{"id":1157680,"date":"2025-01-13T18:31:37","date_gmt":"2025-01-13T10:31:37","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1157680.html"},"modified":"2025-01-13T18:31:39","modified_gmt":"2025-01-13T10:31:39","slug":"python%e4%b8%ad%e5%a6%82%e4%bd%95%e8%a1%a8%e7%a4%ba%e5%af%b9%e6%95%b0","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1157680.html","title":{"rendered":"python\u4e2d\u5982\u4f55\u8868\u793a\u5bf9\u6570"},"content":{"rendered":"

\"python\u4e2d\u5982\u4f55\u8868\u793a\u5bf9\u6570\"<\/p>\n

\u5728Python\u4e2d\uff0c\u8868\u793a\u5bf9\u6570\u7684\u65b9\u6cd5\u6709\u591a\u79cd\uff0c\u4e3b\u8981\u5305\u62ec\u4f7f\u7528math<\/code>\u6a21\u5757\u3001\u4f7f\u7528numpy<\/code>\u6a21\u5757\u3001\u4f7f\u7528scipy<\/code>\u6a21\u5757<\/strong>\u3002\u5176\u4e2d\uff0c\u6700\u5e38\u7528\u7684\u65b9\u6cd5\u662f\u4f7f\u7528math<\/code>\u6a21\u5757\u4e2d\u7684log<\/code>\u51fd\u6570\u3002\u4e0b\u9762\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u8fd9\u51e0\u79cd\u65b9\u6cd5\uff0c\u5e76\u91cd\u70b9\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528math<\/code>\u6a21\u5757\u4e2d\u7684log<\/code>\u51fd\u6570\u3002<\/p>\n<\/p>\n

\u4e00\u3001\u4f7f\u7528math<\/code>\u6a21\u5757<\/h3>\n<\/p>\n

Python\u7684\u6807\u51c6\u5e93math<\/code>\u6a21\u5757\u63d0\u4f9b\u4e86\u8ba1\u7b97\u5bf9\u6570\u7684\u51fd\u6570log<\/code>\u3002\u901a\u8fc7\u8fd9\u4e2a\u51fd\u6570\uff0c\u53ef\u4ee5\u8ba1\u7b97\u81ea\u7136\u5bf9\u6570\uff08\u5373\u4ee5e\u4e3a\u5e95\u7684\u5bf9\u6570\uff09\u548c\u4efb\u610f\u5e95\u6570\u7684\u5bf9\u6570\u3002\u4ee5\u4e0b\u662f\u5177\u4f53\u7528\u6cd5\uff1a<\/p>\n<\/p>\n

import math<\/p>\n
\u8ba1\u7b97\u81ea\u7136\u5bf9\u6570<\/strong><\/h2>\n
natural_log = math.log(10)  # \u4ee5e\u4e3a\u5e95<\/p>\n
\u8ba1\u7b97\u4ee510\u4e3a\u5e95\u7684\u5bf9\u6570<\/strong><\/h2>\n
log_base_10 = math.log(10, 10)<\/p>\n
\u8ba1\u7b97\u4ee52\u4e3a\u5e95\u7684\u5bf9\u6570<\/strong><\/h2>\n
log_base_2 = math.log(10, 2)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8be6\u7ec6\u63cf\u8ff0\uff1a<\/h4>\n<\/p>\n
\u81ea\u7136\u5bf9\u6570<\/strong>\u662f\u6570\u5b66\u4e2d\u975e\u5e38\u91cd\u8981\u7684\u4e00\u79cd\u5bf9\u6570\uff0c\u4ee5\u81ea\u7136\u5e38\u6570e\uff08\u7ea6\u7b49\u4e8e2.71828\uff09\u4e3a\u5e95\u7684\u5bf9\u6570\u3002\u4f7f\u7528math.log<\/code>\u51fd\u6570\u65f6\uff0c\u5982\u679c\u53ea\u4f20\u5165\u4e00\u4e2a\u53c2\u6570\uff0c\u5219\u9ed8\u8ba4\u8ba1\u7b97\u81ea\u7136\u5bf9\u6570\u3002\u4f8b\u5982\uff0cmath.log(10)<\/code>\u8ba1\u7b97\u7684\u662flog_e(10)<\/code>\u3002\u5bf9\u4e8e\u79d1\u5b66\u8ba1\u7b97\u548c\u5de5\u7a0b\u5e94\u7528\uff0c\u8ba1\u7b97\u81ea\u7136\u5bf9\u6570\u662f\u975e\u5e38\u5e38\u89c1\u7684\u9700\u6c42\u3002<\/p>\n<\/p>\n
\u4e8c\u3001\u4f7f\u7528numpy<\/code>\u6a21\u5757<\/h3>\n<\/p>\n
numpy<\/code>\u662f\u4e00\u4e2a\u5f3a\u5927\u7684\u6570\u503c\u8ba1\u7b97\u5e93\uff0c\u4e5f\u63d0\u4f9b\u4e86\u8ba1\u7b97\u5bf9\u6570\u7684\u51fd\u6570\u3002\u901a\u8fc7numpy<\/code>\uff0c\u53ef\u4ee5\u65b9\u4fbf\u5730\u5bf9\u6570\u7ec4\u8fdb\u884c\u5bf9\u6570\u8fd0\u7b97\u3002\u4ee5\u4e0b\u662f\u5177\u4f53\u7528\u6cd5\uff1a<\/p>\n<\/p>\n
import numpy as np<\/p>\n
\u8ba1\u7b97\u81ea\u7136\u5bf9\u6570<\/strong><\/h2>\n
natural_log = np.log(10)<\/p>\n
\u8ba1\u7b97\u4ee510\u4e3a\u5e95\u7684\u5bf9\u6570<\/strong><\/h2>\n
log_base_10 = np.log10(10)<\/p>\n
\u8ba1\u7b97\u4ee52\u4e3a\u5e95\u7684\u5bf9\u6570<\/strong><\/h2>\n
log_base_2 = np.log2(10)<\/p>\n
\u5bf9\u6570\u7ec4\u8fdb\u884c\u5bf9\u6570\u8fd0\u7b97<\/strong><\/h2>\n
array = np.array([1, 10, 100, 1000])<\/p>\n
log_array = np.log(array)  # \u8ba1\u7b97\u6570\u7ec4\u4e2d\u6bcf\u4e2a\u5143\u7d20\u7684\u81ea\u7136\u5bf9\u6570<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e09\u3001\u4f7f\u7528scipy<\/code>\u6a21\u5757<\/h3>\n<\/p>\n
scipy<\/code>\u662f\u4e00\u4e2a\u57fa\u4e8enumpy<\/code>\u7684\u79d1\u5b66\u8ba1\u7b97\u5e93\uff0c\u63d0\u4f9b\u4e86\u66f4\u591a\u9ad8\u7ea7\u7684\u6570\u5b66\u51fd\u6570\u548c\u79d1\u5b66\u8ba1\u7b97\u529f\u80fd\u3002scipy<\/code>\u4e2d\u7684special<\/code>\u6a21\u5757\u4e5f\u63d0\u4f9b\u4e86\u5bf9\u6570\u51fd\u6570\u3002\u4ee5\u4e0b\u662f\u5177\u4f53\u7528\u6cd5\uff1a<\/p>\n<\/p>\n
from scipy import special<\/p>\n
\u8ba1\u7b97\u81ea\u7136\u5bf9\u6570<\/strong><\/h2>\n
natural_log = special.log(10)<\/p>\n
\u8ba1\u7b97\u4ee510\u4e3a\u5e95\u7684\u5bf9\u6570<\/strong><\/h2>\n
log_base_10 = special.log10(10)<\/p>\n
\u8ba1\u7b97\u4ee52\u4e3a\u5e95\u7684\u5bf9\u6570<\/strong><\/h2>\n
log_base_2 = special.log2(10)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u56db\u3001\u5bf9\u6570\u5728\u6570\u636e\u5904\u7406\u4e2d\u7684\u5e94\u7528<\/h3>\n<\/p>\n
\u5bf9\u6570\u5728\u6570\u636e\u5904\u7406\u548c\u5206\u6790\u4e2d\u6709\u7740\u5e7f\u6cdb\u7684\u5e94\u7528\u3002\u4ee5\u4e0b\u662f\u51e0\u4e2a\u5e38\u89c1\u7684\u5e94\u7528\u573a\u666f\uff1a<\/p>\n<\/p>\n
1\u3001\u6570\u636e\u7f29\u653e<\/h4>\n<\/p>\n
\u5728\u5904\u7406\u6570\u636e\u65f6\uff0c\u6709\u65f6\u6570\u636e\u7684\u53d6\u503c\u8303\u56f4\u975e\u5e38\u5927\u3002\u901a\u8fc7\u5bf9\u6570\u636e\u53d6\u5bf9\u6570\uff0c\u53ef\u4ee5\u7f29\u5c0f\u6570\u636e\u7684\u8303\u56f4\uff0c\u4f7f\u5f97\u6570\u636e\u66f4\u52a0\u6613\u4e8e\u5904\u7406\u3002\u4f8b\u5982\uff0c\u5728\u5904\u7406\u91d1\u878d\u6570\u636e\u65f6\uff0c\u7ecf\u5e38\u4f1a\u5bf9\u80a1\u7968\u4ef7\u683c\u53d6\u5bf9\u6570\u3002<\/p>\n<\/p>\n
import numpy as np<\/p>\n
prices = np.array([1, 10, 100, 1000])<\/p>\n
log_prices = np.log(prices)<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001\u6570\u636e\u6b63\u6001\u5316<\/h4>\n<\/p>\n
\u6709\u4e9b\u6570\u636e\u96c6\u4e0d\u7b26\u5408\u6b63\u6001\u5206\u5e03\uff0c\u901a\u8fc7\u5bf9\u6570\u636e\u53d6\u5bf9\u6570\uff0c\u53ef\u4ee5\u4f7f\u5f97\u6570\u636e\u66f4\u52a0\u63a5\u8fd1\u6b63\u6001\u5206\u5e03\u3002\u8fd9\u5728\u673a\u5668\u5b66\u4e60<\/a>\u548c\u7edf\u8ba1\u5206\u6790\u4e2d\u662f\u975e\u5e38\u91cd\u8981\u7684\u3002<\/p>\n<\/p>\n
import numpy as np<\/p>\n
import matplotlib.pyplot as plt<\/p>\n
data = np.random.exponential(scale=2, size=1000)<\/p>\n
log_data = np.log(data)<\/p>\n
plt.hist(data, bins=30, alpha=0.5, label='Original Data')<\/p>\n
plt.hist(log_data, bins=30, alpha=0.5, label='Log Transformed Data')<\/p>\n
plt.legend()<\/p>\n
plt.show()<\/p>\n
<\/code><\/pre>\n<\/p>\n
3\u3001\u7279\u5f81\u5de5\u7a0b<\/h4>\n<\/p>\n
\u5728\u673a\u5668\u5b66\u4e60\u4e2d\uff0c\u5bf9\u6570\u53d8\u6362\u662f\u4e00\u79cd\u5e38\u7528\u7684\u7279\u5f81\u5de5\u7a0b\u624b\u6bb5\u3002\u901a\u8fc7\u5bf9\u7279\u5f81\u53d6\u5bf9\u6570\uff0c\u53ef\u4ee5\u6539\u5584\u6a21\u578b\u7684\u6027\u80fd\u3002<\/p>\n<\/p>\n
import numpy as np<\/p>\n
from sklearn.linear_model import LinearRegression<\/p>\n
from sklearn.metrics import mean_squared_error<\/p>\n
\u751f\u6210\u6570\u636e<\/strong><\/h2>\n
X = np.random.exponential(scale=2, size=(100, 1))<\/p>\n
y = 3 * np.log(X) + np.random.normal(scale=0.5, size=(100, 1))<\/p>\n
\u5bf9\u7279\u5f81\u8fdb\u884c\u5bf9\u6570\u53d8\u6362<\/strong><\/h2>\n
X_log = np.log(X)<\/p>\n
\u5efa\u7acb\u6a21\u578b<\/strong><\/h2>\n
model = LinearRegression()<\/p>\n
model.fit(X_log, y)<\/p>\n
\u9884\u6d4b<\/strong><\/h2>\n
y_pred = model.predict(X_log)<\/p>\n
\u8bc4\u4f30\u6a21\u578b<\/strong><\/h2>\n
mse = mean_squared_error(y, y_pred)<\/p>\n
print(f'Mean Squared Error: {mse}')<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e94\u3001\u5bf9\u6570\u5728\u79d1\u5b66\u8ba1\u7b97\u4e2d\u7684\u5e94\u7528<\/h3>\n<\/p>\n
\u5bf9\u6570\u5728\u79d1\u5b66\u8ba1\u7b97\u4e2d\u4e5f\u6709\u7740\u5e7f\u6cdb\u7684\u5e94\u7528\u3002\u4ee5\u4e0b\u662f\u51e0\u4e2a\u5e38\u89c1\u7684\u5e94\u7528\u573a\u666f\uff1a<\/p>\n<\/p>\n
1\u3001\u5bf9\u6570\u4e0e\u6307\u6570\u51fd\u6570\u7684\u5173\u7cfb<\/h4>\n<\/p>\n
\u5bf9\u6570\u51fd\u6570\u4e0e\u6307\u6570\u51fd\u6570\u4e92\u4e3a\u53cd\u51fd\u6570\uff0c\u8fd9\u5728\u6570\u5b66\u548c\u7269\u7406\u4e2d\u6709\u7740\u91cd\u8981\u7684\u5e94\u7528\u3002\u4f8b\u5982\uff0c\u5728\u8ba1\u7b97\u590d\u5229\u65f6\uff0c\u7ecf\u5e38\u9700\u8981\u7528\u5230\u6307\u6570\u548c\u5bf9\u6570\u51fd\u6570\u3002<\/p>\n<\/p>\n
import math<\/p>\n
\u8ba1\u7b97\u590d\u5229<\/strong><\/h2>\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\u7b97\u590d\u5229\u7ec8\u503c<\/strong><\/h2>\n
future_value = principal * math.exp(rate * time)<\/p>\n
print(f'Future Value: {future_value}')<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001\u5bf9\u6570\u5728\u4fe1\u606f\u8bba\u4e2d\u7684\u5e94\u7528<\/h4>\n<\/p>\n
\u5728\u4fe1\u606f\u8bba\u4e2d\uff0c\u5bf9\u6570\u51fd\u6570\u7528\u4e8e\u8ba1\u7b97\u4fe1\u606f\u71b5\u548c\u4ea4\u53c9\u71b5\u7b49\u5ea6\u91cf\u3002\u4fe1\u606f\u71b5\u662f\u8861\u91cf\u4e0d\u786e\u5b9a\u6027\u7684\u91cd\u8981\u6307\u6807\u3002<\/p>\n<\/p>\n
import numpy as np<\/p>\n
\u8ba1\u7b97\u4fe1\u606f\u71b5<\/strong><\/h2>\n
def entropy(probabilities):<\/p>\n
    return -np.sum(probabilities * np.log2(probabilities))<\/p>\n
probabilities = np.array([0.1, 0.2, 0.3, 0.4])<\/p>\n
info_entropy = entropy(probabilities)<\/p>\n
print(f'Information Entropy: {info_entropy}')<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u516d\u3001\u5bf9\u6570\u5728\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u5e94\u7528<\/h3>\n<\/p>\n
\u5728\u673a\u5668\u5b66\u4e60\u4e2d\uff0c\u5bf9\u6570\u51fd\u6570\u6709\u7740\u91cd\u8981\u7684\u5e94\u7528\u3002\u4ee5\u4e0b\u662f\u51e0\u4e2a\u5e38\u89c1\u7684\u5e94\u7528\u573a\u666f\uff1a<\/p>\n<\/p>\n
1\u3001\u5bf9\u6570\u635f\u5931\u51fd\u6570<\/h4>\n<\/p>\n
\u5728\u5206\u7c7b\u95ee\u9898\u4e2d\uff0c\u5e38\u7528\u7684\u635f\u5931\u51fd\u6570\u662f\u5bf9\u6570\u635f\u5931\u51fd\u6570\uff08Log Loss\uff09\uff0c\u4e5f\u79f0\u4f5c\u4ea4\u53c9\u71b5\u635f\u5931\u3002\u5bf9\u6570\u635f\u5931\u51fd\u6570\u7528\u4e8e\u8861\u91cf\u6a21\u578b\u9884\u6d4b\u7684\u6982\u7387\u5206\u5e03\u4e0e\u771f\u5b9e\u5206\u5e03\u4e4b\u95f4\u7684\u5dee\u5f02\u3002<\/p>\n<\/p>\n
import numpy as np<\/p>\n
\u8ba1\u7b97\u5bf9\u6570\u635f\u5931\u51fd\u6570<\/strong><\/h2>\n
def log_loss(y_true, y_pred):<\/p>\n
    return -np.sum(y_true * np.log(y_pred) + (1 - y_true) * np.log(1 - y_pred))<\/p>\n
y_true = np.array([1, 0, 1, 1, 0])<\/p>\n
y_pred = np.array([0.9, 0.1, 0.8, 0.7, 0.2])<\/p>\n
loss = log_loss(y_true, y_pred)<\/p>\n
print(f'Log Loss: {loss}')<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001\u5bf9\u6570\u5728\u6b63\u5219\u5316\u4e2d\u7684\u5e94\u7528<\/h4>\n<\/p>\n
\u5728\u673a\u5668\u5b66\u4e60\u6a21\u578b\u4e2d\uff0c\u6b63\u5219\u5316\u662f\u4e00\u79cd\u9632\u6b62\u8fc7\u62df\u5408\u7684\u6280\u672f\u3002\u5bf9\u6570\u51fd\u6570\u5728\u6b63\u5219\u5316\u9879\u7684\u6784\u9020\u4e2d\u6709\u7740\u91cd\u8981\u7684\u5e94\u7528\u3002\u4f8b\u5982\uff0c\u5728L1\u6b63\u5219\u5316\u4e2d\uff0c\u4f7f\u7528\u5bf9\u6570\u51fd\u6570\u6765\u7a00\u758f\u5316\u7279\u5f81\u3002<\/p>\n<\/p>\n
import numpy as np<\/p>\n
from sklearn.linear_model import Lasso<\/p>\n
\u751f\u6210\u6570\u636e<\/strong><\/h2>\n
X = np.random.randn(100, 10)<\/p>\n
y = X[:, 0] + 0.5 * X[:, 1] + np.random.randn(100)<\/p>\n
\u8bad\u7ec3\u5e26\u6709L1\u6b63\u5219\u5316\u7684\u56de\u5f52\u6a21\u578b<\/strong><\/h2>\n
model = Lasso(alpha=0.1)<\/p>\n
model.fit(X, y)<\/p>\n
\u6253\u5370\u6a21\u578b\u7cfb\u6570<\/strong><\/h2>\n
print(f'Model Coefficients: {model.coef_}')<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e03\u3001\u5bf9\u6570\u5728\u6570\u503c\u5206\u6790\u4e2d\u7684\u5e94\u7528<\/h3>\n<\/p>\n
\u5bf9\u6570\u51fd\u6570\u5728\u6570\u503c\u5206\u6790\u4e2d\u4e5f\u6709\u7740\u5e7f\u6cdb\u7684\u5e94\u7528\u3002\u4ee5\u4e0b\u662f\u51e0\u4e2a\u5e38\u89c1\u7684\u5e94\u7528\u573a\u666f\uff1a<\/p>\n<\/p>\n
1\u3001\u5bf9\u6570\u79ef\u5206<\/h4>\n<\/p>\n
\u5728\u6570\u503c\u79ef\u5206\u4e2d\uff0c\u5e38\u5e38\u9700\u8981\u5bf9\u5bf9\u6570\u51fd\u6570\u8fdb\u884c\u79ef\u5206\u3002\u4f8b\u5982\uff0c\u5728\u8ba1\u7b97\u67d0\u4e9b\u6982\u7387\u5206\u5e03\u7684\u7d2f\u79ef\u5206\u5e03\u51fd\u6570\u65f6\uff0c\u9700\u8981\u5bf9\u5bf9\u6570\u51fd\u6570\u8fdb\u884c\u79ef\u5206\u3002<\/p>\n<\/p>\n
import scipy.integrate as integrate<\/p>\n
\u5b9a\u4e49\u5bf9\u6570\u51fd\u6570<\/strong><\/h2>\n
def log_func(x):<\/p>\n
    return np.log(x)<\/p>\n
\u8ba1\u7b97\u5bf9\u6570\u51fd\u6570\u7684\u79ef\u5206<\/strong><\/h2>\n
result, error = integrate.quad(log_func, 1, 10)<\/p>\n
print(f'Integral Result: {result}')<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001\u5bf9\u6570\u5fae\u5206<\/h4>\n<\/p>\n
\u5728\u6570\u503c\u5fae\u5206\u4e2d\uff0c\u5bf9\u6570\u51fd\u6570\u7684\u5bfc\u6570\u4e5f\u6709\u7740\u91cd\u8981\u7684\u5e94\u7528\u3002\u4f8b\u5982\uff0c\u5728\u67d0\u4e9b\u4f18\u5316\u7b97\u6cd5\u4e2d\uff0c\u9700\u8981\u8ba1\u7b97\u5bf9\u6570\u51fd\u6570\u7684\u5bfc\u6570\u3002<\/p>\n<\/p>\n
import scipy.misc as misc<\/p>\n
\u5b9a\u4e49\u5bf9\u6570\u51fd\u6570<\/strong><\/h2>\n
def log_func(x):<\/p>\n
    return np.log(x)<\/p>\n
\u8ba1\u7b97\u5bf9\u6570\u51fd\u6570\u7684\u5bfc\u6570<\/strong><\/h2>\n
derivative = misc.derivative(log_func, 10, dx=1e-6)<\/p>\n
print(f'Derivative: {derivative}')<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u516b\u3001\u5bf9\u6570\u5728\u6570\u636e\u53ef\u89c6\u5316\u4e2d\u7684\u5e94\u7528<\/h3>\n<\/p>\n
\u5728\u6570\u636e\u53ef\u89c6\u5316\u4e2d\uff0c\u5bf9\u6570\u53d8\u6362\u4e5f\u662f\u4e00\u79cd\u5e38\u7528\u7684\u6280\u672f\u3002\u4ee5\u4e0b\u662f\u51e0\u4e2a\u5e38\u89c1\u7684\u5e94\u7528\u573a\u666f\uff1a<\/p>\n<\/p>\n
1\u3001\u5bf9\u6570\u523b\u5ea6<\/h4>\n<\/p>\n
\u5728\u7ed8\u5236\u6570\u636e\u56fe\u8868\u65f6\uff0c\u6709\u65f6\u9700\u8981\u4f7f\u7528\u5bf9\u6570\u523b\u5ea6\u6765\u66f4\u597d\u5730\u5c55\u793a\u6570\u636e\u3002\u4f8b\u5982\uff0c\u5728\u7ed8\u5236\u80a1\u7968\u4ef7\u683c\u8d70\u52bf\u56fe\u65f6\uff0c\u4f7f\u7528\u5bf9\u6570\u523b\u5ea6\u53ef\u4ee5\u66f4\u6e05\u6670\u5730\u5c55\u793a\u4ef7\u683c\u53d8\u5316\u3002<\/p>\n<\/p>\n
import matplotlib.pyplot as plt<\/p>\n
import numpy as np<\/p>\n
\u751f\u6210\u6570\u636e<\/strong><\/h2>\n
x = np.linspace(1, 100, 100)<\/p>\n
y = np.exp(x \/ 20)<\/p>\n
\u7ed8\u5236\u5bf9\u6570\u523b\u5ea6\u56fe<\/strong><\/h2>\n
plt.figure()<\/p>\n
plt.plot(x, y)<\/p>\n
plt.xscale('log')<\/p>\n
plt.yscale('log')<\/p>\n
plt.xlabel('X (log scale)')<\/p>\n
plt.ylabel('Y (log scale)')<\/p>\n
plt.title('Logarithmic Scale Plot')<\/p>\n
plt.show()<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001\u5bf9\u6570\u53d8\u6362<\/h4>\n<\/p>\n
\u5728\u7ed8\u5236\u6570\u636e\u5206\u5e03\u56fe\u65f6\uff0c\u6709\u65f6\u9700\u8981\u5bf9\u6570\u636e\u8fdb\u884c\u5bf9\u6570\u53d8\u6362\uff0c\u4ee5\u66f4\u597d\u5730\u5c55\u793a\u6570\u636e\u7684\u5206\u5e03\u3002\u4f8b\u5982\uff0c\u5728\u7ed8\u5236\u6570\u636e\u76f4\u65b9\u56fe\u65f6\uff0c\u5bf9\u6570\u636e\u8fdb\u884c\u5bf9\u6570\u53d8\u6362\u53ef\u4ee5\u66f4\u597d\u5730\u5c55\u793a\u6570\u636e\u7684\u5206\u5e03\u7279\u6027\u3002<\/p>\n<\/p>\n
import matplotlib.pyplot as plt<\/p>\n
import numpy as np<\/p>\n
\u751f\u6210\u6570\u636e<\/strong><\/h2>\n
data = np.random.exponential(scale=2, size=1000)<\/p>\n
log_data = np.log(data)<\/p>\n
\u7ed8\u5236\u5bf9\u6570\u53d8\u6362\u540e\u7684\u76f4\u65b9\u56fe<\/strong><\/h2>\n
plt.figure()<\/p>\n
plt.hist(log_data, bins=30, alpha=0.5, label='Log Transformed Data')<\/p>\n
plt.xlabel('Log Transformed Data')<\/p>\n
plt.ylabel('Frequency')<\/p>\n
plt.title('Histogram of Log Transformed Data')<\/p>\n
plt.legend()<\/p>\n
plt.show()<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u901a\u8fc7\u5bf9\u6570\u636e\u8fdb\u884c\u5bf9\u6570\u53d8\u6362\uff0c\u53ef\u4ee5\u66f4\u597d\u5730\u5c55\u793a\u6570\u636e\u7684\u5206\u5e03\u7279\u6027\uff0c\u4f7f\u5f97\u6570\u636e\u7684\u53ef\u89c6\u5316\u6548\u679c\u66f4\u52a0\u76f4\u89c2\u3002<\/p>\n<\/p>\n
\u4e5d\u3001\u5bf9\u6570\u5728\u7b97\u6cd5\u8bbe\u8ba1\u4e2d\u7684\u5e94\u7528<\/h3>\n<\/p>\n
\u5bf9\u6570\u5728\u7b97\u6cd5\u8bbe\u8ba1\u4e2d\u4e5f\u6709\u7740\u5e7f\u6cdb\u7684\u5e94\u7528\u3002\u4ee5\u4e0b\u662f\u51e0\u4e2a\u5e38\u89c1\u7684\u5e94\u7528\u573a\u666f\uff1a<\/p>\n<\/p>\n
1\u3001\u5bf9\u6570\u5728\u4e8c\u5206\u67e5\u627e\u4e2d\u7684\u5e94\u7528<\/h4>\n<\/p>\n
\u5728\u4e8c\u5206\u67e5\u627e\u7b97\u6cd5\u4e2d\uff0c\u5bf9\u6570\u51fd\u6570\u7528\u4e8e\u8ba1\u7b97\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u3002\u4e8c\u5206\u67e5\u627e\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(log n)\uff0c\u5176\u4e2dn\u662f\u6570\u636e\u7684\u89c4\u6a21\u3002<\/p>\n<\/p>\n
def binary_search(arr, target):<\/p>\n
    left, right = 0, len(arr) - 1<\/p>\n
    while left <= right:<\/p>\n
        mid = left + (right - left) \/\/ 2<\/p>\n
        if arr[mid] == target:<\/p>\n
            return mid<\/p>\n
        elif arr[mid] < target:<\/p>\n
            left = mid + 1<\/p>\n
        else:<\/p>\n
            right = mid - 1<\/p>\n
    return -1<\/p>\n
\u6d4b\u8bd5\u4e8c\u5206\u67e5\u627e\u7b97\u6cd5<\/strong><\/h2>\n
arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]<\/p>\n
target = 7<\/p>\n
result = binary_search(arr, target)<\/p>\n
print(f'Target found at index: {result}')<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001\u5bf9\u6570\u5728\u6392\u5e8f\u7b97\u6cd5\u4e2d\u7684\u5e94\u7528<\/h4>\n<\/p>\n
\u5728\u67d0\u4e9b\u6392\u5e8f\u7b97\u6cd5\u4e2d\uff0c\u5bf9\u6570\u51fd\u6570\u7528\u4e8e\u8ba1\u7b97\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u3002\u4f8b\u5982\uff0c\u5feb\u901f\u6392\u5e8f\u7684\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n log n)\uff0c\u5176\u4e2dn\u662f\u6570\u636e\u7684\u89c4\u6a21\u3002<\/p>\n<\/p>\n
def quicksort(arr):<\/p>\n
    if len(arr) <= 1:<\/p>\n
        return arr<\/p>\n
    pivot = arr[len(arr) \/\/ 2]<\/p>\n
    left = [x for x in arr if x < pivot]<\/p>\n
    middle = [x for x in arr if x == pivot]<\/p>\n
    right = [x for x in arr if x > pivot]<\/p>\n
    return quicksort(left) + middle + quicksort(right)<\/p>\n
\u6d4b\u8bd5\u5feb\u901f\u6392\u5e8f\u7b97\u6cd5<\/strong><\/h2>\n
arr = [3, 6, 8, 10, 1, 2, 1]<\/p>\n
sorted_arr = quicksort(arr)<\/p>\n
print(f'Sorted Array: {sorted_arr}')<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u901a\u8fc7\u5bf9\u6570\u51fd\u6570\u7684\u5e94\u7528\uff0c\u53ef\u4ee5\u66f4\u597d\u5730\u7406\u89e3\u548c\u5206\u6790\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\uff0c\u63d0\u9ad8\u7b97\u6cd5\u8bbe\u8ba1\u7684\u6548\u7387\u548c\u6027\u80fd\u3002<\/p>\n<\/p>\n
\u5341\u3001\u5bf9\u6570\u5728\u91d1\u878d\u4e2d\u7684\u5e94\u7528<\/h3>\n<\/p>\n
\u5bf9\u6570\u5728\u91d1\u878d\u4e2d\u6709\u7740\u5e7f\u6cdb\u7684\u5e94\u7528\u3002\u4ee5\u4e0b\u662f\u51e0\u4e2a\u5e38\u89c1\u7684\u5e94\u7528\u573a\u666f\uff1a<\/p>\n<\/p>\n
1\u3001\u5bf9\u6570\u6536\u76ca\u7387<\/h4>\n<\/p>\n
\u5728\u91d1\u878d\u4e2d\uff0c\u5bf9\u6570\u6536\u76ca\u7387\u662f\u8861\u91cf\u6295\u8d44\u6536\u76ca\u7684\u91cd\u8981\u6307\u6807\u3002\u5bf9\u6570\u6536\u76ca\u7387\u7528\u4e8e\u8ba1\u7b97\u6295\u8d44\u7684\u590d\u5229\u6536\u76ca\u3002<\/p>\n<\/p>\n
import numpy as np<\/p>\n
\u8ba1\u7b97\u5bf9\u6570\u6536\u76ca\u7387<\/strong><\/h2>\n
def log_return(prices):<\/p>\n
    return np.log(prices[1:] \/ prices[:-1])<\/p>\n
prices = np.array([100, 105, 110, 120, 125])<\/p>\n
returns = log_return(prices)<\/p>\n
print(f'Log Returns: {returns}')<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001\u5bf9\u6570\u6b63\u6001\u5206\u5e03<\/h4>\n<\/p>\n
\u5728\u91d1\u878d\u4e2d\uff0c\u80a1\u7968\u4ef7\u683c\u7684\u5bf9\u6570\u5e38\u5e38\u88ab\u5047\u8bbe\u4e3a\u670d\u4ece\u6b63\u6001\u5206\u5e03\u3002\u901a\u8fc7\u5bf9\u4ef7\u683c\u53d6\u5bf9\u6570\uff0c\u53ef\u4ee5\u66f4\u597d\u5730\u5efa\u6a21\u548c\u5206\u6790\u80a1\u7968\u4ef7\u683c\u7684\u53d8\u5316\u3002<\/p>\n<\/p>\n
import numpy as np<\/p>\n
import matplotlib.pyplot as plt<\/p>\n
\u751f\u6210\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u6570\u636e<\/strong><\/h2>\n
mu, sigma = 0, 0.1<\/p>\n
log_normal_data = np.random.lognormal(mu, sigma, 1000)<\/p>\n
\u7ed8\u5236\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u76f4\u65b9\u56fe<\/strong><\/h2>\n
plt.figure()<\/p>\n
plt.hist(log_normal_data, bins=30, alpha=0.5, label='Log Normal Data')<\/p>\n
plt.xlabel('Log Normal Data')<\/p>\n
plt.ylabel('Frequency')<\/p>\n
plt.title('Histogram of Log Normal Data')<\/p>\n
plt.legend()<\/p>\n
plt.show()<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u901a\u8fc7\u5bf9\u6570\u6b63\u6001\u5206\u5e03\uff0c\u53ef\u4ee5\u66f4\u597d\u5730\u5efa\u6a21\u548c\u5206\u6790\u80a1\u7968\u4ef7\u683c\u7684\u53d8\u5316\uff0c\u63d0\u9ad8\u91d1\u878d\u5206\u6790\u7684\u51c6\u786e\u6027\u548c\u53ef\u9760\u6027\u3002<\/p>\n<\/p>\n
\u7efc\u4e0a\u6240\u8ff0\uff0c\u5728Python\u4e2d\u8868\u793a\u5bf9\u6570\u7684\u65b9\u6cd5\u6709\u591a\u79cd\uff0c\u5305\u62ec\u4f7f\u7528math<\/code>\u6a21\u5757\u3001numpy<\/code>\u6a21\u5757\u3001scipy<\/code>\u6a21\u5757\u7b49\u3002\u5bf9\u6570\u5728\u6570\u636e\u5904\u7406\u3001\u79d1\u5b66\u8ba1\u7b97\u3001\u673a\u5668\u5b66\u4e60\u3001\u6570\u503c\u5206\u6790\u3001\u6570\u636e\u53ef\u89c6\u5316\u3001\u7b97\u6cd5\u8bbe\u8ba1\u3001\u91d1\u878d\u7b49\u9886\u57df\u6709\u7740\u5e7f\u6cdb\u7684\u5e94\u7528\u3002\u901a\u8fc7\u5bf9\u6570\u51fd\u6570\u7684\u5e94\u7528\uff0c\u53ef\u4ee5\u66f4\u597d\u5730\u5904\u7406\u548c\u5206\u6790\u6570\u636e\uff0c\u63d0\u9ad8\u8ba1\u7b97\u548c\u5206\u6790\u7684\u6548\u7387\u548c\u51c6\u786e\u6027\u3002<\/p>\n<\/p>\n
\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n
 \u5728Python\u4e2d\uff0c\u5982\u4f55\u8ba1\u7b97\u5bf9\u6570\u7684\u503c\uff1f<\/strong>
Python\u63d0\u4f9b\u4e86\u591a\u79cd\u65b9\u6cd5\u6765\u8ba1\u7b97\u5bf9\u6570\uff0c\u6700\u5e38\u7528\u7684\u662fmath<\/code>\u6a21\u5757\u4e2d\u7684log<\/code>\u51fd\u6570\u3002\u4f7f\u7528math.log(x, base)<\/code>\u53ef\u4ee5\u8ba1\u7b97\u4ee5base<\/code>\u4e3a\u5e95\u7684x<\/code>\u7684\u5bf9\u6570\u3002\u5982\u679c\u4e0d\u6307\u5b9a\u5e95\u6570\uff0c\u9ed8\u8ba4\u662f\u4ee5\u81ea\u7136\u6570e\u4e3a\u5e95\u7684\u5bf9\u6570\u3002\u6b64\u5916\uff0cnumpy<\/code>\u5e93\u4e5f\u63d0\u4f9b\u4e86\u5bf9\u6570\u8ba1\u7b97\u7684\u529f\u80fd\uff0c\u9002\u5408\u5904\u7406\u6570\u7ec4\u548c\u66f4\u590d\u6742\u7684\u6570\u636e\u96c6\u3002<\/p>\n
Python\u4e2d\u7684\u5bf9\u6570\u51fd\u6570\u6709\u54ea\u4e9b\u4e0d\u540c\u7684\u5e95\u6570\u53ef\u4ee5\u4f7f\u7528\uff1f<\/strong>
\u5728Python\u4e2d\uff0c\u53ef\u4ee5\u8ba1\u7b97\u4ee5\u4efb\u610f\u6b63\u6570\u4e3a\u5e95\u7684\u5bf9\u6570\u3002\u5e38\u89c1\u7684\u5e95\u6570\u5305\u62ec10\uff08\u5e38\u7528\u5bf9\u6570\uff09\u30012\uff08\u4ee52\u4e3a\u5e95\u7684\u5bf9\u6570\uff09\u548ce\uff08\u81ea\u7136\u5bf9\u6570\uff09\u3002\u901a\u8fc7math.log10(x)<\/code>\u548cmath.log2(x)<\/code>\u53ef\u4ee5\u5206\u522b\u76f4\u63a5\u8ba1\u7b97\u4ee510\u548c2\u4e3a\u5e95\u7684\u5bf9\u6570\uff0c\u8fd9\u4e9b\u51fd\u6570\u80fd\u7b80\u5316\u8ba1\u7b97\u8fc7\u7a0b\uff0c\u907f\u514d\u624b\u52a8\u6307\u5b9a\u5e95\u6570\u3002<\/p>\n
\u5982\u4f55\u5904\u7406\u5bf9\u6570\u8ba1\u7b97\u4e2d\u7684\u9519\u8bef\u6216\u5f02\u5e38\u60c5\u51b5\uff1f<\/strong>
\u5728\u8fdb\u884c\u5bf9\u6570\u8ba1\u7b97\u65f6\uff0c\u786e\u4fdd\u8f93\u5165\u503c\u662f\u6b63\u6570\uff0c\u56e0\u4e3a\u5bf9\u6570\u51fd\u6570\u5728\u96f6\u548c\u8d1f\u6570\u7684\u60c5\u51b5\u4e0b\u662f\u672a\u5b9a\u4e49\u7684\u3002\u4f7f\u7528try<\/code>\u548cexcept<\/code>\u8bed\u53e5\u53ef\u4ee5\u6709\u6548\u6355\u83b7\u5f02\u5e38\uff0c\u9632\u6b62\u7a0b\u5e8f\u5d29\u6e83\u3002\u4f8b\u5982\uff0c\u53ef\u4ee5\u5728\u8ba1\u7b97\u5bf9\u6570\u524d\u68c0\u67e5\u503c\u7684\u5408\u6cd5\u6027\uff0c\u6216\u8005\u5728\u51fa\u73b0\u9519\u8bef\u65f6\u8fd4\u56de\u4e00\u4e2a\u53cb\u597d\u7684\u63d0\u793a\u4fe1\u606f\uff0c\u8ba9\u7528\u6237\u80fd\u591f\u66f4\u597d\u5730\u7406\u89e3\u95ee\u9898\u6240\u5728\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u5728Python\u4e2d\uff0c\u8868\u793a\u5bf9\u6570\u7684\u65b9\u6cd5\u6709\u591a\u79cd\uff0c\u4e3b\u8981\u5305\u62ec\u4f7f\u7528math\u6a21\u5757\u3001\u4f7f\u7528numpy\u6a21\u5757\u3001\u4f7f\u7528scipy\u6a21\u5757\u3002\u5176\u4e2d […]","protected":false},"author":3,"featured_media":1157686,"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\/1157680"}],"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=1157680"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1157680\/revisions"}],"predecessor-version":[{"id":1157687,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1157680\/revisions\/1157687"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/1157686"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=1157680"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=1157680"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=1157680"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}