perf(math): route ordinary products through MKL and preserve arithmetic

src/fesa/analysis/linear_frequency_procedure.cpp

@@ -32,11 +32,7 @@ Status Failure(const std::string& code, const std::string& identity,
 }
 
 double Dot(const Vector& left, const Vector& right) {
-  double result = 0.0;
-  for (std::size_t index = 0U; index < left.Size(); ++index) {
-    result += left[index] * right[index];
-  }
-  return result;
+  return left.Dot(right);
 }
 
 double Norm(const Vector& vector) {
@@ -318,8 +314,13 @@ Result<EigenAnalysisState> ExecuteCandidate(const Domain& domain) {
                                     (pencil_scale * y_norm) * y_norm);
     const double rayleigh = energy / modal_mass;
     Vector x(a.Rows());
-    for (std::size_t row = 0; row < x.Size(); ++row)
+    for (std::size_t row = 0; row < x.Size(); ++row) {
       x[row] = state.backend.eigenvectors(row, column) * normalization;
+      if (!std::isfinite(x[row]))
+        return Result<EigenAnalysisState>::Failure(
+            Failure("invalid-eigenvalue-result", std::to_string(column),
+                    "Recovered mode is nonfinite or violates constraints."));
+    }
     Vector ax = a.Multiply(x);
     Vector whitened_residual = ax;
     whitened_residual.Axpy(-lambda, x);
@@ -421,6 +422,10 @@ Result<EigenAnalysisState> LinearFrequencyProcedureExecutor::Execute(
     return Result<EigenAnalysisState>::Failure(
         Failure("eigen-index-overflow", "modal-workspace",
                 "Requested workspace exceeds container capacity."));
+  } catch (const std::runtime_error&) {
+    return Result<EigenAnalysisState>::Failure(
+        Failure("eigen-multiplication-failed", "modal-workspace",
+                "Modal sparse multiplication failed."));
   }
 }