From 8008df39ebdf80c9340ce8407e490e7df451c41c Mon Sep 17 00:00:00 2001
From: Arno Solin <arno.solin@aalto.fi>
Date: Sat, 9 Nov 2013 21:09:22 +0000
Subject: [PATCH] Added the sde representation to Matern32

---
 GPy/kern/kern.py           |  5 +++++
 GPy/kern/parts/Matern32.py | 15 +++++++++++++++
 2 files changed, 20 insertions(+)

diff --git a/GPy/kern/kern.py b/GPy/kern/kern.py
index 805c6b43..74def8cd 100644
--- a/GPy/kern/kern.py
+++ b/GPy/kern/kern.py
@@ -574,6 +574,10 @@ class kern(Parameterized):
         else:
             raise NotImplementedError, "Cannot plot a kernel with more than two input dimensions"
 
+    def sde(self):
+         # TODO: should support adding kernels together
+         return self.parts[0].sde()
+
 from GPy.core.model import Model
 
 class Kern_check_model(Model):
@@ -794,3 +798,4 @@ def kern_test(kern, X=None, X2=None, output_ind=None, verbose=False):
         return False
 
     return pass_checks
+
diff --git a/GPy/kern/parts/Matern32.py b/GPy/kern/parts/Matern32.py
index 40da79f0..2828a455 100644
--- a/GPy/kern/parts/Matern32.py
+++ b/GPy/kern/parts/Matern32.py
@@ -137,3 +137,18 @@ class Matern32(Kernpart):
         # print "OLD \n", np.dot(F1lower,F1lower.T), "\n \n"
         # return(G)
         return(self.lengthscale ** 3 / (12.*np.sqrt(3) * self.variance) * G + 1. / self.variance * np.dot(Flower, Flower.T) + self.lengthscale ** 2 / (3.*self.variance) * np.dot(F1lower, F1lower.T))
+
+    def sde(self):
+        """
+        Return the state space representation of the covariance.
+        """
+        foo = np.sqrt(3)/self.lengthscale
+        F  = np.array([[0, 1], [-foo**2, -2*foo]])
+        L  = np.array([[0], [1]])
+        Qc = np.array([12*np.sqrt(3) / self.lengthscale**3 * self.variance])
+        H = np.array([[1, 0]])
+        Pinf = np.array([[self.variance, 0], 
+                        [0,              3*self.variance/(self.lengthscale**2)]])
+        # TODO: return the derivatives as well
+        return (F, L, Qc, H, Pinf) 
+