add unittest for viv (#401)

* add unittest for viv

* Update test_viv.py

test/equation/test_viv.py

@@ -0,0 +1,59 @@
+import paddle
+import pytest
+from paddle import nn
+from paddle.nn import initializer
+
+from ppsci.equation.pde import Vibration
+
+
+@pytest.mark.parametrize("rho,k1,k2", [(1.0, 4.0, -1.0)])
+def test_vibration(rho, k1, k2):
+    """Test for Vibration equation."""
+    batch_size = 13
+    rho = rho
+    k1 = paddle.create_parameter(
+        shape=[],
+        dtype=paddle.get_default_dtype(),
+        default_initializer=initializer.Constant(k1),
+    )
+    k2 = paddle.create_parameter(
+        shape=[],
+        dtype=paddle.get_default_dtype(),
+        default_initializer=initializer.Constant(k2),
+    )
+    # generate input data
+    eta = paddle.randn([batch_size, 1])
+    t_f = paddle.randn([batch_size, 1])
+    eta.stop_gradient = False
+    t_f.stop_gradient = False
+    input_data = paddle.concat([eta, t_f], axis=1)
+    model = nn.Sequential(
+        nn.Linear(2, 1),
+        nn.Tanh(),
+    )
+
+    # manually generate output
+    eta = model(input_data)
+
+    def jacobian(y: paddle.Tensor, x: paddle.Tensor) -> paddle.Tensor:
+        return paddle.grad(y, x, create_graph=True)[0]
+
+    def hessian(y: paddle.Tensor, x: paddle.Tensor) -> paddle.Tensor:
+        return jacobian(jacobian(y, x), x)
+
+    expected_result = (
+        rho * hessian(eta, t_f)
+        + paddle.exp(k1) * jacobian(eta, t_f)
+        + paddle.exp(k2) * eta
+    )
+
+    # compute result using Vibration class
+    vibration_equation = Vibration(rho=rho, k1=k1, k2=k2)
+    data_dict = {"eta": eta, "t_f": t_f}
+    test_result = vibration_equation.equations["f"](data_dict)
+    # check result whether is equal
+    assert paddle.allclose(expected_result, test_result)
+
+
+if __name__ == "__main__":
+    pytest.main()