{"id":928054,"date":"2024-12-26T16:26:42","date_gmt":"2024-12-26T08:26:42","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/928054.html"},"modified":"2024-12-26T16:26:44","modified_gmt":"2024-12-26T08:26:44","slug":"python%e4%b8%ad%e5%a6%82%e4%bd%95%e7%a7%af%e5%88%86","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/928054.html","title":{"rendered":"python\u4e2d\u5982\u4f55\u79ef\u5206"},"content":{"rendered":"

\"python\u4e2d\u5982\u4f55\u79ef\u5206\"<\/p>\n

\u5728Python\u4e2d\u6267\u884c\u79ef\u5206\u7684\u65b9\u6cd5\u5305\u62ec\u4f7f\u7528\u6570\u503c\u79ef\u5206\u5e93\u5982scipy.integrate<\/code>\u3001\u7b26\u53f7\u79ef\u5206\u5e93\u5982sympy<\/code>\u3001\u81ea\u5b9a\u4e49\u6570\u503c\u79ef\u5206\u7b97\u6cd5\u5982\u68af\u5f62\u6cd5\u548c\u8f9b\u666e\u68ee\u6cd5\u3002<\/strong>\u8fd9\u4e09\u79cd\u65b9\u6cd5\u5404\u6709\u5176\u9002\u7528\u7684\u573a\u666f\u548c\u4f18\u7f3a\u70b9\u3002\u5728\u5904\u7406\u590d\u6742\u7684\u51fd\u6570\u65f6\uff0cscipy.integrate<\/code>\u63d0\u4f9b\u4e86\u9ad8\u6548\u7684\u6570\u503c\u89e3\u6cd5\uff0c\u800csympy<\/code>\u5219\u5728\u9700\u8981\u7cbe\u786e\u7684\u7b26\u53f7\u79ef\u5206\u65f6\u8868\u73b0\u51fa\u8272\u3002\u5bf9\u4e8e\u7279\u5b9a\u7684\u7b80\u5355\u79ef\u5206\u95ee\u9898\uff0c\u81ea\u5df1\u7f16\u5199\u7684\u6570\u503c\u79ef\u5206\u7b97\u6cd5\u53ef\u80fd\u66f4\u52a0\u7075\u6d3b\u3002\u4e0b\u9762\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u8fd9\u4e09\u79cd\u65b9\u6cd5\u3002<\/p>\n<\/p>\n

\u4e00\u3001\u4f7f\u7528Scipy\u8fdb\u884c\u6570\u503c\u79ef\u5206<\/h3>\n<\/p>\n

Scipy\u5e93\u4e2d\u7684integrate<\/code>\u6a21\u5757\u662f\u8fdb\u884c\u6570\u503c\u79ef\u5206\u7684\u4e00\u4e2a\u5f3a\u5927\u5de5\u5177\uff0c\u5c24\u5176\u9002\u5408\u4e8e\u89e3\u51b3\u590d\u6742\u51fd\u6570\u7684\u79ef\u5206\u95ee\u9898\u3002Scipy\u4e3b\u8981\u63d0\u4f9b\u4e86quad<\/code>\u51fd\u6570\u7528\u4e8e\u4e00\u7ef4\u79ef\u5206\uff0c\u4ee5\u53cadblquad<\/code>\u548ctplquad<\/code>\u7528\u4e8e\u591a\u91cd\u79ef\u5206\u3002<\/p>\n<\/p>\n

1. Scipy\u7684quad\u51fd\u6570<\/h4>\n<\/p>\n

quad<\/code>\u51fd\u6570\u662fSciPy\u4e2d\u6700\u5e38\u7528\u7684\u7528\u4e8e\u4e00\u7ef4\u6570\u503c\u79ef\u5206\u7684\u5de5\u5177\u3002\u5176\u57fa\u672c\u7528\u6cd5\u662f\uff1a<\/p>\n<\/p>\n

from scipy.integrate import quad<\/p>\n
def integrand(x):<\/p>\n
    return x  2<\/p>\n
result, error = quad(integrand, 0, 1)<\/p>\n
print("Result of integration:", result)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0cintegrand<\/code>\u662f\u88ab\u79ef\u51fd\u6570\uff0c0<\/code>\u548c1<\/code>\u662f\u79ef\u5206\u7684\u4e0a\u4e0b\u9650\u3002quad<\/code>\u51fd\u6570\u8fd4\u56de\u4e24\u4e2a\u503c\uff1a\u79ef\u5206\u7684\u8fd1\u4f3c\u503c\u548c\u4f30\u8ba1\u8bef\u5dee\u3002<\/p>\n<\/p>\n
2. \u591a\u91cd\u79ef\u5206<\/h4>\n<\/p>\n
\u5bf9\u4e8e\u591a\u91cd\u79ef\u5206\uff0cScipy\u63d0\u4f9b\u4e86dblquad<\/code>\u548ctplquad<\/code>\u51fd\u6570\u3002\u4f8b\u5982\uff0c\u8ba1\u7b97\u4e00\u4e2a\u51fd\u6570\u5728\u4e8c\u7ef4\u7a7a\u95f4\u4e0a\u7684\u79ef\u5206\u53ef\u4ee5\u4f7f\u7528dblquad<\/code>\uff1a<\/p>\n<\/p>\n
from scipy.integrate import dblquad<\/p>\n
def integrand(y, x):<\/p>\n
    return x * y<\/p>\n
result, error = dblquad(integrand, 0, 1, lambda x: 0, lambda x: 1)<\/p>\n
print("Result of double integration:", result)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0cintegrand<\/code>\u662f\u4e00\u4e2a\u53cc\u53d8\u91cf\u51fd\u6570\uff0c\u79ef\u5206\u533a\u57df\u662fx<\/code>\u4ece0\u52301\uff0cy<\/code>\u4ece0<\/code>\u52301\u3002<\/p>\n<\/p>\n
\u4e8c\u3001\u4f7f\u7528Sympy\u8fdb\u884c\u7b26\u53f7\u79ef\u5206<\/h3>\n<\/p>\n
Sympy\u662fPython\u7684\u4e00\u4e2a\u7b26\u53f7\u8ba1\u7b97\u5e93\uff0c\u63d0\u4f9b\u4e86\u5f3a\u5927\u7684\u7b26\u53f7\u79ef\u5206\u529f\u80fd\uff0c\u53ef\u4ee5\u7cbe\u786e\u6c42\u89e3\u79ef\u5206\u3002<\/p>\n<\/p>\n
1. \u57fa\u672c\u7b26\u53f7\u79ef\u5206<\/h4>\n<\/p>\n
\u4f7f\u7528Sympy\u8fdb\u884c\u7b26\u53f7\u79ef\u5206\u7684\u57fa\u672c\u6b65\u9aa4\u5982\u4e0b\uff1a<\/p>\n<\/p>\n
from sympy import symbols, integrate<\/p>\n
x = symbols('x')<\/p>\n
expr = x  2<\/p>\n
result = integrate(expr, (x, 0, 1))<\/p>\n
print("Symbolic integration result:", result)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0csymbols<\/code>\u51fd\u6570\u7528\u4e8e\u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf\uff0cintegrate<\/code>\u51fd\u6570\u7528\u4e8e\u6267\u884c\u79ef\u5206\u3002\u7ed3\u679c\u662f\u4e00\u4e2a\u7cbe\u786e\u7684\u7b26\u53f7\u8868\u8fbe\u5f0f\u3002<\/p>\n<\/p>\n
2. \u5904\u7406\u4e0d\u5b9a\u79ef\u5206<\/h4>\n<\/p>\n
Sympy\u540c\u6837\u53ef\u4ee5\u7528\u4e8e\u8ba1\u7b97\u4e0d\u5b9a\u79ef\u5206\uff1a<\/p>\n<\/p>\n
from sympy import symbols, integrate<\/p>\n
x = symbols('x')<\/p>\n
expr = x  2<\/p>\n
result = integrate(expr, x)<\/p>\n
print("Indefinite integration result:", result)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8fd9\u6bb5\u4ee3\u7801\u5c06\u8f93\u51fa\u4e0d\u5b9a\u79ef\u5206\u7684\u7ed3\u679c\uff0c\u5373\u79ef\u5206\u51fd\u6570\u7684\u539f\u51fd\u6570\u3002<\/p>\n<\/p>\n
\u4e09\u3001\u5b9e\u73b0\u81ea\u5b9a\u4e49\u6570\u503c\u79ef\u5206\u7b97\u6cd5<\/h3>\n<\/p>\n
\u5bf9\u4e8e\u7279\u5b9a\u7684\u5e94\u7528\u573a\u666f\uff0c\u6211\u4eec\u53ef\u4ee5\u81ea\u5df1\u5b9e\u73b0\u6570\u503c\u79ef\u5206\u7b97\u6cd5\uff0c\u5982\u68af\u5f62\u6cd5\u548c\u8f9b\u666e\u68ee\u6cd5\u3002<\/p>\n<\/p>\n
1. \u68af\u5f62\u6cd5<\/h4>\n<\/p>\n
\u68af\u5f62\u6cd5\u662f\u4e00\u79cd\u7b80\u5355\u7684\u6570\u503c\u79ef\u5206\u65b9\u6cd5\uff0c\u901a\u8fc7\u5c06\u66f2\u7ebf\u4e0b\u7684\u533a\u57df\u5206\u5272\u6210\u68af\u5f62\u6765\u903c\u8fd1\u79ef\u5206\uff1a<\/p>\n<\/p>\n
def trapezoidal_rule(f, a, b, n):<\/p>\n
    h = (b - a) \/ n<\/p>\n
    s = 0.5 * (f(a) + f(b))<\/p>\n
    for i in range(1, n):<\/p>\n
        s += f(a + i * h)<\/p>\n
    return s * h<\/p>\n
def integrand(x):<\/p>\n
    return x  2<\/p>\n
result = trapezoidal_rule(integrand, 0, 1, 1000)<\/p>\n
print("Trapezoidal rule result:", result)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8fd9\u79cd\u65b9\u6cd5\u9002\u5408\u4e8e\u5206\u6bb5\u7ebf\u6027\u51fd\u6570\u6216\u8005\u79ef\u5206\u533a\u95f4\u8f83\u5c0f\u7684\u60c5\u5f62\u3002<\/p>\n<\/p>\n
2. \u8f9b\u666e\u68ee\u6cd5<\/h4>\n<\/p>\n
\u8f9b\u666e\u68ee\u6cd5\u5229\u7528\u629b\u7269\u7ebf\u6765\u903c\u8fd1\u88ab\u79ef\u51fd\u6570\u7684\u66f2\u7ebf\uff0c\u66f4\u52a0\u7cbe\u786e\uff1a<\/p>\n<\/p>\n
def simpsons_rule(f, a, b, n):<\/p>\n
    if n % 2 == 1:<\/p>\n
        n += 1<\/p>\n
    h = (b - a) \/ n<\/p>\n
    s = f(a) + f(b)<\/p>\n
    for i in range(1, n, 2):<\/p>\n
        s += 4 * f(a + i * h)<\/p>\n
    for i in range(2, n-1, 2):<\/p>\n
        s += 2 * f(a + i * h)<\/p>\n
    return s * h \/ 3<\/p>\n
result = simpsons_rule(integrand, 0, 1, 1000)<\/p>\n
print("Simpson's rule result:", result)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8f9b\u666e\u68ee\u6cd5\u5728\u5927\u591a\u6570\u60c5\u51b5\u4e0b\u6bd4\u68af\u5f62\u6cd5\u66f4\u52a0\u7cbe\u786e\uff0c\u4f46\u8ba1\u7b97\u590d\u6742\u5ea6\u4e5f\u7a0d\u9ad8\u3002<\/p>\n<\/p>\n
\u56db\u3001\u5e94\u7528\u573a\u666f\u4e0e\u9009\u62e9<\/h3>\n<\/p>\n
\u6839\u636e\u4e0d\u540c\u7684\u9700\u6c42\u548c\u573a\u666f\u9009\u62e9\u5408\u9002\u7684\u79ef\u5206\u65b9\u6cd5\u662f\u975e\u5e38\u91cd\u8981\u7684\u3002<\/p>\n<\/p>\n
1. \u6570\u503c\u79ef\u5206\u7684\u5e94\u7528<\/h4>\n<\/p>\n
\u6570\u503c\u79ef\u5206\u9002\u7528\u4e8e\u88ab\u79ef\u51fd\u6570\u590d\u6742\u3001\u65e0\u6cd5\u7b26\u53f7\u79ef\u5206\u6216\u5728\u9ad8\u7cbe\u5ea6\u6570\u503c\u7ed3\u679c\u53ef\u63a5\u53d7\u7684\u60c5\u51b5\u3002Scipy\u7684quad<\/code>\u51fd\u6570\u662f\u5904\u7406\u4e00\u7ef4\u79ef\u5206\u7684\u9996\u9009\uff0cdblquad<\/code>\u548ctplquad<\/code>\u5219\u9002\u7528\u4e8e\u591a\u7ef4\u79ef\u5206\u3002<\/p>\n<\/p>\n
2. \u7b26\u53f7\u79ef\u5206\u7684\u5e94\u7528<\/h4>\n<\/p>\n
\u7b26\u53f7\u79ef\u5206\u9002\u7528\u4e8e\u9700\u8981\u7cbe\u786e\u79ef\u5206\u7ed3\u679c\u7684\u573a\u666f\uff0c\u5c24\u5176\u662f\u5728\u7406\u8bba\u5206\u6790\u6216\u8005\u9700\u8981\u7b26\u53f7\u8868\u8fbe\u5f0f\u7684\u5de5\u7a0b\u5e94\u7528\u4e2d\u3002Sympy\u5728\u5904\u7406\u7b26\u53f7\u79ef\u5206\u65f6\u63d0\u4f9b\u4e86\u5f3a\u5927\u7684\u529f\u80fd\uff0c\u5e76\u4e14\u53ef\u4ee5\u81ea\u52a8\u5316\u5316\u7b80\u590d\u6742\u7684\u79ef\u5206\u5f0f\u3002<\/p>\n<\/p>\n
3. \u81ea\u5b9a\u4e49\u6570\u503c\u79ef\u5206\u7684\u5e94\u7528<\/h4>\n<\/p>\n
\u5728\u7279\u5b9a\u6027\u80fd\u9700\u6c42\u4e0b\uff0c\u81ea\u5df1\u5b9e\u73b0\u6570\u503c\u79ef\u5206\u7b97\u6cd5\u53ef\u4ee5\u63d0\u4f9b\u66f4\u9ad8\u7684\u7075\u6d3b\u6027\u3002\u4f8b\u5982\uff0c\u5f53\u9700\u8981\u5728\u5d4c\u5165\u5f0f\u7cfb\u7edf\u4e2d\u5b9e\u73b0\u7b80\u5355\u7684\u79ef\u5206\u7b97\u6cd5\u65f6\uff0c\u81ea\u5b9a\u4e49\u7684\u68af\u5f62\u6cd5\u6216\u8f9b\u666e\u68ee\u6cd5\u53ef\u4ee5\u66f4\u597d\u5730\u6ee1\u8db3\u8d44\u6e90\u9650\u5236\u3002<\/p>\n<\/p>\n
\u4e94\u3001\u603b\u7ed3\u4e0e\u5efa\u8bae<\/h3>\n<\/p>\n
Python\u63d0\u4f9b\u4e86\u591a\u79cd\u65b9\u6cd5\u6765\u8fdb\u884c\u79ef\u5206\uff0c\u6bcf\u79cd\u65b9\u6cd5\u90fd\u6709\u5176\u72ec\u7279\u7684\u4f18\u52bf\u4e0e\u9002\u7528\u573a\u666f\u3002\u5bf9\u4e8e\u5927\u591a\u6570\u5e94\u7528\uff0c\u4f7f\u7528Scipy\u8fdb\u884c\u6570\u503c\u79ef\u5206\u662f\u6700\u4e3a\u76f4\u63a5\u548c\u9ad8\u6548\u7684\u65b9\u6cd5\uff0c\u4f46\u5f53\u9700\u8981\u7cbe\u786e\u7684\u7b26\u53f7\u79ef\u5206\u65f6\uff0cSympy\u662f\u66f4\u597d\u7684\u9009\u62e9\u3002\u800c\u5728\u7279\u5b9a\u7684\u5e94\u7528\u573a\u666f\u4e0b\uff0c\u81ea\u5b9a\u4e49\u6570\u503c\u79ef\u5206\u7b97\u6cd5\u53ef\u4ee5\u63d0\u4f9b\u6240\u9700\u7684\u7075\u6d3b\u6027\u548c\u6027\u80fd\u3002\u5408\u7406\u9009\u62e9\u548c\u7ec4\u5408\u8fd9\u4e9b\u65b9\u6cd5\uff0c\u53ef\u4ee5\u6709\u6548\u89e3\u51b3\u5927\u591a\u6570\u79ef\u5206\u95ee\u9898\u3002<\/p>\n<\/p>\n
\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n
 \u5728Python\u4e2d\uff0c\u5982\u4f55\u4f7f\u7528SciPy\u8fdb\u884c\u6570\u503c\u79ef\u5206\uff1f<\/strong>
SciPy\u5e93\u63d0\u4f9b\u4e86\u5f3a\u5927\u7684\u6570\u503c\u79ef\u5206\u529f\u80fd\uff0c\u5c24\u5176\u662fscipy.integrate<\/code>\u6a21\u5757\u3002\u7528\u6237\u53ef\u4ee5\u4f7f\u7528quad<\/code>\u51fd\u6570\u5bf9\u4e00\u7ef4\u51fd\u6570\u8fdb\u884c\u79ef\u5206\uff0c\u4f7f\u7528dblquad<\/code>\u548ctplquad<\/code>\u8fdb\u884c\u53cc\u91cd\u548c\u4e09\u91cd\u79ef\u5206\u3002\u4f7f\u7528\u65f6\uff0c\u60a8\u53ea\u9700\u5b9a\u4e49\u8981\u79ef\u5206\u7684\u51fd\u6570\u53ca\u79ef\u5206\u7684\u533a\u95f4\uff0cSciPy\u4f1a\u81ea\u52a8\u8ba1\u7b97\u51fa\u79ef\u5206\u503c\u3002\u4f8b\u5982\uff1a<\/p>\n
from scipy.integrate import quad\n\ndef f(x):\n    return x**2\n\nresult, error = quad(f, 0, 1)\nprint(result)  # \u8f93\u51fa\u79ef\u5206\u7ed3\u679c\n<\/code><\/pre>\n
Python\u4e2d\u662f\u5426\u53ef\u4ee5\u8fdb\u884c\u7b26\u53f7\u79ef\u5206\uff1f<\/strong>
\u662f\u7684\uff0cPython\u652f\u6301\u7b26\u53f7\u79ef\u5206\uff0c\u6700\u5e38\u7528\u7684\u5e93\u662fSymPy\u3002\u901a\u8fc7\u4f7f\u7528SymPy\uff0c\u60a8\u53ef\u4ee5\u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf\uff0c\u5e76\u6267\u884c\u7b26\u53f7\u79ef\u5206\u3002\u4ee5\u4e0b\u662f\u4e00\u4e2a\u7b80\u5355\u7684\u793a\u4f8b\uff1a<\/p>\n
from sympy import symbols, integrate\n\nx = symbols('x')\nintegral_result = integrate(x**2, (x, 0, 1))\nprint(integral_result)  # \u8f93\u51fa\u7ed3\u679c\n<\/code><\/pre>\n
\u5728Python\u4e2d\uff0c\u5982\u4f55\u5904\u7406\u79ef\u5206\u7684\u8bef\u5dee\u548c\u7cbe\u5ea6\uff1f<\/strong>
\u5728\u8fdb\u884c\u6570\u503c\u79ef\u5206\u65f6\uff0c\u7cbe\u5ea6\u548c\u8bef\u5dee\u63a7\u5236\u975e\u5e38\u91cd\u8981\u3002\u4f7f\u7528quad<\/code>\u51fd\u6570\u65f6\uff0c\u53ef\u4ee5\u901a\u8fc7\u8c03\u6574epsabs<\/code>\u548cepsrel<\/code>\u53c2\u6570\u6765\u8bbe\u7f6e\u7edd\u5bf9\u548c\u76f8\u5bf9\u8bef\u5dee\u7684\u5bb9\u5fcd\u5ea6\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u53ef\u4ee5\u67e5\u770b\u8fd4\u56de\u7684\u8bef\u5dee\u4f30\u8ba1\uff0c\u4ee5\u4fbf\u66f4\u597d\u5730\u7406\u89e3\u7ed3\u679c\u7684\u53ef\u9760\u6027\u3002\u5bf9\u4e8e\u7b26\u53f7\u79ef\u5206\uff0cSymPy\u4f1a\u7ed9\u51fa\u7cbe\u786e\u89e3\uff0c\u901a\u5e38\u4e0d\u4f1a\u51fa\u73b0\u8bef\u5dee\u95ee\u9898\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u5728Python\u4e2d\u6267\u884c\u79ef\u5206\u7684\u65b9\u6cd5\u5305\u62ec\u4f7f\u7528\u6570\u503c\u79ef\u5206\u5e93\u5982scipy.integrate\u3001\u7b26\u53f7\u79ef\u5206\u5e93\u5982sympy\u3001\u81ea\u5b9a […]","protected":false},"author":3,"featured_media":928056,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[37],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/928054"}],"collection":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/comments?post=928054"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/928054\/revisions"}],"predecessor-version":[{"id":928058,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/928054\/revisions\/928058"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/928056"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=928054"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=928054"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=928054"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}