[Cherey-Pick]Support 0D for slogdet (#53087)

* add 0D output support for inalg.slogdet,test=allcase

* fix zerom dime test error test=allcase

* fix test error test=allcase

* add static backward test, test=allcase

paddle/phi/kernels/impl/slogdeterminant_kernel_impl.h

@@ -94,7 +94,7 @@ void SlogDeterminantKernel(const Context& dev_ctx,
   std::vector<int> output_dim_vec(input_dim.begin(), input_dim.end() - 2);
   if (input_dim.size() == static_cast<size_t>(2)) {
     // when input is a two-dimension matrix, The det value is a number.
-    output_dim_vec = {1};
+    output_dim_vec = {};
   }
   output_dim_vec.insert(output_dim_vec.begin(),
                         2);  // make the output dims as same as numpy

python/paddle/fluid/tests/unittests/test_zero_dim_tensor.py

@@ -2066,6 +2066,27 @@ def body(i, x):
         self.assertEqual(x.grad.shape, [])
         np.testing.assert_allclose(x.grad, np.array(1.0))
 
+    def test_linalg_slogdet(self):
+        # 2-D input
+        x = paddle.randn([3, 3])
+        x.stop_gradient = False
+        out = paddle.linalg.slogdet(x)
+        out.retain_grads()
+        out.backward()
+
+        self.assertTrue(out.shape, [2])
+        self.assertTrue(x.grad.shape, [3, 3])
+
+        # 3-D input
+        x1 = paddle.randn([3, 3, 3])
+        x1.stop_gradient = False
+        out1 = paddle.linalg.slogdet(x1)
+        out1.retain_grads()
+        out1.backward()
+
+        self.assertTrue(out1.shape, [2, 3])
+        self.assertTrue(x1.grad.shape, [3, 3, 3])
+
 
 class TestSundryAPIStatic(unittest.TestCase):
     def setUp(self):
@@ -3609,6 +3630,30 @@ def test_broadcast_tensors(self):
         self.assertEqual(out1.shape, (2, 3))
         self.assertEqual(out2.shape, (2, 3))
 
+    @prog_scope()
+    def test_linalg_slogdet(self):
+        # 2-D input
+        x = paddle.randn([3, 3])
+        x.stop_gradient = False
+        out = paddle.linalg.slogdet(x)
+        paddle.static.append_backward(out.sum())
+
+        prog = paddle.static.default_main_program()
+        res = self.exe.run(prog, fetch_list=[out, x.grad_name])
+        self.assertEqual(res[0].shape, (2,))
+        self.assertEqual(res[1].shape, (3, 3))
+
+        # 3-D input
+        x1 = paddle.randn([3, 3, 3])
+        x1.stop_gradient = False
+        out1 = paddle.linalg.slogdet(x1)
+        paddle.static.append_backward(out1.sum())
+
+        prog = paddle.static.default_main_program()
+        res = self.exe.run(prog, fetch_list=[out1, x1.grad_name])
+        self.assertEqual(res[0].shape, (2, 3))
+        self.assertEqual(res[1].shape, (3, 3, 3))
+
 
 # Use to test API whose zero-dim input tensors don't have grad and not need to test backward in OpTest.
 class TestNoBackwardAPI(unittest.TestCase):