"""
Example of linear and non-linear models
========================================

This is an example plot from the tutorial which accompanies an explanation
of the support vector machine GUI.
"""

import numpy as np
import matplotlib.pyplot as plt

from sklearn import svm

##############################################################################
# data that is linearly separable

def linear_model(rseed=42, n_samples=30):
    " Generate data according to a linear model"
    np.random.seed(rseed)

    data = np.random.normal(0, 10, (n_samples, 2))
    data[:n_samples // 2] -= 15
    data[n_samples // 2:] += 15

    labels = np.ones(n_samples)
    labels[:n_samples // 2] = -1

    return data, labels


X, y = linear_model()
clf = svm.SVC(kernel='linear')
clf.fit(X, y)

plt.figure(figsize=(6, 4))
ax = plt.subplot(111, xticks=[], yticks=[])
ax.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.bone)

ax.scatter(clf.support_vectors_[:, 0],
            clf.support_vectors_[:, 1],
            s=80, edgecolors="k", facecolors="none")

delta = 1
y_min, y_max = -50, 50
x_min, x_max = -50, 50
x = np.arange(x_min, x_max + delta, delta)
y = np.arange(y_min, y_max + delta, delta)
X1, X2 = np.meshgrid(x, y)
Z = clf.decision_function(np.c_[X1.ravel(), X2.ravel()])
Z = Z.reshape(X1.shape)

ax.contour(X1, X2, Z, [-1.0, 0.0, 1.0], colors='k',
           linestyles=['dashed', 'solid', 'dashed'])


##############################################################################
# data with a non-linear separation

def nonlinear_model(rseed=42, n_samples=30):
    radius = 40 * np.random.random(n_samples)
    far_pts = radius > 20
    radius[far_pts] *= 1.2
    radius[~far_pts] *= 1.1

    theta = np.random.random(n_samples) * np.pi * 2

    data = np.empty((n_samples, 2))
    data[:, 0] = radius * np.cos(theta)
    data[:, 1] = radius * np.sin(theta)

    labels = np.ones(n_samples)
    labels[far_pts] = -1

    return data, labels


X, y = nonlinear_model()
clf = svm.SVC(kernel='rbf', gamma=0.001, coef0=0, degree=3)
clf.fit(X, y)

plt.figure(figsize=(6, 4))
ax = plt.subplot(1, 1, 1, xticks=[], yticks=[])
ax.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.bone, zorder=2)

ax.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],
           s=80, edgecolors="k", facecolors="none")

delta = 1
y_min, y_max = -50, 50
x_min, x_max = -50, 50
x = np.arange(x_min, x_max + delta, delta)
y = np.arange(y_min, y_max + delta, delta)
X1, X2 = np.meshgrid(x, y)
Z = clf.decision_function(np.c_[X1.ravel(), X2.ravel()])
Z = Z.reshape(X1.shape)

ax.contour(X1, X2, Z, [-1.0, 0.0, 1.0], colors='k',
            linestyles=['dashed', 'solid', 'dashed'], zorder=1)

plt.show()