各图形的画图

程序员文章站 2022-03-13 10:54:16

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1.绘制正态分布概率密度函数

mpl.rcParams['font.sans-serif'] = [u'SimHei']  #FangSong/黑体 FangSong/KaiTi
    mpl.rcParams['axes.unicode_minus'] = False
    mu = 0
    sigma = 1
    x = np.linspace(mu - 3 * sigma, mu + 3 * sigma, 51)
    y = np.exp(-(x - mu) ** 2 / (2 * sigma ** 2)) / (math.sqrt(2 * math.pi) * sigma)
    print(x.shape)
    print('x = \n', x)
    print(y.shape)
    print('y = \n', y)
    plt.figure(facecolor='w')
    plt.plot(x, y, 'ro-', linewidth=2)
    # plt.plot(x, y, 'r-', x, y, 'go', linewidth=2, markersize=8)
    plt.xlabel('X', fontsize=15)
    plt.ylabel('Y', fontsize=15)
    plt.title(u'高斯分布函数', fontsize=18)    #
    plt.grid(True)
    plt.show()

2.损失函数：Logistic损失(-1,1)/SVM Hinge损失/ 0/1损失

    plt.figure(figsize=(10,8))
    x = np.linspace(start=-2, stop=3, num=1001, dtype=np.float)
    y_logit = np.log(1 + np.exp(-x)) / math.log(2)
    y_boost = np.exp(-x)
    y_01 = x < 0
    y_hinge = 1.0 - x
    y_hinge[y_hinge < 0] = 0
    plt.plot(x, y_logit, 'r-', label='Logistic Loss', linewidth=2)
    plt.plot(x, y_01, 'g-', label='0/1 Loss', linewidth=2)
    plt.plot(x, y_hinge, 'b-', label='Hinge Loss', linewidth=2)
    plt.plot(x, y_boost, 'm--', label='Adaboost Loss', linewidth=2)
    plt.grid()
    plt.legend(loc='upper right')
    plt.savefig('1.png')
    plt.show()

3.x^x

 plt.figure(facecolor='w')
    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()

4.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), facecolor='w')
    plt.plot(y, x, 'r-', linewidth=2)
    plt.grid(True)
    plt.title(u'胸型线', fontsize=20)
    # plt.savefig('breast.png')
    plt.show()

5.心形线

    t = np.linspace(0, 2*np.pi, 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()

6.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()

7.Bar

    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()

8.均匀分布

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

9.验证中心极限定理

    t = 1000
    a = np.zeros(10000)
    for i in range(t):
        a += np.random.uniform(-5, 5, 10000)
    a /= t
    plt.hist(a, bins=30, color='g', alpha=0.5, normed=True, label=u'均匀分布叠加')
    plt.legend(loc='upper left')
    plt.grid()
    plt.show()

10.其他分布的中心极限定理

 lamda = 7
    p = stats.poisson(lamda)
    y = p.rvs(size=1000)
    mx = 30
    r = (0, mx)
    bins = r[1] - r[0]
    plt.figure(figsize=(15, 8), facecolor='w')
    plt.subplot(121)
    plt.hist(y, bins=bins, range=r, color='g', alpha=0.8, normed=True)
    t = np.arange(0, mx+1)
    plt.plot(t, p.pmf(t), 'ro-', lw=2)
    plt.grid(True)

    N = 1000
    M = 10000
    plt.subplot(122)
    a = np.zeros(M, dtype=np.float)
    p = stats.poisson(lamda)
    for i in np.arange(N):
        a += p.rvs(size=M)
    a /= N
    plt.hist(a, bins=20, color='g', alpha=0.8, normed=True)
    plt.grid(b=True)
    plt.show()

11.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())

12.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='#FFFFA0')
    x = h[1]
    y = norm.pdf(x, loc=mu, scale=sigma)
    plt.plot(x, y, 'r-', x, y, 'ro', linewidth=2, markersize=4)
    plt.grid()
    plt.show()

13.插值

    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 = sp.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()

14.Poisson分布

    size = 1000
    lamda = 5
    p = np.random.poisson(lam=lamda, size=size)
    plt.figure()
    plt.hist(p, bins=range(3 * lamda), histtype='bar', align='left', color='r', rwidth=0.8, normed=True)
    plt.grid(b=True, ls=':')
    # plt.xticks(range(0, 15, 2))
    plt.title('Numpy.random.poisson', fontsize=13)

    plt.figure()
    r = stats.poisson(mu=lamda)
    p = r.rvs(size=size)
    plt.hist(p, bins=range(3 * lamda), color='r', align='left', rwidth=0.8, normed=True)
    plt.grid(b=True, ls=':')
    plt.title('scipy.stats.poisson', fontsize=13)
    plt.show()

15.绘制三维图像

    x, y = np.mgrid[-3:3:7j, -3:3:7j]
    print(x)
    print(y)
    u = np.linspace(-3, 3, 101)
    x, y = np.meshgrid(u, u)
    print(x)
    print(y)
    z = x*y*np.exp(-(x**2 + y**2)/2) / math.sqrt(2*math.pi)
    # z = x*y*np.exp(-(x**2 + y**2)/2) / math.sqrt(2*math.pi)
    fig = plt.figure()
    ax = fig.add_subplot(111, projection='3d')
    # ax.plot_surface(x, y, z, rstride=5, cstride=5, cmap=cm.coolwarm, linewidth=0.1)  #
    ax.plot_surface(x, y, z, rstride=3, cstride=3, cmap=cm.gist_heat, linewidth=0.5)
    plt.show()
    # cmaps = [('Perceptually Uniform Sequential',
    #           ['viridis', 'inferno', 'plasma', 'magma']),
    #          ('Sequential', ['Blues', 'BuGn', 'BuPu',
    #                          'GnBu', 'Greens', 'Greys', 'Oranges', 'OrRd',
    #                          'PuBu', 'PuBuGn', 'PuRd', 'Purples', 'RdPu',
    #                          'Reds', 'YlGn', 'YlGnBu', 'YlOrBr', 'YlOrRd']),
    #          ('Sequential (2)', ['afmhot', 'autumn', 'bone', 'cool',
    #                              'copper', 'gist_heat', 'gray', 'hot',
    #                              'pink', 'spring', 'summer', 'winter']),
    #          ('Diverging', ['BrBG', 'bwr', 'coolwarm', 'PiYG', 'PRGn', 'PuOr',
    #                         'RdBu', 'RdGy', 'RdYlBu', 'RdYlGn', 'Spectral',
    #                         'seismic']),
    #          ('Qualitative', ['Accent', 'Dark2', 'Paired', 'Pastel1',
    #                           'Pastel2', 'Set1', 'Set2', 'Set3']),
    #          ('Miscellaneous', ['gist_earth', 'terrain', 'ocean', 'gist_stern',
    #                             'brg', 'CMRmap', 'cubehelix',
    #                             'gnuplot', 'gnuplot2', 'gist_ncar',
    #                             'nipy_spectral', 'jet', 'rainbow',
    #                             'gist_rainbow', 'hsv', 'flag', 'prism'])]

16.scripy线性回归1

 x = np.linspace(-2, 2, 50)
    A, B, C = 2, 3, -1
    y = (A * x ** 2 + B * x + C) + np.random.rand(len(x))*0.75

    t = leastsq(residual, [0, 0, 0], args=(x, y))
    theta = t[0]
    print('真实值：', A, B, C)
    print('预测值：', theta)
    y_hat = theta[0] * x ** 2 + theta[1] * x + theta[2]
    plt.plot(x, y, 'r-', linewidth=2, label=u'Actual')
    plt.plot(x, y_hat, 'g-', linewidth=2, label=u'Predict')
    plt.legend(loc='upper left')
    plt.grid()
    plt.show()

17.scripy线性回归例2

 x = np.linspace(0, 5, 100)
    a = 5
    w = 1.5
    phi = -2
    y = a * np.sin(w*x) + phi + np.random.rand(len(x))*0.5

    t = leastsq(residual2, [3, 5, 1], args=(x, y))
    theta = t[0]
    print('真实值：', a, w, phi)
    print('预测值：', theta)
    y_hat = theta[0] * np.sin(theta[1] * x) + theta[2]
    plt.plot(x, y, 'r-', linewidth=2, label='Actual')
    plt.plot(x, y_hat, 'g-', linewidth=2, label='Predict')
    plt.legend(loc='lower left')
    plt.grid()
    plt.show()

18.使用scipy计算函数极值

 # a = opt.fmin(f, 1)
    # b = opt.fmin_cg(f, 1)
    # c = opt.fmin_bfgs(f, 1)
    # print(a, 1/a, math.e)
    # print(b)
    # print(c)

    # marker    description
    # ”.”   point
    # ”,”   pixel
    # “o”   circle
    # “v”   triangle_down
    # “^”   triangle_up
    # “<”   triangle_left
    # “>”   triangle_right
    # “1”   tri_down
    # “2”   tri_up
    # “3”   tri_left
    # “4”   tri_right
    # “8”   octagon
    # “s”   square
    # “p”   pentagon
    # “*”   star
    # “h”   hexagon1
    # “H”   hexagon2
    # “+”   plus
    # “x”   x
    # “D”   diamond
    # “d”   thin_diamond
    # “|”   vline
    # “_”   hline
    # TICKLEFT  tickleft
    # TICKRIGHT tickright
    # TICKUP    tickup
    # TICKDOWN  tickdown
    # CARETLEFT caretleft
    # CARETRIGHT    caretright
    # CARETUP   caretup
    # CARETDOWN caretdown

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