Distinguish strategy failures and expose the actual trial tangent

libmeanfield/interface/solver/newton_numerics.cppm

@@ -1,6 +1,7 @@
 module;
 
 #include <concepts>
+#include <cstdint>
 #include <type_traits>
 #include <utility>
 
@@ -22,7 +23,7 @@ export namespace mean_field::solver::nonlinear {
     struct GravitySolveOptions final {
         LinearSolveControl control{.relativeTolerance = 1.0e-10, .absoluteTolerance = 1.0e-14,
                                    .maximumIterations = 300};
-        linear::FGMRESOptions backend{.restartLength = 80};
+        linear::FGMRESOptions backend{.restartLength = 80, .printLevel = -1};
 
         void Validate() const { control.Validate(); backend.Validate(); }
     };
@@ -64,14 +65,18 @@ export namespace mean_field::solver::nonlinear {
     template <typename Candidate>
     concept NewtonNumericalConfiguration = IsNewtonNumerics<std::remove_cvref_t<Candidate>>::value;
 
+    enum class LinearReportSpace : std::uint8_t { full_system, reduced_system, gravity_subsystem };
+
     struct NumericalStrategyDiagnostics final {
         int polynomialChecks{0};
         int directionRepairs{0};
         double lastRepairFraction{0.0};
         double lastMeritDirectionalDerivative{0.0};
-        int gravitySolves{0};
-        int gravityIterations{0};
-        int gravityFailures{0};
+        std::uint64_t gravitySolves{0};
+        std::uint64_t gravityIterations{0};
+        std::uint64_t gravityFailures{0};
+        std::uint64_t gravityPreparedFailures{0};
+        LinearReportSpace lastLinearReportSpace{LinearReportSpace::full_system};
         double gravitySolveSeconds{0.0};
         double lastGravityTrueResidual{0.0};
         double lastGravityCorrectionNorm{0.0};