"""
======================
SVM with custom kernel
======================

Simple usage of Support Vector Machines to classify a sample. It will
plot the decision surface and the support vectors.

"""
import numpy as np
import pylab as pl
from scikits.learn import svm, datasets

# import some data to play with
iris = datasets.load_iris()
X = iris.data[:, :2] # we only take the first two features. We could
                     # avoid this ugly slicing by using a two-dim dataset
Y = iris.target


def my_kernel(x, y):
    """
    We create a custom kernel:

                 (2  0)
    k(x, y) = x  (    ) y.T
                 (0  1)
    """
    M = np.array([[2, 0], [0, 1.0]])
    return np.dot(np.dot(x, M), y.T)
    

h=.02 # step size in the mesh

# we create an instance of SVM and fit out data. 
clf = svm.SVC(kernel=my_kernel)
clf.fit(X, Y)

# Plot the decision boundary. For that, we will asign a color to each
# point in the mesh [x_min, m_max]x[y_min, y_max].
x_min, x_max = X[:,0].min()-1, X[:,0].max()+1
y_min, y_max = X[:,1].min()-1, X[:,1].max()+1
xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])

# Put the result into a color plot
Z = Z.reshape(xx.shape)
pl.set_cmap(pl.cm.Paired)
pl.pcolormesh(xx, yy, Z)

# Plot also the training points
pl.scatter(X[:,0], X[:,1], c=Y)
pl.title('3-Class classification using Support Vector Machine with custom kernel')
pl.axis('tight')
pl.show()