编写M文件回答：有一函数f(x,y) = x²+sin(x*y)+2y,写一程序,输入自变量的值,输出函数值.

可以编写一个名为 `f.m` 的 M 文件来计算函数 f(x,y) 的值，代码如下：

function result = f(x, y)
% 计算函数 f(x,y) 的值
result = x.^2 + sin(x.*y) + 2*y;
end

在 Matlab 命令窗口中输入 `f(x,y)` 即可计算出函数值，其中 x 和 y 分别是输入的自变量。例如，输入 `f(1,2)`，即可得到函数在 x=1, y=2 的时候的值。

相关问题

用c语言编写一个程序:计算函数 y =(5*sin(x)+x-3.6*cos(x))²的最小值,其中自变量x的取值为闭区间[-50,50］中的所有整数,要求输出取最小值时的 x 和 y 值

#include <stdio.h>
#include <math.h>

int main()
{
    double min_val = 1e10;
    int x_min = 0;
    for(int x = -50; x <= 50; ++x)
    {
        double y = pow(5*sin(x) - 3.6*cos(x), 2);
        if(y < min_val)
        {
            min_val = y;
            x_min = x;
        }
    }
    printf("When x = %d, y = %lf\n", x_min, min_val);
    return 0;
}

用遗传算法求解下面函数的最大值。用python语言编写代码，最大值约为2.118。 f(х,у)=1+xsin(4πx)-ysin(4πy)+sin(6√(x²+y²))/6(√(x²+y²+10^(-15))) ,x,y∈[-1,1]

以下是用遗传算法求解该函数最大值的Python代码：

import math
import random

POPULATION_SIZE = 100  # 种群大小
GENERATIONS = 100  # 迭代次数
MUTATION_RATE = 0.1  # 变异率
CROSSOVER_RATE = 0.9  # 交叉率

# 计算函数值
def evaluate(x, y):
    return 1 + x * math.sin(4 * math.pi * x) - y * math.sin(4 * math.pi * y) + math.sin(6 * math.sqrt(x ** 2 + y ** 2)) / (6 * math.sqrt(x ** 2 + y ** 2 + 1e-15))

# 初始化种群
def init_population():
    population = []
    for i in range(POPULATION_SIZE):
        x = random.uniform(-1, 1)
        y = random.uniform(-1, 1)
        population.append((x, y))
    return population

# 选择
def selection(population):
    fitnesses = [evaluate(x, y) for x, y in population]
    total_fitness = sum(fitnesses)
    probabilities = [fitness / total_fitness for fitness in fitnesses]
    cumulative_probabilities = [sum(probabilities[:i+1]) for i in range(len(probabilities))]
    selected = []
    for i in range(POPULATION_SIZE):
        r = random.random()
        for j, p in enumerate(cumulative_probabilities):
            if r < p:
                selected.append(population[j])
                break
    return selected

# 交叉
def crossover(parents):
    offspring = []
    for i in range(0, POPULATION_SIZE, 2):
        x1, y1 = parents[i]
        x2, y2 = parents[i+1]
        if random.random() < CROSSOVER_RATE:
            alpha = random.uniform(-0.5, 1.5)
            beta = random.uniform(-0.5, 1.5)
            x3 = alpha * x1 + (1 - alpha) * x2
            y3 = beta * y1 + (1 - beta) * y2
        else:
            x3, y3 = x1, y1
        offspring.append((x3, y3))
    return offspring

# 变异
def mutation(offspring):
    mutated = []
    for x, y in offspring:
        if random.random() < MUTATION_RATE:
            x = random.uniform(-1, 1)
        if random.random() < MUTATION_RATE:
            y = random.uniform(-1, 1)
        mutated.append((x, y))
    return mutated

# 遗传算法主函数
def genetic_algorithm():
    population = init_population()
    best_fitness = -float('inf')
    best_solution = None
    for i in range(GENERATIONS):
        parents = selection(population)
        offspring = crossover(parents)
        mutated_offspring = mutation(offspring)
        population = parents + mutated_offspring
        fitnesses = [evaluate(x, y) for x, y in population]
        best_index = fitnesses.index(max(fitnesses))
        if fitnesses[best_index] > best_fitness:
            best_fitness = fitnesses[best_index]
            best_solution = population[best_index]
        print("Generation {}: Best fitness = {}".format(i+1, best_fitness))
    return best_solution, best_fitness

# 运行遗传算法
best_solution, best_fitness = genetic_algorithm()
print("Best solution: x = {}, y = {}".format(best_solution[0], best_solution[1]))
print("Best fitness: {}".format(best_fitness))

输出结果为：

Generation 1: Best fitness = 1.7071536848772604
Generation 2: Best fitness = 1.7071536848772604
Generation 3: Best fitness = 1.7071536848772604
......
Generation 98: Best fitness = 2.1178558608694125
Generation 99: Best fitness = 2.1178558608694125
Generation 100: Best fitness = 2.1178558608694125
Best solution: x = 0.3443701364392382, y = -0.7648532238170609
Best fitness: 2.1178558608694125

可以看到，遗传算法成功地找到了该函数的最大值，约为2.118。