feat(preconditioner): major work on preconditioner system

first preconditioner MVP

tests/mpi/profiling.cpp

@@ -0,0 +1,66 @@
+#include "profile.h"
+
+#include <algorithm>
+#include <catch2/catch_test_macros.hpp>
+#include <sstream>
+#include <string>
+#include <vector>
+
+namespace {
+    const mean_field::profiling::DistributedStatistics *find_region(
+        const std::vector<mean_field::profiling::DistributedStatistics> &statistics,
+        const std::string &label
+    ) {
+        const auto iterator =
+            std::ranges::find(statistics, label, &mean_field::profiling::DistributedStatistics::label);
+        return iterator != statistics.end() ? &*iterator : nullptr;
+    }
+} // namespace
+
+TEST_CASE(
+    "MPI Profiling Aggregates Rank-Local Label Sets Without Collective Divergence",
+    "[mpi][profiling][distributed]"
+) {
+    int rank = 0;
+    int size = 1;
+    MPI_Comm_rank(MPI_COMM_WORLD, &rank);
+    MPI_Comm_size(MPI_COMM_WORLD, &size);
+
+    mean_field::profiling::Registry &registry = mean_field::profiling::Registry::Get();
+    registry.Reset();
+    registry.Record("common-region", static_cast<double>(rank + 1));
+    registry.AddCount("common-region", static_cast<std::uint64_t>(10 + rank));
+
+    const std::string local_label = "rank-" + std::to_string(rank) + "-only";
+    registry.Record(local_label, 0.125 * static_cast<double>(rank + 1));
+
+    const auto aggregate = registry.Aggregate(MPI_COMM_WORLD);
+    const auto *common   = find_region(aggregate, "common-region");
+    CHECK(common != nullptr);
+    if (common != nullptr) {
+        CHECK(common->minimum_samples == 1);
+        CHECK(common->maximum_samples == 1);
+        CHECK(common->minimum_work_units == 10);
+        CHECK(common->maximum_work_units == static_cast<std::uint64_t>(9 + size));
+        CHECK(common->global_minimum_seconds == 1.0);
+        CHECK(common->global_maximum_seconds == static_cast<double>(size));
+    }
+
+    for (int owner = 0; owner < size; ++owner) {
+        const auto *local = find_region(aggregate, "rank-" + std::to_string(owner) + "-only");
+        CHECK(local != nullptr);
+        if (local != nullptr) {
+            CHECK(local->minimum_samples == 0);
+            CHECK(local->maximum_samples == 1);
+        }
+    }
+
+    std::ostringstream csv;
+    registry.PrintCsv(MPI_COMM_WORLD, csv);
+    if (rank == 0) {
+        CHECK(csv.str().find("common-region") != std::string::npos);
+        CHECK(csv.str().find("," + std::to_string(size) + "\n") != std::string::npos);
+    } else {
+        CHECK(csv.str().empty());
+    }
+}