Implement unified update prediction cache for (gpu_)hist. (#6860)

* Implement utilites for linalg.
* Unify the update prediction cache functions.
* Implement update prediction cache for multi-class gpu hist.

tests/cpp/common/test_linalg.cc

@@ -0,0 +1,38 @@
+#include <gtest/gtest.h>
+#include <xgboost/linalg.h>
+#include <numeric>
+
+namespace xgboost {
+
+auto MakeMatrixFromTest(HostDeviceVector<float> *storage, size_t n_rows, size_t n_cols) {
+  storage->Resize(n_rows * n_cols);
+  auto& h_storage = storage->HostVector();
+
+  std::iota(h_storage.begin(), h_storage.end(), 0);
+
+  auto m = MatrixView<float>{storage, {n_cols, 1}, {n_rows, n_cols}, -1};
+  return m;
+
+}
+
+TEST(Linalg, Matrix) {
+  size_t kRows = 31, kCols = 77;
+  HostDeviceVector<float> storage;
+  auto m = MakeMatrixFromTest(&storage, kRows, kCols);
+  ASSERT_EQ(m.DeviceIdx(), GenericParameter::kCpuId);
+  ASSERT_EQ(m(0, 0), 0);
+  ASSERT_EQ(m(kRows - 1, kCols - 1), storage.Size() - 1);
+}
+
+TEST(Linalg, Vector) {
+  size_t kRows = 31, kCols = 77;
+  HostDeviceVector<float> storage;
+  auto m = MakeMatrixFromTest(&storage, kRows, kCols);
+  auto v = VectorView<float>(m, 3);
+  for (size_t i = 0; i < v.Size(); ++i) {
+    ASSERT_EQ(v[i], m(i, 3));
+  }
+
+  ASSERT_EQ(v[0], 3);
+}
+} // namespace xgboost