{"id":1011746,"date":"2024-12-27T11:32:43","date_gmt":"2024-12-27T03:32:43","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1011746.html"},"modified":"2024-12-27T11:32:45","modified_gmt":"2024-12-27T03:32:45","slug":"python%e5%a6%82%e4%bd%95%e7%94%a8%e5%87%bd%e6%95%b0%e6%b1%82%e6%a0%b9","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1011746.html","title":{"rendered":"Python\u5982\u4f55\u7528\u51fd\u6570\u6c42\u6839"},"content":{"rendered":"

\"Python\u5982\u4f55\u7528\u51fd\u6570\u6c42\u6839\"<\/p>\n

\u5f00\u5934\u6bb5\u843d\uff1a
Python\u4e2d\u53ef\u4ee5\u4f7f\u7528\u591a\u79cd\u65b9\u6cd5\u6765\u6c42\u89e3\u65b9\u7a0b\u7684\u6839\uff0c\u4f8b\u5982\u4f7f\u7528\u5185\u7f6e\u5e93scipy.optimize\u4e2d\u7684fsolve\u51fd\u6570\u3001\u4f7f\u7528numpy\u5e93\u4e2d\u7684roots\u51fd\u6570\u3001\u4ee5\u53ca\u7f16\u5199\u81ea\u5b9a\u4e49\u7684\u725b\u987f\u8fed\u4ee3\u6cd5\u6216\u4e8c\u5206\u6cd5\u7b49\u3002<\/strong> \u5176\u4e2d\uff0cscipy.optimize\u5e93\u4e2d\u7684fsolve\u51fd\u6570\u662f\u4e00\u4e2a\u5f3a\u5927\u7684\u5de5\u5177\uff0c\u5b83\u80fd\u591f\u6c42\u89e3\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u6839\u3002fsolve\u51fd\u6570\u901a\u8fc7\u6570\u503c\u65b9\u6cd5\u6765\u903c\u8fd1\u65b9\u7a0b\u7684\u89e3\uff0c\u9002\u7528\u4e8e\u591a\u79cd\u590d\u6742\u7684\u65b9\u7a0b\u60c5\u51b5\u3002\u4f7f\u7528fsolve\u51fd\u6570\u65f6\uff0c\u7528\u6237\u9700\u8981\u63d0\u4f9b\u4e00\u4e2a\u521d\u59cb\u731c\u6d4b\u503c\uff0c\u51fd\u6570\u4f1a\u5728\u6b64\u57fa\u7840\u4e0a\u8fdb\u884c\u8fed\u4ee3\u8ba1\u7b97\uff0c\u76f4\u5230\u627e\u5230\u65b9\u7a0b\u7684\u6839\u6216\u8fbe\u5230\u5141\u8bb8\u7684\u8bef\u5dee\u8303\u56f4\u3002\u63a5\u4e0b\u6765\uff0c\u6211\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528fsolve\u51fd\u6570\u6765\u6c42\u89e3\u65b9\u7a0b\u7684\u6839\u3002<\/p>\n<\/p>\n

\u6b63\u6587\uff1a<\/p>\n<\/p>\n

\u4e00\u3001SCIPY.OPTIMIZE\u4e2d\u7684FSOLVE\u51fd\u6570<\/p>\n<\/p>\n

Scipy\u5e93\u662fPython\u4e2d\u4e00\u4e2a\u5f3a\u5927\u7684\u79d1\u5b66\u8ba1\u7b97\u5de5\u5177\u5305\uff0c\u5176\u4e2d\u7684optimize\u6a21\u5757\u63d0\u4f9b\u4e86\u591a\u79cd\u7528\u4e8e\u6c42\u89e3\u65b9\u7a0b\u7684\u6570\u503c\u65b9\u6cd5\u3002fsolve\u51fd\u6570\u662f\u5176\u4e2d\u4e00\u4e2a\u5e38\u7528\u7684\u51fd\u6570\uff0c\u7528\u4e8e\u6c42\u89e3\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4\u3002<\/p>\n<\/p>\n

1.1 FSOLVE\u51fd\u6570\u7684\u57fa\u672c\u7528\u6cd5<\/p>\n<\/p>\n

\u8981\u4f7f\u7528fsolve\u51fd\u6570\uff0c\u9996\u5148\u9700\u8981\u5bfc\u5165scipy.optimize\u6a21\u5757\u3002fsolve\u51fd\u6570\u7684\u57fa\u672c\u4f7f\u7528\u65b9\u6cd5\u5982\u4e0b\uff1a<\/p>\n<\/p>\n

from scipy.optimize import fsolve<\/p>\n
def equation(x):<\/p>\n
    return x2 - 4<\/p>\n
root = fsolve(equation, x0=1)<\/p>\n
print("The root is:", root)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u5b9a\u4e49\u4e86\u4e00\u4e2a\u7b80\u5355\u7684\u65b9\u7a0bx^2 – 4 = 0\u3002fsolve\u51fd\u6570\u9700\u8981\u4e24\u4e2a\u53c2\u6570\uff1a\u4e00\u4e2a\u662f\u9700\u8981\u6c42\u89e3\u7684\u65b9\u7a0b\uff0c\u53e6\u4e00\u4e2a\u662f\u521d\u59cb\u731c\u6d4b\u503cx0\u3002\u5728\u6b64\u4f8b\u4e2d\uff0c\u521d\u59cb\u731c\u6d4b\u503c\u4e3a1\u3002fsolve\u51fd\u6570\u4f1a\u8fd4\u56de\u4e00\u4e2a\u6570\u7ec4\uff0c\u5176\u4e2d\u5305\u542b\u65b9\u7a0b\u7684\u6839\u3002<\/p>\n<\/p>\n
1.2 FSOLVE\u51fd\u6570\u7684\u9ad8\u7ea7\u7528\u6cd5<\/p>\n<\/p>\n
fsolve\u51fd\u6570\u8fd8\u53ef\u4ee5\u63a5\u6536\u5176\u4ed6\u53c2\u6570\u6765\u63a7\u5236\u6c42\u89e3\u8fc7\u7a0b\uff0c\u4f8b\u5982xtol\uff08\u8bef\u5dee\u5bb9\u9650\uff09\u3001maxfev\uff08\u6700\u5927\u51fd\u6570\u8c03\u7528\u6b21\u6570\uff09\u7b49\u3002\u901a\u8fc7\u8c03\u6574\u8fd9\u4e9b\u53c2\u6570\uff0c\u53ef\u4ee5\u63d0\u9ad8\u6c42\u89e3\u7684\u7cbe\u5ea6\u548c\u6548\u7387\u3002<\/p>\n<\/p>\n
root = fsolve(equation, x0=1, xtol=1e-6, maxfev=1000)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u901a\u8fc7\u8bbe\u7f6extol\u53c2\u6570\u4e3a1e-6\uff0c\u53ef\u4ee5\u63d0\u9ad8\u6c42\u89e3\u7684\u7cbe\u5ea6\uff0c\u4f7f\u5f97\u89e3\u7684\u8bef\u5dee\u4e0d\u8d85\u8fc71e-6\u3002maxfev\u53c2\u6570\u9650\u5236\u4e86\u6700\u5927\u51fd\u6570\u8c03\u7528\u6b21\u6570\uff0c\u9632\u6b62\u5728\u6c42\u89e3\u8fc7\u7a0b\u4e2d\u9677\u5165\u65e0\u9650\u5faa\u73af\u3002<\/p>\n<\/p>\n
\u4e8c\u3001NUMPY\u5e93\u4e2d\u7684ROOTS\u51fd\u6570<\/p>\n<\/p>\n
Numpy\u662fPython\u4e2d\u4e00\u4e2a\u57fa\u7840\u7684\u79d1\u5b66\u8ba1\u7b97\u5e93\uff0c\u63d0\u4f9b\u4e86\u8bb8\u591a\u7528\u4e8e\u5904\u7406\u6570\u7ec4\u548c\u77e9\u9635\u7684\u51fd\u6570\u3002roots\u51fd\u6570\u662fNumpy\u5e93\u4e2d\u7684\u4e00\u4e2a\u51fd\u6570\uff0c\u7528\u4e8e\u6c42\u89e3\u591a\u9879\u5f0f\u65b9\u7a0b\u7684\u6839\u3002<\/p>\n<\/p>\n
2.1 ROOTS\u51fd\u6570\u7684\u57fa\u672c\u7528\u6cd5<\/p>\n<\/p>\n
\u8981\u4f7f\u7528roots\u51fd\u6570\uff0c\u9996\u5148\u9700\u8981\u5bfc\u5165numpy\u6a21\u5757\u3002roots\u51fd\u6570\u7684\u4f7f\u7528\u65b9\u6cd5\u5982\u4e0b\uff1a<\/p>\n<\/p>\n
import numpy as np<\/p>\n
coefficients = [1, 0, -4]<\/p>\n
roots = np.roots(coefficients)<\/p>\n
print("The roots are:", roots)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u5b9a\u4e49\u4e86\u4e00\u4e2a\u591a\u9879\u5f0f\u65b9\u7a0bx^2 – 4 = 0\uff0c\u7cfb\u6570\u4e3a[1, 0, -4]\u3002roots\u51fd\u6570\u4f1a\u8fd4\u56de\u4e00\u4e2a\u6570\u7ec4\uff0c\u5176\u4e2d\u5305\u542b\u591a\u9879\u5f0f\u65b9\u7a0b\u7684\u6240\u6709\u6839\u3002<\/p>\n<\/p>\n
2.2 ROOTS\u51fd\u6570\u7684\u5e94\u7528\u573a\u666f<\/p>\n<\/p>\n
roots\u51fd\u6570\u9002\u7528\u4e8e\u6c42\u89e3\u591a\u9879\u5f0f\u65b9\u7a0b\u7684\u6839\uff0c\u5c24\u5176\u662f\u9ad8\u6b21\u591a\u9879\u5f0f\u65b9\u7a0b\u3002\u5728\u5904\u7406\u590d\u6742\u7684\u591a\u9879\u5f0f\u65b9\u7a0b\u65f6\uff0croots\u51fd\u6570\u80fd\u591f\u5feb\u901f\u3001\u51c6\u786e\u5730\u6c42\u89e3\u6240\u6709\u6839\u3002<\/p>\n<\/p>\n
\u4e09\u3001\u81ea\u5b9a\u4e49\u7684\u6570\u503c\u65b9\u6cd5<\/p>\n<\/p>\n
\u9664\u4e86\u4f7f\u7528\u5185\u7f6e\u5e93\u51fd\u6570\uff0cPython\u8fd8\u53ef\u4ee5\u901a\u8fc7\u7f16\u5199\u81ea\u5b9a\u4e49\u7684\u6570\u503c\u65b9\u6cd5\u6765\u6c42\u89e3\u65b9\u7a0b\u7684\u6839\uff0c\u4f8b\u5982\u725b\u987f\u8fed\u4ee3\u6cd5\u548c\u4e8c\u5206\u6cd5\u3002<\/p>\n<\/p>\n
3.1 \u725b\u987f\u8fed\u4ee3\u6cd5<\/p>\n<\/p>\n
\u725b\u987f\u8fed\u4ee3\u6cd5\u662f\u4e00\u79cd\u5feb\u901f\u6536\u655b\u7684\u6570\u503c\u65b9\u6cd5\uff0c\u9002\u7528\u4e8e\u6c42\u89e3\u975e\u7ebf\u6027\u65b9\u7a0b\u7684\u6839\u3002\u5b83\u901a\u8fc7\u8fed\u4ee3\u66f4\u65b0\u521d\u59cb\u731c\u6d4b\u503c\uff0c\u9010\u6b65\u903c\u8fd1\u65b9\u7a0b\u7684\u89e3\u3002<\/p>\n<\/p>\n
def newton_method(func, deriv, x0, tol=1e-6, max_iter=100):<\/p>\n
    x = x0<\/p>\n
    for _ in range(max_iter):<\/p>\n
        x_new = x - func(x) \/ deriv(x)<\/p>\n
        if abs(x_new - x) < tol:<\/p>\n
            return x_new<\/p>\n
        x = x_new<\/p>\n
    rAI<\/a>se ValueError("Failed to converge")<\/p>\n
def func(x):<\/p>\n
    return x2 - 4<\/p>\n
def deriv(x):<\/p>\n
    return 2*x<\/p>\n
root = newton_method(func, deriv, x0=1)<\/p>\n
print("The root is:", root)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u5b9a\u4e49\u4e86\u4e00\u4e2a\u725b\u987f\u8fed\u4ee3\u6cd5\u7684\u51fd\u6570newton_method\uff0c\u63a5\u53d7\u4e00\u4e2a\u65b9\u7a0bfunc\u3001\u65b9\u7a0b\u7684\u5bfc\u6570deriv\u3001\u521d\u59cb\u731c\u6d4b\u503cx0\u3001\u8bef\u5dee\u5bb9\u9650tol\u548c\u6700\u5927\u8fed\u4ee3\u6b21\u6570max_iter\u4f5c\u4e3a\u53c2\u6570\u3002\u901a\u8fc7\u725b\u987f\u8fed\u4ee3\u6cd5\uff0c\u53ef\u4ee5\u6c42\u89e3\u65b9\u7a0b\u7684\u6839\u3002<\/p>\n<\/p>\n
3.2 \u4e8c\u5206\u6cd5<\/p>\n<\/p>\n
\u4e8c\u5206\u6cd5\u662f\u4e00\u79cd\u7b80\u5355\u800c\u7a33\u5065\u7684\u6570\u503c\u65b9\u6cd5\uff0c\u9002\u7528\u4e8e\u6c42\u89e3\u5355\u5cf0\u51fd\u6570\u7684\u6839\u3002\u5b83\u901a\u8fc7\u4e0d\u65ad\u7f29\u5c0f\u533a\u95f4\u8303\u56f4\uff0c\u9010\u6b65\u903c\u8fd1\u65b9\u7a0b\u7684\u89e3\u3002<\/p>\n<\/p>\n
def bisection_method(func, a, b, tol=1e-6, max_iter=100):<\/p>\n
    if func(a) * func(b) >= 0:<\/p>\n
        raise ValueError("The function must have different signs at the endpoints a and b")<\/p>\n
    for _ in range(max_iter):<\/p>\n
        c = (a + b) \/ 2<\/p>\n
        if abs(func(c)) < tol:<\/p>\n
            return c<\/p>\n
        if func(a) * func(c) < 0:<\/p>\n
            b = c<\/p>\n
        else:<\/p>\n
            a = c<\/p>\n
    raise ValueError("Failed to converge")<\/p>\n
root = bisection_method(func, a=0, b=3)<\/p>\n
print("The root is:", root)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u5b9a\u4e49\u4e86\u4e00\u4e2a\u4e8c\u5206\u6cd5\u7684\u51fd\u6570bisection_method\uff0c\u63a5\u53d7\u4e00\u4e2a\u65b9\u7a0bfunc\u3001\u533a\u95f4\u7aef\u70b9a\u548cb\u3001\u8bef\u5dee\u5bb9\u9650tol\u548c\u6700\u5927\u8fed\u4ee3\u6b21\u6570max_iter\u4f5c\u4e3a\u53c2\u6570\u3002\u901a\u8fc7\u4e8c\u5206\u6cd5\uff0c\u53ef\u4ee5\u6c42\u89e3\u65b9\u7a0b\u7684\u6839\u3002<\/p>\n<\/p>\n
\u56db\u3001\u4f7f\u7528MATPLOTLIB\u53ef\u89c6\u5316\u6839\u7684\u6c42\u89e3\u8fc7\u7a0b<\/p>\n<\/p>\n
\u4e3a\u4e86\u66f4\u76f4\u89c2\u5730\u7406\u89e3\u65b9\u7a0b\u6839\u7684\u6c42\u89e3\u8fc7\u7a0b\uff0c\u53ef\u4ee5\u4f7f\u7528Matplotlib\u5e93\u5bf9\u51fd\u6570\u56fe\u50cf\u8fdb\u884c\u53ef\u89c6\u5316\u3002\u901a\u8fc7\u7ed8\u5236\u51fd\u6570\u56fe\u50cf\uff0c\u53ef\u4ee5\u66f4\u6e05\u6670\u5730\u89c2\u5bdf\u65b9\u7a0b\u6839\u7684\u4f4d\u7f6e\u3002<\/p>\n<\/p>\n
4.1 \u5b89\u88c5\u548c\u5bfc\u5165MATPLOTLIB\u5e93<\/p>\n<\/p>\n
\u9996\u5148\uff0c\u9700\u8981\u5b89\u88c5Matplotlib\u5e93\uff0c\u5e76\u5728Python\u811a\u672c\u4e2d\u5bfc\u5165\uff1a<\/p>\n<\/p>\n
pip install matplotlib<\/p>\n
<\/code><\/pre>\n<\/p>\n
import matplotlib.pyplot as plt<\/p>\n
<\/code><\/pre>\n<\/p>\n
4.2 \u7ed8\u5236\u51fd\u6570\u56fe\u50cf<\/p>\n<\/p>\n
\u901a\u8fc7Matplotlib\u5e93\uff0c\u53ef\u4ee5\u7ed8\u5236\u51fd\u6570\u56fe\u50cf\uff0c\u89c2\u5bdf\u65b9\u7a0b\u6839\u7684\u4f4d\u7f6e\uff1a<\/p>\n<\/p>\n
x = np.linspace(-3, 3, 400)<\/p>\n
y = func(x)<\/p>\n
plt.plot(x, y, label='f(x) = x^2 - 4')<\/p>\n
plt.axhline(0, color='black', linewidth=0.8)<\/p>\n
plt.scatter(root, func(root), color='red', label='Root')<\/p>\n
plt.title('Function Graph')<\/p>\n
plt.xlabel('x')<\/p>\n
plt.ylabel('f(x)')<\/p>\n
plt.legend()<\/p>\n
plt.grid(True)<\/p>\n
plt.show()<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u4f7f\u7528numpy\u7684linspace\u51fd\u6570\u751f\u6210\u4e00\u4e2a\u8303\u56f4\u4e3a[-3, 3]\u7684\u6570\u7ec4x\uff0c\u5e76\u8ba1\u7b97\u76f8\u5e94\u7684\u51fd\u6570\u503cy\u3002\u4f7f\u7528Matplotlib\u7684plot\u51fd\u6570\u7ed8\u5236\u51fd\u6570\u56fe\u50cf\uff0c\u5e76\u6807\u8bb0\u51fa\u6c42\u5f97\u7684\u65b9\u7a0b\u6839\u7684\u4f4d\u7f6e\u3002<\/p>\n<\/p>\n
\u4e94\u3001\u603b\u7ed3\u4e0e\u5efa\u8bae<\/p>\n<\/p>\n
\u901a\u8fc7\u672c\u6587\u7684\u4ecb\u7ecd\uff0c\u6211\u4eec\u4e86\u89e3\u4e86Python\u4e2d\u6c42\u89e3\u65b9\u7a0b\u6839\u7684\u591a\u79cd\u65b9\u6cd5\uff0c\u5305\u62ec\u4f7f\u7528scipy.optimize\u5e93\u4e2d\u7684fsolve\u51fd\u6570\u3001numpy\u5e93\u4e2d\u7684roots\u51fd\u6570\uff0c\u4ee5\u53ca\u81ea\u5b9a\u4e49\u7684\u725b\u987f\u8fed\u4ee3\u6cd5\u548c\u4e8c\u5206\u6cd5\u3002\u8fd9\u4e9b\u65b9\u6cd5\u5404\u6709\u4f18\u52bf\uff0c\u9002\u7528\u4e8e\u4e0d\u540c\u7c7b\u578b\u7684\u65b9\u7a0b\u6c42\u89e3\u3002<\/p>\n<\/p>\n
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