要求使用python语言编写一个遗传算法，将一个4*8的二维矩阵进行DCT编码，压缩成2*4的dtc矩阵，要求矩阵内的值限制在-1到1之间，对压缩后矩阵进行优化，在适应度评估时将该矩阵逆变换回4*8的矩阵，目标函数是4*8矩阵的每一列的和分别等于45.2,46.4,47.6,48.8,50,51.2,52.4,53.6。请给出实现上述步骤的代码，并请注意，4*8的矩阵内的值均在-1.3到1.5之间

以下是一个基于Python的遗传算法实现，用于将4x8的矩阵进行DCT编码，并将其压缩为2x4的DTC矩阵，并在适应度评估时将其逆变换回原始矩阵，然后根据给定的约束条件对矩阵进行优化。

import numpy as np
import random

# 定义常量
POPULATION_SIZE = 30
CROSSOVER_RATE = 0.8
MUTATION_RATE = 0.03
NUM_GENERATIONS = 1000
NUM_PARENTS = 2
NUM_BITS = 3

# 定义DCT矩阵
DCT_MATRIX = np.array([
    [0.3536, 0.3536, 0.3536, 0.3536, 0.3536, 0.3536, 0.3536, 0.3536],
    [0.4904, 0.4157, 0.2778, 0.0975, -0.0975, -0.2778, -0.4157, -0.4904],
    [0.4619, 0.1913, -0.1913, -0.4619, -0.4619, -0.1913, 0.1913, 0.4619],
    [0.4157, -0.0975, -0.4904, -0.2778, 0.2778, 0.4904, 0.0975, -0.4157]
])

# 定义逆DCT矩阵
IDCT_MATRIX = np.transpose(DCT_MATRIX)

# 定义目标列和
TARGET_COLUMN_SUMS = [45.2, 46.4, 47.6, 48.8, 50.0, 51.2, 52.4, 53.6]

# 定义矩阵的范围
MIN_VALUE = -1.3
MAX_VALUE = 1.5


def dct_4x8(matrix):
    """对4x8矩阵进行DCT编码"""
    return np.dot(DCT_MATRIX, matrix)


def idct_4x8(matrix):
    """对DCT编码后的2x4矩阵进行逆DCT变换"""
    return np.dot(IDCT_MATRIX, matrix)


def normalize(matrix):
    """将矩阵的值限制在MIN_VALUE和MAX_VALUE之间"""
    return np.clip(matrix, MIN_VALUE, MAX_VALUE)


def fitness(matrix):
    """计算矩阵的适应度"""
    decoded_matrix = idct_4x8(matrix)
    column_sums = np.sum(decoded_matrix, axis=0)
    # 计算每一列与目标列和的差异
    diff = np.abs(column_sums - TARGET_COLUMN_SUMS)
    return np.sum(diff)


def crossover(parent1, parent2):
    """交叉操作"""
    crossover_point = random.randint(1, 7)
    child1 = np.concatenate((parent1[:crossover_point, :], parent2[crossover_point:, :]), axis=0)
    child2 = np.concatenate((parent2[:crossover_point, :], parent1[crossover_point:, :]), axis=0)
    return child1, child2


def mutation(matrix):
    """突变操作"""
    for i in range(matrix.shape[0]):
        for j in range(matrix.shape[1]):
            if random.random() < MUTATION_RATE:
                # 在MIN_VALUE和MAX_VALUE之间随机生成一个值
                matrix[i, j] = random.uniform(MIN_VALUE, MAX_VALUE)
    return matrix


def select_parents(population):
    """选择父代"""
    parents = []
    for i in range(NUM_PARENTS):
        # 选择适应度最佳的个体
        best_fitness = None
        best_individual = None
        for individual in population:
            if best_fitness is None or fitness(individual) < best_fitness:
                best_fitness = fitness(individual)
                best_individual = individual
        parents.append(best_individual)
        # 将已选择的个体从种群中删除
        population.remove(best_individual)
    return parents


def generate_initial_population():
    """生成初始种群"""
    population = []
    for i in range(POPULATION_SIZE):
        # 在MIN_VALUE和MAX_VALUE之间随机生成一个4x8矩阵
        matrix = np.random.uniform(MIN_VALUE, MAX_VALUE, size=(4, 8))
        # 对矩阵进行DCT编码并将其压缩为2x4
        compressed_matrix = dct_4x8(matrix)[:2, :]
        # 将矩阵的值限制在MIN_VALUE和MAX_VALUE之间
        normalized_matrix = normalize(compressed_matrix)
        population.append(normalized_matrix)
    return population


def run_ga():
    """运行遗传算法"""
    population = generate_initial_population()
    for generation in range(NUM_GENERATIONS):
        # 选择父代
        parents = select_parents(population)
        next_population = []
        while len(next_population) < POPULATION_SIZE:
            # 随机选择两个父代进行交叉操作
            parent1, parent2 = random.sample(parents, 2)
            child1, child2 = crossover(parent1, parent2)
            # 对交叉后的子代进行突变操作
            mutated_child1 = mutation(child1)
            mutated_child2 = mutation(child2)
            # 将子代加入下一代种群中
            next_population.append(mutated_child1)
            next_population.append(mutated_child2)
        population = next_population
    # 选择适应度最佳的个体并返回其解码后的矩阵
    best_fitness = None
    best_individual = None
    for individual in population:
        if best_fitness is None or fitness(individual) < best_fitness:
            best_fitness = fitness(individual)
            best_individual = individual
    decoded_matrix = idct_4x8(best_individual)
    return decoded_matrix


if __name__ == '__main__':
    result = run_ga()
    print(result)

该代码生成初始种群，然后在每个代中选择适应度最佳的个体，使用交叉和突变操作生成新的个体，并重复此过程直到达到指定的迭代次数。最后，选择适应度最佳的个体并返回其解码后的矩阵。

注意，这个实现仅用于教学目的，实际上并不是最优的遗传算法实现。在实际应用中，需要对各个参数进行调整以获得更好的结果。