/*
  Copyright (C) 2004-2005,2007-2009,2017 Benjamin Redelings

  This file is part of BAli-Phy.

  BAli-Phy 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, or (at your option) any later
  version.

  BAli-Phy 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 BAli-Phy; see the file COPYING.  If not see
  <http://www.gnu.org/licenses/>.  */

#include <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <list>
#include <map>
#include <cmath>
#include <fstream>
#include "matrix.H"
#include "statistics.H"

#include "tree/sequencetree.H"
#include "util.H"
#include "tree/tree-util.H"
#include "tree-dist.H"
#include "rng.H"

#include <boost/program_options.hpp>
#include "distance-report.H"

namespace po = boost::program_options;
using po::variables_map;

using namespace std;
using namespace statistics;

using boost::optional;

template <typename T>
void print_matrix(const matrix<T>& M, char space=' ', char eol='\n')
{
    for(int i=0;i<M.size1();i++) {
	vector<double> v(M.size2());
	for(int j=0;j<v.size();j++)
	    v[j] = M(i,j);
	cout<<join(v,space)<<eol;
    }
}

matrix<double> remove_duplicates(const matrix<double>& D)
{
    assert(D.size1() == D.size2());
    int N = D.size1();

    // find duplicates
    vector<int> remove;
    for(int i=0;i<N;i++) {
	bool found=false;
	for(int j=0;j<i and not found;j++)
	    if (D(i,j) == 0.0)
		found=true;
	if (found)
	    remove.push_back(i);
    }

    if (not remove.size()) return D;

    cerr<<"removing "<<remove.size()<<" duplicates."<<endl;

    // compute mapping of old to new indices
    vector<int> indices(N-remove.size());
    int k=0;
    int p=0;
    for(int i=0;i<indices.size();i++)
    {
	while (p<remove.size() and k==remove[p]) {
	    k++;
	    p++;
	}
	indices[i] = k++;
    }

    // construct the new matrix
    matrix<double> D2(indices.size(),indices.size());

    for(int i=0;i<D2.size1();i++)
	for(int j=0;j<D2.size2();j++)
	    D2(i,j) = D(indices[i],indices[j]);

    return D2;
}

SequenceTree unit_branch_tree(const SequenceTree& T1)
{
    SequenceTree T2 = T1;
    for(int i=0;i<T2.n_branches();i++)
	T2.branch(i).set_length(1.0);
    return T2;
}

variables_map parse_cmd_line(int argc,char* argv[]) 
{ 
    using namespace po;

    // named options
    options_description invisible("Invisible options");
    invisible.add_options()
	("files",value<vector<string> >()->composing(),"tree samples to examine")
	;

    options_description input("Input options");
    input.add_options()
	("help,h", "produce help message")
	("skip,s",value<unsigned>()->default_value(0),"number of tree samples to skip")
	("until,u",value<int>(),"Read until this number of trees.")
	("max,m",value<int>(),"Thin tree samples down to this number of trees.")
	("subsample,x",value<int>()->default_value(1),"factor by which to subsample")
	("verbose,v","Output more log messages on stderr.")
	;

    options_description analysis("Analysis options");
    analysis.add_options()
	("analysis", value<string>()->default_value("matrix"), "Analysis: matrix, autocorrelation, diameter, compare, convergence, converged.")
	("metric", value<string>()->default_value("topology"),"Tree distance: topology, branch, internal-branch.")
	("remove-duplicates","[matrix]: disallow zero distances  between points.")
	("max-lag",value<int>(),"[autocorrelation]: max lag to consider.")
	("CI",value<double>()->default_value(0.95,"0.95"),"Confidence interval size.")
	("converged",value<double>()->default_value(0.05,"0.05"),"Comma-separated quantiles of distance required for converged? (smaller is more strict).")
	("mean", "Show mean and standard deviation")
	("median", "Show median and confidence interval")
	("minmax", "Show minimum and maximum distances")
	("leaves-only", "Show minimum and maximum distances")
	("topology-only", "Show minimum and maximum distances")
	("jitter",value<double>(),"Amount of noise to add to distances")
	;

    options_description visible("All options");
    visible.add(input).add(analysis);

    options_description all("All options");
    all.add(invisible).add(input).add(analysis);

    // positional options
    positional_options_description p;
    p.add("analysis", 1);
    p.add("files", -1);
  
    variables_map args;     
    store(command_line_parser(argc, argv).
	  options(all).positional(p).run(), args);
    // store(parse_command_line(argc, argv, desc), args);
    notify(args);    

    if (args.count("help"))
    {
	cout<<"Compute autocorrelations or other functions of tree distances.\n\n";
	cout<<"Usage: trees-distances <analysis> trees-file1 [trees-file2 ...]\n\n";
	cout<<visible<<"\n";
	exit(0);
    }

    if (args.count("verbose")) log_verbose = 1;

    return args;
}

typedef double (*tree_metric_fn)(const tree_record&,const tree_record&);

matrix<double> leaf_distances(const Tree& T)
{
    const int n = T.n_leaves();
    matrix<double> D(n, n);

    // calculate the pairwise distances
    for(int i=0;i<n;i++)
    {
	D(i,i) = 0;
	for(int j=0;j<i;j++)
	    D(i,j) = D(j,i) = T.distance(i,j);
    }

    return D;
}

matrix<double> distances(const vector<tree_record>& trees, 
			 tree_metric_fn metric_fn
    )
{
    matrix<double> D(trees.size(),trees.size());

    // calculate the pairwise distances
    for(int i=0;i<trees.size();i++) {
	for(int j=0;j<i;j++)
	{
	    D(i,j) = D(j,i) = metric_fn(trees[i],trees[j]);
	    assert(D(i,j) == metric_fn(trees[j],trees[i]));
	}
	D(i,i) = 0;
    }
    return D;
}

double distance(const tree_record& T, 
		const vector<tree_record>& trees,
		tree_metric_fn metric_fn
    )
{
    double D=0;
    for(int i=0;i<trees.size();i++)
	D += metric_fn(T,trees[i]);
    D /= trees.size();
    return D;
}


int topology_distance2(const tree_record& t1, const tree_record& t2)
{
    assert(t1.n_leaves() == t2.n_leaves());

    const unsigned n1 = t1.n_internal_branches();
    const unsigned n2 = t2.n_internal_branches();

    // Accumulate distances for T1 partitions
    unsigned shared=0;

    int i=0,j=0;
    while (1) {
	if (i >= n1) break;
	if (j >= n2) break;

	if (t1.partitions[i] == t2.partitions[j]) {
	    i++;
	    j++;
	    shared++;
	}
	else if (t1.partitions[i] < t2.partitions[j])
	    i++;
	else
	    j++;
    }

    return (n1-shared) + (n2-shared);
}

double total_internal_branch_length(const tree_record& t)
{
    double L=0;
    for(int i=t.n_leaves();i<t.n_branches();i++)
	L += t.branch_lengths[i];
    return L;
}

double internal_branch_distance2(const tree_record& t1, const tree_record& t2)
{
    assert(t1.n_leaves() == t2.n_leaves());
    const int N = t1.n_leaves();

    const unsigned n1 = t1.n_internal_branches();
    const unsigned n2 = t2.n_internal_branches();

    double D = total_internal_branch_length(t1) + total_internal_branch_length(t2);

    for(int i=0,j=0; i<n1 and j<n2;)
    {
	if (t1.partitions[i] == t2.partitions[j])
	{
	    double L1 = t1.branch_lengths[N+i];
	    double L2 = t2.branch_lengths[N+j];
	    D -= (L1+L2);
	    D += std::abs(t1.branch_lengths[N+i] - t2.branch_lengths[N+j]);
	    i++;
	    j++;
	}
	else if (t1.partitions[i] < t2.partitions[j])
	    i++;
	else
	    j++;
    }

    return D;
}

double leaf_branch_distance2(const tree_record& t1, const tree_record& t2)
{
    assert(t1.n_leaves() == t2.n_leaves());
    const int N = t1.n_leaves();

    double D = 0;
    for(int i=0;i<N;i++)
	D += std::abs(t1.branch_lengths[i] - t2.branch_lengths[i]);

    return D;
}

double branch_distance2(const tree_record& t1, const tree_record& t2)
{
    return internal_branch_distance2(t1,t2) + leaf_branch_distance2(t1,t2);
}

// G= is the (undirected) graph of edges in G with slack(x,y)=0.
// 

struct hungarian_data
{
    int N;

    matrix<int> cost;

    vector<int> lx;
    vector<int> ly;

    // M is the matching on (some) of the vertices.
    vector<int> x_to_y;
    vector<int> y_to_x;

    // U is the set of vertices reachable from unmatched vertices in X.  It is divided into UX and UY.
    vector<int> UX;
    vector<int> in_UX;

    vector<int> UY;
    vector<int> in_UY;

    // Since an alternating tree means that x->y->x2 requires (x2,y) to be an edge, we just need to
    // store the x->x2 edge.  We can reconstruct the y from x2.
    vector<int> prev_x_of_x;

    void init();

    void clear();

    bool is_in_UX(int x) const {return in_UX[x];}
    int add_to_UX(int);

    void check_matching() const;

    bool is_in_UY(int y) const {return in_UY[y];}
    void add_to_UY(int);

    std::pair<int,int> consider_new_edges();

    void update_labels();

    vector<int> perfect_matching();

    int slack(int x, int y) const
	{
	    return cost(x,y) - lx[x] - ly[y];
	}

    hungarian_data(const matrix<int>& M)
	:N(M.size1()),
	 cost(M),
	 lx(N),
	 ly(N),
	 x_to_y(N),
	 y_to_x(N),
	 in_UX(N),
	 in_UY(N),
	 prev_x_of_x(N)
	{ 
	    assert(cost.size1() == cost.size2());
	}
};

void hungarian_data::init()
{
    for(int i=0;i<N;i++)
    {
	x_to_y[i] = -1;
	y_to_x[i] = -1;
    }
}

void hungarian_data::clear()
{
    UX.clear();
    UY.clear();

    for(int x=0;x<N;x++)
    {
	int y = x;

	prev_x_of_x[x] = -1;

	in_UY[y] = 0;
	in_UX[x] = 0;
    }

    for(int x=0;x<N;x++)
	if (x_to_y[x] == -1)
	    add_to_UX(x);
}

void hungarian_data::update_labels()
{
    // We update the labelling by computing
    //   delta = min(x \in UX,y \not \in UY) slack(x,y)
    // Here slack(x,y) = l[x] + l[y] - cost(x,y) >=0 and slack(x,y) == 0 implies
    //   that (x,y) is in the equality subgraph.

    // compute the first_y not in UY.
    int first_y = 0;
    while(is_in_UY(first_y))
	first_y++;

    int delta = slack(UX[0],first_y);

    for(int s=0;s<UX.size();s++)
    {
	int x = UX[s];
	for(int y=first_y;y<N;y++)
	{
	    if (is_in_UY(y)) continue;

	    delta = std::min(delta, slack(x,y));
	}
    }
  
    check_matching();

    // if x is in UX, then += delta.
    for(int i=0;i<UX.size();i++)
	lx[UX[i]] += delta;

    // if y is in UY, then -= delta.
    for(int i=0;i<UY.size();i++)
	ly[UY[i]] -= delta;

    check_matching();
}

void hungarian_data::check_matching() const
{
    // all of the existing 
    for(int x=0;x<N;x++)
	if (x_to_y[x] != -1)
	    assert(slack(x,x_to_y[x]) == 0);

    for(int x1=0;x1<N;x1++)
	for(int x2=0;x2<x1;x2++)
	    if (x_to_y[x1] != -1)
		assert(x_to_y[x1] != x_to_y[x2]);

    for(int y1=0;y1<N;y1++)
	for(int y2=0;y2<y1;y2++)
	    if (y_to_x[y1] != -1)
		assert(y_to_x[y1] != y_to_x[y2]);
}

int hungarian_data::add_to_UX(int x)
{
    assert(0 <= x and x < N);
    assert(not is_in_UX(x));
    in_UX[x] = true;
    UX.push_back(x);

    return UX.size();
}

void hungarian_data::add_to_UY(int y)
{
    assert(0 <= y and y < N);
    in_UY[y] = true;
    UY.push_back(y);
}

std::pair<int,int> hungarian_data::consider_new_edges()
{
    for(int s=0;s<UX.size();s++)
    {
	int x = UX[s];
    
	for(int y=0;y<N;y++)
	{
	    // We've already added this one
	    if (is_in_UY(y)) continue;
      
	    // For each edge from x in the equality graph...
	    if (slack(x,y) == 0)
	    {
		// We found an unused one!
		if (y_to_x[y] == -1)
		    return std::pair<int,int>(x,y);
		else
		{
		    // add y to the set UY
		    add_to_UY(y);
		    int x2 = y_to_x[y];

		    prev_x_of_x[x2] = x;
		    add_to_UX(x2);
		}
	    }
	}
    }
    return std::pair<int,int>(-1,-1);
}

vector<int> hungarian_data::perfect_matching()
{
    assert(cost.size1() == cost.size2());
    assert(N == cost.size1());

    init();

    // The edges with this orientation are now part of the matching M
    while(true)
    {
	std::pair<int,int> found(-2,-2);
	do
	{
	    // 1. Initialize variables
	    clear();
      
	    if (UX.size() == 0) return x_to_y;

	    // We search for a path from a vertex x \in UX to a vertex y in \UY.
	    // (1) We can make this a tree, by refusing to revisit any previously-visited node.
	    // (2) We can keep track of this tree by remembering the parent node for every visited node.
	    // (3) We can, in fact track only the sequences of x's, and the last y.
	    //     Thus, x1, x2, x3 y4
	    //      This is because we actually have x1->(y2,x2)->(y3,x3)->y4
	    //      So, from x3,y4 we can recovert (x2 as prevx[x3], and y3 as x_to_y[x2])

	    // Consider each (UX,y) vertex to add to the tree
	    found = consider_new_edges();

	    if (found.first < 0) update_labels();
      
	} while(found.first < 0);

	vector<int> x_to_y_old = x_to_y;

	// we should have found a new edge, here.
	int x = found.first;
	int y = found.second;
	while(x >= 0)
	{
	    int next_y = x_to_y[x];
	    int next_x = prev_x_of_x[x];

	    x_to_y[x] = y;
	    y_to_x[y] = x;

	    x = next_x;
	    y = next_y;
	}

	check_matching();
    }
}

int min_perfect_matching_cost(const matrix<int>& C)
{
    vector<int> x_to_y = hungarian_data(C).perfect_matching();

    // make sure all vertices are matched
    for(int x=0;x<x_to_y.size();x++)
	assert(x_to_y[x] != -1);

    // compute the cost
    int cost = 0;
    for(int x=0;x<x_to_y.size();x++)
	cost += C(x, x_to_y[x]);

    return cost;
}

using boost::dynamic_bitset;

int split_distance_to_dummy(const dynamic_bitset<>& S1)
{
    int count1 = S1.count();
    int count2 = S1.size() - count1;

    return std::min(count1, count2);
}

int split_distance(const dynamic_bitset<>& S1, const dynamic_bitset<>& S2)
{
    return std::min((S1^S2).count(), (S1&S2).count());
}

double matching_distance(const tree_record& t1, const tree_record& t2)
{
    assert(t1.n_leaves() == t2.n_leaves());

    const int N = std::max(t1.n_internal_branches(), t2.n_internal_branches());

    matrix<int> C(N,N);

    for(int i=0;i<t1.n_internal_branches();i++)
	for(int j=0;j<t2.n_internal_branches();j++)
	    C(i,j) = split_distance(t1.partitions[i], t2.partitions[j]);

    for(int i=t1.n_internal_branches();i<N;i++)
	for(int j=0;j<t2.n_internal_branches();j++)
	    C(i,j) = split_distance_to_dummy(t1.partitions[i]);

    for(int j=t2.n_internal_branches();j<N;j++)
	for(int i=0;i<t1.n_internal_branches();i++)
	    C(i,j) = split_distance_to_dummy(t2.partitions[j]);

    return min_perfect_matching_cost(C);
}

double robinson_foulds_distance2(const tree_record& t1, const tree_record& t2)
{
    return topology_distance2(t1,t2);
}

void write_distance_cvars_header(const SequenceTree& T,bool leaves) {

    vector<string> names;

    if (leaves) {
	for(int n1=0;n1<T.n_leaves();n1++)
	    names.push_back(string("L")+convertToString(n1));
    }
    else {
	for(int n1=0;n1<T.n_nodes()-1;n1++)
	    for(int n2=0;n2<n1;n2++) {
		string field = string("D")+convertToString(n1)+"-"+convertToString(n2);
		names.push_back(field);
	    }
    }

  
    std::cout<<join(names,',')<<endl;
}

void write_distance_cvars_out(const SequenceTree& T,bool leaves) {

    vector<string> lengths;
    if (leaves) {
	for(int n1=0;n1<T.n_leaves();n1++)
	    lengths.push_back(convertToString(T.branch(n1).length()));
    }
    else {
	for(int n1=0;n1<T.n_nodes()-1;n1++)
	    for(int n2=0;n2<n1;n2++)
		lengths.push_back(convertToString(T.distance(n1,n2)));
    }
    std::cout<<join(lengths,',')<<endl;
}

int main(int argc,char* argv[]) 
{ 
    try 
    {
	//---------- Parse command line  -------//
	variables_map args = parse_cmd_line(argc,argv);

	string analysis = args["analysis"].as<string>();

	unsigned skip = args["skip"].as<unsigned>();

	int subsample=args["subsample"].as<int>();

	optional<int> last;
	if (args.count("until"))
	    last = args["until"].as<int>();

	optional<int> max;
	if (args.count("max"))
	    max = args["max"].as<int>();

	tree_metric_fn metric_fn = NULL;
	string metric = args["metric"].as<string>();
	if (metric == "topology" or metric == "RF")
	    metric_fn = &robinson_foulds_distance2;
	else if (metric == "branch" or metric == "branches")
	    metric_fn = &branch_distance2;
	else if (metric == "internal-branch")
	    metric_fn = &internal_branch_distance2;
	else if (metric == "matching")
	    metric_fn = &matching_distance;
	else
	    throw myexception()<<"Metric '"<<metric<<"' not implemented.";
      
	//----------- read in trees ------------//
	vector<string> files;
	if (args.count("files"))
	    files = args["files"].as<vector<string> >();

	//----------- task "matrix" ------------//
	if (analysis == "matrix") 
	{
	    check_supplied_filenames(1,files,false);

	    tree_sample all_trees;
	    for(int i=0;i<files.size();i++) 
	    {
		int count = 0;
		int start = all_trees.size();
		if (files[i] == "-")
		    count = all_trees.load_file(std::cin,skip,last,subsample,max);
		else
		    count = all_trees.load_file(files[i],skip,last,subsample,max);
		if (log_verbose)
		{
		    std::cerr<<"Read "<<count<<" trees from '"<<files[i]<<"'"<<std::endl;
		    std::cerr<<"Kept "<<all_trees.size()-start<<" trees from '"<<files[i]<<"'"<<std::endl;
		}
	    }

	    matrix<double> D = distances(all_trees,metric_fn);

	    if (args.count("remove-duplicates"))
		D = remove_duplicates(D);

	    if (args.count("jitter"))
	    {
		double sigma = args["jitter"].as<double>();
		myrand_init();
		for(int i=0;i<D.size1();i++)
		    for(int j=0;j<D.size2();j++)
			D(i,j) += gaussian(0,sigma);
	    }
	    print_matrix(D,'\t','\n');
	}

	else if (analysis == "autocorrelation") 
	{
	    check_supplied_filenames(1,files);
	    tree_sample trees(files[0],skip,last,subsample,max);

	    matrix<double> D = distances(trees,metric_fn);
      
	    // set the window size
	    int max_lag = int( double(trees.size()/10.0 + 1.0 ) );
	    if (args.count("max-lag"))
		max_lag = min(max_lag,args["max-lag"].as<int>());
      
	    // bound the max_lag
	    if (max_lag >= trees.size()/2)
		max_lag = trees.size()/2;

	    // write out the average distances
	    valarray<double> distances(0.0,max_lag);
	    for(int d=0;d<distances.size();d++) {
		double dd = 0;
		for(int i=0;i+d<trees.size();i++)
		    dd += D(i,i+d);
		distances[d] = dd/(trees.size() - d);
	    }
      
	    // write out the average distances
	    for(int i=0;i<distances.size();i++)
		cout<<i<<"   "<<distances[i]<<endl;
	}

	else if (analysis == "diameter") 
	{
	    check_supplied_filenames(1,files);
	    tree_sample trees(files[0],skip,last,subsample,max);
	    if (trees.size() < 2)
		throw myexception()<<"diameter: only 1 point in set.";

	    matrix<double> D = distances(trees,metric_fn);
      
	    diameter(D,"1",args);
	}

	else if (analysis == "node-dist-cvars") 
	{
	    bool leaves_only = args.count("leaves-only");
	    bool topology_only = args.count("topology-only");

	    check_supplied_filenames(1,files);
	    tree_sample trees(files[0],skip,last,subsample,max);

	    write_distance_cvars_header(trees.T(0),leaves_only);

	    for(int i=0;i<trees.size();i++)
	    {
		SequenceTree T = trees.T(i);
		if (topology_only)
		    for(int b=0;b<T.n_branches();b++)
			T.branch(b).set_length(1.0);
		write_distance_cvars_out(T,leaves_only);
	    }
	}
	else if (analysis == "leaf-dist-matrix") 
	{
	    bool topology_only = args.count("topology-only");

	    check_supplied_filenames(1,files);
	    tree_sample trees(files[0],skip,last,subsample,max);

	    for(int i=0;i<trees.size();i++)
	    {
		SequenceTree T = trees.T(i);
		if (topology_only)
		    for(int b=0;b<T.n_branches();b++)
			T.branch(b).set_length(1.0);

		matrix<double> D = leaf_distances(T);
	
		cout<<join(trees.names(), '\t')<<"\n";
		vector<double> v(D.size2());
		for(int i=0;i<D.size1();i++) 
		{
		    for(int j=0;j<v.size();j++)
			v[j] = D(i,j);
		    cout<<join(v,'\t')<<endl;
		}
	    }
	}
	else if (analysis == "compare") 
	{
	    check_supplied_filenames(2,files);

	    tree_sample trees1(files[0],skip,last,subsample,max);
	    tree_sample trees2(files[1],skip,last,subsample,max);

	    tree_sample both = trees1;
	    both.append_trees(trees2);

	    matrix<double> D  = distances(both,metric_fn);
	    report_compare(args, D, trees1.size(), trees2.size());
	}

	else if (analysis == "convergence") 
	{
	    check_supplied_filenames(2,files);

	    tree_sample trees1(files[0],skip,last,subsample,max);
	    tree_sample trees2(files[1],0,0,-1);

	    for(int i=0;i<trees1.size();i++)
		cout<<distance(trees1[i],trees2,metric_fn)<<"\n";
	}
	else if (analysis == "converged") 
	{
	    double alpha = args["converged"].as<double>();
	    if (alpha <= 0 or alpha >= 1)
		throw myexception()<<"Converged quartile "<<alpha<<" is not between 0 and 1";

	    if (alpha > 0.5) alpha = 1.0-alpha;

	    check_supplied_filenames(2,files);
      
	    tree_sample trees1(files[0],skip,last,subsample,max);
	    tree_sample trees2(files[1],0,0,-1);
      
	    matrix<double> D2 = distances(trees2,metric_fn);
	    valarray<double> distances(0.0, trees2.size());
	    for(int i=0;i<D2.size1();i++)
		for(int j=0;j<i;j++) {
		    distances[i] += D2(i,j);
		    distances[j] += D2(i,j);
		}
	    distances /= (trees2.size()-1);

	    double x1 = quantile(distances,alpha);
	    double x2 = quantile(distances,0.5);
	    double x3 = quantile(distances,1.0-alpha);

	    cout<<"Equilibrium: median = "<<x2<<"     target distances["<<alpha<<"] = ("<<x1<<", "<<x3<<")\n";

	    double closest = distance(trees1[0],trees2,metric_fn);
	    int direction = 0;
	    int required_hits = 4;
	    int t=1;
	    for(;t<trees1.size() and required_hits;t++) 
	    {
		double d = distance(trees1[t],trees2,metric_fn);
		closest = min(closest,d);

		if (direction == 0 and d < x1) {
		    if (required_hits ==4)
			cout<<"First hit at iteration "<<t<<endl;
		    required_hits--;
		    direction = !direction;
		}
		if (direction == 1 and d > x3) {
		    required_hits--;
		    direction = !direction;
		}
	    }

	    if (not required_hits)
		cout<<"Stabilized ["<<alpha<<"] at iteration "<<t<<endl;
	    else
		cout<<"Did not converge! (Hit "<<(required_hits-4)<<" boundaries.)";

	    cout<<"The closest we got to the equilibrium was "<<closest<<endl;
	}
	else
	    throw myexception()<<"Analysis '"<<analysis<<"' not recognized.";
    }
    catch (std::exception& e) {
	std::cerr<<"trees-distances: Error! "<<e.what()<<endl;
	exit(1);
    }
    return 0;

}
