'''
Setup
'''
# Common imports
import numpy as np
import os
from sklearn.svm import SVC
from sklearn import datasets
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import StandardScaler
from sklearn.svm import LinearSVC
from sklearn.datasets import make_moons
from sklearn.preprocessing import PolynomialFeatures
from sklearn.svm import LinearSVR
from sklearn.svm import SVR
from mpl_toolkits.mplot3d import Axes3D


# to make this notebook's output stable across runs
np.random.seed(42)

# To plot pretty figures
import matplotlib as mpl
import matplotlib.pyplot as plt
mpl.rc('axes', labelsize=14)
mpl.rc('xtick', labelsize=12)
mpl.rc('ytick', labelsize=12)

# Where to save the figures
PROJECT_ROOT_DIR = "."
CHAPTER_ID = "svm"

def save_fig(fig_id, tight_layout=True):
    path = os.path.join(PROJECT_ROOT_DIR, "images", CHAPTER_ID, fig_id + ".png")
    print("Saving figure", fig_id)
    if tight_layout:
        plt.tight_layout()
    plt.savefig(path, format='png', dpi=300)

'''
------------------------------------------------------------------------------------------------------------------------
Chapter 5 Support Vector Machine
------------------------------------------------------------------------------------------------------------------------
'''
print('-----------------------------------------------------------------------------------------------------------------\n'
      '                                    5.1 Linear SVM classifier                                                    \n'
      '-----------------------------------------------------------------------------------------------------------------\n')
iris = datasets.load_iris()
X = iris["data"][:, (2, 3)]  # petal length, petal width
y = iris["target"]

setosa_or_versicolor = (y == 0) | (y == 1)
X = X[setosa_or_versicolor]
y = y[setosa_or_versicolor]

# SVM Classifier model
svm_clf = SVC(kernel="linear", C=float("inf"))
svm_clf_fit = svm_clf.fit(X, y)
print('svm_clf_fit = \n{0}'.format(svm_clf_fit))
print()

x_length = iris["data"][:, 2]
x_width = iris["data"][:, 3]

plt.figure(figsize=(12,5))
plt.title("Raw Data", fontsize=15)
plt.xlabel("x_length", fontsize=12)
plt.ylabel("x_width", fontsize=12)
plt.scatter(x_length, x_width)
plt.show()

# Bad models
x0 = np.linspace(0, 5.5, 200)
pred_1 = 5*x0 - 20
pred_2 = x0 - 1.8
pred_3 = 0.1 * x0 + 0.5

def plot_svc_decision_boundary(svm_clf, xmin, xmax):
    w = svm_clf.coef_[0]
    b = svm_clf.intercept_[0]

    # At the decision boundary, w0*x0 + w1*x1 + b = 0
    # => x1 = -w0/w1 * x0 - b/w1
    x0 = np.linspace(xmin, xmax, 200)
    decision_boundary = -w[0]/w[1] * x0 - b/w[1]

    margin = 1/w[1]
    gutter_up = decision_boundary + margin
    gutter_down = decision_boundary - margin

    svs = svm_clf.support_vectors_
    plt.scatter(svs[:, 0], svs[:, 1], s=180, facecolors='#FFAAAA')
    plt.plot(x0, decision_boundary, "k-", linewidth=2)
    plt.plot(x0, gutter_up, "k--", linewidth=2)
    plt.plot(x0, gutter_down, "k--", linewidth=2)


plt.figure(figsize=(12,5))
plt.subplot(121)
plt.title("small margin")
plt.plot(x0, pred_1, "g--", linewidth=2)
plt.plot(x0, pred_2, "m-", linewidth=2)
plt.plot(x0, pred_3, "r-", linewidth=2)
plt.plot(X[:, 0][y==1], X[:, 1][y==1], "bs", label="Iris-Versicolor")
plt.plot(X[:, 0][y==0], X[:, 1][y==0], "yo", label="Iris-Setosa")
plt.xlabel("Petal length", fontsize=14)
plt.ylabel("Petal width", fontsize=14)
plt.legend(loc="upper left", fontsize=14)
plt.axis([0, 5.5, 0, 2])

plt.subplot(122)
plt.title("big margin")
plot_svc_decision_boundary(svm_clf, 0, 5.5)
plt.plot(X[:, 0][y==1], X[:, 1][y==1], "bs")
plt.plot(X[:, 0][y==0], X[:, 1][y==0], "yo")
plt.xlabel("Petal length", fontsize=14)
plt.axis([0, 5.5, 0, 2])
save_fig("large_margin_classification_plot")
plt.show()



'''
---------------------------------------------------------------------------------------------------
Sensitivity to feature scales
---------------------------------------------------------------------------------------------------
'''
Xs = np.array([[1, 50], [5, 20], [3, 80], [5, 60]]).astype(np.float64)
ys = np.array([0, 0, 1, 1])
svm_clf = SVC(kernel="linear", C=100)
svm_clf.fit(Xs, ys)
plt.figure(figsize=(12,3.2))
plt.subplot(121)
plt.plot(Xs[:, 0][ys==1], Xs[:, 1][ys==1], "bo")
plt.plot(Xs[:, 0][ys==0], Xs[:, 1][ys==0], "ms")
plot_svc_decision_boundary(svm_clf, 0, 6)
plt.xlabel("$x_0$", fontsize=20)
plt.ylabel("$x_1$  ", fontsize=20, rotation=0)
plt.title("Unscaled", fontsize=16)
plt.axis([0, 6, 0, 90])

scaler = StandardScaler()
X_scaled = scaler.fit_transform(Xs)
svm_clf.fit(X_scaled, ys)

plt.subplot(122)
plt.plot(X_scaled[:, 0][ys==1], X_scaled[:, 1][ys==1], "bo")
plt.plot(X_scaled[:, 0][ys==0], X_scaled[:, 1][ys==0], "ms")
plot_svc_decision_boundary(svm_clf, -2, 2)
plt.xlabel("$x_0$", fontsize=20)
plt.title("Scaled", fontsize=16)
plt.axis([-2, 2, -2, 2])
save_fig("sensitivity_to_feature_scales_plot")
plt.show()

print()

print('-----------------------------------------------------------------------------------------------------------------\n'
      '                                 5.1.1 Soft margin classification                                                \n'
      '-----------------------------------------------------------------------------------------------------------------\n')
X_outliers = np.array([[3.4, 1.3], [3.2, 0.8]])
y_outliers = np.array([0, 0])
Xo1 = np.concatenate([X, X_outliers[:1]], axis=0)
yo1 = np.concatenate([y, y_outliers[:1]], axis=0)
Xo2 = np.concatenate([X, X_outliers[1:]], axis=0)
yo2 = np.concatenate([y, y_outliers[1:]], axis=0)

svm_clf2 = SVC(kernel="linear", C=10**9)
svm_clf2.fit(Xo2, yo2)

plt.figure(figsize=(12, 3.8))

plt.subplot(121)
plt.title("Hard margin classification", fontsize=16)
plt.plot(Xo1[:, 0][yo1==1], Xo1[:, 1][yo1==1], "bs")
plt.plot(Xo1[:, 0][yo1==0], Xo1[:, 1][yo1==0], "yo")
plt.text(0.3, 1.0, "Impossible!", fontsize=24, color="red")
plt.xlabel("Petal length", fontsize=14)
plt.ylabel("Petal width", fontsize=14)
plt.annotate("Outlier",
             xy=(X_outliers[0][0], X_outliers[0][1]),
             xytext=(2.5, 1.7),
             ha="center",
             arrowprops=dict(facecolor='black', shrink=0.1),
             fontsize=16,
            )
plt.axis([0, 5.5, 0, 2])

plt.subplot(122)
plt.title("Soft margin classification", fontsize=16)
plt.plot(Xo2[:, 0][yo2==1], Xo2[:, 1][yo2==1], "bs")
plt.plot(Xo2[:, 0][yo2==0], Xo2[:, 1][yo2==0], "yo")
plot_svc_decision_boundary(svm_clf2, 0, 5.5)
plt.xlabel("Petal length", fontsize=14)
plt.annotate("Outlier",
             xy=(X_outliers[1][0], X_outliers[1][1]),
             xytext=(3.2, 0.08),
             ha="center",
             arrowprops=dict(facecolor='black', shrink=0.1),
             fontsize=16,
            )
plt.axis([0, 5.5, 0, 2])
save_fig("sensitivity_to_outliers_plot")
plt.show()

print('-----------------------------------------------------------------------------------------------------------------\n'
      '                                Large margin vs margin violations                                                \n'
      '-----------------------------------------------------------------------------------------------------------------\n')
iris = datasets.load_iris()
X = iris["data"][:, (2, 3)]  # petal length, petal width
'''
Iris-Virginica is set to y = 1, otherwise y = 0.
'''
y = (iris["target"] == 2).astype(np.float64)  # Iris-Virginica

svm_clf = Pipeline([
        ("scaler", StandardScaler()),
        ("linear_svc", LinearSVC(C=1, loss="hinge", random_state=42)),
    ])

svm_clf_fit = svm_clf.fit(X, y)
print('svm_clf_fit = \n{0}'.format(svm_clf_fit))
print()
svm_clf_predit = svm_clf.predict([[5.5, 1.7]])
print('svm_clf_predict([[5.5, 1.7]] = {0}'.format(svm_clf_predit))
print()

print('---< Now let us generate the graph comparing different regularization settings: >---')

scaler = StandardScaler()
svm_clf1 = LinearSVC(C=1, loss="hinge", random_state=42)
svm_clf2 = LinearSVC(C=100, loss="hinge", random_state=42)

scaled_svm_clf1 = Pipeline([
        ("scaler", scaler),
        ("linear_svc", svm_clf1),
    ])
scaled_svm_clf2 = Pipeline([
        ("scaler", scaler),
        ("linear_svc", svm_clf2),
    ])

scaled_svm_clf1.fit(X, y)
scaled_svm_clf2.fit(X, y)

# Convert to unscaled parameters
b1 = svm_clf1.decision_function([-scaler.mean_ / scaler.scale_])
b2 = svm_clf2.decision_function([-scaler.mean_ / scaler.scale_])
w1 = svm_clf1.coef_[0] / scaler.scale_
w2 = svm_clf2.coef_[0] / scaler.scale_
svm_clf1.intercept_ = np.array([b1])
svm_clf2.intercept_ = np.array([b2])
svm_clf1.coef_ = np.array([w1])
svm_clf2.coef_ = np.array([w2])

# Find support vectors (LinearSVC does not do this automatically)
t = y * 2 - 1
support_vectors_idx1 = (t * (X.dot(w1) + b1) < 1).ravel()
support_vectors_idx2 = (t * (X.dot(w2) + b2) < 1).ravel()
svm_clf1.support_vectors_ = X[support_vectors_idx1]
svm_clf2.support_vectors_ = X[support_vectors_idx2]

plt.figure(figsize=(12,3.2))
plt.subplot(121)
plt.plot(X[:, 0][y==1], X[:, 1][y==1], "g^", label="Iris-Virginica")
plt.plot(X[:, 0][y==0], X[:, 1][y==0], "bs", label="Iris-Versicolor")
plot_svc_decision_boundary(svm_clf1, 4, 6)
plt.xlabel("Petal length", fontsize=14)
plt.ylabel("Petal width", fontsize=14)
plt.legend(loc="upper left", fontsize=14)
plt.title("$C = {}$".format(svm_clf1.C), fontsize=16)
plt.axis([4, 6, 0.8, 2.8])

plt.subplot(122)
plt.plot(X[:, 0][y==1], X[:, 1][y==1], "g^")
plt.plot(X[:, 0][y==0], X[:, 1][y==0], "bs")
plot_svc_decision_boundary(svm_clf2, 4, 6)
plt.xlabel("Petal length", fontsize=14)
plt.title("$C = {}$".format(svm_clf2.C), fontsize=16)
plt.axis([4, 6, 0.8, 2.8])

save_fig("regularization_plot")
plt.show()

print('-----------------------------------------------------------------------------------------------------------------\n'
      '                                  5.2 Non-linear classification                                                  \n'
      '-----------------------------------------------------------------------------------------------------------------\n')
X1D = np.linspace(-4, 4, 9).reshape(-1, 1)
X2D = np.c_[X1D, X1D**2]
y = np.array([0, 0, 1, 1, 1, 1, 1, 0, 0])

plt.figure(figsize=(11, 5))

plt.subplot(121)
plt.grid(True, which='both')
plt.axhline(y=0, color='k')
plt.plot(X1D[:, 0][y==0], np.zeros(4), "bs")
plt.plot(X1D[:, 0][y==1], np.zeros(5), "g^")
plt.gca().get_yaxis().set_ticks([])
plt.xlabel(r"$x_1$", fontsize=20)
plt.axis([-4.5, 4.5, -0.2, 0.2])

plt.subplot(122)
plt.grid(True, which='both')
plt.axhline(y=0, color='k')
plt.axvline(x=0, color='k')
plt.plot(X2D[:, 0][y==0], X2D[:, 1][y==0], "bs")
plt.plot(X2D[:, 0][y==1], X2D[:, 1][y==1], "g^")
plt.xlabel(r"$x_1$", fontsize=20)
plt.ylabel(r"$x_2$", fontsize=20, rotation=0)
plt.gca().get_yaxis().set_ticks([0, 4, 8, 12, 16])
plt.plot([-4.5, 4.5], [6.5, 6.5], "r--", linewidth=3)
plt.axis([-4.5, 4.5, -1, 17])

save_fig("higher_dimensions_plot", tight_layout=False)
plt.show()

X, y = make_moons(n_samples=100, noise=0.15, random_state=42)

def plot_dataset(X, y, axes):
    plt.plot(X[:, 0][y==0], X[:, 1][y==0], "bs")
    plt.plot(X[:, 0][y==1], X[:, 1][y==1], "g^")
    plt.axis(axes)
    plt.grid(True, which='both')
    plt.xlabel(r"$x_1$", fontsize=20)
    plt.ylabel(r"$x_2$", fontsize=20, rotation=0)

plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])
plt.show()

print('---< Linear SVM classifier using polynomial features >---')

polynomial_svm_clf = Pipeline([
        ("poly_features", PolynomialFeatures(degree=3)),
        ("scaler", StandardScaler()),
        ("svm_clf", LinearSVC(C=10, loss="hinge", random_state=42))
    ])

polynomial_svm_clf_fit = polynomial_svm_clf.fit(X, y)
print('polynomial_svm_clf_fit = \n{0}'.format(polynomial_svm_clf_fit))
print()

def plot_predictions(clf, axes):
    x0s = np.linspace(axes[0], axes[1], 100)
    x1s = np.linspace(axes[2], axes[3], 100)
    x0, x1 = np.meshgrid(x0s, x1s)
    X = np.c_[x0.ravel(), x1.ravel()]
    y_pred = clf.predict(X).reshape(x0.shape)
    y_decision = clf.decision_function(X).reshape(x0.shape)
    plt.contourf(x0, x1, y_pred, cmap=plt.cm.brg, alpha=0.2)
    plt.contourf(x0, x1, y_decision, cmap=plt.cm.brg, alpha=0.1)

plot_predictions(polynomial_svm_clf, [-1.5, 2.5, -1, 1.5])
plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])
plt.title("moons_polynomial_svc_plot", fontsize=20)
save_fig("moons_polynomial_svc_plot")
plt.show()

print('-----------------------------------------------------------------------------------------------------------------\n'
      '                                  5.2.1 Polynomial kernel                                                        \n'
      '-----------------------------------------------------------------------------------------------------------------\n')
X, y = make_moons(n_samples=100, noise=0.15, random_state=42)

poly_kernel_svm_clf = Pipeline([
    ("scaler", StandardScaler()),
    ("svm_clf", SVC(C=5, kernel="poly", degree=3, coef0=1))
])

poly_kernel_svm_clf_fit = poly_kernel_svm_clf.fit(X, y)

print('poly_kernel_svm_clf_fit = \n{0}'.format(poly_kernel_svm_clf_fit))
print()

poly100_kernel_svm_clf = Pipeline([
    ("scaler", StandardScaler()),
    ("svm_clf", SVC(C=5, kernel="poly", degree=10, coef0=100))
])

poly100_kernel_svm_clf_fit = poly100_kernel_svm_clf.fit(X, y)

print('poly100_kernel_svm_clf_fit = \n{0}'.format(poly100_kernel_svm_clf_fit))
print()

plt.figure(figsize=(11, 4))

plt.subplot(121)
plot_predictions(poly_kernel_svm_clf, [-1.5, 2.5, -1, 1.5])
plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])
plt.title(r"$d=3, r=1, C=5$", fontsize=18)

plt.subplot(122)
plot_predictions(poly100_kernel_svm_clf, [-1.5, 2.5, -1, 1.5])
plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])
plt.title(r"$d=10, r=100, C=5$", fontsize=18)
save_fig("moons_polynomial_svc_plot")
plt.show()

print('-----------------------------------------------------------------------------------------------------------------\n'
      '                                5.2.2 Add similarity feature                                                     \n'
      '-----------------------------------------------------------------------------------------------------------------\n')
def gaussian_rbf(x, landmark, gamma):
    return np.exp(-gamma * np.linalg.norm(x - landmark, axis=1) ** 2)


gamma = 0.3

x1s = np.linspace(-4.5, 4.5, 200).reshape(-1, 1)
x2s = gaussian_rbf(x1s, -2, gamma)
x3s = gaussian_rbf(x1s, 1, gamma)

XK = np.c_[gaussian_rbf(X1D, -2, gamma), gaussian_rbf(X1D, 1, gamma)]
yk = np.array([0, 0, 1, 1, 1, 1, 1, 0, 0])

plt.figure(figsize=(15, 5))

plt.subplot(121)
plt.grid(True, which='both')
plt.axhline(y=0, color='k')
plt.scatter(x=[-2, 1], y=[0, 0], s=150, alpha=0.5, c="red")
plt.plot(X1D[:, 0][yk == 0], np.zeros(4), "bs")
plt.plot(X1D[:, 0][yk == 1], np.zeros(5), "g^")
plt.plot(x1s, x2s, "g--")
plt.plot(x1s, x3s, "b:")
plt.gca().get_yaxis().set_ticks([0, 0.25, 0.5, 0.75, 1])
plt.xlabel(r"$x_1$", fontsize=20)
plt.ylabel(r"Similarity", fontsize=14)
plt.annotate(r'$\mathbf{x}$',
             xy=(X1D[3, 0], 0),
             xytext=(-0.5, 0.20),
             ha="center",
             arrowprops=dict(facecolor='black', shrink=0.1),
             fontsize=18,
             )
plt.text(-2, 0.9, "$x_2$", ha="center", fontsize=20)
plt.text(1, 0.9, "$x_3$", ha="center", fontsize=20)
plt.axis([-4.5, 4.5, -0.1, 1.1])

plt.subplot(122)
plt.grid(True, which='both')
plt.axhline(y=0, color='k')
plt.axvline(x=0, color='k')
plt.plot(XK[:, 0][yk == 0], XK[:, 1][yk == 0], "bs")
plt.plot(XK[:, 0][yk == 1], XK[:, 1][yk == 1], "g^")
plt.xlabel(r"$x_2$", fontsize=20)
plt.ylabel(r"$x_3$  ", fontsize=20, rotation=0)
plt.annotate(r'$\phi\left(\mathbf{x}\right)$',
             xy=(XK[3, 0], XK[3, 1]),
             xytext=(0.65, 0.50),
             ha="center",
             arrowprops=dict(facecolor='black', shrink=0.1),
             fontsize=18,
             )
plt.plot([-0.1, 1.1], [0.57, -0.1], "r--", linewidth=3)
plt.axis([-0.1, 1.1, -0.1, 1.1])
plt.show()

print('-----------------------------------------------------------------------------------------------------------------\n'
      '                                5.2.3 Gaussian RBF kernel                                                        \n'
      '-----------------------------------------------------------------------------------------------------------------\n')
rbf_kernel_svm_clf = Pipeline([
        ("scaler", StandardScaler()),
        ("svm_clf", SVC(kernel="rbf", gamma=5, C=0.001))
    ])

print('rbf_kernel_svm_clf.fit(X, y) = \n{0}'.format(rbf_kernel_svm_clf.fit(X, y)))
print()

gamma1, gamma2 = 0.1, 5
C1, C2 = 0.001, 1000
hyperparams = (gamma1, C1), (gamma1, C2), (gamma2, C1), (gamma2, C2)

svm_clfs = []
for gamma, C in hyperparams:
    rbf_kernel_svm_clf = Pipeline([
            ("scaler", StandardScaler()),
            ("svm_clf", SVC(kernel="rbf", gamma=gamma, C=C))
        ])
    rbf_kernel_svm_clf.fit(X, y)
    svm_clfs.append(rbf_kernel_svm_clf)

plt.figure(figsize=(11, 7))

for i, svm_clf in enumerate(svm_clfs):
    plt.subplot(221 + i)
    plot_predictions(svm_clf, [-1.5, 2.5, -1, 1.5])
    plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])
    gamma, C = hyperparams[i]
    plt.title(r"$\gamma = {}, C = {}$".format(gamma, C), fontsize=16)

save_fig("moons_rbf_svc_plot")
plt.show()
print()

print('-----------------------------------------------------------------------------------------------------------------\n'
      '                                5.3 SVM Regression                                                               \n'
      '-----------------------------------------------------------------------------------------------------------------\n')
print('---< SVM Regression with Linear type >---')
np.random.seed(42)
m = 50
X = 2 * np.random.rand(m, 1)
y = (4 +3 * X + np.random.randn(m, 1))

# plot scatter
plt.figure(figsize=(9, 4))
plt.scatter(X, y)
plt.title("SVM Regression with Linear type")
plt.xlabel("X")
plt.ylabel("y")
plt.grid(True)
plt.show()

y = y.ravel()

svm_reg = LinearSVR(epsilon=1.5, random_state=42)
svm_reg_fit = svm_reg.fit(X, y)
print('svm_reg_fit = \n{0}'.format(svm_reg_fit))
print()

svm_reg1 = LinearSVR(epsilon=1.5, random_state=42)
svm_reg2 = LinearSVR(epsilon=0.5, random_state=42)
svm_reg1.fit(X, y)
svm_reg2.fit(X, y)

def find_support_vectors(svm_reg, X, y):
    y_pred = svm_reg.predict(X)
    off_margin = (np.abs(y - y_pred) >= svm_reg.epsilon)
    return np.argwhere(off_margin)

svm_reg1.support_ = find_support_vectors(svm_reg1, X, y)
svm_reg2.support_ = find_support_vectors(svm_reg2, X, y)

eps_x1 = 1
eps_y_pred = svm_reg1.predict([[eps_x1]])

def plot_svm_regression(svm_reg, X, y, axes):
    x1s = np.linspace(axes[0], axes[1], 100).reshape(100, 1)
    y_pred = svm_reg.predict(x1s)
    plt.plot(x1s, y_pred, "k-", linewidth=2, label=r"$\hat{y}$")
    plt.plot(x1s, y_pred + svm_reg.epsilon, "k--")
    plt.plot(x1s, y_pred - svm_reg.epsilon, "k--")
    plt.scatter(X[svm_reg.support_], y[svm_reg.support_], s=180, facecolors='#FFAAAA')
    plt.plot(X, y, "bo")
    plt.xlabel(r"$x_1$", fontsize=18)
    plt.legend(loc="upper left", fontsize=18)
    plt.axis(axes)

plt.figure(figsize=(9, 4))
plt.subplot(121)
plot_svm_regression(svm_reg1, X, y, [0, 2, 3, 11])
plt.title(r"$\epsilon = {}$".format(svm_reg1.epsilon), fontsize=18)
plt.ylabel(r"$y$", fontsize=18, rotation=0)
#plt.plot([eps_x1, eps_x1], [eps_y_pred, eps_y_pred - svm_reg1.epsilon], "k-", linewidth=2)
plt.annotate(
        '', xy=(eps_x1, eps_y_pred), xycoords='data',
        xytext=(eps_x1, eps_y_pred - svm_reg1.epsilon),
        textcoords='data', arrowprops={'arrowstyle': '<->', 'linewidth': 1.5}
    )
plt.text(0.91, 5.6, r"$\epsilon$", fontsize=20)
plt.subplot(122)
plot_svm_regression(svm_reg2, X, y, [0, 2, 3, 11])
plt.title(r"$\epsilon = {}$".format(svm_reg2.epsilon), fontsize=18)
save_fig("svm_regression_plot")
plt.show()
print()

print('---< SVM regression using quadratic polynomial kernel >---')
np.random.seed(42)
m = 100
X = 2 * np.random.rand(m, 1) - 1
y = (0.2 + 0.1 * X + 0.5 * X**2 + np.random.randn(m, 1)/10)

# plot scatter
plt.figure(figsize=(9, 4))
plt.scatter(X, y)
plt.title("SVM regression using quadratic polynomial kernel")
plt.xlabel("X")
plt.ylabel("y")
plt.grid(True)
plt.show()

y = y.ravel()

svm_poly_reg = SVR(kernel="poly", degree=2, C=100, epsilon=0.1, gamma="auto")
svm_poly_reg_fit = svm_poly_reg.fit(X, y)
print('svm_poly_reg_fit = \n{0}'.format(svm_poly_reg_fit))
print()

svm_poly_reg1 = SVR(kernel="poly", degree=2, C=100, epsilon=0.1, gamma="auto")
svm_poly_reg2 = SVR(kernel="poly", degree=2, C=0.01, epsilon=0.1, gamma="auto")
svm_poly_reg1.fit(X, y)
svm_poly_reg2.fit(X, y)

plt.figure(figsize=(9, 4))
plt.subplot(121)
plot_svm_regression(svm_poly_reg1, X, y, [-1, 1, 0, 1])
plt.title(r"$degree={}, C={}, \epsilon = {}$".format(svm_poly_reg1.degree, svm_poly_reg1.C, svm_poly_reg1.epsilon), fontsize=18)
plt.ylabel(r"$y$", fontsize=18, rotation=0)
plt.subplot(122)
plot_svm_regression(svm_poly_reg2, X, y, [-1, 1, 0, 1])
plt.title(r"$degree={}, C={}, \epsilon = {}$".format(svm_poly_reg2.degree, svm_poly_reg2.C, svm_poly_reg2.epsilon), fontsize=18)
save_fig("svm_with_polynomial_kernel_plot")
plt.show()

'''
------------------------------------------------------------------------------------------------------------------------
                                   5.4 Under the hood
------------------------------------------------------------------------------------------------------------------------
'''

print('-----------------------------------------------------------------------------------------------------------------\n'
      '                                5.4.1 Decision functions and predictions                                         \n'
      '-----------------------------------------------------------------------------------------------------------------\n')
iris = datasets.load_iris()

print(iris.DESCR)

# petal length, petal width
X = iris["data"][:, (2, 3)]

# Iris-Virginica
y = (iris["target"] == 2).astype(np.float)

def plot_3D_decision_function(ax, w, b, x1_lim=[4, 6], x2_lim=[0.8, 2.8]):
    x1_in_bounds = (X[:, 0] > x1_lim[0]) & (X[:, 0] < x1_lim[1])
    X_crop = X[x1_in_bounds]
    y_crop = y[x1_in_bounds]
    x1s = np.linspace(x1_lim[0], x1_lim[1], 20)
    x2s = np.linspace(x2_lim[0], x2_lim[1], 20)
    x1, x2 = np.meshgrid(x1s, x2s)
    xs = np.c_[x1.ravel(), x2.ravel()]
    df = (xs.dot(w) + b).reshape(x1.shape)
    m = 1 / np.linalg.norm(w)
    boundary_x2s = -x1s*(w[0]/w[1])-b/w[1]
    margin_x2s_1 = -x1s*(w[0]/w[1])-(b-1)/w[1]
    margin_x2s_2 = -x1s*(w[0]/w[1])-(b+1)/w[1]
    ax.plot_surface(x1s, x2, np.zeros_like(x1),
                    color="b", alpha=0.2, cstride=100, rstride=100)
    ax.plot(x1s, boundary_x2s, 0, "k-", linewidth=2, label=r"$h=0$")
    ax.plot(x1s, margin_x2s_1, 0, "k--", linewidth=2, label=r"$h=\pm 1$")
    ax.plot(x1s, margin_x2s_2, 0, "k--", linewidth=2)
    ax.plot(X_crop[:, 0][y_crop==1], X_crop[:, 1][y_crop==1], 0, "g^")
    ax.plot_wireframe(x1, x2, df, alpha=0.3, color="k")
    ax.plot(X_crop[:, 0][y_crop==0], X_crop[:, 1][y_crop==0], 0, "bs")
    ax.axis(x1_lim + x2_lim)
    ax.text(4.5, 2.5, 3.8, "Decision function $h$", fontsize=15)
    ax.set_xlabel(r"Petal length", fontsize=15)
    ax.set_ylabel(r"Petal width", fontsize=15)
    ax.set_zlabel(r"$h = \mathbf{w}^T \mathbf{x} + b$", fontsize=18)
    ax.legend(loc="upper left", fontsize=16)

fig = plt.figure(figsize=(11, 6))
ax1 = fig.add_subplot(111, projection='3d')
plot_3D_decision_function(ax1, w=svm_clf2.coef_[0], b=svm_clf2.intercept_[0])

#save_fig("iris_3D_plot")
plt.show()

print('-----------------------------------------------------------------------------------------------------------------\n'
      '                                5.4.2 Training goals                                                             \n'
      '-----------------------------------------------------------------------------------------------------------------\n')

print('---< Small weight vector results in a large margin >---')

def plot_2D_decision_function(w, b, ylabel=True, x1_lim=[-3, 3]):
    x1 = np.linspace(x1_lim[0], x1_lim[1], 200)
    y = w * x1 + b
    m = 1 / w

    plt.plot(x1, y)
    plt.plot(x1_lim, [1, 1], "k:")
    plt.plot(x1_lim, [-1, -1], "k:")
    plt.axhline(y=0, color='k')
    plt.axvline(x=0, color='k')
    plt.plot([m, m], [0, 1], "k--")
    plt.plot([-m, -m], [0, -1], "k--")
    plt.plot([-m, m], [0, 0], "k-o", linewidth=3)
    plt.axis(x1_lim + [-2, 2])
    plt.xlabel(r"$x_1$", fontsize=16)
    if ylabel:
        plt.ylabel(r"$w_1 x_1$  ", rotation=0, fontsize=16)
    plt.title(r"$w_1 = {}$".format(w), fontsize=16)

plt.figure(figsize=(12, 3.2))
plt.subplot(121)
plot_2D_decision_function(1, 0)
plt.subplot(122)
plot_2D_decision_function(0.5, 0, ylabel=False)
save_fig("small_w_large_margin_plot")
plt.show()
print()

X = iris["data"][:, (2, 3)] # petal length, petal width
y = (iris["target"] == 2).astype(np.float64) # Iris-Virginica

svm_clf = SVC(kernel="linear", C=1)
svm_clf.fit(X, y)
svm_clf_predit = svm_clf.predict([[5.3, 1.3]])
print('svm_clf_predit = {0}'.format(svm_clf_predit))
print()

print('-----------------------------------------------------------------------------------------------------------------\n'
      '                                5.4.6 on-line SVM                                                                \n'
      '-----------------------------------------------------------------------------------------------------------------\n')
print('---< hingle loss >---')

t = np.linspace(-2, 4, 200)
h = np.where(1 - t < 0, 0, 1 - t)  # max(0, 1-t)

plt.figure(figsize=(5,2.8))
plt.plot(t, h, "b-", linewidth=2, label="$max(0, 1 - t)$")
plt.grid(True, which='both')
plt.axhline(y=0, color='k')
plt.axvline(x=0, color='k')
plt.yticks(np.arange(-1, 2.5, 1))
plt.xlabel("$t$", fontsize=16)
plt.axis([-2, 4, -1, 2.5])
plt.legend(loc="upper right", fontsize=16)
save_fig("hinge_plot")
plt.show()
print()

