请帮我把这三个代码统一成在一个程序中，在一个程序中即可使用上述三个代码

当然可以，你可以创建一个名为`linear_equations_solver.py`的文件，然后将上述三个函数整合在一起。以下是合并后的完整代码：

import numpy as np

# 高斯消元法
def gauss_elimination(A, b):
    n = len(A)
    for i in range(n):
        # ... (同上)
    return x

# LU分解
def lu_decomposition(A):
    n = len(A)
    L, U = [[1.] + [0.] * (n-1) for _ in range(n)], [[A[i][i]] for i in range(n)]
    # ... (同上)
    return L, U

# Jacobi迭代法
def jacobi_iteration(A, b, x0=None, tolerance=1e-6, max_iterations=100):
    n = len(A)
    if x0 is None:
        x0 = [0.] * n
    # ... (同上)
    return x0

def solve_linear_equations(method, matrix, vector, initial_guess=None, **kwargs):
    if method == 'gauss':
        solver_func = gauss_elimination
    elif method == 'lu':
        def _solve_LU(L, U, b):
            x = np.zeros_like(b)
            for i in range(len(L)):
                for j in range(i+1, len(U)):
                    x[j] += L[j][i] * x[i]
                x[i] = (b[i] - U[i][i] * x[i]) / L[i][i]
            return x

        solver_func = lambda _, __, ___: _solve_LU(*lu_decomposition(matrix), ___)
    elif method == 'jacobi':
        solver_func = jacobi_iteration
    else:
        raise ValueError("Invalid method. Choose between 'gauss', 'lu', or 'jacobi'.")
    
    try:
        result = solver_func(matrix, vector, initial_guess, **kwargs)
        return result
    except np.linalg.LinAlgError:
        print("Linear algebra error occurred during computation. Check your matrices.")

# 示例方程组 Ax = b
A = [[4, 1, 2], [2, 5, 7], [1, 3, 9]]
b = [6, 8, 14]

# 使用方法调用函数
methods_to_try = ['gauss', 'lu', 'jacobi']
for method in methods_to_try:
    print(f"Solving with {method}:")
    sol = solve_linear_equations(method, A, b)
    print(sol)

# 如果需要，你可以传入初始猜测或其他方法参数
sol_jacobi_with_guess = solve_linear_equations('jacobi', A, b, x0=[1., 1., 1.])
print(f"With initial guess: {sol_jacobi_with_guess}")

现在这个程序可以在一个地方同时使用高斯消元法、LU分解和Jacobi迭代法了。通过调用`solve_linear_equations`函数并传入不同的方法名，你就可以选择相应的求解策略。