diff --git a/GPy/kern/_src/coregionalize.py b/GPy/kern/_src/coregionalize.py
index 69fc27ef..0d99ce21 100644
--- a/GPy/kern/_src/coregionalize.py
+++ b/GPy/kern/_src/coregionalize.py
@@ -5,6 +5,7 @@ from kern import Kern
 import numpy as np
 from scipy import weave
 from ...core.parameterization import Param
+from ...core.parameterization.transformations import Logexp
 
 class Coregionalize(Kern):
     """
@@ -20,7 +21,7 @@ class Coregionalize(Kern):
        k_2(x, y)=\mathbf{B} k(x, y)
 
     it is obtained as the tensor product between a covariance function
-    k(x,y) and B.
+    k(x, y) and B.
 
     :param output_dim: number of outputs to coregionalize
     :type output_dim: int
@@ -29,7 +30,7 @@ class Coregionalize(Kern):
     :param W: a low rank matrix that determines the correlations between the different outputs, together with kappa it forms the coregionalization matrix B
     :type W: numpy array of dimensionality (num_outpus, W_columns)
     :param kappa: a vector which allows the outputs to behave independently
-    :type kappa: numpy array of dimensionality  (output_dim,)
+    :type kappa: numpy array of dimensionality  (output_dim, )
 
     .. note: see coregionalization examples in GPy.examples.regression for some usage.
     """
@@ -37,18 +38,18 @@ class Coregionalize(Kern):
         super(Coregionalize, self).__init__(input_dim=1, name=name)
         self.output_dim = output_dim
         self.rank = rank
-        if self.rank>output_dim-1:
+        if self.rank>output_dim:
             print("Warning: Unusual choice of rank, it should normally be less than the output_dim.")
         if W is None:
-            W = 0.5*np.random.randn(self.output_dim,self.rank)/np.sqrt(self.rank)
+            W = 0.5*np.random.randn(self.output_dim, self.rank)/np.sqrt(self.rank)
         else:
-            assert W.shape==(self.output_dim,self.rank)
-        self.W = Param('W',W)
+            assert W.shape==(self.output_dim, self.rank)
+        self.W = Param('W', W)
         if kappa is None:
             kappa = 0.5*np.ones(self.output_dim)
         else:
-            assert kappa.shape==(self.output_dim,)
-        self.kappa = Param('kappa', kappa)
+            assert kappa.shape==(self.output_dim, )
+        self.kappa = Param('kappa', kappa, Logexp())
         self.add_parameters(self.W, self.kappa)
         self.parameters_changed()
 
@@ -56,54 +57,58 @@ class Coregionalize(Kern):
     def parameters_changed(self):
         self.B = np.dot(self.W, self.W.T) + np.diag(self.kappa)
 
-    def K(self,index,index2,target):
-        index = np.asarray(index,dtype=np.int)
+    def K(self, X, X2=None):
+        index = np.asarray(X, dtype=np.int)
 
         #here's the old code (numpy)
         #if index2 is None:
             #index2 = index
         #else:
-            #index2 = np.asarray(index2,dtype=np.int)
+            #index2 = np.asarray(index2, dtype=np.int)
         #false_target = target.copy()
-        #ii,jj = np.meshgrid(index,index2)
-        #ii,jj = ii.T, jj.T
-        #false_target += self.B[ii,jj]
+        #ii, jj = np.meshgrid(index, index2)
+        #ii, jj = ii.T, jj.T
+        #false_target += self.B[ii, jj]
 
-        if index2 is None:
+
+        if X2 is None:
+            target = np.empty((X.shape[0], X.shape[0]), dtype=np.float64)
             code="""
             for(int i=0;i<N; i++){
-              target[i+i*N] += B[index[i]+output_dim*index[i]];
+              target[i+i*N] = B[index[i]+output_dim*index[i]];
               for(int j=0; j<i; j++){
-                  target[j+i*N] += B[index[i]+output_dim*index[j]];
-                  target[i+j*N] += target[j+i*N];
+                  target[j+i*N] = B[index[i]+output_dim*index[j]];
+                  target[i+j*N] = target[j+i*N];
                 }
               }
             """
-            N,B,output_dim = index.size, self.B, self.output_dim
-            weave.inline(code,['target','index','N','B','output_dim'])
+            N, B, output_dim = index.size, self.B, self.output_dim
+            weave.inline(code, ['target', 'index', 'N', 'B', 'output_dim'])
         else:
-            index2 = np.asarray(index2,dtype=np.int)
+            index2 = np.asarray(X2, dtype=np.int)
+            target = np.empty((X.shape[0], X2.shape[0]), dtype=np.float64)
             code="""
             for(int i=0;i<num_inducing; i++){
               for(int j=0; j<N; j++){
-                  target[i+j*num_inducing] += B[output_dim*index[j]+index2[i]];
+                  target[i+j*num_inducing] = B[output_dim*index[j]+index2[i]];
                 }
               }
             """
-            N,num_inducing,B,output_dim = index.size,index2.size, self.B, self.output_dim
-            weave.inline(code,['target','index','index2','N','num_inducing','B','output_dim'])
+            N, num_inducing, B, output_dim = index.size, index2.size, self.B, self.output_dim
+            weave.inline(code, ['target', 'index', 'index2', 'N', 'num_inducing', 'B', 'output_dim'])
+        return target
 
 
-    def Kdiag(self,index,target):
-        target += np.diag(self.B)[np.asarray(index,dtype=np.int).flatten()]
+    def Kdiag(self, X):
+        return np.diag(self.B)[np.asarray(X, dtype=np.int).flatten()]
 
-    def update_gradients_full(self,dL_dK, index, index2=None):
-        index = np.asarray(index,dtype=np.int)
+    def update_gradients_full(self, dL_dK, X, X2=None):
+        index = np.asarray(X, dtype=np.int)
         dL_dK_small = np.zeros_like(self.B)
-        if index2 is None:
+        if X2 is None:
             index2 = index
         else:
-            index2 = np.asarray(index2,dtype=np.int)
+            index2 = np.asarray(X2, dtype=np.int)
 
         code="""
         for(int i=0; i<num_inducing; i++){
@@ -113,28 +118,20 @@ class Coregionalize(Kern):
         }
         """
         N, num_inducing, output_dim = index.size, index2.size, self.output_dim
-        weave.inline(code, ['N','num_inducing','output_dim','dL_dK','dL_dK_small','index','index2'])
+        weave.inline(code, ['N', 'num_inducing', 'output_dim', 'dL_dK', 'dL_dK_small', 'index', 'index2'])
 
         dkappa = np.diag(dL_dK_small)
         dL_dK_small += dL_dK_small.T
-        dW = (self.W[:,None,:]*dL_dK_small[:,:,None]).sum(0)
+        dW = (self.W[:, None, :]*dL_dK_small[:, :, None]).sum(0)
 
         self.W.gradient = dW
         self.kappa.gradient = dkappa
 
-    def update_gradients_sparse(self, dL_dKmm, dL_dKnm, dL_dKdiag, X, Z):
-        raise NotImplementedError, "some code below"
-    #def dKdiag_dtheta(self,dL_dKdiag,index,target):
-        #index = np.asarray(index,dtype=np.int).flatten()
-        #dL_dKdiag_small = np.zeros(self.output_dim)
-        #for i in range(self.output_dim):
-            #dL_dKdiag_small[i] += np.sum(dL_dKdiag[index==i])
-        #dW = 2.*self.W*dL_dKdiag_small[:,None]
-        #dkappa = dL_dKdiag_small
-        #target += np.hstack([dW.flatten(),dkappa])
+    def update_gradients_diag(self, dL_dKdiag, X):
+        index = np.asarray(X, dtype=np.int).flatten()
+        dL_dKdiag_small = np.array([dL_dKdiag[index==i] for i in xrange(output_dim)])
+        self.W.gradient = 2.*self.W*dL_dKdiag_small[:, None]
+        self.kappa.gradient = dL_dKdiag_small
 
-    def gradients_X(self,dL_dK,X,X2):
-        if X2 is None:
-            return np.zeros((X.shape[0], X.shape[0]))
-        else:
-            return np.zeros((X.shape[0], X2.shape[0]))
+    def gradients_X(self, dL_dK, X, X2=None):
+        return np.zeros(X.shape)