feat(dynamic-engine): added derivitves for energy generation rate. dε/dT and dε/dρ have been added to NetOut and computed with auto diff

src/include/gridfire/engine/diagnostics/dynamic_engine_diagnostics.h

@@ -0,0 +1,34 @@
+#pragma once
+
+#include "gridfire/engine/engine_abstract.h"
+
+#include <vector>
+#include <string>
+
+namespace gridfire::diagnostics {
+    void report_limiting_species(
+        const DynamicEngine& engine,
+        const std::vector<double>& Y_full,
+        const std::vector<double>& E_full,
+        const std::vector<double>& dydt_full,
+        double relTol,
+        double absTol,
+        size_t top_n = 10
+    );
+
+    void inspect_species_balance(
+        const DynamicEngine& engine,
+        const std::string& species_name,
+        const std::vector<double>& Y_full,
+        double T9,
+        double rho
+    );
+
+    void inspect_jacobian_stiffness(
+        const DynamicEngine& engine,
+        const std::vector<double>& Y_full,
+        double T9,
+        double rho
+    );
+
+}