/* call-seq:
* graph.layout_sphere -> IGraphMatrix
*
* Places vertices (more or less) uniformly on a sphere.
*
* The algorithm was described in the following paper: Distributing many
* points on a sphere by E.B. Saff and A.B.J. Kuijlaars, Mathematical
* Intelligencer 19.1 (1997) 5--11.
*/
VALUE cIGraph_layout_sphere(VALUE self) {
igraph_t *graph;
igraph_matrix_t *res = malloc(sizeof(igraph_matrix_t));
Data_Get_Struct(self, igraph_t, graph);
igraph_matrix_init(res,0,0);
igraph_layout_sphere(graph,res);
return Data_Wrap_Struct(cIGraphMatrix, 0, cIGraph_matrix_free, res);
}
int igraph_layout_kamada_kawai_3d(const igraph_t *graph, igraph_matrix_t *res,
igraph_bool_t use_seed, igraph_integer_t maxiter,
igraph_real_t epsilon, igraph_real_t kkconst,
const igraph_vector_t *weights,
const igraph_vector_t *minx, const igraph_vector_t *maxx,
const igraph_vector_t *miny, const igraph_vector_t *maxy,
const igraph_vector_t *minz, const igraph_vector_t *maxz) {
igraph_integer_t no_nodes=igraph_vcount(graph);
igraph_integer_t no_edges=igraph_ecount(graph);
igraph_real_t L, L0=sqrt(no_nodes);
igraph_matrix_t dij, lij, kij;
igraph_real_t max_dij;
igraph_vector_t D1, D2, D3;
igraph_integer_t i, j, m;
if (maxiter < 0) {
IGRAPH_ERROR("Number of iterations must be non-negatice in "
"Kamada-Kawai layout", IGRAPH_EINVAL);
}
if (kkconst <= 0) {
IGRAPH_ERROR("`K' constant must be positive in Kamada-Kawai layout",
IGRAPH_EINVAL);
}
if (use_seed && (igraph_matrix_nrow(res) != no_nodes ||
igraph_matrix_ncol(res) != 3)) {
IGRAPH_ERROR("Invalid start position matrix size in "
"3d Kamada-Kawai layout", IGRAPH_EINVAL);
}
if (weights && igraph_vector_size(weights) != no_edges) {
IGRAPH_ERROR("Invalid weight vector length", IGRAPH_EINVAL);
}
if (minx && igraph_vector_size(minx) != no_nodes) {
IGRAPH_ERROR("Invalid minx vector length", IGRAPH_EINVAL);
}
if (maxx && igraph_vector_size(maxx) != no_nodes) {
IGRAPH_ERROR("Invalid maxx vector length", IGRAPH_EINVAL);
}
if (minx && maxx && !igraph_vector_all_le(minx, maxx)) {
IGRAPH_ERROR("minx must not be greater than maxx", IGRAPH_EINVAL);
}
if (miny && igraph_vector_size(miny) != no_nodes) {
IGRAPH_ERROR("Invalid miny vector length", IGRAPH_EINVAL);
}
if (maxy && igraph_vector_size(maxy) != no_nodes) {
IGRAPH_ERROR("Invalid maxy vector length", IGRAPH_EINVAL);
}
if (miny && maxy && !igraph_vector_all_le(miny, maxy)) {
IGRAPH_ERROR("miny must not be greater than maxy", IGRAPH_EINVAL);
}
if (minz && igraph_vector_size(minz) != no_nodes) {
IGRAPH_ERROR("Invalid minz vector length", IGRAPH_EINVAL);
}
if (maxz && igraph_vector_size(maxz) != no_nodes) {
IGRAPH_ERROR("Invalid maxz vector length", IGRAPH_EINVAL);
}
if (minz && maxz && !igraph_vector_all_le(minz, maxz)) {
IGRAPH_ERROR("minz must not be greater than maxz", IGRAPH_EINVAL);
}
if (!use_seed) {
if (minx || maxx || miny || maxy || minz || maxz) {
const igraph_real_t width=sqrt(no_nodes), height=width, depth=width;
IGRAPH_CHECK(igraph_matrix_resize(res, no_nodes, 3));
RNG_BEGIN();
for (i=0; i<no_nodes; i++) {
igraph_real_t x1=minx ? VECTOR(*minx)[i] : -width/2;
igraph_real_t x2=maxx ? VECTOR(*maxx)[i] : width/2;
igraph_real_t y1=miny ? VECTOR(*miny)[i] : -height/2;
igraph_real_t y2=maxy ? VECTOR(*maxy)[i] : height/2;
igraph_real_t z1=minz ? VECTOR(*minz)[i] : -depth/2;
igraph_real_t z2=maxz ? VECTOR(*maxz)[i] : depth/2;
if (!igraph_finite(x1)) { x1 = -width/2; }
if (!igraph_finite(x2)) { x2 = width/2; }
if (!igraph_finite(y1)) { y1 = -height/2; }
if (!igraph_finite(y2)) { y2 = height/2; }
if (!igraph_finite(z1)) { z1 = -depth/2; }
if (!igraph_finite(z2)) { z2 = depth/2; }
MATRIX(*res, i, 0) = RNG_UNIF(x1, x2);
MATRIX(*res, i, 1) = RNG_UNIF(y1, y2);
MATRIX(*res, i, 2) = RNG_UNIF(z1, z2);
}
RNG_END();
} else {
igraph_layout_sphere(graph, res);
}
}
if (no_nodes <= 1) { return 0; }
IGRAPH_MATRIX_INIT_FINALLY(&dij, no_nodes, no_nodes);
IGRAPH_MATRIX_INIT_FINALLY(&kij, no_nodes, no_nodes);
IGRAPH_MATRIX_INIT_FINALLY(&lij, no_nodes, no_nodes);
IGRAPH_CHECK(igraph_shortest_paths_dijkstra(graph, &dij, igraph_vss_all(),
igraph_vss_all(), weights,
IGRAPH_ALL));
max_dij = 0.0;
for (i=0; i<no_nodes; i++) {
for (j=i+1; j<no_nodes; j++) {
if (!igraph_finite(MATRIX(dij, i, j))) { continue; }
if (MATRIX(dij, i, j) > max_dij) { max_dij = MATRIX(dij, i, j); }
}
}
for (i=0; i<no_nodes; i++) {
for (j=0; j<no_nodes; j++) {
if (MATRIX(dij, i, j) > max_dij) { MATRIX(dij, i, j) = max_dij; }
}
}
L = L0 / max_dij;
for (i=0; i<no_nodes; i++) {
for (j=0; j<no_nodes; j++) {
igraph_real_t tmp=MATRIX(dij, i, j) * MATRIX(dij, i, j);
if (i==j) { continue; }
MATRIX(kij, i, j) = kkconst / tmp;
MATRIX(lij, i, j) = L * MATRIX(dij, i, j);
}
}
/* Initialize delta */
IGRAPH_VECTOR_INIT_FINALLY(&D1, no_nodes);
IGRAPH_VECTOR_INIT_FINALLY(&D2, no_nodes);
IGRAPH_VECTOR_INIT_FINALLY(&D3, no_nodes);
for (m=0; m<no_nodes; m++) {
igraph_real_t myD1=0.0, myD2=0.0, myD3=0.0;
for (i=0; i<no_nodes; i++) {
if (i==m) { continue; }
igraph_real_t dx=MATRIX(*res, m, 0) - MATRIX(*res, i, 0);
igraph_real_t dy=MATRIX(*res, m, 1) - MATRIX(*res, i, 1);
igraph_real_t dz=MATRIX(*res, m, 2) - MATRIX(*res, i, 2);
igraph_real_t mi_dist=sqrt(dx * dx + dy * dy + dz * dz);
myD1 += MATRIX(kij, m, i) * (dx - MATRIX(lij, m, i) * dx / mi_dist);
myD2 += MATRIX(kij, m, i) * (dy - MATRIX(lij, m, i) * dy / mi_dist);
myD3 += MATRIX(kij, m, i) * (dz - MATRIX(lij, m, i) * dz / mi_dist);
}
VECTOR(D1)[m] = myD1;
VECTOR(D2)[m] = myD2;
VECTOR(D3)[m] = myD3;
}
for (j=0; j<maxiter; j++) {
igraph_real_t Ax=0.0, Ay=0.0, Az=0.0;
igraph_real_t Axx=0.0, Axy=0.0, Axz=0.0, Ayy=0.0, Ayz=0.0, Azz=0.0;
igraph_real_t max_delta, delta_x, delta_y, delta_z;
igraph_real_t old_x, old_y, old_z, new_x, new_y, new_z;
igraph_real_t detnum;
/* Select maximal delta */
m=0; max_delta=-1;
for (i=0; i<no_nodes; i++) {
igraph_real_t delta=(VECTOR(D1)[i] * VECTOR(D1)[i] +
VECTOR(D2)[i] * VECTOR(D2)[i] +
VECTOR(D3)[i] * VECTOR(D3)[i]);
if (delta > max_delta) {
m=i; max_delta=delta;
}
}
if (max_delta < epsilon) { break; }
old_x=MATRIX(*res, m, 0);
old_y=MATRIX(*res, m, 1);
old_z=MATRIX(*res, m, 2);
/* Calculate D1, D2 and D3, and other coefficients */
for (i=0; i<no_nodes; i++) {
if (i==m) { continue; }
igraph_real_t dx=old_x - MATRIX(*res, i, 0);
igraph_real_t dy=old_y - MATRIX(*res, i, 1);
igraph_real_t dz=old_z - MATRIX(*res, i, 2);
igraph_real_t dist=sqrt(dx * dx + dy * dy + dz *dz);
igraph_real_t den=dist * (dx * dx + dy * dy + dz * dz);
igraph_real_t k_mi=MATRIX(kij, m, i);
igraph_real_t l_mi=MATRIX(lij, m, i);
Axx += k_mi * (1 - l_mi * (dy*dy + dz*dz) / den);
Ayy += k_mi * (1 - l_mi * (dx*dx + dz*dz) / den);
Azz += k_mi * (1 - l_mi * (dx*dx + dy*dy) / den);
Axy += k_mi * l_mi * dx * dy / den;
Axz += k_mi * l_mi * dx * dz / den;
Ayz += k_mi * l_mi * dy * dz / den;
}
Ax = -VECTOR(D1)[m];
Ay = -VECTOR(D2)[m];
Az = -VECTOR(D3)[m];
/* Need to solve some linear equations, we just use Cramer's rule */
#define DET(a,b,c,d,e,f,g,h,i) ((a*e*i+b*f*g+c*d*h)-(c*e*g+b*d*i+a*f*h))
detnum = DET(Axx,Axy,Axz, Axy,Ayy,Ayz, Axz,Ayz,Azz);
delta_x = DET(Ax ,Ay ,Az , Axy,Ayy,Ayz, Axz,Ayz,Azz) / detnum;
delta_y = DET(Axx,Axy,Axz, Ax ,Ay ,Az , Axz,Ayz,Azz) / detnum;
delta_z = DET(Axx,Axy,Axz, Axy,Ayy,Ayz, Ax ,Ay ,Az ) / detnum;
new_x = old_x + delta_x;
new_y = old_y + delta_y;
new_z = old_z + delta_z;
/* Limits, if given */
if (minx && new_x < VECTOR(*minx)[m]) { new_x = VECTOR(*minx)[m]; }
if (maxx && new_x > VECTOR(*maxx)[m]) { new_x = VECTOR(*maxx)[m]; }
if (miny && new_y < VECTOR(*miny)[m]) { new_y = VECTOR(*miny)[m]; }
if (maxy && new_y > VECTOR(*maxy)[m]) { new_y = VECTOR(*maxy)[m]; }
if (minz && new_z < VECTOR(*minz)[m]) { new_z = VECTOR(*minz)[m]; }
if (maxz && new_z > VECTOR(*maxz)[m]) { new_z = VECTOR(*maxz)[m]; }
/* Update delta, only with/for the affected node */
VECTOR(D1)[m] = VECTOR(D2)[m] = VECTOR(D3)[m] = 0.0;
for (i=0; i<no_nodes; i++) {
if (i==m) { continue; }
igraph_real_t old_dx=old_x - MATRIX(*res, i, 0);
igraph_real_t old_dy=old_y - MATRIX(*res, i, 1);
igraph_real_t old_dz=old_z - MATRIX(*res, i, 2);
igraph_real_t old_mi_dist=sqrt(old_dx * old_dx + old_dy * old_dy +
old_dz * old_dz);
igraph_real_t new_dx=new_x - MATRIX(*res, i, 0);
igraph_real_t new_dy=new_y - MATRIX(*res, i, 1);
igraph_real_t new_dz=new_z - MATRIX(*res, i, 2);
igraph_real_t new_mi_dist=sqrt(new_dx * new_dx + new_dy * new_dy +
new_dz * new_dz);
VECTOR(D1)[i] -= MATRIX(kij, m, i) *
(-old_dx + MATRIX(lij, m, i) * old_dx / old_mi_dist);
VECTOR(D2)[i] -= MATRIX(kij, m, i) *
(-old_dy + MATRIX(lij, m, i) * old_dy / old_mi_dist);
VECTOR(D3)[i] -= MATRIX(kij, m, i) *
(-old_dz + MATRIX(lij, m, i) * old_dz / old_mi_dist);
VECTOR(D1)[i] += MATRIX(kij, m, i) *
(-new_dx + MATRIX(lij, m, i) * new_dx / new_mi_dist);
VECTOR(D2)[i] += MATRIX(kij, m, i) *
(-new_dy + MATRIX(lij, m, i) * new_dy / new_mi_dist);
VECTOR(D3)[i] += MATRIX(kij, m, i) *
(-new_dz + MATRIX(lij, m, i) * new_dz / new_mi_dist);
VECTOR(D1)[m] += MATRIX(kij, m, i) *
(new_dx - MATRIX(lij, m, i) * new_dx / new_mi_dist);
VECTOR(D2)[m] += MATRIX(kij, m, i) *
(new_dy - MATRIX(lij, m, i) * new_dy / new_mi_dist);
VECTOR(D3)[m] += MATRIX(kij, m, i) *
(new_dz - MATRIX(lij, m, i) * new_dz / new_mi_dist);
}
/* Update coordinates*/
MATRIX(*res, m, 0) = new_x;
MATRIX(*res, m, 1) = new_y;
MATRIX(*res, m, 2) = new_z;
}
igraph_vector_destroy(&D3);
igraph_vector_destroy(&D2);
igraph_vector_destroy(&D1);
igraph_matrix_destroy(&lij);
igraph_matrix_destroy(&kij);
igraph_matrix_destroy(&dij);
IGRAPH_FINALLY_CLEAN(6);
return 0;
}
