Define core multi-target regression tree structure. (#8884)

- Define a new tree struct embedded in the `RegTree`.
- Provide dispatching functions in `RegTree`.
- Fix some c++-17 warnings about the use of nodiscard (currently we disable the warning on
  the CI).
- Use uint32_t instead of size_t for `bst_target_t` as it has a defined size and can be used
  as part of dmlc parameter.
- Hide the `Segment` struct inside the categorical split matrix.

tests/cpp/tree/test_multi_target_tree_model.cc

@@ -0,0 +1,48 @@
+/**
+ * Copyright 2023 by XGBoost Contributors
+ */
+#include <gtest/gtest.h>
+#include <xgboost/context.h>     // for Context
+#include <xgboost/multi_target_tree_model.h>
+#include <xgboost/tree_model.h>  // for RegTree
+
+namespace xgboost {
+TEST(MultiTargetTree, JsonIO) {
+  bst_target_t n_targets{3};
+  bst_feature_t n_features{4};
+  RegTree tree{n_targets, n_features};
+  ASSERT_TRUE(tree.IsMultiTarget());
+  linalg::Vector<float> base_weight{{1.0f, 2.0f, 3.0f}, {3ul}, Context::kCpuId};
+  linalg::Vector<float> left_weight{{2.0f, 3.0f, 4.0f}, {3ul}, Context::kCpuId};
+  linalg::Vector<float> right_weight{{3.0f, 4.0f, 5.0f}, {3ul}, Context::kCpuId};
+  tree.ExpandNode(RegTree::kRoot, /*split_idx=*/1, 0.5f, true, base_weight.HostView(),
+                  left_weight.HostView(), right_weight.HostView());
+  ASSERT_EQ(tree.param.num_nodes, 3);
+  ASSERT_EQ(tree.param.size_leaf_vector, 3);
+  ASSERT_EQ(tree.GetMultiTargetTree()->Size(), 3);
+  ASSERT_EQ(tree.Size(), 3);
+
+  Json jtree{Object{}};
+  tree.SaveModel(&jtree);
+
+  auto check_jtree = [](Json jtree, RegTree const& tree) {
+    ASSERT_EQ(get<String const>(jtree["tree_param"]["num_nodes"]),
+              std::to_string(tree.param.num_nodes));
+    ASSERT_EQ(get<F32Array const>(jtree["base_weights"]).size(),
+              tree.param.num_nodes * tree.param.size_leaf_vector);
+    ASSERT_EQ(get<I32Array const>(jtree["parents"]).size(), tree.param.num_nodes);
+    ASSERT_EQ(get<I32Array const>(jtree["left_children"]).size(), tree.param.num_nodes);
+    ASSERT_EQ(get<I32Array const>(jtree["right_children"]).size(), tree.param.num_nodes);
+  };
+  check_jtree(jtree, tree);
+
+  RegTree loaded;
+  loaded.LoadModel(jtree);
+  ASSERT_TRUE(loaded.IsMultiTarget());
+  ASSERT_EQ(loaded.param.num_nodes, 3);
+
+  Json jtree1{Object{}};
+  loaded.SaveModel(&jtree1);
+  check_jtree(jtree1, tree);
+}
+}  // namespace xgboost

tests/cpp/tree/test_tree_model.cc

@@ -477,7 +477,7 @@ TEST(Tree, JsonIO) {
   auto tparam = j_tree["tree_param"];
   ASSERT_EQ(get<String>(tparam["num_feature"]), "0");
   ASSERT_EQ(get<String>(tparam["num_nodes"]), "3");
-  ASSERT_EQ(get<String>(tparam["size_leaf_vector"]), "0");
+  ASSERT_EQ(get<String>(tparam["size_leaf_vector"]), "1");
 
   ASSERT_EQ(get<I32Array const>(j_tree["left_children"]).size(), 3ul);
   ASSERT_EQ(get<I32Array const>(j_tree["right_children"]).size(), 3ul);