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#include <eigen3/Eigen/Dense>
#include <random>
#include <getopt.h>
#include "pcg-cpp/include/pcg_random.hpp"
#include "randutils/randutils.hpp"
template <class Real>
using Vector = Eigen::Matrix<Real, Eigen::Dynamic, 1>;
template <class Real>
using Matrix = Eigen::Matrix<Real, Eigen::Dynamic, Eigen::Dynamic>;
template <class Real>
class Model {
private:
Matrix<Real> A;
Vector<Real> b;
public:
template <class Generator>
Model(Real σ, unsigned N, unsigned M, Generator& r) : A(M, N), b(M) {
std::normal_distribution<Real> aDistribution(0, 1);
for (unsigned i = 0; i < M; i++) {
for (unsigned j =0; j < N; j++) {
A(i, j) = aDistribution(r);
}
}
std::normal_distribution<Real> bDistribution(0, σ);
for (unsigned i = 0; i < M; i++) {
b(i) = bDistribution(r);
}
}
const unsigned N() {
return A.cols();
}
const unsigned M() {
return A.rows();
}
const Vector<Real> V(const Vector<Real>& x) {
return A * x + b;
}
const Matrix<Real> dV(const Vector<Real>& x) {
return A;
}
// const Real ddV(const Vector<Real>& x) {
// return Matrix::Zero(;
// }
const Real H(const Vector<Real>& x) {
return V(x).squaredNorm();
}
const Vector<Real> dH(const Vector<Real>& x) {
return dV(x).transpose() * V(x);
}
const Matrix<Real> ddH(const Vector<Real>& x) {
return dV(x).transpose() * dV(x);
}
const Vector<Real> ∇H(const Vector<Real>& x){
return dH(x) - dH(x).dot(x) * x / x.squaredNorm();
}
const Matrix<Real> HessH(const Vector<Real>& x) {
Matrix<Real> hess = ddH(x) - x.dot(dH(x)) * Matrix<Real>::Identity(N(), N());
return hess - (hess * x) * x.transpose() / x.squaredNorm();
}
};
using Rng = randutils::random_generator<pcg32>;
using Real = double;
int main(int argc, char* argv[]) {
unsigned N = 10;
unsigned M = 10;
Real σ = 1;
int opt;
while ((opt = getopt(argc, argv, "N:M:s:")) != -1) {
switch (opt) {
case 'N':
N = (unsigned)atof(optarg);
break;
case 'M':
M = (unsigned)atof(optarg);
break;
case 's':
σ = atof(optarg);
break;
default:
exit(1);
}
}
Rng r;
Model<Real> leastSquares(σ, N, M, r.engine());
Vector<Real> x = Vector<Real>::Zero(N);
x(0) = N;
std::cout << leastSquares.H(x) << std::endl;
std::cout << leastSquares.∇H(x) << std::endl;
std::cout << leastSquares.HessH(x) << std::endl;
return 0;
}
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