function [xopt, fopt, niter, gnorm, dx ] = grad_descent2(varargin)
if nargin==0

 x0 = [3,3];
elseif nargin==1
 x0 = varargin{1};
end

tol = 1e-6;
maxiter = 1000;
dxmin = 1e-6;
alpha = 0.1;

gnorm = inf; x=x0; niter=0; dx=inf;

f = @(x1,x2) x1.^2+x1.*x2+3*x2.^2;
figure(1); clf; ezcontour(f, [-5 5 -5 5]); axis equal; hold on
f2 = @(x) f(x(1),x(2));

while and(gnorm>=tol, and(niter<=maxiter, dx>=dxmin))

    g=grad(x);
    gnorm=norm(g);

    xnew = x - alpha*g;

%    if -isfinite(xnew)
%        niter
%        error('x is inf or NaN');
    end

    plot([x(1) xnew(1)], [x(2) xnew(2)], 'o')
    reflesh
    niter = niter + 1;
    dx = norm(xnew - x);
    x = xnew;
end
xopt = x
fopt = f2(xopt);
niter = niter - 1;

function g = grad(x)
g=[2*x(1) + x(2)
x(1) + 6*x(2)];

end
end