// ch13_bootstrap_fit.cpp
// Companion code for Chapter 13: Optimization and Data Fitting.
// Standalone C++11; standard library only; console output without plotting.
// Compile: c++ -std=c++11 -O2 -Wall -Wextra -pedantic ch13_bootstrap_fit.cpp -o ch13_bootstrap_fit
// Edit the example settings in main(); routines above main() can be reused.
// Fixed seeds reproduce runs with the same standard-library implementation.
// Random distributions need not give identical sequences across compilers/languages.

#include <algorithm>
#include <array>
#include <cmath>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <numeric>
#include <random>
#include <stdexcept>
#include <string>
#include <utility>
#include <vector>

using Vec = std::vector<double>;
using Mat = std::vector<Vec>;
using Function = std::function<double(const Vec&)>;
using ScalarFunction = std::function<double(double)>;
const double pi = std::acos(-1.0);

void require(bool condition, const std::string& message) {
    if (!condition) throw std::invalid_argument(message);
}
void finite_vector(const Vec& x) {
    require(!x.empty(), "A nonempty vector is required.");
    for (double v : x) require(std::isfinite(v), "Data must be finite.");
}
void check_bounds(const Vec& lo, const Vec& hi) {
    finite_vector(lo); finite_vector(hi);
    require(lo.size() == hi.size(), "Bounds must have matching dimensions.");
    for (std::size_t j=0; j<lo.size(); ++j)
        require(hi[j]>lo[j] && std::isfinite(hi[j]-lo[j]), "Require finite upper > lower.");
}
double objective_value(double value) {
    require(std::isfinite(value), "Objective must return a finite real scalar.");
    return value;
}
double clip(double x, double lo, double hi) { return std::max(lo,std::min(hi,x)); }
Vec linspace(double a, double b, int n) {
    require(n>=2, "Grid needs at least two points.");
    Vec x(n);
    for (int i=0; i<n; ++i) x[i]=a+(b-a)*i/(n-1);
    return x;
}
struct Random {
    std::mt19937 engine;
    std::uniform_real_distribution<double> uniform{0.0,1.0};
    std::normal_distribution<double> normal{0.0,1.0};
    explicit Random(unsigned int seed) : engine(seed) {}
    double u() { return uniform(engine); }
    double z() { return normal(engine); }
    int index(int n) { return std::uniform_int_distribution<int>(0,n-1)(engine); }
};
struct Result {
    Vec point;
    double value=0.0;
    long long evaluations=0;
    int iterations=0;
    std::string status;
};
void print_result(const Result& r) {
    std::cout << std::setprecision(12);
    for (std::size_t j=0; j<r.point.size(); ++j)
        std::cout << "p(" << j+1 << ") = " << r.point[j] << '\n';
    std::cout << "Objective value: " << r.value << "\nIterations/updates: " << r.iterations
              << "\nFunction calls: " << r.evaluations << "\nStatus: " << r.status << '\n';
}

Vec line_coefficients(const Vec& x, const Vec& y) {
    double xb=std::accumulate(x.begin(),x.end(),0.0)/x.size();
    double yb=std::accumulate(y.begin(),y.end(),0.0)/y.size(), Sxx=0,Sxy=0;
    for (std::size_t i=0;i<x.size();++i) { double dx=x[i]-xb; Sxx+=dx*dx; Sxy+=dx*(y[i]-yb); }
    require(std::isfinite(Sxx) && Sxx>0,"Degenerate data/resample: slope undefined; bootstrap aborted.");
    double slope=Sxy/Sxx; return {yb-slope*xb,slope};
}
struct Bootstrap { Vec estimate,standard_errors,bias; Mat covariance,samples; };
// Independent pairs bootstrap. For fixed experimental x consider residual or
// parametric resampling; dependent data need a scheme preserving that dependence.
// Aborts explicitly on degenerate resamples rather than discarding them silently.
Bootstrap bootstrap_line(const Vec& x, const Vec& y, int B, Random& rng) {
    finite_vector(x); finite_vector(y);
    require(x.size()==y.size() && x.size()>=3 && B>=2,"Invalid bootstrap data or resample count.");
    Bootstrap r; r.estimate=line_coefficients(x,y); r.samples.resize(B); Vec mean(2,0.0);
    for (int b=0;b<B;++b) {
        Vec xx(x.size()),yy(x.size());
        for (std::size_t i=0;i<x.size();++i) { int j=rng.index(static_cast<int>(x.size())); xx[i]=x[j]; yy[i]=y[j]; }
        r.samples[b]=line_coefficients(xx,yy);
        for (int j=0;j<2;++j) mean[j]+=r.samples[b][j]/B;
    }
    r.covariance=Mat(2,Vec(2,0.0)); r.standard_errors=Vec(2); r.bias=Vec(2);
    for (const Vec& a:r.samples) for (int i=0;i<2;++i) for (int j=0;j<2;++j)
        r.covariance[i][j]+=(a[i]-mean[i])*(a[j]-mean[j])/(B-1);
    for (int j=0;j<2;++j) { r.standard_errors[j]=std::sqrt(r.covariance[j][j]); r.bias[j]=mean[j]-r.estimate[j]; }
    return r;
}

int main() {
  try {
    const unsigned int seed = 1;
    Random rng(seed);
    // Alternative: comment out the previous line and seed from system entropy.
    // Random rng(std::random_device{}());
    Vec x=linspace(0,1,25),y(x.size());
    for (std::size_t i=0;i<x.size();++i) y[i]=2+.5*x[i]+.15*rng.z();
    int B=2000;
    // Replace x,y with observed independent pairs; resample pairs together.
    Bootstrap r=bootstrap_line(x,y,B,rng);
    std::cout << std::setprecision(12);
    for (int j=0;j<2;++j)
        std::cout << (j==0 ? "Intercept" : "Slope") << ": " << r.estimate[j] << "; bootstrap SE: " << r.standard_errors[j]
                  << "; bootstrap bias: " << r.bias[j] << '\n';
    std::cout << "Resamples: " << B << "\nStandard errors are not confidence intervals.\n";
    return 0;
  } catch (const std::exception& e) {
    std::cerr << "Error: " << e.what() << '\n'; return 1;
  }
}