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#include <vector>
#include <algorithm>
#include <iostream>
#include "var_alea.hpp"
#include <gsl/gsl_cdf.h>
using namespace std;
vector<double> quantile_norm(int n, double sigma);
struct gaussian_truncated : var_alea<double>
{
gaussian_truncated(double a, double b, double mu = 0, double sigma = 1)
:a(a), b(b), V(gsl_cdf_ugaussian_P(a), gsl_cdf_ugaussian_P(b)), mu(mu), sigma(sigma) {};
double operator()() {
double v = V();
return mu + gsl_cdf_gaussian_Pinv(v,sigma);
}
private:
double a, b;
uniform V;
double mu;
double sigma;
};
struct multi_gaussian_truncated : public var_alea<std::vector<double> >
{
multi_gaussian_truncated(double a, double b, const std::vector<double> u)
:a(a), b(b), V(gsl_cdf_ugaussian_P(a), gsl_cdf_ugaussian_P(b)), G(0,1), u(u), d(u.size()) {};
std::vector<double> operator()() {
double v = V();
double Z = gsl_cdf_gaussian_Pinv(v,1);
std::vector<double> Y(d);
for(int i=0; i<d; i++){
Y[i] = G();
}
double scal = 0;
for(int j=0; j<d; j++){
scal += Y[j]*u[j];
}
std::vector<double> X(d);
for(int i=0; i<d; i++){
X[i] = u[i]*Z + Y[i] - u[i]*scal;
}
return X;
}
private:
double a, b;
uniform V;
gaussian G;
std::vector<double> u;
int d;
};
template <typename L>
struct stratified_sampling {
stratified_sampling(vector<double> p, vector<L> X)
:p(p), X(X), mean(p.size(), 0), sigma2(p.size(), 0), I(p.size()){};
void draw(int N);
vector<double> get_mean() const;
vector<double> get_var() const;
void print_mean() const;
void print_sigma() const;
pair<double,double> estimator() const;
private:
void update(int N);
vector<double> p;
vector<L> X;
vector<int> M;
vector<int> cumM;
vector<double> mean;
vector<double> sigma2;
const int I;
};
//actualisation du nombre de tirages à faire par strates
template <typename L>
void stratified_sampling<L>::update(int Nk) {
bool first_step = M.empty();
//reinitialistation du vecteur M du nombre de tirages par strates
if (first_step) {
M.resize(I,1);
cumM.resize(I,0);
}
else {
for(int i=0; i<I; i++){
cumM[i]=cumM[i]+M[i];
M[i]=1;
}
}
std::vector<double> m(I, 0); //le vecteur des m_i idéals
if (first_step) {
for (int i=0; i<I; i++) {
m[i] = (Nk-I)*p[i];
}
}
else {
//On remplit un vecter des écarts types à parti de notre vecteur de variance
std::vector<double> sigma(p.size(),0);
for (int i=0; i < I; i++) {
sigma[i]=sqrt(sigma2[i]);
}
double scal = std::inner_product(p.begin(), p.end(), sigma.begin(), (double) 0);
for (int i=0; i < I; i++) {
m[i] = (Nk-I)*p[i]*sigma[i]/scal;
//std::cout<<m[i]<<std::endl;
}
}
M[0]+=floor(m[0]);
double current = m[0];
for (int i=1; i<I-1; i++){
M[i] += floor(current+m[i]) - floor(current);
current += m[i];
}
M[I-1]+=Nk-I-floor(current);
}
template <typename L>
void stratified_sampling<L>::draw(int N) {
update(N);
double m, s, oldmean;
for(int i=0;i<I;i++){
m=0;
s=0;
for(int j=0;j<M[i];j++){
double temp = X[i]();
m=m+temp;
s=s+temp*temp;
}
oldmean=mean[i];
mean[i]=(mean[i]*cumM[i]+m)/(cumM[i]+M[i]);
sigma2[i]=((sigma2[i]+oldmean*oldmean)*cumM[i] + s)/(cumM[i]+M[i]) - mean[i]*mean[i];
}
};
template <typename L>
vector<double> stratified_sampling<L>::get_mean() const {
return mean;
};
template <typename L>
vector<double> stratified_sampling<L>::get_var() const {
return sigma2;
};
template <typename L>
void stratified_sampling<L>::print_mean() const {
cout<<"les espérances :"<<endl;
for(int i=0;i<I;i++){
cout<<mean[i]<<"\t";
}
cout<<endl;
};
template <typename L>
void stratified_sampling<L>::print_sigma() const {
cout<<"les écarts types :"<<endl;
for(int i=0;i<I;i++){
cout<<sqrt(sigma2[i])<<"\t";
}
cout<<endl;
};
template <typename L>
pair<double,double> stratified_sampling<L>::estimator() const {
double est_mean = 0;
double est_std = 0;
for (int i=0; i<I; i++) {
est_mean += mean[i]*p[i];
est_std += sqrt(sigma2[i])*p[i];
}
return {est_mean, est_std};
}
template <typename Fct>
struct exponential_tilt : public std::unary_function<std::vector<double>, double>
{
exponential_tilt(std::vector<double> mu, Fct f) : mu(mu), f(f){
norm_mu = 0;
for(unsigned int i=0; i<mu.size(); i++) {
norm_mu += mu[i]*mu[i];
}
};
double operator()(std::vector<double> X) {
std::vector<double> Y(X.size());
double scal = 0;
for (unsigned int i=0; i<X.size(); i++){
Y[i] = X[i] + mu[i];
scal+=X[i]*mu[i];
}
return f(Y) * exp(-scal-0.5*norm_mu);
};
private:
std::vector<double> mu;
Fct f;
double norm_mu;
};
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