constrained_majorization_ipsep.c

Go to the documentation of this file.

/* $Id$ $Revision$ */
/* vim:set shiftwidth=4 ts=8: */

/**********************************************************
 * Based on constrained_majorization.c
 *
 * Perform stress majorization subject
 * to separation constraints, for background see the paper:
 * "IPSep-CoLa: An Incremental Procedure for Separation Constraint Layout of Graphs"
 * by Tim Dwyer, Yehuda Koren and Kim Marriott
 *
 * Available separation constraints so far are:
 *  o Directed edge constraints
 *  o Node non-overlap constraints
 *  o Cluster containment constraints
 *  o Cluster/node non-overlap constraints
 *
 * Tim Dwyer, 2006
 **********************************************************/

#include "digcola.h"
#ifdef IPSEPCOLA
#include <math.h>
#include <stdlib.h>
#include <time.h>
#include <stdio.h>
#include <float.h>
#include "stress.h"
#include "dijkstra.h"
#include "bfs.h"
#include "matrix_ops.h"
#include "kkutils.h"
#include "conjgrad.h"
#include <csolve_VPSC.h>
#include "quad_prog_vpsc.h"
#include "quad_prog_solver.h"
#include "matrix_ops.h"

#define localConstrMajorIterations 1000

int stress_majorization_cola(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)  */
                             node_t ** nodes,   /* Original nodes */
                             int dim,   /* Dimemsionality of layout */
                             int model, /* difference model */
                             int maxi,  /* max iterations */
                             ipsep_options * opt)
{
    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;
    float *lap1 = NULL;
    float *dist_accumulator = NULL;
    float *tmp_coords = NULL;
    float **b = NULL;
    double *degrees = NULL;
    float *lap2 = NULL;
    int lap_length;
    float *f_storage = NULL;
    float **coords = NULL;
    int orig_n = n;

    /*double conj_tol=tolerance_cg; *//* tolerance of Conjugate Gradient */
    CMajEnvVPSC *cMajEnvHor = NULL;
    CMajEnvVPSC *cMajEnvVrt = NULL;
    double y_0;
    int length;
    DistType diameter;
    float *Dij = NULL;
    float constant_term;
    int count;
    double degree;
    int step;
    float val;
    double old_stress, new_stress = 0;
    boolean converged;
    int len;
    double nsizeScale = 0;
    float maxEdgeLen = 0;
    double max = 1;

    initLayout(graph, n, dim, d_coords, nodes);
    if (n == 1)
        return 0;

    for (i = 0; i < n; i++) {
        for (j = 1; j < graph[i].nedges; j++) {
            maxEdgeLen = MAX(graph[i].ewgts[j], maxEdgeLen);
        }
    }

        /****************************************************
        ** Compute the all-pairs-shortest-distances matrix **
        ****************************************************/

    if (maxi == 0)
        return iterations;

    if (Verbose)
        start_timer();

    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");
        }
    } else if (model == MODEL_MDS) {
        if (Verbose)
            fprintf(stderr, "Calculating MDS model");
        Dij = mdsModel(graph, n);
    }
    if (!Dij) {
        if (Verbose)
            fprintf(stderr, "Calculating shortest paths");
        Dij = compute_apsp_packed(graph, n);
    }
    if (Verbose) {
        fprintf(stderr, ": %.2f sec\n", elapsed_sec());
        fprintf(stderr, "Setting initial positions");
        start_timer();
    }

    diameter = -1;
    length = n + n * (n - 1) / 2;
    for (i = 0; i < length; i++) {
        if (Dij[i] > diameter) {
            diameter = (int) Dij[i];
        }
    }

    /* for numerical stability, scale down layout                */
    /* No Jiggling, might conflict with constraints                      */
    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;
        }
    }

        /**************************
        ** 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;
    }
    if (Verbose)
        fprintf(stderr, ": %.2f sec", elapsed_sec());

        /**************************
        ** 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);

    if (opt->clusters->nclusters > 0) {
        int nn = n + opt->clusters->nclusters * 2;
        int clap_length = nn + nn * (nn - 1) / 2;
        float *clap = N_GNEW(clap_length, float);
        int c0, c1;
        float v;
        c0 = c1 = 0;
        for (i = 0; i < nn; i++) {
            for (j = 0; j < nn - i; j++) {
                if (i < n && j < n - i) {
                    v = lap2[c0++];
                } else {
                    /* v=j==1?i%2:0; */
                    if (j == 1 && i % 2 == 1) {
                        v = maxEdgeLen;
                        v *= v;
                        if (v > 0.01) {
                            v = 1.0 / v;
                        }
                    } else
                        v = 0;
                }
                clap[c1++] = v;
            }
        }
        free(lap2);
        lap2 = clap;
        n = nn;
        lap_length = clap_length;
    }
    /* 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];
    }

    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] = j < orig_n ? (float) (d_coords[i][j]) : 0;
        }
    }

    /* compute constant term in stress sum
     * which is \sum_{i<j} w_{ij}d_{ij}^2
     */
    constant_term = (float) (n * (n - 1) / 2);

        /*************************
        ** 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);

    old_stress = DBL_MAX;       /* at least one iteration */

    if ((cMajEnvHor = initCMajVPSC(n, lap2, graph, opt, 0)) == NULL) {
        iterations = -1;
        goto finish;
    }
    if ((cMajEnvVrt = initCMajVPSC(n, lap2, graph, opt, opt->diredges)) == NULL) {
        iterations = -1;
        goto finish;
    }

    lap1 = N_GNEW(lap_length, float);

    for (converged = FALSE, iterations = 0;
         iterations < maxi && !converged; iterations++) {

        /* First, construct Laplacian of 1/(d_ij*|p_i-p_j|)  */
        set_vector_val(n, 0, degrees);
        sqrt_vecf(lap_length, lap2, lap1);
        for (count = 0, i = 0; i < n - 1; i++) {
            len = n - i - 1;
            /* init 'dist_accumulator' with zeros */
            set_vector_valf(n, 0, dist_accumulator);

            /* put into 'dist_accumulator' all squared distances 
             * between 'i' and 'i'+1,...,'n'-1
             */
            for (k = 0; k < dim; k++) {
                set_vector_valf(len, coords[k][i], tmp_coords);
                vectors_mult_additionf(len, tmp_coords, -1,
                                       coords[k] + i + 1);
                square_vec(len, tmp_coords);
                vectors_additionf(len, tmp_coords, dist_accumulator,
                                  dist_accumulator);
            }

            /* convert to 1/d_{ij} */
            invert_sqrt_vec(len, dist_accumulator);
            /* detect overflows */
            for (j = 0; j < len; j++) {
                if (dist_accumulator[j] >= FLT_MAX
                    || dist_accumulator[j] < 0) {
                    dist_accumulator[j] = 0;
                }
            }

            count++;            /* save place for the main diagonal entry */
            degree = 0;
            for (j = 0; j < len; j++, count++) {
                val = lap1[count] *= dist_accumulator[j];
                degree += val;
                degrees[i + j + 1] -= val;
            }
            degrees[i] -= degree;
        }
        for (step = n, count = 0, i = 0; i < n; i++, count += step, step--) {
            lap1[count] = (float) degrees[i];
        }

        /* Now compute b[] (L^(X(t))*X(t)) */
        for (k = 0; k < dim; k++) {
            /* b[k] := lap1*coords[k] */
            right_mult_with_vector_ff(lap1, n, coords[k], b[k]);
        }

        /* compute new stress
         * remember that the Laplacians are negated, so we subtract 
         * instead of add and vice versa
         */
        new_stress = 0;
        for (k = 0; k < dim; k++) {
            new_stress += vectors_inner_productf(n, coords[k], b[k]);
        }
        new_stress *= 2;
        new_stress += constant_term;    /* only after mult by 2 */
        for (k = 0; k < dim; k++) {
            right_mult_with_vector_ff(lap2, n, coords[k], tmp_coords);
            new_stress -= vectors_inner_productf(n, coords[k], tmp_coords);
        }

#ifdef ALTERNATIVE_STRESS_CALC
        {
            double mat_stress = new_stress;
            double compute_stress(float **coords, float *lap, int dim,
                                  int n);
            new_stress = compute_stress(coords, lap2, dim, n);
            if (fabs(mat_stress - new_stress) /
                min(mat_stress, new_stress) > 0.001) {
                fprintf(stderr,
                        "Diff stress vals: %lf %lf (iteration #%d)\n",
                        mat_stress, new_stress, iterations);
            }
        }
#endif
        /* check for convergence */
        if (Verbose && (iterations % 1 == 0)) {
            fprintf(stderr, "%.3f ", new_stress);
            if (iterations % 10 == 0)
                fprintf(stderr, "\n");
        }
        converged = new_stress < old_stress
            && fabs(new_stress - old_stress) / fabs(old_stress + 1e-10) <
            Epsilon;
        /*converged = converged || (iterations>1 && new_stress>old_stress); */
        /* in first iteration we allowed stress increase, which 
         * might result ny imposing constraints
         */
        old_stress = new_stress;

        /* in determining non-overlap constraints we gradually scale up the
         * size of nodes to avoid local minima
         */
        if ((iterations >= maxi - 1 || converged) && opt->noverlap == 1
            && nsizeScale < 0.999) {
            nsizeScale += 0.1;
            if (Verbose)
                fprintf(stderr, "nsizescale=%f,iterations=%d\n",
                        nsizeScale, iterations);
            iterations = 0;
            converged = FALSE;
        }


        /* now we find the optimizer of trace(X'LX)+X'B by solving 'dim' 
         * system of equations, thereby obtaining the new coordinates.
         * If we use the constraints (given by the var's: 'ordering', 
         * 'levels' and 'num_levels'), we cannot optimize 
         * trace(X'LX)+X'B by simply solving equations, but we have
         * to use a quadratic programming solver
         * note: 'lap2' is a packed symmetric matrix, that is its 
         * upper-triangular part is arranged in a vector row-wise
         * also note: 'lap2' is really the negated laplacian (the 
         * laplacian is -'lap2')
         */

        if (opt->noverlap == 1 && nsizeScale > 0.001) {
            generateNonoverlapConstraints(cMajEnvHor, nsizeScale, coords,
                                          0,
                                          nsizeScale < 0.5 ? FALSE : TRUE,
                                          opt);
        }
        if (cMajEnvHor->m > 0) {
#ifdef MOSEK
            if (opt->mosek) {
                mosek_quad_solve_sep(cMajEnvHor->mosekEnv, n, b[0],
                                     coords[0]);
            } else
#endif                          /* MOSEK */
                constrained_majorization_vpsc(cMajEnvHor, b[0], coords[0],
                                              localConstrMajorIterations);
        } else {
            /* if there are no constraints then use conjugate gradient
             * optimisation which should be considerably faster
             */
            if (conjugate_gradient_mkernel(lap2, coords[0], b[0], n,
                                       tolerance_cg, n) < 0) {
                iterations = -1;
                goto finish;
            }
        }
        if (opt->noverlap == 1 && nsizeScale > 0.001) {
            generateNonoverlapConstraints(cMajEnvVrt, nsizeScale, coords,
                                          1, FALSE, opt);
        }
        if (cMajEnvVrt->m > 0) {
#ifdef MOSEK
            if (opt->mosek) {
                mosek_quad_solve_sep(cMajEnvVrt->mosekEnv, n, b[1],
                                     coords[1]);
            } else
#endif                          /* MOSEK */
                if (constrained_majorization_vpsc(cMajEnvVrt, b[1], coords[1],
                                              localConstrMajorIterations) < 0) {
                iterations = -1;
                goto finish;
            }
        } else {
            conjugate_gradient_mkernel(lap2, coords[1], b[1], n,
                                       tolerance_cg, n);
        }
    }
    if (Verbose) {
        fprintf(stderr, "\nfinal e = %f %d iterations %.2f sec\n",
                new_stress, iterations, elapsed_sec());
    }
    deleteCMajEnvVPSC(cMajEnvHor);
    deleteCMajEnvVPSC(cMajEnvVrt);

    if (opt->noverlap == 2) {
        /* fprintf(stderr, "Removing overlaps as post-process...\n"); */
        removeoverlaps(orig_n, coords, opt);
    }

finish:
    if (coords != NULL) {
        for (i = 0; i < dim; i++) {
            for (j = 0; j < orig_n; j++) {
                d_coords[i][j] = coords[i][j];
            }
        }
        free(coords[0]);
        free(coords);
    }

    if (b) {
        free(b[0]);
        free(b);
    }
    free(tmp_coords);
    free(dist_accumulator);
    free(degrees);
    free(lap2);
    free(lap1);

    return iterations;
}
#endif                          /* IPSEPCOLA */