RBTreeInsert(treey, &(scanpointsy[k+n]), NULL);
} else {
assert(scanpointsx[i].node >= n);
newNode = newNode0 = RBExactQuery(treey, &(scanpointsy[k + n]));
#ifdef DEBUG_RBTREE
fprintf(stderr, "poping..%d....", scanpointsy[k + n].node);
treey->PrintKey(newNode->key);
#endif
assert(treey->nil != newNode);
while ((newNode) && ((newNode = TreePredecessor(treey, newNode)) != treey->nil) && ((scan_point *)newNode->key)->node != k){
neighbor = (((scan_point *)newNode->key)->node)%n;
A = SparseMatrix_coordinate_form_add_entries(A, 1, &neighbor, &k, &one);
#ifdef DEBUG_RBTREE
fprintf(stderr,"%d %d\n",k,neighbor);
#endif
}
#ifdef DEBUG_RBTREE
fprintf(stderr, "deleteing...");
treey->PrintKey(newNode0->key);
#endif
if (newNode0) RBDelete(treey,newNode0);
if (newNode != treey->nil && newNode != newNode0) {
#ifdef DEBUG_RBTREE
fprintf(stderr, "deleting2...");
treey->PrintKey(newNode->key)
#endif
if (newNode0) RBDelete(treey,newNode);
}
}
}
UniformStressSmoother UniformStressSmoother_new(int dim, SparseMatrix A, real *x, real alpha, real M, int *flag){
UniformStressSmoother sm;
int i, j, k, m = A->m, *ia = A->ia, *ja = A->ja, *iw, *jw, *id, *jd;
int nz;
real *d, *w, *a = (real*) A->a;
real diag_d, diag_w, dist, epsilon = 0.01;
assert(SparseMatrix_is_symmetric(A, FALSE));
sm = MALLOC(sizeof(struct StressMajorizationSmoother_struct));
sm->data = NULL;
sm->scheme = SM_SCHEME_UNIFORM_STRESS;
sm->lambda = NULL;
sm->data = MALLOC(sizeof(real)*2);
((real*) sm->data)[0] = alpha;
((real*) sm->data)[1] = M;
sm->data_deallocator = FREE;
/* Lw and Lwd have diagonals */
sm->Lw = SparseMatrix_new(m, m, A->nz + m, MATRIX_TYPE_REAL, FORMAT_CSR);
sm->Lwd = SparseMatrix_new(m, m, A->nz + m, MATRIX_TYPE_REAL, FORMAT_CSR);
iw = sm->Lw->ia; jw = sm->Lw->ja;
id = sm->Lwd->ia; jd = sm->Lwd->ja;
w = (real*) sm->Lw->a; d = (real*) sm->Lwd->a;
if (!(sm->Lw) || !(sm->Lwd)) {
StressMajorizationSmoother_delete(sm);
return NULL;
}
iw = sm->Lw->ia; jw = sm->Lw->ja;
id = sm->Lwd->ia; jd = sm->Lwd->ja;
w = (real*) sm->Lw->a; d = (real*) sm->Lwd->a;
iw[0] = id[0] = 0;
nz = 0;
for (i = 0; i < m; i++){
diag_d = diag_w = 0;
for (j = ia[i]; j < ia[i+1]; j++){
k = ja[j];
if (k != i){
dist = MAX(ABS(a[j]), epsilon);
jd[nz] = jw[nz] = k;
w[nz] = -1/(dist*dist);
w[nz] = -1.;
d[nz] = w[nz]*dist;
diag_w += w[nz];
diag_d += d[nz];
nz++;
}
}
jd[nz] = jw[nz] = i;
w[nz] = -diag_w;
d[nz] = -diag_d;
nz++;
iw[i+1] = nz;
id[i+1] = nz;
}
sm->Lw->nz = nz;
sm->Lwd->nz = nz;
return sm;
}
