{"id":1104523,"date":"2025-01-08T16:21:35","date_gmt":"2025-01-08T08:21:35","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1104523.html"},"modified":"2025-01-08T16:21:39","modified_gmt":"2025-01-08T08:21:39","slug":"python%e4%b8%ad%e5%a6%82%e4%bd%95%e5%af%b9%e6%a0%b7%e6%9c%ac%e7%82%b9%e6%95%b0%e6%8d%ae%e8%bf%9b%e8%a1%8c%e6%8b%9f%e5%90%88","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1104523.html","title":{"rendered":"python\u4e2d\u5982\u4f55\u5bf9\u6837\u672c\u70b9\u6570\u636e\u8fdb\u884c\u62df\u5408"},"content":{"rendered":"

\"python\u4e2d\u5982\u4f55\u5bf9\u6837\u672c\u70b9\u6570\u636e\u8fdb\u884c\u62df\u5408\"<\/p>\n

\u5728Python\u4e2d\uff0c\u5bf9\u6837\u672c\u70b9\u6570\u636e\u8fdb\u884c\u62df\u5408\u53ef\u4ee5\u4f7f\u7528\u591a\u79cd\u65b9\u6cd5\uff0c\u5e38\u89c1\u7684\u6709\u4f7f\u7528numpy\u5e93\u7684polyfit\u51fd\u6570\u3001scipy\u5e93\u7684curve_fit\u51fd\u6570\u3001\u4ee5\u53ca\u673a\u5668\u5b66\u4e60<\/a>\u5e93\u5982scikit-learn\u7684\u7ebf\u6027\u56de\u5f52\u7b49\u65b9\u6cd5\u3002<\/strong><\/p>\n<\/p>\n

\u4e00\u3001\u4f7f\u7528numpy\u5e93\u7684polyfit\u51fd\u6570\uff1a<\/p>\n

numpy\u7684polyfit\u51fd\u6570\u53ef\u4ee5\u7528\u4e8e\u591a\u9879\u5f0f\u62df\u5408\uff0c\u9002\u5408\u4e8e\u7b80\u5355\u7684\u6570\u636e\u62df\u5408\u4efb\u52a1\u3002\u591a\u9879\u5f0f\u62df\u5408\u7684\u672c\u8d28\u662f\u627e\u5230\u4e00\u4e2a\u591a\u9879\u5f0f\u51fd\u6570\uff0c\u4f7f\u5176\u5c3d\u53ef\u80fd\u5730\u8d34\u5408\u7ed9\u5b9a\u7684\u6837\u672c\u70b9\u3002<\/p>\n<\/p>\n

import numpy as np<\/p>\n
import matplotlib.pyplot as plt<\/p>\n
\u6837\u672c\u70b9\u6570\u636e<\/strong><\/h2>\n
x = np.array([1, 2, 3, 4, 5])<\/p>\n
y = np.array([1, 4, 9, 16, 25])<\/p>\n
\u62df\u5408\u4e8c\u6b21\u591a\u9879\u5f0f<\/strong><\/h2>\n
coefficients = np.polyfit(x, y, 2)<\/p>\n
polynomial = np.poly1d(coefficients)<\/p>\n
\u7ed8\u5236\u62df\u5408\u66f2\u7ebf<\/strong><\/h2>\n
x_fit = np.linspace(min(x), max(x), 100)<\/p>\n
y_fit = polynomial(x_fit)<\/p>\n
plt.scatter(x, y, label='Sample Points')<\/p>\n
plt.plot(x_fit, y_fit, label='Fitted Polynomial')<\/p>\n
plt.legend()<\/p>\n
plt.show()<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e8c\u3001\u4f7f\u7528scipy\u5e93\u7684curve_fit\u51fd\u6570\uff1a<\/p>\n
scipy\u7684curve_fit\u51fd\u6570\u53ef\u4ee5\u7528\u4e8e\u975e\u7ebf\u6027\u66f2\u7ebf\u62df\u5408\uff0c\u66f4\u52a0\u7075\u6d3b\u548c\u5f3a\u5927\u3002curve_fit\u51fd\u6570\u5141\u8bb8\u7528\u6237\u5b9a\u4e49\u4efb\u4f55\u5f62\u5f0f\u7684\u51fd\u6570\uff0c\u53ea\u8981\u63d0\u4f9b\u5408\u9002\u7684\u521d\u59cb\u53c2\u6570\u5373\u53ef\u3002<\/p>\n<\/p>\n
import numpy as np<\/p>\n
import matplotlib.pyplot as plt<\/p>\n
from scipy.optimize import curve_fit<\/p>\n
\u6837\u672c\u70b9\u6570\u636e<\/strong><\/h2>\n
x = np.array([1, 2, 3, 4, 5])<\/p>\n
y = np.array([1, 4, 9, 16, 25])<\/p>\n
\u5b9a\u4e49\u62df\u5408\u51fd\u6570<\/strong><\/h2>\n
def func(x, a, b, c):<\/p>\n
    return a * x2 + b * x + c<\/p>\n
\u62df\u5408\u53c2\u6570<\/strong><\/h2>\n
params, params_covariance = curve_fit(func, x, y)<\/p>\n
\u7ed8\u5236\u62df\u5408\u66f2\u7ebf<\/strong><\/h2>\n
x_fit = np.linspace(min(x), max(x), 100)<\/p>\n
y_fit = func(x_fit, *params)<\/p>\n
plt.scatter(x, y, label='Sample Points')<\/p>\n
plt.plot(x_fit, y_fit, label='Fitted Curve')<\/p>\n
plt.legend()<\/p>\n
plt.show()<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e09\u3001\u4f7f\u7528scikit-learn\u5e93\u7684\u7ebf\u6027\u56de\u5f52\uff1a<\/p>\n
scikit-learn\u5e93\u63d0\u4f9b\u4e86\u66f4\u52a0\u5168\u9762\u7684\u673a\u5668\u5b66\u4e60\u5de5\u5177\uff0c\u5176\u4e2d\u7684\u7ebf\u6027\u56de\u5f52\u53ef\u4ee5\u7528\u4e8e\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u548c\u591a\u9879\u5f0f\u56de\u5f52\u3002<\/p>\n<\/p>\n
import numpy as np<\/p>\n
import matplotlib.pyplot as plt<\/p>\n
from sklearn.linear_model import LinearRegression<\/p>\n
from sklearn.preprocessing import PolynomialFeatures<\/p>\n
\u6837\u672c\u70b9\u6570\u636e<\/strong><\/h2>\n
x = np.array([1, 2, 3, 4, 5]).reshape(-1, 1)<\/p>\n
y = np.array([1, 4, 9, 16, 25])<\/p>\n
\u591a\u9879\u5f0f\u7279\u5f81\u8f6c\u6362<\/strong><\/h2>\n
poly = PolynomialFeatures(degree=2)<\/p>\n
x_poly = poly.fit_transform(x)<\/p>\n
\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u62df\u5408<\/strong><\/h2>\n
model = LinearRegression()<\/p>\n
model.fit(x_poly, y)<\/p>\n
\u9884\u6d4b<\/strong><\/h2>\n
x_fit = np.linspace(min(x), max(x), 100).reshape(-1, 1)<\/p>\n
x_fit_poly = poly.transform(x_fit)<\/p>\n
y_fit = model.predict(x_fit_poly)<\/p>\n
plt.scatter(x, y, label='Sample Points')<\/p>\n
plt.plot(x_fit, y_fit, label='Fitted Curve')<\/p>\n
plt.legend()<\/p>\n
plt.show()<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u56db\u3001\u4f7f\u7528\u591a\u79cd\u65b9\u6cd5\u8fdb\u884c\u6570\u636e\u62df\u5408\u5bf9\u6bd4\uff1a<\/p>\n
\u4e0d\u540c\u7684\u65b9\u6cd5\u9002\u7528\u4e8e\u4e0d\u540c\u7c7b\u578b\u7684\u62df\u5408\u4efb\u52a1\uff0c\u901a\u8fc7\u5bf9\u6bd4\u4e0d\u540c\u65b9\u6cd5\u7684\u62df\u5408\u6548\u679c\uff0c\u53ef\u4ee5\u9009\u62e9\u6700\u5408\u9002\u7684\u62df\u5408\u65b9\u6cd5\u3002<\/p>\n<\/p>\n
\u4e00\u3001POLYFIT \u51fd\u6570\u7684\u8be6\u7ec6\u4ecb\u7ecd<\/h3>\n<\/p>\n
numpy\u7684polyfit\u51fd\u6570\u662f\u4e00\u79cd\u57fa\u4e8e\u6700\u5c0f\u4e8c\u4e58\u6cd5\u7684\u591a\u9879\u5f0f\u62df\u5408\u65b9\u6cd5\u3002\u5b83\u9002\u7528\u4e8e\u7b80\u5355\u7684\u6570\u636e\u62df\u5408\u4efb\u52a1\uff0c\u5c24\u5176\u662f\u5f53\u6570\u636e\u5448\u73b0\u4e00\u5b9a\u7684\u591a\u9879\u5f0f\u5173\u7cfb\u65f6\u3002polyfit\u51fd\u6570\u7684\u4f7f\u7528\u975e\u5e38\u7b80\u5355\uff0c\u53ea\u9700\u6307\u5b9a\u6837\u672c\u70b9\u6570\u636e\u548c\u591a\u9879\u5f0f\u7684\u9636\u6570\u5373\u53ef\u3002<\/p>\n<\/p>\n
import numpy as np<\/p>\n
import matplotlib.pyplot as plt<\/p>\n
\u6837\u672c\u70b9\u6570\u636e<\/strong><\/h2>\n
x = np.array([1, 2, 3, 4, 5])<\/p>\n
y = np.array([1, 4, 9, 16, 25])<\/p>\n
\u62df\u5408\u4e8c\u6b21\u591a\u9879\u5f0f<\/strong><\/h2>\n
coefficients = np.polyfit(x, y, 2)<\/p>\n
polynomial = np.poly1d(coefficients)<\/p>\n
\u7ed8\u5236\u62df\u5408\u66f2\u7ebf<\/strong><\/h2>\n
x_fit = np.linspace(min(x), max(x), 100)<\/p>\n
y_fit = polynomial(x_fit)<\/p>\n
plt.scatter(x, y, label='Sample Points')<\/p>\n
plt.plot(x_fit, y_fit, label='Fitted Polynomial')<\/p>\n
plt.legend()<\/p>\n
plt.show()<\/p>\n
<\/code><\/pre>\n<\/p>\n
polyfit\u51fd\u6570\u7684\u4f18\u52bf\u5728\u4e8e\u5176\u7b80\u5355\u548c\u9ad8\u6548\uff0c\u9002\u5408\u5904\u7406\u5c0f\u89c4\u6a21\u6570\u636e\u96c6\u3002\u7136\u800c\uff0c\u5f53\u6570\u636e\u91cf\u8f83\u5927\u6216\u6570\u636e\u5173\u7cfb\u590d\u6742\u65f6\uff0cpolyfit\u53ef\u80fd\u65e0\u6cd5\u63d0\u4f9b\u8db3\u591f\u597d\u7684\u62df\u5408\u6548\u679c\u3002<\/p>\n<\/p>\n
\u4e8c\u3001CURVE_FIT \u51fd\u6570\u7684\u8be6\u7ec6\u4ecb\u7ecd<\/h3>\n<\/p>\n
scipy\u7684curve_fit\u51fd\u6570\u662f\u4e00\u79cd\u66f4\u4e3a\u7075\u6d3b\u548c\u5f3a\u5927\u7684\u975e\u7ebf\u6027\u66f2\u7ebf\u62df\u5408\u65b9\u6cd5\u3002curve_fit\u51fd\u6570\u5141\u8bb8\u7528\u6237\u5b9a\u4e49\u4efb\u4f55\u5f62\u5f0f\u7684\u51fd\u6570\uff0c\u53ea\u8981\u63d0\u4f9b\u5408\u9002\u7684\u521d\u59cb\u53c2\u6570\u5373\u53ef\u3002<\/p>\n<\/p>\n
import numpy as np<\/p>\n
import matplotlib.pyplot as plt<\/p>\n
from scipy.optimize import curve_fit<\/p>\n
\u6837\u672c\u70b9\u6570\u636e<\/strong><\/h2>\n
x = np.array([1, 2, 3, 4, 5])<\/p>\n
y = np.array([1, 4, 9, 16, 25])<\/p>\n
\u5b9a\u4e49\u62df\u5408\u51fd\u6570<\/strong><\/h2>\n
def func(x, a, b, c):<\/p>\n
    return a * x2 + b * x + c<\/p>\n
\u62df\u5408\u53c2\u6570<\/strong><\/h2>\n
params, params_covariance = curve_fit(func, x, y)<\/p>\n
\u7ed8\u5236\u62df\u5408\u66f2\u7ebf<\/strong><\/h2>\n
x_fit = np.linspace(min(x), max(x), 100)<\/p>\n
y_fit = func(x_fit, *params)<\/p>\n
plt.scatter(x, y, label='Sample Points')<\/p>\n
plt.plot(x_fit, y_fit, label='Fitted Curve')<\/p>\n
plt.legend()<\/p>\n
plt.show()<\/p>\n
<\/code><\/pre>\n<\/p>\n
curve_fit\u51fd\u6570\u7684\u4f18\u52bf\u5728\u4e8e\u5176\u7075\u6d3b\u6027\uff0c\u80fd\u591f\u5904\u7406\u5404\u79cd\u5f62\u5f0f\u7684\u975e\u7ebf\u6027\u51fd\u6570\u3002\u7136\u800c\uff0ccurve_fit\u51fd\u6570\u5bf9\u521d\u59cb\u53c2\u6570\u8f83\u4e3a\u654f\u611f\uff0c\u53ef\u80fd\u9700\u8981\u8fdb\u884c\u591a\u6b21\u5c1d\u8bd5\u624d\u80fd\u627e\u5230\u5408\u9002\u7684\u62df\u5408\u53c2\u6570\u3002<\/p>\n<\/p>\n
\u4e09\u3001LINEAR REGRESSION \u51fd\u6570\u7684\u8be6\u7ec6\u4ecb\u7ecd<\/h3>\n<\/p>\n
scikit-learn\u7684\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u662f\u4e00\u79cd\u5e7f\u6cdb\u5e94\u7528\u4e8e\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u62df\u5408\u65b9\u6cd5\u3002\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u4e0d\u4ec5\u53ef\u4ee5\u7528\u4e8e\u7b80\u5355\u7ebf\u6027\u56de\u5f52\uff0c\u8fd8\u53ef\u4ee5\u901a\u8fc7\u591a\u9879\u5f0f\u7279\u5f81\u8f6c\u6362\uff0c\u5b9e\u73b0\u591a\u9879\u5f0f\u56de\u5f52\u3002<\/p>\n<\/p>\n
import numpy as np<\/p>\n
import matplotlib.pyplot as plt<\/p>\n
from sklearn.linear_model import LinearRegression<\/p>\n
from sklearn.preprocessing import PolynomialFeatures<\/p>\n
\u6837\u672c\u70b9\u6570\u636e<\/strong><\/h2>\n
x = np.array([1, 2, 3, 4, 5]).reshape(-1, 1)<\/p>\n
y = np.array([1, 4, 9, 16, 25])<\/p>\n
\u591a\u9879\u5f0f\u7279\u5f81\u8f6c\u6362<\/strong><\/h2>\n
poly = PolynomialFeatures(degree=2)<\/p>\n
x_poly = poly.fit_transform(x)<\/p>\n
\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u62df\u5408<\/strong><\/h2>\n
model = LinearRegression()<\/p>\n
model.fit(x_poly, y)<\/p>\n
\u9884\u6d4b<\/strong><\/h2>\n
x_fit = np.linspace(min(x), max(x), 100).reshape(-1, 1)<\/p>\n
x_fit_poly = poly.transform(x_fit)<\/p>\n
y_fit = model.predict(x_fit_poly)<\/p>\n
plt.scatter(x, y, label='Sample Points')<\/p>\n
plt.plot(x_fit, y_fit, label='Fitted Curve')<\/p>\n
plt.legend()<\/p>\n
plt.show()<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u7684\u4f18\u52bf\u5728\u4e8e\u5176\u5e7f\u6cdb\u7684\u5e94\u7528\u548c\u7a33\u5b9a\u6027\uff0c\u9002\u5408\u5904\u7406\u5927\u89c4\u6a21\u6570\u636e\u96c6\u3002\u7136\u800c\uff0c\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u5728\u5904\u7406\u9ad8\u5ea6\u975e\u7ebf\u6027\u6570\u636e\u65f6\uff0c\u53ef\u80fd\u9700\u8981\u8fdb\u884c\u590d\u6742\u7684\u7279\u5f81\u5de5\u7a0b\u3002<\/p>\n<\/p>\n
\u56db\u3001\u591a\u79cd\u65b9\u6cd5\u7684\u5bf9\u6bd4\u548c\u9009\u62e9<\/h3>\n<\/p>\n
\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u4e0d\u540c\u7684\u65b9\u6cd5\u9002\u7528\u4e8e\u4e0d\u540c\u7684\u62df\u5408\u4efb\u52a1\u3002polyfit\u51fd\u6570\u9002\u5408\u7b80\u5355\u7684\u591a\u9879\u5f0f\u62df\u5408\u4efb\u52a1\uff0ccurve_fit\u51fd\u6570\u9002\u5408\u590d\u6742\u7684\u975e\u7ebf\u6027\u66f2\u7ebf\u62df\u5408\u4efb\u52a1\uff0c\u800c\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u5219\u9002\u5408\u5e7f\u6cdb\u7684\u673a\u5668\u5b66\u4e60\u5e94\u7528\u3002\u901a\u8fc7\u5bf9\u6bd4\u4e0d\u540c\u65b9\u6cd5\u7684\u62df\u5408\u6548\u679c\uff0c\u53ef\u4ee5\u9009\u62e9\u6700\u5408\u9002\u7684\u62df\u5408\u65b9\u6cd5\u3002<\/p>\n<\/p>\n
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