def tv_shrinkage(x, lambda_, num_iter=100):
    """
    Chambolle的TV投影算法实现
    """
    # 参数
    tau = 0.125
    sigma = 1.0 / tau
    theta = 1.0

    # 初始化
    p = np.zeros_like(x)
    x_tilde = x.copy()

    for _ in range(num_iter):
        # 梯度计算
        grad_x_tilde = compute_gradient(x_tilde)

        # p的更新
        p = p + sigma * grad_x_tilde
        norm_p = np.sqrt(p[:, 0]**2 + p[:, 1]**2)
        p = p / np.maximum(1, norm_p[:, :, np.newaxis])

        # x的更新
        x_new = x_tilde - tau * compute_divergence(p)

        # 外推
        x_tilde = x_new + theta * (x_new - x)

    return x_new

def compute_gradient(image):
    """计算图像梯度"""
    grad_x = np.zeros_like(image)
    grad_y = np.zeros_like(image)

    grad_x[:, :-1] = image[:, 1:] - image[:, :-1]
    grad_y[:-1, :] = image[1:, :] - image[:-1, :]

    return np.stack([grad_x, grad_y], axis=-1)

def compute_divergence(p):
    """计算散度"""
    div = np.zeros(p.shape[:2])

    div[:, :-1] += p[:, :-1, 0]
    div[:, 1:] -= p[:, :-1, 0]
    div[:-1, :] += p[:-1, :, 1]
    div[1:, :] -= p[:-1, :, 1]

    return div

def lp_shrinkage(x, lambda_, p):
    """
    Lp范数广义软阈值
    """
    if p == 1:
        return np.sign(x) * np.maximum(np.abs(x) - lambda_, 0)

    elif p == 2:
        return x / (1 + lambda_)

    elif p == np.inf:
        return np.clip(x, -lambda_, lambda_)

    else:
        # 数值求解Lp收缩
        return _solve_lp_shrinkage(x, lambda_, p)

def _solve_lp_shrinkage(y, lambda_, p):
    """
    数值求解Lp收缩问题：min_x (1/2)||x-y||^2 + lambda_|x|_p^p
    """
    x = np.zeros_like(y)

    for i in range(len(y)):
        if abs(y[i]) < 1e-10:
            x[i] = 0
        else:
            # 二分法求解
            low = 0
            high = abs(y[i])

            for _ in range(50):
                mid = (low + high) / 2
                if abs(mid - y[i]) - lambda_ * p * (mid ** (p-1)) > 0:
                    high = mid
                else:
                    low = mid

            x[i] = mid * np.sign(y[i])

    return x

def robot_path_planning_twist(start_config, goal_config, obstacles, robot_model):
    """
    使用TWIST算法进行机器人路径规划
    """
    # 问题维度
    dim = len(start_config)

    # 构建观测算子（包含动力学约束）
    H = build_dynamics_operator(robot_model, dim)

    # 正则化项（路径平滑性）
    def path_regularizer(path):
        # 二阶差分惩罚（平滑性）
        smoothness = np.sum(np.diff(path, n=2, axis=0)**2)

        # 长度惩罚
        length = np.sum(np.diff(path, axis=0)**2)

        # 避障惩罚
        collision = collision_penalty(path, obstacles, robot_model)

        return smoothness + alpha * length + beta * collision

    # 构建TWIST求解器
    def twist_path_solver():
        # 初始化路径（直线插值）
        initial_path = linear_interpolation(start_config, goal_config, num_points=100)

        # 使用TWIST优化
        optimized_path = TWIST_optimizer(
            initial_path=initial_path,
            H=H,
            regularizer=path_regularizer,
            lambda_=0.1,
            alpha=0.5
        )

        return optimized_path

    return twist_path_solver()

class DynamicTwistPlanner:
    """动态环境下的TWIST路径规划器"""

    def __init__(self, robot_model):
        self.robot_model = robot_model
        self.current_path = None
        self.twist_solver = None

    def plan(self, start, goal, obstacles):
        """初始规划"""
        self.current_path = self._plan_with_twist(start, goal, obstacles)
        return self.current_path

    def replan(self, new_obstacles, execution_point_idx):
        """动态重规划"""
        if self.current_path is None:
            return None

        # 从执行点开始重规划
        remaining_path = self.current_path[execution_point_idx:]
        new_goal = remaining_path[-1]
        new_start = remaining_path[0]

        # 局部重规划
        local_path = self._plan_with_twist(new_start, new_goal, new_obstacles)

        # 组合路径
        self.current_path = np.concatenate([
            self.current_path[:execution_point_idx],
            local_path[1:]
        ])

        return self.current_path

    def _plan_with_twist(self, start, goal, obstacles):
        """使用TWIST进行路径规划"""
        # 实现细节见上文
        pass

class MemoryEfficientTWIST:
    """内存优化的TWIST实现"""

    def __init__(self, chunk_size=1000):
        self.chunk_size = chunk_size

    def solve_large_problem(self, y, H, lambda_, Psi):
        """分块求解大规模问题"""
        n = len(y)
        num_chunks = (n + self.chunk_size - 1) // self.chunk_size

        # 分块处理
        for i in range(num_chunks):
            start_idx = i * self.chunk_size
            end_idx = min((i + 1) * self.chunk_size, n)

            # 提取子问题
            y_chunk = y[start_idx:end_idx]
            H_chunk = self._extract_operator_chunk(H, start_idx, end_idx)

            # TWIST求解
            x_chunk = self._solve_chunk(y_chunk, H_chunk, lambda_, Psi)

            # 存储结果
            self._store_result(x_chunk, start_idx, end_idx)

import multiprocessing as mp

def parallel_twist(y, H, lambda_, Psi, num_processes=None):
    """并行TWIST实现"""
    if num_processes is None:
        num_processes = mp.cpu_count()

    # 数据分割
    chunks = split_data(y, H, num_processes)

    # 创建进程池
    with mp.Pool(num_processes) as pool:
        # 并行处理
        results = pool.starmap(
            solve_twist_chunk,
            [(chunk['y'], chunk['H'], lambda_, Psi) for chunk in chunks]
        )

    # 合并结果
    return merge_results(results)

import cupy as cp

class GPUTWIST:
    """GPU加速的TWIST实现"""

    def __init__(self):
        self.use_gpu = cp.cuda.is_available()

    def solve(self, y, H, lambda_, Psi):
        """GPU求解"""
        if self.use_gpu:
            # 转移到GPU
            y_gpu = cp.array(y)
            H_gpu = cp.array(H)

            # GPU上的TWIST迭代
            x_gpu = self._gpu_twist_iteration(y_gpu, H_gpu, lambda_, Psi)

            # 转移回CPU
            return cp.asnumpy(x_gpu)
        else:
            # CPU回退
            return self._cpu_twist_iteration(y, H, lambda_, Psi)

class AutoTwistTuner:
    """自动TWIST参数调优"""

    def __init__(self):
        self.param_history = []

    def tune_parameters(self, problem_type, data_characteristics):
        """基于问题特性自动调参"""

        # 分析数据特性
        condition_number = self._estimate_condition_number(data_characteristics)
        noise_level = self._estimate_noise_level(data_characteristics)

        # 参数选择规则
        if problem_type == 'image_deconvolution':
            if condition_number > 1000:
                alpha = 0.3  # 重度病态
                lambda_ = 0.01
            elif condition_number > 100:
                alpha = 0.5  # 中度病态
                lambda_ = 0.05
            else:
                alpha = 0.7  # 轻度病态
                lambda_ = 0.1

        elif problem_type == 'robot_path_planning':
            alpha = 0.6  # 路径规划常用值
            lambda_ = 0.1 / noise_level  # 基于噪声水平调整

        # 记录参数
        self.param_history.append({
            'problem_type': problem_type,
            'condition_number': condition_number,
            'alpha': alpha,
            'lambda': lambda_
        })

        return alpha, lambda_

class TwistConvergenceMonitor:
    """TWIST收敛监控器"""

    def __init__(self):
        self.objective_history = []
        self.gradient_norms = []

    def monitor(self, x_k, objective, gradient_norm):
        """监控迭代过程"""
        self.objective_history.append(objective)
        self.gradient_norms.append(gradient_norm)

        # 检查停滞
        if len(self.objective_history) > 10:
            recent_improvement = (
                self.objective_history[-10] -
                self.objective_history[-1]
            ) / self.objective_history[-10]

            if recent_improvement < 1e-6:
                return "stalled"

        # 检查发散
        if len(self.objective_history) > 2:
            if self.objective_history[-1] > self.objective_history[-2] * 1.1:
                return "diverging"

        # 检查收敛
        if gradient_norm < 1e-8:
            return "converged"

        return "continuing"

    def plot_convergence(self):
        """绘制收敛曲线"""
        import matplotlib.pyplot as plt

        fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(10, 8))

        # 目标函数曲线
        ax1.semilogy(self.objective_history)
        ax1.set_ylabel('Objective Value')
        ax1.set_title('TWIST Convergence')
        ax1.grid(True)

        # 梯度范数曲线
        ax2.semilogy(self.gradient_norms)
        ax2.set_ylabel('Gradient Norm')
        ax2.set_xlabel('Iteration')
        ax2.grid(True)

        plt.tight_layout()
        plt.show()

def compare_convergence_rates(algorithms, test_problems):
    """比较不同算法的收敛速度"""
    results = {}

    for problem in test_problems:
        results[problem.name] = {}

        for alg_name, alg_class in algorithms.items():
            # 运行算法
            solver = alg_class()
            x, history = solver.solve(problem)

            # 计算收敛速度
            convergence_rate = compute_convergence_rate(history)

            results[problem.name][alg_name] = {
                'iterations': len(history),
                'final_error': history[-1],
                'convergence_rate': convergence_rate,
                'time_per_iter': solver.time_per_iteration
            }

    return results

def compute_convergence_rate(history, window_size=10):
    """计算收敛速度"""
    if len(history) < window_size * 2:
        return None

    # 计算最近窗口的收敛率
    recent = history[-window_size:]
    earlier = history[-window_size*2:-window_size]

    rate = np.mean(recent) / np.mean(earlier)
    return rate ** (1.0 / window_size)

def robustness_test():
    """测试算法对参数和噪声的鲁棒性"""

    # 参数敏感性测试
    alpha_values = np.linspace(0.1, 0.9, 9)
    lambda_values = [0.001, 0.01, 0.1, 1.0]
    noise_levels = [0.01, 0.05, 0.1, 0.2]

    results = np.zeros((len(alpha_values), len(lambda_values), len(noise_levels)))

    for i, alpha in enumerate(alpha_values):
        for j, lambda_ in enumerate(lambda_values):
            for k, noise in enumerate(noise_levels):
                # 生成测试问题
                problem = generate_test_problem(noise)

                # 运行TWIST
                solver = TWIST(alpha=alpha, lambda_=lambda_)
                x, history = solver.solve(problem)

                # 记录最终误差
                results[i, j, k] = history[-1]

    return results