/*
  Copyright (C) 2004-2008 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/>.  */

///
/// \file imodel.H
///
/// \brief This file implements classes and functions related to insertions and deletions.
///

#include <cmath>
#include "imodel/imodel.H"
#include "rng.H"
#include "myexception.H"
#include "probability/probability.H"
#include "util.H"
#include "dp/2way.H"

using std::vector;
using std::string;
using namespace A2;

void remove_one_state(Matrix& Q,int S) {
    assert(Q.size1() == Q.size2());

    double temp = 1.0 - Q(S,S);

    // compute transitions from i!=S -> j  [ depends on Q(S->j) ]
    for(int i=0;i<Q.size1();i++) {
	if (i != S) {
	    // compute transitions from i!=S -> j!=S  [ depends on Q(i->S) and Q(S->j) ]
	    for(int j=0;j<Q.size2();j++) 
		if (j != S)
		    Q(i,j) +=  Q(i,S) * Q(S,j) / temp;
	}
	Q(i,S) = 0;
    }

    // compute transitions from S -> j  
    for(int j=0;j<Q.size2();j++) 
	Q(S,j) /= temp;

}

namespace indel 
{
    PairHMM::PairHMM()
	: Matrix(5,5),
	  start_pi_(5,0) 
    {
	for(int i=0;i<size1();i++)
	    for(int j=0;j<size2();j++)
		(*this)(i,j) = 0;
    }

    double PairHMM::start(int s) const {
	double total = 0;
	for(int i=0;i<n_states();i++)
	    total += start_pi(i)*(*this)(i,s);
	return total;
    }

    //------------------------------------------------------------------------//

    bool PairTransducer::is_match(int i)  const {return e1[i]>=0 and e2[i]>=0;}
    bool PairTransducer::is_insert(int i) const {return e1[i]< 0 and e2[i]>=0;}
    bool PairTransducer::is_delete(int i) const {return e1[i]>=0 and e2[i]< 0;}
    bool PairTransducer::is_silent(int i) const {return e1[i]< 0 and e2[i]< 0;}
    bool PairTransducer::is_start(int i)  const {return i == start_;}
    bool PairTransducer::is_end(int i)    const {return i == end_;}

    // find a set of non-silent states (along with start and end) to use instead
    void PairTransducer::remove_silent()
    {
	// construct the new set of states, and mark the (single) start and (single) end
	int new_start = -1;
	int new_end = -1;
	vector<int> keep;
	for(int i=0;i<n_states();i++)
	    if (is_start(i) or is_end(i) or not is_silent(i)) {
		if (is_start(i))
		    new_start = keep.size();
		if (is_end(i))
		    new_end = keep.size();
		keep.push_back(i);
	    }
	    else
		remove_one_state(*this,i);

	// This only works because we already REMOVED the other states
	Matrix Q(keep.size(),keep.size());
	for(int i=0;i<Q.size1();i++)
	    for(int j=0;j<Q.size2();j++)
		Q(i,j) = (*this)(keep[i],keep[j]);
    
	// only keep the emission information for states we are going to keep
	e1 = apply_indices(e1,keep);
	e2 = apply_indices(e2,keep);

	// swap in the new start and end
	start_ = new_start;
	end_ = new_end;

	// swap in the new transition probs
	this->swap(Q);

	for(int i=0;i<n_states();i++)
	    assert(is_start(i) or is_end(i) or not is_silent(i));
    }

    void PairTransducer::check_states() 
    {
	Matrix& Q = *this;

	// store a copy of our transition probabilities to restore at the end
	Matrix temp = Q;

	vector<int> from;

	// Collect states that emit in Seq1 and remove others
	for(int i=0;i<n_states();i++) 
	{
	    if (is_end(i))
		continue;
	    else if (is_start(i) or e1[i] >= 0)
		from.push_back(i);
	    else
		remove_one_state(*this,i);
	}

	// Collect all sets of states which have transition probability of 1.0
	vector< vector<int> > to;
	for(int l=0;l<n_letters();l++) {
	    to.push_back(vector<int>());
	    for(int i=0;i<n_states();i++)
		if (e1[i] == l)
		    to.back().push_back(i);
	}
	to.push_back(vector<int>(1,end_state()));

	// Check transitions from each reading state j to each letter i
	for(int i=0;i<to.size();i++)
	    for(int j=0;j<from.size();j++)
	    {
		double total = 0;
		for(int k=0;k<to[i].size();k++)
		    total += Q(from[j],to[i][k]);

		if (std::abs(total - 1.0) > 1.0e-9) {
		    std::cerr<<"Transition from state "<<j<<" to letter "<<i<<" was "<<total<<", not 1.0!"<<std::endl;
		    abort();
		}
	  
	    }

	// restore the saved copy of our transition probabilities
	Q = temp;
    }

    PairTransducer::PairTransducer(int s,int e,const vector<int>& v1, const vector<int>& v2)
	:Matrix(v1.size(), v1.size(), 0.0),e1(v1),e2(v2),start_(s),end_(e)
    {
	assert(e1.size() == n_states());
	assert(e2.size() == n_states());

	n_letters_ = 1+std::max(max(v1),max(v2));
    }
}

void IndelModel::set_training(bool b)
{
    in_training = b;
}

bool IndelModel::is_training() const
{
    return in_training;
}

double IndelModel::get_heat() const
{
    return heat;
}

void IndelModel::set_heat(double h)
{
    assert(0<= h and h <= 1);
    heat = h;
}

IndelModel::IndelModel(const std::shared_ptr<module_loader>& L)
    :Model(L),in_training(false), heat(1)
{ }

IndelModel::~IndelModel() {}


// Get a bitmask of the list of possible next letters emitted in sequence 1 after state @s0
// The mask is indexed by letter1, letter2, ... , E
vector<int> get_possible_next_letters(int s0, const indel::PairTransducer& PTM)
{
    vector<int> visited(PTM.n_states(),0);

    vector<int> next;
    next.push_back(s0);

    vector<int> possible(PTM.n_letters()+1,0);

    while (next.size())
    {
	// states to consider next time around
	vector<int> next2;

	// For each next (unvisited) letter s1
	for(int i=0;i<next.size();i++)
	{
	    int s1 = next[i];

	    if (visited[s1]) continue;

	    visited[s1] = 1;

	    // For each unvisited neighbor s2 of s1
	    for(int s2=0;s2<PTM.n_states();s2++)
	    {
		if (PTM(s1,s2) > 0) 
		{
		    // If it emits a letter in sequence1, then that letter is possible;
		    if (PTM.emits_1(s2) != -1) {
			possible[PTM.emits_1(s2)] = 1;
			visited[s2] = 1;
		    }
		    // If it is the end state, then the end state is possible
		    else if (s2 == PTM.end_state()) {
			possible.back() = 1;
			visited[s2] = 1;
		    }
		    // If is silent in sequence 1 and not the end state, the consider
		    // that state's neighbors.
		    else if (not visited[s2])
			next2.push_back(s2);
		}
	    }
	}

	next = next2;
    }

    return possible;
}

transducer_state_info::transducer_state_info(const indel::PairTransducer& PTM)
    :M(PTM.n_letters()+1,PTM.n_letters()+1),
     D(PTM.n_letters()+1,PTM.n_letters()+1),
     I(PTM.n_letters()+1,PTM.n_letters()+1)
{
    // Find possible next letters
    vector< vector<int> > possible;
    for(int i=0;i<PTM.n_states();i++)
	possible.push_back(get_possible_next_letters(i,PTM));

    // Find unique states S[i,j] of type Si that next emit j in sequence 1
    const int o = PTM.n_letters()+1;

    for(int i=0;i<o;i++)
	for(int j=0;j<o;j++)
	    M(i,j) = D(i,j) = I(i,j) = -1;

    for(int i=0;i<PTM.n_states();i++)
    {
	int t1 = PTM.emits_1(i);
	if (t1 == -1)
	    t1 = PTM.emits_2(i);
	if (t1 == -1)
	    continue;

	for(int t2=0;t2<PTM.n_letters()+1;t2++) 
	    if (possible[i][t2]) {

		if (PTM.is_match(i)) {
		    assert(M(t1,t2) == -1);
		    M(t1,t2) = i;
		}
		if (PTM.is_delete(i)) {
		    assert(D(t1,t2) == -1);
		    D(t1,t2) = i;
		}
		if (PTM.is_insert(i)) {
		    assert(I(t1,t2) == -1);
		    I(t1,t2) = i;
		}
	    }
    }


}

string i_parameter_name(int i,int n) {
    if (i>=n)
	throw myexception()<<"substitution model: referred to parameter "<<i<<" but there are only "<<n<<" parameters.";
    return string("pI") + convertToString(i);
}

/// Add an edge from S1 to S2 with probability t, and scale back other outgoing edges (including any existing edge from S1 to S2).
void exitize(Matrix& Q,double t,int S1,int S2)
{
    for(int i=0;i<5;i++)
	Q(S1,i) *= (1.0-t);
    Q(S1,S2) += t;
}

/// Only continue from S, it we don't stay in the fragment
void fragmentize(Matrix& Q,double e,int S)
{
    exitize(Q,e,S,S);
}


/// Modify a model on residues to a model on fragments of length L ~ Geometric(e)
void fragmentize(Matrix& Q,double e)
{
    using namespace states;

    fragmentize(Q,e,M);
    fragmentize(Q,e,G1);
    fragmentize(Q,e,G2);
}

// f_M(s) = [ ME  + s(MGxGE - MExGG) ] / [ 1 - s(GG + MM) + s^2(MMxGG - MGxGM) ]

log_double_t SimpleIndelModel::lengthp(int l) const 
{
    using namespace states;

    //--------------- Remove the 'G2' State ----------------------//
    double MM = QE(M,M);
    double MG = QE(M,G1);
    double ME = QE(M,E);

    double GM = QE(G1,M);
    double GG = QE(G1,G1);
    double GE = QE(G1,E);

    //----- Calculate roots of q(s); we assume its quadratic -----//
    double C = 1;
    double B = -(GG + MM);
    double A = MM*GG - MG*GM;

    double sqr_det = sqrt(B*B-4.0*A*C);
    double r1 = (-B - sqr_det)/(2*A);
    double r2 = (-B + sqr_det)/(2*A);

    //------------ Calculate the coefficients f_M[l] ------------//
    double P;
    if (l==0)
	P = ME;
    else {
	double P1 = pow(r1,-l-1);
	double P2 = pow(r2,-l-1);

	// Calculate q[l] and q[l-i] (I've proved that all q[i]>=0)
	double q_l   = 1.0/ (A*(r2-r1)) * (P1 - P2);
	double q_lm1 = 1.0/ (A*(r2-r1)) * (P1*r1 - P2*r2);

	// Calculate f_M[l] from the q[i] (*IS* this always positive?)
	P = ME*q_l + (MG*GE - ME*GG)*q_lm1;
    }
    return P;
}

indel::PairHMM SimpleIndelModel::get_branch_HMM(double) const 
{
    using namespace states;

    double delta   = exp(get_parameter_value(0).as_double());
    double e       = exp(get_parameter_value(1).as_double());
    double t       = exp(get_parameter_value(2).as_double());

    if (is_training()) delta = std::min(delta,0.005);

    // Return a model with all probabilities zero if e==1.
    if (e >= 1)
	return indel::PairHMM();

    if (t < -0.5)
	delta = 0.5;
    else
    {
	double f = 0.1; //unaligned fraction
	delta = pow(delta, get_heat()) * pow(f/(1+f),1-get_heat());
	e = 1.0 - pow(1.0 - e, get_heat());
    }

    if (delta > 0.5)
	throw myexception()<<"indel model: we need (delta <= 0.5), but delta = "<<delta;

    if (e > 1.0)
	throw myexception()<<"indel model: we need (epsilon <= 1), but epsilon = "<<e;

    assert(delta >= 0.0 and delta <= 1.0);
    assert(e >= 0.0 and e < 1.0);

    indel::PairHMM Q;

    Q(S ,S ) = 0;
    Q(S ,M ) = 1 - 2*delta;
    Q(S ,G1) = delta;
    Q(S ,G2) = delta;
    Q(S ,E ) = 0;

    Q(M ,S ) = 1;
    Q(G1,S ) = 1;
    Q(G2,S ) = 1;

    // For the states G1, G2 fragment lengths are Geometric(e)
    fragmentize(Q,e,G1);
    fragmentize(Q,e,G2);

    // For the states M, G1, G2 we might exit with probability t
    exitize(Q,t,M ,E);
    exitize(Q,t,G1,E);
    exitize(Q,t,G2,E);

    // When moving from another state, continue until we are not in S
    remove_one_state(Q,S);

    Q.start_pi(S)  = 0;
    Q.start_pi(M)  = 1;
    Q.start_pi(G1) = 0;
    Q.start_pi(G2) = 0;
    Q.start_pi(E)  = 0;

    return Q;
}


void SimpleIndelModel::recalc()
{
    /* Chain with transitions to End state */
    Q1 = get_branch_HMM(1);

    remove_one_state(Q1,states::G2);

    QE = Q1;
}

log_double_t SimpleIndelModel::prior() const 
{
    double D = 0.5;
    log_double_t Pr = 1;

    // Calculate prior on lambda_O
    double lambda_O = get_parameter_value(0).as_double();
    double pdel =  lambda_O-logdiff(0,lambda_O);
    double rate =  log(-logdiff(0,pdel)) - log(D);

    Pr *= laplace_pdf(rate,-5, 0.5);

    // Calculate prior on lambda_E - shouldn't depend on lambda_O
    double lambda_E = get_parameter_value(1).as_double();
    if (lambda_E >= 0) return 0;

    double E_length = lambda_E - logdiff(0,lambda_E);
    double E_length_mean = 5.0;

    Pr *= exp_exponential_pdf(E_length,E_length_mean);

    return Pr;
}

string SimpleIndelModel::name() const {return "RS05";}

SimpleIndelModel::SimpleIndelModel(const std::shared_ptr<module_loader>& L)
    :IndelModel(L),QE(Q1.size1(),Q1.size2())
{
    add_modifiable_parameter_with_value("delta",  -5.0);
    add_modifiable_parameter_with_value("epsilon",-0.25); // no upper bound on transformed scale
    add_modifiable_parameter_with_value("tau",    log(0.001));
}

indel::PairHMM RS07_branch_HMM_(double e, double D, double heat, bool in_training)
{
    using namespace states;

    // Here D = rate * t

    // Return a model with all probabilities zero if e==1.
    // Scaling time by 1/(1.0-e) doesn't work if e==1.
    if (e >= 1)
	return indel::PairHMM();

    // (1-e) * delta / (1-delta) = P(indel)
    // But move the (1-e) into the RATE to make things work
    double mu = D/(1.0-e);
    double P_indel = 1.0 - exp(-mu);
    double A = P_indel;

    if (in_training) A = std::min(A,0.005);

    double delta = A/(1+A);

    // Note: If the branch is disconnected, then t < -0.5
    //  if (t < -0.5) delta = 0.5;

    double f = 0.1; //unaligned fraction
    delta = pow(delta, heat) * pow(f/(1+f),1-heat);
    e = 1.0 - pow(1.0 - e, heat);

    if (1 - 2*delta <0)
	throw myexception()<<"indel model: we need (delta <= 0.5), but delta = "<<delta;

    if (e > 1)
	throw myexception()<<"indel model: we need (epsilon <= 1), but epsilon = "<<e;
    
    assert(delta >= 0 and delta <= 1);
    assert(e >= 0 and e < 1);

    // transition probabilities default to *zero*
    indel::PairHMM Q;

    Q(S ,S ) = 0;
    Q(S ,M ) = 1 - 2*delta;
    Q(S ,G1) = delta;
    Q(S ,G2) = delta;
    Q(S ,E ) = 1 - delta;

    Q(M ,S ) = 1;
    Q(G1,S ) = 1;
    Q(G2,S ) = 1;

    //  if (t < -0.5)  then don't fragmentize

    // turn the model into a fragment model
    fragmentize(Q,e);

    remove_one_state(Q,S);

    Q.start_pi(S)  = 0;
    Q.start_pi(M)  = 1;
    Q.start_pi(G1) = 0;
    Q.start_pi(G2) = 0;
    Q.start_pi(E)  = 0;

    return Q;
}

log_double_t TKF1::prior() const 
{
    log_double_t Pr = 1;

    // Calculate prior on lambda
    Pr *= laplace_pdf(get_parameter_value(0).as_double(), get_parameter_value(2).as_double(), get_parameter_value(3).as_double());

    // Calculate prior on mean sequence length
    Pr *= exponential_pdf(get_parameter_value(1).as_double(), get_parameter_value(4).as_double());

    return Pr;
}


// lambda is the insertion rate.
// mu     is the deletion  rate.
indel::PairHMM get_TKF1_HMM(double t,double lambda, double mu)
{
    using namespace states;

    indel::PairHMM Q;

    double U = exp(-mu*t);
    double B = (1.0 - exp((lambda-mu)*t))/(mu - lambda*exp((lambda - mu)*t));

    Q(S ,S ) = 0;
    Q(S ,M ) = (1.0 - lambda*B) * (lambda/mu) * U;
    Q(S ,G1) = lambda * B;
    Q(S ,G2) = (1.0 - lambda*B) * (lambda/mu) * (1.0-U);
    Q(S ,E)  = (1.0 - lambda*B) * (1.0 - lambda/mu);

    Q(M ,S ) = 0;
    Q(M ,M ) = Q(S, M);
    Q(M ,G1) = Q(S, G1);
    Q(M ,G2) = Q(S, G2);
    Q(M ,E)  = Q(S, E);

    Q(G1,S ) = 0;
    Q(G1,M ) = lambda * B * U/(1.0-U);
    Q(G1,G1) = lambda * B;
    Q(G1,G2) = (1.0 - U - mu*B)/(1.0-U);
    Q(G1,E ) = (mu-lambda)*B/(1.0-U);

    Q(G2,S ) = 0;
    Q(G2,M ) = Q(S, M);
    Q(G2,G1) = Q(S, G1);
    Q(G2,G2) = Q(S, G2);
    Q(G2,E ) = Q(S, E);

    Q(E, S ) = 0;
    Q(E ,M ) = 0;
    Q(E ,G1) = 0;
    Q(E ,G2) = 0;

    Q.start_pi(S)  = 0;
    Q.start_pi(M)  = 1;
    Q.start_pi(G1) = 0;
    Q.start_pi(G2) = 0;
    Q.start_pi(E)  = 0;

    return Q;
}

indel::PairHMM TKF1::get_branch_HMM(double t) const 
{
    if (not time_dependant)
	t = 1;

    double lambda = exp(get_parameter_value(0).as_double());
    double mean_length = get_parameter_value(1).as_double();
    double sigma = mean_length/(1.0 + mean_length); // E L = s/(1-s)
    double mu = lambda/sigma;                       // s = lambda/mu

    assert(lambda < mu);

    return get_TKF1_HMM(t,lambda,mu);
}

string TKF1::name() const 
{
    return "TKF1";
}

log_double_t TKF1::lengthp(int l) const 
{
    double mean_length = get_parameter_value(1).as_double();

    double sigma = mean_length/(1.0 + mean_length);

    return (1.0-sigma)*pow(log_double_t(sigma),l);
}

TKF1::TKF1(const std::shared_ptr<module_loader>& L, bool b)
    :IndelModel(L),time_dependant(b)
{
    add_modifiable_parameter_with_value("lambda",-5.0);
    add_modifiable_parameter_with_value("meanLength",100.0);
    add_modifiable_parameter_with_value("lambdaPriorMedian", -5.0);
    add_modifiable_parameter_with_value("lambdaPriorStddev", 1.5);
    add_modifiable_parameter_with_value("meanLengthPriorMean", 1.5);
}


log_double_t TKF2::prior() const 
{
    log_double_t Pr = 1;

    // Calculate prior on lambda
    Pr *= laplace_pdf(get_parameter_value(0).as_double(), get_parameter_value(3).as_double(), get_parameter_value(4).as_double());

    // Calculate prior on epsilon
    double lambda_E = get_parameter_value(1).as_double();
    double E_length = lambda_E - logdiff(0,lambda_E);
    double E_length_mean = get_parameter_value(5).as_double();

    Pr *= exp_exponential_pdf(E_length,E_length_mean);

    // Calculate prior on mean sequence length
    Pr *= exponential_pdf(get_parameter_value(2).as_double(), get_parameter_value(6).as_double());

    return Pr;
}

indel::PairHMM TKF2::get_branch_HMM(double t) const 
{
    using namespace states;

    if (not time_dependant)
	t = 1;

    double lambda = exp(get_parameter_value(0).as_double());
    double e = exp(get_parameter_value(1).as_double());
    double mean_length = get_parameter_value(2).as_double();
    double sigma = mean_length/(1.0 + mean_length); // E L = s/(1-s)
    double mu = lambda/sigma;                       // s = lambda/mu

    assert(lambda < mu);

    indel::PairHMM Q = get_TKF1_HMM(t,lambda,mu);
    fragmentize(Q,e);
    return Q;
}

string TKF2::name() const 
{
    return "TKF2";
}

log_double_t TKF2::lengthp(int l) const 
{
    // FIXME -  this is wrong
    std::abort();
    double mean_length = get_parameter_value(1).as_double();

    double sigma = mean_length/(1.0 + mean_length);

    return (1.0-sigma)*pow(log_double_t(sigma),l);
}

TKF2::TKF2(const std::shared_ptr<module_loader>& L, bool b)
    :IndelModel(L), time_dependant(b)
{
    add_modifiable_parameter_with_value("lambda",-5.0);
    add_modifiable_parameter_with_value("epsilon",-0.25);
    add_modifiable_parameter_with_value("mean_length",100.0);
    add_modifiable_parameter_with_value("lambdaPriorMedian", -5.0);
    add_modifiable_parameter_with_value("lambdaPriorStddev", 1.5);
    add_modifiable_parameter_with_value("epsilonPriorLength", 10.0);
    add_modifiable_parameter_with_value("meanLengthPriorMean", 1.5);
}

TransducerIndelModel::TransducerIndelModel(const std::shared_ptr<module_loader>& module_path)
    :Model(module_path)
{ }

TransducerIndelModel::~TransducerIndelModel() {}

log_double_t TKF1_Transducer::prior() const 
{
    log_double_t Pr = 1;

    // Calculate prior on lambda
    Pr *= laplace_pdf(get_parameter_value(0).as_double(), get_parameter_value(2).as_double(), get_parameter_value(3).as_double());

    // Calculate prior on mean sequence length
    Pr *= exponential_pdf(get_parameter_value(1).as_double(), get_parameter_value(4).as_double());

    return Pr;
}

// States: S, letters, E
Matrix TKF1_Transducer::root_chain() const
{
    double lambda = exp(get_parameter_value(0).as_double());
    double mean_length = get_parameter_value(1).as_double();
    double sigma = mean_length/(1.0 + mean_length); // E L = s/(1-s)
    double mu = lambda/sigma;                       // s = lambda/mu

    Matrix M(3,3);

    for(int i=0;i<M.size1();i++)
	for(int j=0;j<M.size2();j++)
	    M(i,j) = 0;

    M(0,1) = lambda/mu;
    M(0,2) = 1 - M(0,1);

    M(1,1) = lambda/mu;
    M(1,2) = 1 - M(1,1);

    return M;
}

// lambda is the insertion rate.
// mu     is the deletion  rate.
indel::PairTransducer get_TKF1_Transducer(double t,double lambda, double mu)
{
    const int S = 0;
    const int M = 1;
    const int D = 2;
    const int I = 3;
    const int E = 4;
    const int W = 6;

    vector<int> e1(7);
    e1[S] = -1;
    e1[M] =  0;
    e1[D] =  0;
    e1[I] = -1;
    e1[E] = -1;
    e1[5] = -1;
    e1[W] = -1;

    vector<int> e2(7);
    e2[S] = -1;
    e2[M] =  0;
    e2[D] = -1;
    e2[I] =  0;
    e2[E] = -1;
    e2[5] = -1;
    e2[W] = -1;

    indel::PairTransducer Q(0,4,e1,e2);

    double U = exp(-mu*t);
    double B = (1.0 - exp((lambda-mu)*t))/(mu - lambda*exp((lambda - mu)*t));

    Q(S ,5 ) = 1;

    Q(M, 5)  = 1.0;

    Q(D, W)  = mu*B/(1.0 - U);
    Q(D, I)  = 1.0 - Q(D,W);

    Q(I, I)  = lambda*B;
    Q(I, W)  = 1.0 - Q(I,I);

    Q(5, I ) = lambda * B;
    Q(5, W ) = 1.0 - Q(5,I);

    Q(W, M ) = U;
    Q(W, D ) = 1.0 - U;
    Q(W, E ) = 1.0;


    Q.remove_silent();

#ifndef NDEBUG
    Q.check_states();
#endif

    return Q;
  
}

indel::PairTransducer TKF1_Transducer::get_branch_Transducer(double t) const 
{
    if (not time_dependent)
	t = 1;

    double lambda = exp(get_parameter_value(0).as_double());
    double mean_length = get_parameter_value(1).as_double();
    double sigma = mean_length/(1.0 + mean_length); // E L = s/(1-s)
    double mu = lambda/sigma;                       // s = lambda/mu

    assert(lambda < mu);

    return get_TKF1_Transducer(t,lambda,mu);
}

string TKF1_Transducer::name() const 
{
    return "TKF1_Transducer";
}

TKF1_Transducer::TKF1_Transducer(const std::shared_ptr<module_loader>& L,bool b)
    :TransducerIndelModel(L),time_dependent(b)
{
    add_modifiable_parameter_with_value("lambda",-5.0);
    add_modifiable_parameter_with_value("meanLength",100.0);
    add_modifiable_parameter_with_value("lambdaPriorMedian", -5.0);
    add_modifiable_parameter_with_value("lambdaPriorStddev", 1.5);
    add_modifiable_parameter_with_value("meanLengthPriorMean", 1.5);
}


// States: S, letters, E
Matrix FS_Transducer::root_chain() const
{
    double tau      = get_parameter_value(5).as_double();
    double mean_s   = get_parameter_value(3).as_double();
    double mean_f   = get_parameter_value(4).as_double();

    double e_s = mean_s/(1+mean_s);
    double e_f = mean_f/(1+mean_f);

    Matrix M(4,4);

    for(int i=0;i<M.size1();i++)
	for(int j=0;j<M.size2();j++)
	    M(i,j) = 0;

    M(0,1) = mean_s/(mean_s+mean_f);
    M(0,2) = mean_f/(mean_s+mean_f);

    M(1,1) = e_s/(1 - tau*tau*(1-e_s)*(1-e_f) );
    M(1,2) = tau*(1-e_s)*e_f/(1 - tau*tau*(1-e_s)*(1-e_f) );
    M(1,3) = 1 - M(1,1) - M(1,2);

    M(2,1) = tau*(1-e_f)*e_s/(1 - tau*tau*(1-e_f)*(1-e_s) );
    M(2,2) = e_f/(1 - tau*tau*(1-e_f)*(1-e_s) );
    M(2,3) = 1 - M(2,1) - M(2,2);

    return M;
}

log_double_t FS_Transducer::prior() const 
{
    log_double_t Pr = 1;

    // Calculate prior on indel rate
    double lambda_s = get_parameter_value(0).as_double();
    double lambda_f = get_parameter_value(1).as_double();

    if (lambda_f < lambda_s) return 0;

    Pr *= laplace_pdf(lambda_s, get_parameter_value(6).as_double(), get_parameter_value(8).as_double());
    Pr *= laplace_pdf(lambda_f, get_parameter_value(7).as_double(), get_parameter_value(8).as_double());

    // Calculate prior on indel length
    double E_length_mean = get_parameter_value(9).as_double();
    double log_r = get_parameter_value(2).as_double();
    double E_length_r = log_r - logdiff(0,log_r);

    Pr *= exp_exponential_pdf(E_length_r,E_length_mean);

    // uniform prior on switch

    return Pr;
}


// Currently, multiple insertions in a row are not allowed, 
// even though multiple deletions are.  This is because I
// would have to figure out a way not to keep track of the LEFT
// end of the insertion also.
// 
// -- Um... couldn't we just have the (1-r) simply go to Rij where 
//    i is the type of residue we last inserted?

// Insertions into FF, FS and SF are delta_f, insertions into SS are delta_s

// Deletions delete only one type (no mixed-type deletions) and are 
//  independent of their left and right neighbors.
// (Currently, we model deletions as occuring at the first letter
//  or the deletion.  The deletion may continue until the first time
//  it either choose to terminate OR sees a letter of another type.
//  Thus, the rate of deletions depends on how close other types are.)

indel::PairTransducer get_FS_Transducer(double /* t */,double delta_s,double delta_f, double r, double Rsf, double Rfs)
{
    double Rss = 1.0-Rsf;
    double Rff = 1.0-Rfs;

    const int S = 0;    // 0

    const int Ms  = 1;  // 1
    const int Ds  = 2;  // 2
    const int IsS = 3;  // 3
    const int IsF = 4;  // 4
    const int Ws  = 5;
    const int WsD = 6;
    const int TsS = 7;
    const int TsF = 8;
    const int E   = 9;  // 5

    const int Mf  = 10; // 6
    const int Df  = 11; // 7
    const int IfF = 12; // 8
    const int IfS = 13; // 9
    const int Wf  = 14;
    const int WfD = 15;
    const int TfF = 16;
    const int TfS = 17;

    const int TsE = 18;
    const int IsE = 19; // 10
    const int TfE = 20;
    const int IfE = 21; // 11

    // Rij means that, having emitted an @i, we will now go on to emit a @j
    const int RSS = 22;
    const int RSF = 23;
    const int RSE = 24;
    const int RFS = 25;
    const int RFF = 26;
    const int RFE = 27;


    vector<int> e1(28, -1);
    vector<int> e2(28, -1);

    // matches
    e1[Ms]  =  e2[Ms]  =  0;
    e1[Mf]  =  e2[Mf]  =  1;

    // deletes
    e1[Ds]  =  0;
    e1[Df]  =  1;

    // inserts - conditional on the next letter in the input sequence
    e2[IsS] =  0;
    e2[IsF] =  0;
    e2[IsE] =  0;

    e2[IfS] =  1;
    e2[IfF] =  1;
    e2[IfE] =  1;

    indel::PairTransducer Q(S,E,e1,e2);

    // This is not F/S symmetric: it treats start like an F

    Q(S,RFS)    = 1;
    Q(S,RFF)    = 1;
    Q(S,RFE)    = 1;

    /*************************************************/

    // Except for the link-outs (below) these probs should all sum to 1

    Q(Ws,Ms)    = (1-2*delta_s)/(1-delta_s);
    Q(Ws,Ds)    = 1 - Q(Ws,Ms);

    Q(Ms,RSS)   = 1;

    Q(Ds,RSS)   = 1 - r;
    Q(Ds,WsD)   = r;

    Q(WsD,Ds)   = 1;

    Q(RSS,Ws)   = 1-delta_s;
    Q(RSS,TsS)  = delta_s;      // Pr(Insertion between two SS)

    // given that the last column was an S, and the next letter in seq1 is an S, do we insert S or F?
    Q(TsS,IsS)  = Rss*Rss/(Rss*Rss+Rsf*Rfs);
    Q(TsS,IfS)  = Rsf*Rfs/(Rss*Rss+Rsf*Rfs);

    // given that the last column was an S, and the next letter in seq1 is an S, do we insert S or F?
    Q(TfS,IsS)  = Rfs*Rss/(Rfs*Rss+Rff*Rfs);
    Q(TfS,IfS)  = Rff*Rfs/(Rfs*Rss+Rff*Rfs);
  
    Q(IsS,TsS)  = r;            // go back and insert another letter .. of undecided type.
    Q(IsS,Ws)   = 1 - r;        // we are done inserting

    Q(IfS,TfS)  = r;
    Q(IfS,Ws)   = 1 - r;

  
    //  This is different than coming from the START state
    //  because we are conditioning on the previous state being an S.
    Q(Ms,RSF)   = Q(Ds,RSF) = 1;    // Link to path out of S into F
    Q(Ms,RSE)   = Q(Ds,RSE) = 1;    // Link to path out of S into E

    Q(RSF,TsF)  = delta_f;
    Q(RSF,Wf)   = 1-delta_f;

    Q(RSE,TsE)  = delta_f;
    Q(RSE,E)    = 1-delta_f;

    /*************************************************/

    // Except for the link-outs (below) these probs should all sum to 1

    Q(Wf,Mf)    = (1-2*delta_f)/(1-delta_f);
    Q(Wf,Df)    = 1 - Q(Wf,Mf);

    Q(Mf,RFF)   = 1;

    Q(Df,RFF)   = 1 - r;
    Q(Df,WfD)   = r;

    Q(WfD,Df)   = 1;

    Q(RFF,Wf)   = 1-delta_f;
    Q(RFF,TfF)  = delta_f;      // Pr(Insertion between two SS)

    // given that the last column was an S, and the next letter in seq1 is an F, do we insert S or F?
    Q(TsF,IsF)  = Rss*Rsf/(Rss*Rsf+Rsf*Rff);
    Q(TsF,IfF)  = Rsf*Rff/(Rss*Rsf+Rsf*Rff);

    // given that the last column was an S, and the next letter in seq1 is an F, do we insert S or F?
    Q(TfF,IsF)  = Rfs*Rsf/(Rfs*Rsf+Rff*Rff);
    Q(TfF,IfF)  = Rff*Rff/(Rfs*Rsf+Rff*Rff);
  
    Q(IsF,TsF)  = r;            // go back and insert another letter .. of undecided type.
    Q(IsF,Wf)   = 1 - r;        // we are done inserting

    Q(IfF,TfF)  = r;
    Q(IfF,Wf)   = 1 - r;

  
    //  This is different than coming from the START state
    //  because we are conditioning on the previous state being an S.
    Q(Mf,RFS)   = Q(Df,RFS) = 1;    // Link to path out of F into S
    Q(Mf,RFE)   = Q(Df,RFE) = 1;    // Link to path out of F into E

    Q(RFS,TfS)  = delta_f;
    Q(RFS,Ws)   = 1-delta_f;

    Q(RFE,TfE)  = delta_f;
    Q(RFE,E)    = 1-delta_f;

    /*************************************************/

    // given that the last column was an S, and the next letter in seq1 is an E (F), do we insert S or F?
    Q(TsE,IsE)  = Rss*Rsf/(Rss*Rsf+Rsf*Rff);
    Q(TsE,IfE)  = Rsf*Rff/(Rss*Rsf+Rsf*Rff);

    // given that the last column was an S, and the next letter in seq1 is an E (F), do we insert S or F?
    Q(TfE,IsE)  = Rfs*Rsf/(Rfs*Rsf+Rff*Rff);
    Q(TfE,IfE)  = Rff*Rff/(Rfs*Rsf+Rff*Rff);
  
    Q(IsE,TsE)  = r;            // go back and insert another letter .. of undecided type.
    Q(IsE,E)    = 1 - r;        // we are done inserting

    Q(IfE,TfE)  = r;
    Q(IfE,E)    = 1 - r;


    Q.remove_silent();

#ifndef NDEBUG
    Q.check_states();
#endif

    return Q;
}

indel::PairTransducer FS_Transducer::get_branch_Transducer(double t) const 
{
    if (not time_dependent)
	t = 1;

    double lambda_s      = exp(get_parameter_value(0).as_double());
    double lambda_f      = exp(get_parameter_value(1).as_double());
    double r             = exp(get_parameter_value(2).as_double());
    double mean_length_s = get_parameter_value(3).as_double();
    double mean_length_f = get_parameter_value(4).as_double();
    //  double tau           = get_parameter_value(5).as_double();

    double sigma_s = mean_length_s/(1.0 + mean_length_s); // E L = s/(1-s)
    double mu_s = lambda_s/sigma_s;                       // s = lambda/mu

    double sigma_f = mean_length_f/(1.0 + mean_length_f); // E L = s/(1-s)
    double mu_f = lambda_f/sigma_f;                       // s = lambda/mu

    assert(lambda_s < mu_s);
    assert(lambda_f < mu_f);

    double A_s = lambda_s*t;
    double B_s = 1.0 - exp(-A_s);
    double delta_s = B_s/(1+B_s);

    double A_f = lambda_f*t;
    double B_f = 1.0 - exp(-A_f);
    double delta_f = B_f/(1+B_f);

    double Rsf = -1;
    double Rfs = -1;
    {
	Matrix R = root_chain();
	//    int start = 0;
	int S     = 1;
	int F     = 2;
	int end   = 3;
	Rsf = R(S,F)/(1-R(S,end));
	Rfs = R(F,S)/(1-R(F,end));
    }

    return get_FS_Transducer(t, delta_s, delta_f, r, Rsf, Rfs);
}

string FS_Transducer::name() const 
{
    return "FS_Transducer";
}

FS_Transducer::FS_Transducer(const std::shared_ptr<module_loader>& L,bool b)
    :TransducerIndelModel(L),time_dependent(b)
{
    add_modifiable_parameter_with_value("lambdaS", -5.0);                  // 0
    add_modifiable_parameter_with_value("lambdaF", -3.0);                  // 1
    add_modifiable_parameter_with_value("r", -0.3);                       // 2
    add_modifiable_parameter_with_value("meanLengthS", 20);             // 3
    add_modifiable_parameter_with_value("meanLengthF", 20);             // 4
    add_modifiable_parameter_with_value("switch", 0.1);                   // 5
    add_modifiable_parameter_with_value("lambdaPriorMedianS", -5.0);    // 6
    add_modifiable_parameter_with_value("lambdaPriorMedianF", -3.0);    // 7
    add_modifiable_parameter_with_value("lambdaPriorStddev", 1.5);     // 8
    add_modifiable_parameter_with_value("meanLengthPriorMean", 1.5);  // 9
}

