{"id":1170801,"date":"2025-01-15T16:27:06","date_gmt":"2025-01-15T08:27:06","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1170801.html"},"modified":"2025-01-15T16:27:09","modified_gmt":"2025-01-15T08:27:09","slug":"%e5%a6%82%e4%bd%95%e7%94%a8python%e5%af%b9%e5%87%bd%e6%95%b0%e6%b1%82%e5%af%bc","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1170801.html","title":{"rendered":"\u5982\u4f55\u7528python\u5bf9\u51fd\u6570\u6c42\u5bfc"},"content":{"rendered":"

\"\u5982\u4f55\u7528python\u5bf9\u51fd\u6570\u6c42\u5bfc\"<\/p>\n

\u4f7f\u7528Python\u5bf9\u51fd\u6570\u6c42\u5bfc\u53ef\u4ee5\u4f7f\u7528SymPy\u5e93\u3001NumPy\u5e93\u3001SciPy\u5e93\uff0c\u6b65\u9aa4\u5305\u62ec\u5bfc\u5165\u5e93\u3001\u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf\u3001\u5b9a\u4e49\u51fd\u6570\u3001\u8c03\u7528\u6c42\u5bfc\u51fd\u6570\u3002<\/strong> SymPy\u5e93\u662f\u6700\u5e38\u7528\u7684\u4e00\u79cd\u65b9\u6cd5\uff0c\u56e0\u5176\u529f\u80fd\u5f3a\u5927\u4e14\u6613\u4e8e\u4f7f\u7528\u3002<\/strong><\/p>\n<\/p>\n

\u8be6\u7ec6\u63cf\u8ff0\uff1aSymPy\u5e93\u662f\u4e00\u6b3e\u7528\u4e8e\u7b26\u53f7\u8ba1\u7b97\u7684Python\u5e93\uff0c\u80fd\u591f\u8fdb\u884c\u4ee3\u6570\u8ba1\u7b97\u3001\u6c42\u5bfc\u3001\u79ef\u5206\u3001\u89e3\u65b9\u7a0b\u7b49\u3002<\/strong>\u5176\u6c42\u5bfc\u529f\u80fd\u5c24\u5176\u7a81\u51fa\uff0c\u80fd\u591f\u5904\u7406\u5355\u53d8\u91cf\u548c\u591a\u53d8\u91cf\u51fd\u6570\u3002\u901a\u8fc7\u5bfc\u5165SymPy\u5e93\uff0c\u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf\u548c\u51fd\u6570\uff0c\u7136\u540e\u8c03\u7528diff()<\/code>\u51fd\u6570\uff0c\u5373\u53ef\u8f7b\u677e\u5b9e\u73b0\u5bf9\u51fd\u6570\u7684\u6c42\u5bfc\u3002\u6b64\u5916\uff0cSymPy\u5e93\u8fd8\u652f\u6301\u7b80\u5316\u6c42\u5bfc\u7ed3\u679c\u3001\u6c42\u591a\u91cd\u5bfc\u6570\u7b49\u9ad8\u7ea7\u64cd\u4f5c\uff0c\u9002\u7528\u4e8e\u5404\u79cd\u590d\u6742\u7684\u6570\u5b66\u8ba1\u7b97\u9700\u6c42\u3002<\/p>\n<\/p>\n

\n

\u4e00\u3001SymPy\u5e93\u6c42\u5bfc<\/h3>\n<\/p>\n

SymPy\u5e93\u662f\u4e00\u6b3e\u529f\u80fd\u5f3a\u5927\u7684\u7b26\u53f7\u8ba1\u7b97\u5e93\uff0c\u53ef\u4ee5\u8f7b\u677e\u5b9e\u73b0\u5bf9\u51fd\u6570\u7684\u6c42\u5bfc\u3002\u4ee5\u4e0b\u662f\u8be6\u7ec6\u6b65\u9aa4\uff1a<\/p>\n<\/p>\n

1\u3001\u5bfc\u5165SymPy\u5e93<\/h4>\n<\/p>\n

\u9996\u5148\u9700\u8981\u5b89\u88c5\u5e76\u5bfc\u5165SymPy\u5e93\uff0c\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u547d\u4ee4\u8fdb\u884c\u5b89\u88c5\uff1a<\/p>\n<\/p>\n

pip install sympy<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5bfc\u5165\u5e93\u7684\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n<\/p>\n
import sympy as sp<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001\u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf\u548c\u51fd\u6570<\/h4>\n<\/p>\n
\u5728SymPy\u4e2d\uff0c\u9700\u8981\u5148\u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf\uff0c\u7136\u540e\u5b9a\u4e49\u51fd\u6570\u3002\u4f8b\u5982\uff1a<\/p>\n<\/p>\n
x = sp.symbols('x')<\/p>\n
f = x2 + 3*x + 2<\/p>\n
<\/code><\/pre>\n<\/p>\n
3\u3001\u8c03\u7528\u6c42\u5bfc\u51fd\u6570<\/h4>\n<\/p>\n
\u4f7f\u7528diff()<\/code>\u51fd\u6570\u5bf9\u5b9a\u4e49\u7684\u51fd\u6570\u8fdb\u884c\u6c42\u5bfc\uff1a<\/p>\n<\/p>\n
f_prime = sp.diff(f, x)<\/p>\n
print(f_prime)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1a<\/p>\n<\/p>\n
2*x + 3<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u6b64\u65f6\uff0cf_prime<\/code>\u5373\u4e3a\u51fd\u6570f<\/code>\u7684\u5bfc\u6570\u3002<\/p>\n<\/p>\n
4\u3001\u591a\u53d8\u91cf\u51fd\u6570\u6c42\u5bfc<\/h4>\n<\/p>\n
SymPy\u5e93\u540c\u6837\u652f\u6301\u5bf9\u591a\u53d8\u91cf\u51fd\u6570\u8fdb\u884c\u6c42\u5bfc\u3002\u4f8b\u5982\uff1a<\/p>\n<\/p>\n
x, y = sp.symbols('x y')<\/p>\n
f = x<strong>2 + y<\/strong>2 + 3*x*y<\/p>\n
f_prime_x = sp.diff(f, x)<\/p>\n
f_prime_y = sp.diff(f, y)<\/p>\n
print(f_prime_x)<\/p>\n
print(f_prime_y)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1a<\/p>\n<\/p>\n
2*x + 3*y<\/p>\n
2*y + 3*x<\/p>\n
<\/code><\/pre>\n<\/p>\n
5\u3001\u9ad8\u9636\u5bfc\u6570<\/h4>\n<\/p>\n
SymPy\u5e93\u53ef\u4ee5\u8ba1\u7b97\u9ad8\u9636\u5bfc\u6570\uff0c\u4f8b\u5982\u8ba1\u7b97\u51fd\u6570\u7684\u4e8c\u9636\u5bfc\u6570\uff1a<\/p>\n<\/p>\n
f_double_prime = sp.diff(f, x, 2)<\/p>\n
print(f_double_prime)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1a<\/p>\n<\/p>\n
2<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e8c\u3001NumPy\u5e93\u6c42\u5bfc<\/h3>\n<\/p>\n
NumPy\u5e93\u4e3b\u8981\u7528\u4e8e\u6570\u503c\u8ba1\u7b97\uff0c\u867d\u7136\u4e0d\u5177\u5907\u7b26\u53f7\u8ba1\u7b97\u7684\u80fd\u529b\uff0c\u4f46\u901a\u8fc7\u6570\u503c\u65b9\u6cd5\u53ef\u4ee5\u8fd1\u4f3c\u6c42\u5bfc\u3002\u4f8b\u5982\uff0c\u4f7f\u7528\u6709\u9650\u5dee\u5206\u6cd5\uff1a<\/p>\n<\/p>\n
1\u3001\u5bfc\u5165NumPy\u5e93<\/h4>\n<\/p>\n
\u5b89\u88c5\u5e76\u5bfc\u5165NumPy\u5e93\uff1a<\/p>\n<\/p>\n
pip install numpy<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5bfc\u5165\u5e93\u7684\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n<\/p>\n
import numpy as np<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001\u5b9a\u4e49\u51fd\u6570<\/h4>\n<\/p>\n
\u5b9a\u4e49\u9700\u8981\u6c42\u5bfc\u7684\u51fd\u6570\uff1a<\/p>\n<\/p>\n
def f(x):<\/p>\n
    return x2 + 3*x + 2<\/p>\n
<\/code><\/pre>\n<\/p>\n
3\u3001\u6709\u9650\u5dee\u5206\u6cd5\u6c42\u5bfc<\/h4>\n<\/p>\n
\u901a\u8fc7\u6709\u9650\u5dee\u5206\u6cd5\u8fd1\u4f3c\u6c42\u5bfc\uff1a<\/p>\n<\/p>\n
def numerical_derivative(f, x, h=1e-5):<\/p>\n
    return (f(x + h) - f(x)) \/ h<\/p>\n
x_val = 2<\/p>\n
f_prime_val = numerical_derivative(f, x_val)<\/p>\n
print(f_prime_val)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1a<\/p>\n<\/p>\n
7.000010000027032<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8fd9\u4e2a\u7ed3\u679c\u662f\u8fd1\u4f3c\u503c\uff0c\u968f\u7740h<\/code>\u7684\u51cf\u5c0f\uff0c\u7ed3\u679c\u4f1a\u8d8a\u6765\u8d8a\u7cbe\u786e\u3002<\/p>\n<\/p>\n
\u4e09\u3001SciPy\u5e93\u6c42\u5bfc<\/h3>\n<\/p>\n
SciPy\u5e93\u540c\u6837\u53ef\u4ee5\u7528\u4e8e\u6570\u503c\u8ba1\u7b97\uff0c\u63d0\u4f9b\u4e86\u4e00\u4e9b\u6c42\u5bfc\u7684\u5de5\u5177\u3002<\/p>\n<\/p>\n
1\u3001\u5bfc\u5165SciPy\u5e93<\/h4>\n<\/p>\n
\u5b89\u88c5\u5e76\u5bfc\u5165SciPy\u5e93\uff1a<\/p>\n<\/p>\n
pip install scipy<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5bfc\u5165\u5e93\u7684\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n<\/p>\n
import scipy.misc<\/p>\n
import numpy as np<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001\u5b9a\u4e49\u51fd\u6570<\/h4>\n<\/p>\n
\u5b9a\u4e49\u9700\u8981\u6c42\u5bfc\u7684\u51fd\u6570\uff1a<\/p>\n<\/p>\n
def f(x):<\/p>\n
    return x2 + 3*x + 2<\/p>\n
<\/code><\/pre>\n<\/p>\n
3\u3001\u4f7f\u7528SciPy\u5e93\u6c42\u5bfc<\/h4>\n<\/p>\n
\u4f7f\u7528SciPy\u5e93\u4e2d\u7684derivative<\/code>\u51fd\u6570\u6c42\u5bfc\uff1a<\/p>\n<\/p>\n
f_prime_val = scipy.misc.derivative(f, 2.0, dx=1e-6)<\/p>\n
print(f_prime_val)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1a<\/p>\n<\/p>\n
7.000000000013102<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8fd9\u4e2a\u7ed3\u679c\u4e5f\u662f\u8fd1\u4f3c\u503c\uff0c\u4f46\u7cbe\u5ea6\u8f83\u9ad8\u3002<\/p>\n<\/p>\n
\u56db\u3001\u591a\u53d8\u91cf\u51fd\u6570\u6c42\u5bfc<\/h3>\n<\/p>\n
1\u3001\u5bfc\u5165SymPy\u5e93<\/h4>\n<\/p>\n
\u6211\u4eec\u5df2\u7ecf\u5728\u4e0a\u9762\u7684SymPy\u5e93\u6c42\u5bfc\u4e2d\u4ecb\u7ecd\u4e86\u5982\u4f55\u5bfc\u5165SymPy\u5e93\uff0c\u8fd9\u91cc\u4e0d\u518d\u8d58\u8ff0\u3002<\/p>\n<\/p>\n
2\u3001\u5b9a\u4e49\u591a\u53d8\u91cf\u51fd\u6570<\/h4>\n<\/p>\n
\u5b9a\u4e49\u4e00\u4e2a\u5305\u542b\u591a\u4e2a\u53d8\u91cf\u7684\u51fd\u6570\uff0c\u4f8b\u5982\uff1a<\/p>\n<\/p>\n
x, y = sp.symbols('x y')<\/p>\n
f = x<strong>2 + y<\/strong>2 + 3*x*y<\/p>\n
<\/code><\/pre>\n<\/p>\n
3\u3001\u5bf9\u591a\u4e2a\u53d8\u91cf\u6c42\u5bfc<\/h4>\n<\/p>\n
\u4f7f\u7528diff()<\/code>\u51fd\u6570\u5206\u522b\u5bf9\u4e0d\u540c\u53d8\u91cf\u6c42\u5bfc\uff1a<\/p>\n<\/p>\n
f_prime_x = sp.diff(f, x)<\/p>\n
f_prime_y = sp.diff(f, y)<\/p>\n
print(f_prime_x)<\/p>\n
print(f_prime_y)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1a<\/p>\n<\/p>\n
2*x + 3*y<\/p>\n
2*y + 3*x<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e94\u3001\u9690\u51fd\u6570\u6c42\u5bfc<\/h3>\n<\/p>\n
\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\uff0c\u51fd\u6570\u7684\u5f62\u5f0f\u53ef\u80fd\u662f\u9690\u5f0f\u7684\uff0c\u5373\u65e0\u6cd5\u76f4\u63a5\u5199\u6210\u663e\u5f0f\u51fd\u6570\u7684\u5f62\u5f0f\u3002SymPy\u5e93\u540c\u6837\u80fd\u591f\u5904\u7406\u8fd9\u79cd\u60c5\u51b5\u3002<\/p>\n<\/p>\n
1\u3001\u5b9a\u4e49\u9690\u51fd\u6570<\/h4>\n<\/p>\n
\u4f8b\u5982\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u9690\u51fd\u6570\uff1a<\/p>\n<\/p>\n
x, y = sp.symbols('x y')<\/p>\n
f = x<strong>2 + y<\/strong>2 - 1<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001\u6c42\u9690\u51fd\u6570\u7684\u5bfc\u6570<\/h4>\n<\/p>\n
\u4f7f\u7528diff()<\/code>\u51fd\u6570\u5bf9\u9690\u51fd\u6570\u6c42\u5bfc\uff1a<\/p>\n<\/p>\n
f_prime_x = sp.diff(f, x)<\/p>\n
f_prime_y = sp.diff(f, y)<\/p>\n
print(f_prime_x)<\/p>\n
print(f_prime_y)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1a<\/p>\n<\/p>\n
2*x<\/p>\n
2*y<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u6b64\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u6c42\u89e3\u4e0a\u8ff0\u65b9\u7a0b\u7ec4\uff0c\u5f97\u5230\u9690\u51fd\u6570\u7684\u5bfc\u6570\u5173\u7cfb\u3002<\/p>\n<\/p>\n
\u516d\u3001\u53c2\u6570\u51fd\u6570\u6c42\u5bfc<\/h3>\n<\/p>\n
\u5728\u67d0\u4e9b\u5e94\u7528\u4e2d\uff0c\u51fd\u6570\u53ef\u80fd\u4f9d\u8d56\u4e8e\u591a\u4e2a\u53c2\u6570\u3002SymPy\u5e93\u540c\u6837\u53ef\u4ee5\u5904\u7406\u8fd9\u79cd\u60c5\u51b5\u3002<\/p>\n<\/p>\n
1\u3001\u5b9a\u4e49\u53c2\u6570\u51fd\u6570<\/h4>\n<\/p>\n
\u4f8b\u5982\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u53c2\u6570\u51fd\u6570\uff1a<\/p>\n<\/p>\n
x, a, b = sp.symbols('x a b')<\/p>\n
f = a*x2 + b*x + 1<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001\u5bf9\u53c2\u6570\u6c42\u5bfc<\/h4>\n<\/p>\n
\u4f7f\u7528diff()<\/code>\u51fd\u6570\u5bf9\u53c2\u6570\u6c42\u5bfc\uff1a<\/p>\n<\/p>\n
f_prime_a = sp.diff(f, a)<\/p>\n
f_prime_b = sp.diff(f, b)<\/p>\n
print(f_prime_a)<\/p>\n
print(f_prime_b)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1a<\/p>\n<\/p>\n
x2<\/p>\n
x<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u6b64\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u53c2\u6570\u51fd\u6570\u7684\u5bfc\u6570\u5173\u7cfb\u3002<\/p>\n<\/p>\n
\u4e03\u3001\u94fe\u5f0f\u6cd5\u5219\u6c42\u5bfc<\/h3>\n<\/p>\n
\u94fe\u5f0f\u6cd5\u5219\u662f\u6c42\u5bfc\u7684\u91cd\u8981\u6cd5\u5219\u4e4b\u4e00\uff0cSymPy\u5e93\u53ef\u4ee5\u65b9\u4fbf\u5730\u5904\u7406\u94fe\u5f0f\u6cd5\u5219\u7684\u6c42\u5bfc\u3002<\/p>\n<\/p>\n
1\u3001\u5b9a\u4e49\u590d\u5408\u51fd\u6570<\/h4>\n<\/p>\n
\u4f8b\u5982\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u590d\u5408\u51fd\u6570\uff1a<\/p>\n<\/p>\n
x, y = sp.symbols('x y')<\/p>\n
f = sp.sin(x)<\/p>\n
g = sp.exp(f)<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u6c42\u5bfc<\/h4>\n<\/p>\n
\u4f7f\u7528diff()<\/code>\u51fd\u6570\u5bf9\u590d\u5408\u51fd\u6570\u6c42\u5bfc\uff1a<\/p>\n<\/p>\n
g_prime = sp.diff(g, x)<\/p>\n
print(g_prime)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1a<\/p>\n<\/p>\n
exp(sin(x))*cos(x)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u6b64\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u590d\u5408\u51fd\u6570\u7684\u5bfc\u6570\u5173\u7cfb\u3002<\/p>\n<\/p>\n
\u516b\u3001\u6570\u503c\u79ef\u5206\u4e2d\u7684\u6c42\u5bfc<\/h3>\n<\/p>\n
\u5728\u6570\u503c\u79ef\u5206\u4e2d\uff0c\u6c42\u5bfc\u540c\u6837\u662f\u4e00\u4e2a\u91cd\u8981\u6b65\u9aa4\u3002NumPy\u548cSciPy\u5e93\u53ef\u4ee5\u65b9\u4fbf\u5730\u5904\u7406\u8fd9\u79cd\u60c5\u51b5\u3002<\/p>\n<\/p>\n
1\u3001\u5bfc\u5165\u5fc5\u8981\u7684\u5e93<\/h4>\n<\/p>\n
\u5b89\u88c5\u5e76\u5bfc\u5165NumPy\u548cSciPy\u5e93\uff1a<\/p>\n<\/p>\n
pip install numpy scipy<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5bfc\u5165\u5e93\u7684\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n<\/p>\n
import numpy as np<\/p>\n
import scipy.integrate as spi<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001\u5b9a\u4e49\u88ab\u79ef\u51fd\u6570<\/h4>\n<\/p>\n
\u5b9a\u4e49\u9700\u8981\u8fdb\u884c\u6570\u503c\u79ef\u5206\u7684\u51fd\u6570\uff1a<\/p>\n<\/p>\n
def f(x):<\/p>\n
    return x2 + 3*x + 2<\/p>\n
<\/code><\/pre>\n<\/p>\n
3\u3001\u6570\u503c\u79ef\u5206\u6c42\u5bfc<\/h4>\n<\/p>\n
\u4f7f\u7528SciPy\u5e93\u4e2d\u7684quad<\/code>\u51fd\u6570\u8fdb\u884c\u6570\u503c\u79ef\u5206\uff0c\u5e76\u6c42\u5bfc\uff1a<\/p>\n<\/p>\n
integral_val, error = spi.quad(f, 0, 1)<\/p>\n
print(integral_val)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1a<\/p>\n<\/p>\n
3.833333333333333<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u6b64\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u88ab\u79ef\u51fd\u6570\u5728\u6307\u5b9a\u533a\u95f4\u5185\u7684\u79ef\u5206\u503c\u3002<\/p>\n<\/p>\n
\u4e5d\u3001\u4f18\u5316\u95ee\u9898\u4e2d\u7684\u6c42\u5bfc<\/h3>\n<\/p>\n
\u5728\u4f18\u5316\u95ee\u9898\u4e2d\uff0c\u6c42\u5bfc\u540c\u6837\u662f\u4e00\u4e2a\u91cd\u8981\u6b65\u9aa4\u3002SymPy\u5e93\u53ef\u4ee5\u65b9\u4fbf\u5730\u5904\u7406\u8fd9\u79cd\u60c5\u51b5\u3002<\/p>\n<\/p>\n
1\u3001\u5b9a\u4e49\u76ee\u6807\u51fd\u6570<\/h4>\n<\/p>\n
\u4f8b\u5982\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u76ee\u6807\u51fd\u6570\uff1a<\/p>\n<\/p>\n
x = sp.symbols('x')<\/p>\n
f = x2 + 3*x + 2<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001\u6c42\u68af\u5ea6<\/h4>\n<\/p>\n
\u4f7f\u7528diff()<\/code>\u51fd\u6570\u5bf9\u76ee\u6807\u51fd\u6570\u6c42\u68af\u5ea6\uff1a<\/p>\n<\/p>\n
f_prime = sp.diff(f, x)<\/p>\n
print(f_prime)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1a<\/p>\n<\/p>\n
2*x + 3<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u6b64\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u76ee\u6807\u51fd\u6570\u7684\u68af\u5ea6\uff0c\u7528\u4e8e\u4f18\u5316\u95ee\u9898\u7684\u6c42\u89e3\u3002<\/p>\n<\/p>\n
\u5341\u3001\u504f\u5fae\u5206\u65b9\u7a0b\u4e2d\u7684\u6c42\u5bfc<\/h3>\n<\/p>\n
\u504f\u5fae\u5206\u65b9\u7a0b\u662f\u63cf\u8ff0\u7269\u7406\u73b0\u8c61\u7684\u91cd\u8981\u5de5\u5177\uff0cSymPy\u5e93\u53ef\u4ee5\u65b9\u4fbf\u5730\u5904\u7406\u504f\u5fae\u5206\u65b9\u7a0b\u7684\u6c42\u5bfc\u3002<\/p>\n<\/p>\n
1\u3001\u5b9a\u4e49\u504f\u5fae\u5206\u65b9\u7a0b<\/h4>\n<\/p>\n
\u4f8b\u5982\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u504f\u5fae\u5206\u65b9\u7a0b\uff1a<\/p>\n<\/p>\n
x, y = sp.symbols('x y')<\/p>\n
u = sp.Function('u')(x, y)<\/p>\n
pde = sp.Eq(sp.diff(u, x, 2) + sp.diff(u, y, 2), 0)<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001\u6c42\u504f\u5bfc\u6570<\/h4>\n<\/p>\n
\u4f7f\u7528diff()<\/code>\u51fd\u6570\u5bf9\u504f\u5fae\u5206\u65b9\u7a0b\u6c42\u504f\u5bfc\u6570\uff1a<\/p>\n<\/p>\n
u_xx = sp.diff(u, x, 2)<\/p>\n
u_yy = sp.diff(u, y, 2)<\/p>\n
print(u_xx)<\/p>\n
print(u_yy)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1a<\/p>\n<\/p>\n
Derivative(u(x, y), (x, 2))<\/p>\n
Derivative(u(x, y), (y, 2))<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u6b64\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u504f\u5fae\u5206\u65b9\u7a0b\u7684\u504f\u5bfc\u6570\u5173\u7cfb\u3002<\/p>\n<\/p>\n
\u5341\u4e00\u3001\u6c42\u5bfc\u7684\u5e94\u7528\u5b9e\u4f8b<\/h3>\n<\/p>\n
1\u3001\u7269\u7406\u5b66\u4e2d\u7684\u5e94\u7528<\/h4>\n<\/p>\n
\u5728\u7269\u7406\u5b66\u4e2d\uff0c\u6c42\u5bfc\u662f\u63cf\u8ff0\u7269\u7406\u73b0\u8c61\u7684\u91cd\u8981\u5de5\u5177\u3002\u4f8b\u5982\uff0c\u901f\u5ea6\u662f\u4f4d\u79fb\u5bf9\u65f6\u95f4\u7684\u5bfc\u6570\uff0c\u52a0\u901f\u5ea6\u662f\u901f\u5ea6\u5bf9\u65f6\u95f4\u7684\u5bfc\u6570\u3002<\/p>\n<\/p>\n
import sympy as sp<\/p>\n
t = sp.symbols('t')<\/p>\n
s = 5*t2 + 3*t + 2<\/p>\n
v = sp.diff(s, t)<\/p>\n
a = sp.diff(v, t)<\/p>\n
print(v)<\/p>\n
print(a)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1a<\/p>\n<\/p>\n
10*t + 3<\/p>\n
10<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u6b64\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u7269\u4f53\u7684\u901f\u5ea6\u548c\u52a0\u901f\u5ea6\u3002<\/p>\n<\/p>\n
2\u3001\u7ecf\u6d4e\u5b66\u4e2d\u7684\u5e94\u7528<\/h4>\n<\/p>\n
\u5728\u7ecf\u6d4e\u5b66\u4e2d\uff0c\u6c42\u5bfc\u662f\u63cf\u8ff0\u7ecf\u6d4e\u73b0\u8c61\u7684\u91cd\u8981\u5de5\u5177\u3002\u4f8b\u5982\uff0c\u8fb9\u9645\u6210\u672c\u662f\u603b\u6210\u672c\u5bf9\u4ea7\u91cf\u7684\u5bfc\u6570\uff0c\u8fb9\u9645\u6536\u76ca\u662f\u603b\u6536\u76ca\u5bf9\u4ea7\u91cf\u7684\u5bfc\u6570\u3002<\/p>\n<\/p>\n
import sympy as sp<\/p>\n
q = sp.symbols('q')<\/p>\n
C = 5*q2 + 3*q + 2<\/p>\n
MC = sp.diff(C, q)<\/p>\n
print(MC)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1a<\/p>\n<\/p>\n
10*q + 3<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u6b64\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u8fb9\u9645\u6210\u672c\u3002<\/p>\n<\/p>\n
3\u3001\u751f\u7269\u5b66\u4e2d\u7684\u5e94\u7528<\/h4>\n<\/p>\n
\u5728\u751f\u7269\u5b66\u4e2d\uff0c\u6c42\u5bfc\u662f\u63cf\u8ff0\u751f\u7269\u73b0\u8c61\u7684\u91cd\u8981\u5de5\u5177\u3002\u4f8b\u5982\uff0c\u79cd\u7fa4\u589e\u957f\u7387\u662f\u79cd\u7fa4\u6570\u91cf\u5bf9\u65f6\u95f4\u7684\u5bfc\u6570\u3002<\/p>\n<\/p>\n
import sympy as sp<\/p>\n
t = sp.symbols('t')<\/p>\n
N = 100*sp.exp(0.02*t)<\/p>\n
growth_rate = sp.diff(N, t)<\/p>\n
print(growth_rate)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1a<\/p>\n<\/p>\n
2.0*exp(0.02*t)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u6b64\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u79cd\u7fa4\u7684\u589e\u957f\u7387\u3002<\/p>\n<\/p>\n
\u5341\u4e8c\u3001\u603b\u7ed3<\/h3>\n<\/p>\n
Python\u63d0\u4f9b\u4e86\u591a\u79cd\u65b9\u6cd5\u6765\u5bf9\u51fd\u6570\u8fdb\u884c\u6c42\u5bfc\u3002SymPy\u5e93<\/strong>\u662f\u6700\u5e38\u7528\u7684\u65b9\u6cd5\uff0c\u56e0\u5176\u529f\u80fd\u5f3a\u5927\u4e14\u6613\u4e8e\u4f7f\u7528\uff0c\u9002\u7528\u4e8e\u7b26\u53f7\u8ba1\u7b97\u3002NumPy\u5e93<\/strong>\u548cSciPy\u5e93<\/strong>\u5219\u4e3b\u8981\u7528\u4e8e\u6570\u503c\u8ba1\u7b97\uff0c\u901a\u8fc7\u6709\u9650\u5dee\u5206\u6cd5\u548c\u6570\u503c\u79ef\u5206\u7b49\u65b9\u6cd5\u6765\u8fd1\u4f3c\u6c42\u5bfc\u3002\u94fe\u5f0f\u6cd5\u5219\u6c42\u5bfc\u3001\u53c2\u6570\u51fd\u6570\u6c42\u5bfc\u3001\u591a\u53d8\u91cf\u51fd\u6570\u6c42\u5bfc<\/strong>\u7b49\u9ad8\u7ea7\u64cd\u4f5c\u5728SymPy\u5e93\u4e2d\u4e5f\u80fd\u8f7b\u677e\u5b9e\u73b0\u3002\u901a\u8fc7\u8fd9\u4e9b\u65b9\u6cd5\uff0c\u6211\u4eec\u53ef\u4ee5\u89e3\u51b3\u7269\u7406\u5b66\u3001\u7ecf\u6d4e\u5b66\u3001\u751f\u7269\u5b66\u7b49\u9886\u57df\u4e2d\u7684\u5b9e\u9645\u95ee\u9898\u3002\u5e0c\u671b\u672c\u6587\u5bf9\u60a8\u4e86\u89e3\u548c\u5e94\u7528Python\u6c42\u5bfc\u6709\u6240\u5e2e\u52a9\u3002<\/p>\n<\/p>\n
\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n
 \u5982\u4f55\u4f7f\u7528Python\u81ea\u52a8\u6c42\u5bfc\uff1f<\/strong>
\u5728Python\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528\u4e00\u4e9b\u5e93\u6765\u5b9e\u73b0\u81ea\u52a8\u6c42\u5bfc\uff0c\u5982SymPy\u548cAutograd\u3002SymPy\u662f\u4e00\u4e2a\u7528\u4e8e\u7b26\u53f7\u6570\u5b66\u7684\u5e93\uff0c\u80fd\u591f\u65b9\u4fbf\u5730\u8fdb\u884c\u7b26\u53f7\u6c42\u5bfc\u3002\u60a8\u53ea\u9700\u5b9a\u4e49\u4e00\u4e2a\u7b26\u53f7\u53d8\u91cf\u5e76\u4f7f\u7528diff\u51fd\u6570\u5373\u53ef\u3002\u4f8b\u5982\uff1a<\/p>\n
import sympy as sp\n\nx = sp.symbols('x')\nfunction = x**2 + 3*x + 2\nderivative = sp.diff(function, x)\nprint(derivative)\n<\/code><\/pre>\n
Python\u4e2d\u6709\u54ea\u4e9b\u5e93\u53ef\u4ee5\u8fdb\u884c\u6570\u503c\u6c42\u5bfc\uff1f<\/strong>
\u5728Python\u4e2d\uff0c\u9664\u4e86SymPy\u5916\uff0c\u8fd8\u6709SciPy\u548cNumPy\u7b49\u5e93\u53ef\u4ee5\u8fdb\u884c\u6570\u503c\u6c42\u5bfc\u3002SciPy\u7684scipy.misc.derivative<\/code>\u51fd\u6570\u53ef\u4ee5\u7528\u6765\u8ba1\u7b97\u51fd\u6570\u7684\u6570\u503c\u5bfc\u6570\u3002\u4f8b\u5982\uff1a<\/p>\n
from scipy.misc import derivative\n\ndef f(x):\n    return x**2 + 3*x + 2\n\nresult = derivative(f, 1.0, dx=1e-6)\nprint(result)\n<\/code><\/pre>\n
\u5982\u4f55\u5728Python\u4e2d\u5904\u7406\u591a\u53d8\u91cf\u51fd\u6570\u7684\u6c42\u5bfc\uff1f<\/strong>
\u5bf9\u4e8e\u591a\u53d8\u91cf\u51fd\u6570\uff0cSymPy\u540c\u6837\u652f\u6301\u7b26\u53f7\u6c42\u5bfc\u3002\u60a8\u53ef\u4ee5\u5b9a\u4e49\u591a\u4e2a\u7b26\u53f7\u53d8\u91cf\u5e76\u4f7f\u7528diff\u51fd\u6570\u5bf9\u7279\u5b9a\u53d8\u91cf\u8fdb\u884c\u6c42\u5bfc\u3002\u793a\u4f8b\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n
import sympy as sp\n\nx, y = sp.symbols('x y')\nfunction = x<strong>2 + y<\/strong>2 + 3*x*y\nderivative_x = sp.diff(function, x)\nderivative_y = sp.diff(function, y)\nprint(derivative_x)\nprint(derivative_y)\n<\/code><\/pre>\n
\u901a\u8fc7\u8fd9\u4e9b\u65b9\u6cd5\uff0c\u60a8\u53ef\u4ee5\u8f7b\u677e\u5730\u5728Python\u4e2d\u8fdb\u884c\u51fd\u6570\u7684\u6c42\u5bfc\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u4f7f\u7528Python\u5bf9\u51fd\u6570\u6c42\u5bfc\u53ef\u4ee5\u4f7f\u7528SymPy\u5e93\u3001NumPy\u5e93\u3001SciPy\u5e93\uff0c\u6b65\u9aa4\u5305\u62ec\u5bfc\u5165\u5e93\u3001\u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf\u3001\u5b9a\u4e49 […]","protected":false},"author":3,"featured_media":1170808,"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\/1170801"}],"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=1170801"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1170801\/revisions"}],"predecessor-version":[{"id":1170812,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1170801\/revisions\/1170812"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/1170808"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=1170801"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=1170801"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=1170801"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}