function [V,K] = economics_vk(expense,income,rnd)

% function to find V and K parameters using scaled conjugate gradients over
% each round returning the time dependent parameters V and K for each
% income (i.e. Cnorm + Fnorm + Nnorm) against expense (e.g. Cnorm).

options = foptions; % options for Netlab gradient descent algorithm
options(9) = 0; % do a gradient check? 1 = yes, 0 = no
options(1) = -1; % show error at iterations? 1 = yes, -1 = no.

N = length(income);
index = find((rnd(1:end-1)-rnd(2:end))<0);
index = [0,index']; index(end+1) = N;

rounds = length(index)-1;

for i = 1:rounds
%pars(i,:) = scg('economics_vk_err',rand(2,1)',options,'economics_vk_grad',expense(index(i)+1:index(i+1)),income(index(i)+1:index(i+1)));

% do gradient descent internally instead of using netlab
pars(i,:) = rand(1,2);
err_old = economics_vk_err(pars(i,:),expense(index(i)+1:index(i+1)),income(index(i)+1:index(i+1)));
success = 1; eta = 0.8;
for ind1 = 1:150
    if success
        grad = economics_vk_grad(pars(i,:),expense(index(i)+1:index(i+1)),income(index(i)+1:index(i+1)));
    end
    pars(i,:) = pars(i,:) - eta*grad;
    
    err_new = economics_vk_err(pars(i,:),expense(index(i)+1:index(i+1)),income(index(i)+1:index(i+1)));
    
    if err_new < err_old
        success = 1;
        eta = eta*1.2;
        err_old = err_new;
    else
        success = 0;
        pars(i,:) = pars(i,:) + eta*grad;
        eta = eta*0.2;
        
    end
end
    
end

V = pars(:,1);
K = pars(:,2);

end