Add tests for prediction cache. (#7650)

* Extract the test from approx for other tree methods.
* Add note on how it works.

src/tree/updater_approx.cc

@@ -216,6 +216,16 @@ class GloablApproxBuilder {
     bst_node_t num_leaves = 1;
     auto expand_set = driver.Pop();
 
+    /**
+     * Note for update position
+     * Root:
+     *   Not applied: No need to update position as initialization has got all the rows ordered.
+     *   Applied: Update position is run on applied nodes so the rows are partitioned.
+     * Non-root:
+     *   Not applied: That node is root of the subtree, same rule as root.
+     *   Applied: Ditto
+     */
+
     while (!expand_set.empty()) {
       // candidates that can be further splited.
       std::vector<CPUExpandEntry> valid_candidates;

src/tree/updater_gpu_hist.cu

@@ -692,6 +692,9 @@ struct GPUHistMakerDevice {
         if (GPUExpandEntry::ChildIsValid(param, tree.GetDepth(left_child_nidx),
                                          num_leaves)) {
           monitor.Start("UpdatePosition");
+          // Update position is only run when child is valid, instead of right after apply
+          // split (as in approx tree method).  Hense we have the finalise position call
+          // in GPU Hist.
           this->UpdatePosition(candidate.nid, p_tree);
           monitor.Stop("UpdatePosition");