Add C document to sphinx, fix arrow. (#8300)

- Group C API.
- Add C API sphinx doc.
- Consistent use of `OptionalArg` and the parameter name `config`.
- Remove call to deprecated functions in demo.
- Fix some formatting errors.
- Add links to c examples in the document (only visible with doxygen pages)
- Fix arrow.

src/data/adapter.h

@@ -1078,10 +1078,8 @@ class ArrowColumnarBatch {
 using ArrowColumnarBatchVec = std::vector<std::unique_ptr<ArrowColumnarBatch>>;
 class RecordBatchesIterAdapter: public dmlc::DataIter<ArrowColumnarBatchVec> {
  public:
-  RecordBatchesIterAdapter(XGDMatrixCallbackNext *next_callback,
-                          int nthread)
-    : next_callback_{next_callback},
-      nbatches_{nthread} {}
+  RecordBatchesIterAdapter(XGDMatrixCallbackNext* next_callback, int nbatch)
+      : next_callback_{next_callback}, nbatches_{nbatch} {}
 
   void BeforeFirst() override {
     CHECK(at_first_) << "Cannot reset RecordBatchesIterAdapter";

src/data/simple_dmatrix.cc

@@ -263,6 +263,8 @@ template SimpleDMatrix::SimpleDMatrix(
 
 template <>
 SimpleDMatrix::SimpleDMatrix(RecordBatchesIterAdapter* adapter, float missing, int nthread) {
+  ctx_.nthread = nthread;
+
   auto& offset_vec = sparse_page_->offset.HostVector();
   auto& data_vec = sparse_page_->data.HostVector();
   uint64_t total_batch_size = 0;
@@ -275,7 +277,7 @@ SimpleDMatrix::SimpleDMatrix(RecordBatchesIterAdapter* adapter, float missing, i
     size_t num_elements = 0;
     size_t num_rows = 0;
     // Import Arrow RecordBatches
-#pragma omp parallel for reduction(+ : num_elements, num_rows) num_threads(nthread)
+#pragma omp parallel for reduction(+ : num_elements, num_rows) num_threads(ctx_.Threads())
     for (int i = 0; i < static_cast<int>(batches.size()); ++i) {  // NOLINT
       num_elements += batches[i]->Import(missing);
       num_rows += batches[i]->Size();
@@ -297,7 +299,7 @@ SimpleDMatrix::SimpleDMatrix(RecordBatchesIterAdapter* adapter, float missing, i
     data_vec.resize(total_elements);
     offset_vec.resize(total_batch_size + 1);
     // Copy data into DMatrix
-#pragma omp parallel num_threads(nthread)
+#pragma omp parallel num_threads(ctx_.Threads())
     {
 #pragma omp for nowait
       for (int i = 0; i < static_cast<int>(batches.size()); ++i) {  // NOLINT