ENH: Added templates for state-space kernels.

Those are childs of regular kernels with extra "sde" function.

GPy/examples/state_space.py

@@ -4,12 +4,12 @@ import matplotlib.pyplot as plt
 
 import GPy.models.state_space_new as SS_new
 
-#X = np.linspace(0, 10, 2000)[:, None]
+X = np.linspace(0, 10, 4000)[:, None]
-#Y = np.sin(X) + np.random.randn(*X.shape)*0.1
+Y = np.sin(X) + np.random.randn(*X.shape)*0.1
 
 # Need to run these lines when X and Y are imported ->
-X.shape = (X.shape[0],1)
+#X.shape = (X.shape[0],1)
-Y.shape = (Y.shape[0],1)
+#Y.shape = (Y.shape[0],1)
 # Need to run these lines when X and Y are imported <-
 
 ## Generation of minimal example data ->

GPy/kern/__init__.py

@@ -29,3 +29,11 @@ from .src.splitKern import SplitKern,DEtime
 from .src.splitKern import DEtime as DiffGenomeKern
 from .src.spline import Spline
 from .src.basis_funcs import LogisticBasisFuncKernel, LinearSlopeBasisFuncKernel, BasisFuncKernel, ChangePointBasisFuncKernel, DomainKernel
+
+from .src.sde_matern import sde_Matern32
+from .src.sde_matern import sde_Matern52
+from .src.sde_linear import sde_Linear
+from .src.sde_standard_periodic import sde_StdPeriodic
+from .src.sde_static import sde_White, sde_Bias
+from .src.sde_stationary import sde_RBF,sde_Exponential,sde_RatQuad
+from .src.sde_brownian import sde_Brownian

GPy/kern/_src/sde_linear.py

@@ -0,0 +1,35 @@
+# -*- coding: utf-8 -*-
+"""
+Classes in this module enhance Matern covariance functions with the
+Stochastic Differential Equation (SDE) functionality.
+"""
+from .linear import Linear
+
+import numpy as np
+
+class sde_Linear(Linear):
+    """
+    
+    Class provide extra functionality to transfer this covariance function into
+    SDE form.
+    
+    Linear kernel:
+
+    .. math::
+
+       k(x,y) = \sum_{i=1}^{input dim} \sigma^2_i x_iy_i
+
+    """
+
+    def sde(self): 
+        """ 
+        Return the state space representation of the covariance. 
+        """ 
+        
+        # Arno, insert your code here
+
+        # Params to use:
+
+        # self.variances
+
+        #return (F, L, Qc, H, Pinf, dF, dQc, dPinf)

GPy/kern/_src/sde_matern.py

@@ -4,6 +4,7 @@ Classes in this module enhance Matern covariance functions with the
 Stochastic Differential Equation (SDE) functionality.
 """
 from .stationary import Matern32
+from .stationary import Matern52
 import numpy as np
 
 class sde_Matern32(Matern32):
@@ -16,7 +17,7 @@ class sde_Matern32(Matern32):
 
     .. math::
 
-       k(r) = \\sigma^2 (1 + \\sqrt{3} r) \exp(- \sqrt{3} r) \\ \\ \\ \\  \\text{ where  } r = \sqrt{\sum_{i=1}^input_dim \\frac{(x_i-y_i)^2}{\ell_i^2} }
+       k(r) = \sigma^2 (1 + \sqrt{3} r) \exp(- \sqrt{3} r) \\ \\ \\ \\  \text{ where  } r = \sqrt{\sum_{i=1}^{input dim} \frac{(x_i-y_i)^2}{\ell_i^2} }
 
     """
 
@@ -56,3 +57,30 @@ class sde_Matern32(Matern32):
         dPinf[:,:,1] = dPinflengthscale 
 
         return (F, L, Qc, H, Pinf, dF, dQc, dPinf)
+
+class sde_Matern52(Matern52):
+    """
+    
+    Class provide extra functionality to transfer this covariance function into
+    SDE forrm.
+    
+    Matern 5/2 kernel:
+
+    .. math::
+
+       k(r) = \sigma^2 (1 + \sqrt{5} r + \frac{5}{3}r^2) \exp(- \sqrt{5} r) \\ \\ \\ \\  \text{ where  } r = \sqrt{\sum_{i=1}^{input dim} \frac{(x_i-y_i)^2}{\ell_i^2} }
+
+    """
+
+    def sde(self): 
+        """ 
+        Return the state space representation of the covariance. 
+        """ 
+        
+        # Arno, insert your code here
+
+        # Params to use:
+        # self.lengthscale
+        # self.variance
+
+        #return (F, L, Qc, H, Pinf, dF, dQc, dPinf)  

GPy/kern/_src/sde_standard_periodic.py

@@ -0,0 +1,40 @@
+# -*- coding: utf-8 -*-
+"""
+Classes in this module enhance Matern covariance functions with the
+Stochastic Differential Equation (SDE) functionality.
+"""
+from .standard_periodic import StdPeriodic
+
+import numpy as np
+
+class sde_StdPeriodic(StdPeriodic):
+    """
+    
+    Class provide extra functionality to transfer this covariance function into
+    SDE form.
+    
+    Standard Periodic kernel:
+
+    .. math::
+
+       k(x,y) = \theta_1 \exp \left[  - \frac{1}{2} {}\sum_{i=1}^{input\_dim}  
+       \left( \frac{\sin(\frac{\pi}{\lambda_i} (x_i - y_i) )}{l_i} \right)^2 \right] }
+
+    """
+
+    def sde(self): 
+        """ 
+        Return the state space representation of the covariance. 
+        """ 
+        
+        # Arno, insert your code here
+
+        # Params to use:
+        #self.variance
+        #self.wavelengths
+        #self.lengthscales
+        
+        # Arno, you could visualize the Latex version of the kernel formula
+        # and assume inputs are 1D, so no ARD is used. Then use parameters aboove.        
+        
+        #return (F, L, Qc, H, Pinf, dF, dQc, dPinf)

GPy/kern/_src/sde_static.py

@@ -0,0 +1,61 @@
+# -*- coding: utf-8 -*-
+"""
+Classes in this module enhance Matern covariance functions with the
+Stochastic Differential Equation (SDE) functionality.
+"""
+from .static import White
+from .static import Bias
+
+import numpy as np
+
+class sde_White(White):
+    """
+    
+    Class provide extra functionality to transfer this covariance function into
+    SDE forrm.
+    
+    Linear kernel:
+
+    .. math::
+
+       k(x,y) = \alpha
+
+    """
+
+    def sde(self): 
+        """ 
+        Return the state space representation of the covariance. 
+        """ 
+        
+        # Arno, insert your code here
+
+        # Params to use:
+        # self.variance
+
+        #return (F, L, Qc, H, Pinf, dF, dQc, dPinf)
+
+class sde_Bias(Bias):
+    """
+    
+    Class provide extra functionality to transfer this covariance function into
+    SDE forrm.
+    
+    Linear kernel:
+
+    .. math::
+
+       k(x,y) = \alpha*\delta(x-y)
+
+    """
+
+    def sde(self): 
+        """ 
+        Return the state space representation of the covariance. 
+        """ 
+        
+        # Arno, insert your code here
+        
+        # Params to use:
+        # self.variance
+        
+        #return (F, L, Qc, H, Pinf, dF, dQc, dPinf)

GPy/kern/_src/sde_stationary.py

@@ -0,0 +1,103 @@
+# -*- coding: utf-8 -*-
+"""
+Classes in this module enhance several stationary covariance functions with the
+Stochastic Differential Equation (SDE) functionality.
+"""
+from .rbf import RBF
+from .stationary import Exponential
+from .stationary import RatQuad
+
+import numpy as np
+
+class sde_RBF(RBF):
+    """
+    
+    Class provide extra functionality to transfer this covariance function into
+    SDE form.
+    
+    Radial Basis Function kernel:
+
+    .. math::
+
+        k(r) = \sigma^2 \exp \\bigg(- \\frac{1}{2} r^2 \\bigg) \\ \\ \\ \\  \text{ where  } r = \sqrt{\sum_{i=1}^{input dim} \frac{(x_i-y_i)^2}{\ell_i^2} }
+
+    """
+
+    def sde(self): 
+        """ 
+        Return the state space representation of the covariance. 
+        """ 
+        
+        # Arno, insert your code here
+
+        # Params to use:
+
+        # self.lengthscale
+        # self.variance
+        
+        #return (F, L, Qc, H, Pinf, dF, dQc, dPinf)
+
+class sde_Exponential(Exponential):
+    """
+    
+    Class provide extra functionality to transfer this covariance function into
+    SDE form.
+    
+    Exponential kernel:
+
+    .. math::
+
+       k(r) = \sigma^2 \exp \\bigg(- \\frac{1}{2} r \\bigg) \\ \\ \\ \\  \text{ where  } r = \sqrt{\sum_{i=1}^{input dim} \frac{(x_i-y_i)^2}{\ell_i^2} }
+
+    """
+
+    def sde(self): 
+        """ 
+        Return the state space representation of the covariance. 
+        """ 
+        F  = np.array([[-1/self.lengthscale]]) 
+        L  = np.array([[1]]) 
+        Qc = np.array([[2*self.variance/self.lengthscale]]) 
+        H = np.array([[1]]) 
+        Pinf = np.array([[self.variance]]) 
+        # TODO: return the derivatives as well 
+        
+        return (F, L, Qc, H, Pinf)
+        
+        # Arno, insert your code here
+        
+        # Params to use:
+
+        # self.lengthscale
+        # self.variance
+
+        #return (F, L, Qc, H, Pinf, dF, dQc, dPinf) 
+
+class sde_RatQuad(RatQuad):
+    """
+    
+    Class provide extra functionality to transfer this covariance function into
+    SDE form.
+    
+    Rational Quadratic kernel:
+
+    .. math::
+
+       k(r) = \sigma^2 \\bigg( 1 + \\frac{r^2}{2} \\bigg)^{- \alpha} \\ \\ \\ \\  \text{ where  } r = \sqrt{\sum_{i=1}^{input dim} \frac{(x_i-y_i)^2}{\ell_i^2} }
+
+    """
+
+    def sde(self):
+        """ 
+        Return the state space representation of the covariance. 
+        """ 
+        
+        # Arno, insert your code here
+        
+        # Params to use:
+
+        # self.lengthscale
+        # self.variance
+        #self.power
+        
+        #return (F, L, Qc, H, Pinf, dF, dQc, dPinf)  

GPy/kern/src/stationary.py

@@ -320,18 +320,18 @@ class Exponential(Stationary):
     def dK_dr(self, r):
         return -0.5*self.K_of_r(r)
 
-    def sde(self): 
+#    def sde(self): 
-        """ 
+#        """ 
-        Return the state space representation of the covariance. 
+#        Return the state space representation of the covariance. 
-        """ 
+#        """ 
-        F  = np.array([[-1/self.lengthscale]]) 
+#        F  = np.array([[-1/self.lengthscale]]) 
-        L  = np.array([[1]]) 
+#        L  = np.array([[1]]) 
-        Qc = np.array([[2*self.variance/self.lengthscale]]) 
+#        Qc = np.array([[2*self.variance/self.lengthscale]]) 
-        H = np.array([[1]]) 
+#        H = np.array([[1]]) 
-        Pinf = np.array([[self.variance]]) 
+#        Pinf = np.array([[self.variance]]) 
-        # TODO: return the derivatives as well 
+#        # TODO: return the derivatives as well 
-        
+#        
-        return (F, L, Qc, H, Pinf)  
+#        return (F, L, Qc, H, Pinf)