create_3d.py

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import axes3d
# 리스트 4-4-(9)
def gauss(mu, sigma, a):
    return a * np.exp(-(x - mu)**2 / sigma**2)
x = np.linspace(-4, 4, 100)
plt.figure(figsize=(4, 4))
plt.plot(x, gauss(0, 1, 1), 'black', linewidth=3)
plt.plot(x, gauss(2, 3, 0.5), 'gray', linewidth=3)
plt.ylim(-.5, 1.5)
plt.xlim(-4, 4)
plt.grid(True)
plt.show()
# 리스트 4-5-(1)
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import axes3d
#matplotlib inline
# 가우스 함수
def gauss(x, mu, sigma):
    N, D = x.shape
    c1 = 1 / (2 * np.pi)**(D / 2)
    c2 = 1 / (np.linalg.det(sigma)**(1 / 2))
    inv_sigma = np.linalg.inv(sigma)
    c3 = x - mu
    c4 = np.dot(c3, inv_sigma)
    c5 = np.zeros(N)
    for d in range(D):
        c5 = c5 + c4[:, d] * c3[:, d]
    p = c1 * c2 * np.exp(-c5 / 2)
    return p
# 리스트 4-5-(3)
X_range0=[-3,3]
X_range1=[-3,3]
# 등고선 표시 --------------------------------
def show_contour_gauss(mu, sig):
    xn = 40 # 등고선 표시 해상도
    x0 = np.linspace(X_range0[0], X_range0[1], xn)
    x1 = np.linspace(X_range1[0], X_range1[1], xn)
    xx0, xx1 = np.meshgrid(x0, x1)
    x = np.c_[np.reshape(xx0, xn * xn, 1), np.reshape(xx1, xn * xn, 1)]
    f = gauss(x, mu, sig)
    f = f.reshape(xn, xn)
    f = f.T
    cont = plt.contour(xx0, xx1, f, 15, colors='k')
    plt.grid(True)
# 3D 표시 ----------------------------------
def show3d_gauss(ax, mu, sig):
    xn = 40 # 등고선 표시 해상도
    x0 = np.linspace(X_range0[0], X_range0[1], xn)
    x1 = np.linspace(X_range1[0], X_range1[1], xn)
    xx0, xx1 = np.meshgrid(x0, x1)
    x = np.c_[np.reshape(xx0, xn * xn, 1), np.reshape(xx1, xn * xn, 1)]
    f = gauss(x, mu, sig)
    f = f.reshape(xn, xn)
    f = f.T
    ax.plot_surface(xx0, xx1, f,
                    rstride=2, cstride=2, alpha=0.3,
                    color='blue', edgecolor='black')
# 메인 -----------------------------------
mu = np.array([1, 0.5]) # (A)
sigma = np.array([[2, 1], [1, 1]]) # (B)
Fig = plt.figure(1, figsize=(7, 3))
Fig.add_subplot(1, 2, 1)
show_contour_gauss(mu, sigma)
plt.xlim(X_range0)
plt.ylim(X_range1)
plt.xlabel('$x_0$', fontsize=14)
plt.ylabel('$x_1$', fontsize=14)
Ax = Fig.add_subplot(1, 2, 2, projection='3d')
show3d_gauss(Ax, mu, sigma)
Ax.set_zticks([0.05, 0.10])
Ax.set_xlabel('$x_0$', fontsize=14)
Ax.set_ylabel('$x_1$', fontsize=14)
Ax.view_init(40, -100)
plt.show()