test_utils to make it easier for downstream implementations to check correctness

gpflow/test_utils.py

@@ -0,0 +1,32 @@
+import numpy as np
+
+from .kernels import Kernel
+
+
+def assert_psd_matrix(A: np.ndarray, tol: float = 1e-12):
+    assert np.linalg.eigvals(A).min() > -tol, "test for positive semi definite matrix"
+
+
+def test_kernel(kernel: Kernel, X: np.ndarray, X2: np.ndarray):
+    N, D = X.shape
+    N2, D2 = X2.shape
+    assert D == D2
+    assert N1 != N2
+
+    kX = kernel(X).numpy()
+    assert kX.shape == (N, N)
+    kXX = kernel(X, X).numpy()
+    assert kXX.shape == (N, N)
+    np.testing.assert_allclose(kX, kXX)
+    np.testing.assert_allclose(kX, kX.T)
+    assert_psd_matrix(kX)
+
+    kXX2 = kernel(X, X2).numpy()
+    assert kXX2.shape == (N, N2)
+
+    kX2X = kernel(X2, X).numpy()
+    np.testing.assert_allclose(kXX2, kX2X.T)
+
+    kXdiag = kernel(X, full_cov=False).numpy()
+    assert kXdiag.shape == (N,)
+    np.testing.assert_allclose(np.diag(kX), kXdiag)

tests/gpflow/kernels/test_positive_semidefinite.py

@@ -20,7 +20,7 @@
 from numpy.testing import assert_array_less
 
 import gpflow.ci_utils
-from gpflow import kernels
+from gpflow import kernels, test_utils
 
 KERNEL_CLASSES = [
     kernel
@@ -32,23 +32,17 @@
 rng = np.random.RandomState(42)
 
 
-def pos_semidefinite(kernel: kernels.Kernel) -> None:
-    N, D = 100, 5
-    X = rng.randn(N, D)
-
-    cov = kernel(X)
-    eig = tf.linalg.eigvalsh(cov).numpy()
-    assert_array_less(-1e-12, eig)
-
-
 @pytest.mark.parametrize("kernel_class", KERNEL_CLASSES)
-def test_positive_semidefinite(kernel_class: Type[kernels.Kernel]) -> None:
+def test_kernel_interface(kernel_class: Type[kernels.Kernel]) -> None:
     """
     A valid kernel is positive semidefinite. Some kernels are only valid for
     particular input shapes, see https://github.com/GPflow/GPflow/issues/1328
     """
+    N, N2, D = 101, 103, 5
+    X = rng.randn(N, D)
+    X2 = rng.randn(N2, D)
     kernel = kernel_class()
-    pos_semidefinite(kernel)
+    test_utils.test_kernel(kernel, X, X2)
 
 
 @pytest.mark.parametrize(
@@ -60,4 +54,8 @@ def test_positive_semidefinite_periodic(base_class: Type[kernels.IsotropicStatio
     particular input shapes, see https://github.com/GPflow/GPflow/issues/1328
     """
     kernel = kernels.Periodic(base_class())
-    pos_semidefinite(kernel)
+
+    N, N2, D = 101, 103, 5
+    X = rng.randn(N, D)
+    X2 = rng.randn(N2, D)
+    test_utils.test_kernel(kernel, X, X2)