www.gusucode.com > 增广拉格朗日函数 > augumented lagrangian function/smooth function.m

    %% plot smoothed function and its original function
times = 2;

mu = 0.5; %精度控制参数：accuracy control parameter
step = 0.05; % 粒度

% first part
[X,Y] = meshgrid(-mu:step:mu);

X1 =reshape(X,[numel(X) 1]);
Y1 = reshape(Y,[numel(Y) 1]);

M = [X1 Y1];

f = sum(abs(M),2).^2 /(2*mu);
f = reshape(f,[size(X,1),size(X,2)]);
% l1 norm
f0 = sum(abs(M),2);
f0 = reshape(f0,[size(X,1),size(X,2)]);
%  second part
[X0,Y0] = meshgrid(mu:step:times*mu);


X2 =reshape(X0,[numel(X0) 1]);
Y2 = reshape(Y0,[numel(Y0) 1]);

M2 = [X2 Y2];
f2 = bsxfun(@minus,sum(abs(M2),2) ,mu/2);

f2 = reshape(f2,[size(X0,1),size(X0,2)]);

% third part

[X3,Y3] = meshgrid(-times*mu:step:-mu);


X4 =reshape(X3,[numel(X3) 1]);
Y4 = reshape(Y3,[numel(Y3) 1]);

M3 = [X4 Y4];
f3 = bsxfun(@minus,sum(abs(M3),2) ,mu/2);

f3 = reshape(f3,[size(X3,1),size(X3,2)]);

% forth part
tim = 2;
[X5,Y5] = meshgrid(-tim*mu:step:tim*mu);


X6 =reshape(X5,[numel(X5) 1]);
Y6 = reshape(Y5,[numel(Y5) 1]);

M4 = [X6 Y6];
f4 = bsxfun(@minus,sum(abs(M4),2) ,mu/2);

f4 = reshape(f4,[size(X5,1),size(X5,2)]);

figure(1);
subplot(2,2,1);
surf(X,Y,f);
hold on;
surf(X,Y,f0);
title('smoothed and its original');
%hold on;
% surf(X0,Y0,f2);
% hold on ;
% surf(X3,Y3,f3);
% hold on;
subplot(2,2,2);
surf(X5,Y5,f4);
title('original');
subplot(2,2,3);
surf(X,Y,f);
hold on;
surf(X5,Y5,f4);

subplot(2,2,4);
surf(X,Y,f0);
hold on;
% for point: [-1 -2],[-1 2] => val: 3

plot3(-0.1,-0.2,0.3,'.r','markersize',30);
plot3(-0.1,0.2,0.3,'.k','markersize',30);