feat(analysis): execute solid generalized frequency pencil

include/fesa/solvers/eigen/mkl_feast_eigen_solver.h

@@ -58,7 +58,7 @@ struct FeastEigenResult {
   std::string upper_search_termination;
 };
 
-/// @brief Solves a whitened real-symmetric eigenproblem with oneMKL FEAST.
+/// @brief Adapts standard and symmetric-definite sparse pencils to FEAST.
 class MklFeastEigenSolver final {
  public:
   /// @brief Computes all validated interval pairs for a requested lowest-mode
@@ -76,6 +76,28 @@ class MklFeastEigenSolver final {
   Result<FeastEigenResult> Solve(const SparseMatrix& whitened_operator,
                                  std::size_t requested_modes,
                                  double zero_operator_scale) const;
+  /// @brief Solves the original sparse symmetric definite K/M pencil.
+  /// @param mass_lower_bound Certified positive lower spectral bound of M,
+  /// including floating-point assembly uncertainty; never a diagonal estimate.
+  /// @param classification_scale Positive max |Kii|/Mii in physical units.
+  /// @note Eigenvectors are mass-normalized. For this API the historical
+  /// whitened_residuals field contains original-pencil eta_r; no whitening
+  /// is performed. Intervals/eigenvalues in normalized backend evidence use
+  /// classification_scale, while eigenvalues are returned in physical units.
+  Result<FeastEigenResult> SolveGeneralized(const SparseMatrix& stiffness,
+                                            const SparseMatrix& mass,
+                                            std::size_t requested_modes,
+                                            double mass_lower_bound,
+                                            double classification_scale) const;
+
+ private:
+  /// @brief Shares deterministic count/search controls without changing
+  /// pencils.
+  Result<FeastEigenResult> SolveImpl(const SparseMatrix& stiffness,
+                                     const SparseMatrix* mass,
+                                     std::size_t requested_modes,
+                                     double physical_scale,
+                                     double mass_lower_bound) const;
 };
 
 }  // namespace fesa