Python曲线拟合(polyfit , curve_fit, interp1d插值)

python 拟合回归 2023-09-15 11:09:45 575人浏览薄情痞子

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摘要

文章目录 np.polyfit 多项式拟合例1例2 curve_fit () 自定义函数拟合scipy.interpolate.interpnd 插值拟合References

文章目录

np.polyfit 多项式拟合

在python中，Numpy.polyfit()是一个在多项式函数内拟合数据的方法。当最小二乘法的拟合条件很差时，polyfit会发出RankWarning。

对散点进行多项式拟合并打印出拟合函数以及拟合后的图形程序如下

例1

在这个程序中，首先，导入matplotlib和numpy库。设置x、y、p和t的值。然后，使用这个x、y、p和t的值，通过拟合绘制多项式。

import numpy as npimport matplotlib.pyplot as pltnp.random.seed(46)x = np.linspace(0, 1, 25)y = np.cos(x) + 0.3 * np.random.rand(25)p = np.poly1d(np.polyfit(x, y, 4))t = np.linspace(0, 1, 250)plt.plot(x, y, 'o', t, p(t), '-')plt.show()

例2

在这个程序中，也是如此，首先，导入matplotlib和numpy库。设置x和y的值。然后，计算多项式并设置x和y的新值。一旦完成，使用函数polyfit()拟合多项式。

import numpy as npimport matplotlib.pyplot as pltnp.random.seed(12)x = np.linspace(-20, 20, 10)y = 3.6 * pow(x, 3) + 8.3 * pow(x, 2) + 5.1 * pow(x, 1) + 5func = np.polyfit(x, y, 4)xn = np.linspace(-20, 20, 1000)yn = np.poly1d(func)plt.plot(xn, yn(xn), x, y, 'o')plt.show()

curve_fit () 自定义函数拟合

能拟合的函数不止下面这些，只要你写出想要使用的函数的表达式，就可以得到函数的参数！！！

import numpy as np  # NumPy https://numpy.org/import matplotlib.pyplot as plt  # Matplotlib Https://matplotlib.org/from scipy.optimize import curve_fit  # https://www.scipy.org/# 三次 - 跟前面所说的poly_fit一个意思def func_poly_3(x, a, b, c , d):    return a*x*x*x + b*x*x + c*x + d# 幂函数def func_power(x, a, b):    return x**a + b# 指数函数def func_exp(x, a, b):    return a**x + bdef Hyperb(x, a1, a2, qi):    y = qi / np.power(1 + a1 * a2 * x, 1 / a2)    return yxdata=[1.0, 1.0185728, 1.0371457, 1.0557185, 1.0742913, 1.0928641, 1.111437, 1.1300098, 1.1485826, 1.1671554, 1.1857283, 1.2043011, 1.2228739, 1.2414467, 1.2600196, 1.2785924, 1.2971652, 1.315738, 1.3343109, 1.3528837, 1.3714565, 1.3900293, 1.4086022, 1.427175, 1.4457478, 1.4643206, 1.4828935, 1.5014663, 1.5200391, 1.5386119, 1.5571848, 1.5757576, 1.5943304, 1.6129032, 1.6314761, 1.6500489, 1.6686217, 1.6871945, 1.7057674, 1.7243402, 1.742913, 1.7614858, 1.7800587, 1.7986315, 1.8172043, 1.8357771, 1.85435, 1.8729228, 1.8914956, 1.9100684, 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-1.923807, -1.9478237, -1.9720384, -1.996452, -2.0210651, -2.0458786, -2.0708932, -2.0961095, -2.1215284, -2.1471505, -2.1729764, -2.199007, -2.2252427, -2.2516843, -2.2783324, -2.3051877, -2.3322506, -2.3595217, -2.3870017, -2.414691, -2.4425902, -2.4706997, -2.4990201, -2.5275517, -2.5562949, -2.5852503, -2.6144181, -2.6437987, -2.6733924, -2.7031995, -2.7332203, -2.7634549, -2.7939036, -2.8245666, -2.8554439, -2.8865356, -2.9178419, -2.9493627, -2.981098, -3.0130477]popt, pcov = curve_fit(func_poly_3, xdata, ydata, method='lm',maxfev = 8866)plot1 = plt.plot(np.array(xdata), ydata, 'r*', label='original values')plot2 = plt.plot(np.array(xdata), [func_poly_3(i, *popt) for i in xdata], 'b', label='curvefit values')plt.show()

scipy.interpolate.interpnd 插值拟合

前两种都限于你得提前知道待拟合的是什么函数, 可不可以通过大量的点插值得到函数呢?

Python的scipy.interpolate模块有一维插值函数interp1d，二维插值函数interp2d，多维插值函数interpnd.

在此只对一维插值做演示.

import numpy as npfrom scipy.interpolate import interp1dimport matplotlib.pyplot as pltxdata=[1.0, 1.0185728, 1.0371457, 1.0557185, 1.0742913, 1.0928641, 1.111437, 1.1300098, 1.1485826, 1.1671554, 1.1857283, 1.2043011, 1.2228739, 1.2414467, 1.2600196, 1.2785924, 1.2971652, 1.315738, 1.3343109, 1.3528837, 1.3714565, 1.3900293, 1.4086022, 1.427175, 1.4457478, 1.4643206, 1.4828935, 1.5014663, 1.5200391, 1.5386119, 1.5571848, 1.5757576, 1.5943304, 1.6129032, 1.6314761, 1.6500489, 1.6686217, 1.6871945, 1.7057674, 1.7243402, 1.742913, 1.7614858, 1.7800587, 1.7986315, 1.8172043, 1.8357771, 1.85435, 1.8729228, 1.8914956, 1.9100684, 1.9286413, 1.9472141, 1.9657869, 1.9843597, 2.0029326, 2.0215054, 2.0400782, 2.058651, 2.0772239, 2.0957967, 2.1143695, 2.1329423, 2.1515152, 2.170088, 2.1886608, 2.2072336, 2.2258065, 2.2443793, 2.2629521, 2.2815249, 2.3000978, 2.3186706, 2.3372434, 2.3558162, 2.3743891, 2.3929619, 2.4115347, 2.4301075, 2.4486804, 2.4672532, 2.485826, 2.5043988, 2.5229717, 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-10.202608, -10.231554, -10.260545, -10.289581, -10.318663, -10.34779, -10.376963, -10.40618, -10.435443, -10.464751, -10.494104, -10.523502, -10.552944, -10.582431, -10.611963, -10.641539, -10.671159, -10.700824, -10.730533, -10.760285, -10.790082, -10.819922, -10.849805, -10.879733, -10.909703, -10.939716, -10.969773, -10.999872, -11.030014, -11.060198, -11.090425, -11.120694, -11.151005, -11.181357, -11.211751, -11.242187, -11.272663, -11.303181, -11.333739, -11.364338, -11.394978, -11.425657, -11.456377, -11.487136, -11.517934, -11.548772, -11.579648, -11.610563, -11.641517, -11.672509, -11.703538, -11.734605, -11.76571, -11.796851, -11.82803, -11.859244, -11.890495, -11.921781, -11.953103, -11.98446, -12.015852, -12.047278, -12.078738, -12.110232, -12.14176]# method: 插值方法: 可选 {‘linear’, ‘nearest’, ‘cubic’} 之一# ‘linear’: 分段线性, ‘nearest’: 最近邻点, ‘cubic’: 三次样条（cubic spline）插值func = interp1d(xdata, ydata, kind='cubic')x_new = np.linspace(start=min(xdata), stop=max(xdata), num=10)y_new = func(x_new)plot1 = plt.plot(xdata, ydata, 'r', label='original values')plt.scatter(x_new, y_new)  # 此时即为平滑曲线plt.show()