41 lines
935 B
Matlab
Executable File
41 lines
935 B
Matlab
Executable File
function [Ax,Ay,b,K] = convexhullConvex(varargin)
|
|
% Two upper bounds from tangents
|
|
% y > f(xL) + (x-xL)*df(xL)
|
|
% y > f(xU) + (x-xL)*df(xU)
|
|
% Upper bound from conneting extreme points
|
|
% y < f(xU)(x-xL)/(xU-xL) + f(xL)(xU-x)/(xU-xL)
|
|
% can be wrtitten as
|
|
% Ax*x + Ay*y < b
|
|
|
|
if rem(nargin,3)
|
|
error('The convex hull generator assumes n triplets (x,f,df).')
|
|
end
|
|
m = nargin/3;
|
|
x = [varargin{(1:m)}]';
|
|
f = [varargin{(1:m)+m}]';
|
|
df = [varargin{(1:m)+2*m}]';
|
|
|
|
if all(diff(x)>0)
|
|
Ay = [-ones(m,1);1];
|
|
b = [-f + x.*df; -f(end)*x(1)/(x(end)-x(1)) + f(1)*x(end)/(x(end)-x(1))];
|
|
Ax = [df;-f(end)/(x(end)-x(1)) + f(1)/(x(end)-x(1))];
|
|
|
|
% Don't use ill-conditioned cuts
|
|
if df(1)<-1000
|
|
Ax(1)=[];
|
|
Ay(1) = [];
|
|
b(1) = [];
|
|
end
|
|
if df(end)>1000
|
|
Ax(end)=[];
|
|
Ay(end) = [];
|
|
b(end) = [];
|
|
end
|
|
|
|
else
|
|
Ax = [];
|
|
Ay = [];
|
|
b = [];
|
|
end
|
|
K.f = 0;
|
|
K.l = length(b); |