adding file for gaussian-kronrod integration, test cases and calculating gradients of log marginal wrt theta-likelihood params

GPy/testing/quadrature_tests.py

@@ -0,0 +1,39 @@
+from __future__ import print_function, division
+import numpy as np
+import GPy
+import warnings
+from  ..util.quad_integrate import quadgk_int, quadvgk
+
+
+
+class QuadTests(np.testing.TestCase):
+    """
+    test file for checking implementation of gaussian-kronrod quadrature.
+    we will take a function which can be integrated analytically and check if quadgk result is similar or not!
+    through this file we can test how numerically accurate quadrature implementation in native numpy or manual code is.
+    """
+    def setUp(self):
+        pass
+
+    def test_infinite_quad(self):
+        def f(x):
+            return np.exp(-0.5*x**2)*np.power(x,np.arange(3)[:,None])
+        quad_int_val = quadgk_int(f)
+        real_val = np.sqrt(np.pi * 2)
+        np.testing.assert_almost_equal(real_val, quad_int_val[0], decimal=7)
+
+    def test_finite_quad(self):
+        def f2(x):
+            return x**2
+        quad_int_val = quadvgk(f2, 1.,2.)
+        real_val = 7/3.
+        np.testing.assert_almost_equal(real_val, quad_int_val, decimal=5)
+
+if __name__ == '__main__':
+    def f(x):
+        return np.exp(-0.5 * x ** 2) * np.power(x, np.arange(3)[:, None])
+
+    quad_int_val = quadgk_int(f)
+    real_val = np.sqrt(np.pi*2)
+    np.testing.assert_almost_equal(real_val, quad_int_val[0], decimal=7)
+    print(quadgk_int(f))