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qile11
V2EX  ›  Python

Python 做拟合后如何让折线变为平滑曲线,用 1d 插值拟合后曲率变大

  •  
  •   qile11 · 2018-06-30 14:03:23 +08:00 · 7243 次点击
    这是一个创建于 2337 天前的主题,其中的信息可能已经有所发展或是发生改变。

    代码如下

    import matplotlib.pyplot as plt
    import numpy as np
    
    x = [1,5,30,200]
    y = [27,12,7,5]
    x = np.array(x)
    y = np.array(y)
    # x = np.arange(1, 17, 1)
    # y = np.array([4.00, 6.40, 8.00, 8.80, 9.22, 9.50, 9.70, 9.86, 10.00, 10.20, 10.32, 10.42, 10.50, 10.55, 10.58, 10.60])
    z1 = np.polyfit(x, y, 3)#用 3 次多项式拟合
    p1 = np.poly1d(z1)
    print(p1) #在屏幕上打印拟合多项式
    yvals=p1(x)#也可以使用 yvals=np.polyval(z1,x)
    plot1=plt.plot(x, y, '*',label='original values')
    plot2=plt.plot(x, yvals, 'r',label='polyfit values')
    plt.xlabel('x axis')
    plt.ylabel('y axis')
    plt.legend(loc=1)#指定 legend 的位置,读者可以自己 help 它的用法
    plt.title('polyfitting')
    plt.show()
    

    使用插值拟合后,产生一个波峰一个波谷,我只想要个平滑的曲线,不知道有啥好办法

    fq1 = interp1d(x, y1, kind='quadratic')
    fq2 = interp1d(x, y2, kind='zero')
    

    下面代码是一个粘度曲线测试程序,请参考程序运行结果

    
    import numpy as np
    from scipy.interpolate import interp1d
    
    
    #创建待插值的数据
    # x = np.linspace(0, 10*np.pi, 20)
    # y = np.cos(x)
    x = [1,5,30,200]
    # x = [1,100,150,200]
    y = [27,12,7,5]
    x = np.array(x)
    y = np.array([27,12,7,5])
    
    
    # 分别用 linear 和 quadratic 插值
    fl = interp1d(x, y, kind='linear')
    fq = interp1d(x, y, kind='quadratic')
    
    #设置 x 的最大值和最小值以防止插值数据越界
    xint = np.linspace(x.max(), x.min(), 200)
    y1 = np.array([21.350,11,6.62,5.05])
    y2 = np.array([15.630,8.31,5.18,3.53])
    # x1 = np.array([50,150,200])
    # xint1 = np.linspace(x1.min(), x1.max(), 110)
    yintl = fl(xint)
    yintq = fq(xint)
    fq1 = interp1d(x, y1, kind='quadratic')
    fq2 = interp1d(x, y2, kind='zero')
    import pylab as pl
    
    fig, ax = pl.subplots()
    
    # make ticks and tick labels
    # xticks = range(min(x), max(x) + 1, 3)
    
    # xticks = range(1, 200 + 50,30)
    xticklabels = [1,3,10,"",30,100,200]
    # #设置网格样式
    # ax.set_xticks(xticks)
    ax.set_xticklabels(xticklabels, rotation=0)
    ax.grid(True, linestyle='-.',color="b")
    yfq2=fq2(xint)
    yfq1=fq1(xint)
    # pl.plot(xint,fl(xint), color="green", label = "Linear")
    pl.plot(xint,fq(xint), color="red", label ="Quadratic")
    pl.plot(xint,yfq1, "b--", label ="QuadraticL")
    pl.plot(xint,yfq2, color="green", label ="QuadraticH")
    x3= np.array([1,5,30,200])
    y3 = np.array([27,12,7,5])
    pl.plot(x3,y3,"b-", label ="QuadraticZ")
    pl.legend(loc = "best")
    
    
    pl.ylim(1,50,10)
    pl.xlim(0,200,70)
    pl.show()
    
    4 条回复    2018-07-03 21:51:45 +08:00
    qile1
        1
    qile1  
       2018-07-01 21:57:03 +08:00 via Android
    没人知道?写个函数计算是不是可以实现
    daya0576
        2
    daya0576  
       2018-07-02 01:40:27 +08:00
    ```python
    import matplotlib.pyplot as plt
    import numpy as np

    x = np.array([1,5,30,200])
    y = np.array([27,12,7,5])
    plot1=plt.plot(x, y, 'x',label='original values')

    # calculate polynomial
    z = np.polyfit(x, y, 2)
    f = np.poly1d(z)
    x_new = np.linspace(x[0], x[-1], 200)
    y_new = f(x_new)
    plot2=plt.plot(x_new, y_new, 'r',label='polyfit values')

    plt.show()
    ```
    都拿到 3 元函数了, 那就是画图的问题, 多取几个点就好了.
    ---
    但是拟合的曲线会有 overfitting 的问题, 不知道怎么解决.
    ![]( http://p24a7yp7l.bkt.clouddn.com/dd345a805f1425d17d29aea471690113.png)
    qile11
        4
    qile11  
    OP
       2018-07-03 21:51:45 +08:00
    @daya0576
    @Ballacuda
    感谢回复,可能我方向不对,我画的是黏度曲线,不可能出现负数,上面画出来的都有负数,
    [![PE2kbF.md.png]( https://s1.ax1x.com/2018/07/03/PE2kbF.md.png)]( https://imgchr.com/i/PE2kbF)
    [img]https://s1.ax1x.com/2018/07/03/PE2kbF.png[/img]
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