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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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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
}
}
}