Added spline kernel (from P. Hennig) to GPy

Had to modify the base_plots and model_plots.py, since I had troubles
installing GPy in anaconda on debian linux due to the dependency on
Tango. Why is Tango needed to represent colors that can also be typed in
Hex format thus eliminating further dependencies.

GPy/kern/__init__.py

@@ -13,6 +13,7 @@ from _src.ODE_UYC import ODE_UYC
 from _src.ODE_st import ODE_st
 from _src.ODE_t import ODE_t
 from _src.poly import Poly
+from _src.spline import Spline
 
 from _src.trunclinear import TruncLinear,TruncLinear_inf
 from _src.splitKern import SplitKern,DiffGenomeKern

GPy/kern/_src/spline.py

@@ -0,0 +1,47 @@
+# Copyright (c) 2014, James Hensman
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+import numpy as np
+from kern import Kern
+from ...core.parameterization import Param
+from ...core.parameterization.transformations import Logexp
+class Spline(Kern):
+    """
+    Spline kernel
+    """
+
+    def __init__(self, input_dim, variance=1., c=1., active_dims=None, name='spline'):
+        super(Spline, self).__init__(input_dim, active_dims, name)
+        self.variance = Param('variance', variance, Logexp())
+        self.c = Param('c', c)
+        self.link_parameters(self.variance,self.c)
+
+
+    def K(self, X, X2=None):
+        if X2 is None: X2=X
+        term1 = (X+8.)*(X2.T+8.)/16.
+        term2 = abs((X-X2.T)/16.)**3
+        term3 = ((X+8.)/16.)**3 + ((X2.T+8.)/16.)**3
+        return (self.variance**2 * (1. + (1.+self.c) * term1 + self.c/3. * (term2 - term3)))
+
+    def Kdiag(self, X):
+        term1 = np.square(X+8.,X+8.)/16.
+        term3 = 2. * ((X+8.)/16.)**3
+        return (self.variance**2 * (1. + (1.+self.c) * term1 - self.c/3. * term3))[:,0]
+
+    def update_gradients_full(self, dL_dK, X, X2=None):
+        if X2 is None: X2=X
+        term1 = (X+8.)*(X2.T+8.)/16.
+        term2 = abs((X-X2.T)/16.)**3
+        term3 = ((X+8.)/16.)**3 + ((X2.T+8.)/16.)**3
+        self.variance.gradient = np.sum(dL_dK * (2*self.variance * (1. + (1.+self.c) * term1 + self.c/3. * ( term2 - term3))))
+        self.c.gradient = np.sum(dL_dK * (self.variance**2* (term1 + 1./3.*(term2 - term3))))
+
+    def update_gradients_diag(self, dL_dKdiag, X):
+        raise NotImplementedError
+
+    def gradients_X(self, dL_dK, X, X2=None):
+        raise NotImplementedError
+
+    def gradients_X_diag(self, dL_dKdiag, X):
+        raise NotImplementedError

GPy/plotting/matplot_dep/base_plots.py

@@ -3,7 +3,7 @@
 
 
 try:
-    import Tango
+    #import Tango
     import pylab as pb
 except:
     pass
@@ -17,11 +17,11 @@ def ax_default(fignum, ax):
         fig = ax.figure
     return fig, ax
 
-def meanplot(x, mu, color=Tango.colorsHex['darkBlue'], ax=None, fignum=None, linewidth=2,**kw):
+def meanplot(x, mu, color='#3300FF', ax=None, fignum=None, linewidth=2,**kw):
     _, axes = ax_default(fignum, ax)
     return axes.plot(x,mu,color=color,linewidth=linewidth,**kw)
 
-def gpplot(x, mu, lower, upper, edgecol=Tango.colorsHex['darkBlue'], fillcol=Tango.colorsHex['lightBlue'], ax=None, fignum=None, **kwargs):
+def gpplot(x, mu, lower, upper, edgecol='#3300FF', fillcol='#33CCFF', ax=None, fignum=None, **kwargs):
     _, axes = ax_default(fignum, ax)
 
     mu = mu.flatten()

GPy/plotting/matplot_dep/models_plots.py

@@ -2,7 +2,7 @@
 # Licensed under the BSD 3-clause license (see LICENSE.txt)
 
 try:
-    import Tango
+#    import Tango
     import pylab as pb
 except:
     pass
@@ -16,7 +16,7 @@ def plot_fit(model, plot_limits=None, which_data_rows='all',
         which_data_ycols='all', fixed_inputs=[],
         levels=20, samples=0, fignum=None, ax=None, resolution=None,
         plot_raw=False,
-        linecol=Tango.colorsHex['darkBlue'],fillcol=Tango.colorsHex['lightBlue'], Y_metadata=None, data_symbol='kx'):
+        linecol='#3300FF',fillcol='#00FFFF', Y_metadata=None, data_symbol='kx'):
     """
     Plot the posterior of the GP.
       - In one dimension, the function is plotted with a shaded region identifying two standard deviations.
@@ -107,7 +107,7 @@ def plot_fit(model, plot_limits=None, which_data_rows='all',
         if samples: #NOTE not tested with fixed_inputs
             Ysim = model.posterior_samples(Xgrid, samples)
             for yi in Ysim.T:
-                plots['posterior_samples'] = ax.plot(Xnew, yi[:,None], Tango.colorsHex['darkBlue'], linewidth=0.25)
+                plots['posterior_samples'] = ax.plot(Xnew, yi[:,None], '#3300FF', linewidth=0.25)
                 #ax.plot(Xnew, yi[:,None], marker='x', linestyle='--',color=Tango.colorsHex['darkBlue']) #TODO apply this line for discrete outputs.