【0D output】support 0D output for matrix_rank/multi_dot (#52861)

* support_0D_output_for_matrix_rank_multi_dot, test=allcase

* add 0D output test for matrox_rank and mutli_dot test=allcase

* fix assert error ,test=allcase

* fix test error, test=allcase

* fix other test error, test=allcase

* fix other test error, test=allcase

* fix test error, test=allcase

* fix matrix_rank and multi dot test err test=allcase

* fix test error test=allcase

* fix test zero dim test, test=allcase

* add static backward test for multi_dot, test=allcase

* add tol 2d broadcast test case, test=allcase

paddle/phi/infermeta/binary.cc

@@ -72,7 +72,7 @@ static void BinarySameInputDimsCheck(const MetaTensor& x,
 static DDim CheckAndGetOutputDim(const DDim& dim_x) {
   auto x_vec = phi::vectorize(dim_x);
   if (x_vec.size() == 2) {
-    return phi::make_ddim({1});
+    return phi::make_ddim({});
   }
   x_vec.erase(x_vec.end() - 2, x_vec.end());
   return phi::make_ddim(x_vec);

paddle/phi/infermeta/multiary.cc

@@ -2345,7 +2345,7 @@ void MultiDotInferMeta(const std::vector<const MetaTensor*>& x,
   // If the last tensor is 1D of size n view it as a column vector (n, 1)
   if (last_dim.size() == 1) {
     last_dim = phi::make_ddim({static_cast<int>(last_dim[0]), 1});
-    out_dim = is_vector ? phi::make_ddim({1}) : phi::make_ddim({first_dim[0]});
+    out_dim = is_vector ? phi::make_ddim({}) : phi::make_ddim({first_dim[0]});
   } else {
     out_dim = is_vector ? phi::make_ddim({last_dim[1]})
                         : phi::make_ddim({first_dim[0], last_dim[1]});

paddle/phi/infermeta/unary.cc

@@ -38,7 +38,7 @@ namespace detail {
 static DDim CheckAndGetOutputDim(const DDim& dim_x) {
   auto x_vec = phi::vectorize(dim_x);
   if (x_vec.size() == 2) {
-    return phi::make_ddim({1});
+    return phi::make_ddim({});
   }
   x_vec.erase(x_vec.end() - 2, x_vec.end());
   return phi::make_ddim(x_vec);

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

@@ -2123,6 +2123,23 @@ class TestSundryAPI(unittest.TestCase):
         self.assertTrue(out1.shape, [2, 3])
         self.assertTrue(x1.grad.shape, [3, 3, 3])
 
+    def test_multi_dot(self):
+        a = paddle.randn([4])
+        a.stop_gradient = False
+        b = paddle.randn([4, 5])
+        b.stop_gradient = False
+        c = paddle.randn([5])
+        c.stop_gradient = False
+
+        out = paddle.linalg.multi_dot([a, b, c])
+        out.retain_grads()
+        out.backward()
+
+        self.assertEqual(out.shape, [])
+        self.assertEqual(a.grad.shape, [4])
+        self.assertEqual(b.grad.shape, [4, 5])
+        self.assertEqual(c.grad.shape, [5])
+
 
 class TestSundryAPIStatic(unittest.TestCase):
     def setUp(self):
@@ -3710,6 +3727,26 @@ class TestSundryAPIStatic(unittest.TestCase):
         self.assertEqual(res[0].shape, (2, 3))
         self.assertEqual(res[1].shape, (3, 3, 3))
 
+    @prog_scope()
+    def test_multi_dot(self):
+        a = paddle.randn([4])
+        a.stop_gradient = False
+        b = paddle.randn([4, 5])
+        b.stop_gradient = False
+        c = paddle.randn([5])
+        c.stop_gradient = False
+
+        out = paddle.linalg.multi_dot([a, b, c])
+        paddle.static.append_backward(out.sum())
+        prog = paddle.static.default_main_program()
+        res = self.exe.run(
+            prog, fetch_list=[out, a.grad_name, b.grad_name, c.grad_name]
+        )
+        self.assertEqual(res[0].shape, ())
+        self.assertEqual(res[1].shape, (4,))
+        self.assertEqual(res[2].shape, (4, 5))
+        self.assertEqual(res[3].shape, (5,))
+
 
 # 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):
@@ -3901,6 +3938,38 @@ class TestNoBackwardAPI(unittest.TestCase):
             self.assertEqual(inverse.shape, [1])
             self.assertEqual(counts.shape, [1])
 
+    def test_matrix_rank(self):
+        x = paddle.eye(10)
+        x.stop_gradient = False
+        out = paddle.linalg.matrix_rank(x)
+
+        self.assertEqual(out.shape, [])
+        np.testing.assert_equal(out, np.array(10))
+
+        c = paddle.ones(shape=[3, 4, 5])
+        c.stop_gradient = False
+        out_c = paddle.linalg.matrix_rank(c)
+        self.assertEqual(out_c.shape, [3])
+        np.testing.assert_equal(out_c, np.array([1, 1, 1]))
+
+        # 2D, tol->float : OUTPUT 0D
+        x_tol = paddle.eye(10)
+        x_tol.stop_gradient = False
+        out_tol = paddle.linalg.matrix_rank(x_tol, tol=0.1)
+        self.assertEqual(out_tol.shape, [])
+
+        # 3D, tol->float : OUTPUT 1D
+        c_tol = paddle.ones(shape=[3, 4, 5])
+        c_tol.stop_gradient = False
+        out_c_tol = paddle.linalg.matrix_rank(c_tol, tol=0.1)
+        self.assertEqual(out_c_tol.shape, [3])
+
+        tol_2 = paddle.randn([2])
+        # 2D, tol->Tensor[1,2] : OUTPUT 1D
+        d = paddle.eye(10)
+        out_d = paddle.linalg.matrix_rank(d, tol=tol_2)
+        self.assertEqual(out_d.shape, [2])
+
 
 class TestNoBackwardAPIStatic(unittest.TestCase):
     def setUp(self):
@@ -4135,6 +4204,51 @@ class TestNoBackwardAPIStatic(unittest.TestCase):
         self.assertEqual(res[2].shape, (1,))
         self.assertEqual(res[3].shape, (1,))
 
+    @prog_scope()
+    def test_static_matrix_rank(self):
+        # 2D : OUTPUT 0D
+        x = paddle.eye(10)
+        x.stop_gradient = False
+        out = paddle.linalg.matrix_rank(x)
+        prog = paddle.static.default_main_program()
+        res = self.exe.run(prog, fetch_list=[out])
+        self.assertEqual(res[0].shape, ())
+
+        # 3D : OUTPUT 1D
+        c = paddle.ones(shape=[3, 4, 5])
+        c.stop_gradient = False
+        out_c = paddle.linalg.matrix_rank(c)
+        prog = paddle.static.default_main_program()
+        self.exe.run(paddle.static.default_startup_program())
+        res = self.exe.run(prog, fetch_list=[out_c])
+        self.assertEqual(res[0].shape, (3,))
+
+        # 2D, tol->float : OUTPUT 0D
+        x_tol = paddle.eye(10)
+        x_tol.stop_gradient = False
+        out_tol = paddle.linalg.matrix_rank(x_tol, tol=0.1)
+        prog = paddle.static.default_main_program()
+        res = self.exe.run(prog, fetch_list=[out_tol])
+        self.assertEqual(res[0].shape, ())
+
+        # 3D, tol->float : OUTPUT 1D
+        c_tol = paddle.ones(shape=[3, 4, 5])
+        c_tol.stop_gradient = False
+        out_c_tol = paddle.linalg.matrix_rank(c_tol, tol=0.1)
+        prog = paddle.static.default_main_program()
+        self.exe.run(paddle.static.default_startup_program())
+        res = self.exe.run(prog, fetch_list=[out_c_tol])
+        self.assertEqual(res[0].shape, (3,))
+
+        tol_2 = paddle.randn([2])
+        # 2D, tol->Tensor[1,2] : OUTPUT 1D
+        d = paddle.eye(10)
+        out_d = paddle.linalg.matrix_rank(d, tol=tol_2)
+        prog = paddle.static.default_main_program()
+        self.exe.run(paddle.static.default_startup_program())
+        res = self.exe.run(prog, fetch_list=[out_d])
+        self.assertEqual(res[0].shape, (2,))
+
 
 unary_apis_with_complex_input = [
     paddle.real,