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collapsed.cpp
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collapsed.cpp
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#include <iostream>
#include <fstream>
#include <vector>
#include <cstdlib>
#include <string>
#include <sstream>
#include <algorithm> // std::sort
#include <math.h>
#include <numeric>
#include <iomanip>
#include <ctime>
#include <time.h>
#include <boost/foreach.hpp>
#include "omp.h"
#include "get_k_split.h"
#include "infiles.h"
//#include "gen_dir.h"
#include "boost/random/mersenne_twister.hpp"
#include "boost/random/gamma_distribution.hpp"
#include "boost/random/normal_distribution.hpp"
#include <boost/math/distributions/beta.hpp>
#include <boost/random.hpp>
#include <boost/math/special_functions/digamma.hpp> //needed for computing the modified Dirichlet bound
#include <boost/math/special_functions/gamma.hpp>
//#include <boost/random/uniform_01.hpp>
//#include "omp.h"
using namespace std;
using namespace boost::math::policies;
using namespace boost::math;
//****************************************************************************************************************************************
//sample A
vector< vector <double> > x_1; // double x[n][p]: pdfvalues
vector< int > y_1; // int y[n]: number of mappings per read
vector< vector <int> > c_1; // int c_new[n][p]: relabelled index of mapping components per read.
//sample B
vector< vector <double> > x_2; // double x[n][p]: pdfvalues
vector< int > y_2; // int y[n]: number of mappings per read
vector< vector <int> > c_2; // int c_new[n][p]: relabelled index of mapping components per read.
vector< int > r;
vector< int > s;
vector< int > z_alloc; //z = (z_1,...,z_r)
vector< int > xi_alloc; //xi = (xi_1,...,xi_s)
//double * theta;
//double * w;
vector<double> theta (K,0.0);
vector<double> w (K,0.0);
vector<double> sum_1 (K,0.0);
vector<double> sum_2 (K,0.0);
vector<double> sum_1_new (K,0.0);
vector<double> sum_2_new (K,0.0);
vector<int> cum_sum_1 (n_1,0);
vector<int> cum_sum_2 (n_2,0);
double p_alloc, p_alloc_new, myStheta, mySw;
double log_likelihood, log_likelihood_new, gPrior;
// gPrior denotes the probability of being DE, and it follows: gPrior ~ Beta(0.5,0.5), that is, the Jefreys Prior for a Bernoulli trial
vector<int> c_vec (K,1); //c_vector
vector<int> c_new (K,0); //c_vector
vector<int> permutation (K,0);
vector<int> inv_permutation (K,0);
vector<int> permutation_new (K,0);
vector<int> inv_permutation_new (K,0);
//double * u;
//double * v;
vector<double> u (K,0.0);
vector<double> v (K,0.0);
double u_sum_c1, ty1, ty2;
double u_sum_c1_new;
vector<double> alpha_prior (K,1.0); //prior for u
vector<double> gamma_prior (K,1.0); //prior for v
vector<double> v_new (K,0.0);
int nMIX = 5, mixID, kRest, myClustID;
vector<double> beta_paramNEW (nMIX,1.0); //beta parameters of mixture
const double threshold = pow(10.0,-80.0);
void gen_dir(vector<double>&, vector<double>&, int);
void dir(vector<double>&, int);
double allocate(int , int );
double allocate_new(int , int );
double allocateCollapsed(int , int );
double unifRand();
void log_like();
void log_like_new();
void permutation_current();
void permutation_current_collapsed();
void permutation_prop();
void permutation_prop_collapsed();
double bp(int);
double dp(int);
double beta_rand( double , double );
double log_beta(double , double , double );
double log_f_c_old();
double log_f_c_new();
double birth_accept_prob(double , double ,double , double ,int ,int ,double );
double birth_mh(double , double , int ,int );
//****************************************************************************************************************************************
int n_obs, c_sum, c_sum_new; // number of components and number of observations
//****************************************************************************************************************************************
// temp vectors
vector<double> z_prob (K,0.0);
vector<double> alpha_gd(K ,0.0);
vector<double> beta_gd(K ,0.0);
vector<double> w_temp (K,0.0);
vector<double> u_temp (K,0.0);
vector<double> u_temp1 (K,0.0);
vector<double> papasA;
vector<double> papasB;
int main()
{
int iterNEW, myBurn;
myBurn = burn;
//if(K > 200){
// myBurn = 3*burn;
//}
beta_paramNEW[0] = 1.0;
beta_paramNEW[1] = 10.0;
beta_paramNEW[2] = 100.0;
beta_paramNEW[3] = 250.0;
beta_paramNEW[4] = 500.0;
iterNEW = iterations + myBurn;
//if(K > 200){
// iterNEW = 5*iterations + myBurn;
//}
ifstream inFile, trFile;
int i, j, num, k, h, place = 0, step = 0, iter, nan_number = 0, cluster, tid, d_minus_index;
double temp, expZero;
expZero = threshold;
string line, sample;
string result;
ostringstream convert;
//tid: the first number of prob line denotes the cluster of each row
inFile.open(tr_info_file.data(), ifstream::in);
// inFile.ignore(3);
inFile.ignore(1000,' ');
inFile >> kRest;
cout<< "kRest = "<< kRest<<endl;
//alpha_prior[K-1] = kRest + 0.0;
inFile >> temp;
inFile >> cluster;
cout<< "cluster = "<< cluster<<endl;
myClustID = cluster;
inFile.close();
srand(time(NULL)) ;
//clock_t start, end;
//double index[K];
inFile.open("conditionA.weights", ifstream::in);
if (!inFile) {
cerr << "Unable to open conditionA.weights file\n";
exit(1); // call system to stop
}
double malakia;
for(h = 0; h < n_1; h++){
inFile >> malakia;
papasA.push_back(malakia);
}
inFile.close();
inFile.open("conditionB.weights", ifstream::in);
if (!inFile) {
cerr << "Unable to open conditionB.weights file\n";
exit(1); // call system to stop
}
for(h = 0; h < n_2; h++){
inFile >> malakia;
papasB.push_back(malakia);
}
inFile.close();
for(h = 0; h < n_1; h++){
cout << papasA[h]<< " ";
}
cout << endl;
for(h = 0; h < n_2; h++){
cout << papasB[h]<< " ";
}
cout << endl;
//exit(1);
//read conditionA files
cout<<"Reading Condition A"<<endl;
for (h = 0; h < n_1; h++){
convert << h + 1;
sample = prob_file_1.data();
sample += "_";
sample += convert.str();
sample += ".panos";
//cout<<"name = "<< sample.data()<<endl;
convert.str("");
//for (i = 0; i < K; ++i) index[i] = 1.0;
inFile.open(sample.data(), ifstream::in);
cout<< " Reading "<< sample.data()<<" file: ";
if (!inFile) {
cerr << "Unable to open file .panos file\n";
exit(1); // call system to stop
}
i = -1;
while (i<0){
getline( inFile, line );
//cout <<line << endl;
if (line[0] != '#'){
i = 0;
inFile.seekg(place); // this sets the ifstream to the previous line
}
place = inFile.tellg(); // this reads the current position of the ifstream
}
i = 0;
inFile >> tid;
if (tid == cluster){
inFile >> num;
y_1.push_back(num);
xi_alloc.push_back(num);
vector<double> row(num);
vector<int> c_row(num);
temp = 0.0;
for ( j = 0; j < num; ++j){
inFile >> c_row[j] >> row[j];
row[j] = exp(row[j]);
if (row[j] < threshold){row[j] = threshold;nan_number++;}
}
x_1.push_back(row);
c_1.push_back(c_row);
inFile.ignore(10000000,'\n');
i = i+1;
}else{
inFile.ignore(10000000,'\n');
//cout << "line ignored"<< endl;
}
while( inFile.good() ){
inFile >> tid;
if (tid == cluster){
inFile >> num;
y_1.push_back(num);
xi_alloc.push_back(num);
vector<double> row(num);
vector<int> c_row(num);
//cout << "i = "<< i + 1 << ", nMap = "<< num << " ";
for ( j = 0; j < num; ++j){
inFile >> c_row[j] >> row[j];
row[j] = exp(row[j]);
if (row[j] < threshold){row[j] = threshold;nan_number++;}
//cout << c_row[j] << ", " << row[j]<< " ";
}
//cout << endl;
x_1.push_back(row);
x_1[i][num - 1] = expZero;
c_1.push_back(c_row);
inFile.ignore(10000000,'\n');
i = i+1;
}else{
inFile.ignore(10000000,'\n');
}
}
inFile.close();
n_obs = i;
r.push_back(n_obs);
cout << "replicate "<< h + 1 << ", r["<< h<<"] = "<< r[h] <<", total reads = "<< x_1.size() <<endl;
step += n_obs;
cum_sum_1[h] = step;
}
if(nan_number>0){
cout<<"WARNING: found "<< nan_number <<" alignments with weird pdf value."<<endl;
nan_number = 0;
}
cout<<"Reading Condition B"<<endl;
step = 0;
for (h = 0; h < n_2; h++){
convert << h + 1;
sample = prob_file_2.data();
sample += "_";
sample += convert.str();
sample += ".panos";
convert.str("");
//for (i = 0; i < K; ++i) index[i] = 1.0;
inFile.open(sample.data(), ifstream::in);
cout<< " Reading "<< sample.data()<<" file: ";
if (!inFile) {
cerr << "Unable to open file .panos file\n";
exit(1); // call system to stop
}
i = -1;
while (i<0){
getline( inFile, line );
if (line[0] != '#'){
i = 0;
inFile.seekg(place); // this sets the ifstream to the previous line
}
place = inFile.tellg(); // this reads the current position of the ifstream
}
i = 0;
inFile >> tid;
if (tid == cluster){
inFile >> num;
y_2.push_back(num);
z_alloc.push_back(num);
vector<double> row(num);
vector<int> c_row(num);
temp = 0.0;
for ( j = 0; j < num; ++j){
inFile >> c_row[j] >> row[j];
row[j] = exp(row[j]);
if (row[j] < threshold){row[j] = threshold;nan_number++;}
}
x_2.push_back(row);
c_2.push_back(c_row);
inFile.ignore(10000000,'\n');
i = i+1;
}else{
inFile.ignore(10000000,'\n');
}
while( inFile.good() ){
inFile >> tid;
if (tid == cluster){
inFile >> num;
y_2.push_back(num);
z_alloc.push_back(num);
vector<double> row(num);
vector<int> c_row(num);
for ( j = 0; j < num; ++j){
inFile >> c_row[j] >> row[j];
row[j] = exp(row[j]);
if (row[j] < threshold){row[j] = threshold;nan_number++;}
}
x_2.push_back(row);
x_2[i][num - 1] = expZero;
c_2.push_back(c_row);
inFile.ignore(10000000,'\n');
i = i+1;
}else{
inFile.ignore(10000000,'\n');
}
}
inFile.close();
n_obs = i ;
s.push_back(n_obs) ;
cout << "replicate "<< h +1 << ", s["<< h<<"] = "<< s[h] <<", total reads = "<< x_2.size() <<endl;
step += n_obs;
cum_sum_2[h] = step;
}
if(nan_number>0){
cout<<"WARNING: found "<< nan_number <<" alignments with weird pdf value."<<endl;
}
//*******************************************************************************************
int initial_state;
double t_start, t_end;
vector<double> a_pars, b_pars;
int chain, switchCondition = 0;
t_start = omp_get_wtime( );
// ofstream de_file ( output_file.data() );
// ofstream theta_out ( theta_file.data() );
// ofstream w_out ( w_file.data() );
// ofstream gThan ( xgty_file.data() );
vector<double> thetaMEAN (K,0.0);
vector<double> wMEAN (K,0.0);
vector<double> stateMEAN (K,0.0);
int nIterations = 0;
string myString;
int numberChains = nChains;
if (x_2.size() + x_1.size()> 2000000){
numberChains = 4;
}
if (x_2.size() + x_1.size()> 10000000){
numberChains = 2;
}
if (x_2.size() + x_1.size()> 30000000){
numberChains = 2;
iterNEW = (iterations - 1)/5 + 1;
myBurn = 100;
}
if (K > 200){ numberChains = 2; }
ofstream ar_out ( ar_file.data() );
for(chain = 0; chain < numberChains; chain++){
convert << chain + 1;
myString = output_file.data();
myString += "_";
myString += convert.str();
cout<<"name = "<< myString.data()<<endl;
convert.str("");
ofstream de_file ( myString.data() );
if (chain == numberChains/2){
cout << "swap:"<<endl;
x_1.swap(x_2);
y_1.swap(y_2);
c_1.swap(c_2);
z_alloc.swap(xi_alloc);
cum_sum_1.swap(cum_sum_2);
papasA.swap(papasB);
r.swap(s);
switchCondition = 1;
}
convert << chain + 1;
myString = theta_file.data();
myString += "_";
myString += convert.str();
cout<<"name = "<< myString.data()<<endl;
convert.str("");
ofstream theta_out ( myString.data() );
convert << chain + 1;
myString = w_file.data();
myString += "_";
myString += convert.str();
cout<<"name = "<< myString.data()<<endl;
convert.str("");
ofstream w_out ( myString.data() );
//if( chain < numberChains/2){
// initial_state = 0;
//}else{
// initial_state = 1;
//}
if ((chain+1) % 2 == 0){
initial_state = 1;
}else{
initial_state = 0;
}
//if (K > 200){ initial_state = 0; }
//**************************************************************************************************
// Algorithm begins by default from full DE. Otherwise: **
// **
//this corresponds to initialization from zero. **
if (initial_state == 0){ // **
for (k = 1; k< K - 1; k++){ // **
c_vec[k] = 0; // **
}
c_vec[0] = 1; // **
c_vec[K-1] = 1;
}else{
for (k = 1; k< K - 1; k++){ // **
c_vec[k] = 1; // **
}
}
//initialization
iter = 0;
c_sum =accumulate(c_vec.begin(),c_vec.end(),0);
//gamma_prior[c_sum - 1] = kRest + 0.0;
cout << "Initializing chain " << chain+1 << " from nDE = " << c_sum <<"... " << endl;
/*
##################################################################################################################################
*/
dir(alpha_prior,K); //generates v
for (k = 0; k<K; k++){
u[k] = v[k]; //set u equal to v
}
permutation_current(); //this computes the permutation and sets theta as a function of u. It should be called AFTER u.
//computing w
if (c_sum>0){
dir(gamma_prior,c_sum);
for (k = 0; k < K - c_sum; k++){
w_temp[k] = u[k];
}
for (k = K-c_sum; k < K; k++){
w_temp[k] = v[k - K + c_sum]*u_sum_c1;
}
for (k = 0; k < K; k++){
w[k] = w_temp[inv_permutation[k]];
}
}else{
for (k = 0; k< K; k++){
w[k] = theta[k];
}
}
/*
##################################################################################################################################
*/
int sample1, sample2;
double cum_sum1, cum_sum2, tot_sum1, tot_sum2, uni, rj_rate = 0.0;
/* Burn-in period
##################################################################################################################################
*/
tot_sum1 = r[0]/papasA[0] + s[0]/papasB[0] + K;
tot_sum2 = r[0]/papasA[0] + K;
sample1 = 1;
sample2 = 1;
ty1 = r[0]/papasA[0] - r[0];
ty2 = s[0]/papasB[0] - s[0];
for(iter = 1; iter<burn;iter++){
//generate random integers in 1,...,n_1 and 1,...,n_2
//sample1 = 1 + rand() % n_1;
//sample2 = 1 + rand() % n_2;
allocate(sample1, sample2); // generate allocations
// compute GD hyperparameters
//tot_sum1 = r[sample1 - 1]/papasA[sample1 - 1] + s[sample2 - 1]/papasB[sample2 - 1] + K;
//tot_sum2 = r[sample1 - 1]/papasA[sample1 - 1] + K;
cum_sum1 = 0.0;
cum_sum2 = 0.0;
for (k = 0; k < K - c_sum; k++){
alpha_gd[k] = alpha_prior[permutation[k]] + sum_1[permutation[k]] + sum_2[permutation[k]];
beta_gd[k] = tot_sum1 - (alpha_gd[k] + cum_sum1);
cum_sum1 += alpha_gd[k];
cum_sum2 += alpha_gd[k] - sum_2[permutation[k]];
}
if (c_sum>0){
for (k = K - c_sum; k < K ; k++){
alpha_gd[k] = alpha_prior[permutation[k]] + sum_1[permutation[k]];
beta_gd[k] = tot_sum2 - (alpha_gd[k] + cum_sum2);
cum_sum2 += alpha_gd[k];
w_temp[k - K + c_sum] = gamma_prior[permutation[k -K + c_sum]] + sum_2[permutation[k]];
}
}
gen_dir(alpha_gd,beta_gd,K); //generate u
permutation_current();
log_like();
if (c_sum>0){
dir(w_temp,c_sum); //generate v
for (k = 0; k < K - c_sum; k++){
w_temp[k] = u[k];
}
for (k = K-c_sum; k < K; k++){
w_temp[k] = v[k - K + c_sum]*u_sum_c1;
}
for (k = 0; k < K; k++){
w[k] = w_temp[inv_permutation[k]];
}
}else{
for (k = 0; k< K; k++){
w[k] = theta[k];
}
}
}
t_end = omp_get_wtime( );
cout << "Burn-in done. Time: "<< setprecision(5)<< t_end - t_start<<" sec."<< "\n\n";
/* Sampler
##################################################################################################################################
*/
vector<double> xgty (K,0.0);
vector<double> ygtx (K,0.0);
vector<double> cDist (2,0.0);
tot_sum1 = r[0]/papasA[0] + s[0]/papasB[0] + K;
tot_sum2 = r[0]/papasA[0] + K;
vector<int> componentsIndex(K-2);
//cout << tot_sum1 << ", " << tot_sum2 <<endl;
sample1 = 1;
sample2 = 1;
gPrior = beta_rand(0.5,0.5);
for(iter = 1; iter<iterNEW;iter++){
//cout << iter <<endl;
allocateCollapsed(sample1, sample2); // generate allocations (and compute c_sum)
permutation_current_collapsed();
if (K < 20){
for (k = 1; k < K - 1; k++){
d_minus_index = c_sum - c_vec[k];
//k = 1 + rand() % (K-2);
for (i = 0; i < K; i++){
c_new[i] = c_vec[i];
}
uni = unifRand();
c_new[k] = 0;
cDist[0] = log_f_c_new() + log(1.0-gPrior);
c_new[k] = 1;
cDist[1] = log_f_c_new() + log(gPrior);
// Prosoxi: o pollaplasiasmos me d_minus_index isxuei mono otan gamma_prior = 1
cDist[0] = 1.0/(1.0 + d_minus_index*exp(cDist[1] - cDist[0]));
//cout << cDist[0] << endl;
if(uni < cDist[0]){
//edw koitaw ti itan to proigoumeno value wste na aukosmeiwsw c_sum
//if(c_vec[k] == 0) tote einai idio
if(c_vec[k] == 1){c_sum = c_sum - 1;}
c_vec[k] = 0;
}else{
//if(c_vec[k] == 1) tote einai idio
if(c_vec[k] == 0){c_sum = c_sum + 1;}
c_vec[k] = 1;
}
}
}else{
for (k = 0; k < K - 2; k++) componentsIndex[k] = k + 1; // 1 2 ... K - 2
random_shuffle ( componentsIndex.begin(), componentsIndex.end() ); //random permutation
// update first 5 elements of random permutation
for (j = 0; j < 5; j++){
k = componentsIndex[j];
d_minus_index = c_sum - c_vec[k];
for (i = 0; i < K; i++){
c_new[i] = c_vec[i];
}
uni = unifRand();
c_new[k] = 0;
cDist[0] = log_f_c_new() + log(1.0-gPrior);
c_new[k] = 1;
cDist[1] = log_f_c_new() + log(gPrior);
cDist[0] = 1.0/(1.0 + d_minus_index*exp(cDist[1] - cDist[0]));
//cout << cDist[0] << endl;
if(uni < cDist[0]){
if(c_vec[k] == 1){c_sum = c_sum - 1;}
c_vec[k] = 0;
}else{
if(c_vec[k] == 0){c_sum = c_sum + 1;}
c_vec[k] = 1;
}
}
}
c_sum = 0;
for (k = 0; k < K; k++){
c_sum += c_vec[k];
gamma_prior[k] = 1.0;
}
permutation_current_collapsed(); //update permutation
// Update gPrior:
gPrior = beta_rand(c_sum + 0.5, K - c_sum + 0.5);
//gPrior = 0.99;
if (iter % saveStep == 0){
if(iter > myBurn){
nIterations++;
}
//###########################################################################################
//###########################################################################################
cum_sum1 = 0.0;
cum_sum2 = 0.0;
if(c_sum<K){
for (k = 0; k < K - c_sum; k++){
alpha_gd[k] = alpha_prior[permutation[k]] + sum_1[permutation[k]] + sum_2[permutation[k]];
beta_gd[k] = tot_sum1 - (alpha_gd[k] + cum_sum1);
cum_sum1 += alpha_gd[k];
cum_sum2 += alpha_gd[k] - sum_2[permutation[k]];
}
}
if (c_sum>0){
for (k = K - c_sum; k < K ; k++){
alpha_gd[k] = alpha_prior[permutation[k]] + sum_1[permutation[k]];
beta_gd[k] = tot_sum2 - (alpha_gd[k] + cum_sum2);
cum_sum2 += alpha_gd[k];
w_temp[k - K + c_sum] = gamma_prior[permutation[k -K + c_sum]] + sum_2[permutation[k]];
}
}
gen_dir(alpha_gd,beta_gd,K);
permutation_current();
if (c_sum>0){
dir(w_temp,c_sum);
for (k = 0; k < K - c_sum; k++){
w_temp[k] = u[k];
}
for (k = K-c_sum; k < K; k++){
w_temp[k] = v[k - K + c_sum]*u_sum_c1;
}
for (k = 0; k < K; k++){
w[k] = w_temp[inv_permutation[k]];
}
}else{
for (k = 0; k< K; k++){
w[k] = theta[k];
}
}
//###########################################################################################
//###########################################################################################
for (i = 0; i<K; ++i){
de_file << c_vec[i] << " ";
if (switchCondition == 0){
theta_out << theta[i] << " ";
w_out << w[i] << " ";
}else{
theta_out << w[i] << " ";
w_out << theta[i] << " ";
}
if(iter > myBurn){
if (switchCondition == 0){
thetaMEAN[i] += theta[i];
wMEAN[i] += w[i];
}else{
thetaMEAN[i] += w[i];
wMEAN[i] += theta[i];
}
stateMEAN[i] += c_vec[i];
}
}
de_file << endl;
theta_out << endl;
w_out << endl;
if (iter % 1000 == 0){
t_end = omp_get_wtime( );
cout << "Iteration " << iter <<": RJ rate = "<<setprecision(3)<<100.0*rj_rate/iter <<"%, time: "<< setprecision(5)<< t_end - t_start<<" sec."<< "\n\n";
cout << sum_1[0] << ", " << sum_2[0]<<"\n";
}
}
//##################################################################################################################
}
ar_out << rj_rate/iter << endl;
}
ofstream de_file ( output_file.data() );
ofstream theta_out ( theta_file.data() );
ofstream w_out ( w_file.data() );
for (i = 0; i<K; ++i){
thetaMEAN[i] /= (nIterations + 0.0);
wMEAN[i] /= (nIterations + 0.0);
stateMEAN[i] /= (nIterations + 0.0);
de_file << stateMEAN[i] << endl;
theta_out << thetaMEAN[i] << endl;
w_out << wMEAN[i] << endl;
}
cout << "Sampling done."<<endl;
return(0);
}
void gen_dir( vector<double>& a_pars, vector<double>& b_pars, int n_comps){
int i;
//double *theta_vec = new double[n_comps];
double sum_theta, g1, g2; // g1 and g2 are the two gamma rv's in order to simulate a beta rv
int seed = rand();
boost::mt19937 rng(seed);
i = 0;
boost::gamma_distribution<double> gd1(a_pars[i]), gd2(b_pars[i]);
boost::variate_generator<boost::mt19937&,boost::gamma_distribution<> > var_gamma1( rng, gd1 ), var_gamma2( rng, gd2 );
g1 = var_gamma1(); // g1 ~ Gamma(a_pars[], 1)
g2 = var_gamma2(); // g2 ~ Gamma(b_pars[], 1)
u[i] = g1/(g1 + g2); // theta[] ~ Beta(a_pars[], b_pars[])
sum_theta = u[i];
for (i = 1; i< n_comps-1; ++i){
boost::gamma_distribution<double> gd1(a_pars[i]), gd2(b_pars[i]);
boost::variate_generator<boost::mt19937&,boost::gamma_distribution<> > var_gamma1( rng, gd1 ), var_gamma2( rng, gd2 );
g1 = var_gamma1(); // g1 ~ Gamma(a_pars[], 1)
g2 = var_gamma2(); // g2 ~ Gamma(b_pars[], 1)
u[i] = g1*(1.0-sum_theta)/(g1 + g2); // theta[] ~ Beta(a_pars[], b_pars[])
sum_theta += u[i];
}
u[n_comps-1] = 1.0-sum_theta;
}
/*
*****************************************************************************************
Function to simulate Beta(a1,a2) r.v *
*****************************************************************************************
*/
double beta_rand( double a1, double a2){
double theta_vec, g1, g2; // g1 and g2 are the two gamma rv's in order to simulate a beta rv
int seed = rand();
boost::mt19937 rng(seed);
boost::gamma_distribution<double> gd1(a1), gd2(a2);
boost::variate_generator<boost::mt19937&,boost::gamma_distribution<> > var_gamma1( rng, gd1 ), var_gamma2( rng, gd2 );
g1 = var_gamma1(); // g1 ~ Gamma(a_pars[], 1)
g2 = var_gamma2(); // g2 ~ Gamma(b_pars[], 1)
theta_vec = g1/(g1 + g2); // theta[] ~ Beta(a_pars[], b_pars[])
return theta_vec;
}
/*
*****************************************************************************************
Function to compute the log pdf Beta(a1,a2) *
*****************************************************************************************
*/
double log_beta(double b, double a1, double a2){
double pdf;
pdf = boost::math::lgamma(a1) + boost::math::lgamma(a2) - boost::math::lgamma(a1+a2); //beta function
pdf = (a1-1.0)*log(b) + (a2-1.0)*log(1.0-b) - pdf;
return pdf;
}
/*
*****************************************************************************************
Function to compute the log f(xi_alloc,z_alloc|c), given xi_alloc, z_alloc, c *
*****************************************************************************************
*/
double log_f_c_old(){
double pdf, u1, talHeads, talHeads2, sum_lg_c0, lg_sum_c1, lg_sum_c1_2, sum_lg_c1, lg_sum_c1_3, sum_lg_c1_3;
int k;
sum_lg_c0 = 0.0;
lg_sum_c1 = 0.0;
lg_sum_c1_2 = 0.0;
sum_lg_c1 = 0.0;
lg_sum_c1_3 = 0.0;
sum_lg_c1_3 = 0.0;
c_sum = 0;
for(k = 0; k < K; k++){
talHeads2 = alpha_prior[k] + sum_1[k];
talHeads = talHeads2 + sum_2[k];
if(c_vec[k] == 0){
sum_lg_c0 += boost::math::lgamma(talHeads);
}else{
lg_sum_c1 += talHeads;
lg_sum_c1_2 += talHeads2;
sum_lg_c1 += boost::math::lgamma(talHeads2);
u1 = gamma_prior[0] + sum_2[k];
sum_lg_c1_3 += boost::math::lgamma(u1);
lg_sum_c1_3 += u1;
c_sum++;
}
}
lg_sum_c1 = boost::math::lgamma(lg_sum_c1);
lg_sum_c1_2 = boost::math::lgamma(lg_sum_c1_2);
lg_sum_c1_3 = boost::math::lgamma(lg_sum_c1_3);
pdf = lg_sum_c1 + sum_lg_c0 + sum_lg_c1 + sum_lg_c1_3 - lg_sum_c1_2 - lg_sum_c1_3;
return pdf;
}
/*
*****************************************************************************************
Function to compute the log f(xi,z|c_new) *
*****************************************************************************************
*/
double log_f_c_new(){
double pdf, u1, talHeads, talHeads2, sum_lg_c0, lg_sum_c1, lg_sum_c1_2, sum_lg_c1, lg_sum_c1_3, sum_lg_c1_3;
int k;
sum_lg_c0 = 0.0;
lg_sum_c1 = 0.0;
lg_sum_c1_2 = 0.0;
sum_lg_c1 = 0.0;
lg_sum_c1_3 = 0.0;
sum_lg_c1_3 = 0.0;
for(k = 0; k < K; k++){
talHeads2 = alpha_prior[k] + sum_1[k];
talHeads = talHeads2 + sum_2[k];
if(c_new[k] == 0){
sum_lg_c0 += boost::math::lgamma(talHeads);
}else{
lg_sum_c1 += talHeads;
lg_sum_c1_2 += talHeads2;
sum_lg_c1 += boost::math::lgamma(talHeads2);
u1 = gamma_prior[0] + sum_2[k];
sum_lg_c1_3 += boost::math::lgamma(u1);
lg_sum_c1_3 += u1;
}
}
lg_sum_c1 = boost::math::lgamma(lg_sum_c1);
lg_sum_c1_2 = boost::math::lgamma(lg_sum_c1_2);
lg_sum_c1_3 = boost::math::lgamma(lg_sum_c1_3);
pdf = lg_sum_c1 + sum_lg_c0 + sum_lg_c1 + sum_lg_c1_3 - lg_sum_c1_2 - lg_sum_c1_3;
return pdf;
}
void dir( vector<double>& a_pars, int n_comps){
int i;
double sum_theta;
int seed = rand();
boost::mt19937 rng(seed);
i = 0;
//boost::gamma_distribution<double> gd1(a_pars[i]);
//boost::variate_generator<boost::mt19937&,boost::gamma_distribution<> > var_gamma1( rng, gd1 );
sum_theta = 0.0;
for (i = 0; i< n_comps; ++i){
boost::gamma_distribution<double> gd1(a_pars[i]);
boost::variate_generator<boost::mt19937&,boost::gamma_distribution<> > var_gamma1( rng, gd1 );
v[i] = var_gamma1(); // g1 ~ Gamma(a_pars[], 1)
sum_theta += v[i];
}
for (i = 0; i< n_comps; ++i){
v[i] = v[i]/sum_theta; // theta[] ~ Beta(a_pars[], b_pars[])
}
}
/*
*****************************************************************************************
Function to simulate U(0,1) r.v's *
*****************************************************************************************
*/
//double unifRand()
//{
// int seed = rand();
// boost::mt19937 rng(seed);
// boost::uniform_01<double> gd1;
// boost::variate_generator<boost::mt19937&,boost::uniform_01<> > uni( rng, gd1 );
// return uni();
//}
double unifRand()
{
return rand() / double(RAND_MAX);
}
double allocateCollapsed(int sample1, int sample2){
int z,i,k,sample_start, sample_end;
double uni, z_prob_sum, z_dist, u1, u2, talHeads;
sample_start = cum_sum_1[sample1-1] - r[sample1-1];
sample_end = cum_sum_1[sample1-1];
// sum_1 = {s_k(xi); k = 1, ..., K}
// sum_2 = {s_k(z); k = 1, ..., K}
for (i = sample_start; i < sample_end; i++){
z = xi_alloc[i];
//cout<<", "<< i << ", previous alloc_i = " << z << " ---------"<< endl;
u1 = 0.0;
u2 = 0.0;
z_prob_sum = 0.0;
for (k = 0; k < K; k++){
talHeads = alpha_prior[k] + sum_1[k];
if(c_vec[k] == 0){
theta[k] = talHeads + sum_2[k];
}else{
theta[k] = talHeads;
u1 += talHeads + sum_2[k];
u2 += talHeads;
}
}
theta[z] = theta[z] - 1.0;
if(c_vec[z] == 1){
u1 = u1 - 1.0;
u2 = u2 - 1.0;
}
for (k = 0; k < y_1[i]; k++){
if(c_vec[c_1[i][k]] == 0){
theta[c_1[i][k]] *= x_1[i][k];