added tutorial in examples

GPy/examples/tuto_GP_regression.py

@@ -0,0 +1,56 @@
+# The detailed explanations of the commands used in this file can be found in the tutorial section
+
+import pylab as pb
+pb.ion()
+import numpy as np
+import GPy
+
+X = np.random.uniform(-3.,3.,(20,1))
+Y = np.sin(X) + np.random.randn(20,1)*0.05
+
+kernel = GPy.kern.rbf(D=1, variance=1., lengthscale=1.)
+
+m = GPy.models.GP_regression(X,Y,kernel)
+
+print m
+m.plot()
+
+m.constrain_positive('')
+
+m.unconstrain('')                            # Required to remove the previous constrains
+m.constrain_positive('rbf_variance')
+m.constrain_bounded('lengthscale',1.,10. )
+m.constrain_fixed('noise',0.0025)
+
+m.optimize()
+
+m.optimize_restarts(Nrestarts = 10)
+
+###########################
+#  2-dimensional example  #
+###########################
+
+import pylab as pb
+pb.ion()
+import numpy as np
+import GPy
+
+# sample inputs and outputs
+X = np.random.uniform(-3.,3.,(50,2))
+Y = np.sin(X[:,0:1]) * np.sin(X[:,1:2])+np.random.randn(50,1)*0.05
+
+# define kernel
+ker = GPy.kern.Matern52(2,ARD=True) + GPy.kern.white(2)
+
+# create simple GP model
+m = GPy.models.GP_regression(X,Y,ker)
+
+# contrain all parameters to be positive
+m.constrain_positive('')
+
+# optimize and plot
+pb.figure()
+m.optimize('tnc', max_f_eval = 1000)
+
+m.plot()
+print(m)

GPy/examples/tuto_kernel_overview.py

@@ -0,0 +1,139 @@
+# The detailed explanations of the commands used in this file can be found in the tutorial section
+
+import pylab as pb
+import numpy as np
+import GPy
+pb.ion()
+
+ker1 = GPy.kern.rbf(1)  # Equivalent to ker1 = GPy.kern.rbf(D=1, variance=1., lengthscale=1.)
+ker2 = GPy.kern.rbf(D=1, variance = .75, lengthscale=2.)
+ker3 = GPy.kern.rbf(1, .5, .5)
+
+print ker2
+ker1.plot()
+ker2.plot()
+ker3.plot()
+
+k1 = GPy.kern.rbf(1,1.,2.)
+k2 = GPy.kern.Matern32(1, 0.5, 0.2)
+
+# Product of kernels
+k_prod = k1.prod(k2)
+k_prodorth = k1.prod_orthogonal(k2)
+
+# Sum of kernels
+k_add = k1.add(k2)
+k_addorth = k1.add_orthogonal(k2)    
+
+pb.figure(figsize=(8,8))
+pb.subplot(2,2,1)
+k_prod.plot()
+pb.title('prod')
+pb.subplot(2,2,2)
+k_prodorth.plot()
+pb.title('prod_orthogonal')
+pb.subplot(2,2,3)
+k_add.plot()
+pb.title('add')
+pb.subplot(2,2,4)
+k_addorth.plot()
+pb.title('add_orthogonal')
+pb.subplots_adjust(wspace=0.3, hspace=0.3)
+
+k1 = GPy.kern.rbf(1,1.,2)
+k2 = GPy.kern.periodic_Matern52(1,variance=1e3, lengthscale=1, period = 1.5, lower=-5., upper = 5)
+
+k = k1 * k2  # equivalent to k = k1.prod(k2)
+print k
+
+# Simulate sample paths
+X = np.linspace(-5,5,501)[:,None]
+Y = np.random.multivariate_normal(np.zeros(501),k.K(X),1)
+
+# plot
+pb.figure(figsize=(10,4))
+pb.subplot(1,2,1)
+k.plot()
+pb.subplot(1,2,2)
+pb.plot(X,Y.T)
+pb.ylabel("Sample path")
+pb.subplots_adjust(wspace=0.3)
+
+k = (k1+k2)*(k1+k2)
+print k.parts[0].name, '\n', k.parts[1].name, '\n', k.parts[2].name, '\n', k.parts[3].name
+
+k1 = GPy.kern.rbf(1)
+k2 = GPy.kern.Matern32(1)
+k3 = GPy.kern.white(1)
+
+k = k1 + k2 + k3
+print k
+
+k.constrain_positive('var')
+k.constrain_fixed(np.array([1]),1.75)
+k.tie_param('len')
+k.unconstrain('white')
+k.constrain_bounded('white',lower=1e-5,upper=.5)
+print k
+
+k_cst = GPy.kern.bias(1,variance=1.)
+k_mat = GPy.kern.Matern52(1,variance=1., lengthscale=3)
+Kanova = (k_cst + k_mat).prod_orthogonal(k_cst + k_mat)
+print Kanova
+
+# sample inputs and outputs
+X = np.random.uniform(-3.,3.,(40,2))
+Y = 0.5*X[:,:1] + 0.5*X[:,1:] + 2*np.sin(X[:,:1]) * np.sin(X[:,1:])
+
+# Create GP regression model
+m = GPy.models.GP_regression(X,Y,Kanova)
+pb.figure(figsize=(5,5))
+m.plot()
+
+pb.figure(figsize=(20,3))
+pb.subplots_adjust(wspace=0.5)
+pb.subplot(1,5,1)
+m.plot()
+pb.subplot(1,5,2)
+pb.ylabel("=   ",rotation='horizontal',fontsize='30')
+pb.subplot(1,5,3)
+m.plot(which_functions=[False,True,False,False])
+pb.ylabel("cst          +",rotation='horizontal',fontsize='30')
+pb.subplot(1,5,4)
+m.plot(which_functions=[False,False,True,False])
+pb.ylabel("+   ",rotation='horizontal',fontsize='30')
+pb.subplot(1,5,5)
+pb.ylabel("+   ",rotation='horizontal',fontsize='30')
+m.plot(which_functions=[False,False,False,True])
+
+import pylab as pb
+import numpy as np
+import GPy
+pb.ion()
+
+ker1 = GPy.kern.rbf(D=1)  # Equivalent to ker1 = GPy.kern.rbf(D=1, variance=1., lengthscale=1.)
+ker2 = GPy.kern.rbf(D=1, variance = .75, lengthscale=3.)
+ker3 = GPy.kern.rbf(1, .5, .25)
+
+ker1.plot()
+ker2.plot()
+ker3.plot()
+#pb.savefig("Figures/tuto_kern_overview_basicdef.png")
+
+kernels = [GPy.kern.rbf(1), GPy.kern.exponential(1), GPy.kern.Matern32(1), GPy.kern.Matern52(1),  GPy.kern.Brownian(1), GPy.kern.bias(1), GPy.kern.linear(1), GPy.kern.spline(1), GPy.kern.periodic_exponential(1), GPy.kern.periodic_Matern32(1), GPy.kern.periodic_Matern52(1), GPy.kern.white(1)]
+kernel_names = ["GPy.kern.rbf", "GPy.kern.exponential", "GPy.kern.Matern32", "GPy.kern.Matern52", "GPy.kern.Brownian", "GPy.kern.bias", "GPy.kern.linear", "GPy.kern.spline", "GPy.kern.periodic_exponential", "GPy.kern.periodic_Matern32", "GPy.kern.periodic_Matern52", "GPy.kern.white"]
+
+pb.figure(figsize=(16,12))
+pb.subplots_adjust(wspace=.5, hspace=.5)
+for i, kern in enumerate(kernels):
+   pb.subplot(3,4,i+1)
+   kern.plot(x=7.5,plot_limits=[0.00001,15.])
+   pb.title(kernel_names[i]+ '\n')
+
+# actual plot for the noise
+i = 11
+X = np.linspace(0.,15.,201)
+WN = 0*X
+WN[100] = 1.
+pb.subplot(3,4,i+1)
+pb.plot(X,WN,'b')

doc/tuto_GP_regression.rst

@@ -2,7 +2,7 @@
 Gaussian process regression tutorial
 *************************************
 
-We will see in this tutorial the basics for building a 1 dimensional and a 2 dimensional Gaussian process regression model, also known as a kriging model.
+We will see in this tutorial the basics for building a 1 dimensional and a 2 dimensional Gaussian process regression model, also known as a kriging model. The code shown in this tutorial can be found without the comments at GPy/examples/tuto_GP_regression.py.
 
 We first import the libraries we will need: ::
 

doc/tuto_kernel_overview.rst

@@ -2,6 +2,7 @@
 ****************************
 tutorial : A kernel overview
 ****************************
+The aim of this tutorial is to give a better understanding of the kernel objects in GPy and to list the ones that are already implemented. The code shown in this tutorial can be found without the comments at GPy/examples/tuto_kernel_overview.py.
 
 First we import the libraries we will need ::