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

src/fesa/analysis/solid_frequency_procedure.cpp

@@ -248,8 +248,13 @@ Result<SolidFrequencyState> ExecuteCandidate(const Domain& domain) {
   mass_phi.reserve(count);
   for (std::size_t c = 0; c < count; ++c) {
     Vector vector(k.Rows());
-    for (std::size_t row = 0; row < k.Rows(); ++row)
+    for (std::size_t row = 0; row < k.Rows(); ++row) {
       vector[row] = state.backend.eigenvectors(row, c);
+      if (!std::isfinite(vector[row]))
+        return Result<SolidFrequencyState>::Failure(
+            Failure("solid-eigenpair-validation-failed",
+                    "Modal mass is not finite positive."));
+    }
     Vector mv = m.Multiply(vector);
     const double raw_mass = vector.Dot(mv);
     if (!(raw_mass > 0.0) || !std::isfinite(raw_mass))
@@ -257,6 +262,12 @@ Result<SolidFrequencyState> ExecuteCandidate(const Domain& domain) {
           Failure("solid-eigenpair-validation-failed",
                   "Modal mass is not finite positive."));
     vector.Scale(1.0 / std::sqrt(raw_mass));
+    for (std::size_t row = 0; row < vector.Size(); ++row) {
+      if (!std::isfinite(vector[row]))
+        return Result<SolidFrequencyState>::Failure(
+            Failure("solid-eigenpair-validation-failed",
+                    "Normalized modal vector is not finite."));
+    }
     mv = m.Multiply(vector);
     const Vector kv = k.Multiply(vector);
     const double lambda = state.backend.eigenvalues[c];
@@ -362,6 +373,10 @@ Result<SolidFrequencyState> SolidFrequencyProcedureExecutor::Execute(
     return Result<SolidFrequencyState>::Failure(
         Failure("eigen-allocation-failed",
                 "Solid modal workspace exceeds addressable storage."));
+  } catch (const std::runtime_error&) {
+    return Result<SolidFrequencyState>::Failure(
+        Failure("eigen-multiplication-failed",
+                "Solid modal sparse multiplication failed."));
   }
 }
 }  // namespace fesa