From 16b64f41d6c35074802b3b8eddd9b9f8e4a6bf96 Mon Sep 17 00:00:00 2001
From: Max Zwiessele <ibinbei@gmail.com>
Date: Fri, 26 Apr 2013 16:33:17 +0100
Subject: [PATCH] kern psi statistic tests

---
 GPy/testing/kern_psi_stat_tests.py | 78 ++++++++++++++++++++++++++++++
 1 file changed, 78 insertions(+)
 create mode 100644 GPy/testing/kern_psi_stat_tests.py

diff --git a/GPy/testing/kern_psi_stat_tests.py b/GPy/testing/kern_psi_stat_tests.py
new file mode 100644
index 00000000..4099d984
--- /dev/null
+++ b/GPy/testing/kern_psi_stat_tests.py
@@ -0,0 +1,78 @@
+'''
+Created on 26 Apr 2013
+
+@author: maxz
+'''
+import unittest
+import GPy
+import numpy as np
+import pylab
+
+class Test(unittest.TestCase):
+    D = 9
+    M = 5
+    Nsamples = 3e6
+
+    def setUp(self):
+        self.kerns = (
+                      GPy.kern.rbf(self.D), GPy.kern.rbf(self.D, ARD=True),
+                      GPy.kern.linear(self.D), GPy.kern.linear(self.D, ARD=True),
+                      GPy.kern.linear(self.D) + GPy.kern.bias(self.D),
+                      GPy.kern.rbf(self.D) + GPy.kern.bias(self.D),
+                      GPy.kern.linear(self.D) + GPy.kern.bias(self.D) + GPy.kern.white(self.D),
+                      GPy.kern.rbf(self.D) + GPy.kern.bias(self.D) + GPy.kern.white(self.D),
+                      GPy.kern.bias(self.D), GPy.kern.white(self.D),
+                      )
+        self.q_x_mean = np.random.randn(self.D)
+        self.q_x_variance = np.exp(np.random.randn(self.D))
+        self.q_x_samples = np.random.randn(self.Nsamples, self.D) * np.sqrt(self.q_x_variance) + self.q_x_mean
+        self.Z = np.random.randn(self.M, self.D)
+        self.q_x_mean.shape = (1, self.D)
+        self.q_x_variance.shape = (1, self.D)
+
+    def test_psi0(self):
+        for kern in self.kerns:
+            psi0 = kern.psi0(self.Z, self.q_x_mean, self.q_x_variance)
+            Kdiag = kern.Kdiag(self.q_x_samples)
+            self.assertAlmostEqual(psi0, np.mean(Kdiag), 1)
+            # print kern.parts[0].name, np.allclose(psi0, np.mean(Kdiag))
+
+    def test_psi1(self):
+        for kern in self.kerns:
+            Nsamples = 100
+            psi1 = kern.psi1(self.Z, self.q_x_mean, self.q_x_variance)
+            K_ = np.zeros((self.N, self.M))
+            diffs = []
+            for i, q_x_sample_stripe in enumerate(np.array_split(self.q_x_samples, self.Nsamples / Nsamples)):
+                K = kern.K(q_x_sample_stripe, self.Z)
+                K_ += K
+                diffs.append(((psi1 - (K_ / (i + 1))) ** 2).mean())
+            K_ /= self.Nsamples / Nsamples
+#             pylab.figure("+".join([p.name for p in kern.parts]) + "psi1")
+#             pylab.plot(diffs)
+            self.assertTrue(np.allclose(psi1.flatten() , K.mean(0), rtol=1e-1))
+
+    def test_psi2(self):
+        for kern in self.kerns:
+            Nsamples = 100
+            psi2 = kern.psi2(self.Z, self.q_x_mean, self.q_x_variance)
+            K_ = np.zeros((self.M, self.M))
+            diffs = []
+            for i, q_x_sample_stripe in enumerate(np.array_split(self.q_x_samples, self.Nsamples / Nsamples)):
+                K = kern.K(q_x_sample_stripe, self.Z)
+                K = (K[:, :, None] * K[:, None, :]).mean(0)
+                K_ += K
+                diffs.append(((psi2 - (K_ / (i + 1))) ** 2).mean())
+            K_ /= self.Nsamples / Nsamples
+            try:
+#                 pylab.figure("+".join([p.name for p in kern.parts]) + "psi2")
+#                 pylab.plot(diffs)
+                self.assertTrue(np.allclose(psi2.squeeze(), K_,
+                                            rtol=1e-1, atol=.1),
+                                msg="{}: not matching".format("+".join([p.name for p in kern.parts])))
+            except:
+                print "{}: not matching".format(kern.parts[0].name)
+
+if __name__ == "__main__":
+    import sys;sys.argv = ['', 'Test.test_psi2']
+    unittest.main()