% Illustration of gradient descent function main()   % the ploting window    figure(1);    clf; hold on;    set(gcf, 'color', 'white');    set(gcf, 'InvertHardCopy', 'off');    axis equal; axis off;   % the box     Lx1=-2; Lx2=2; Ly1=-2; Ly2=2;   % the function whose contours will be plotted    N=60; h=1/N;    XX=Lx1:h:Lx2;    YY=Ly1:h:Ly2;    [X, Y]=meshgrid(XX, YY);    f=inline('-((y+1).^4/25+(x-1).^4/10+x.^2+y.^2-1)');    Z=f(X, Y);   % the contours    h=0.3; l0=-1; l1=20;    l0=h*floor(l0/h);    l1=h*floor(l1/h);    v=[l0:1.5*h:0 0:h:l1 0.8 0.888];    [c,h] = contour(X, Y, Z, v, 'b');    % graphing settings    small=0.08;    small_rad = 0.01;    thickness=1; arrowsize=0.06; arrow_type=2;    fontsize=13;    red = [1, 0, 0];    white = 0.99*[1, 1, 1];   % initial guess for gradient descent    x=-0.6498; y=-1.0212;      % run several iterations of gradient descent    for i=0:4       H=text(x-1.5*small, y+small/2, sprintf('x_%d', i));       set(H, 'fontsize', fontsize, 'color', 0*[1 1 1]);        % the derivatives in x and in y, the step size       u=-2/5*(x-1)^3-2*x;       v=-4/25*(y+1)^3-2*y;       alpha=0.11;         if i< 4          plot([x, x+alpha*u], [y, y+alpha*v]);          arrow([x, y], [x, y]+alpha*[u, v], thickness, arrowsize, pi/8, ...                arrow_type, [1, 0, 0])          x=x+alpha*u; y=y+alpha*v;       end      end   % some dummy text, to expand the saving window a bit    text(-0.9721, -1.5101, '*', 'color', white);    text(1.5235,   1.1824, '*', 'color', white);   % save to eps    saveas(gcf, 'Gradient_descent.eps', 'psc2')   function arrow(start, stop, thickness, arrow_size, sharpness, arrow_type, color)   % Function arguments: % start, stop:  start and end coordinates of arrow, vectors of size 2 % thickness:    thickness of arrow stick % arrow_size:   the size of the two sides of the angle in this picture -> % sharpness:    angle between the arrow stick and arrow side, in radians % arrow_type:   1 for filled arrow, otherwise the arrow will be just two segments % color:        arrow color, a vector of length three with values in [0, 1]   % convert to complex numbers    i=sqrt(-1);    start=start(1)+i*start(2); stop=stop(1)+i*stop(2);    rotate_angle=exp(i*sharpness);   % points making up the arrow tip (besides the "stop" point)    point1 = stop - (arrow_size*rotate_angle)*(stop-start)/abs(stop-start);    point2 = stop - (arrow_size/rotate_angle)*(stop-start)/abs(stop-start);      if arrow_type==1 % filled arrow   % plot the stick, but not till the end, looks bad       t=0.5*arrow_size*cos(sharpness)/abs(stop-start); stop1=t*start+(1-t)*stop;       plot(real([start, stop1]), imag([start, stop1]), 'LineWidth', thickness, 'Color', color);   % fill the arrow       H=fill(real([stop, point1, point2]), imag([stop, point1, point2]), color);       set(H, 'EdgeColor', 'none')      else % two-segment arrow       plot(real([start, stop]), imag([start, stop]),   'LineWidth', thickness, 'Color', color);       plot(real([stop, point1]), imag([stop, point1]), 'LineWidth', thickness, 'Color', color);       plot(real([stop, point2]), imag([stop, point2]), 'LineWidth', thickness, 'Color', color);    end   function ball(x, y, r, color)    Theta=0:0.1:2*pi;    X=r*cos(Theta)+x;    Y=r*sin(Theta)+y;    H=fill(X, Y, color);    set(H, 'EdgeColor', 'none');  %plot2svg must be retrieved from http://www.zhinst.com/blogs/schwizer/ plot2svg;