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')