lab2

function [ptr,fval] = finmin( func, start, step, eps, varargin )

nargs = length(varargin);

f_hl = matlabFunction(func);
grad = gradient(func);
max_iter = 400;


%% gradient cell array for speed optimisation purposes
grad_arr = [sym()];
for i=1:length(start)
    grad_arr(i) = grad(i);
end
grad_hl_arr = num2cell(grad_arr);
for i=1:length(grad_hl_arr)
    grad_hl_arr{i} = matlabFunction( grad_arr(i) );
end


%% getting vararign params
if nargs == 0
    delta = eps;
elseif nargs == 1
    delta  = varargin{1};
elseif nargs == 2
    delta  = varargin{1};
    max_iter = varargin{2};
end

%% function wrappers
    function r = func_wrapper(ptr)
        cell_ptr = num2cell(ptr);
        r = f_hl(cell_ptr{1:length(cell_ptr)});
    end

    function r = gradient_wrapper(i, x)
        vars = symvar(grad_arr(i));
        args = {};
        for j = 1:length(vars)
            for k = 1:length(x)
                if vars(j) == strcat('x', num2str(k))
                    args{length(args) + 1} = x(k);
                    % TODO: remove matlab warning
                    break;
                end
            end
        end
        r = grad_hl_arr{i}(args{1:length(args)});
    end

    function draw_wrapper(ptr, ptr_n)
        cell_ptr = num2cell(ptr);
        plot(cell_ptr{1:length(cell_ptr)}, 'x');
    end

    function draw_plot(xV, yV, step);
        [x,y] = meshgrid(-yV:step:yV);
        z = f_hl(x,y);
        contour(x,y,z,32);
    end

    function r = f_min_search_wrapper(h, ptr, g)
        z = num2cell(ptr + h*g);
        r    = f_hl(z{1:length(z)});
    end

%% prepare for computation
ptr = start

hold on
draw_plot(2.1, 2.1, 0.1);

%% options for fminunc
options = optimset('Display', 'off') ;
options.LargeScale = 'off';

for index=1:max_iter
    %% computing gradient
    g = zeros([1 length(ptr)]);
    for i = 1:length(ptr)
        g(i) = -gradient_wrapper(i, ptr);
    end

    %% searcing optimal step
    step = fminunc(@(h)f_min_search_wrapper(h, ptr, g), step, options);

    %% main computing
    ptr_n = ptr + (step/4) * g;

    %% check result condition to exit loop
    if abs(norm(ptr_n) - norm(ptr)) < delta
        fprintf('DELTA condition worked\n');
        break;
    elseif abs(func_wrapper(ptr_n) - func_wrapper(ptr)) < eps
        fprintf('EPS condition worked\n');
        break;
    end

    %% drawing point
    draw_wrapper(ptr, ptr_n);

    %% prepare for next itaretion
    ptr = ptr_n;

    fprintf('iteration %i\n', index);
end

%% drawing last red point
cell_ptr = num2cell(ptr);
plot(cell_ptr{1:length(cell_ptr)},'r*');

hold off
%% returning variables
fval = func_wrapper(ptr);
x = ptr;

end