drl_graph_3d.cpp

/* 
 * Copyright 2007 Sandia Corporation. Under the terms of Contract
 * DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
 * certain rights in this software.
 * 
 * All rights reserved.
 * 
 * Redistribution and use in source and binary forms, with or without 
 * modification, are permitted provided that the following conditions are 
 * met:
 * 
 *     * Redistributions of source code must retain the above copyright 
 * notice, this list of conditions and the following disclaimer.
 *     * Redistributions in binary form must reproduce the above copyright 
 * notice, this list of conditions and the following disclaimer in the 
 * documentation and/or other materials provided with the distribution.
 *     * Neither the name of Sandia National Laboratories nor the names of 
 * its contributors may be used to endorse or promote products derived from 
 * this software without specific prior written permission.
 * 
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
 * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT 
 * OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 
 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED 
 * TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
 * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
 * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
 * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */
// This file contains the member definitions of the master class

#include <iostream>
#include <fstream>
#include <map>
#include <vector>
#include <cstdlib>
#include <cmath>
#include <cstring>

using namespace std;

#include "drl_graph_3d.h"
#include "igraph_random.h"
#include "igraph_interface.h"
#include "igraph_progress.h"
#include "igraph_interrupt_internal.h"
#ifdef MUSE_MPI
  #include <mpi.h>
#endif

namespace drl3d {

graph::graph(const igraph_t *igraph, 
	     const igraph_layout_drl_options_t *options,
	     const igraph_vector_t *weights) {
  myid = 0;
  num_procs = 1;
  
  STAGE = 0;
  iterations = options->init_iterations;
  temperature = options->init_temperature;
  attraction = options->init_attraction;
  damping_mult = options->init_damping_mult;
  min_edges = 20;
  first_add = fine_first_add = true;
  fineDensity = false;
  
  // Brian's original Vx schedule
  liquid.iterations = options->liquid_iterations;
  liquid.temperature = options->liquid_temperature;
  liquid.attraction = options->liquid_attraction;
  liquid.damping_mult = options->liquid_damping_mult;
  liquid.time_elapsed = 0;
  
  expansion.iterations = options->expansion_iterations;
  expansion.temperature = options->expansion_temperature;
  expansion.attraction = options->expansion_attraction;
  expansion.damping_mult = options->expansion_damping_mult;
  expansion.time_elapsed = 0;
  
  cooldown.iterations = options->cooldown_iterations;
  cooldown.temperature = options->cooldown_temperature;
  cooldown.attraction = options->cooldown_attraction;
  cooldown.damping_mult = options->cooldown_damping_mult;
  cooldown.time_elapsed = 0;
  
  crunch.iterations = options->crunch_iterations;
  crunch.temperature = options->crunch_temperature;
  crunch.attraction = options->crunch_attraction;
  crunch.damping_mult = options->crunch_damping_mult;
  crunch.time_elapsed = 0;
  
  simmer.iterations = options->simmer_iterations;
  simmer.temperature = options->simmer_temperature;
  simmer.attraction = options->simmer_attraction;
  simmer.damping_mult = options->simmer_damping_mult;
  simmer.time_elapsed = 0;
  
  // scan .int file for node info
  highest_sim = 1.0;
  num_nodes=igraph_vcount(igraph);
  long int no_of_edges=igraph_ecount(igraph);
  for (long int i=0; i<num_nodes; i++) {
    id_catalog[i] = 1;
  }
  map< int, int>::iterator cat_iter;
  for ( cat_iter = id_catalog.begin();
	cat_iter != id_catalog.end(); cat_iter++) {
    cat_iter->second = cat_iter->first;
  }
  
  // populate node positions and ids  
  positions.reserve ( num_nodes );
  for ( cat_iter = id_catalog.begin();
	cat_iter != id_catalog.end();
	cat_iter++ ) {
    positions.push_back ( Node( cat_iter->first ) );
  }
  
  // read .int file for graph info
  long int node_1, node_2;
  double weight;
  for (long int i=0; i<no_of_edges; i++) {
    node_1=IGRAPH_FROM(igraph, i);
    node_2=IGRAPH_TO(igraph,i);
    weight = weights ? VECTOR(*weights)[i] : 1.0 ;
    (neighbors[id_catalog[node_1]])[id_catalog[node_2]] = weight;    
    (neighbors[id_catalog[node_2]])[id_catalog[node_1]] = weight;  
  }
  
  // initialize density server
  density_server.Init();
    
}

// init_parms -- this subroutine initializes the edge_cut variables
// used in the original VxOrd starting with the edge_cut parameter.
// In our version, edge_cut = 0 means no cutting, 1 = maximum cut.
// We also set the random seed here.

void graph::init_parms ( int rand_seed, float edge_cut, float real_parm )
{

        IGRAPH_UNUSED(rand_seed);
	// first we translate edge_cut the former tcl sliding scale
	//CUT_END = cut_length_end = 39000.0 * (1.0 - edge_cut) + 1000.0;
	CUT_END = cut_length_end = 40000.0 * (1.0 - edge_cut);
	
	// cut_length_end cannot actually be 0
	if ( cut_length_end <= 1.0 )
	  cut_length_end = 1.0;
	  
	float cut_length_start = 4.0 * cut_length_end;
	
	// now we set the parameters used by ReCompute
	cut_off_length = cut_length_start;
	cut_rate = ( cut_length_start - cut_length_end ) / 400.0;
	
	// finally set the number of iterations to leave .real coords fixed
	int full_comp_iters;
	full_comp_iters = liquid.iterations + expansion.iterations +
					  cooldown.iterations + crunch.iterations + 3;
    
	// adjust real parm to iterations (do not enter simmer halfway)
	if ( real_parm < 0 )
		real_iterations = (int)real_parm;
	else if ( real_parm == 1)
		real_iterations = full_comp_iters + simmer.iterations + 100;
	else
		real_iterations = (int)(real_parm*full_comp_iters);
		
	tot_iterations = 0;
	if ( real_iterations > 0 )
		real_fixed = true;
	else
		real_fixed = false;

    // calculate total expected iterations (for progress bar display)
    tot_expected_iterations = liquid.iterations +
                              expansion.iterations + cooldown.iterations +
                              crunch.iterations + simmer.iterations;

	/*
	// output edge_cutting parms (for debugging)
	cout << "Processor " << myid << ": "
	     << "cut_length_end = CUT_END = " << cut_length_end
	     << ", cut_length_start = " << cut_length_start
	     << ", cut_rate = " << cut_rate << endl;
	*/
	
	// set random seed
	// srand ( rand_seed ); // Don't need this in igraph
	
}

void graph::init_parms(const igraph_layout_drl_options_t *options) {
  double rand_seed = 0.0;
  double real_in = -1.0;
  init_parms(rand_seed, options->edge_cut, real_in);
}

int graph::read_real ( const igraph_matrix_t *real_mat, 
		       const igraph_vector_bool_t *fixed) {
  long int n=igraph_matrix_nrow(real_mat);
  for (long int i=0; i<n; i++) {
    positions[id_catalog[i]].x = MATRIX(*real_mat, i, 0);
    positions[id_catalog[i]].y = MATRIX(*real_mat, i, 1);
    positions[id_catalog[i]].z = MATRIX(*real_mat, i, 2);
    positions[id_catalog[i]].fixed = fixed ? VECTOR(*fixed)[i] : false;
    
    if ( real_iterations > 0 ) {
      density_server.Add ( positions[id_catalog[i]], fineDensity );
    }
  }

  return 0;
}

/*********************************************
 * Function: ReCompute				         *
 * Description: Compute the graph locations	 *
 * Modified from original code by B. Wylie   *
 ********************************************/

int graph::ReCompute( ) 
{

  // carryover from original VxOrd
  int MIN = 1;
  
  /*
  // output parameters (for debugging)
  cout << "ReCompute is using the following parameters: "<< endl;
  cout << "STAGE: " << STAGE << ", iter: " << iterations << ", temp = " << temperature
       << ", attract = " << attraction << ", damping_mult = " << damping_mult
	   << ", min_edges = " << min_edges << ", cut_off_length = " << cut_off_length
	   << ", fineDensity = " << fineDensity << endl; 
  */

  /* igraph progress report */
  float progress = (tot_iterations * 100.0 / tot_expected_iterations);

  switch (STAGE) {
    case 0:
      if (iterations == 0)
        IGRAPH_PROGRESS("DrL layout (initialization stage)", progress, 0);
      else
        IGRAPH_PROGRESS("DrL layout (liquid stage)", progress, 0);
      break;
    case 1:
      IGRAPH_PROGRESS("DrL layout (expansion stage)", progress, 0); break;
    case 2:
      IGRAPH_PROGRESS("DrL layout (cooldown and cluster phase)", progress, 0); break;
    case 3:
      IGRAPH_PROGRESS("DrL layout (crunch phase)", progress, 0); break;
    case 5:
      IGRAPH_PROGRESS("DrL layout (simmer phase)", progress, 0); break;
    case 6:
      IGRAPH_PROGRESS("DrL layout (final phase)", 100.0, 0); break;
    default:
      IGRAPH_PROGRESS("DrL layout (unknown phase)", 0.0, 0); break;
  }

  /* Compute Energies for individual nodes */
  update_nodes ();
  
  // check to see if we need to free fixed nodes
  tot_iterations++;
  if ( tot_iterations >= real_iterations )
	 real_fixed = false;


  	// ****************************************
	// AUTOMATIC CONTROL SECTION
	// ****************************************

	// STAGE 0: LIQUID
	if (STAGE == 0) {

		if ( iterations == 0 )
		{
			start_time = time( NULL );
// 			if ( myid == 0 )
// 				cout << "Entering liquid stage ...";
		}

		if (iterations < liquid.iterations) {
			temperature = liquid.temperature;
			attraction = liquid.attraction;
			damping_mult = liquid.damping_mult;
			iterations++;
// 			if ( myid == 0 )
// 				cout << "." << flush;
		
		} else {

			stop_time = time( NULL );
			liquid.time_elapsed = liquid.time_elapsed + (stop_time - start_time);
			temperature = expansion.temperature;
			attraction = expansion.attraction;
			damping_mult = expansion.damping_mult;
			iterations = 0;

			// go to next stage
			STAGE = 1;
			start_time = time( NULL );
			
// 			if ( myid == 0 )
// 				cout << "Entering expansion stage ...";
		}
	}

	// STAGE 1: EXPANSION
	if (STAGE == 1) {

		if (iterations < expansion.iterations) {
				
			// Play with vars
			if (attraction > 1) attraction -= .05;
			if (min_edges > 12) min_edges -= .05;
			cut_off_length -= cut_rate;
			if (damping_mult > .1) damping_mult -= .005;
			iterations++;
// 			if ( myid == 0 ) cout << "." << flush;
	
		} else {

			stop_time = time( NULL );
			expansion.time_elapsed = expansion.time_elapsed + (stop_time - start_time);
		  	min_edges = 12;
			damping_mult = cooldown.damping_mult;
			
			STAGE = 2;
			attraction = cooldown.attraction;
			temperature = cooldown.temperature;
			iterations = 0;
			start_time = time( NULL );
			
// 			if ( myid == 0 )
// 				cout << "Entering cool-down stage ...";
		}
	}

	// STAGE 2: Cool down and cluster
	else if(STAGE==2) {

		if (iterations < cooldown.iterations) {

			// Reduce temperature
			if (temperature > 50) temperature -= 10;

			// Reduce cut length
			if (cut_off_length > cut_length_end) cut_off_length -= cut_rate*2;
			if (min_edges > MIN) min_edges -= .2;
			//min_edges = 99;
			iterations++;
// 			if ( myid == 0 )
// 				cout << "." << flush;
			
		} else {

			stop_time = time( NULL );
			cooldown.time_elapsed = cooldown.time_elapsed + (stop_time - start_time);
			cut_off_length = cut_length_end;
			temperature = crunch.temperature;
			damping_mult = crunch.damping_mult;
			min_edges = MIN;
			//min_edges = 99; // In other words: no more cutting
			
			STAGE = 3;
			iterations = 0;
			attraction = crunch.attraction;
			start_time = time( NULL );
			
// 			if ( myid == 0 )
// 				cout << "Entering crunch stage ...";
		}  
	}

	// STAGE 3: Crunch
	else if(STAGE==3) {
	
		if (iterations < crunch.iterations)
		{
			iterations++;
// 			if ( myid == 0 ) cout << "." << flush;
		}
		else {
		
			stop_time = time( NULL );
			crunch.time_elapsed = crunch.time_elapsed + (stop_time - start_time);
			iterations = 0;
			temperature = simmer.temperature;
			attraction = simmer.attraction;
			damping_mult = simmer.damping_mult;
			min_edges = 99;
			fineDensity = true;
			
			STAGE = 5;
			start_time = time( NULL );
				
// 			if ( myid == 0 )
// 				cout << "Entering simmer stage ...";
		}  
	}

	// STAGE 5: Simmer
	else if( STAGE==5 ) {

		if (iterations < simmer.iterations) {
			if (temperature > 50) temperature -= 2;
			iterations++;
// 			if ( myid == 0 ) cout << "." << flush;
		} else {
			stop_time = time( NULL );
			simmer.time_elapsed = simmer.time_elapsed + (stop_time - start_time);
			
			STAGE = 6;
			
// 			if ( myid == 0 )
// 				cout << "Layout calculation completed in " <<
// 				  ( liquid.time_elapsed + expansion.time_elapsed +
// 				    cooldown.time_elapsed + crunch.time_elapsed +
// 				    simmer.time_elapsed )
// 				     << " seconds (not including I/O)." 
// 				     << endl;
		}
	}

	// STAGE 6: All Done!
	else if ( STAGE == 6)
	{
	  
	  /*
	  // output parameters (for debugging)
	  cout << "ReCompute is using the following parameters: "<< endl;
      cout << "STAGE: " << STAGE << ", iter: " << iterations << ", temp = " << temperature
           << ", attract = " << attraction << ", damping_mult = " << damping_mult
	       << ", min_edges = " << min_edges << ", cut_off_length = " << cut_off_length
	       << ", fineDensity = " << fineDensity << endl; 
	  */
	  
	  return 0;
	}
	
	// ****************************************
	// END AUTOMATIC CONTROL SECTION
	// ****************************************

	// Still need more recomputation
	return 1;

}

// update_nodes -- this function will complete the primary node update
// loop in layout's recompute routine.  It follows exactly the same
// sequence to ensure similarity of parallel layout to the standard layout

void graph::update_nodes ( )
{
	
	vector<int> node_indices;			// node list of nodes currently being updated
	float old_positions[2*MAX_PROCS];	// positions before update
	float new_positions[2*MAX_PROCS];	// positions after update
    
	bool all_fixed;						// check if all nodes are fixed
	
	// initial node list consists of 0,1,...,num_procs
	for ( int i = 0; i < num_procs; i++ )
	  node_indices.push_back( i );

	// next we calculate the number of nodes there would be if the
	// num_nodes by num_procs schedule grid were perfectly square
	int square_num_nodes = (int)(num_procs + num_procs*floor ((float)(num_nodes-1)/(float)num_procs ));

	for ( int i = myid; i < square_num_nodes; i += num_procs )
	{
	
		// get old positions
		get_positions ( node_indices, old_positions );
		
		// default new position is old position
		get_positions ( node_indices, new_positions );
		
		if ( i < num_nodes )
		{

		  // advance random sequence according to myid
		  for ( int j = 0; j < 2*myid; j++ )
		    RNG_UNIF01();
		    // rand();

		  // calculate node energy possibilities
		  if ( !(positions[i].fixed && real_fixed) )
			update_node_pos ( i, old_positions, new_positions );

		  // advance random sequence for next iteration
		  for ( unsigned int j = 2*myid; j < 2*(node_indices.size()-1); j++ )
		    RNG_UNIF01();
		    // rand();

		}
		else
		{
		  // advance random sequence according to use by
		  // the other processors
		  for ( unsigned int j = 0; j < 2*(node_indices.size()); j++ )
		    RNG_UNIF01();
		    //rand();
		}
		
		// check if anything was actually updated (e.g. everything was fixed)
		all_fixed = true;
		for ( unsigned int j = 0; j < node_indices.size (); j++ )
		  if ( !(positions [ node_indices[j] ].fixed && real_fixed) )
		    all_fixed = false;
		  
		// update positions across processors (if not all fixed)
		if ( !all_fixed )
		{
		  #ifdef MUSE_MPI
  		    MPI_Allgather ( &new_positions[2*myid], 2, MPI_FLOAT,
			  	            new_positions, 2, MPI_FLOAT, MPI_COMM_WORLD ); 
		  #endif
		
		  // update positions (old to new)
		  update_density ( node_indices, old_positions, new_positions );
		}
		
		/*
		if ( myid == 0 )
		  {
		    // output node list (for debugging)
		    for ( unsigned int j = 0; j < node_indices.size(); j++ )
		      cout << node_indices[j] << " ";
		    cout << endl;
		  }
		*/

		// compute node list for next update
		for ( unsigned int j = 0; j < node_indices.size(); j++ )
		  node_indices [j] += num_procs;
		
		while ( !node_indices.empty() && node_indices.back() >= num_nodes )
		  node_indices.pop_back ( );
			
	}
	
	// update first_add and fine_first_add
	first_add = false;
	if ( fineDensity ) fine_first_add = false;
	
}

// The get_positions function takes the node_indices list
// and returns the corresponding positions in an array.

void graph::get_positions ( vector<int> &node_indices,
			    float return_positions[3*MAX_PROCS]  )
{
	
	// fill positions
	for(unsigned int i=0; i < node_indices.size(); i++)
	{
		return_positions[3*i] = positions[ node_indices[i] ].x;
		return_positions[3*i+1] = positions[ node_indices[i] ].y;
		return_positions[3*i+2] = positions[ node_indices[i] ].z;
	}
	
}

// update_node_pos -- this subroutine does the actual work of computing
// the new position of a given node.  num_act_proc gives the number
// of active processes at this level for use by the random number
// generators.

void graph::update_node_pos ( int node_ind,
			      float old_positions[3*MAX_PROCS],
			      float new_positions[3*MAX_PROCS] )
{	

		float energies[2];			// node energies for possible positions
		float updated_pos[2][3];	// possible positions
		float pos_x, pos_y, pos_z;
		
		// old VxOrd parameter
		float jump_length = .010 * temperature;
		
		// subtract old node
		density_server.Subtract ( positions[node_ind], first_add, fine_first_add, fineDensity );

		// compute node energy for old solution
		energies[0] = Compute_Node_Energy ( node_ind );

	        // move node to centroid position
		Solve_Analytic ( node_ind, pos_x, pos_y, pos_z );
		positions[node_ind].x = updated_pos[0][0] = pos_x;
		positions[node_ind].y = updated_pos[0][1] = pos_y;
		positions[node_ind].z = updated_pos[0][2] = pos_z;

		/*
		// ouput random numbers (for debugging)
		int rand_0, rand_1;
		rand_0 = rand();
		rand_1 = rand();
		cout << myid << ": " << rand_0 << ", " << rand_1 << endl;
		*/

		// Do random method (RAND_MAX is C++ maximum random number)
		updated_pos[1][0] = updated_pos[0][0] + (.5 - RNG_UNIF01()) * jump_length;
		updated_pos[1][1] = updated_pos[0][1] + (.5 - RNG_UNIF01()) * jump_length;
		updated_pos[1][2] = updated_pos[0][2] + (.5 - RNG_UNIF01()) * jump_length;
		
		// compute node energy for random position
		positions[node_ind].x = updated_pos[1][0];
		positions[node_ind].y = updated_pos[1][1];
		positions[node_ind].z = updated_pos[1][2];
		energies[1] = Compute_Node_Energy ( node_ind );
		
		/*
		// output update possiblities (debugging):
		cout << node_ind << ": (" << updated_pos[0][0] << "," << updated_pos[0][1]
			 << "), " << energies[0] << "; (" << updated_pos[1][0] << ","
			 << updated_pos[1][1] << "), " << energies[1] << endl;
		*/
			 
		// add back old position
		positions[node_ind].x = old_positions[3*myid];
		positions[node_ind].y = old_positions[3*myid+1];
		positions[node_ind].z = old_positions[3*myid+2];
		if ( !fineDensity && !first_add )
			density_server.Add ( positions[node_ind], fineDensity );
		else if ( !fine_first_add )
			density_server.Add ( positions[node_ind], fineDensity );
		
		// choose updated node position with lowest energy
		if ( energies[0] < energies[1] )
		{
			new_positions[3*myid] = updated_pos[0][0];
			new_positions[3*myid+1] = updated_pos[0][1];
			new_positions[3*myid+2] = updated_pos[0][2];
			positions[node_ind].energy = energies[0];
		}
		else
		{
			new_positions[3*myid] = updated_pos[1][0];
			new_positions[3*myid+1] = updated_pos[1][1];
			new_positions[3*myid+2] = updated_pos[1][2];
			positions[node_ind].energy = energies[1];
		}
		
}

// update_density takes a sequence of node_indices and their positions and
// updates the positions by subtracting the old positions and adding the
// new positions to the density grid.

void graph::update_density ( vector<int> &node_indices,
			     float old_positions[3*MAX_PROCS],
			     float new_positions[3*MAX_PROCS] )
{
	
	// go through each node and subtract old position from
	// density grid before adding new position
	for ( unsigned int i = 0; i < node_indices.size(); i++ )
	{
		positions[node_indices[i]].x = old_positions[3*i];
		positions[node_indices[i]].y = old_positions[3*i+1];
		positions[node_indices[i]].z = old_positions[3*i+2];
		density_server.Subtract ( positions[node_indices[i]],
					  first_add, fine_first_add, fineDensity );
		
		positions[node_indices[i]].x = new_positions[3*i];
		positions[node_indices[i]].y = new_positions[3*i+1];
		positions[node_indices[i]].z = new_positions[3*i+2];
		density_server.Add ( positions[node_indices[i]], fineDensity );
	}	

}

/********************************************
* Function: Compute_Node_Energy			    *
* Description: Compute the node energy		*
* This code has been modified from the      *
* original code by B. Wylie.                *
*********************************************/

float graph::Compute_Node_Energy( int node_ind )
{
	
	/* Want to expand 4th power range of attraction */
	float attraction_factor = attraction*attraction*
			attraction*attraction*2e-2;
	
	map <int,float>::iterator EI;
	float x_dis,y_dis,z_dis;
	float energy_distance, weight;
	float node_energy=0;
	
	// Add up all connection energies
	for(EI = neighbors[node_ind].begin(); EI != neighbors[node_ind].end(); ++EI) {

		// Get edge weight
		weight = EI->second;
				
		// Compute x,y distance
		x_dis = positions[ node_ind ].x - positions[ EI->first ].x;
		y_dis = positions[ node_ind ].y - positions[ EI->first ].y;
		z_dis = positions[ node_ind ].z - positions[ EI->first ].z;
		
		// Energy Distance
		energy_distance = x_dis*x_dis + y_dis*y_dis + z_dis*z_dis;
		if (STAGE<2) energy_distance *= energy_distance;

		// In the liquid phase we want to discourage long link distances
		if (STAGE==0) energy_distance *= energy_distance;

		node_energy += weight * attraction_factor * energy_distance;
	}

	// output effect of density (debugging)
	//cout << "[before: " << node_energy;
	
	// add density
	node_energy += density_server.GetDensity ( positions[ node_ind ].x, positions[ node_ind ].y,
						   positions[ node_ind ].z, fineDensity );

	// after calling density server (debugging)
	//cout << ", after: " << node_energy << "]" << endl;
	
	// return computated energy
	return node_energy;
}


/*********************************************
* Function: Solve_Analytic			         *
* Description: Compute the node position     *
* This is a modified version of the function *
* originally written by B. Wylie		     *
*********************************************/

void graph::Solve_Analytic( int node_ind, float &pos_x, float &pos_y,
			    float &pos_z)
{

   map <int,float>::iterator EI;
   float total_weight = 0;
   float x_dis, y_dis, z_dis, x_cen=0, y_cen=0, z_cen=0;
   float x=0,y=0,z=0,dis;
   float damping,weight;

   // Sum up all connections
   for(EI = neighbors[node_ind].begin(); EI != neighbors[node_ind].end(); ++EI) {
		weight = EI->second;
		total_weight += weight;
		x +=  weight * positions[ EI->first ].x;  
		y +=  weight * positions[ EI->first ].y;
		z +=  weight * positions[ EI->first ].z;
   }

   // Now set node position
   if (total_weight > 0) {

		// Compute centriod
		x_cen = x/total_weight;
		y_cen = y/total_weight;
		z_cen = z/total_weight;
		damping = 1.0 - damping_mult;
		pos_x = damping*positions[ node_ind ].x + (1.0-damping) * x_cen;
		pos_y = damping*positions[ node_ind ].y + (1.0-damping) * y_cen;
		pos_z = damping*positions[ node_ind ].z + (1.0-damping) * z_cen;
   }
   
   // No cut edge flag (?)
   if (min_edges == 99) return;

   // Don't cut at end of scale
   if ( CUT_END >= 39500 ) return;

   float num_connections = (float)sqrt((float)neighbors[node_ind].size());
   float maxLength = 0;

   map<int, float>::iterator maxIndex;

   // Go through nodes edges... cutting if necessary
   for(EI = maxIndex = neighbors[node_ind].begin();
	   EI !=neighbors[node_ind].end(); ++EI) {

		// Check for at least min edges
		if (neighbors[node_ind].size() < min_edges) continue;

		x_dis = x_cen - positions[ EI->first ].x;
		y_dis = y_cen - positions[ EI->first ].y;
		z_dis = z_cen - positions[ EI->first ].z;
		dis = x_dis*x_dis+y_dis*y_dis+z_dis*z_dis;
		dis *= num_connections;

		// Store maximum edge
		if (dis > maxLength) {maxLength = dis; maxIndex=EI;}
   }

   // If max length greater than cut_length then cut
   if (maxLength > cut_off_length) neighbors[ node_ind ].erase( maxIndex ); 
   
}


// get_tot_energy adds up the energy for each node to give an estimate of the
// quality of the minimization.

float graph::get_tot_energy ( )
{

	float my_tot_energy, tot_energy;
	my_tot_energy = 0;
	for ( int i = myid; i < num_nodes; i += num_procs )
	  my_tot_energy += positions[i].energy;
	  
	//vector<Node>::iterator i;
    //for ( i = positions.begin(); i != positions.end(); i++ )
	//	tot_energy += i->energy;
	
	#ifdef MUSE_MPI
		MPI_Reduce ( &my_tot_energy, &tot_energy, 1, MPI_FLOAT, MPI_SUM, 0, MPI_COMM_WORLD );
	#else
		tot_energy = my_tot_energy;
	#endif
	
	return tot_energy;
	
}


int graph::draw_graph(igraph_matrix_t *res) {
  int count_iter=0;
  while (ReCompute()) {
    IGRAPH_ALLOW_INTERRUPTION();
    count_iter++;
  }
  long int n=positions.size();
  IGRAPH_CHECK(igraph_matrix_resize(res, n, 3));
  for (long int i=0; i<n; i++) {
    MATRIX(*res, i, 0) = positions[i].x;
    MATRIX(*res, i, 1) = positions[i].y;
    MATRIX(*res, i, 2) = positions[i].z;
  }
  return 0;
}

} // namespace drl3d