feat: add autodiff example

examples/derivatives/main.cpp

@@ -0,0 +1,46 @@
+// Copyright (c) 2024 Alvin Zhang.
+
+#include <suboptimal/autodiff/Variable.h>
+#include <suboptimal/autodiff/derivatives.h>
+
+#include <cmath>
+#include <format>
+#include <iostream>
+#include <vector>
+
+int main() {
+  suboptimal::Variable x{};
+  const suboptimal::Variable y = 1.0 / (1.0 + suboptimal::exp(-x));  // Sigmoid function
+  const suboptimal::Variable dydx = suboptimal::derivative(y, x);
+
+  constexpr double min = -1.0;
+  constexpr double max = 1.0;
+  constexpr double step = 0.1;
+
+  std::vector<double> x_vals(static_cast<int>((max - min) / step) + 1);
+  for (unsigned int i = 0; i < x_vals.size(); i++) {
+    x_vals[i] = min + i * step;
+  }
+
+  std::cout << std::format("Differentiating y = 1 / (1 + e^(-x)), on x ∈ [{}, {}]\n", min, max) << std::endl;
+
+  std::cout << std::format("{:^10}|{:^10}|{:^20}|{:^20}\n", "x", "y", "dy/dx (manual)", "dy/dx (autodiff)")
+            << std::format("{:=<63}", "") << std::endl;
+  for (double x_val : x_vals) {
+    x.setValue(x_val);
+    double dydx_manual = std::exp(-x_val) / std::pow(1.0 + std::exp(-x_val), 2);
+    double dydx_ad = dydx.getValue();
+    std::cout << std::format("{:^10.4f}|{:^10.4f}|{:^20.4f}|{:^20.4f}", x_val, y.getValue(), dydx_manual, dydx_ad)
+              << std::endl;
+
+    if (std::abs(dydx_manual - dydx_ad) > 1e-9) {
+      std::cerr << std::format(
+          "Error: autodiff result is incorrect\n "
+          "Manual: {}\n "
+          "Autodiff: {}\n",
+          dydx_manual, dydx_ad);
+      return 1;
+    }
+  }
+  return 0;
+}