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

tests/unit/results/result_recovery_components_test.cpp

@@ -6,6 +6,7 @@
 #include <filesystem>
 #include <limits>
 #include <memory>
+#include <optional>
 #include <stdexcept>
 #include <string>
 #include <utility>
@@ -353,6 +354,41 @@ TEST(ResultRecoveryComponents,
   }
 }
 
+TEST(ResultRecoveryComponents, PartitionedScaleKeepsCancelledInternalTerms) {
+  auto definition = MakeShellDefinition();
+  definition.node_sets = {{"Fixed", std::optional<std::string>{"Shell-1"},
+                           {0U}, {definition.source_path, 60U}}};
+  definition.steps[0].boundaries = {
+      {"Fixed", 1, 1, 1.0, {definition.source_path, 61U}}};
+  const auto fixture = MakeShellFixture(std::move(definition));
+  const auto count = fixture.dofs->FullDofCount();
+  fesa::SparsePattern pattern;
+  pattern.row_offsets = {0U, 1U, 3U};
+  pattern.row_offsets.resize(count + 1U, 3U);
+  pattern.column_indices = {0U, 0U, 1U};
+  auto matrix = fesa::SparseMatrix::FromCoo(
+      count, count,
+      {{0U, 0U, 1.0, 0U, 0U}, {1U, 0U, -1.0, 0U, 1U},
+       {1U, 1U, 1.0, 0U, 2U}}, pattern);
+  ASSERT_TRUE(matrix.HasValue());
+  fesa::Vector displacement{count};
+  displacement[0U] = 1.0;
+  displacement[1U] = 1.0;
+  fesa::Vector external{count};
+  external[1U] = 1.0e-12;
+  const auto result = fesa::results_internal::GlobalEquilibriumRecovery(
+      *fixture.domain, *fixture.dofs, matrix.Value(), displacement, external);
+  ASSERT_TRUE(result.HasValue());
+  EXPECT_DOUBLE_EQ(result.Value().internal_force[1U], 0.0);
+  EXPECT_DOUBLE_EQ(result.Value().normalized_free_residual, 1.0e-12);
+  displacement[1U] = std::numeric_limits<double>::quiet_NaN();
+  const auto rejected = fesa::results_internal::GlobalEquilibriumRecovery(
+      *fixture.domain, *fixture.dofs, matrix.Value(), displacement, external);
+  ASSERT_FALSE(rejected.HasValue());
+  ExpectStatusCode(rejected.GetStatus(), "nonfinite-recovery-value");
+  EXPECT_DOUBLE_EQ(result.Value().reaction[1U], -1.0e-12);
+}
+
 // C-MODULE-002
 TEST(ResultRecoveryComponents,
      BeamResultRecoveryKeepsEndpointGaussAndStressIdentities) {