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#include <getopt.h>
#include <iomanip>
#include <list>
#include "pcg-cpp/include/pcg_random.hpp"
#include "randutils/randutils.hpp"
#include "eigen/Eigen/Dense"
using Rng = randutils::random_generator<pcg32>;
using Real = double;
using Vector = Eigen::Matrix<Real, Eigen::Dynamic, 1>;
/*
inline Real basisFunctions(unsigned N, unsigned i, Real x) {
if (i == 0) {
return 1;
} else {
return pow(x, i);
}
}
*/
inline Real basisFunctions(unsigned N, unsigned i, Real x) {
return std::legendre(i, 2.0 * (x - 0.5));
}
/*
inline Real basisFunctions(unsigned N, unsigned i, Real x) {
return abs(x - i / (N - 1.0));
}
*/
Real value(const Vector& coeffs, Real x) {
Real v = 0;
for (unsigned j = 0; j < coeffs.size(); j++) {
v += coeffs[j] * basisFunctions(coeffs.size(), j, x);
}
return v;
}
Real cost(const std::vector<std::tuple<Real, Real>>& data, const Vector& coeffs) {
Real c = 0;
#pragma omp parallel for reduction(+:c)
for (const std::tuple<Real, Real>& xy : data) {
Real x = std::get<0>(xy);
Real y = std::get<1>(xy);
c += 0.5 * pow(value(coeffs, x) - y, 2);
}
return c;
}
Vector dCost(const std::vector<std::tuple<Real, Real>>& data, const Vector& coeffs) {
Vector dC = Vector::Zero(coeffs.size());
for (const std::tuple<Real, Real>& xy : data) {
Real x = std::get<0>(xy);
Real y = std::get<1>(xy);
Real Δc = value(coeffs, x) - y;
#pragma omp parallel for
for (unsigned j = 0; j < coeffs.size(); j++) {
dC[j] += Δc * basisFunctions(coeffs.size(), j, x);
}
}
return dC;
}
Vector gradientDescent(const std::vector<std::tuple<Real, Real>>& data, const Vector& a₀, unsigned maxSteps, Real ε = 1e-12) {
Vector xₜ = a₀;
Real Hₜ = cost(data, a₀);
Real α = 1.0;
Real m;
Vector ∇H;
unsigned steps = 0;
while (
∇H = dCost(data, xₜ), m = ∇H.squaredNorm(),
m > ε && steps < maxSteps
) {
Vector xₜ₊₁;
Real Hₜ₊₁;
while (
xₜ₊₁ = xₜ - α * ∇H, Hₜ₊₁ = cost(data, xₜ₊₁),
Hₜ₊₁ > Hₜ - 0.25 * α * m
) {
α /= 2;
}
xₜ = xₜ₊₁;
Hₜ = Hₜ₊₁;
α *= 1.25;
steps++;
}
return xₜ;
}
Vector dCostRand(const std::vector<std::tuple<Real, Real>>& data, const Vector& coeffs, Real batchP, Rng& r) {
Vector dC = Vector::Zero(coeffs.size());
for (unsigned j = 0; j < coeffs.size(); j++) {
for (const std::tuple<Real, Real>& xy : data) {
if (batchP > r.uniform(0.0, 1.0)) {
Real x = std::get<0>(xy);
Real y = std::get<1>(xy);
dC[j] += (value(coeffs, x) - y) * basisFunctions(coeffs.size(), j, x);
}
}
}
return dC;
}
Vector stochasticGradientDescent(std::vector<std::tuple<Real, Real>>& data, const Vector& a₀, Rng& r, unsigned maxSteps, Real ε = 1e-12) {
Vector xₜ = a₀;
Real α = 1e-3;
Real m;
Vector ∇H;
unsigned steps = 0;
while (
∇H = dCostRand(data, xₜ, 0.1, r), m = ∇H.squaredNorm(),
m > ε && steps < maxSteps
) {
xₜ = xₜ - α * ∇H;
steps++;
}
return xₜ;
}
std::vector<std::tuple<Real, Real>> generateData(Real(*f)(Real), unsigned M, Real σ, Rng& r) {
std::vector<std::tuple<Real, Real>> data;
data.reserve(M);
for (unsigned i = 0; i < M; i++) {
Real x = ((Real)i) / (M - 1.0);
data.push_back({x, f(x) + r.variate<Real, std::normal_distribution>(0, σ)});
}
return data;
}
int main(int argc, char* argv[]) {
unsigned N = 10;
unsigned M = 10;
Real σ = 0.2;
long unsigned maxSteps = 1e12;
int opt;
while ((opt = getopt(argc, argv, "N:M:s:S:")) != -1) {
switch (opt) {
case 'N':
N = (unsigned)atof(optarg);
break;
case 'M':
M = (unsigned)atof(optarg);
break;
case 's':
σ = atof(optarg);
break;
case 'S':
maxSteps = (long unsigned)atof(optarg);
break;
default:
exit(1);
}
}
Rng r;
std::vector<std::tuple<Real, Real>> data = generateData([](Real x) {return std::cos(2 * M_PI * x);}, M, σ, r);
std::cout << std::setprecision(15);
for (std::tuple<Real, Real> datum : data) {
std::cout << std::get<0>(datum) << " " << std::get<1>(datum) << " ";
}
std::cout << std::endl;
Vector a₀ = Vector::Zero(N);
for (Real& aa : a₀) {
aa = r.variate<Real, std::normal_distribution>(0, 0);
}
Vector a = gradientDescent(data, a₀, maxSteps);
for (unsigned i = 0; i < N; i++) {
std::cout << a[i] << " ";
}
std::cout << std::endl;
return 0;
}
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