util.m

来自「这是一个超宽带的源码」· M 代码 · 共 49 行

%
%	[A,b,umin] = util(xmax,n,f)
%
%  Arguments:
%	xmax - approximate between (0,xmax]  (default xmax=10)
%  n - number of points for linear interpolation (default n=4)
%  f - utility function default (f=@log)
%
%	gives a linear aproximation of a utility function (log by default)
% 	in points xmax.^[-n+2:1] (default [0.01,0.1,1,10]). 
%
%  A, b - such that for every x, U(x) <= Ax + b
%  umin - min U (for x=0)
%


function [A,b,umin] = util(xrange,n,f)

if nargin < 3
	% define default utility f. here
	f=@log;
	if nargin < 2
		n = 4;
		if nargin < 1
			xrange = [10 1e-3];
		end
	end
end

xmax = xrange(1);
if length(xrange) < 2
    xmin = 10^(-n+1+log10(xmax));
else
    xmin = xrange(2);
end


% interpolation points
x = logspace(log10(xmin), log10(xmax), n);
fx = feval(f,x);
A = zeros(size(x,2)-1,1);
b = zeros(size(x,2)-1,1);

for i=1:size(x,2)-1
    A(i) = (fx(i+1)-fx(i))/(x(i+1)-x(i));
    b(i) = fx(i) - A(i)*x(i);
end

umin = b(1);