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/* -*- mode: C -*- */
/* vim:set ts=2 sw=2 sts=2 et: */
/*
IGraph R package.
Copyright (C) 2014 Gabor Csardi <csardi.gabor@gmail.com>
334 Harvard street, Cambridge, MA 02139 USA
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301 USA
*/
#include "igraph_layout.h"
#include "igraph_interface.h"
#include "igraph_random.h"
#include <math.h>
/**
* \ingroup layout
* \function igraph_layout_gem
*
* The GEM layout algorithm, as described in Arne Frick, Andreas Ludwig,
* Heiko Mehldau: A Fast Adaptive Layout Algorithm for Undirected Graphs,
* Proc. Graph Drawing 1994, LNCS 894, pp. 388-403, 1995.
* \param graph The input graph. Edge directions are ignored in
* directed graphs.
* \param res The result is stored here. If the \p use_seed argument
* is true (non-zero), then this matrix is also used as the
* starting point of the algorithm.
* \param use_seed Boolean, whether to use the supplied coordinates in
* \p res as the starting point. If false (zero), then a
* uniform random starting point is used.
* \param maxiter The maximum number of iterations to
* perform. Updating a single vertex counts as an iteration.
* A reasonable default is 40 * n * n, where n is the number of
* vertices. The original paper suggests 4 * n * n, but this
* usually only works if the other parameters are set up carefully.
* \param temp_max The maximum allowed local temperature. A reasonable
* default is the number of vertices.
* \param temp_min The global temperature at which the algorithm
* terminates (even before reaching \p maxiter iterations). A
* reasonable default is 1/10.
* \param temp_init Initial local temperature of all vertices. A
* reasonable default is the square root of the number of
* vertices.
* \return Error code.
*
* Time complexity: O(t * n * (n+e)), where n is the number of vertices,
* e is the number of edges and t is the number of time steps
* performed.
*/
int igraph_layout_gem(const igraph_t *graph, igraph_matrix_t *res,
igraph_bool_t use_seed, igraph_integer_t maxiter,
igraph_real_t temp_max, igraph_real_t temp_min,
igraph_real_t temp_init) {
igraph_integer_t no_nodes = igraph_vcount(graph);
igraph_vector_int_t perm;
igraph_vector_float_t impulse_x, impulse_y, temp, skew_gauge;
igraph_integer_t i;
float temp_global;
igraph_integer_t perm_pointer = 0;
float barycenter_x = 0.0, barycenter_y = 0.0;
igraph_vector_t phi;
igraph_vector_t neis;
const float elen_des2 = 128 * 128;
const float gamma = 1/16.0;
const float alpha_o = M_PI;
const float alpha_r = M_PI / 3.0;
const float sigma_o = 1.0 / 3.0;
const float sigma_r = 1.0 / 2.0 / no_nodes;
if (maxiter < 0) {
IGRAPH_ERROR("Number of iterations must be non-negative in GEM layout",
IGRAPH_EINVAL);
}
if (use_seed && (igraph_matrix_nrow(res) != no_nodes ||
igraph_matrix_ncol(res) != 2)) {
IGRAPH_ERROR("Invalid start position matrix size in GEM layout",
IGRAPH_EINVAL);
}
if (temp_max <= 0) {
IGRAPH_ERROR("Maximum temperature should be positive in GEM layout",
IGRAPH_EINVAL);
}
if (temp_min <= 0) {
IGRAPH_ERROR("Minimum temperature should be positive in GEM layout",
IGRAPH_EINVAL);
}
if (temp_init <= 0) {
IGRAPH_ERROR("Initial temperature should be positive in GEM layout",
IGRAPH_EINVAL);
}
if (temp_max < temp_init || temp_init < temp_min) {
IGRAPH_ERROR("Minimum <= Initial <= Maximum temperature is required "
"in GEM layout", IGRAPH_EINVAL);
}
if (no_nodes == 0) { return 0; }
IGRAPH_CHECK(igraph_vector_float_init(&impulse_x, no_nodes));
IGRAPH_FINALLY(igraph_vector_float_destroy, &impulse_x);
IGRAPH_CHECK(igraph_vector_float_init(&impulse_y, no_nodes));
IGRAPH_FINALLY(igraph_vector_float_destroy, &impulse_y);
IGRAPH_CHECK(igraph_vector_float_init(&temp, no_nodes));
IGRAPH_FINALLY(igraph_vector_float_destroy, &temp);
IGRAPH_CHECK(igraph_vector_float_init(&skew_gauge, no_nodes));
IGRAPH_FINALLY(igraph_vector_float_destroy, &skew_gauge);
IGRAPH_CHECK(igraph_vector_int_init_seq(&perm, 0, no_nodes-1));
IGRAPH_FINALLY(igraph_vector_int_destroy, &perm);
IGRAPH_VECTOR_INIT_FINALLY(&phi, no_nodes);
IGRAPH_VECTOR_INIT_FINALLY(&neis, 10);
RNG_BEGIN();
/* Initialization */
igraph_degree(graph, &phi, igraph_vss_all(), IGRAPH_ALL, IGRAPH_LOOPS);
if (!use_seed) {
const igraph_real_t width_half=no_nodes*100, height_half=width_half;
IGRAPH_CHECK(igraph_matrix_resize(res, no_nodes, 2));
for (i=0; i<no_nodes; i++) {
MATRIX(*res, i, 0) = RNG_UNIF(-width_half, width_half);
MATRIX(*res, i, 1) = RNG_UNIF(-height_half, height_half);
barycenter_x += MATRIX(*res, i, 0);
barycenter_y += MATRIX(*res, i, 1);
VECTOR(phi)[i] *= (VECTOR(phi)[i] / 2.0 + 1.0);
}
} else {
for (i=0; i<no_nodes; i++) {
barycenter_x += MATRIX(*res, i, 0);
barycenter_y += MATRIX(*res, i, 1);
VECTOR(phi)[i] *= (VECTOR(phi)[i] / 2.0 + 1.0);
}
}
igraph_vector_float_fill(&temp, temp_init);
temp_global = temp_init * no_nodes;
while (temp_global > temp_min * no_nodes && maxiter > 0) {
/* choose a vertex v to update */
igraph_integer_t u, v, nlen, j;
float px, py, pvx, pvy;
if (!perm_pointer) {
igraph_vector_int_shuffle(&perm);
perm_pointer=no_nodes-1;
}
v=VECTOR(perm)[perm_pointer--];
/* compute v's impulse */
px = (barycenter_x/no_nodes - MATRIX(*res, v, 0)) * gamma * VECTOR(phi)[v];
py = (barycenter_y/no_nodes - MATRIX(*res, v, 1)) * gamma * VECTOR(phi)[v];
px += RNG_UNIF(-32.0, 32.0);
py += RNG_UNIF(-32.0, 32.0);
for (u = 0; u < no_nodes; u++) {
float dx, dy, dist2;
if (u == v) { continue; }
dx=MATRIX(*res, v, 0) - MATRIX(*res, u, 0);
dy=MATRIX(*res, v, 1) - MATRIX(*res, u, 1);
dist2=dx * dx + dy * dy;
if (dist2 != 0) {
px += dx * elen_des2 / dist2;
py += dy * elen_des2 / dist2;
}
}
IGRAPH_CHECK(igraph_neighbors(graph, &neis, v, IGRAPH_ALL));
nlen=igraph_vector_size(&neis);
for (j = 0; j < nlen; j++) {
igraph_integer_t u=VECTOR(neis)[j];
float dx=MATRIX(*res, v, 0) - MATRIX(*res, u, 0);
float dy=MATRIX(*res, v, 1) - MATRIX(*res, u, 1);
float dist2= dx * dx + dy * dy;
px -= dx * dist2 / (elen_des2 * VECTOR(phi)[v]);
py -= dy * dist2 / (elen_des2 * VECTOR(phi)[v]);
}
/* update v's position and temperature */
if (px != 0 || py != 0) {
float plen = sqrtf(px * px + py * py);
px *= VECTOR(temp)[v] / plen;
py *= VECTOR(temp)[v] / plen;
MATRIX(*res, v, 0) += px;
MATRIX(*res, v, 1) += py;
barycenter_x += px;
barycenter_y += py;
}
pvx=VECTOR(impulse_x)[v]; pvy=VECTOR(impulse_y)[v];
if (pvx != 0 || pvy != 0) {
float beta = atan2f(pvy - py, pvx - px);
float sin_beta = sinf(beta);
float sign_sin_beta = (sin_beta > 0) ? 1 : ((sin_beta < 0) ? -1 : 0);
float cos_beta = cosf(beta);
float abs_cos_beta = fabsf(cos_beta);
float old_temp=VECTOR(temp)[v];
if (sin(beta) >= sin(M_PI_2 + alpha_r / 2.0)) {
VECTOR(skew_gauge)[v] += sigma_r * sign_sin_beta;
}
if (abs_cos_beta >= cosf(alpha_o / 2.0)) {
VECTOR(temp)[v] *= sigma_o * cos_beta;
}
VECTOR(temp)[v] *= (1 - fabsf(VECTOR(skew_gauge)[v]));
if (VECTOR(temp)[v] > temp_max) { VECTOR(temp)[v] = temp_max; }
VECTOR(impulse_x)[v] = px;
VECTOR(impulse_y)[v] = py;
temp_global += VECTOR(temp)[v] - old_temp;
}
maxiter--;
} /* while temp && iter */
RNG_END();
igraph_vector_destroy(&neis);
igraph_vector_destroy(&phi);
igraph_vector_int_destroy(&perm);
igraph_vector_float_destroy(&skew_gauge);
igraph_vector_float_destroy(&temp);
igraph_vector_float_destroy(&impulse_y);
igraph_vector_float_destroy(&impulse_x);
IGRAPH_FINALLY_CLEAN(7);
return 0;
}
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