// ch13_differential_evolution.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_differential_evolution.cpp -o ch13_differential_evolution
// 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';
}

// Frozen-generation current-to-best/1/bin; no polishing or convergence claim.
Result differential_evolution(const Function& f, const Vec& lo, const Vec& hi,
                              Random& rng, int n, int generations, double F, double CR) {
    check_bounds(lo,hi); std::size_t d=lo.size();
    require(n>=4 && generations>0 && F>0 && F<=2 && CR>=0 && CR<=1, "Invalid DE settings.");
    Mat pop(n,Vec(d)); Vec values(n);
    for (int i=0;i<n;++i) {
        for (std::size_t j=0;j<d;++j) pop[i][j]=lo[j]+(hi[j]-lo[j])*rng.u();
        values[i]=objective_value(f(pop[i]));
    }
    for (int k=0;k<generations;++k) {
        int idx=static_cast<int>(std::min_element(values.begin(),values.end())-values.begin());
        Vec best=pop[idx]; Mat next=pop; Vec next_values=values;
        for (int i=0;i<n;++i) {
            int a,b; do { a=rng.index(n); } while (a==i);
            do { b=rng.index(n); } while (b==i || b==a);
            int forced=rng.index(static_cast<int>(d)); Vec trial=pop[i];
            for (std::size_t j=0;j<d;++j) {
                if (rng.u()<CR || static_cast<int>(j)==forced)
                    trial[j]=pop[i][j]+F*(best[j]-pop[i][j])+F*(pop[a][j]-pop[b][j]);
                if (!std::isfinite(trial[j]) || trial[j]<lo[j] || trial[j]>hi[j])
                    trial[j]=lo[j]+(hi[j]-lo[j])*rng.u();
            }
            double ft=objective_value(f(trial));
            if (ft<=values[i]) { next[i]=trial; next_values[i]=ft; }
        }
        pop=next; values=next_values;
    }
    int idx=static_cast<int>(std::min_element(values.begin(),values.end())-values.begin());
    Result r; r.point=pop[idx]; r.value=values[idx]; r.iterations=generations;
    r.evaluations=static_cast<long long>(n)*(generations+1LL); r.status="Search budget completed.";
    return r;
}

int main() {
  try {
    const unsigned int seed = 3;
    Random rng(seed);
    // Alternative: comment out the previous line and seed from system entropy.
    // Random rng(std::random_device{}());
    Function f=[](const Vec& p) { double sum=0; for (double x:p) sum+=(x-.5)*(x-.5)+10*(1-std::cos(2*pi*(x-.5))); return sum; };
    Vec lower={-4.5,-4.5},upper={5.5,5.5};
    int population_size=50,max_generations=400; double F=.9,CR=.9;
    print_result(differential_evolution(f,lower,upper,rng,population_size,max_generations,F,CR));
    std::cout << "Repeat with other seeds; global optimality is not guaranteed.\n";
    return 0;
  } catch (const std::exception& e) {
    std::cerr << "Error: " << e.what() << '\n'; return 1;
  }
}