Python曲线拟合多项式深入详解

import numpy as np
import matplotlib.pyplot as plt
np.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()

import numpy as np
import matplotlib.pyplot as plt
np.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) + 5
func = 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()

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 + b
def Hyperb(x, a1, a2, qi):
    y = qi / np.power(1 + a1 * a2 * x, 1 / a2)
    return y
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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()

import numpy as np
from scipy.interpolate import interp1d
import matplotlib.pyplot as plt
xdata=[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, 2.5415445, 2.5601173, 2.5786901, 2.597263, 2.6158358, 2.6344086, 2.6529814, 2.6715543, 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# 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()