[Lang] Support LU sparse solver on CUDA backend (taichi-dev#6967)

Issue: taichi-dev#2906 

### Brief Summary
To be consistent with API on CPU backend, this pr provides LU sparse
solver on CUDA backend. CuSolver just provides a CPU version API of LU
sparse solver which is used in this PR. The cuSolverRF provides a GPU
version LU solve, but it only supports `double` datatype. Thus, it's not
used in this PR.

Besides, the `print_triplets` is refactored to resolve the ndarray
`read` constraints (the `read` and `write` data should be the same
datatype).

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

python/taichi/linalg/sparse_matrix.py

@@ -243,7 +243,11 @@ def _get_ndarray_addr(self):
 
     def print_triplets(self):
         """Print the triplets stored in the builder"""
-        self.ptr.print_triplets()
+        taichi_arch = get_runtime().prog.config().arch
+        if taichi_arch == _ti_core.Arch.x64 or taichi_arch == _ti_core.Arch.arm64:
+            self.ptr.print_triplets_eigen()
+        elif taichi_arch == _ti_core.Arch.cuda:
+            self.ptr.print_triplets_cuda()
 
     def build(self, dtype=f32, _format='CSR'):
         """Create a sparse matrix using the triplets"""

python/taichi/linalg/sparse_solver.py

@@ -100,32 +100,13 @@ def solve(self, b):  # pylint: disable=R1710
             return self.solver.solve(b)
         if isinstance(b, Ndarray):
             x = ScalarNdarray(b.dtype, [self.matrix.m])
-            self.solve_rf(self.matrix, b, x)
+            self.solver.solve_rf(get_runtime().prog, self.matrix.matrix, b.arr,
+                                 x.arr)
             return x
         raise TaichiRuntimeError(
             f"The parameter type: {type(b)} is not supported in linear solvers for now."
         )
 
-    def solve_cu(self, sparse_matrix, b):
-        if isinstance(sparse_matrix, SparseMatrix) and isinstance(b, Ndarray):
-            x = ScalarNdarray(b.dtype, [sparse_matrix.m])
-            self.solver.solve_cu(get_runtime().prog, sparse_matrix.matrix,
-                                 b.arr, x.arr)
-            return x
-        raise TaichiRuntimeError(
-            f"The parameter type: {type(sparse_matrix)}, {type(b)} and {type(x)} is not supported in linear solvers for now."
-        )
-
-    def solve_rf(self, sparse_matrix, b, x):
-        if isinstance(sparse_matrix, SparseMatrix) and isinstance(
-                b, Ndarray) and isinstance(x, Ndarray):
-            self.solver.solve_rf(get_runtime().prog, sparse_matrix.matrix,
-                                 b.arr, x.arr)
-        else:
-            raise TaichiRuntimeError(
-                f"The parameter type: {type(sparse_matrix)}, {type(b)} and {type(x)} is not supported in linear solvers for now."
-            )
-
     def info(self):
         """Check if the linear systems are solved successfully.
 

taichi/program/sparse_matrix.cpp

@@ -99,17 +99,53 @@ SparseMatrixBuilder::SparseMatrixBuilder(int rows,
       prog_, dtype_, std::vector<int>{3 * (int)max_num_triplets_ + 1});
 }
 
-void SparseMatrixBuilder::print_triplets() {
-  num_triplets_ = ndarray_data_base_ptr_->read_int(std::vector<int>{0});
+template <typename T, typename G>
+void SparseMatrixBuilder::print_triplets_template() {
+  auto ptr = get_ndarray_data_ptr();
+  G *data = reinterpret_cast<G *>(ptr);
+  num_triplets_ = data[0];
   fmt::print("n={}, m={}, num_triplets={} (max={})\n", rows_, cols_,
              num_triplets_, max_num_triplets_);
+  data += 1;
   for (int i = 0; i < num_triplets_; i++) {
-    auto idx = 3 * i + 1;
-    auto row = ndarray_data_base_ptr_->read_int(std::vector<int>{idx});
-    auto col = ndarray_data_base_ptr_->read_int(std::vector<int>{idx + 1});
-    auto val = ndarray_data_base_ptr_->read_float(std::vector<int>{idx + 2});
+    fmt::print("[{}, {}] = {}\n", data[i * 3], data[i * 3 + 1],
+               taichi_union_cast<T>(data[i * 3 + 2]));
+  }
+}
+
+void SparseMatrixBuilder::print_triplets_eigen() {
+  auto element_size = data_type_size(dtype_);
+  switch (element_size) {
+    case 4:
+      print_triplets_template<float32, int32>();
+      break;
+    case 8:
+      print_triplets_template<float64, int64>();
+      break;
+    default:
+      TI_ERROR("Unsupported sparse matrix data type!");
+      break;
+  }
+}
+
+void SparseMatrixBuilder::print_triplets_cuda() {
+#ifdef TI_WITH_CUDA
+  CUDADriver::get_instance().memcpy_device_to_host(
+      &num_triplets_, (void *)get_ndarray_data_ptr(), sizeof(int));
+  fmt::print("n={}, m={}, num_triplets={} (max={})\n", rows_, cols_,
+             num_triplets_, max_num_triplets_);
+  auto len = 3 * num_triplets_ + 1;
+  std::vector<float32> trips(len);
+  CUDADriver::get_instance().memcpy_device_to_host(
+      (void *)trips.data(), (void *)get_ndarray_data_ptr(),
+      len * sizeof(float32));
+  for (auto i = 0; i < num_triplets_; i++) {
+    int row = taichi_union_cast<int>(trips[3 * i + 1]);
+    int col = taichi_union_cast<int>(trips[3 * i + 2]);
+    auto val = trips[i * 3 + 3];
     fmt::print("[{}, {}] = {}\n", row, col, val);
   }
+#endif
 }
 
 intptr_t SparseMatrixBuilder::get_ndarray_data_ptr() const {

taichi/program/sparse_matrix.h

@@ -22,7 +22,8 @@ class SparseMatrixBuilder {
                       const std::string &storage_format,
                       Program *prog);
 
-  void print_triplets();
+  void print_triplets_eigen();
+  void print_triplets_cuda();
 
   intptr_t get_ndarray_data_ptr() const;
 
@@ -36,6 +37,9 @@ class SparseMatrixBuilder {
   template <typename T, typename G>
   void build_template(std::unique_ptr<SparseMatrix> &);
 
+  template <typename T, typename G>
+  void print_triplets_template();
+
  private:
   uint64 num_triplets_{0};
   std::unique_ptr<Ndarray> ndarray_data_base_ptr_{nullptr};