X**X、胸型线、心型线、均匀分布、中心极限定理，泊松分布，直方图

x**x

# x ** x        x > 0
# (-x) ** (-x)  x < 0
def f(x):
    y = np.ones_like(x)
    i = x > 0
    y[i] = np.power(x[i], x[i])
    i = x < 0
    y[i] = np.power(-x[i], -x[i])
    return y

 x = np.linspace(-1.3, 1.3, 101)
 y = f(x)
 plt.plot(x, y, 'g-', label='x^x', linewidth=2)
 plt.grid()
 plt.legend(loc='upper left')
 plt.show()

胸型线：

    x = np.arange(1, 0, -0.001)
    y = (-3 * x * np.log(x) + np.exp(-(40 * (x - 1 / np.e)) ** 4) / 25) / 2
    plt.figure(figsize=(5,7))
    plt.plot(y, x, 'r-', linewidth=2)
    plt.grid(True)
    plt.show()

心型线

    t = np.linspace(0, 7, 100)
    x = 16 * np.sin(t) ** 3
    y = 13 * np.cos(t) - 5 * np.cos(2*t) - 2 * np.cos(3*t) - np.cos(4*t)
    plt.plot(x, y, 'r-', linewidth=2)
    plt.grid(True)
    plt.show()

渐开线

    t = np.linspace(0, 50, num=1000)
    x = t*np.sin(t) + np.cos(t)
    y = np.sin(t) - t*np.cos(t)
    plt.plot(x, y, 'r-', linewidth=2)
    plt.grid()
    plt.show()

Bar

    matplotlib.rcParams['font.sans-serif'] = [u'SimHei']  #黑体 
    FangSong/KaiTi
    matplotlib.rcParams['axes.unicode_minus'] = False
    x = np.arange(0, 10, 0.1)
    y = np.sin(x)
    plt.bar(x, y, width=0.04, linewidth=0.2)
    plt.plot(x, y, 'r--', linewidth=2)
    plt.title(u'Sin曲线')
    plt.xticks(rotation=-60)
    plt.xlabel('X')
    plt.ylabel('Y')
    plt.grid()
    plt.show()

均匀分布

    x = np.random.rand(10000)
    t = np.arange(len(x))
    plt.hist(x, 30, color='m', alpha=0.5)
    # plt.plot(t, x, 'r-', label=u'均匀分布')
    plt.legend(loc='upper left')
    plt.grid()
    plt.show()

验证中心极限定理

    t = 10000
    a = np.zeros(1000)
    for i in range(t):
    　　a += np.random.uniform(-5, 5, 1000)
    a /= t
    plt.hist(a, bins=30, color='g', alpha=0.5, normed=True)
    plt.grid()
    plt.show()

Poisson分布

    x = np.random.poisson(lam=5, size=10000)
    print x
    pillar = 15
    a = plt.hist(x, bins=pillar, normed=True, range=[0, pillar], color='g', alpha=0.5)
    plt.grid()
    # plt.show()
    print a
    print a[0].sum()

直方图的使用

    mu = 2
    sigma = 3
    data = mu + sigma * np.random.randn(1000)
    h = plt.hist(data, 30, normed=1, color='#a0a0ff')
    x = h[1]
    y = norm.pdf(x, loc=mu, scale=sigma)　　#概率密度函数
    plt.plot(x, y, 'r--', x, y, 'ro', linewidth=2, markersize=4)
    plt.grid()
    plt.show()

差值

    rv = poisson(5)
    x1 = a[1]
    y1 = rv.pmf(x1)
    itp = BarycentricInterpolator(x1, y1)  # 重心插值
    x2 = np.linspace(x.min(), x.max(), 50)
    y2 = itp(x2)
    cs = scipy.interpolate.CubicSpline(x1, y1)       # 三次样条插值
    plt.plot(x2, cs(x2), 'm--', linewidth=5, label='CubicSpine')           # 三次样条插值
    plt.plot(x2, y2, 'g-', linewidth=3, label='BarycentricInterpolator')   # 重心插值
    plt.plot(x1, y1, 'r-', linewidth=1, label='Actural Value')             # 原始值
    plt.legend(loc='upper right')
    plt.grid()
    plt.show()