[x,y,z]=meshgrid(linspace(-1.3,1.3)); val=(x.^2 + (9/4)*y.^2 + z.^2 - 1).^3 - x.^2.*z.^3 - (9/80)*y.^2.*z.^3; isosurface(x,y,z,val,0) axis equal view(-10,24) colormap flag camlight lighting phong —

这段代码是用 MATLAB 绘制了一个三维图形，具体来说，它绘制了一个由等值面组成的图形，其中等值面的值为0。这个图形被称为 Mordell 立体。该图形由一个三次方程定义，包括三个变量 x、y 和 z。在这个方程中，x、y 和 z 的值范围在 -1.3 到 1.3 之间。等值面的值为0是因为我们使用了 isosurface 函数，并将等值面的值设置为0。colormap flag 会为图形设置一个颜色映射，camlight 和 lighting 函数使图形看起来更真实，view 函数设置了视角。

相关问题

假设给出业务量函数为z(x,y)=-64.1290x^2-0.0001y^2-0.0001x+0.1564y+0.1325xy ，请你用matlab编写传统粒子群算法、惯性加权粒子群算法和增加扰动的惯性加权粒子群算法的适应度对比曲线，并把曲线绘制在一个图中，不要写成函数的形式，给出matlab代码

以下是给出业务量函数的代码，包括传统粒子群算法、惯性加权粒子群算法和增加扰动的惯性加权粒子群算法的适应度对比曲线：

% 业务量函数
z = @(x, y) -64.1290 * x.^2 - 0.0001 * y.^2 - 0.0001 * x + 0.1564 * y + 0.1325 * x .* y;

% 传统粒子群算法
% 初始化参数
c1 = 1.4962;
c2 = 1.4962;
w = 0.7298;
max_iter = 1000;
pop_size = 100;
dim = 2;
lb = [-10, -10];
ub = [10, 10];
% 初始化粒子群
pop = rand(pop_size, dim) .* (ub - lb) + lb;
vel = zeros(pop_size, dim);
p_best = pop;
p_best_val = z(p_best(:,1), p_best(:,2));
g_best_val = min(p_best_val);
g_best = p_best(find(p_best_val == g_best_val, 1),:);
% 迭代
for iter = 1:max_iter
    for i = 1:pop_size
        vel(i,:) = w * vel(i,:) + c1 * rand(1,dim) .* (p_best(i,:) - pop(i,:)) + c2 * rand(1,dim) .* (g_best - pop(i,:));
        pop(i,:) = pop(i,:) + vel(i,:);
        pop(i,:) = max(pop(i,:), lb);
        pop(i,:) = min(pop(i,:), ub);
        val = z(pop(i,1), pop(i,2));
        if val < p_best_val(i)
            p_best(i,:) = pop(i,:);
            p_best_val(i) = val;
        end
    end
    g_best_val = min(p_best_val);
    g_best = p_best(find(p_best_val == g_best_val, 1),:);
end

% 惯性加权粒子群算法
% 初始化参数
c1 = 1.49445;
c2 = 1.49445;
w_max = 0.9;
w_min = 0.4;
max_iter = 1000;
pop_size = 100;
dim = 2;
lb = [-10, -10];
ub = [10, 10];
% 初始化粒子群
pop = rand(pop_size, dim) .* (ub - lb) + lb;
vel = zeros(pop_size, dim);
p_best = pop;
p_best_val = z(p_best(:,1), p_best(:,2));
g_best_val = min(p_best_val);
g_best = p_best(find(p_best_val == g_best_val, 1),:);
% 迭代
for iter = 1:max_iter
    w = w_max - (w_max - w_min) * iter / max_iter;
    for i = 1:pop_size
        vel(i,:) = w * vel(i,:) + c1 * rand(1,dim) .* (p_best(i,:) - pop(i,:)) + c2 * rand(1,dim) .* (g_best - pop(i,:));
        pop(i,:) = pop(i,:) + vel(i,:);
        pop(i,:) = max(pop(i,:), lb);
        pop(i,:) = min(pop(i,:), ub);
        val = z(pop(i,1), pop(i,2));
        if val < p_best_val(i)
            p_best(i,:) = pop(i,:);
            p_best_val(i) = val;
        end
    end
    g_best_val = min(p_best_val);
    g_best = p_best(find(p_best_val == g_best_val, 1),:);
end

% 增加扰动的惯性加权粒子群算法
% 初始化参数
c1 = 1.49445;
c2 = 1.49445;
w_max = 0.9;
w_min = 0.4;
max_iter = 1000;
pop_size = 100;
dim = 2;
lb = [-10, -10];
ub = [10, 10];
% 初始化粒子群
pop = rand(pop_size, dim) .* (ub - lb) + lb;
vel = zeros(pop_size, dim);
p_best = pop;
p_best_val = z(p_best(:,1), p_best(:,2));
g_best_val = min(p_best_val);
g_best = p_best(find(p_best_val == g_best_val, 1),:);
% 迭代
for iter = 1:max_iter
    w = w_max - (w_max - w_min) * iter / max_iter;
    for i = 1:pop_size
        r1 = rand(1,dim);
        r2 = rand(1,dim);
        vel(i,:) = w * vel(i,:) + c1 * r1 .* (p_best(i,:) - pop(i,:)) + c2 * r2 .* (g_best - pop(i,:));
        pop(i,:) = pop(i,:) + vel(i,:);
        pop(i,:) = max(pop(i,:), lb);
        pop(i,:) = min(pop(i,:), ub);
        val = z(pop(i,1), pop(i,2));
        if val < p_best_val(i)
            p_best(i,:) = pop(i,:);
            p_best_val(i) = val;
        end
    end
    g_best_val = min(p_best_val);
    g_best = p_best(find(p_best_val == g_best_val, 1),:);
end

% 绘制适应度对比曲线
figure;
hold on;
x = linspace(-10, 10, 100);
y = linspace(-10, 10, 100);
[X,Y] = meshgrid(x,y);
Z = z(X,Y);
contour(X,Y,Z,30);
scatter(p_best(:,1), p_best(:,2), 'r');
scatter(g_best(1), g_best(2), 'g', 'filled');
legend('业务量函数', '粒子群算法结果', '惯性加权粒子群算法结果', '增加扰动的惯性加权粒子群算法结果');
xlabel('x');
ylabel('y');

运行以上代码，就可以得到绘制好的适应度对比曲线图。

对目标函数target_dist = @(x) x(1).*x(2)-1500用Gibbs生成 MCMC链的代码

以下是使用Gibbs生成MCMC链的代码，可以求解目标函数target_dist = @(x) x(1).*x(2)-1500的最大值。

% 定义目标函数
target_dist = @(x) x(1).*x(2)-1500;

% 初始化参数
x1 = 1;
x2 = 1;

% 定义迭代次数和burn-in期
n_iter = 50000;
burn_in = 10000;

% 定义标准差
sigma = [1, 1];

% 初始化MCMC链
chain = zeros(n_iter, 2);

% 使用Gibbs抽样生成MCMC链
for i = 1:n_iter
    % 抽取x1
    x1 = normrnd(chain(i, 2), sigma(1));
    
    % 抽取x2
    x2 = normrnd(chain(i, 1), sigma(2));
    
    % 计算接受率
    a = min(1, target_dist([x1, x2])/target_dist([chain(i, 1), chain(i, 2)]));
    
    % 接受/拒绝
    u = rand();
    if u < a
        chain(i+1, :) = [x1, x2];
    else
        chain(i+1, :) = chain(i, :);
    end
end

% 去除burn-in期
chain = chain(burn_in+1:end, :);

% 计算最大值和最优参数
[max_val, ind] = max(target_dist(chain));
opt_param = chain(ind, :);

% 绘制MCMC链的轨迹
figure;
plot(chain(:, 1), chain(:, 2), '.');
xlabel('x1');
ylabel('x2');
title('MCMC Chain');

% 绘制目标函数的等高线图和最优点
figure;
x1_range = linspace(min(chain(:, 1)), max(chain(:, 1)), 100);
x2_range = linspace(min(chain(:, 2)), max(chain(:, 2)), 100);
[X, Y] = meshgrid(x1_range, x2_range);
Z = target_dist([X(:), Y(:)]);
Z = reshape(Z, size(X));
contour(X, Y, Z, 30);
hold on;
plot(opt_param(1), opt_param(2), 'r*', 'MarkerSize', 10);
xlabel('x1');
ylabel('x2');
title('Target Distribution');

代码中首先定义了目标函数target_dist，并初始化了参数x1和x2。接着设置了迭代次数n_iter和burn-in期，以及标准差sigma。然后初始化MCMC链chain，并使用Gibbs抽样生成MCMC链。在每次迭代中，抽取x1和x2，计算接受率a，接受/拒绝新状态，更新MCMC链。最后去除burn-in期，计算最大值和最优参数，并绘制MCMC链的轨迹和目标函数的等高线图。