% SDQ script demonstrates steepest descent
%     with a quadratic objective function.
%     
% Requires: sampleq.m [function M-file]
%
close all
clc
%
% Coefficients of the quadratic objective function
%
% q(x) = (1/2) x'*H*x  -  b'*x  +  c
%
H = [7 5; 5 6]; 
b = [15; -30]; 
c = 21;
% 
% Minimizer
xstar = H \ b;
% 
% First draw a contour map, showing the minimizer as a magenta star.
% 
x = linspace(xstar(1)-2,xstar(1)+3,65);
y = linspace(xstar(2)-3,xstar(2)+2,65);
Z = sampleq(x,y,H,b,c);
contour(x,y,Z,15);
axis('equal')
xlabel('x'), ylabel('y')
hold on
plot(xstar(1),xstar(2),'m*')
%
% User clicks mouse to set initial point for steepest descent
% 
xc = zeros(2,1);
title('Click to select starting point for Steepest Descent')
[xc(1),xc(2)] = ginput(1)
title('Minimizing a quadratic function by Steepest Descent')
m = 0;                      % m counts completed iterations
while (m<10)                % Quit when 10 iterations completed
  pc = b - H*xc;            % Steepest descent direction = residual
  t  = (pc'*pc)/(pc'*H*pc); % Calculate distance to new xc
  xn = xc + t*pc;

% Show the line segment from current point to new point.
% Add the contour thru the new point to the plot.

  plot([xc(1) xn(1)],[xc(2) xn(2)],'r')
  qc = sampleq(xn(1),xn(2),H,b,c);
  contour(x,y,Z,[qc qc]);

  xc = xn;                  % Move to the new point
  m = m+1;                  % Bump the iteration counter
end