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add blts

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This commit is contained in:
Valentin Leon Stöcker
2026-01-21 15:27:17 +01:00
parent 650e5cc6b8
commit 16334e4834
7 changed files with 195 additions and 143 deletions
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CMakeLists.txt
+3
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@@ -6,8 +6,11 @@ set(CMAKE_CXX_STANDARD 23)
add_compile_options(-Wall -Werror -Wpedantic)
find_package(Eigen3 REQUIRED)
add_library(autoopt INTERFACE)
target_include_directories(autoopt INTERFACE include)
target_link_libraries(autoopt INTERFACE Eigen3::Eigen)
install(DIRECTORY include/autoopt DESTINATION include)
flake.nix
+2
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@@ -22,6 +22,7 @@
cmake,
ninja,
lib,
eigen,
gtest,
withTests ? false,
}:
@@ -46,6 +47,7 @@
nativeBuildInputs = [
cmake
ninja
eigen
];
};
in
include/autoopt/btls.hpp
+49
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@@ -0,0 +1,49 @@
#pragma once
#include <iostream>
#include "autoopt/optimization_problem.hpp"
namespace autoopt {
template <typename T>
struct btls_parameters {
T step_decrease = T{0.5};
T step_increase = T{1.5};
T sufficient_decrease = T{1e-2};
T tolerance = T{1e-9};
size_t max_iters = 1000;
};
template <typename T>
void btls(optimization_problem<T>& problem,
const btls_parameters<T>& params = btls_parameters<T>()) {
Eigen::VectorX<T>& x = problem.x();
T step_size = T{1.0};
for (size_t iter = 0; iter < params.max_iters; ++iter) {
T obj_value = problem.objective(x);
std::cout << "Iter " << iter << ": obj = " << obj_value
<< ", x = " << x.transpose() << ", step_size = " << step_size
<< std::endl;
Eigen::VectorX<T> grad = -problem.gradient(x);
Eigen::VectorX<T> step_dir = grad.normalized();
while (problem.objective(x + step_size * step_dir) >
obj_value +
params.sufficient_decrease * step_size * grad.dot(step_dir)) {
step_size *= params.step_decrease;
}
x += step_size * step_dir;
if (step_size < params.tolerance) {
break;
}
}
problem.x() = x;
}
} // namespace autoopt
include/autoopt/derivative.hpp
+28 -31
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@@ -1,6 +1,6 @@
#pragma once
#include <array>
#include <Eigen/Eigen>
#include "autoopt/dual.hpp"
@@ -13,49 +13,46 @@ T derivative(Func&& f, const T& x) {
return b._dx;
}
template <typename T, std::size_t N, class Func>
std::array<T, N> gradient(Func&& f, const std::array<T, N>& x) {
std::array<T, N> grad{};
std::array<dual<T>, N> dual_x{};
for (std::size_t i = 0; i < N; ++i) {
dual_x[i] = dual<T>(x[i], T(0));
template <typename T, class Func>
Eigen::VectorX<T> gradient(Func&& f, const Eigen::VectorX<T>& x) {
Eigen::VectorX<T> grad{x.size()};
Eigen::VectorX<dual<T>> dual_x{x.size()};
for (int i = 0; i < x.size(); ++i) {
dual_x(i) = dual<T>(x(i), T(0));
}
for (std::size_t i = 0; i < N; ++i) {
dual_x[i]._dx = T(1);
for (int i = 0; i < x.size(); ++i) {
dual_x(i)._dx = T(1);
dual<T> dual_y = f(dual_x);
grad[i] = dual_y._dx;
dual_x[i]._dx = T(0);
grad(i) = dual_y._dx;
dual_x(i)._dx = T(0);
}
return grad;
}
template <typename T, std::size_t N, std::size_t M>
using matrix_t = std::array<std::array<T, M>, N>;
template <typename T, std::size_t N, std::size_t M, class Func>
matrix_t<T, M, N> jacobian(Func&& f, const std::array<T, N>& x) {
matrix_t<T, M, N> jacob{};
std::array<dual<T>, N> dual_x{};
for (std::size_t i = 0; i < N; ++i) {
dual_x[i] = dual<T>(x[i], T(0));
template <typename T, class Func>
Eigen::MatrixX<T> jacobian(Func&& f, const Eigen::VectorX<T>& x) {
Eigen::MatrixX<T> jacob(f(x).size(), x.size());
Eigen::VectorX<dual<T>> dual_x(x.size());
for (int i = 0; i < x.size(); ++i) {
dual_x(i) = dual<T>(x(i), T(0));
}
for (std::size_t i = 0; i < N; ++i) {
dual_x[i]._dx = T(1);
std::array<dual<T>, M> dual_y = f(dual_x);
for (std::size_t j = 0; j < M; ++j) {
jacob[j][i] = dual_y[j]._dx;
for (int i = 0; i < x.size(); ++i) {
dual_x(i)._dx = T(1);
Eigen::VectorX<dual<T>> dual_y = f(dual_x);
for (int j = 0; j < dual_y.size(); ++j) {
jacob(j, i) = dual_y(j)._dx;
}
dual_x[i]._dx = T(0);
dual_x(i)._dx = T(0);
}
return jacob;
}
template <typename T, std::size_t N, class Func>
matrix_t<T, N, N> hessian(Func&& f, const std::array<T, N>& x) {
auto helper_func = [&f]<typename U>(const std::array<U, N>& y) {
return gradient<U, N>(f, y);
template <typename T, class Func>
Eigen::MatrixX<T> hessian(Func&& f, const Eigen::VectorX<T>& x) {
auto helper_func = [&f]<typename U>(const Eigen::VectorX<U>& y) {
return gradient<U>(f, y);
};
return jacobian<T, N, N>(helper_func, x);
return jacobian<T>(helper_func, x);
}
} // namespace autoopt
include/autoopt/optimization_problem.hpp
+47 -46
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@@ -1,108 +1,109 @@
#pragma once
#include <array>
#include <cstddef>
#include "autoopt/derivative.hpp"
namespace autoopt {
template <typename T, size_t N>
template <typename T>
struct optimization_problem {
virtual std::array<T, N> initial_guess() = 0;
virtual Eigen::VectorX<T>& initial_guess() = 0;
virtual Eigen::VectorX<T>& x() = 0;
virtual T objective(const std::array<T, N>& params) = 0;
virtual std::array<T, N> gradient(const std::array<T, N>& params) = 0;
virtual matrix_t<T, N, N> hessian(const std::array<T, N>& params) = 0;
virtual T objective(const Eigen::VectorX<T>& params) = 0;
virtual Eigen::VectorX<T> gradient(const Eigen::VectorX<T>& params) = 0;
virtual Eigen::MatrixX<T> hessian(const Eigen::VectorX<T>& params) = 0;
};
template <typename T, size_t N, class Func>
struct auto_diff_optimization_problem : public optimization_problem<T, N> {
template <typename T, class Func>
struct auto_diff_optimization_problem : public optimization_problem<T> {
Func _objective_func;
std::array<T, N> _initial_guess;
Eigen::VectorX<T> _initial_guess;
Eigen::VectorX<T> _x;
auto_diff_optimization_problem(
Func objective_func, std::array<T, N> initial_guess = std::array<T, N>{})
: _objective_func(objective_func), _initial_guess(initial_guess) {}
Func objective_func, Eigen::VectorX<T> initial_guess = Eigen::VectorX<T>{})
: _objective_func(objective_func), _initial_guess(initial_guess), _x(initial_guess) {}
std::array<T, N> initial_guess() override { return _initial_guess; }
Eigen::VectorX<T>& initial_guess() override { return _initial_guess; }
T objective(const std::array<T, N>& params) override {
Eigen::VectorX<T>& x() override { return _x; }
T objective(const Eigen::VectorX<T>& params) override {
return _objective_func(params);
}
std::array<T, N> gradient(const std::array<T, N>& params) override {
return autoopt::gradient<T, N>(_objective_func, params);
Eigen::VectorX<T> gradient(const Eigen::VectorX<T>& params) override {
return autoopt::gradient<T>(_objective_func, params);
}
matrix_t<T, N, N> hessian(const std::array<T, N>& params) override {
return autoopt::hessian<T, N>(_objective_func, params);
Eigen::MatrixX<T> hessian(const Eigen::VectorX<T>& params) override {
return autoopt::hessian<T>(_objective_func, params);
}
};
template <typename T, size_t N>
template <typename T>
struct log_barrier_optimization_problem
: public optimization_problem<T, N> {
optimization_problem<T, N>& _base_problem;
std::array<T, N> _delta;
: public optimization_problem<T> {
optimization_problem<T>& _base_problem;
Eigen::VectorX<T> _delta;
T _barrier_strength;
log_barrier_optimization_problem(
optimization_problem<T, N>& base_problem,
std::array<T, N> delta,
optimization_problem<T>& base_problem,
Eigen::VectorX<T> delta,
T barrier_strength = T{1e-3})
: _base_problem(base_problem),
_delta(delta),
_barrier_strength(barrier_strength) {}
std::array<T, N> initial_guess() override {
Eigen::VectorX<T>& initial_guess() override {
return _base_problem.initial_guess();
}
T objective(const std::array<T, N>& params) override {
Eigen::VectorX<T>& x() override {
return _base_problem.x();
}
T objective(const Eigen::VectorX<T>& params) override {
T base_obj = _base_problem.objective(params);
T barrier = barrier_term(params);
return base_obj + barrier;
}
std::array<T, N> gradient(const std::array<T, N>& params) override {
Eigen::VectorX<T> gradient(const Eigen::VectorX<T>& params) override {
auto base_grad = _base_problem.gradient(params);
std::array<T, N> barrier_grad = autoopt::gradient<T, N>(
[this]<typename U>(const std::array<U, N>& p) {
Eigen::VectorX<T> barrier_grad = autoopt::gradient<T>(
[this]<typename U>(const Eigen::VectorX<U>& p) {
return barrier_term<U>(p);
},
params);
std::array<T, N> total_grad;
for (size_t i = 0; i < N; ++i) {
total_grad[i] = base_grad[i] + barrier_grad[i];
}
Eigen::VectorX<T> total_grad(params.size());
total_grad = base_grad + barrier_grad;
return total_grad;
}
matrix_t<T, N, N> hessian(const std::array<T, N>& params) override {
Eigen::MatrixX<T> hessian(const Eigen::VectorX<T>& params) override {
auto base_hess = _base_problem.hessian(params);
matrix_t<T, N, N> barrier_hess = autoopt::hessian<T, N>(
[this]<typename U>(const std::array<U, N>& p) {
Eigen::MatrixX<T> barrier_hess = autoopt::hessian<T>(
[this]<typename U>(const Eigen::VectorX<U>& p) {
return barrier_term<U>(p);
},
params);
matrix_t<T, N, N> total_hess;
for (size_t i = 0; i < N; ++i) {
for (size_t j = 0; j < N; ++j) {
total_hess[i][j] = base_hess[i][j] + barrier_hess[i][j];
}
}
Eigen::MatrixX<T> total_hess(params.size(), params.size());
total_hess = base_hess + barrier_hess;
return total_hess;
}
private:
template <typename U>
U barrier_term(const std::array<U, N>& params) {
U barrier_term(const Eigen::VectorX<U>& params) {
U barrier = U{0};
for (size_t i = 0; i < N; ++i) {
U lb = _base_problem.initial_guess()[i] - _delta[i];
U ub = _base_problem.initial_guess()[i] + _delta[i];
barrier = barrier + std::log(params[i] - lb) + std::log(ub - params[i]);
for (int i = 0; i < params.size(); ++i) {
U lb = U{_base_problem.initial_guess()(i) - _delta(i)};
U ub = U{_base_problem.initial_guess()(i) + _delta(i)};
barrier = barrier + std::log(params(i) - lb) + std::log(ub - params(i));
}
return -U{_barrier_strength} * barrier;
}
tests/dual.cpp
+42 -36
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@@ -50,58 +50,63 @@ TEST(DualTest, DerivativeFunction) {
}
TEST(DualTest, GradientFunction) {
auto func = []<typename T>(const std::array<T, 2>& x) {
return x[0] * x[0] + std::sin(x[1]);
auto func = []<typename T>(const Eigen::VectorX<T>& x) {
return x(0) * x(0) + std::sin(x(1));
};
std::array<double, 2> point = {1.0, 0.0};
std::array<double, 2> grad = gradient(func, point);
Eigen::VectorX<double> point(2);
point << 1.0, 0.0;
Eigen::VectorX<double> grad = gradient(func, point);
EXPECT_DOUBLE_EQ(grad[0], 2.0 * point[0]); // d/dx1
EXPECT_DOUBLE_EQ(grad[1], std::cos(point[1])); // d/dx2
EXPECT_DOUBLE_EQ(grad(0), 2.0 * point(0)); // d/dx1
EXPECT_DOUBLE_EQ(grad(1), std::cos(point(1))); // d/dx2
}
TEST(DualTest, JacobianFunction) {
auto func = []<typename T>(const std::array<T, 2>& x) {
return std::array<T, 2>{x[0] * x[0], std::sin(x[1])};
auto func = []<typename T>(const Eigen::VectorX<T>& x) {
Eigen::VectorX<T> y(2);
y << x(0) * x(0), std::sin(x(1));
return y;
};
std::array<double, 2> point = {1.0, 0.0};
auto jacob = jacobian<double, 2, 2>(func, point);
Eigen::VectorX<double> point(2);
point << 1.0, 0.0;
auto jacob = jacobian<double>(func, point);
EXPECT_DOUBLE_EQ(jacob[0][0], 2.0 * point[0]); // d(f1)/d(x1)
EXPECT_DOUBLE_EQ(jacob[0][1], 0.0); // d(f1)/d(x2)
EXPECT_DOUBLE_EQ(jacob[1][0], 0.0); // d(f2)/d(x1)
EXPECT_DOUBLE_EQ(jacob[1][1], std::cos(point[1])); // d(f2)/d(x2)
EXPECT_DOUBLE_EQ(jacob(0, 0), 2.0 * point(0)); // d(f1)/d(x1)
EXPECT_DOUBLE_EQ(jacob(0, 1), 0.0); // d(f1)/d(x2)
EXPECT_DOUBLE_EQ(jacob(1, 0), 0.0); // d(f2)/d(x1)
EXPECT_DOUBLE_EQ(jacob(1, 1), std::cos(point(1))); // d(f2)/d(x2)
}
TEST(DualTest, HessianFunction) {
auto func = []<typename T>(const std::array<T, 2>& x) {
return x[0] * x[0] + x[1] * x[1];
auto func = []<typename T>(const Eigen::VectorX<T>& x) {
return x(0) * x(0) + x(1) * x(1);
};
std::array<double, 2> point = {1.0, 2.0};
auto hess = hessian<double, 2>(func, point);
Eigen::VectorX<double> point(2);
point << 1.0, 2.0;
auto hess = hessian<double>(func, point);
EXPECT_DOUBLE_EQ(hess[0][0], 2.0); // d²f/dx1²
EXPECT_DOUBLE_EQ(hess[0][1], 0.0); // d²f/dx1dx2
EXPECT_DOUBLE_EQ(hess[1][0], 0.0); // d²f/dx2dx1
EXPECT_DOUBLE_EQ(hess[1][1], 2.0); // d²f/dx2²
EXPECT_DOUBLE_EQ(hess(0, 0), 2.0); // d²f/dx1²
EXPECT_DOUBLE_EQ(hess(0, 1), 0.0); // d²f/dx1dx2
EXPECT_DOUBLE_EQ(hess(1, 0), 0.0); // d²f/dx2dx1
EXPECT_DOUBLE_EQ(hess(1, 1), 2.0); // d²f/dx2²
}
struct opti_func {
std::vector<std::array<double, 2>> test_data;
std::vector<Eigen::Vector2<double>> test_data;
// loss function
template <typename T>
T operator()(const std::array<T, 3>& params) const {
T operator()(const Eigen::VectorX<T>& params) const {
T sum = T(0);
for (const auto& data_point : test_data) {
T x = T{data_point[0]};
T y_true = T{data_point[1]};
T a = params[0];
T b = params[1];
T c = params[2];
T x = T{data_point(0)};
T y_true = T{data_point(1)};
T a = params(0);
T b = params(1);
T c = params(2);
T y_pred = a * x * x + b * x + c;
T error = y_pred - y_true;
sum = sum + error * error;
@@ -120,18 +125,19 @@ TEST(DualTest, OptimizationFunction) {
{4.0, 4.0},
};
std::array<double, 3> params = {1.0, -4.0, 4.0};
Eigen::VectorX<double> params(3);
params << 1.0, -4.0, 4.0;
auto grad = gradient<double, 3>(f, params);
auto grad = gradient<double>(f, params);
EXPECT_DOUBLE_EQ(grad[0], 0.0); // dL/da
EXPECT_DOUBLE_EQ(grad[1], 0.0); // dL/db
EXPECT_DOUBLE_EQ(grad[2], 0.0); // dL/dc
EXPECT_DOUBLE_EQ(grad(0), 0.0); // dL/da
EXPECT_DOUBLE_EQ(grad(1), 0.0); // dL/db
EXPECT_DOUBLE_EQ(grad(2), 0.0); // dL/dc
auto hess = hessian<double, 3>(f, params);
auto hess = hessian<double>(f, params);
for (std::size_t i = 0; i < 3; ++i) {
for (std::size_t j = 0; j < 3; ++j) {
EXPECT_GE(hess[i][j], 0.0); // Hessian should be positive semi-definite
EXPECT_GE(hess(i, j), 0.0); // Hessian should be positive semi-definite
}
}
}
tests/ellipse.cpp
+24 -30
View File
@@ -3,6 +3,7 @@
#include <autoopt/ellipse.hpp>
#include <autoopt/optimization_problem.hpp>
#include <autoopt/util.hpp>
#include <autoopt/btls.hpp>
#include <iomanip>
#include <iostream>
@@ -21,11 +22,12 @@ TEST(Ellipse, ParamGradient) {
std::vector<std::pair<double, double>> data_points = {
{-10.0, -0.001}, {0.0, 0.0}, {10, 0.0009}};
std::array<double, 4> params = {100, 1000, deg2rad(1.0), 0.0};
Eigen::VectorX<double> params(4);
params << 100, 1000, deg2rad(1.0), 0.0;
auto loss_func = [&data_points]<typename T>(const std::array<T, 4>& p) {
ellipse<T> e{T{p[0]}, T{p[1]}, T{p[2]}};
quadric<T> q = e.to_quadric().rotated_by(T{p[3]});
auto loss_func = [&data_points]<typename T>(const Eigen::VectorX<T>& p) {
ellipse<T> e{T{p(0)}, T{p(1)}, T{p(2)}};
quadric<T> q = e.to_quadric().rotated_by(T{p(3)});
T loss = T{0};
for (const auto& [x, y_true] : data_points) {
T y_pred = q.slope_at(T{x});
@@ -35,44 +37,36 @@ TEST(Ellipse, ParamGradient) {
return loss / T(data_points.size());
};
auto_diff_optimization_problem<double, 4, decltype(loss_func)> problem(loss_func, params);
auto_diff_optimization_problem<double, decltype(loss_func)> problem(loss_func, params);
auto grad = problem.gradient(params);
EXPECT_NEAR(grad[0], -2.0789313126683308e-10, 1e-15); // d/d(left_arm)
EXPECT_NEAR(grad[1], -1.7464984353858657e-12, 1e-15); // d/d(right_arm)
EXPECT_NEAR(grad[2], 1.2013025455499119e-06, 1e-15); // d/d(entrance_angle)
EXPECT_NEAR(grad[3], -2.0332702665822054e-05, 1e-15); // d/d(rotation_angle)
std::cout << "Gradient:\n";
for (size_t i = 0; i < 4; ++i) {
std::cout << grad[i] << "\n";
}
std::cout << grad << std::endl;
EXPECT_NEAR(grad(0), -2.0789313126683308e-10, 1e-15); // d/d(left_arm)
EXPECT_NEAR(grad(1), -1.7464984353858657e-12, 1e-15); // d/d(right_arm)
EXPECT_NEAR(grad(2), 1.2013025455499119e-06, 1e-15); // d/d(entrance_angle)
EXPECT_NEAR(grad(3), -2.0332702665822054e-05, 1e-15); // d/d(rotation_angle)
auto hess = problem.hessian(params);
// set formatting for easier reading
std::cout << std::scientific;
// set field width for alignment
std::cout << "Hessian matrix:\n";
std::cout << hess << std::endl;
for (size_t i = 0; i < 4; ++i) {
;
for (size_t j = 0; j < 4; ++j) {
std::cout << std::setprecision(5) << std::setw(15) << hess[i][j];
}
std::cout << "\n";
}
Eigen::VectorX<double> params_delta(4);
params_delta << 1.0, 1.0, deg2rad(0.1), deg2rad(0.1);
params(0) += 0.9; // left_arm
// log barrier
log_barrier_optimization_problem<double, 4> log_barrier_problem(
log_barrier_optimization_problem<double> log_barrier_problem(
problem,
{1.0, 1.0, deg2rad(0.1), deg2rad(0.1)},
params_delta,
1e-3);
auto log_barrier_grad = log_barrier_problem.gradient(params);
std::cout << "Log Barrier Gradient:\n";
for (size_t i = 0; i < 4; ++i) {
std::cout << log_barrier_grad[i] << "\n";
}
std::cout << "Log barrier gradient:" << std::endl;
std::cout << log_barrier_grad << std::endl;
btls(problem);
}