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import mathimport numpy as npimport matplotlib.pyplot as pltif 1:    def generx2(sta, end, num): # 生成y=x^2的测试集        # 随机干扰因子        sampleNo = num        mu = 0.01        sigma = 0.1        np.random.seed(0)        s = np.random.normal(mu, sigma, sampleNo)        X = np.linspace(sta, end, num)  # 在返回（-1, 1）范围内的等差序列        Y = X * X + s        x = X.reshape(-1, 1)        y = Y.reshape(-1, 1)        return x, y    def generx3(sta, end, num): # 生成y=x^3的测试集        # 随机干扰因子        sampleNo = num        mu = 0.01        sigma = 0.1        np.random.seed(0)        s = np.random.normal(mu, sigma, sampleNo)        X = np.linspace(sta, end, num)  # 在返回（-1, 1）范围内的等差序列        Y = X * X * X + s        x = X.reshape(-1, 1)        y = Y.reshape(-1, 1)        return x, y    def polyfunc(x, dim):  # 多项式作为基函数的线性模型        px = []        for i in x:            cell = []            for j in range(dim):  # 基函数 y = [1, x, x^2, x^3 ... , x^9]                cell.append(i[0] ** j)            px.append(cell)        px = np.matrix(px)        print('px shape:', np.shape(px))        return px    def trigofunc(x, dim):  # 三角函数作为基函数的线性模型        px = []        for i in x:            cell = []            for j in range(dim):  # 基函数 y = [1, x, x^2, x^3 ... , x^9]                if j == 0:                    cell.append(1)                else:                    ers = j >> 1                    cou = j & 0x1                    if cou == 0:                        res = math.sin(ers * i[0])                    else:                        res = math.cos(ers * i[0])                    cell.append(res)            px.append(cell)        px = np.matrix(px)        print('px shape:', np.shape(px))        return px    def corefunc(x):    # 高斯核模型        h = 1        temp = 2 * h * h        Kx = []        for i in x:            cell = 0            for j in x:                cell = cell + (i - j) ** 2            cell = cell ** 0.5            cell = np.exp(- (cell / temp))            Kx.append(cell)        Kx = np.matrix(Kx)        print('Kx shape:', np.shape(Kx))        return Kx    def linear_model_test(i, dim):  #线性模型        x, y = generx2(-1, 1, 400)        plt.plot(x, y)        px = trigofunc(x, dim)        pfunc = y.T * np.linalg.pinv(px).T        # 生成测试集        tx, ty = generx2(-1.5, 1.5, 2000)        tempx = trigofunc(tx, dim)        predict = pfunc * tempx.T        plt.plot(tx, predict.T, label=str(i))    def core_model_test():  # 核模型        x, y = generx2(-1, 1, 400)        print(x.shape, y.shape)        plt.plot(x, y)        px = corefunc(x)        pfunc = y * np.linalg.pinv(px)        # 生成测试集        tx, ty = generx2(-1, 1, 400)        tempx = corefunc(tx)        predict = pfunc * tempx        plt.plot(tx, predict)if __name__ == '__main__':    for i in range(10):        linear_model_test(i, i)    plt.legend()    plt.show()

y = x ^ 2 在不同多项式基函数维度下的曲线