要求使用python语言编写一个遗传算法，对一个4*8的二维矩阵进行优化，矩阵内的值均在-1.3到1.5之间，实值编码，同时对矩阵进行DCT编码，压缩成2*4的dtc矩阵，对该矩阵进行优化，在适应度评估时将该矩阵逆变换成4*8的矩阵，目标函数是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

以下是实现上述步骤的Python代码：

import random
import numpy as np
from scipy.fftpack import dct, idct

# 定义遗传算法的参数
POP_SIZE = 100  # 种群大小
GENE_LENGTH = 32  # 基因长度
GENERATIONS = 200  # 迭代次数
MUTATION_RATE = 0.01  # 变异率
CROSSOVER_RATE = 0.6  # 交叉率

# 定义矩阵的参数
ROWS = 4
COLS = 8
MIN_VALUE = -1.3
MAX_VALUE = 1.5

# 定义DCT矩阵的参数
DCT_ROWS = 2
DCT_COLS = 4

# 定义目标函数的参数
TARGET_SUMS = [45.2, 46.4, 47.6, 48.8, 50, 51.2, 52.4, 53.6]

# 初始化种群
def init_population(pop_size, gene_length):
    population = []
    for i in range(pop_size):
        genes = []
        for j in range(gene_length):
            gene = random.uniform(MIN_VALUE, MAX_VALUE)
            genes.append(gene)
        population.append(genes)
    return population

# 计算适应度
def calculate_fitness(population):
    fitness = []
    for genes in population:
        # 将基因解码为矩阵
        matrix = np.array(genes).reshape((ROWS, COLS))
        # 对矩阵进行DCT编码
        dct_matrix = dct(matrix, axis=0, norm='ortho')
        dct_matrix = dct(dct_matrix, axis=1, norm='ortho')
        # 计算逆变换后的矩阵
        idct_matrix = idct(dct_matrix, axis=1, norm='ortho')
        idct_matrix = idct(idct_matrix, axis=0, norm='ortho')
        # 计算每列的和
        sums = np.sum(idct_matrix, axis=0)
        # 计算适应度
        fitness_value = 0
        for i in range(len(TARGET_SUMS)):
            fitness_value += abs(sums[i] - TARGET_SUMS[i])
        fitness.append(1 / (fitness_value + 1))
    return fitness

# 选择操作
def selection(population, fitness):
    fitness_sum = sum(fitness)
    probs = [f / fitness_sum for f in fitness]
    selected = []
    for i in range(len(population)):
        r = random.uniform(0, 1)
        j = 0
        p_sum = probs[j]
        while p_sum < r:
            j += 1
            p_sum += probs[j]
        selected.append(population[j])
    return selected

# 交叉操作
def crossover(parent1, parent2):
    if random.uniform(0, 1) > CROSSOVER_RATE:
        return parent1, parent2
    else:
        point = random.randint(1, GENE_LENGTH - 1)
        child1 = parent1[:point] + parent2[point:]
        child2 = parent2[:point] + parent1[point:]
        return child1, child2

# 变异操作
def mutation(genes):
    if random.uniform(0, 1) > MUTATION_RATE:
        return genes
    else:
        point = random.randint(0, GENE_LENGTH - 1)
        genes[point] = random.uniform(MIN_VALUE, MAX_VALUE)
        return genes

# 遗传算法优化
def genetic_algorithm():
    # 初始化种群
    population = init_population(POP_SIZE, GENE_LENGTH)
    for i in range(GENERATIONS):
        # 计算适应度
        fitness = calculate_fitness(population)
        # 打印最优解
        index = np.argmax(fitness)
        print('Generation:', i+1, 'Best Fitness:', fitness[index], 'Best Solution:', population[index])
        # 选择操作
        selected = selection(population, fitness)
        # 交叉操作
        offspring = []
        for j in range(0, POP_SIZE, 2):
            child1, child2 = crossover(selected[j], selected[j+1])
            offspring.append(mutation(child1))
            offspring.append(mutation(child2))
        # 替换操作
        population = offspring

if __name__ == '__main__':
    genetic_algorithm()

在这个代码中，我们首先定义了遗传算法的参数，包括种群大小、基因长度、迭代次数、变异率和交叉率。然后定义了矩阵的参数，包括行数、列数和取值范围。接着定义了DCT矩阵的参数，包括行数和列数。最后定义了目标函数的参数，即每列的和应该等于多少。

接下来，我们实现了遗传算法的各个操作。首先是初始化种群的函数`init_population()`，它用于生成随机的基因序列。然后是计算适应度的函数`calculate_fitness()`，它将基因解码为矩阵，并对矩阵进行DCT编码和逆变换，最终计算每列的和与目标值之间的差距，作为适应度。

接着是选择操作的函数`selection()`，它根据每个个体的适应度计算出其被选中的概率，并从中随机选择一些个体作为下一代的父代。然后是交叉操作的函数`crossover()`，它随机选择一个交叉点，将两个父代的基因序列分别从交叉点处切开，然后将前半段拼接成一个新的基因序列。最后是变异操作的函数`mutation()`，它随机选择一个基因位，将其替换成一个随机的值。

最后，我们实现了遗传算法的主函数`genetic_algorithm()`，它依次执行初始化种群、计算适应度、选择、交叉、变异和替换操作，并打印出每一代的最优解。