quad_prog_vpsc.c

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/**********************************************************
 *
 * Solve a quadratic function f(X) = X' e->A X + b X
 * subject to a set of separation constraints e->cs
 *
 * Tim Dwyer, 2006
 **********************************************************/
 
#include <cgraph/alloc.h>
#include <neatogen/digcola.h>
#include <stdbool.h>
#ifdef IPSEPCOLA
#include <math.h>
#include <stdlib.h>
#include <time.h>
#include <stdio.h>
#include <float.h>
#include <assert.h>
#include <neatogen/matrix_ops.h>
#include <neatogen/kkutils.h>
#include <vpsc/csolve_VPSC.h>
#include <neatogen/quad_prog_vpsc.h>
#include <neatogen/quad_prog_solver.h>
 
/* #define CONMAJ_LOGGING 1 */
#define quad_prog_tol 1e-4
 
/*
 * Use gradient-projection to solve Variable Placement with Separation Constraints problem.
 */
int
constrained_majorization_vpsc(CMajEnvVPSC * e, float *b, float *place,
                              int max_iterations)
{
    int i, j, counter;
    float *g, *old_place, *d;
    /* for laplacian computation need number of real vars and those
     * dummy vars included in lap
     */
    int n = e->nv + e->nldv;
    bool converged = false;
#ifdef CONMAJ_LOGGING
    static int call_no = 0;
#endif                          /* CONMAJ_LOGGING */
 
    if (max_iterations == 0)
        return 0;
    g = e->fArray1;
    old_place = e->fArray2;
    d = e->fArray3;
    if (e->m > 0) {
        for (i = 0; i < n; i++) {
            setVariableDesiredPos(e->vs[i], place[i]);
        }
        satisfyVPSC(e->vpsc);
        for (i = 0; i < n; i++) {
            place[i] = getVariablePos(e->vs[i]);
        }
    }
#ifdef CONMAJ_LOGGING
    float prev_stress = 0;
    for (i = 0; i < n; i++) {
        prev_stress += 2 * b[i] * place[i];
        for (j = 0; j < n; j++) {
            prev_stress -= e->A[i][j] * place[j] * place[i];
        }
    }
    FILE *logfile = fopen("constrained_majorization_log", "a");
#endif
 
    for (counter = 0; counter < max_iterations && !converged; counter++) {
        float test = 0;
        float alpha, beta;
        float numerator = 0, denominator = 0, r;
        converged = true;
        /* find steepest descent direction */
        for (i = 0; i < n; i++) {
            old_place[i] = place[i];
            g[i] = 2 * b[i];
            for (j = 0; j < n; j++) {
                g[i] -= 2 * e->A[i][j] * place[j];
            }
        }
        for (i = 0; i < n; i++) {
            numerator += g[i] * g[i];
            r = 0;
            for (j = 0; j < n; j++) {
                r += 2 * e->A[i][j] * g[j];
            }
            denominator -= r * g[i];
        }
        if (denominator != 0)
            alpha = numerator / denominator;
        else
            alpha = 1.0;
        for (i = 0; i < n; i++) {
            place[i] -= alpha * g[i];
        }
        if (e->m > 0) {
            /* project to constraint boundary */
            for (i = 0; i < n; i++) {
                setVariableDesiredPos(e->vs[i], place[i]);
            }
            satisfyVPSC(e->vpsc);
            for (i = 0; i < n; i++) {
                place[i] = getVariablePos(e->vs[i]);
            }
        }
        /* set place to the intersection of old_place-g and boundary and 
         * compute d, the vector from intersection pnt to projection pnt
         */
        for (i = 0; i < n; i++) {
            d[i] = place[i] - old_place[i];
        }
        /* now compute beta */
        numerator = 0, denominator = 0;
        for (i = 0; i < n; i++) {
            numerator += g[i] * d[i];
            r = 0;
            for (j = 0; j < n; j++) {
                r += 2 * e->A[i][j] * d[j];
            }
            denominator += r * d[i];
        }
        if (denominator != 0.0)
            beta = numerator / denominator;
        else
            beta = 1.0;
 
        for (i = 0; i < n; i++) {
            /* beta > 1.0 takes us back outside the feasible region
             * beta < 0 clearly not useful and may happen due to numerical imp.
             */
            if (beta > 0 && beta < 1.0) {
                place[i] = old_place[i] + beta * d[i];
            }
            test += fabsf(place[i] - old_place[i]);
        }
#ifdef CONMAJ_LOGGING
        float stress = 0;
        for (i = 0; i < n; i++) {
            stress += 2 * b[i] * place[i];
            for (j = 0; j < n; j++) {
                stress -= e->A[i][j] * place[j] * place[i];
            }
        }
        fprintf(logfile, "%d: stress=%f, test=%f, %s\n", call_no, stress,
                test, (stress >= prev_stress) ? "No Improvement" : "");
        prev_stress = stress;
#endif
        if (test > quad_prog_tol) {
            converged = false;
        }
    }
#ifdef CONMAJ_LOGGING
    call_no++;
    fclose(logfile);
#endif
    return counter;
}
 
/*
 * 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;
    /* nv is the number of real nodes */
    int nConCs;
    CMajEnvVPSC *e = gv_alloc(sizeof(CMajEnvVPSC));
    e->A = NULL;
    /* 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 = gv_calloc(n, sizeof(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 (size_t j = 1; j < graph[i].nedges; 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 (size_t 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 = gv_calloc(n + e->ndv, sizeof(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 (int 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 (int 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);
        }
    }
    if (opt->clusters.nclusters > 0) {
        Constraint **ecs = e->gcs;
        nConCs = 2 * opt->clusters.nvars;
        e->gcs = newConstraints(e->gm + nConCs);
        for (i = 0; i < e->gm; i++) {
            e->gcs[i] = ecs[i];
        }
        if (ecs != NULL)
            deleteConstraints(0, ecs);
        for (i = 0; i < opt->clusters.nclusters; i++) {
            for (int j = 0; j < opt->clusters.clustersizes[i]; j++) {
                Variable *v = e->vs[opt->clusters.clusters[i][j]];
                Variable *cl = e->vs[e->nv + 2 * i];
                Variable *cr = e->vs[e->nv + 2 * i + 1];
                e->gcs[e->gm++] = newConstraint(cl, v, 0);
                e->gcs[e->gm++] = newConstraint(v, cr, 0);
            }
        }
    }
 
    e->m = 0;
    e->cs = NULL;
    if (e->gm > 0) {
        e->vpsc = newIncVPSC(n + e->ndv, e->vs, e->gm, e->gcs);
        e->m = e->gm;
        e->cs = e->gcs;
    }
    if (packedMat != NULL) {
        e->A = unpackMatrix(packedMat, n);
    }
 
    e->fArray1 = gv_calloc(n, sizeof(float));
    e->fArray2 = gv_calloc(n, sizeof(float));
    e->fArray3 = gv_calloc(n, sizeof(float));
    if (Verbose)
        fprintf(stderr,
                "  initCMajVPSC done: %d global constraints generated.\n",
                e->m);
    return e;
}
 
void deleteCMajEnvVPSC(CMajEnvVPSC * e)
{
    int i;
    if (e->A != NULL) {
        free(e->A[0]);
        free(e->A);
    }
    if (e->m > 0) {
        deleteVPSC(e->vpsc);
        if (e->cs != e->gcs && e->gcs != NULL)
            deleteConstraints(0, e->gcs);
        deleteConstraints(e->m, e->cs);
        for (i = 0; i < e->nv + e->nldv + e->ndv; i++) {
            deleteVariable(e->vs[i]);
        }
        free(e->vs);
    }
    free(e->fArray1);
    free(e->fArray2);
    free(e->fArray3);
    free(e);
}
 
/* generate non-overlap constraints inside each cluster, including dummy
 * nodes at bounds of cluster
 * generate constraints again for top level nodes and clusters treating
 * clusters as rectangles of dim (l,r,b,t)
 * for each cluster map in-constraints to l out-constraints to r 
 *
 * For now, we'll keep the global containment constraints already
 * generated for each cluster, and simply generate non-overlap constraints
 * for all nodes and then an additional set of non-overlap constraints for
 * clusters that we'll map back to the dummy vars as above.
 */
void generateNonoverlapConstraints(CMajEnvVPSC * e,
                                   float nsizeScale,
                                   float **coords,
                                   int k,
                                   bool transitiveClosure,
                                   ipsep_options * opt)
{
    Constraint **csol, **csolptr;
    int i, j, mol = 0;
    int n = e->nv + e->nldv;
    boxf* bb = gv_calloc(n, sizeof(boxf));
    bool genclusters = opt->clusters.nclusters > 0;
    if (genclusters) {
        /* n is the number of real variables, not dummy cluster vars */
        n -= 2 * opt->clusters.nclusters;
    }
    if (k == 0) {
        /* grow a bit in the x dimension, so that if overlap is resolved
         * horizontally then it won't be considered overlapping vertically
         */
        nsizeScale *= 1.0001f;
    }
    for (i = 0; i < n; i++) {
        bb[i].LL.x =
            coords[0][i] - nsizeScale * opt->nsize[i].x / 2.0 -
            opt->gap.x / 2.0;
        bb[i].UR.x =
            coords[0][i] + nsizeScale * opt->nsize[i].x / 2.0 +
            opt->gap.x / 2.0;
        bb[i].LL.y =
            coords[1][i] - nsizeScale * opt->nsize[i].y / 2.0 -
            opt->gap.y / 2.0;
        bb[i].UR.y =
            coords[1][i] + nsizeScale * opt->nsize[i].y / 2.0 +
            opt->gap.y / 2.0;
    }
    if (genclusters) {
        Constraint ***cscl = gv_calloc(opt->clusters.nclusters + 1,
                                       sizeof(Constraint**));
        int* cm = gv_calloc(opt->clusters.nclusters + 1, sizeof(int));
        for (i = 0; i < opt->clusters.nclusters; i++) {
            int cn = opt->clusters.clustersizes[i];
            Variable** cvs = gv_calloc(cn + 2, sizeof(Variable*));
            boxf* cbb = gv_calloc(cn + 2, sizeof(boxf));
            /* compute cluster bounding bb */
            boxf container;
            container.LL.x = container.LL.y = DBL_MAX;
            container.UR.x = container.UR.y = -DBL_MAX;
            for (j = 0; j < cn; j++) {
                int iv = opt->clusters.clusters[i][j];
                cvs[j] = e->vs[iv];
                B2BF(bb[iv], cbb[j]);
                EXPANDBB(container, bb[iv]);
            }
            B2BF(container, opt->clusters.bb[i]);
            cvs[cn] = e->vs[n + 2 * i];
            cvs[cn + 1] = e->vs[n + 2 * i + 1];
            B2BF(container, cbb[cn]);
            B2BF(container, cbb[cn + 1]);
            if (k == 0) {
                cbb[cn].UR.x = container.LL.x + 0.0001;
                cbb[cn + 1].LL.x = container.UR.x - 0.0001;
                cm[i] =
                    genXConstraints(cn + 2, cbb, cvs, &cscl[i],
                                    transitiveClosure);
            } else {
                cbb[cn].UR.y = container.LL.y + 0.0001;
                cbb[cn + 1].LL.y = container.UR.y - 0.0001;
                cm[i] = genYConstraints(cn + 2, cbb, cvs, &cscl[i]);
            }
            mol += cm[i];
            free (cvs);
            free (cbb);
        }
        /* generate top level constraints */
        {
            int cn = opt->clusters.ntoplevel + opt->clusters.nclusters;
            Variable** cvs = gv_calloc(cn, sizeof(Variable*));
            boxf* cbb = gv_calloc(cn, sizeof(boxf));
            for (i = 0; i < opt->clusters.ntoplevel; i++) {
                int iv = opt->clusters.toplevel[i];
                cvs[i] = e->vs[iv];
                B2BF(bb[iv], cbb[i]);
            }
            /* make dummy variables for clusters */
            for (i = opt->clusters.ntoplevel; i < cn; i++) {
                cvs[i] = newVariable(123 + i, 1, 1);
                j = i - opt->clusters.ntoplevel;
                B2BF(opt->clusters.bb[j], cbb[i]);
            }
            i = opt->clusters.nclusters;
            if (k == 0) {
                cm[i] =
                    genXConstraints(cn, cbb, cvs, &cscl[i],
                                    transitiveClosure);
            } else {
                cm[i] = genYConstraints(cn, cbb, cvs, &cscl[i]);
            }
            /* remap constraints from tmp dummy vars to cluster l and r vars */
            for (i = opt->clusters.ntoplevel; i < cn; i++) {
                double dgap;
                j = i - opt->clusters.ntoplevel;
                /* dgap is the change in required constraint gap.
                 * since we are going from a source rectangle the size
                 * of the cluster bounding box to a zero width (in x dim,
                 * zero height in y dim) rectangle, the change will be
                 * half the bb width.
                 */
                if (k == 0) {
                    dgap = -(cbb[i].UR.x - cbb[i].LL.x) / 2.0;
                } else {
                    dgap = -(cbb[i].UR.y - cbb[i].LL.y) / 2.0;
                }
                remapInConstraints(cvs[i], e->vs[n + 2 * j], dgap);
                remapOutConstraints(cvs[i], e->vs[n + 2 * j + 1], dgap);
                /* there may be problems with cycles between
                 * cluster non-overlap and diredge constraints,
                 * to resolve:
                 * 
                 * for each constraint c:v->cvs[i]:
                 *   if exists diredge constraint u->v where u in c:
                 *     remap v->cl to cr->v (gap = height(v)/2)
                 *
                 * in = getInConstraints(cvs[i])
                 * for(c : in) {
                 *   assert(c.right==cvs[i]);
                 *   vin = getOutConstraints(v=c.left)
                 *   for(d : vin) {
                 *     if(d.left.cluster==i):
                 *       tmp = d.left
                 *       d.left = d.right
                 *       d.right = tmp
                 *       d.gap = height(d.right)/2
                 *   }
                 * }
                 *       
                 */
                deleteVariable(cvs[i]);
            }
            mol += cm[opt->clusters.nclusters];
            free (cvs);
            free (cbb);
        }
        csolptr = csol = newConstraints(mol);
        for (i = 0; i < opt->clusters.nclusters + 1; i++) {
            /* copy constraints into csol */
            for (j = 0; j < cm[i]; j++) {
                *csolptr++ = cscl[i][j];
            }
            deleteConstraints(0, cscl[i]);
        }
        free (cscl);
        free (cm);
    } else {
        if (k == 0) {
            mol = genXConstraints(n, bb, e->vs, &csol, transitiveClosure);
        } else {
            mol = genYConstraints(n, bb, e->vs, &csol);
        }
    }
    /* remove constraints from previous iteration */
    if (e->m > 0) {
        /* can't reuse instance of VPSC when constraints change! */
        deleteVPSC(e->vpsc);
        for (i = e->gm; i < e->m; i++) {
            /* delete previous overlap constraints */
            deleteConstraint(e->cs[i]);
        }
        /* just delete the array, not the elements */
        if (e->cs != e->gcs)
            deleteConstraints(0, e->cs);
    }
    /* if we have no global constraints then the overlap constraints
     * are all we have to worry about.
     * Otherwise, we have to copy the global and overlap constraints 
     * into the one array
     */
    if (e->gm == 0) {
        e->m = mol;
        e->cs = csol;
    } else {
        e->m = mol + e->gm;
        e->cs = newConstraints(e->m);
        for (i = 0; i < e->m; i++) {
            if (i < e->gm) {
                e->cs[i] = e->gcs[i];
            } else {
                e->cs[i] = csol[i - e->gm];
            }
        }
        /* just delete the array, not the elements */
        deleteConstraints(0, csol);
    }
    if (Verbose)
        fprintf(stderr, "  generated %d constraints\n", e->m);
    e->vpsc = newIncVPSC(e->nv + e->nldv + e->ndv, e->vs, e->m, e->cs);
    free (bb);
}
 
/*
 * Statically remove overlaps, that is remove all overlaps by moving each node as
 * little as possible.
 */
void removeoverlaps(int n, float **coords, ipsep_options * opt)
{
    int i;
    CMajEnvVPSC *e = initCMajVPSC(n, NULL, NULL, opt, 0);
    generateNonoverlapConstraints(e, 1.0, coords, 0, true, opt);
    solveVPSC(e->vpsc);
    for (i = 0; i < n; i++) {
        coords[0][i] = getVariablePos(e->vs[i]);
    }
    generateNonoverlapConstraints(e, 1.0, coords, 1, false, opt);
    solveVPSC(e->vpsc);
    for (i = 0; i < n; i++) {
        coords[1][i] = getVariablePos(e->vs[i]);
    }
    deleteCMajEnvVPSC(e);
}
 
/*
 unpack the "ordering" array into an array of DigColaLevel
*/
DigColaLevel *assign_digcola_levels(int *ordering, int n, int *level_inds,
                                    int num_divisions)
{
    int i, j;
    DigColaLevel *l = gv_calloc(num_divisions + 1, sizeof(DigColaLevel));
    /* first level */
    l[0].num_nodes = level_inds[0];
    l[0].nodes = gv_calloc(l[0].num_nodes, sizeof(int));
    for (i = 0; i < l[0].num_nodes; i++) {
        l[0].nodes[i] = ordering[i];
    }
    /* second through second last level */
    for (i = 1; i < num_divisions; i++) {
        l[i].num_nodes = level_inds[i] - level_inds[i - 1];
        l[i].nodes = gv_calloc(l[i].num_nodes, sizeof(int));
        for (j = 0; j < l[i].num_nodes; j++) {
            l[i].nodes[j] = ordering[level_inds[i - 1] + j];
        }
    }
    /* last level */
    if (num_divisions > 0) {
        l[num_divisions].num_nodes = n - level_inds[num_divisions - 1];
        l[num_divisions].nodes = gv_calloc(l[num_divisions].num_nodes, sizeof(int));
        for (i = 0; i < l[num_divisions].num_nodes; i++) {
            l[num_divisions].nodes[i] =
                ordering[level_inds[num_divisions - 1] + i];
        }
    }
    return l;
}
 
/*********************
get number of separation constraints based on the number of nodes in each level
ie, num_sep_constraints = sum_i^{num_levels-1} (|L[i]|+|L[i+1]|)
**********************/
int get_num_digcola_constraints(DigColaLevel * levels, int num_levels)
{
    int i, nc = 0;
    for (i = 1; i < num_levels; i++) {
        nc += levels[i].num_nodes + levels[i - 1].num_nodes;
    }
    nc += levels[0].num_nodes + levels[num_levels - 1].num_nodes;
    return nc;
}
 
#endif                          /* IPSEPCOLA */