hw5¶

import os
import random

# 生成文件的函数
def generate_files(folder_path):
    if not os.path.exists(folder_path):
        os.makedirs(folder_path)
    # 生成100个文件
    for i in range(1, 101):
        file_name = f"assignment_{i}.txt"
        file_path = os.path.join(folder_path, file_name)
        # 写入文本内容为绝对路径
        with open(file_path, 'w') as file:
            file.write(os.path.abspath(file_path))

# 随机删除5个文件
def delete_random_files(folder_path):
    # 筛选文件名和后缀名避免误删
    files = [f for f in os.listdir(folder_path) if f.startswith('assignment_') and f.endswith('.txt')]
    to_delete = random.sample(files, 5)
    for file in to_delete:
        file_path = os.path.join(folder_path, file)
        os.remove(file_path)


if __name__ == "__main__":
    folder_path = "hw5_problem1_folder"
    generate_files(folder_path)
    delete_random_files(folder_path)

import os

# 找出缺失的5个文件
def find_missing_files(folder_path):
    existing_files = [f for f in os.listdir(folder_path) if f.startswith('assignment_') and f.endswith('.txt')]
    # 找出未被删除的文件
    existing_numbers = [int(f.split('_')[1].split('.')[0]) for f in existing_files]
    all_numbers = set(range(1, 101))
    missing_numbers = all_numbers - set(existing_numbers)
    return missing_numbers


def recover_missing_files(folder_path, missing_numbers):
    for num in missing_numbers:
        file_name = f"assignment_{num}.txt"
        file_path = os.path.join(folder_path, file_name)
        with open(file_path, 'w') as file:
            file.write(os.path.abspath(file_path))


if __name__ == "__main__":
    folder_path = "hw5_problem1_folder"
    missing_numbers = find_missing_files(folder_path)
    # 检验操作
    print(missing_numbers)
    # 恢复
    recover_missing_files(folder_path, missing_numbers)
    # 再检验一次
    missing_numbers = find_missing_files(folder_path)
    print(missing_numbers)

import numpy as np

# 定义要生成的矩阵大小
sizes = [10, 100, 1000]

# 遍历不同大小
for size in sizes:
    # 使用 numpy.random.randn 创建指定大小的矩阵
    matrix = np.random.randn(size, size)
    # 计算矩阵的均值
    mean = np.mean(matrix)
    # 计算矩阵的标准差
    std_dev = np.std(matrix)
    print(f"{size}x{size} 矩阵的均值: {mean}")
    print(f"{size}x{size} 矩阵的标准差: {std_dev}")
    print()

import numpy as np
import matplotlib.pyplot as plt

# 定义的函数，计算滑动平均值
def moving_average(a, n):
    ret = np.cumsum(a, dtype=float)
    ret[n:] = ret[n:] - ret[:-n]
    return ret[n - 1:] / n


# 示例数组 长度和区间长度
a = np.random.randn(20)
n = 3
moving_avg = moving_average(a, n)

# 绘图
plt.figure(figsize=(12, 6))
plt.plot(a, label = "Original Array")
plt.plot(np.arange(n - 1, len(a)), moving_avg, label = f"Moving Average (window size={n})")
plt.title("Original Array vs Moving Average")
plt.xlabel("Index")
plt.ylabel("Value")
plt.legend()
plt.grid(True)
plt.show()

import numpy as np


def extract_square_matrix(arr, i, j, l):

    # 增加输入检查功能
    # 检查输入数组是否为二维数组
    if len(arr.shape) != 2:
        raise ValueError("输入数组必须是二维数组。")
    # 检查输入的 i、j、l 是否为有效整数
    if not isinstance(i, int) or not isinstance(j, int) or not isinstance(l, int):
        raise ValueError("i、j、l 必须是整数。")

    # 获取输入数组的行数和列数 
    # 修正坐标
    i -= 1
    j -= 1

    rows, cols = arr.shape
    # 初始化结果矩阵，大小为 (2l+1, 2l+1)，初始值全为 0
    result = np.zeros((2 * l + 1, 2 * l + 1))

    # 计算方阵在原数组中的起始行索引，确保不小于 0
    start_row = max(0, i - l)
    # 计算方阵在原数组中的结束行索引，确保不超过数组行数
    end_row = min(rows, i + l + 1)
    # 计算方阵在原数组中的起始列索引，确保不小于 0
    start_col = max(0, j - l)
    # 计算方阵在原数组中的结束列索引，确保不超过数组列数
    end_col = min(cols, j + l + 1)

    # 计算方阵在结果矩阵中的起始行偏移量
    offset_row_start = start_row - (i - l)
    # 计算方阵在结果矩阵中的结束行偏移量
    offset_row_end = offset_row_start + (end_row - start_row)
    # 计算方阵在结果矩阵中的起始列偏移量
    offset_col_start = start_col - (j - l)
    # 计算方阵在结果矩阵中的结束列偏移量
    offset_col_end = offset_col_start + (end_col - start_col)

    # 将原数组中提取的方阵赋值给结果矩阵的相应位置
    result[offset_row_start:offset_row_end, offset_col_start:offset_col_end] = arr[start_row:end_row, start_col:end_col]

    return result


# 多测试点

arr = np.array([[1, 2, 3, 4],
                [5, 6, 7, 8],
                [9, 10, 11, 12],
                [13, 14, 15, 16]])
i, j = 2, 3
l = 1
submatrix = extract_square_matrix(arr, i, j, l)
print(submatrix)
print("\n")

i, j = 2, 1
l = 3
submatrix = extract_square_matrix(arr, i, j, l)
print(submatrix)
print("\n")

i, j = 2, 1
l = 2
submatrix = extract_square_matrix(arr, i, j, l)
print(submatrix)
print("\n")


i, j = 2, 3
l = 4
submatrix = extract_square_matrix(arr, i, j, l)
print(submatrix)

import numpy as np


# 利用基本的线性代数知识求解
def find_coefficients(points):
    # 构建线性方程组的系数矩阵 A 和常数矩阵 B
    A = []
    B = []
    for x, y in points:
        A.append([x**2, x, 1])
        B.append(y)
    A = np.array(A)
    B = np.array(B)
    # 求解线性方程组
    try:
        coefficients = np.linalg.solve(A, B)
        return coefficients
    except np.linalg.LinAlgError:
        print("线性方程组无解或有无穷多解。")
        return None


# 示例点
points = [(-1, 1), (0, -1), (2, 7)]
coefficients = find_coefficients(points)
if coefficients is not None:
    a, b, c = coefficients
    print(f"二次函数系数: a = {a}, b = {b}, c = {c}")