{"id":1187491,"date":"2025-01-15T20:06:11","date_gmt":"2025-01-15T12:06:11","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1187491.html"},"modified":"2025-01-15T20:06:15","modified_gmt":"2025-01-15T12:06:15","slug":"python%e5%a6%82%e4%bd%95%e8%a1%a8%e7%a4%ba%e6%8c%87%e6%95%b0%e5%87%bd%e6%95%b0","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1187491.html","title":{"rendered":"python\u5982\u4f55\u8868\u793a\u6307\u6570\u51fd\u6570"},"content":{"rendered":"

\"python\u5982\u4f55\u8868\u793a\u6307\u6570\u51fd\u6570\"<\/p>\n

Python\u8868\u793a\u6307\u6570\u51fd\u6570\u7684\u65b9\u5f0f\u6709\u591a\u79cd\uff0c\u4e3b\u8981\u5305\u62ec\u4f7f\u7528\u5185\u7f6e\u7684\u5e42\u8fd0\u7b97\u7b26\u3001math\u6a21\u5757\u4e2d\u7684exp\u51fd\u6570\u548cnumpy\u6a21\u5757\u4e2d\u7684exp\u51fd\u6570\u3002<\/strong>\u5176\u4e2d\uff0c\u4f7f\u7528\u5185\u7f6e\u7684\u5e42\u8fd0\u7b97\u7b26<\/strong>\u662f\u6700\u5e38\u89c1\u548c\u76f4\u63a5\u7684\u65b9\u5f0f\uff0c\u4e0b\u9762\u5c06\u8be6\u7ec6\u63cf\u8ff0\u5176\u7528\u6cd5\u3002<\/p>\n<\/p>\n

\u4f7f\u7528\u5185\u7f6e\u7684\u5e42\u8fd0\u7b97\u7b26<\/strong>\uff1a\u5728Python\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528\u53cc\u661f\u53f7<strong><\/code>\u8868\u793a\u6307\u6570\u8fd0\u7b97\u3002\u4f8b\u5982\uff0c2<\/strong>3<\/code>\u8868\u793a2\u7684\u4e09\u6b21\u65b9\uff0c\u7ed3\u679c\u662f8\u3002\u8fd9\u79cd\u65b9\u5f0f\u7b80\u5355\u6613\u61c2\uff0c\u9002\u7528\u4e8e\u57fa\u672c\u7684\u6307\u6570\u8ba1\u7b97\u3002<\/p>\n<\/p>\n

\u4f7f\u7528\u5185\u7f6e\u7684\u5e42\u8fd0\u7b97\u7b26\u7684\u793a\u4f8b\uff1a<\/p>\n<\/p>\n

# \u8ba1\u7b972\u76843\u6b21\u65b9<\/p>\n
result = 2  3<\/p>\n
print(result)  # \u8f93\u51fa: 8<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8fd9\u79cd\u65b9\u5f0f\u9002\u7528\u4e8e\u7b80\u5355\u7684\u6307\u6570\u8fd0\u7b97\uff0c\u4f46\u5982\u679c\u9700\u8981\u66f4\u590d\u6742\u7684\u6570\u5b66\u8ba1\u7b97\uff0c\u7279\u522b\u662f\u6d89\u53ca\u81ea\u7136\u6307\u6570\u51fd\u6570\u65f6\uff0c\u4f7f\u7528math<\/code>\u6a21\u5757\u6216numpy<\/code>\u6a21\u5757\u4f1a\u66f4\u52a0\u65b9\u4fbf\u3002<\/p>\n<\/p>\n
\n
\u4e00\u3001MATH\u6a21\u5757<\/h3>\n<\/p>\n
Python\u7684math<\/code>\u6a21\u5757\u63d0\u4f9b\u4e86\u8bb8\u591a\u6570\u5b66\u51fd\u6570\uff0c\u5176\u4e2d\u5305\u62ecexp<\/code>\u51fd\u6570\uff0c\u7528\u4e8e\u8ba1\u7b97e\u7684\u6307\u6570\u5e42\u3002<\/p>\n<\/p>\n
1\u3001math.exp\u51fd\u6570<\/h4>\n<\/p>\n
math.exp(x)<\/code>\u51fd\u6570\u7528\u4e8e\u8ba1\u7b97e\u7684x\u6b21\u65b9\uff0c\u5176\u4e2de\u662f\u81ea\u7136\u5bf9\u6570\u7684\u5e95\u6570\uff0c\u7ea6\u7b49\u4e8e2.71828\u3002<\/p>\n<\/p>\n
\u4f7f\u7528\u793a\u4f8b\uff1a<\/p>\n<\/p>\n
import math<\/p>\n
\u8ba1\u7b97e\u76842\u6b21\u65b9<\/strong><\/h2>\n
result = math.exp(2)<\/p>\n
print(result)  # \u8f93\u51fa: 7.3890560989306495<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001math.pow\u51fd\u6570<\/h4>\n<\/p>\n
\u9664\u4e86exp<\/code>\u51fd\u6570\u5916\uff0cmath<\/code>\u6a21\u5757\u8fd8\u63d0\u4f9b\u4e86pow<\/code>\u51fd\u6570\uff0c\u7528\u4e8e\u8ba1\u7b97\u4efb\u610f\u6570\u7684\u5e42\u3002<\/p>\n<\/p>\n
\u4f7f\u7528\u793a\u4f8b\uff1a<\/p>\n<\/p>\n
import math<\/p>\n
\u8ba1\u7b972\u76843\u6b21\u65b9<\/strong><\/h2>\n
result = math.pow(2, 3)<\/p>\n
print(result)  # \u8f93\u51fa: 8.0<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e8c\u3001NUMPY\u6a21\u5757<\/h3>\n<\/p>\n
\u5bf9\u4e8e\u6d89\u53ca\u5927\u91cf\u6570\u503c\u8ba1\u7b97\u7684\u60c5\u51b5\uff0cnumpy<\/code>\u6a21\u5757\u63d0\u4f9b\u4e86\u66f4\u591a\u9ad8\u6548\u7684\u6570\u5b66\u51fd\u6570\uff0c\u5305\u62ecnumpy.exp<\/code>\u51fd\u6570\u3002<\/p>\n<\/p>\n
1\u3001numpy.exp\u51fd\u6570<\/h4>\n<\/p>\n
numpy.exp(x)<\/code>\u51fd\u6570\u7528\u4e8e\u8ba1\u7b97e\u7684\u6bcf\u4e2a\u5143\u7d20\u7684\u6307\u6570\u5e42\uff0c\u9002\u7528\u4e8e\u6570\u7ec4\u64cd\u4f5c\u3002<\/p>\n<\/p>\n
\u4f7f\u7528\u793a\u4f8b\uff1a<\/p>\n<\/p>\n
import numpy as np<\/p>\n
\u521b\u5efa\u4e00\u4e2a\u6570\u7ec4<\/strong><\/h2>\n
arr = np.array([1, 2, 3])<\/p>\n
\u8ba1\u7b97\u6570\u7ec4\u4e2d\u6bcf\u4e2a\u5143\u7d20\u7684\u6307\u6570\u5e42<\/strong><\/h2>\n
result = np.exp(arr)<\/p>\n
print(result)  # \u8f93\u51fa: [ 2.71828183  7.3890561  20.08553692]<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001numpy.power\u51fd\u6570<\/h4>\n<\/p>\n
numpy<\/code>\u6a21\u5757\u8fd8\u63d0\u4f9b\u4e86power<\/code>\u51fd\u6570\uff0c\u7528\u4e8e\u8ba1\u7b97\u6570\u7ec4\u4e2d\u6bcf\u4e2a\u5143\u7d20\u7684\u5e42\u3002<\/p>\n<\/p>\n
\u4f7f\u7528\u793a\u4f8b\uff1a<\/p>\n<\/p>\n
import numpy as np<\/p>\n
\u521b\u5efa\u4e00\u4e2a\u6570\u7ec4<\/strong><\/h2>\n
arr = np.array([1, 2, 3])<\/p>\n
\u8ba1\u7b97\u6570\u7ec4\u4e2d\u6bcf\u4e2a\u5143\u7d20\u76843\u6b21\u65b9<\/strong><\/h2>\n
result = np.power(arr, 3)<\/p>\n
print(result)  # \u8f93\u51fa: [ 1  8 27]<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e09\u3001SYMPY\u6a21\u5757<\/h3>\n<\/p>\n
SymPy<\/code>\u662f\u4e00\u4e2aPython\u7684\u7b26\u53f7\u6570\u5b66\u5e93\uff0c\u9002\u7528\u4e8e\u7b26\u53f7\u8ba1\u7b97\u548c\u6570\u5b66\u516c\u5f0f\u7684\u8868\u793a\u3002<\/p>\n<\/p>\n
1\u3001\u7b26\u53f7\u8868\u8fbe\u5f0f<\/h4>\n<\/p>\n
\u4f7f\u7528SymPy<\/code>\u53ef\u4ee5\u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf\u5e76\u8fdb\u884c\u6307\u6570\u8fd0\u7b97\u3002<\/p>\n<\/p>\n
\u4f7f\u7528\u793a\u4f8b\uff1a<\/p>\n<\/p>\n
import sympy as sp<\/p>\n
\u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf<\/strong><\/h2>\n
x = sp.symbols('x')<\/p>\n
\u8868\u793a\u6307\u6570\u51fd\u6570<\/strong><\/h2>\n
expr = sp.exp(x)<\/p>\n
print(expr)  # \u8f93\u51fa: exp(x)<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001\u6c42\u5bfc\u548c\u79ef\u5206<\/h4>\n<\/p>\n
SymPy<\/code>\u53ef\u4ee5\u5bf9\u7b26\u53f7\u8868\u8fbe\u5f0f\u8fdb\u884c\u6c42\u5bfc\u548c\u79ef\u5206\u64cd\u4f5c\u3002<\/p>\n<\/p>\n
\u4f7f\u7528\u793a\u4f8b\uff1a<\/p>\n<\/p>\n
import sympy as sp<\/p>\n
\u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf<\/strong><\/h2>\n
x = sp.symbols('x')<\/p>\n
\u8868\u793a\u6307\u6570\u51fd\u6570<\/strong><\/h2>\n
expr = sp.exp(x)<\/p>\n
\u6c42\u5bfc<\/strong><\/h2>\n
derivative = sp.diff(expr, x)<\/p>\n
print(derivative)  # \u8f93\u51fa: exp(x)<\/p>\n
\u79ef\u5206<\/strong><\/h2>\n
integral = sp.integrate(expr, x)<\/p>\n
print(integral)  # \u8f93\u51fa: exp(x)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u56db\u3001SCIPY\u6a21\u5757<\/h3>\n<\/p>\n
SciPy<\/code>\u662f\u4e00\u4e2a\u7528\u4e8e\u79d1\u5b66\u8ba1\u7b97\u7684Python\u5e93\uff0c\u63d0\u4f9b\u4e86\u66f4\u591a\u9ad8\u7ea7\u6570\u5b66\u51fd\u6570\u3002<\/p>\n<\/p>\n
1\u3001scipy.special.expit\u51fd\u6570<\/h4>\n<\/p>\n
SciPy<\/code>\u7684special<\/code>\u6a21\u5757\u63d0\u4f9b\u4e86\u8bb8\u591a\u7279\u6b8a\u51fd\u6570\uff0c\u5305\u62ecexpit<\/code>\u51fd\u6570\uff0c\u7528\u4e8e\u8ba1\u7b97\u903b\u8f91\u51fd\u6570\u3002<\/p>\n<\/p>\n
\u4f7f\u7528\u793a\u4f8b\uff1a<\/p>\n<\/p>\n
from scipy.special import expit<\/p>\n
\u8ba1\u7b97\u903b\u8f91\u51fd\u6570\u503c<\/strong><\/h2>\n
result = expit(2)<\/p>\n
print(result)  # \u8f93\u51fa: 0.8807970779778823<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001scipy.optimize.curve_fit\u51fd\u6570<\/h4>\n<\/p>\n
SciPy<\/code>\u7684optimize<\/code>\u6a21\u5757\u63d0\u4f9b\u4e86\u8bb8\u591a\u4f18\u5316\u548c\u62df\u5408\u51fd\u6570\uff0c\u5305\u62eccurve_fit<\/code>\u51fd\u6570\uff0c\u7528\u4e8e\u6307\u6570\u51fd\u6570\u62df\u5408\u3002<\/p>\n<\/p>\n
\u4f7f\u7528\u793a\u4f8b\uff1a<\/p>\n<\/p>\n
import numpy as np<\/p>\n
from scipy.optimize import curve_fit<\/p>\n
import matplotlib.pyplot as plt<\/p>\n
\u5b9a\u4e49\u6307\u6570\u51fd\u6570<\/strong><\/h2>\n
def exp_func(x, a, b):<\/p>\n
    return a * np.exp(b * x)<\/p>\n
\u751f\u6210\u6570\u636e<\/strong><\/h2>\n
x_data = np.linspace(0, 4, 50)<\/p>\n
y_data = exp_func(x_data, 2, 1.5) + 0.5 * np.random.normal(size=len(x_data))<\/p>\n
\u62df\u5408\u6570\u636e<\/strong><\/h2>\n
params, params_covariance = curve_fit(exp_func, x_data, y_data, p0=[2, 1.5])<\/p>\n
\u7ed8\u5236\u7ed3\u679c<\/strong><\/h2>\n
plt.scatter(x_data, y_data, label='Data')<\/p>\n
plt.plot(x_data, exp_func(x_data, params[0], params[1]), label='Fitted function', color='red')<\/p>\n
plt.legend()<\/p>\n
plt.show()<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e94\u3001\u5176\u5b83\u5e38\u89c1\u7684\u6307\u6570\u51fd\u6570\u5e94\u7528\u573a\u666f<\/h3>\n<\/p>\n
1\u3001\u91d1\u878d\u8ba1\u7b97<\/h4>\n<\/p>\n
\u6307\u6570\u51fd\u6570\u5728\u91d1\u878d\u8ba1\u7b97\u4e2d\u6709\u5e7f\u6cdb\u5e94\u7528\uff0c\u5982\u8ba1\u7b97\u590d\u5229\u3001\u503a\u5238\u5b9a\u4ef7\u7b49\u3002<\/p>\n<\/p>\n
\u4f7f\u7528\u793a\u4f8b\uff1a<\/p>\n<\/p>\n
# \u8ba1\u7b97\u590d\u5229<\/p>\n
principal = 1000  # \u672c\u91d1<\/p>\n
rate = 0.05  # \u5e74\u5229\u7387<\/p>\n
time = 10  # \u65f6\u95f4\uff08\u5e74\uff09<\/p>\n
\u8ba1\u7b9710\u5e74\u540e\u7684\u672c\u606f\u548c<\/strong><\/h2>\n
amount = principal * (1 + rate)  time<\/p>\n
print(amount)  # \u8f93\u51fa: 1628.8946267774415<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001\u4fe1\u53f7\u5904\u7406<\/h4>\n<\/p>\n
\u6307\u6570\u51fd\u6570\u5728\u4fe1\u53f7\u5904\u7406\u4e2d\u7684\u5e94\u7528\u5305\u62ec\u6ee4\u6ce2\u5668\u8bbe\u8ba1\u3001\u65f6\u57df\u5206\u6790\u7b49\u3002<\/p>\n<\/p>\n
\u4f7f\u7528\u793a\u4f8b\uff1a<\/p>\n<\/p>\n
import numpy as np<\/p>\n
import matplotlib.pyplot as plt<\/p>\n
\u751f\u6210\u4fe1\u53f7<\/strong><\/h2>\n
t = np.linspace(0, 1, 500)<\/p>\n
signal = np.exp(-t) * np.sin(2 * np.pi * 5 * t)<\/p>\n
\u7ed8\u5236\u4fe1\u53f7<\/strong><\/h2>\n
plt.plot(t, signal)<\/p>\n
plt.xlabel('Time [s]')<\/p>\n
plt.ylabel('Amplitude')<\/p>\n
plt.title('Damped Sine Wave')<\/p>\n
plt.show()<\/p>\n
<\/code><\/pre>\n<\/p>\n
3\u3001\u673a\u5668\u5b66\u4e60<\/a><\/h4>\n<\/p>\n
\u5728\u673a\u5668\u5b66\u4e60\u4e2d\uff0c\u6307\u6570\u51fd\u6570\u88ab\u5e7f\u6cdb\u5e94\u7528\u4e8e\u6fc0\u6d3b\u51fd\u6570\u3001\u635f\u5931\u51fd\u6570\u7b49\u3002<\/p>\n<\/p>\n
\u4f7f\u7528\u793a\u4f8b\uff1a<\/p>\n<\/p>\n
import numpy as np<\/p>\n
\u5b9a\u4e49sigmoid\u6fc0\u6d3b\u51fd\u6570<\/strong><\/h2>\n
def sigmoid(x):<\/p>\n
    return 1 \/ (1 + np.exp(-x))<\/p>\n
\u751f\u6210\u6570\u636e<\/strong><\/h2>\n
x = np.linspace(-10, 10, 100)<\/p>\n
y = sigmoid(x)<\/p>\n
\u7ed8\u5236\u7ed3\u679c<\/strong><\/h2>\n
import matplotlib.pyplot as plt<\/p>\n
plt.plot(x, y)<\/p>\n
plt.xlabel('x')<\/p>\n
plt.ylabel('sigmoid(x)')<\/p>\n
plt.title('Sigmoid Activation Function')<\/p>\n
plt.show()<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u516d\u3001\u6307\u6570\u51fd\u6570\u7684\u6570\u5b66\u6027\u8d28\u548c\u5e94\u7528<\/h3>\n<\/p>\n
1\u3001\u6307\u6570\u51fd\u6570\u7684\u57fa\u672c\u6027\u8d28<\/h4>\n<\/p>\n
\u6307\u6570\u51fd\u6570\u5177\u6709\u4ee5\u4e0b\u57fa\u672c\u6027\u8d28\uff1a<\/p>\n<\/p>\n