关于Python中math 和 decimal 模块的解析与实践

import math

angle = math.radians(30)  # 将角度转换为弧度
sin_value = math.sin(angle)

print(f"sin(30°) 的值为：{sin_value}")

import math

random_number = math.random()
print(f"随机数：{random_number}")

import math

pi_value = math.pi
e_value = math.e

print(f"π 的值为：{pi_value}")
print(f"e 的值为：{e_value}")

from decimal import Decimal

decimal_number = Decimal('3.1415926535')
print(f"Decimal 对象的值：{decimal_number}")

from decimal import Decimal, getcontext

# 设置精度上下文
getcontext().prec = 10

# 高精度加法
result = Decimal('1.23456789') + Decimal('2.34567890')

print(f"高精度加法的结果：{result}")

import math

def compound_interest(principal, rate, time):
    # 复利计算公式：A = P * (1 + r/n)^(nt)
    n = 12  # 假设每年复利12次
    compound_amount = principal * math.pow((1 + rate/n), n*time)
    return compound_amount

# 示例：计算1000元本金，年利率5%，存款5年后的本息和
principal_amount = 1000
annual_interest_rate = 0.05
years = 5

result = compound_interest(principal_amount, annual_interest_rate, years)
print(f"复利计算结果：{result:.2f} 元")

from decimal import Decimal, getcontext

def decimal_compound_interest(principal, rate, time):
    # 复利计算公式：A = P * (1 + r/n)^(nt)
    n = 12  # 假设每年复利12次

    # 初始化Decimal对象
    principal_decimal = Decimal(str(principal))
    rate_decimal = Decimal(str(rate/n))
    time_decimal = Decimal(str(n*time))

    # 高精度复利计算
    compound_amount = principal_decimal * (1 + rate_decimal)**time_decimal
    return compound_amount

# 设置精度上下文
getcontext().prec = 15

# 示例：计算1000元本金，年利率5%，存款5年后的本息和（高精度计算）
result_decimal = decimal_compound_interest(principal_amount, annual_interest_rate, years)
print(f"高精度复利计算结果：{result_decimal:.15f} 元")

import math
import matplotlib.pyplot as plt
import numpy as np

# 生成正弦函数的数据
x = np.linspace(0, 2 * math.pi, 100)  # 在0到2π之间生成100个点
y = np.sin(x)

# 绘制正弦函数图形
plt.plot(x, y, label='sin(x)')
plt.title('Sin Function')
plt.xlabel('x')
plt.ylabel('sin(x)')
plt.legend()
plt.grid(True)
plt.show()

from decimal import Decimal, getcontext

# 设置精度上下文
getcontext().prec = 30

# 使用Decimal进行高精度计算
x_decimal = [Decimal(str(val)) for val in x]
y_decimal = [Decimal(str(math.sin(val))) for val in x_decimal]

# 绘制高精度正弦函数图形
plt.plot(x_decimal, y_decimal, label='sin(x) (High Precision)')
plt.title('High Precision Sin Function')
plt.xlabel('x')
plt.ylabel('sin(x)')
plt.legend()
plt.grid(True)
plt.show()

import numpy as np

# 系数矩阵
coefficients = np.array([[2, 1], [4, -3]])

# 右侧常数向量
constants = np.array([5, 2])

# 解线性方程组
solution = np.linalg.solve(coefficients, constants)

print(f"线性方程组的解为：x = {solution[0]}, y = {solution[1]}")

import math

# 计算*方根
square_root_result = math.sqrt(9)

print(f"*方根的计算结果：{square_root_result}")

import math

def binary_search_sqrt(num, epsilon=1e-6):
    if num < 0:
        raise ValueError("负数没有实数*方根")

    if num == 0 or num == 1:
        return num

    low, high = 0, num
    mid = (low + high) / 2

    while abs(mid**2 - num) > epsilon:
        if mid**2 < num:
            low = mid
        else:
            high = mid

        mid = (low + high) / 2

    return mid

# 示例：计算 16 的*方根
result = binary_search_sqrt(16)
print(f"通过二分查找计算的*方根：{result}")

# 对比使用math模块的sqrt函数
math_result = math.sqrt(16)
print(f"math模块的sqrt函数计算的*方根：{math_result}")

import numpy as np
import math

def loan_payment(principal, annual_interest_rate, loan_term):
    # 将年利率转换为月利率
    monthly_interest_rate = annual_interest_rate / 12 / 100

    # 计算每月还款金额
    monthly_payment = (principal * monthly_interest_rate) / (1 - math.pow(1 + monthly_interest_rate, -loan_term))

    return monthly_payment

# 示例：借款金额 10000 元，年利率 5%，贷款期限 3 年
loan_amount = 10000
annual_rate = 5
loan_period = 3

monthly_payment_result = loan_payment(loan_amount, annual_rate, loan_period)
print(f"每月还款金额：{monthly_payment_result:.2f} 元")

import numpy as np
import math
import matplotlib.pyplot as plt

# 生成示例数据
np.random.seed(42)
X = 2 * np.random.rand(100, 1)
y = 4 + 3 * X + np.random.randn(100, 1)

# 使用numpy进行线性回归
X_b = np.c_[np.ones((100, 1)), X]
theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)

# 打印线性回归参数
print("线性回归参数：", theta_best)

# 绘制原始数据和回归线
plt.scatter(X, y, color='blue', label='原始数据')
plt.plot(X, X_b.dot(theta_best), color='red', label='线性回归')
plt.title('线性回归示例')
plt.xlabel('X')
plt.ylabel('y')
plt.legend()
plt.show()